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Physical aging behavior in glassy polymers - polystyrene and a miscible blend

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Physical aging behavior in glassy polymers - polystyrene and a miscible blend
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Liburd, Bernard A., 1965-
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English
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xvi, 228 leaves : ill. ; 29 cm.

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Calibration ( jstor )
Cooling ( jstor )
Dilatometry ( jstor )
Enthalpy ( jstor )
Heating ( jstor )
Polymer blends ( jstor )
Polymers ( jstor )
Temperature dependence ( jstor )
Transition temperature ( jstor )
Volume ( jstor )
Chemistry thesis, Ph. D ( lcsh )
Dissertations, Academic -- Chemistry -- UF ( lcsh )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

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Thesis:
Thesis (Ph. D.)--University of Florida, 1999.
Bibliography:
Includes bibliographical references (leaves 217-227).
Additional Physical Form:
Also available online.
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Printout.
General Note:
Vita.
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by Bernard A. Liburd.

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University of Florida
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Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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PHYSICAL AGING BEHAVIOR IN GLASSY POLYMERS POLYSTYRENE
AND A MISCIBLE BLEND















By

BERNARD A. LIBURD


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


1999
















To my wife, Coleen,

with deepest love and gratitude



To my daughters, Kibirsha and Ijunanyah,

rays of sunshine

who make forgetting the workday frustrations quite easy



and



To my dad, James Phipps,

whose never-waning faith

inspires my every effort














ACKNOWLEDGMENTS


Many persons have contributed in making this dissertation a reality. First and

foremost, I would like to thank my research advisor, Dr. Randy Duran, for his support and

guidance during my tenure in his group. Dr. Duran allowed me the opportunity to

explore a fascinating field of chemistry I never knew existed before I came to the

University of Florida. To him I express my sincere appreciation.

During the initial stages of this research, one of the more daunting tasks was that

of assembling and learning to use the automated dilatometer. No one was more

instrumental in getting me started than Dr. Pedro Bemal at Rollins College in Florida.

Dr. Bemal invited me to his institution and gave freely of his time as he recounted his

experiences with the instrument and the necessary initial preparations for performing

experiments. I would like to express my deepest gratitude to him for his time and the

many helpful discussions.

Further thanks are extended to Joe Caruso, without whom volume measurements

in this dissertation would not have been possible. Joe is an excellent glassblower and

utilized his expertise and skill in fabricating the many dilatometers I requested of him. I

could always count on Joe to repair or replace my broken dilatometers in a timely

manner. He would frequently find the time to get my jobs done ahead of schedule even

though he often had a heavy workload. I cannot thank him enough for his contributions









to this project. Knowing he was there in the glass shop, in support of my research efforts,

was always a comforting thought.

I must also thank past and present members of the Duran research group and

members of the Butler Polymer Research Laboratory for enriching my graduate

experience and for making the Polymer Floor one of the best places to do research at the

University of Florida.

Special thanks go to Drs. Roslyn White, Michelle Fletcher, Thandi Buthelezi, and

Sophia Cummings for their friendship and encouragement. Also, thanks must be given to

the many members of the UF chapter of the National Organization for the Professional

Advancement of Black Chemists and Chemical Engineers (NOBCChE), who not only

served as a support group, but also undertook the positive work of going into area schools

and encouraging minority students to pursue future careers in science.

Appreciation is expressed to the University of Florida and the National Science

Foundation for providing the financial support for my graduate education and research.

Finally, I would like to thank my wife, Coleen, to whom I owe an immense debt.

She has given more in understanding and genuine compassion than I can ever hope to

repay. Despite the many lost weekends and rare family activities, she has never wavered

in her support and encouragement. She made the more trying times pleasant and

bearable. That she put up with all of this while taking care of our two young daughters

(not an easy task by any means), with very little assistance from me, is much more than

any man should ask for. She has my deepest love and respect, for she is truly my better

half.














TABLE OF CONTENTS


page

ACKNOW LEDGM ENTS................................................................................................. iii

LIST OF TABLES............................................................................................................. vii

LIST OF FIGURES ......................................................................................................... viii

ABSTRACT .....................................................................................................................xvi

CHAPTERS

1 INTRODUCTION ......................................................................................................... 1

1.1 The Nature of Physical Aging................................................................................. 1
1.2 The Glass Transition Tem perature ......................................................................... 3
1.3 The Basic Features of Structural Recovery....................................................... 7
1.4 Theoretical Treatm ents of Physical Aging ........................................................... 14
1.5 Summ ary of Theoretical Aspects.......................................................................... 36
1.6 Com prison of Volum e and Enthalpy Studies...................................................... 37
1.7 Objectives of This Research ................................................................................ 40

2 AUTOMATED VOLUME DILATOMETRY ............................................................ 42

Chapter Overview ........................................................................................................ 42
2.1 Background........................................................................................................... 42
2.2 Instrum ent Description ......................................................................................... 45
2.3 Data M manipulation ................................................................................................ 50
2.4 Preparation of a Specim en Dilatom eter................................................................ 50
2.5 Volum e M easurem ents ......................................................................................... 51
2.6 Quantitative Aspects............................................................................................. 54
2.7 Calibration of the LVDT....................................................................................... 55
2.8 Test M easurem ents on Polystyrene ...................................................................... 56
2.9 Error Considerations and Analysis ....................................................................... 67









3 DIFFERENTIAL SCANNING CALORIMETRY ......................................................71

Chapter Overview ........................................................................................................ 71
3.1 Introduction........................................................................................................... 71
3.2 Instrumental Features............................................................................................ 73
3.3 Calibration of the DSC ......................................................................................... 75
3.4 Therm al Treatments.............................................................................................. 82

4 THE TIME-DEPENDENT BEHAVIOR OF VOLUME AND ENTHALPY IN
POLYSTYRENE...................................................................................................... 97

4.1 Introduction........................................................................................................... 97
4.2 Experimental......................................................................................................... 99
4.3 Results and Discussion....................................................................................... 103

5 PHYSICAL AGING IN A POLYSTYRENE / POLY(2,6-DIMETHYL-1,4-
PHENYLENE OXIDE) BLEND ............................................................................ 145

5.1 Introduction......................................................................................................... 145
5.2 Experimental....................................................................................................... 153
5.3 Results and Discussion....................................................................................... 156

6 SUM M ARY AND CONCLUSIONS........................................................................ 191

6.1 Introduction......................................................................................................... 191
6.2 Instrum entation................................................................................................... 191
6.3 Volume and Enthalpy Recovery Within PS and PS/PPO................................... 193
6.4 Aging in PS/PPO Versus Aging in PS................................................................ 195

APPENDIX A CONSTANT TEMPERATURE AGING PROGRAM...................... 196

APPENDIX B TEMPERATURE SCANNING PROGRAM .................................... 200

APPENDIX C CALCULATIONS OF REFERENCE SPECIFIC VOLUME
AND TRAPPED GAS VOLUME IN DILATOMETER ................ 212

REFERENCES ................................................................................................................ 217

BIOGRAPHICAL SKETCH ........................................................................................... 228














LIST OF TABLES


Table pag

2-1 Volume thermal expansion coefficients for PS................................................... 64

3-1 Aging data for the enthalpy recovery of PS at 98.6 C................................... 92

4-1 Physical aging rate data for PS at various aging temperatures.......................... 120

4-2 Aging param eters for PS ................................................................................... 134

4-3 Quantification of the energy per unit free volume for PS ................................. 143

5-1 Quantification of the energy per unit free volume for 90/10 PS/PPO............... 180














LIST OF FIGURES


Figure page

1-1 illustration of the relationship between specific volume and
temperature for a glassy polymer......................................................................... 4

1-2 The cooling-rate dependence of the specific volumeof a
glass-forming amorphous polymer...................................................................... 5

1-3 Nonlinear effect of volume recovery of atactic polystyrene.
Samples were equilibrated at various temperatures
(and 1 atm.) as shown adjacent to each recovery curve
and then quenched to the aging temperature, Ta = 98.6 C.
The equilibrium volume at 98.6 C is denoted by v ........................................ 8

1-4 Asymmetric effect of isothermal volume recovery of atactic
polystyrene. Samples were annealed above Tg, quenched to
95.8 C and 101.4 C, equilibrated at those temperatures and
reheated to 98.6 C. The equilibrium volume at 98.6 C is
denoted by v ................................................................................................ 9

1-5 Memory effects of the volume recovery of poly(vinyl acetate)
after double temperature jumps. Samples were quenched from
40 C to different temperatures and then aged for different
amounts of time before reheating to 30 C: (1) direct quenching
from 40 C to 30 C; (2) 40 C to 10 C, aging time = 160 hrs;
(3) 40 C to 15 C, aging time = 140 hrs; (4) 40 C to 25 C,
aging time = 90 hrs. The equilibrium volume at 30 C is denoted
by V- (reprinted after ref. 18 with permission of publisher).............................. 10

1-6 DSC traces of polystyrene showing the endothermic peak associated
w ith aging .......................................................................................................... 12

1-7 Schematic plot of specific volume or enthalpy as a function of time
during isothermal structural recovery in response to a quench from
a one temperature to a lower temperature.......................................................... 13









1-8 Schematic specific volume temperature plot of a glassy polymer
showing the temperature dependence of the free volume................................... 15

2-1 Schematic illustration of the dilatometer and its measuring system:
(A) LVDT coil, (B) LVDT core, (C) wire lead to LVDT
readout/controller, (D) micrometer, (E) sample, (F) stainless steel
connecting rod, (G) stainless steel cylindrical float, (H) glass
dilatometer, (I) metal rod support...................................................................... 47

2-2 Schematic diagram of the components of the automated dilatometer :
(A) & (D) analog to digital converters; (B) & (C) personal computers;
(E) & (G) high precision digital thermometers; (F) LVDT readout/controller;
(H) automated dilatometer; (I) TMV-40DD/aging bath; (J) & (N) platinum
resistance temperature probes; (K), (M) & (P) silicon oils; (L) EX-251
HT/annealing bath; (0) Hart Scientific High Precision bath............................. 49

2-3 Plot of core displacement vs. LVDT voltage. The connecting rod was
turned in both clockwise (o) and counterclockwise (+) directions
by a micrometer-type gage head calibrator. The slope is 2.5504 x 10 -3
2.2464 x 10 -6 cmmV -1'. Calibration temperature was 28.5 1.0 C ...........57

2-4 LVDT voltage as a function of temperature for a mercury-only
dilatometer. Data collected at a constant scan rate of 0.100 Cmin-1
(A = heating data; 0 = cooling data) .................................................................. 58

2-5 Temperature dependence of the LVDT voltage in the
volume measurements of polystyrene for (a) three scans
(a cooling-heating-cooling sequence) (b) a cooling scan after
the dilatometer was removed from the bath and allowed to
cool at room temperature. Temperature scans performed at
a rate of 0.100 C'm in .................................................................................... 60

2-6 Deviations of experimental values from best-fit straight lines drawn
through the linear portions of the voltage versus temperature curves
(symbols correspond to those in Figure 2-5) ..................................................... 61

2-7 Specific volume as a function of temperature for PS. The average Tg,
calculated from the intersections of the glassy and liquid lines of four
curves obtained at a scan rate of 0.100 Cmin -, was 97.1 1.5 C.
(Some data points have been excluded for clarity)............................................ 62

2-8 Specific volume as a function of temperature for two different PS
specimens. (Six curves representing three heating and three
cooling scans are superimposed) ....................................................................... 63









2-9 Specific volume change showing the structural recovery of two
specimens of glassy PS at 95.6 C and 98.6 C. Experiments
performed at normal atmospheric pressure (0, D = specimen 1,
A = specim en 2).................................................................................................. 65

2-10 Relative specific volume change as a function of time showing
the long time stability of the LVDT. The time interval is from
the initial attainment of equilibrium until the end of the experiment.
Measurement temperature was 95.6 C............................................................. 66

3-1 (A) Block diagram and (B) schematic diagram of a power
compensated DSC system (reprinted after ref. 126 with permission of
publisher)........................................................................................................... 74

3-2 Dependence of the heat calibration factor, KQ, on heating rate and
mass of indium, tin, and lead (9 = sample mass 11.6 mg,
o = sam ple m ass 3.5 m g) ................................................................................... 78

3-3 Heat calibration curve determined with indium, tin, and lead for the
DSC 7. ( o, A, o = sample mass 3.5 mg; U, A, = sample mass 11.6 mg)........79

3-4 Heat flow rate calibration curve determined from several runs with
two different masses of sapphire for the DSC 7. The solid line is
the average heat calibration factor..................................................................... 81

3-5 DSC curve for PS obtained at a heating rate of 10 Cmin -1 following
a quench at 100 C m in -i ................................................................................... 84

3-6 Illustration of procedural steps for measuring enthalpy changes in DSC .............86

3-7 Output power (P) of the aged and unaged PS specimen, and the
difference between the two output signals (AP). Aging condition
is 98.6 C for 6 h................................................................................................ 87

3-8 Schematic diagram describing the pathway of enthalpy evolution
during DSC measurements. Path ABCO'CA represents the
physical aging process and path ABOBA is without aging............................... 88

3-9 The change in enthalpy versus log ta for isothermal aging of PS at
98.6 C. The data level off when equilibrium is reached ................................. 93

4-1 M olecular structure of polystyrene.................................................................... 100








4-2 Schematic diagram of volume and enthalpy evolution during
physical aging. The material is annealed above the Tg ( = Tf) for
a period of time and then cooled to and aged at Ta (path ABC).
Path CD represents the excess enthalpy or specific volume............................ 101

4-3 Specific volume temperature curve for PS obtained with the
volume dilatometer at a cooling rate of 0.100 Cmin -1. The
discontinuity at ~ 70 C is an experimental artifact. (Not all data
points are included; linear fit ranges were indicated in Chapter 2
where the data first appeared).......................................................................... 104

4-4 The normalized output power (P/m) (symbol 0) and calculated
specific heat capacity (symbol A) of PS as a functions of temperature
and time. Curve obtained at a heating rate of 10 Cmin -1 following
a rapid quench at 100 C min .. ..................................................................... 105

4-5 Determination of the fictive and glass transition temperatures of
PS by the D SC ................................................................................................. 106

4-6 Av- (circles) and AHl (squares) as a function of aging temperature
for P S ............................................................................................................... 108

4-7 Isochronal (time = 137 s) specific volume (squares) and equilibrium
specific volume (triangles) versus temperature for the quenched PS,
compared with data (circles) on the same polymer from slow cooling
(rate = 0.100 Cmin -1) experiments. (Observed peak at about 70 C
is an experim ental artifact) .............................................................................. 109

4-8 Isothermal volume contraction of PS at various aging temperatures
after a quench from Teq = 116.6 C ................................................................. 111

4-9 Isothermal volume contraction of PS at various aging temperatures
following a quench from Teq = 116.6 C (8v is calculated as indicated
in text). Data at 93.6 C are included for comparison .................................... 112

4-10 The change in enthalpy versus log aging time for PS at various
temperatures. Each curve, except the bottom curve, is shifted
vertically by 0.5 Jg -1 for clarity...................................................................... 113

4-11 The change in enthalpy versus log aging time for PS at 81.6 C and
91.6 C. For clarity, the curve at 91.6 C is shifted vertically by
0.5 J g ............................................................................................................ 114

4-12 Isothermal enthalpy contraction of PS aged at the indicated temperatures
following a quench from To = 138.6 C .......................................................... 115








4-13 Isothermal enthalpy contraction of PS aged at 81.6 C and 91.6 C
following a quench from To = 138.6 C (calculation of OH is
described in the text). The isotherm from 93.6 C is also added
for com prison ................................................................................................. 116

4-14 Physical aging rate, r, as a function of temperature, for PS (o = r'v and
= rH), over the same time interval................................................................ 119

4-15 Time necessary for the attainment of thermodynamic equilibrium, t,
for volume (open circles) and enthalpy (solid circles) recovery at
different tem peratures for PS............................................................................ 121

4-16 The effective retardation time of enthalpy recovery versus the
effective retardation time of volume recovery for PS aged at various
tem peratures..................................................................................................... 123

4-17 Plots of In teff for volume recovery (P = v, open symbols) and enthalpy
recovery (P = H, filled symbols) as a function of the excess specific
volume of PS at different aging temperatures ................................................. 126

4-18 Plots of In Teff, H as a function of the distance of the PS polymer from
enthalpy equilibrium ........................................................................................ 128

4-19 Arrhenius plot of In A'(Ta) versus 1/Ta for volume recovery in PS................... 132

4-20 Arrhenius plot of In A'(Ta) versus 1/Ta for enthalpy recovery in PS................. 133

4-21 The enthalpy change per unit volume change with time at (a) 98.6 and
97.6 C, (b) 95.6 and 93.6 C, and (c) 91.6 and 81.6 C (lines are
included only as visual aids)............................................................................ 135

4-22 Comparison of volume (empty shapes) and enthalpy (filled shapes)
isotherms at 100.6 C and 98.6 C as a function of aging time....................... 138

4-23 Comparison of volume (empty shapes) and enthalpy (filled shapes)
isotherms at 97.6 C and 95.6 C as a function of aging time......................... 139

4-24 Comparison of volume (empty shapes) and enthalpy (shapes with
error bars) isotherms at 93.6 C and 91.6 C as a function of aging
tim e .................................................................................................................. 140

4-25 Comparison of volume (dotted shapes) and enthalpy (shapes with
error bars) isotherms at 81.6 C as a function of aging time........................... 141








5-1 Molecular structures of (a) polystyrene and
(b) poly(2,6-dimethyl- 1,4-phenylene oxide).................................................... 149

5-2 TGA curve of 90/10 PS/PPO blend showing the range over which
the blend thermally decomposes. The arrow indicates where phase
separation begins (~ 355 C). The specimen was purged with air while
varying the temperature rate at 30 C'min '.................................................... 154

5-3 Specific volume-temperature curve for the PS/PPO (90/10) blend and
the PS homopolymer obtained at a cooling rate of 0.100 C'min in
the volume dilatometer. Peaks at ~ 70 C on each curve are experimental
artifacts. (Linear fits were from 45 to 65 C and 120 to 136 C for
PS/PPO; fits for PS have been previously indicated in the text)..................... 157

5-4 The mass normalized output power and calculated specific heat
capacity as a function of temperature and time for PS/PPO (90/10)
and PS. Curves obtained at a heating rate of 10 C'min -1 following
a rapid quench at 100 Cmin '. (Triangles = specific heat capacity;
circles and squares = power; linear ranges for Tf determination were
65 to 80 C and 133 to 143 C for PS/PPO and for PS, as previously
indicated in the text) ........................................................................................ 158

5-5 DSC trace of 90/10 PS/PPO blend showing the single Tg, compared
with DSC traces of PS and PPO. Data was obtained at heating rate of
10.0 C m in .' ................................................................................................... 159

5-6 Av- (circles) and AH, (squares) as a function of aging temperature for
PS/PPO blend .................................................................................................. 161

5-7 Isochronal (time = 137 s) specific volume (circles) and equilibrium
specific volume (triangles) versus temperature for the quenched
PS/PPO, compared with data (squares) on the same polymer from slow
cooling (rate = 0.100 Cmin -1) experiments (observed peak at about
70 C is an experimental artifact).................................................................... 162

5-8 Isothermal volume contraction of PS/PPO blend at various aging
temperatures after a quench from Teq = 130.8 C............................................ 163

5-9 Isothermal enthalpy contraction of PS/PPO blend aged at the indicated
temperatures following a quench from To = 150.0 C..................................... 166

5-10 Volume recovery data for two specimens of 90/10 PS/PPO during
isothermal aging at Ta = 106.8 C following a quench from 130.8 C.
Tests for thermo-reversibility are represented by "+" symbols; solid
circles and diamonds are first runs for the two specimens.............................. 167








5-11 Time necessary for the attainment of thermodynamic equilibrium, t,
for volume (open circles) and enthalpy (solid circles) recovery at
different temperatures for PS/PPO.................................................................. 169

5-12 Plots of In teff for volume recovery (P = v, open symbols) and enthalpy
recovery (P = H, closed symbols) as a function of the excess specific
volume of PS/PPO at five aging temperatures................................................. 171

5-13 Plots of In teff, H as a function of the distance of the PS/PPO system from
enthalpy equilibrium for five aging temperatures............................................ 172

5-14 Arrhenius plots of In A'(Ta) versus 1/Ta for (a) volume recovery and
(b) enthalpy recovery in 90/10 PS/PPO........................................................... 174

5-15 The enthalpy change per unit volume change of the 90/10 PS/PPO
blend as a function of aging time at 100.8- and 106.8-C............................... 175

5-16 Comparison of volume (empty shapes) and enthalpy (filled shapes)
isotherms at 115.8- and 112.8-C as a function of aging time in 90/10
PS/PPO blend .................................................................................................. 177

5-17 Comparison of volume (empty shapes) and enthalpy (filled shapes)
isotherms at 109.8- and 106.8-C as a function of aging time in
90/10 PS/PPO blend ........................................................................................ 178

5-18 Comparison of volume (empty shapes) and enthalpy (filled shapes)
isotherms at 100.8 C as a function of aging time in 90/10 PS/PPO
blend ................................................................................................................ 179

5-19 Volume recovery curves of 90/10 PS/PPO (open symbols) and PS (filled
symbols) at (a) Ta = Tg 7.4 C (curves 1 & 2), (b) Ta = Tg 4.4 C
(curves 3 & 4), and (c) Ta = Tg 9.4 C (curves 5 & 6)................................... 182

5-20 Plots of In Teff versus excess volume of 90/10 PS/PPO (open
symbols) and PS (filled symbols) from volume recovery curves at
(a) Ta = Tg 7.4 C (1 & 2), (b) Ta = Tg 4.4 C (3 & 4), and
(c) Ta = Tg 9.4 C (5 & 6).............................................................................. 184

5-21 Cooling curves of PS/PPO and PS compared at Tf = 97.1 1.5 C.
The original PS/PPO curve was shifted by -7.3 C and + 0.016350
cm3 g -1 (peaks observed around 70 C on each curve are experimental
artifacts) .......................................................................................................... 189














Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

PHYSICAL AGING BEHAVIOR IN GLASSY POLYMERS POLYSTYRENE
AND A MISCIBLE BLEND


By

Bernard A. Liburd

December 1999


Chairman: Randolph S. Duran
Major Department: Chemistry


Isothermal volume and enthalpy recovery due to physical aging in polystyrene

(PS) and a miscible blend of polystyrene/poly(2,6-dimethyl-l,4-phenylene oxide)

(PS/PPO) were measured by dilatometry and calorimetry. The aim of these

measurements was to directly compare volume and enthalpy recovery within the same

polymer, and possibly between polymer systems.

Volume data were collected with a custom-built automated volume dilatometer.

Automation was accomplished by use of a linear variable differential transformer, which

not only provided high resolution, precision and good accuracy of the data, but most

significantly, automated the entire data taking process. Enthalpy data were collected with

a differential scanning calorimeter following procedures that allowed accurate monitoring

of enthalpy changes.









Excess volume (8) and enthalpy (61) quantities were calculated, compared and

analyzed for PS and a 90/10 % (by mass) PS/PPO polymer blend. Blend miscibility was

assessed by the single glass transition temperature criterion. It was found that the times

for both excess quantities to attain equilibrium in each polymer were the same within the

limits of experimental error. In both polymers, recovery rates determined from single

effective retardation times (teff 's) were found to be dissimilar at high aging temperatures

(Ta's), but similar or identical at lower Ta's. A single parameter approach was used to

calculate aging parameters that showed some of the similarities and differences between

volume and enthalpy recovery functions. Comparison of Teff's at the same value of 8

clearly showed that enthalpy recovered faster than volume in each polymer system.

The data was analyzed for the energy to create unit free volume. Values for PS

were consistent with the measurements of Oleinik, but were smaller than those for

PS/PPO. Further, it was shown that volume and enthalpy approached equilibrium

differently with volume initially recovering faster in both polymers.

Volume recoveries in PS/PPO and the constituent PS homopolymer were also

examined at equal temperature distances, Tg T. The blend aged faster and had a total 8v

much smaller than that for the pure PS homopolymer. These features were interpreted in

terms of greater free volume in the blend and the presence of concentration fluctuations.














CHAPTER 1
INTRODUCTION


Glasses, which are by a broad definition amorphous solids, are among the oldest

materials known to mankind. In the last three decades there has been considerable

renewed interest in these materials spurred by their newly found applications in advanced

technologies, such as electronics, telecommunications, and aerospace. This interest has

led to considerable research efforts aimed at understanding the fundamental

characteristics of the glassy state, mainly using synthetic organic polymers.

It is well known that glasses exist in a non-equilibrium state. If, after its

formation history, a glass is kept at constant environmental conditions, it undergoes a

process whereby it tries to reach an equilibrium state. 1'2 This process is commonly called

structural recovery,3-6 structural relaxation,7 or in general physical aging 8 and manifests

itself in structural and property changes of glassy and partially glassy polymers.


1.1 The Nature of Physical Aging


Physical aging 2, 8- 12 refers to the time-dependent observed change that occurs in a

property of any amorphous material at a constant temperature. It occurs because of the

long-lived unstable states that are produced during the cooling of a glassy polymer from a

temperature above its glass transition temperature (Tg), to a temperature in the vicinity of,

or below the Tg. As a glassy polymer is cooled under normal conditions, it passes from









the liquid through the glass transition and into the glassy state. A rapid decrease in

molecular motion occurs as the transition temperature is approached. The polymer

molecules are not able to reach their equilibrium conformation and packing with respect

to the rate of cooling. Further cooling results in the molecules essentially being "frozen"

into a non-equilibrium state of high energy. Thermodynamic quantities such as specific

volume, enthalpy and entropy are in higher energy states than they would be in the

corresponding equilibrium state at the same temperature.8 Although molecular motion is

greatly decreased in the glassy state compared to the liquid state, there remains some

finite motion which allows the excess thermodynamic quantities to decrease toward

equilibrium. As a result, there is a driving force for molecular rearrangement and

continued packing of the polymer chains. This drive toward equilibrium, which results in

densification of the polymer, is commonly referred to as physical aging. It is generally

viewed as a recovery phenomenon and can be determined through a number of processes,

among them, volume recovery and enthalpy recovery. In contrast to chemical aging or

degradation which leads to permanent chemical modification, physical aging is a thermo-

reversible process. By re-heating the aged material to above the Tg, the original state of

thermodynamic equilibrium is recovered; a renewed quench through the Tg will induce

the same aging effects as before.

Physical aging affects many material properties of polymers: elastic modulus and

yield stress increase progressively while impact strength, fracture toughness, ultimate

elongation, and creep rate 8,9 decrease. Whenever polymers are in the glassy state, they

tend to become more brittle as they age and this affects their utility in any long-term

application. Therefore, physical aging must be considered in the design and








manufacturing of polymers, especially if their applications are to be at temperatures

below their Tg's.

Numerous studies have been conducted on the variation of various physical

properties with time. Volume and enthalpy, which are thermodynamically analogous to

one another, have been two frequently measured properties. However, rarely have

parallel measurements of both quantities been made on the same batch of materials. The

research contained herein provide these data; in this work sensitive experimental

techniques are systematically applied to the same polymers to collect specific volume (or

volume) and enthalpy data for glassy polymers.


1.2 The Glass Transition Temperature


The glass transition occurs over a temperature interval for which no single

temperature is unique, but merely representative. A temperature called the glass

transition temperature, Tg, represents the transition, which is not a typical phase

transition. The Tg distinguishes an amorphous, polymeric solid from its melt, rubbery or

liquid state. At Tg, a large number of physical properties change. These include but are

not restricted to the specific heat capacity, expansitivity, compressibility, and dielectric

permittivity which change abruptly, and entropy, specific volume and enthalpy which

show gradual changes. Only the latter two properties will be discussed in this work.

Specific volume may be continuously measured in a mercury dilatometer. Figure

1-1 illustrates the relationship between specific volume and temperature for a glassy

polymer. If the polymer, in its liquid state, could be cooled infinitely slowly through the

glass transition, the dotted line would be followed, as all modes of molecular relaxation











would have enough time to completely relax. In practice however, finite cooling rates


cause the specific volume decrease to become retarded and the solid line is followed. The


point at which the retardation occurs is the (conventional) Tg.


Since the transition to the glassy state is a continuous curve, and the Tg is not well


defined, it is often more convenient to use the fictive temperature, Tf, concept. 6,13,14 The


fictive temperature is defined as a (hypothetical) temperature at which the glass would be


in metastable equilibrium if it could be brought to Tf instantaneously. It is located at the


9
I
*
I
I
sS
f
f#
f
ss^


Temperature









Figure 1-1 illustration of the relationship between specific volume and temperature for a
glassy polymer.









intersection of the extrapolated liquid and glass lines as shown in Figure 1-1, and is in

fact the same as the conventional Tg of the material. Although it appears that Tg and Tf

are precise temperatures, this is not the case as they both depend on the rate of cooling.

Each value shifts to a higher temperature if the cooling rate is faster (Figure 1-2);

experimental work has shown that Tg is changed by approximately 3 C per factor of ten

change in the cooling rate. 15, 16 At higher cooling rates, the time for molecular

rearrangement is shorter than at the slower cooling rates, and the curve begins to deviate

from the equilibrium line at a higher temperature.


GLASSY REGION




Oell^


LIQUIDUS REGION


Temperature


Figure 1-2 The cooling-rate dependence of the specific volume of a glass-forming
amorphous polymer.








Differential scanning calorimetry, DSC, is an easier and more convenient

technique for locating Tg. The technique is used to determine the enthalpy of a glassy

polymer and is analogous to the specific volume determined by dilatometry. Only a few

milligrams (~ 10 mg) of material is required. Consequently, faster rates of temperature

change are used in DSC experiments. Unlike dilatometery where samples are

characterized by cooling from the liquid to the glassy state, DSC characterizes samples

most commonly by heating up from the glassy state. When heating an amorphous

polymer, the glass transition phenomenon is observed as an abrupt change in the heat

capacity of the material. Integration of the heat capacity-temperature curve yields

enthalpy. An enthalpy-temperature plot is similar to the plot shown in Figure 1-1 except

that the curvature on both sides of the glass transition is slightly more developed. The

temperature at which the liquid and glass enthalpy curves intersect is the fictive

temperature and is similar to the temperature at which the specific volume of the glass

and liquid intersect. For any material at enthalpic or volumetric equilibrium at some

temperature, the Tf will simply be equal to that temperature.

Enthalpy is not the measured variable in DSC (the power is). Accordingly, the

method of determination of both the Tg and the Tf is not immediately obvious, as it is in

volume dilatometry (refer to Figure 1-1). There is considerable confusion in the literature

regarding these determinations. Adding to the confusion are frequently used terms such

as "onset Tg", "mid-point Tg" and "end Tg", which are determined at the step change in

heat capacity, but at best are only approximations to the conventional Tg. The problem,

however, is easily identified. The term Tg is an operational definition of a temperature

obtained when cooling occurs from the liquid to the glassy state, whereas the DSC uses a








heating scan from the glassy to the liquid state. The path by which the glass is formed

(i.e. its thermal history) will have an influence on the heating scan. In fact, Richardson

and Saville23 have demonstrated that it is incorrect to determine Tg directly from DSC

curves because of the kinetic effects associated with aged glasses. Therefore, instead of

referring to a "glass transition temperature" of a material characterized by a heating scan,

it is more relevant and meaningful to use the fictive temperature (Tf). Values of Tf and

Tg are identical for unaged glasses, but for aged glasses the two move in opposite

directions as the amount of aging increases: Tf decreases, but the heat capacity curve

measured during heating moves to higher temperatures, thus higher Tg values.


1.3 The Basic Features of Structural Recovery


Volume recovery of polymers has been extensively studied by Kovacs,17'18 Endo

et al.,19 Hozumi et al.,20 and Adachi et al.21'22 Their works show three qualitative features

of the recovery process: non-linearity, asymmetry and memory effect. The first two

features result from single temperature jumps. The memory effects are observed after

two or more successive temperature jumps.

The non-linearity is shown in Figure 1-3. After equilibration at different

temperatures above a new equilibration temperature (98.6 C), amorphous atactic

polystyrene is quenched to that temperature. Different temperature steps result in

different response rates as initially excessive volume states approach the same

equilibrium volume in a non-linear way. The asymmetry is observed when the

contraction and expansion curves with the same temperature step are compared, as

demonstrated in Figure 1-4. The contracting polymer is always closer to the equilibrium








than the expanding polymer. The rate of structural recovery depends on the magnitude

and the sign of the initial departure from the equilibrium state.


log(t-t1) (s)











Figure 1-3 Nonlinear effect of volume recovery of atactic polystyrene. Samples were
equil ibrated at various temperatures (and 1 atm.) as shown adjacent to each recovery
curve and then quenched to the aging temperature, Ta = 98.6 C. The equilibrium volume
at 98.6 C is denoted by v,.


































0.0 ....................


-0.5


-1.0


1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0I I I I
1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0


log(t-t,) (S)











Figure 1-4 Asymmetric effect of isothermal volume recovery of atactic polystyrene.
Samples were annealed above Tg, quenched to 95.8 C and 101.4 C, equilibrated at those
temperatures and reheated to 98.6 C. The equilibrium volume at 98.6 C is denoted by
V_0.


1~1~1'1~1~I I I *


A 101.4 C

AA-.


95.8 C
,-0


' 1 I








The memory effect, illustrated by Figure 1-5, is the response from a glassy system

as it 'remembers' its previous thermal history. It is a more complex behavior than the

other two features and is the result of two successive temperature jumps of opposite

signs. The observed volume maximum appears only in samples that have not reached


t-ti, (hrs)


Figure 1-5 Memory effects of the volume recovery of poly(vinyl acetate) after double
temperature jumps. Samples were quenched from 40 C to different temperatures and
then aged for different amounts of time before reheating to 30 C: (1) direct quenching
from 40 C to 30 C; (2) 40 C to 10 C, aging time = 160 hrs; (3) 40 C to 15 C, aging
time = 140 hrs; (4) 40 C to 25 C, aging time = 90 hrs. The equilibrium volume at 30 C
is denoted by vo (reprinted from ref. 18 with permission of publisher).








equilibrium at the lower temperature. Past the volume peaks, all of the curves

interestingly decrease to the same equilibrium volume.

Enthalpy recovery curves that are measured in situ 22'24 show the same features as

volume recovery. In DSC, however, the scan of an aged polymer usually shows the

presence of an endothermic peak (Figure 1-6) whose position and intensity depend on the

aging conditions, both temperature and time. An amorphous polymer quenched from the

melt has excess enthalpy. During isothermal aging below the Tg, the excess enthalpy

decreases with aging time. On reheating the polymer above the Tg, the absorption of heat

results in the recovery of this enthalpy, also called the "Tg overshoot". This recovery to

establish equilibrium generates the endothermic peak which appears superposed on the Tg

in the DSC scan. Pioneering studies of this phenomenon were made by Foltz and

McKinney25 and Petrie, 26 who all demonstrated that the magnitude of the endotherm

was a quantitative measure of the enthalpy relaxation that had occurred during aging.

These and other published results on amorphous polymers systems 27-37 have shown that

an endothermic peak is a general feature of structural recovery of glassy polymers and

that the peak area is a measure of the amount of enthalpy recovery or physical aging.

Thermal histories that combine high cooling rates and low aging temperatures

may produce endothermic peaks on the lower temperature side of the Tg. These

endotherms are called sub-Tg peaks. They have been observed in a number of polymers

systems including poly(vinyl chloride) (PVC), 34,38,39 polystyrene (PS),40' 42 and

poly(methyl methacrylate) (PMMA).43 46 Sub-Tg peaks increase in height and shift to

higher temperatures as aging time increases. 34,47 Their formation can also be explained









in terms of the evolution of the enthalpy during the heating scan due to the structural

recovery of the polymer.














E


S,
0
MU
E~


Temperature (C)













Figure 1-6 DSC traces of polystyrene showing the endothermic peak associated with
aging.








The generic response of the specific volume (v) or enthalpy (H) of a glassy

polymer following a quench from an equilibrium state at T, to a lower temperature T2 is

shown schematically in Figure 1-7. The quench begins at time t = 0 and initially the

liquid polymer displays a "fast" or glass-like change in v and H associated primarily with








T Ti
TT



fast--



v,H H



slow______

........ ..... _.............. ....................... ................ ........ .................. ......... T 2


0
time








Figure 1-7 Schematic plot of specific volume or enthalpy as a function of time during
isothermal structural recovery in response to a quench from a one temperature to a lower
temperature.








the vibrational degrees of freedom. This is further followed by a "slow" or kinetically

impeded change in v or H associated with the structural recovery process, and continues

until equilibrium is reached at the new temperature.


1.4 Theoretical Treatments of Physical Aging


A complete theoretical understanding of the physical aging phenomenon is not yet

available. The existing theories can be divided into three main groups: free volume

theories, kinetic theories and thermodynamic theories. Although these theories may at

first appear to be very different, they really examine three aspects of the same basic

phenomenon and can be unified in a qualitative way. However, their degree of success in

quantitatively describing the phenomenon varies greatly.


1.4.1 Free Volume Theory


The bulk state of an amorphous polymer contains many voids or empty spaces.

The presence of these empty spaces can be inferred from a simple demonstration of

dissolving a polystyrene glass in benzene. One observes a contraction in the total volume

of the polymer when dissolved in the solvent. This observation indicates that a polymer

can occupy less volume and that there must have been some unused space in the glassy

matrix, which allowed for greater packing of the polymer chains. Collectively, the empty

or unused spaces are referred to as the free volume, vf, which is more accurately defined

as the unoccupied space in a material, arising from the inefficient packing of disordered

chains in the amorphous regions of the material. Mathematically, vf is defined by the

relationship:











Vf = V-V,


where v is the observed specific volume of the sample and Vo is the specific volume

actually occupied by the polymer molecules. Each volume term is temperature

dependent. Figure 1-8 shows schematically the temperature dependence of free volume.







Total specific
volume (v)


O Free volume (v,)
atTg


specific
volume (vj


Temperature


Figure 1-8 Schematic specific volume temperature plot of a glassy polymer showing the
temperature dependence of the free volume.


(1-1)









The free volume is a measure of the space available for the polymer to adjust from one

conformational state to another. When the polymer is in the liquid or rubbery state the

amount of free volume will increase with temperature due to faster molecular motions.

The dependence of free volume on temperature above Tg can be expressed in terms of a

fractional free volume, f, as:




fT = fg + af/(T- T) (1-2)




where fT is the fractional free volume at a temperature, T, above Tg, fg is the fractional

free volume at Tg, (f = Vf / v), and af is the expansion coefficient of the fractional free

volume above Tg.

The concept of free volume was first developed to explain the variation of the

48 -57
viscosity, il, of liquids above Tg.4857 The starting point of the theory is the relationship

between viscosity and free volume, which is expressed by the empirical Doolittle 49-52

equation:



B
l= A exp (VfIV,) (1-3)



where A and B are constants with B being close to unity. According to this equation, if

Vo is greater than Vf, (i.e., the polymer chain is larger than the average hole size) the

viscosity will be high, whereas if Vo is smaller than Vf, the viscosity will be low. This

means that the viscosity is intimately linked to internal mobility, which in turn is closely








related to free volume. Hence, as free volume increases, the viscosity rapidly decreases.

Equation 1-3 has been found to be highly accurate in describing the viscosity dependence

of simple liquids. Moreover, because the mobility of a system is reflected by its viscosity

and there is an inverse relationship between free volume and viscosity, many researchers

have adopted the free volume theory to describe the volume recovery process that occurs

in glassy polymers.

Another important empirically derived relationship is the William, Landel and

Ferry (WLF) equation.'5 It was developed to describe the change in viscoelastic

properties of polymers above Tg and is often employed to describe the time temperature

dependence of physical aging. The WLF equation expressed in general terms, is:



C (T-T)
log a -CTT (1-4)
C2 + T- T,



where the temperature shift factor, aT = 1iT / TIT, = TT / TtTr (T is a characteristic segmental

relaxation time at temperatures T and Tr (reference temperature)), C1 and C2 are

constants. When Tr is set equal to Tg, C1 and C2 are 17.44 and 51.6 K, respectively.

These values were once thought to be universal but variations have been shown from

polymer to polymer. Substitution of these values into equation 1-4 results in the relation:



17.44 (T-T,)
log aT = 7.44 (T-) (1-5)
51.6 +T-T,








This empirical expression is valid in the temperature range Tg < T < (Tg + 100 C) and is

applicable to many linear amorphous polymers independent of chemical structure. Since

aT = TT / tTg in equation 1-5, the WLF equation can be used to determine the relaxation

time of polymer melt behavior at one temperature in reference to another such as Tg. If

applied to the phenomenon of physical aging, this equation restricts molecular relaxation

times to a small temperature interval Tg to Tg 51.6 K, and predicts that at T < Tg 51.6

K molecular relaxation times are infinite, i.e., T = oo. This suggests that for a quenched

amorphous polymer, physical aging effects will not be observed 52 K below Tg since

relaxation times far exceed experimental times. Despite this prediction, there is strong
58
evidence 58 that aging occurs well below Tg 51.6 K and involves molecular relaxations

associated with localized segmental motions (rotations of side groups and restricted main-

chain motions) and cooperative motions of the polymer chains. The connection between

the WLF equation and free volume is found in the mathematical definitions of the

"universal" constants C, and C2. The relationship is demonstrated in the following

paragraph.

Expressing the shift factor, aT in terms of the Doolittle equation and the fractional

free volume, f, the following is obtained:




aT 1T exp[B(i/f 1)] exp[B(I (1-6)
7 exp[B(l/f1 -1)] [f f



If the reference temperature is set to Tg and then equation 1-2 inserted into equation 1-6,

the expression becomes:









aT = -= exp[B I -I
RT, [fg+faf(T-Tg) fgJ
rl i L^a(r-r ) ^-

Sexp af- (T T)
f + f (T T.)


-B ](T- Tg)
=exp f9 1(1-7)
f9 +T T
laf 1-


The following equation is obtained by taking the logarithm of equation 1-7:


-B ](T-T)
[ -]2.303/,
log aT 2.303 ]T-- (1-8)
f] + T-Tg]
laf


This equation predicts a rapid increase in viscosity as the Tg is approached and free
volume decreases. By comparing equation 1-8 with equation 1-5, fg and af can be
evaluated from:








B_
233f C =-17.44 = fg = 0.025 (when B= 1) (1-9)
2.303 ff




fg = 51.6K =* f f 0.025 = 4.8 x 10-4 K-' (1-10)
0f 51.6K 51.6K



These expressions show the dependence of the "universal" constants, C1 and C2 on free

volume. The outcome of the fact that the WLF equation exhibits these constants is that

the fractional free volume at the glass transition temperature and the thermal expansion

coefficient of free volume also have "universal" values. These values are valid for a

wide range of materials, although by no means for all glass former. The development of

the above ideas forms the core of the free volume theory which suggests that free volume

at Tg is of the order of 2.5 % for most materials.

The concept of free volume can describe quite well the mobility of many simple

and polymeric fluids. Two remarkable strengths of the free volume theory are its

conceptual appeal and relative simplicity, and the fact that the famous WLF equation can

be derived from it leading to "universal" parameters that have physically reasonable

values. Nevertheless, the free volume theory has a number of drawbacks. One drawback

is the free volume and occupied volume are not very clearly defined thus quantitative

interpretations of both are not obvious. Another drawback is the theory does not provide

insight into the molecular processes associated with physical aging and provides very

little information about the molecular motion itself. For more detailed information on the

free volume concept in glassy polymers, the reader is referred to the literature. 4,56,57, 59,60








1.4.2 Kinetic Theory


The WLF equation was derived from free volume considerations in the previous

section. This equation can also serve to introduce some kinetic aspects of physical aging.

For example, if the time frame of an experiment is decreased by a factor of ten near Tg,

use of various forms of equation 1-5 indicate that Tg should be raised by ~ 3 C:




lim(logaT lim -17.44 0.338

(1-11)
-1.0
T- T = -0.338 +3.0
s -0.338



For larger changes in time, values of 6 7 C are obtained from equation 1-5, in

agreement with many experiments.

The kinetic theory to be developed in the next two subsections considers the

single-parameter model based on the free volume concept, and multi-parameter models

based on non-linearity and non-exponentiality (or distribution of retardation times), two

aspects of physical aging. Single parameter models are the simplest models and are

useful for qualitative descriptions of many of the features of aging. The model

summarized by Kovacs 61 is among the best and will be the one discussed here. Multi-

parameter models are extensions of single parameter models and are more useful for

quantitative descriptions of aging behavior. Only the descriptions provided by the Tool-

Narayanaswamy-Moynihan-KAHR5 7, 18,62, 63 models will be considered.








1.4.2.1 Single-parameter approach

In general, the properties of a pure substance in its equilibrium state can be

completely specified by its temperature (T) and pressure (p). However, in a non-

equilibrium glassy state, additional parameters are required to specify the state of the

system. In the single-parameter model it is assumed that in addition to T and p, one

ordering parameter (free volume) is required to fully describe the non-equilibrium state of

a polymer glass. Early theories for the structural recovery of glasses were proposed by

Tool 5.6 and Davies and Jones.' These researchers assumed that the departure of glasses

from equilibrium depended upon a single ordering parameter and used a single

retardation time, t, to describe the process. Using this single retardation time and the

presumption that the rate of specific volume change is proportional to its deviation from

the equilibrium value, v-, Kovacs 9' 18 64,65 proposed the following equation for isobaric

volume recovery:



dv v(t) v (112)
dt agvoq -(1-12
dtT



in which Oag = (1/v-) (&v/OT)p is the thermal expansion in the glassy state, v is the

instantaneous specific volume, v- is the equilibrium specific volume and q = (dT/dt) is

the experimental rate of cooling (q < 0) or heating (q > 0).

At this point two new variables are introduced: 8, a dimensionless parameter that

represents the volume departure from equilibrium, and 8H (in J g -1), the enthalpy

departure from equilibrium or excess enthalpy. Both variables are defined as follows:










8 v(t) v v(t) 1 (1-13)
V_0 V_



SH = H(t)-HH0 (1-14)



where H is the actual enthalpy, Hoo is the equilibrium enthalpy and the other terms are as

previously defined. Either variable can be used as the ordering parameter. For volume

changes, equation 1-12 becomes:



=qAa + (1-15)
dt) I-,



where Aa is the difference between the liquid and glass expansion coefficients, t is time

and Tv is the isobaric volume retardation time. A similar expression for isobaric enthalpy

recovery is:



dt = qAcp + '- (1-16)
dt TH



in which Acp is the difference between the liquid and glass specific heat capacities and TH

is the enthalpy retardation time. Tool5,6,61 used the fictive temperature (Tf) to define the

structure of a glass and proposed a general form of equation 1-15 in terms of Tf, i.e.,










dT,/dt = -(T T)/T, (1-17)



where Tf = T + 8Aa and Tf = T + 8 H Acp are for volume and enthalpy recovery,

respectively. The solution to this expression determines how well actual glassy behavior

is described by the model.

Under isothermal conditions, equation 1-15 becomes:



d8- 8 (1-18)
dt



which has the solution




8 =8exp(-L1 (1-19)
(- I t


where 60 characterizes the volumetric state of the polymer at time, t = 0. Equation 1-19

cannot, however, be fitted to experimental isothermal volume recovery data. To

overcome this shortcoming of the model, Tool 5,6 assumed that Tv was not a constant, but

that in addition to depending on T and p, it was also dependent on the instantaneous state

of the glass, i.e. on 5 or Tf. Utilizing the Doolittle viscosity equation in a form analogous

to equation 1-6, one can write the relationship between Tv and Tvg as:








S= exp B (1-20)
( f f9


where tv is the volume relaxation time at temperature T, tvg is the volume relaxation time

at equilibrium at a reference temperature Tg, B is a constant, and f and fg are the fractional

free volume at T and the equilibrium fractional free volume at Tg, respectively. Inserting

equation 1-20 into equation 1-15 leads to:



8exp B
L = qAaf (1-21)
dt) (B}
( f}


A similar expression can be derived for enthalpy changes. It turns out that this

modification to give the retardation time a free volume dependence provides a qualitative

description of the isothermal physical aging of polymer glasses after a single temperature

jump and under constant rate of cooling or heating. In particular, the isotherms and the

asymmetry of approach towards equilibrium (see Figures 1-3 and 1-4) are reasonably well

described by this model. Despite these successes, however, single-parameter models fail

completely in describing memory effects (see Figure 1-5). This is because they predict

that d8/dt would be 0 at the start when 8 =0.








1.4.2.2 Multi-parameter approach

Multi-parameter models were developed in an attempt to separate the effects of

temperature and structure during physical aging of materials. Kovacs et al.63 attributed

memory effects to the contributions of at least two independent relaxation mechanisms

involving two or more retardation times. These authors proposed a multi-parameter

approach called the KAHR 63 (Kovacs-Aklonis-Hutchinson-Ramos) model. In this

model, the aging process is divided into N sub-processes, which in the case of volume

recovery may be represented as:



dt~i 8~i
-- = qAcx + (1< i dt Ti



in which Aao = giAc4 is the weighted contribution of the i-th parameter to Aa (= (XL -

ac) with



N
gi =1 (1-23)
i=1



Each ordering parameter, i, contributes an amount 4 to the departure of the fractional free

volume from equilibrium and is directly associated with a unique retardation time, Ti.

Further, the KAHR model assumes that the 8i's do not affect each other. Although it is

unlikely this assumption is true, it does simplify the mathematics involved greatly. The

total departure from equilibrium is then given by the sum of all the individual -, i.e.











= 4i(1-24)
i=1



Similar equations can be written for the enthalpy.

Assuming that the retardation time depends on both temperature and structure, the

solution to equation 1-22, is:



ri(T, 8) = ir exp[0(Tr T)]exp[-(l x)08/Aca] (1-25)




where Ti, r is the value of ti in equilibrium at the reference temperature, Tr, 0 is a structure

parameter which, within a limited temperature interval around Tg, is approximately equal

to Ah*/RTg2 (Ah* is activation energy), and x (0 < x < 1) is a partitioning parameter (or

the non-linearity term) that determines the relative contributions of temperature and

structure to Ti: x = 0 expresses a pure structure dependence whereas x = 1 expresses a pure

temperature dependence. The corresponding equation for enthalpy recovery is:



ri(T, 8H) = rir exp[O(T, T)]exp[-(l x)08, /Acp] (1-26)



Both equations account for the non-linear aspect of the aging process. The distribution of

retardation times is non-continuous and is seen in equations 1-25 and 1-26 where the

subscript i refers to the i-th sub-process of a discrete distribution of N sub-processes.








A discrete distribution is advantageous as it allows examination of 4 (or 8H. ) at any point

during the aging process.

The temperature dependence of ti at constant 8 is given by the temperature shift

function, aT:




aT = T exp[a(T, T)] (1-27)
Ti(Tr, I)



while the structural dependence is given by the structural shift function az:




a = (T, exp[-(1 x)OS/Aa] (1-28)
Tri (T, 0)



where =0 denotes equilibrium. A combination of equations 1-27 and 1-28 leads to the

following expression:



Ti(T,8) = iT,rara6 (1-29)



The retardation time spectrum, G(ti, r) is obtained from the parameters gi and t, r.

The spectrum has a constant shape, assured by assuming that the gj's are independent of T

and 8, whereas ti (at the same T and 8) is given by equation 1-29. A change in

temperature from Tr to T or a change in 8 will thus shift the spectrum along the log t axis

by amounts log aT or log as, respectively. This fundamental assumption of the spectrum








of retardation times shifting its position with respect to the internal structure but not

changing its shape, is referred to as the thermorheological simplicity of physical aging.

For any thermal history of the type



T(t) = To + qdt (1-30)




where To, is the temperature at which an equilibrium state (all 4js = 0) is initially

established, the thermal history dependence of 8 can be written in a compact form using a

reduced time variable z:



z = (aa)- 'dt (1-31)



which reduces the instantaneous rates of change of structure (4i) at any temperature and 8

to those obtained in equilibrium at T. The relevant expression for S(t) (which depends on

the thermal history and material properties) is then given by:




8(z) = -Aafo R(z z') d 'd (1-32)
dz



where R(z), the normalized retardation (recovery) function of the system, is determined

from:








N
R(z) = .giexp(-z/rir,,) (1-33)
i =1



This function describes the non-exponential behavior of the recovery process. The value

of R(z) changes from unity to zero as z (or t) increases from zero to infinity and must be

determined from experiment. All other material functions (aT, a8, Aa) must also be

determined experimentally.

The KAHR model is capable of predicting the experimental data obtained at

different cooling rates (Figure 1-2), isothermal recovery following a single "down"

temperature jump (Figurel-3 and 1-4 ) and a single "up" temperature jump (Figurel-4).

The KAHR model is also quite successful in describing asymmetry of isothermal

approach curves (Figure 1-4). It reproduces all of the features of the memory effects

(Figure 1-5) which can only be explained by the multiplicity of retardation times.

Reliable fits to peaks obtained on constant heating through the transition range (Figure

1-6) have also been performed with the KAHR model.

Common descriptions of the kinetics of structural recovery are found in the multi-

parameter models of Tool5, Narayanaswamy 63 and Moynihan 66 (TNM). These models

show the required dependence of t on both temperature and structure and are generally

represented by the equation:



,rjrr[ x^Jh* (1 xc)AA*
r(T, Tf) = ro0exp-- + (1-34)
RTRTf








This non-linear equation is applicable at temperatures close to Tg; it clearly separates the

temperature and structure dependence of t. The characteristic retardation time, to, is the

retardation time in equilibrium (Tf = T) at an infinitely high temperature, x has the same

definition as in the KAHR model, and R is the molar gas constant. In the limit of small

departures from equilibrium (Tf -- T), this equation becomes an Arrhenius type equation

(T = Toexp[Ah*/RT]) with an activation energy, Ah*.

The second requirement for physical aging is non-exponential character or a

distribution of retardation times. This is introduced into the TNM model by use of the

stretched exponential response function:



( = exp[-(t/r) ] (1-35)



known as the Kohlrausch 67 -Williams-Watts 68 (KWW) function. The non-exponential

parameter 0 (0 < < 1) is inversely proportional to the width of a corresponding

distribution of retardation times, whereas 'T is given by equation 1-34.

When equations 1-34 and 1-35 are combined with a constitutive kinetic equation,

in which the isothermal rate of approach to equilibrium is proportional to the departure

from equilibrium, equation 1-17 is generated. The TNM model can then describe the

response of the glass to any thermal history.

The TNM model has been remarkably successful in describing isothermal

enthalpy recovery and DSC endotherms on heating at constant rate.32 35, 43,44,69

However, there has only been partial success in evaluating the parameters defining the

kinetics (x, p, Ah*) for different polymer glasses as there is quite a wide variation in these








values. A possible explanation of these discrepancies might be that the KWW type

continuous distribution used is not appropriate for such recovery in all polymers.


1.4.3 Thermodynamic Theory


The thermodynamic theory of glasses was formulated by both Gibbs and

DiMarzio 71 -73 (G-D) who argued that, even though the observed glass transition is

indeed a kinetic phenomenon, the underlying true transition can possess equilibrium

properties, even if it is difficult to realize. At infinitely long times, they predict a true

second-order transition, when the material finally reaches equilibrium. The

thermodynamic theory attempted to explain the Kauzmann 74 paradox, which can be

stated as follows. If the equilibrium thermodynamic quantities of a material, e.g. entropy

(S), volume (V), and enthalpy (H), are extrapolated through the glass transition, the

values of S, V and H for the glass will be lower than for the corresponding crystals. The

G-D theory resolves the problem by predicting a thermodynamic glass transition when the

conformational entropy, Sc, goes to zero.

The G-D theory of the glass transition is based on an application of the Flory-

Huggins 75'76 lattice model for polymer solutions. One of these scientists, DiMarzio,77

has argued that the use of a lattice model is more promising for the study of polymers

rather than for simple liquids, because in polymers it is possible to form glasses from

systems with no underlying crystalline phase. Atactic polymers are such systems because

their irregular structures do not, in general, permit them to crystallize.

The G-D theory employs a lattice of coordination number z filled with polymer

molecules (nx) each with a degree of polymerization x, and vacant sites (no). Each








polymer chain has a lowest energy shape, and the more the shape deviates from it, the

greater the internal energy of the molecule. This energy is expressed as two energies,

intramolecular energy and intermolecular energy. The intramolecular energy is given by

xfAe, where f is the number of bonds in the high-energy state (state 2) and AE = C2 SI is

the energy difference between high- and low-energy conformational states. The

intermolecular energy is proportional to the number of vacant sites (no) and the non-

bonded interaction energy, AEh. The partition function is calculated by the same method

used by Flory and Huggins78 and Sc which describes the location of vacant sites and

polymer molecules, is derived from it.

A second-order transition is included in the partition function in the Ehrenfest

sense. The Ehrenfest equation for a second-order transition is:



dp Aa (1-36)
-f ( 1-36)
dT AKc



where p is the pressure, T is the transition temperature, Aa and AK are the changes in

volumetric thermal expansion and compressibility, respectively, associated with the

transition. The lattice model predicts the existence of a true second-order transition at a

temperature T2. The transition occurs at Sc = 0, and the Kauzmann74 paradox is resolved

for thermodynamic reasons rather than kinetic ones. Thus, extrapolation of high

temperature behavior through the glass transition is not allowed, for as the material is

cooled, a break in the S T (or V T or H T) curves occurs because of a second-order

transition. As a glass-forming material is cooled down, at a given pressure, the number of








possible arrangements (i.e. the conformational entropy) of the molecules decreases with

decreasing temperature. This is due to a decrease in the number of holes (a volume

decrease), a decrease in the permutation of holes and chain segments, and the gradual

approach of the chains towards populating the low-energy state (state 1). Finally when

Sc = 0 the temperature T2 is reached. The G-D theory also allows the glassy state as a

metastable state of energy greater than that of the low-energy crystalline state for

crystallizable materials.

The temperature T2 is not of course an experimentally measurable quantity but

lies below the experimental Tg and can be related to Tg on this basis. Evidently, Gibbs

and DiMarzio were making comparisons with experimental data and used the

experimental (kinetic) Tg in their equations. Nevertheless, the theory is capable of

describing a whole range of experimentally established phenomena such as the molecular

weight dependence of Tg7179, the variation of Tg with the molecular weight of

crosslinked polymers 80,81, the change in specific heat capacity associated with the glass

transition 2,83 (typical values for amorphous polymers are 0.3 0.6 J g -I K ), the

change in Tg due to plasticization84 and deformation 80 and the dependence of Tg on the

compositions of copolymers85 and polymer blends. 71,86,87

Adam and Gibbs84 attempted to unify the theories relating the rate effect of the

observed glass transition and the equilibrium behavior of the hypothetical second-order

transition. They proposed the concept of "co-operatively rearranging regions," defined

as regions in which conformational changes can take place without influencing their

surroundings. At T2, this region becomes equal to the size of the sample, since only one

conformation is available to each molecule.






35

Adam and Gibbs derived the following expression for viscosity:



C
In i = B + (1-37)
TS,



where B and C are constants. By assigning a temperature dependence to Sc, it is possible

to derive the WLF equation (equation 1-4) from equation 1-37. The temperature (T2) at

which the second-order transition would occur may then be calculated from the WLF

equation as follows: To shift an experiment from a finite time-scale to an infinite one

requires a value of log aT approaching infinity. Clearly, this will be the case (at Tr = Tg) if

the denominator on the right hand side of equation 1-4 goes to zero while the numerator

remains finite, i.e.,



C2 + T2 Tg = 0 (1-38)



Since C2 is relatively constant for most polymers, then



T, = Tg C2 = T, 52 (1-39)



Thus, T2 would be observed about 50 C below Tg for an experiment carried out infinitely

slowly. Equation 1-39 holds for a wide range of glass-forming systems, both polymeric

and low molecular weight. Thus, the incorporation of co-operativity into the G-D theory








appears to resolve most of the differences between the kinetic and thermodynamic

interpretations of the glass transition.


1.5 Summary of Theoretical Aspects


From the discussion above, it is clear that the phenomenon of physical aging is

very complex and that no single theory, as yet, is capable of accounting for all the aspects

of it. The current theories can be divided into three main groups: free volume, kinetic and

thermodynamic theories. The free volume theory introduces free volume in the form of

segment-size voids as a requirement for the onset of co-ordinated molecular motion, and

provides relationships between coefficients of thermal expansion below and above Tg. It

treats the glass transition as a temperature at which the polymer has a certain universal

free volume (i.e. as an iso-free volume state) and yields equations relating viscoelastic

motion to variables of temperature and time. According to the kinetic theory, there is no

thermodynamic glass transition; the phenomenon is purely kinetic. The transition

temperature (Tg) is defined as the temperature at which the retardation time for the

segmental motions in the main polymer chain is of the same order of magnitude as the

time scale of the experiment. The kinetic theory is concerned with the rate of approach to

equilibrium of the system, taking the respective motions of holes and molecules into

account. It provides quantitative information about the heat capacities below and above

Tg, and the material parameters defining the kinetics of the system. The 3 C and

sometimes 6 7 C shift in the glass transition per decade of time scale of the experiment

is also explained by the kinetic theory. The thermodynamic theory introduces the notion

of equilibrium and the requirements for a true second-order transition, albeit at infinitely









long time scales. The equilibrium properties of the true second-order transition are

described by the Ehrenfest equation. The theory postulates the existence of a true second-

order transition, which the glass transition approaches as a limit when measurements are

carried out more and more slowly. This limit is the hypothetical thermodynamic

transition temperature (T2) at which the theory postulates the conformational entropy is

zero. The thermodynamic theory successfully predicts the variation of Tg with molecular

weight and cross-link density, composition, and other variables. Adam and Gibbs

incorporated the idea of co-operativity into the theory and rederived the WLF equation

from which the relationship (Tg T2) = 50 C is obtained.

All the models discussed above incorporate the two aspects of non-linearity and

non-exponentiality (or distribution of retardation times) which have long been recognized

as essential. In this way they all provide a qualitatively good description of many aging

phenomena. The details of the ways in which these aspects are introduced are obviously

different between models, for example free volume versus conformational entropy, or

discrete distribution functions versus continuous KWW functions. Nevertheless, these

differences are of little importance in comparison with the common features of the

models.


1.6 Comparison of Volume and Enthalpy Studies


There are numerous reports in the literature on enthalpy recovery in polymers

and fewer on volume recovery in polymers. Even less than these are the number of

studies in which comparable volume and enthalpy recovery data are obtained. Only a few








of these studies have been performed on identical samples of materials and there is yet to

be a clear conclusion about volume and enthalpy.

Weitz and Wunderlich88 prepared densified glasses of polymers by slowly

cooling them from the liquid state under elevated pressures. These researchers then

measured the enthalpy and volume recovery of the densified polymers by DSC and

volume dilatometry, respectively, at atmospheric pressure. Their findings for volume and

enthalpy showed a difference in the times to reach a specific percent recovery. Volume

was faster than enthalpy in reaching this specified percentage in PS whereas in PMMA it

was slower.

Sasabe and Moynihan 89 used DSC at constant atmospheric pressure to investigate

enthalpy recovery in poly(vinyl acetate) (PVAc) at different constant heating rates and

then compared their results with volume data from the work of McKinney and

Goldstein.90 After performing curve-fitting with their mathematical model, they found

that the average equilibrium volume recovery time was smaller by a factor of two than the

corresponding enthalpy recovery time.

Roe privately communicated to Prest et al.91 that enthalpy changed more rapidly

than volume in PVC. The supporting data, however, were not published. Prest et al. 91

reported volume and enthalpy data on an anionically polymerized PS sample. The

enthalpy changes were collected at 5, 10 and 20 C min -1 and corrected to zero heating

rate. Volume recovery data on the same sample were obtained in the laboratory of A. J.

Kovacs. From different representations of the data, Prest et al.91 concluded that in this

particular PS sample, volume equilibrium was reached long before the enthalpy had fully

recovered, and that the two processes had significantly different temperature








dependence. Cowie et al. 92 also used volume data from A. J. Kovacs to compare with

their enthalpy measurements on PVAc. DSC was used to obtain the excess enthalpy data

for PVAc aged at 10 K below its Tg. From a plot of effective retardation times versus

aging times, these authors were able to show that the enthalpy recovery was faster than

the volume recovery in the PVAc glass.

In another study, Adachi and Kotaka22 investigated the enthalpy recovery of PS

by isothermal microcalorimetry and the volume recovery of the same sample by volume

dilatometry. Following a double-step temperature jump (as in Kovacs memory

experiments 18), they observed that the time to reach maximum volume for PS near its Tg

was 0.4 decades longer than that for reaching maximum enthalpy. Adachi and Kotaka22

also found that, for a broad and narrow molecular weight distribution PS, volume and

enthalpy recovery were very similar, but not the same. They calculated that it required

2.0 kJ cm3 of enthalpy to create free volumes in PS.

Using a Calvet-type calorimeter with a precision mercury dilatometer in the

calorimeter cell, Oleinik 93 simultaneously measured enthalpy and volume recovery on

atactic PS, following simple up-and down- temperature jumps. He found a one-to-one

correspondence between volume and enthalpy and related their rates of approach to

equilibrium by a constant. In a similar recent study, Takahara et al. 94 simultaneously

measured volume and enthalpy recovery in a PS sample near Tg and demonstrated that the

times for both processes to reach equilibrium were the same within experimental error.

As part of their investigation, Perez et al. 95 used length dilatometry and DSC to

study the aging of PMMA at various temperatures below its Tg. From the corresponding

volume and enthalpy measurements on the same material, they concluded that the time








scales for volume recovery were shorter than those for enthalpy recovery. The authors

used a defect theory to explain their findings.

More recently, Simon et al. reported on the time scales of recovery for volume and

enthalpy in polyetherimide 96 (PEI) and PS 97 at various aging temperatures. Analysis of

the data led to the findings that the times required to reach equilibrium for both properties

were the same within experimental error, for both polymers. These researchers also

observed differences in the approach to equilibrium for volume and enthalpy. In both

polymers, volume approach to equilibrium was faster than enthalpy approach at short

times.

Finally, in the only relevant study this author has seen on miscible polymer

blends, Robertson and Wilkes 98 examined the physical aging in different compositions of

blends of poly(2,6-dimethyl-1,4-phenylene oxide) (PPO) and atactic PS, by measuring

volume and enthalpy changes. Using DSC and dilatometry, they collected aging data at

30 C below the Tgs of the blends. They found that the dependence of the enthalpy and

volume recovery rates on PPO content were similar in all of the blends.



1.7 Objectives of This Research


The overall objectives of this investigation are to compare volume and enthalpy

recovery behavior in the same amorphous glassy polymer and across glassy polymers,

from isothermal physical aging experiments. Volume dilatometry and differential

scanning calorimetry are used as tools to investigate the structural recovery at different

aging temperatures following a quench from the equilibrium liquid state.








Physical aging was monitored at several temperatures for times ranging up to

several days. The large quantities of comparable volume and enthalpy recovery data

generated were analyzed in detail to gain insight into the structural recovery process that

occurs in glassy polymers as they age. Comparisons between volume and enthalpy data

included times to reach equilibrium, relative approaches to equilibrium, evolution of

effective retardation times, and aging parameters.

Two polymer systems were studied: a homopolymer of polystyrene (PS) and

miscible blend of polystyrene/poly(2,6-dimethyl-l,4-phenylene oxide). Both systems are

well known, as over the years, they have been subjected to numerous and extensive

studies. The choice of these two systems were based on five important points:

1. the measurement range of the automated dilatometer.

2. both polymer systems are completely amorphous.

3. availability of each homopolymer and ease of preparation of the blend from the

component homopolymers.

4. compatibility of the components in all blend ratios.

5. the glass transition temperatures and experimental conditions for aging

are in an easily accessible temperature range for both homopolymer and blend.

The blend composition selected was one in which one component was highly

dilute. Specifically, a blend composition of 90 % by mass of atactic PS and 10 % by

mass of PPO (90/10 PS/PPO) was chosen. The homopolymer and binary system were

prepared in accordance with accepted procedures, aged, and their volume and enthalpy

recovery data evaluated.














CHAPTER 2
AUTOMATED VOLUME DILATOMETRY


Chapter Overview


The data in this dissertation were collected with two pieces of analytical

instrumentation. This chapter describes one of them, a custom-built automated

dilatometer, and its performance capabilities. The section that immediately follows this

overview provides background information on the conventional technique of volume

dilatometry and discusses previous successful attempts at automation of this technique.

The remainder of the chapter gives a detailed description of the instrument, its operational

procedures, test measurements on polystyrene and a discussion and analysis of possible

errors associated with its measurements.



2.1 Background


The determination of the change in length or volume of a sample as a function of

temperature constitutes the technique termed dilatometry. When this change is a

variation in length the term length dilatometry is used; volume dilatometry is the term

applied to volume changes. Over the years, volume changes in materials have been

measured with various forms of capillary type dilatometers.18' 90,99 II In its simplest

form 100, a volume dilatometer consists of a capillary attached to a sample reservoir;

temperature is controlled by immersing the dilatometer (without the capillary) in a








heating or cooling liquid. In general, a column of mercury surrounds the material and

any change in its dimensions is observed as a change in the mercury height. The height

of the mercury column is usually measured with a cathetometer and then multiplied by

the cross-sectional area of the capillary (calibrated separately) to give the volume change

of the sample and confining liquid. In all volume dilatometry experiments, only the

volume changes are measured directly. To convert these volume changes to actual

volumes, the volume of the sample at some convenient temperature must be determined

by measuring its specific volume. Manual measurements with this type of dilatometer are

very slow, quite laborious, and require constant attention by the observer. Therefore,

many attempts have been made to automate the data collection process by using various

automatic techniques to follow the height of the mercury in the capillary. One such

attempt involves a device called a linear variable differential transformer (LVDT).

An LVDT is an electromechanical transducer that is commonly used in

Thermomechanical Analysis (TMA) and produces an electrical output proportional to the

displacement of a moveable core. Tung 12 was the first to fit an LVDT to a dilatometer.

He measured polymer crystallization rates and found excellent reproducibility between

measurements on different specimens of the same polymer. He also measured

crystallization rates with a conventional dilatometer and found very good agreement

between the measurements from both instruments. H6jfors and Flodin 113 extended

Tung's design in what they referred to as "differential dilatometry" to measure polymer

crystallization rates and melting temperatures. In their set-up, two dilatometers--one

with sample and one without--were fitted with LVDTs whose differential electrical








outputs were registered by a recorder. Very reproducible results were obtained with this

instrument.

Recently, LVDTs have been used to monitor volume changes of polymers held at

various temperatures. In 1990, Duran and McKenna 114 floated an LVDT on the mercury

surface of a dilatometer and measured volume changes of a polymer subjected to

torsional deformations. The computer to which the LVDT was interfaced automatically

recorded the volume changes. Sobieski et al.115 employed a modified version of the

Zoller 09 designed bellows dilatometer to automatically measure volume changes of a

polymer during physical aging experiments. Similar measurements were made with a

conventional capillary dilatometer ; the results demonstrated that the automated

dilatometer was just as reliable as the proven technique of capillary dilatometry.

In this work, a fully automated dilatometer with some features of both the

McKenna and Zoller designs, was used to measure volumes and volume changes. This

instrument was originally conceived by Drs. Gregory B. McKenna and Randy Duran but

was designed by and constructed under the direction of Drs. Randy Duran and Pedro

Bernal at the University of Florida. Automation and the design of the instrument afforded

a number of advantages : (i) data collection over several days or even weeks without

constant attention by the researcher, (ii) the instrument is a complete measuring system

(no external calibration necessary for volume measurements) and (iii) high precision and

good accuracy of measurements.









2.2 Instrument Description


2.2.1 Dilatometer Design


All the dilatometers used in the experiments reported herein are U-shaped in

design (Figure 2-1) and are constructed entirely from clear fused quartz using routine

glassblowing skills. Each has two main components: the specimen compartment which

has walls of ca. 1 mm thickness and a capillary column which is made of precision bore

quartz tubing (Wilmad Glass, Buena, N.J., Catalog Number 902) of internal diameter

5.0190 0.00051mm. The main advantage of this dilatometer design is it minimizes the

length of capillary extending above the bath.


2.2.2 Dilatometer Confining Liquid


Mercury was chosen for the confining liquid to be used in the dilatometer because

it offered many advantages. These included: (1) total insolubility and nonreactivity with

the polymer, (2) stability, nonvolatility, and very accurately known expansion over the

temperature range of interest, and (3) a large density that enhances precision of the

dilatometer calibration. Clean mercury that was thrice distilled (three repeated vacuum

distillations were necessary to remove all the visible particulate matter from the mercury)

was stored in the distilling flask of a cleaned one-piece glass distillation apparatus

situated in a fume hood. The dilatometer was filled by directly attaching it to the

receiving end of the distillation apparatus and further distilling the cleaned distillate into

it.









Repeated distillation of the mercury was necessary because the expansion of any

impurities can contribute to noise in the measured signal and lead to erroneous volume

results for the specimen. However, the repeatability of data collected with the dilatometer

(see Figures 2-4, 5, 7, 8 and 9) demonstrated the negligible effect of any noise in the

signal.


2.2.3 Measurement System


Figure 2-1 shows a simplified schematic diagram of the automated measuring

system. An LVDT and an extension rod-core-float assembly measure the mercury height

in the capillary column. The LVDT consists of a primary coil, two secondary coils that

give opposing outputs, and a free moving rod-shaped ferro magnetic core. The core is

floated on the mercury surface by a threaded stainless steel extension rod and float. The

rod makes contact with the mercury via a flat cylindrical stainless steel float of 5 mm

diameter that is screwed onto one end. The purpose of the float is to increase the volume

of the mercury displaced due to the weight of the rod and core which is attached to the

extension rod that extends out of the capillary to the LVDT transformer. The LVDT is

attached to a device which is fastened to a micrometer, which in turn is supported by a

metal rod. The device permits lateral and vertical movements of the core to align the hole

in the transformer with the capillary due to variations in temperature of the experiments

and in the amount of mercury used to fill the dilatometer. An auto-calibrated digital

readout/controller (Lucas Schaevitz Microprocessor (MP) Series 1000) provides the

excitation voltage across the LVDT and reads the output voltage. This real time output is

linearly proportional to the LVDT core displacement. Data is communicated to a




















































Figure 2-1 Schematic illustration of the dilatometer and its measuring system: (A) LVDT
coil, (B) LVDT core, (C) wire lead to LVDT readout/controller, (D) micrometer,
(E) sample, (F) stainless steel connecting rod, (G) stainless steel cylindrical float, (H)
glass dilatometer, (I) metal rod support.








personal computer through an RS-232 interface on the digital readout/controller using

two personally modified QuickBasic programs. The entire data collection system is

therefore automated making it possible to collect data in real time over very long periods.

The LVDT (model 100 MHR, Lucas Schaevitz, Inc., Pennsauken, N.J.) is a

miniature highly reliable (MHR) device that has a measurement range of 0.100 in.

( 0.254 cm) and can operate from 55 C to 150 C. The small mass of the core and its

freedom of movement enhance the response capabilities for dynamic measurements and

gives the LVDT infinite resolution. However, because the LVDT is connected to the

analog to digital board on the digital readout/controller, a more realistic resolution is

about 1 x 10 -5 in. (0.254 Vm). For the capillary of internal diameter 5.0190 mm, the

volume resolution is 5.03 x 10 -6 cm3.


2.2.4 Constant Temperature Baths


Three constant temperature oil baths--a Neslab TMV-40DD, an EX-251 HT, and a

Hart Scientific High Precision Bath (Model 6035)--were all part of the fully automated

set-up depicted in Figure 2-2. Silicon oils (Dow Coming 510 & 710) were the heat

transfer media used in these baths. All baths were equipped with stirrers so as to

maintain uniform temperature throughout the baths. The temperature of the TMV-40DD

and the Hart Bath were internally controlled to within 0.005 C and the EX-251 HT to

within 0.05 C. Calibrated high precision digital platinum resistance thermometers

(Hart Scientific Micro-Therm Thermometer, Models 1006 & 1506) with resolutions of

0.001 C were used to externally monitor the temperatures of the baths and the indicated

temperatures were the ones recorded in all experiments. The EX-251 HT bath was





49





A B C D
\ \ V-/ /




o JLJLJULIUL n p LJU UL g-J-
FU NBHoHHHHppg rU:

E


G








J I GN
H. r !
"" 1 L M



Sp
jI S N- "









Figure 2-2 Schematic diagram of the components of the automated dilatometer:
(A) & (D) analog to digital converters; (B) & (C) personal computers; (E) & (G) high
precision digital thermometers; (F) LVDT readout/controller; (H) automated dilatometer;
(I) TMV-40DD/aging bath; (J) & (N) platinum resistance temperature probes; (K), (M) &
(P) silicon oils; (L) EX-251 HT/annealing bath; (0) Hart Scientific High Precision bath.








maintained at a high temperature to anneal the specimen to equilibrium volume and the

TMV-40DD was maintained at the desired temperature for aging experiments.

Measurements of volume change as a function of temperature were conducted in the Hart

Bath. This bath, a digital thermometer, and a digital readout/controller were all interfaced

to a personal computer, which commanded them using the constant temperature scan

program in Appendix B. Temperature, time and LVDT voltage were simultaneously

recorded so that measurements of volume versus temperature at constant scan rates were

easily obtained.


2.3 Data Manipulation


All data were collected and stored on the dilatometer computers in ASCII file

format and then transferred via floppy disks to other computers in the lab. Microcal's

software Origin 5.0 was used to construct graphs for analysis of the data.


2.4 Preparation of a Specimen Dilatometer


The dilatometer was first cleaned with Nochromix solution, rinsed repeatedly with

Millipore water (18.0 Mi'm), and dried in a vacuum oven. Approximately 1 g of dried

polymer was weighed out on a microbalance and placed in the dilatometer. To avoid

heating the specimen during sealing, the dilatometer was placed upright in a container

filled with ice so that the sample was about 4 cm below the ice level. The specimen

compartment was then rapidly sealed a few centimeters above the ice level using a

hydrogen flame. The sealed dilatometer was degassed at a temperature above the glass

transition of the specimen for 24 h under a vacuum of -1.3 x 10-2 Nm -2 (-10 4 torr).








Following this evacuation, the dilatometer and its contents were allowed to cool to room

temperature under vacuum and then weighed to correct for any mass loss from the

specimen. Afterwards, the dilatometer was again attached to the distillation apparatus

and evacuated for 24 h. With the vacuum still applied, clean mercury (section 2.1.2.2)

was then distilled into the dilatometer. The mass of mercury was determined after

weighing the filled dilatometer.

The vacuum quality has to be quite good during degassing and filling of the

dilatometer because air has to be removed from the confining spaces of the dilatometer

and also from the specimen. Gases should be removed as quantitatively as possible

because their expansitivities are much different from that of the specimen and can lead to

very noisy signals and inflated volume data for the specimen. Quantification of the total

gas volume in the dilatometer is addressed in the following section. In some instances

after filling, microbubbles of air were present in the capillary arm of the dilatometer. A

procedure, which required gentle tapping of the arm and dipping the dilatometer

alternately in warm and cold water a few times, was quite adequate for dislodging the air

bubbles.


2.5 Volume Measurements


To perform a measurement, the dilatometer was suspended from a support rod and

immersed in the oil baths such that the mercury meniscus was always below the oil level.

A stem correction, similar to that used for thermometers 116, is usually applied to most

capillary dilatometers because part of the capillary emerges from the bath. This

correction term is dependent on the capillary diameter and the differential thermal








expansions of the glass dilatometer and the mercury and can be on the order of a few

millimeters. However, in the present instrument no stem correction is necessary since the

mercury never rises above oil level. Consequently, the mercury in the dilatometer is

always uniformly heated.

Measurements of volume as a function temperature were performed on all

specimen dilatometers and a dilatometer filled only with mercury. Before and between

measurements, the dilatometer was always allowed to sit at room temperature and the

core position was set to give a stable negative voltage reading. Setting of the core

position was achieved by adjustment of the connecting rod such that it floated on the

mercury surface. With the variation of the temperature in the room, the signal was usually

stable after 40 50 min. For consistency and measurement comparison, the dilatometer

was always allowed to sit for the same amount of time before each run. Once the voltage

signal (displayed by the digital readout/controller) was stable, the initial voltage was

recorded. The dilatometer was carefully raised from its position in a stand away from the

baths, and suspended in the Hart Bath. The computer was then instructed to collect data

at a constant rate of 0.100 C'min -.

Reference specific volumes of the polymer specimens were also determined by

measurements conducted in the high precision Hart Bath. The specific volume of each

polymer was determined at a reference temperature above its Tg (see Appendix C, Part I

for a specimen calculation), which was necessary to obtain absolute and reproducible

values. The specimen and dilatometer were prepared as described earlier. Afterwards,

the dilatometer was supported in a vertical position by a clamp and leveled with a

leveling device. A thin strip of graph paper (used as a guide) was attached to the mercury








column. A reference mark was placed on the graph paper a few millimeters below the

mercury meniscus and the position of the meniscus was also marked. With the aid of a

set of vernier calipers (accuracy 0.001 in.; resolution 0.0005 in.), the distance between the

two marks was measured. The initial voltage was stabilized as before and the computer

was instructed (through the QuickBasic program in Appendix A) to record all signals.

Eight measurements were performed on the specimen at the reference temperature. The

mercury was removed from the dilatometer and the specimen was extracted with

chloroform. After rinsing four times with chloroform, the dilatometer was cleaned as

described in section 2.4 and refilled with mercury. Adjustment and recording of the

mercury column height were repeated as before and voltage measurements were again

taken. Any contribution to volume change from the glassware is cancelled out by this

procedure.

In the preparation of mercury-only dilatometers, it was often observed that a

gaseous void--the result of poor vacuum quality--existed in the bulb of the dilatometers.

The vacuum produced at the pump vacuum inlet was earlier stated as -10 -4 torr.

However, this value was never realized at the dilatometer due to many factors including

the narrow bore imposed by the dilatometer capillary. By the technique shown in part II

of Appendix C, it was estimated that a gas void of volume 0.01265 cm 3, which is 2 %

of the total sample volume, consistently remained in the dilatometer. Inevitably, due to

equipment design, these voids added some uncertainty (~ 2 %) to the reference specific

volume calculation, but are not expected to significantly affect the aging results presented

in Chapters 4 and 5.








2.6 Quantitative Aspects


The volume change of the specimen, AVs (in cm3) in volume dilatometry is

generally corrected according to the following equation:



AVs = AV,o, A V/ AVQ (2-1)



where AVtot, AVHg, and AVQ are the total volume change, the volume change of mercury,

and the volume change of quartz, respectively. However, it is more useful to express

volume change of the specimen as specific volume change of the specimen (Avs).

Dividing through by the mass of the specimen and keeping the terms in the same order,

equation 2-1 can be rewritten to show how Avs (in cm3 .g -1) is calculated:



[{(vdt),- (lvdt),}(] [(latmHgvHTg(T T2)]
Av (2-2)
S- [aQ (mQ/pQ )(T T2)r)




V"= r (J h' (2-3)



Both equations are valid over the linear measurement range of the LVDT (or, in terms of

temperature, from ~ 145- to ~ 45-C). The various quantities are defined as follows: ms

(in g) is the mass of the specimen; (lvdt)to (in mV) is the LVDT voltage at time, t = 0 at

Ti; (lvdt)t (in mV) is the LVDT voltage after time, t, during the quench and subsequent








specimen recovery at T2; T| and T2 (in C) were previously defined (see Figure 1-7);

V is 5.046 x 10 -4 cm3 mV -1, the volume sensitivity of the LVDT; d (0.50190 cm) is the

measured internal diameter of the precision capillary column; h' (in cmmV -1 ) is the

displacement per unit voltage of the LVDT core; VHg (0.073556 cm3 g -1) is the mercury

specific volume at 0 C 117; mHg (in g) is the mass of mercury in the dilatometer; aHg is

1.8145 x 10 -4 C-1, the mercury volume coefficient of thermal expansion at 0 C 118; OQ

is 1.65 x 10 -'6 C -, the volume coefficient of thermal expansion of quartz 119; mo (in g)

is the mass of the quartz; pQ is 2.20 gcm -3, the volume density of the quartz.

Once the specific volume change at some temperature, (Avs)r, and the reference

specific volume, VTr, are known, the total specific volume at the same temperature,

(Vs) T, can then be determined from the relationship:



(vs), (in cm3g -') = {(AVs), + V} (2-4)


2.7 Calibration of the LVDT


Two calibrations were performed on the LVDT. The first was done to calibrate

the LVDT core for displacement per unit voltage, h'. With the LVDT connected to a

digital readout/controller, the connecting rod was placed on a micrometer calibration

stand. The micrometer wheel was turned in both clockwise and counterclockwise

directions in increments of 0.01 in. and the voltages due to the new core positions were

recorded from the digital readout/controller. During the calibration, the temperature of

the room varied between 27.5- and 29.5-C. However, even though an LVDT is very









sensitive to temperature variations, no significant drifts were observed in the voltage

signals for up to 20 min after the core was displaced, indicating very good control of the

signal by the digital readout/controller.

The calibration curve is displayed in Figure 2-3. Using linear regression, a slope

of 2.5504 x 10 -3 cmmV with an uncertainty of 2.2464 x 10 -6 cmmV -1 was

obtained, which indicates that the LVDT signal has excellent repeatability and linearity

throughout its measurement range.

For the second calibration, the LVDT was fitted to the mercury-only dilatometer

and both cooling and heating temperature scans were performed. This calibration

provided information on the effect of temperature on the LVDT signal. The curves in

Figure 2-4 show that the LVDT produces a stable highly linear output over a wide

temperature range.


2.8 Test Measurements on Polystyrene


Atactic PS was chosen to test the performance of the dilatometer. Two

dilatometers containing PS specimens were prepared following the procedure outlined in

section 2.4.


2.8.1 Reference Specific Volume


As mentioned earlier, the specific volume of the material is required to convert

volume changes into actual volumes. Measurements were performed on each of the

two specimens at 115.000 0.005 C and 1 atm. pressure following the procedure

described in section 2.5. The average reference specific volumes for the two specimens









were calculated as 0.95857 0.00017 cm3 .g -1 (see Appendix C, Part I) and 0.95412

0.00017 cm3 g -1. This difference in specific volume for the two PS specimens from

the same sample was somewhat surprising because at the reference temperature, PS is in


0.30000


0.20000


0.10000


0.00000


-0.10000


-0.20000


-0.30000


-80.00 -40.00 0.00 40.00 80.00


120.00


LVDT Voltage (mV)


Figure 2-3 Plot of core displacement vs. LVDT voltage. The connecting rod was turned
in both clockwise (0) and counterclockwise (+) directions by a micrometer-type gage
head calibrator. The slope is 2.5504 x 10-3 2.2464 x 10 -6 cm'mV -'. Calibration
temperature was 28.5 1.0 C.






58

the equilibrium liquid state. However, such differences have been reported before. 120

Therefore, it was necessary to determine the specific volume of each specimen for

comparison of their results.


-50


-100


60 80 100 120 140

Temperature (C)


Figure 2-4 LVDT voltage as a function of temperature for a mercury-only dilatometer.
Data collected at a constant scan rate of 0.100 C'min '. (A = heating data; 0 = cooling
data).








2.8.2 Volume Change Measurements


In order to test the precision of volume measurements, a number of experiments

were performed on the PS. Three different procedures were followed: (i) the dilatometer

was subjected to repeated scans in the oil bath, (ii) the dilatometer was removed from the

oil bath, allowed to cool at room temperature, placed back in the oil bath and then re-

scanned, and (iii) a second specimen was scanned.

Figure 2-5 displays the raw data obtained using procedures (i) and (ii). Different

initial voltages were used in both cases and the scans were made at a rate of 0.100 C

min -1. The two curves at (a) are quite repeatable and are virtually parallel to curve (b);

a simple vertical shift will superpose the curves. The data from 140 C to 105 C and

90 C to 50 C on all the curves were fitted with best-fit straight lines using the method of

least squares. The deviations from the straight lines are plotted as functions of

temperature in Figure 2-6. The deviations of the data are all within 0.8 mV, which

corresponds to 0.8 % of the maximum voltage (100 mV) meaning that the overall

precision in the LVDT measurements is better than 1 %.

The 0.8 mV deviation also corresponds to a maximum uncertainty of

4.0 x 10 -4 cm3 in the volume change measurements. However, in reality, the volume

uncertainty is less than this, because below the transition region, the curves are not

necessarily straight lines. This portion of the curves may be slightly curved due to the

decreasing rate of structural recovery that occurs in the polymer as it is slowly cooled

well into its non-equilibrium glassy state.









The LVDT signals in Figure 2-5 were converted to specific volumes using

equations (2-2, 3,4). The curves of specific volumes against temperature (Figure 2-7) are

typical of a glassy polymer. Linear regression was used to draw straight lines from 140 C

to 120 C and from 50 C to 65 C. The intersection of these lines is generally assigned

as Tg of the polymer, and at a constant cooling rate of 0.100 C'min -1, the average Tg is

97.1 1.5 C.


120.00


80.00


40.00


0.00


-40.00


-80.00


-120.00
4(


0


60 80 100 120 140

Temperature (C)


Figure 2-5 Temperature dependence of the LVDT voltage in the volume measurements
of polystyrene for (a) three scans (a cooling-heating-cooling sequence) (b) a cooling scan
after the dilatometer vwas removed from the bath and allowed to cool at room temperature.
Temperature scans performed at a rate of 0.100 Cmin-.


I I I I


- -~ _I


m I m





















1.00

0.80

0.60

0.40

0.20

0.00

-0.20

-0.40

-0.60

-0.80

-1.00
4(


0
I I I I I *





0
@@
- o< "



.............


Ma0
-~ ~~E 'B El' ^ ^

El 0


0
Q 1E 20 1





I I I I I *
O 60 80 100 120 140 1


Temperature


(OC)


Figure 2-6 Deviations of experimental values from best-fit straight lines drawn through
the linear portions of the voltage versus temperature curves (symbols correspond to those
in Figure 2-5).






















0.9800



0.9700


0.9600



0.9500


0.9400 F


0.9300 L
4C


I 60 80 100 120 140


Temperature (C)













Figure 2-7 Specific volume as a function of temperature for PS. The averaged Tg,
calculated from the intersections of the glassy and liquid lines of four curves obtained at a
scan rate of 0.100 C min -1, was 97.1 1.5 C. (Some data points have been excluded
for clarity).


Tg= 97.1 1.5 *C
























0.9900


0.9800 -


0.9700 -


0.9600 -


0.9500 -


0.9400 -


0.9300 I I* I i- I I-
40 60 80 100 120 140


Temperature


(oC)


Figure 2-8 Specific volume as a function of temperature for two different PS specimens.
(Six curves representing three heating and three cooling scans are superimposed).


0.69227 g Sample


0.77338 g Sample








Results from the second specimen are displayed in Figure 2-8 along with the

curves from Figure 2-7 for comparison. The curves have similar slopes above Tg, but

slightly different slopes below Tg due to the instability of the glassy state. Volume

coefficients of thermal expansion were determined from the six curves, by the method of

least squares using the formula a = d (In v)/dT. Table 2-1 shows the calculated glass

(o0) and liquid (aL) expansion coefficients and their literature values 120, 121 for PS. The

calculated values fall within the literature ranges indicating that the accuracy of the

experimental data is quite good.


Table 2-1 Volume thermal expansion coefficients for PS.

Expansion coefficients Literature* Calculated
(C-1)__________
o (x l0 -4) 1.7-2.5 2.28 0.22

aL (xl 0 -4) 5.7-6.0 5.97 0.09

values obtained from references 120 and 121.


2.8.3 Aging Experiments


When a polymer is cooled from an equilibrium state above its Tg to some

temperature below Tg, its specific volume (or volume) decreases until it can establish a

new equilibrium. This recovery phenomenon is referred to as physical aging and was

investigated in PS at a number of different temperatures. Only part of the results is

presented here to demonstrate the capability of the instrument. Details and discussion of

this study will be given in Chapter 4.








The specific volume changes due to structural recovery at 95.6- and 98.6-C are displayed

in Figure 2-9. The abscissa of the graph is log (t ti) where t is the elapsed time from the

start of the quench and t, is the thermal equilibration time (~ 137 s) of the sample after

transfer to the aging bath. The ordinate is 8 (the normalized volume departure from

equilibrium) and the horizontal line from the origin of the ordinate


1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

log(t-ti) (s)


Figure 2-9 Specific volume change showing the structural recovery of two specimens of
glassy PS at 95.6 C and 98.6 C. Experiments performed at normal atmospheric
pressure. ( 0, = specimen 1, A = specimen 2).









represents equilibrium values. The two curves at 95.6 C show aging of two different

specimens. Two aging runs on the same specimen are shown at 98.6 C. By observation,

the precision of the data is quite good, as in general the curves at both temperatures are

superimposable.

The curves also show that PS achieves an equilibrium structure in the time frame

of the experiment. At the lower temperature, the aging of one of the specimens was

carried out for more than three days. Figure 2-10 displays the relative specific volume as


-1.0 F


-2.0 F


2.0

Time(s)x 105


Figure 2-10 Relative specific volume change as a function of time showing the long time
stability of the LVDT. The time interval is from the initial attainment of equilibrium
until the end of the experiment. Measurement temperature was 95.6 C.


- 0 0
-WO 000 00 0 0000 0 00 ~0
0 0
0


0
oOOooOof









a function of time after equilibrium is initially established. The specific volume and

hence, the LVDT signal remained stable for more than 45 h. Therefore, the electronics

of the instrument are very stable and consequently the dilatometer can be used to collect

data over long periods of time.


2.9 Error Considerations and Analysis


In any measurement, there is always a degree of uncertainty resulting from

measurement error. A combination of the errors from all possible sources results in the

overall measurement error. Static errors, introduced by the components of the measuring

system in the automated dilatometer are usually the major contributors to overall

measurement error. Static errors result from the physical nature of the various

components of the measuring system as that system responds to a stimulus that is time-

invariant during measurement. Three types of errors combine to give the static error:

reading errors, characteristic (instrumental) errors and environmental errors. In the

present measuring system, reading errors which apply exclusively to the readout or

display device, are eliminated by use of the digital readout/display; characteristic errors

are minimized or eliminated by the signal conditioning electronics of the LVDT

readout/controller, calibration, and the LVDT design. 122

Environmental errors, on the other hand, affect not only the measuring system but

also the physical quantity to be measured. Such errors are usually due to temperature,

pressure, humidity and moisture, magnetic or electric fields, vibration or shock, and

periodic or random motion. The design of the LVDT 122, the careful handling of the

measurement system during measurements, the thermostated room temperature and








constant external pressure (atmospheric pressure), either minimized or eliminated most of

these errors in the output signals for our measurements.

The output signal from the LVDT is a measure of volume changes occurring in

the dilatometer. The error associated with the volume changes can be assessed through

two procedures: (i) a propagation of errors calculation, and (ii) the error in our reference

specific volume measurements.

The propagation of errors calculation is performed by taking the total differential

of equation 2-2:


a(Avs) =


( V){V [a(lvdt), a(lvdt),] [aftgV (T- T2)]am
kaQ/PQ)(l T2)]amQ + [((lvdt), (lvdt),)] V'}


2fV',[((Ivdt) (ivdt))] kgmHgVHg(, T2)]

[Q(mQ/pQ)(Ti -A)]} ms


in which


V' = 5.0459 x 10 -4 cm3 .mV-1 V = +4.4444 x 10 -7 cm3 "mV -'

[(lvdt)to (lvdt)t] = 200.00 mV, [a(lvdt)to )(lvdt)t] = 0.01 mV

mHg = 45.4652 g, amHg = rmQ = ims = 0.00001 g

ms= 0.69227 g, mQ = 29.72601 g

T =115.000 'C, T2 = 28.5 C.

Substitution of the experimental numbers above, into the differential equation gives a

maximum specific volume change error of approximately 1.35 x 104 cm3 .g -1.








Our unique approach to reference specific volume determination resulted in good

agreement between the specific volume of PS under ordinary temperature conditions and

that found in the literature obtained under similar conditions. 22,58.98,120,123 For example,

the extrapolation of the lower (glassy) region of Figure 2-7 to a temperature of 23 C,

gives a specific volume of 0.93253 cm3 .g -1 for PS. The value deduced at the same

temperature from literature data is ~ 0.955 cm3 .g -1. Thus, the difference of ~ 0.022

cm3 g -1 results in an error of ~ 2.3 % (most probably caused by the trapped gas in the

mercury-only dilatometer) in our specific volume measurements.

Based on equation 2-4, the measured specific volume depends on both the specific

volume change and the reference specific volume. Accordingly, any error in the

measured specific volume is related to errors in the other two quantities by the equation:




s((V)) = )+ (v (2-5)



where s represents the uncertainty or error in each term. Substitution of the two

calculated uncertainties above into this equation yields a maximum overall error of

0.022 cm3 g -1 or 2.2 % error in specific volume measurements of the PS specimen.

The absolute accuracy of the specific volume is, of course, limited by the accuracy

of the previously mentioned dilatometric determination of VTr. In the work to be

presented later, however, the absolute accuracy of VTr is not very critical. The interest,

for example, is not in the general level of specific volume; the only requirement is that the

volume recovery curves measured with different dilatometers, or repeatedly with one








dilatometer coincide. By definition, however, all dilatometers give the same specific

volume, that is VTrr, at the reference temperature, T, Therefore, it is the (absolute) error in

the specific volume change, VT VTr, that is of primary interest, because it is this error

which determines the deviations and scatter in recovery data such as is observed in

Figures 2-9 and 5-9. This error, which is dependent on the measuring temperature, was

earlier estimated by error propagation to be 1.35 x 10 -4 cm 3 g -1 over the temperature

range 28.5 to 115.000 C.

Finally, the automated dilatometer has several advantages: it is very reliable (high

precision and good accuracy), simple to build, records voltages due to very slow changes

in mercury height, and the linear relationship between the LVDT signal and displacement

of the core simplifies the use of results. Perhaps the most significant advantage of this

instrument is that volume change measurements are completely automated thus

eliminating the need for constant attention. With a volume sensitivity of 5.046 x 10 -4

cm3 mV -1 and resolution of 5.03 x 10 -6 cm 3, the automated dilatometer is an ideal

instrument for accurately following the small volume changes induced in a polymer by

variations in its thermal environment.














CHAPTER 3
DIFFERENTIAL SCANNING CALORIMETRY


Chapter Overview


The other analytical instrument used in this study is a differential scanning

calorimeter (DSC). The chapter begins with the basis for thermal measurements by DSC

and then provides a brief treatment of the features of the instrument. The DSC must be

properly calibrated before measurements are made and therefore emphasis has to be

placed on the calibration procedures. Accordingly, in section 3.3 calibrant data are

presented in order to determine the characteristics of the DSC. Enthalpy data on PS are

presented to demonstrate instrument capability, and methods of data analysis are

discussed. Procedures for ensuring the collection of highly reliable data are also

mentioned. The chapter ends with an evaluation of the experimental uncertainty

associated with the enthalpy measurements.



3.1 Introduction


The first DSC was introduced in 1964 by Watson et al.124 at Perkin-Elmer. Since

then, there have been a number of improvements to the instrument; temperature scanning,

and data collection and analysis are now computer-controlled. These improvements,









along with the speed of experimentation, ease of operation, and the high reproducibility

of the technique, have made DSC very popular.

In today's laboratories, DSC is a widely used method for the study of thermal

events in materials. Thermal events are the result of stored thermal energy in materials.

In simple substances thermal energy arises mainly from translational motion of

molecules, while in polymers it comes from motions of polymer segments. The stored

energy changes whenever the state of the system changes and every change is

accompanied by an input or output of energy in the form of heat. The ability of the

material to absorb or release this heat is expressed as heat capacity (Cp), the magnitude of

which depends on the type of molecular motion in a material and, in general, increases

with temperature. In DSC, the temperature of a material is usually varied through a

region of transition or reaction by means of a programmed heating or cooling rate, and the

power which is a measure of the material's heat capacity, recorded as a function of

temperature. In the case of an amorphous material being heated, when its temperature

reaches Tg its heat capacity changes abruptly (no change in enthalpy). At this

temperature, the material absorbs more heat because it has a higher heat capacity, and the

thermal event appears as a deviation from the DSC baseline. The deviations are either in

the endothermic (positive) direction for heating or in the exothermic (negative) direction

on cooling.

A very frequent application of DSC is to the glass transition region of amorphous

polymers. The goals of such efforts are to characterize and to model structural recovery

in glasses. The usual approach is to first anneal the specimen to equilibrium at a

temperature above Tg, to cool it at a constant rate, then to age it for a fixed period of time









at a temperature below Tg, and finally to heat it through the transition region. The DSC

output is proportional to the specimen's specific heat capacity (cp), which typically

produces a peak on heating, going from a value characteristic of the glass, cpg, to one

characteristic of the liquid, Cpi. The area under the peak, found by integration, is the

amount of enthalpy recovered. Petrie's26 pioneering work laid the foundations for this

kind of study by DSC. She established the equivalence between energy absorbed through

the glass transition region during heating and the enthalpy released during the preceding

aging period. Some years later, Lagasse 125 took a possible thermal lag into account and

suggested a modified experimental procedure. His work greatly expanded the feasibility

of enthalpy recovery measurements by DSC.

The DSC typically ramps the temperature in a linear fashion and requires the input

of an initial temperature, a final temperature, and a rate to achieve the final temperature.

Additionally, it has the capability of maintaining the sample at the initial or final

temperature for a specified amount of time. Many types of commercial DSCs exist;

however, since the measurements presented here were made on a Perkin-Elmer

instrument, only the key features of this instrument will be discussed.


3.2 Instrumental Features


In this work, a Perkin Elmer Differential Scanning Calorimeter 7 Series (DSC 7)

was used to make calorimetry measurements and to characterize polymer specimens.

Figure 3-1 shows the diagrams of the DSC 7. The measuring system consists of two

microfumaces ( a sample holder and a reference holder) of the same type made of a

platinum-iridium alloy, each of which contains a temperature sensor (platinum resistance











Sample Holder


num Fogl



older Supporl Rod

Gas Inte


Fig 3-1 (A) Block diagram and (B) schematic diagram of a power compensated DSC
system (reprinted from ref. 126 with permission of publisher).








thermometer) and a heating resistor (made of platinum wire). Both microfurnaces are

separately heated and are positioned in an aluminum block whose base is surrounded by

coolant. The (DEC) computer controls the DSC via a temperature controller (TAC 7 /

DX). Under the control of the computer, the DSC 7 can be operated in both the normal

temperature scanning mode and the isothermal mode. Data is analyzed by the Perkin

Elmer 7 Series / UNIX Thermal Analysis System software installed in the computer.

The DSC 7 operates on the power compensated "null-balance" principle, in which

energy absorbed or liberated by the specimen is exactly compensated by adding or

subtracting an equivalent amount of electrical energy to a heater located in the sample

holder. The power (energy per unit time) to the furnaces is continuously and

automatically adjusted in response to any thermal effects in the sample, so as to maintain

sample and reference holders at identical temperatures. The differential power, AP,

required to achieve this condition is recorded as the ordinate with the temperature or time

as the abscissa.



3.3 Calibration of the DSC


A calibration procedure provides a vital check of the reproducibility and accuracy

of the DSC measurements 127-129 as it the only way of checking the many varying

experimental parameters and their interaction. A DSC measures the differential power

output as a function of the programmed temperature and not the true specimen

temperature. Therefore, it is imperative that the proportionality factors, KQ (the heat

calibration factor) and Kp (the heat flow rate calibration factor), that relate the indicated

signal to the true heat and heat flow rate, be determined through calibration.








The DSC 7 was calibrated according to the guidelines of E. Gmelin and St. M.

Sarge. 130 Three calibrations were performed: (i) temperature calibration, (ii) heat (energy

output) calibration, and (iii) heat flow rate (power output) calibration.

Temperature and heat calibrations were carried out using high purity (> 99.99 %)

indium, tin, and lead as calibration standards. Two different masses of each "fresh"

(oxide layer removed) metal were weighed in aluminum pans that were then hermetically

sealed. With each calibration sample, the thermal effect was recorded at heating rates of

0.1-, 0.5-, 1.0-, 2.5-, 5.0-, and 10.0-Cmin -1. The experiments for each heating rate were

performed twice. The first experiments were never used to compute calibration

parameters usually, because of insufficient contact between sample and pan. After the

first melting, the contact area increases causing better heat transfer thus second runs were

used. Using a two standard calibration procedure, average values of the extrapolated

peak onset temperature for indium (156.57 0.10 C) and tin (231.30 0.15 C) at 10.0

C'min -1 were entered into the DSC 7 calibration set for the temperature scale

calibration. The literature value of the true transition heat (the area in J'g -1 under a

transition peak) of indium (28.45 Jg -') was also entered to calibrate the energy output

scale of the instrument. For each metal, the area under the melt transition was obtained

by integration using the DSC software. The heat calibration factor, KQ, was calculated

from




KQ = Qtrue (3-1)
A








where Qtue is the true transition heat and A is the measured peak area. Figure 3-2

displays KQ values as a function of both the heating rate and mass of the calibrant.

Because there are no significant differences between the values of KQ for each mass or

the different heating rates (most obvious at the higher heating rates), the mean calibration

curve in Figure 3-3 was calculated. The scatter observed in Figure 3-3 data is typical for

a power compensated DSC.'30' 131 An average value of KQ = 1.04 0.02 was calculated

and used to correct all measured peak areas prior to data analysis. This value was

determined from the data obtained at 10 Cmin -1 on the larger mass of each calibrant.

(The same heating rate, and similar masses of polymer specimens will be employed in the

enthalpy recovery experiments).

The heat flow rate of the DSC 7 was checked with synthetic sapphire (a-A1203,

corundum) over the range 25 to 180 C using a heating rate of 10.0 Cmin -1. Runs were

performed on two sapphire samples of different masses and an empty aluminum pan.

Each calibration, which consisted of measuring the calibrant and measurement with the

empty pan, was repeated three times. Values of Kp which are necessary to determine the

actual heat flow rate of the sample, were calculated from the data using the relation:




K, (T) = Cps,,p (T).q (3-2)
0.060. [P,, (T) P( (T)]



where: Cp. Sapp = heat capacity of sapphire (in JYK-)

q = heating rate (in Kmin -')

Pm = measured heat flow rate of the sapphire (in mW)


























1.2


1.0


Heating rate, q


(C min 1)


Figure 3-2 Dependence of the heat calibration factor, KQ, on heating rate and mass of
indium, tin, and lead (e = sample mass 11.6 mg, D = sample mass 3.5 mg).


0




- *0

*


0
0]










I I I I *
























13
0


*

A








0
1I I 2 I 3 I
150 200 250 300 3


T,, (C)









Figure 3-3 Heat calibration curve determined with indium, tin, and lead for the DSC 7
(D1. A, o = sample mass 3.5 mg; m, A, @ = sample mass 11.6 mg)








PO = measured heat flow rate of the empty pan (in mW).

T = temperature (in Kelvin (K))

The heat capacity of sapphire was determined by multiplying the mass of the sapphire by

its specific heat capacity which was calculated from the equation: 130



Cp. sapp = 5.81126x 101 + 8.25981 x 10-3 T 1.76767x 10-T2

+ 2.17663 x 108 T3 1.60541 x 10 -" T4 + 7.01732 x 10-'5 T5

1.67621 x 10-18 T 6 + 1.68486 x 10-22 T7,

290 K < T(K) < 2250 K (3-3)



Figure 3-4 shows only part of Kp(T) as a function of both temperature and mass

for the DSC 7. There is very little dependence of Kp(T) on temperature or mass;

therefore, an average calibration curve (the solid line) can be calculated. Average values

of Kp are fairly constant for this instrument. The values at various temperatures were

used to adjust measured power outputs to actual sample power outputs (Ptrue) using the

relation:




Kp (T)- P,,.(T) (3-4)
P, (T)


All adjustments were made prior to data analyses.













































0.4
3


10


320 330 340 350 360 370 380 390


Temperature (K)












Figure 3-4 Heat flow rate calibration curve determined from several runs with two
different masses of sapphire for the DSC 7. The solid line is the average heat calibration
factor.


m =14.31 mg

... -t t*llls = .. .. m



m = 9.21 mg






I I I I I I *









Data from a DSC can be very reliable and reproducible if certain necessary

procedures are followed. To ensure these aspects in the DSC data presented in this

dissertation, careful attention was given to the following parameters: (i) flat, thin

specimens were used in all situations, (ii) flat aluminum DSC pans were matched to

within 0.01 mg, (iii) the specimen and reference pans were always placed in the center of

the DSC furnaces, (iv) the vented platinum lids used to cover both furnaces were always

oriented in the same position, (v) the furnaces were purged with dry helium gas at a rate

of 25 mLmin -1, (vi) the DSC outer enclosure (the dry box) was constantly purged with

dry nitrogen gas, (vii) the ice and water coolant was always kept at the same level in the

reservoir, (viii) identical scanning rates were employed on all polymer specimens, and

(ix) the mass of the polymer specimen was selected to be as close as possible or equal to

that of the sapphire standard.


3.4 Thermal Treatments


Following the calibration, thermal effects in PS were investigated. The PS

specimen was cut from the same atactic PS sample as the dilatometer specimens. The

study is discussed in greater detail in Chapter 4. Below, however, the approach taken is

discussed and analyses are shown using a representative data set from the PS study. Note

that key results on all polymer samples used in this research were obtained by following

similar methods and analyses.








3.4.1 Specimen Characterization


Before initiating enthalpy recovery experiments, the PS specimen has to be

characterized. The previously dried and weighed specimen was hermetically sealed in an

aluminum pan and placed in the DSC furnace. This single specimen of PS was used

throughout and left untouched in the instrument furnace in an attempt to reduce

experimental scatter due to differences in heat transfer effects. A check of the structural

thermal stability of the specimen was made by cycling the instrument between 35- and

180-C several times. Structural equilibrium was achieved in the specimen when the

heating and cooling curves were superimposed. After the third set of scans this was the

case for the PS specimen.

The glass transition temperature of PS was measured next. The specimen was

first annealed at a high temperature for some time to ensure it was in equilibrium and to

erase the effects of previous thermal histories, was quenched at a cooling rate of 100 C

min -1, and then was immediately reheated at 10 'Cmin -1. The mid-point of the

inflection on the power output curve in the glass transition region was calculated as Tg

(Figure 3-5). The enthalpic glass transition temperature (or the fictive temperature), Tf, H,

was also calculated. Both calculations were performed by the UNIX software on the DSC

computer.





























I..
0 g







I I I I I I I I i ,
50 60 70 80 90 100 110 120 130 140 150

Temperature (C)









Figure 3-5 DSC curve for PS obtained at a heating rate of 10 C'min -1 following a
quench at 100 C'min -1.




Full Text

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AGREEMENT_INFO ACCOUNT UF PROJECT UFDC
FILES


PHYSICAL AGING BEHAVIOR IN GLASSY POLYMERS - POLYSTYRENE
AND A MISCIBLE BLEND
By
BERNARD A. LIBURD
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1999

To my wife, Coleen,
with deepest love and gratitude
To my daughters, Kibirsha and Ijunanyah,
rays of sunshine
who make forgetting the workday frustrations quite easy
and
To my dad, James Phipps,
whose never-waning faith
inspires my every effort

ACKNOWLEDGMENTS
Many persons have contributed in making this dissertation a reality. First and
foremost, I would like to thank my research advisor, Dr. Randy Duran, for his support and
guidance during my tenure in his group. Dr. Duran allowed me the opportunity to
explore a fascinating field of chemistry I never knew existed before I came to the
University of Florida. To him I express my sincere appreciation.
During the initial stages of this research, one of the more daunting tasks was that
of assembling and learning to use the automated dilatometer. No one was more
instrumental in getting me started than Dr. Pedro Bernal at Rollins College in Florida.
Dr. Bernal invited me to his institution and gave freely of his time as he recounted his
experiences with the instrument and the necessary initial preparations for performing
experiments. I would like to express my deepest gratitude to him for his time and the
many helpful discussions.
Further thanks are extended to Joe Caruso, without whom volume measurements
in this dissertation would not have been possible. Joe is an excellent glassblower and
utilized his expertise and skill in fabricating the many dilatometers I requested of him. I
could always count on Joe to repair or replace my broken dilatometers in a timely
manner. He would frequently find the time to get my jobs done ahead of schedule even
though he often had a heavy workload. I cannot thank him enough for his contributions

to this project. Knowing he was there in the glass shop, in support of my research efforts,
was always a comforting thought.
I must also thank past and present members of the Duran research group and
members of the Butler Polymer Research Laboratory for enriching my graduate
experience and for making the Polymer Floor one of the best places to do research at the
University of Florida.
Special thanks go to Drs. Roslyn White, Michelle Fletcher, Thandi Buthelezi, and
Sophia Cummings for their friendship and encouragement. Also, thanks must be given to
the many members of the UF chapter of the National Organization for the Professional
Advancement of Black Chemists and Chemical Engineers (NOBCChE), who not only
served as a support group, but also undertook the positive work of going into area schools
and encouraging minority students to pursue future careers in science.
Appreciation is expressed to the University of Florida and the National Science
Foundation for providing the financial support for my graduate education and research.
Finally, I would like to thank my wife, Coleen, to whom I owe an immense debt.
She has given more in understanding and genuine compassion than I can ever hope to
repay. Despite the many lost weekends and rare family activities, she has never wavered
in her support and encouragement. She made the more trying times pleasant and
bearable. That she put up with all of this while taking care of our two young daughters
(not an easy task by any means), with very little assistance from me, is much more than
any man should ask for. She has my deepest love and respect, for she is truly my better
half.
IV

TABLE OF CONTENTS
page
ACKNOWLEDGMENTS iii
LIST OF TABLES vii
LIST OF FIGURES viii
ABSTRACT xvi
CHAPTERS
1 INTRODUCTION 1
1.1 The Nature of Physical Aging 1
1.2 The Glass Transition Temperature 3
1.3 The Basic Features of Structural Recovery 7
1.4 Theoretical Treatments of Physical Aging 14
1.5 Summary of Theoretical Aspects 36
1.6 Comparison of Volume and Enthalpy Studies 37
1.7 Objectives of This Research 40
2 AUTOMATED VOLUME DILATOMETRY 42
Chapter Overview 42
2.1 Background 42
2.2 Instrument Description 45
2.3 Data Manipulation 50
2.4 Preparation of a Specimen Dilatometer 50
2.5 Volume Measurements 51
2.6 Quantitative Aspects 54
2.7 Calibration of the LVDT 55
2.8 Test Measurements on Polystyrene 56
2.9 Error Considerations and Analysis 67
v

3 DIFFERENTIAL SCANNING CALORIMETRY 71
Chapter Overview 71
3.1 Introduction 71
3.2 Instrumental Features 73
3.3 Calibration of the DSC 75
3.4 Thermal Treatments 82
4 THE TIME-DEPENDENT BEHAVIOR OF VOLUME AND ENTHALPY IN
POLYSTYRENE 97
4.1 Introduction 97
4.2 Experimental 99
4.3 Results and Discussion 103
5 PHYSICAL AGING IN A POLYSTYRENE / POLY(2,6-DIMETHYL-1,4-
PHENYLENE OXIDE) BLEND 145
5.1 Introduction 145
5.2 Experimental 153
5.3 Results and Discussion 156
6 SUMMARY AND CONCLUSIONS 191
6.1 Introduction 191
6.2 Instrumentation 191
6.3 Volume and Enthalpy Recovery Within PS and PS/PPO 193
6.4 Aging in PS/PPO Versus Aging in PS 195
APPENDIX A CONSTANT TEMPERATURE AGING PROGRAM 196
APPENDIX B TEMPERATURE SCANNING PROGRAM 200
APPENDIX C CALCULATIONS OF REFERENCE SPECIFIC VOLUME
AND TRAPPED GAS VOLUME IN DILATOMETER 212
REFERENCES 217
BIOGRAPHICAL SKETCH 228
vi

LIST OF TABLES
Table page
2-1 Volume thermal expansion coefficients for PS 64
3-1 Aging data for the enthalpy recovery of PS at 98.6 °C 92
4-1 Physical aging rate data for PS at various aging temperatures 120
4-2 Aging parameters for PS 134
4-3 Quantification of the energy per unit free volume for PS 143
5-1 Quantification of the energy per unit free volume for 90/10 PS/PPO 180
Vll

LIST OF FIGURES
Figure page
1-1 Illustration of the relationship between specific volume and
temperature for a glassy polymer 4
1-2 The cooling-rate dependence of the specific volumeof a
glass-forming amorphous polymer 5
1-3 Nonlinear effect of volume recovery of atactic polystyrene.
Samples were equilibrated at various temperatures
(and 1 atm.) as shown adjacent to each recovery curve
and then quenched to the aging temperature, Ta = 98.6 °C.
The equilibrium volume at 98.6 °C is denoted by v» 8
1-4 Asymmetric effect of isothermal volume recovery of atactic
polystyrene. Samples were annealed above Tg, quenched to
95.8 °C and 101.4 °C, equilibrated at those temperatures and
reheated to 98.6 °C. The equilibrium volume at 98.6 °C is
denoted by v,*, 9
1-5 Memory effects of the volume recovery of poly(vinyl acetate)
after double temperature jumps. Samples were quenched from
40 °C to different temperatures and then aged for different
amounts of time before reheating to 30 °C: (1) direct quenching
from 40 °C to 30 °C; (2) 40 °C to 10 °C, aging time = 160 hrs;
(3) 40 °C to 15 °C, aging time = 140 hrs; (4) 40 °C to 25 °C,
aging time = 90 hrs. The equilibrium volume at 30 °C is denoted
by Vo» (reprinted after ref. 18 with permission of publisher) 10
1-6 DSC traces of polystyrene showing the endothermic peak associated
with aging 12
1-7 Schematic plot of specific volume or enthalpy as a function of time
during isothermal structural recovery in response to a quench from
a one temperature to a lower temperature 13
vm

1-8
\
Schematic specific volume - temperature plot of a glassy polymer
showing the temperature dependence of the free volume 15
2-1 Schematic illustration of the dilatometer and its measuring system:
(A) LVDT coil, (B) LVDT core, (C) wire lead to LVDT
readout/controller, (D) micrometer, (E) sample, (F) stainless steel
connecting rod, (G) stainless steel cylindrical float, (H) glass
dilatometer, (I) metal rod support 47
2-2 Schematic diagram of the components of the automated dilatometer :
(A) & (D) analog to digital converters; (B) & (C) personal computers;
(E) & (G) high precision digital thermometers; (F) LVDT readout/controller;
(H) automated dilatometer; (I) TMV-40DD/aging bath; (J) & (N) platinum
resistance temperature probes; (K), (M) & (P) silicon oils; (L) EX-251
HT/annealing bath; (O) Hart Scientific High Precision bath 49
2-3 Plot of core displacement vs. LVDT voltage. The connecting rod was
turned in both clockwise (o) and counterclockwise (+) directions
by a micrometer-type gage head calibrator. The slope is 2.5504 x 10 3
± 2.2464 x 10 6 cm mV Calibration temperature was 28.5 ± 1.0 °C 57
2-4 LVDT voltage as a function of temperature for a mercury-only
dilatometer. Data collected at a constant scan rate of 0.100 °C min
(A = heating data; O = cooling data) 58
2-5 Temperature dependence of the LVDT voltage in the
volume measurements of polystyrene for (a) three scans
(a cooling-heating-cooling sequence) (b) a cooling scan after
the dilatometer was removed from the bath and allowed to
cool at room temperature. Temperature scans performed at
arate of 0.100 °Cmin 60
2-6 Deviations of experimental values from best-fit straight lines drawn
through the linear portions of the voltage versus temperature curves
(symbols correspond to those in Figure 2-5) 61
2-7 Specific volume as a function of temperature for PS. The average Tg,
calculated from the intersections of the glassy and liquid lines of four
curves obtained at a scan rate of 0.100 °C min -1, was 97.1 ± 1.5 °C.
(Some data points have been excluded for clarity) 62
2-8 Specific volume as a function of temperature for two different PS
specimens. (Six curves representing three heating and three
cooling scans are superimposed) 63
IX

2-9 Specific volume change showing the structural recovery of two
specimens of glassy PS at 95.6 °C and 98.6 °C. Experiments
performed at normal atmospheric pressure (•, □ = specimen 1,
A = specimen 2) 65
2-10 Relative specific volume change as a function of time showing
the long time stability of the LVDT. The time interval is from
the initial attainment of equilibrium until the end of the experiment.
Measurement temperature was 95.6 °C 66
3-1 (A) Block diagram and (B) schematic diagram of a power
compensated DSC system (reprinted after ref. 126 with permission of
publisher) 74
3-2 Dependence of the heat calibration factor, Kq, on heating rate and
mass of indium, tin, and lead (• = sample mass 11.6 mg,
â–¡ = sample mass 3.5 mg) 78
3-3 Heat calibration curve determined with indium, tin, and lead for the
DSC 7. ( □, A, o = sample mass 3.5 mg; ■,▲,• = sample mass 11.6 mg) 79
3-4 Heat flow rate calibration curve determined from several runs with
two different masses of sapphire for the DSC 7. The solid line is
the average heat calibration factor 81
3-5 DSC curve for PS obtained at a heating rate of 10 °C min 1 following
a quench at 100 °C min _1 84
3-6 Illustration of procedural steps for measuring enthalpy changes in DSC 86
3-7 Output power (P) of the aged and unaged PS specimen, and the
difference between the two output signals (AP). Aging condition
is 98.6 °C for 6 h 87
3-8 Schematic diagram describing the pathway of enthalpy evolution
during DSC measurements. Path ABCO'CA represents the
physical aging process and path ABOBA is without aging 88
3-9 The change in enthalpy versus log ta for isothermal aging of PS at
98.6 °C. The data level off when equilibrium is reached 93
4-1 Molecular structure of polystyrene 100
x

4-2 Schematic diagram of volume and enthalpy evolution during
physical aging. The material is annealed above the Tg ( = Tf) for
a period of time and then cooled to and aged at Ta (path ABC).
Path CD represents the excess enthalpy or specific volume 101
4-3 Specific volume - temperature curve for PS obtained with the
volume dilatometer at a cooling rate of 0.100 °C min '. The
discontinuity at ~ 70 °C is an experimental artifact. (Not all data
points are included; linear fit ranges were indicated in Chapter 2
where the data first appeared) 104
4-4 The normalized output power (P/m) (symbol O) and calculated
specific heat capacity (symbol A) of PS as a functions of temperature
and time. Curve obtained at a heating rate of 10 °C min '* following
a rapid quench at 100 °C min '* 105
4-5 Determination of the Active and glass transition temperatures of
PS by the DSC 106
4-6 Av»c (circles) and AFU (squares) as a function of aging temperature
for PS 108
4-7 Isochronal (time = 137 s) specific volume (squares) and equilibrium
specific volume (triangles) versus temperature for the quenched PS,
compared with data (circles) on the same polymer from slow cooling
(rate = 0.100 °C min “') experiments. (Observed peak at about 70 °C
is an experimental artifact) 109
4-8 Isothermal volume contraction of PS at various aging temperatures
after a quench from Teq = 116.6 °C Ill
4-9 Isothermal volume contraction of PS at various aging temperatures
following a quench from Teq = 116.6 °C (8v is calculated as indicated
in text). Data at 93.6 °C are included for comparison 112
4-10 The change in enthalpy versus log aging time for PS at various
temperatures. Each curve, except the bottom curve, is shifted
vertically by 0.5 J g 1 for clarity 113
4-11 The change in enthalpy versus log aging time for PS at 81.6 °C and
91.6 °C. For clarity, the curve at 91.6 °C is shifted vertically by
0.5 J g •' 114
4-12 Isothermal enthalpy contraction of PS aged at the indicated temperatures
following a quench from T0 = 138.6 °C 115

4-13 Isothermal enthalpy contraction of PS aged at 81.6 °C and 91.6 °C
following a quench from T0 = 138.6 °C (calculation of 8h is
described in the text). The isotherm from 93.6 °C is also added
for comparison 116
4-14 Physical aging rate, r, as a function of temperature, for PS (o = r'v and
• = Th), over the same time interval 119
4-15 Time necessary for the attainment of thermodynamic equilibrium, U,
for volume (open circles) and enthalpy (solid circles) recovery at
different temperatures for PS 121
4-16 The effective retardation time of enthalpy recovery versus the
effective retardation time of volume recovery for PS aged at various
temperatures 123
4-17 Plots of In xeff for volume recovery (P = v, open symbols) and enthalpy
recovery (P = H, filled symbols) as a function of the excess specific
volume of PS at different aging temperatures 126
4-18 Plots of In Teff, h as a function of the distance of the PS polymer from
enthalpy equilibrium 128
4-19 Arrhenius plot of In A'(Ta) versus 1/Ta for volume recovery in PS 132
4-20 Arrhenius plot of In A'(Ta) versus 1/Ta for enthalpy recovery in PS 133
4-21 The enthalpy change per unit volume change with time at (a) 98.6 and
97.6 °C, (b) 95.6 and 93.6 °C, and (c) 91.6 and 81.6 °C (lines are
included only as visual aids) 135
4-22 Comparison of volume (empty shapes) and enthalpy (filled shapes)
isotherms at 100.6 °C and 98.6 °C as a function of aging time 138
4-23 Comparison of volume (empty shapes) and enthalpy (filled shapes)
isotherms at 97.6 °C and 95.6 °C as a function of aging time 139
4-24 Comparison of volume (empty shapes) and enthalpy (shapes with
error bars) isotherms at 93.6 °C and 91.6 °C as a function of aging
time 140
4-25 Comparison of volume (dotted shapes) and enthalpy (shapes with
error bars) isotherms at 81.6 °C as a function of aging time 141
xii

5-1 Molecular structures of (a) polystyrene and
(b) poly(2,6-dimethyl-1,4-phenylene oxide) 149
5-2 TGA curve of 90/10 PS/PPO blend showing the range over which
the blend thermally decomposes. The arrow indicates where phase
separation begins (~ 355 °C). The specimen was purged with air while
varying the temperature rate at 30 °C min -1 154
5-3 Specific volume-temperature curve for the PS/PPO (90/10) blend and
the PS homopolymer obtained at a cooling rate of 0.100 °C min 1 in
the volume dilatometer. Peaks at ~ 70 °C on each curve are experimental
artifacts. (Linear fits were from 45 to 65 °C and 120 to 136 °C for
PS/PPO; fits for PS have been previously indicated in the text) 157
5-4 The mass normalized output power and calculated specific heat
capacity as a function of temperature and time for PS/PPO (90/10)
and PS. Curves obtained at a heating rate of 10 °C min _1 following
a rapid quench at 100 °C min (Triangles = specific heat capacity;
circles and squares = power; linear ranges for Tf determination were
65 to 80 °C and 133 to 143 °C for PS/PPO and for PS, as previously
indicated in the text) 158
5-5 DSC trace of 90/10 PS/PPO blend showing the single Tg, compared
with DSC traces of PS and PPO. Data was obtained at heating rate of
10.0 °C min _1 159
5-6 AVo„ (circles) and APL, (squares) as a function of aging temperature for
PS/PPO blend 161
5-7 Isochronal (time = 137 s) specific volume (circles) and equilibrium
specific volume (triangles) versus temperature for the quenched
PS/PPO, compared with data (squares) on the same polymer from slow
cooling (rate = 0.100 °C min _1) experiments (observed peak at about
70 °C is an experimental artifact) 162
5-8 Isothermal volume contraction of PS/PPO blend at various aging
temperatures after a quench from Teq = 130.8 °C 163
5-9 Isothermal enthalpy contraction of PS/PPO blend aged at the indicated
temperatures following a quench from T0 = 150.0 °C 166
5-10 Volume recovery data for two specimens of 90/10 PS/PPO during
isothermal aging at Ta = 106.8 °C following a quench from 130.8 °C.
Tests for thermo-reversibility are represented by "+" symbols; solid
circles and diamonds are first runs for the two specimens 167
Xlll

5-11 Time necessary for the attainment of thermodynamic equilibrium, U,
for volume (open circles) and enthalpy (solid circles) recovery at
different temperatures for PS/PPO 169
5-12 Plots of In Teff for volume recovery (P = v, open symbols) and enthalpy
recovery (P = H, closed symbols) as a function of the excess specific
volume of PS/PPO at five aging temperatures 171
5-13 Plots of In Teff, h as a function of the distance of the PS/PPO system from
enthalpy equilibrium for five aging temperatures 172
5-14 Arrhenius plots of In A’(Ta) versus 1/Ta for (a) volume recovery and
(b) enthalpy recovery in 90/10 PS/PPO 174
5-15 The enthalpy change per unit volume change of the 90/10 PS/PPO
blend as a function of aging time at 100.8- and 106.8-°C 175
5-16 Comparison of volume (empty shapes) and enthalpy (filled shapes)
isotherms at 115.8- and 112.8-°C as a function of aging time in 90/10
PS/PPO blend 177
5-17 Comparison of volume (empty shapes) and enthalpy (filled shapes)
isotherms at 109.8- and 106.8-°C as a function of aging time in
90/10 PS/PPO blend 178
5-18 Comparison of volume (empty shapes) and enthalpy (filled shapes)
isotherms at 100.8 °C as a function of aging time in 90/10 PS/PPO
blend 179
5-19 Volume recovery curves of 90/10 PS/PPO (open symbols) and PS (filled
symbols) at (a) Ta = Tg - 7.4 °C (curves 1 & 2), (b) Ta = Tg - 4.4 °C
(curves 3 & 4), and (c) Ta = Tg - 9.4 °C (curves 5 & 6) 182
5-20 Plots of In Teff versus excess volume of 90/10 PS/PPO (open
symbols) and PS (filled symbols) from volume recovery curves at
(a) Ta = Tg - 7.4 °C (1 & 2), (b) Ta = Tg - 4.4 °C (3 & 4), and
(c) Ta = Tg - 9.4 °C (5 & 6) 184
5-21 Cooling curves of PS/PPO and PS compared at Tf = 97.1 ± 1.5 °C.
The original PS/PPO curve was shifted by -7.3 °C and + 0.016350
cm 3 g 1 (peaks observed around 70 °C on each curve are experimental
artifacts) 189
xiv

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
PHYSICAL AGING BEHAVIOR IN GLASSY POLYMERS - POLYSTYRENE
AND A MISCIBLE BLEND
By
Bernard A. Liburd
December 1999
Chairman: Randolph S. Duran
Major Department: Chemistry
Isothermal volume and enthalpy recovery due to physical aging in polystyrene
(PS) and a miscible blend of polystyrene/poly(2,6-dimethyl-1,4-phenylene oxide)
(PS/PPO) were measured by dilatometry and calorimetry. The aim of these
measurements was to directly compare volume and enthalpy recovery within the same
polymer, and possibly between polymer systems.
Volume data were collected with a custom-built automated volume dilatometer.
Automation was accomplished by use of a linear variable differential transformer, which
not only provided high resolution, precision and good accuracy of the data, but most
significantly, automated the entire data taking process. Enthalpy data were collected with
a differential scanning calorimeter following procedures that allowed accurate monitoring
of enthalpy changes.
xv

Excess volume (6v) and enthalpy (5h) quantities were calculated, compared and
analyzed for PS and a 90/10 % (by mass) PS/PPO polymer blend. Blend miscibility was
assessed by the single glass transition temperature criterion. It was found that the times
for both excess quantities to attain equilibrium in each polymer were the same within the
limits of experimental error. In both polymers, recovery rates determined from single
effective retardation times (Xeff’s) were found to be dissimilar at high aging temperatures
(Ta’s), but similar or identical at lower Ta’s. A single parameter approach was used to
calculate aging parameters that showed some of the similarities and differences between
volume and enthalpy recovery functions. Comparison of xeff’s at the same value of 5y
clearly showed that enthalpy recovered faster than volume in each polymer system.
The data was analyzed for the energy to create unit free volume. Values for PS
were consistent with the measurements of Oleinik, but were smaller than those for
PS/PPO. Further, it was shown that volume and enthalpy approached equilibrium
differently with volume initially recovering faster in both polymers.
Volume recoveries in PS/PPO and the constituent PS homopolymer were also
examined at equal temperature distances, Tg - T. The blend aged faster and had a total Sy
much smaller than that for the pure PS homopolymer. These features were interpreted in
terms of greater free volume in the blend and the presence of concentration fluctuations.
xvi

CHAPTER 1
INTRODUCTION
Glasses, which are by a broad definition amorphous solids, are among the oldest
materials known to mankind. In the last three decades there has been considerable
renewed interest in these materials spurred by their newly found applications in advanced
technologies, such as electronics, telecommunications, and aerospace. This interest has
led to considerable research efforts aimed at understanding the fundamental
characteristics of the glassy state, mainly using synthetic organic polymers.
It is well known that glasses exist in a non-equilibrium state. If, after its
formation history, a glass is kept at constant environmental conditions, it undergoes a
process whereby it tries to reach an equilibrium state. ’ This process is commonly called
structural recovery, structural relaxation, or in general physical aging and manifests
itself in structural and property changes of glassy and partially glassy polymers.
1.1 The Nature of Physical Aging
Physical aging - 8 12 refers to the time-dependent observed change that occurs in a
property of any amorphous material at a constant temperature. It occurs because of the
long-lived unstable states that are produced during the cooling of a glassy polymer from a
temperature above its glass transition temperature (Tg), to a temperature in the vicinity of,
or below the Tg. As a glassy polymer is cooled under normal conditions, it passes from
1

2
the liquid through the glass transition and into the glassy state. A rapid decrease in
molecular motion occurs as the transition temperature is approached. The polymer
molecules are not able to reach their equilibrium conformation and packing with respect
to the rate of cooling. Further cooling results in the molecules essentially being “frozen”
into a non-equilibrium state of high energy. Thermodynamic quantities such as specific
volume, enthalpy and entropy are in higher energy states than they would be in the
corresponding equilibrium state at the same temperature. Although molecular motion is
greatly decreased in the glassy state compared to the liquid state, there remains some
finite motion which allows the excess thermodynamic quantities to decrease toward
equilibrium. As a result, there is a driving force for molecular rearrangement and
continued packing of the polymer chains. This drive toward equilibrium, which results in
densification of the polymer, is commonly referred to as physical aging. It is generally
viewed as a recovery phenomenon and can be determined through a number of processes,
among them, volume recovery and enthalpy recovery. In contrast to chemical aging or
degradation which leads to permanent chemical modification, physical aging is a thermo-
reversible process. By re-heating the aged material to above the Tg, the original state of
thermodynamic equilibrium is recovered; a renewed quench through the Tg will induce
the same aging effects as before.
Physical aging affects many material properties of polymers: elastic modulus and
yield stress increase progressively while impact strength, fracture toughness, ultimate
elongation, and creep rate 8'9 decrease. Whenever polymers are in the glassy state, they
tend to become more brittle as they age and this affects their utility in any long-term
application. Therefore, physical aging must be considered in the design and

3
manufacturing of polymers, especially if their applications are to be at temperatures
below their Tg’s.
Numerous studies have been conducted on the variation of various physical
properties with time. Volume and enthalpy, which are thermodynamically analogous to
one another, have been two frequently measured properties. However, rarely have
parallel measurements of both quantities been made on the same batch of materials. The
research contained herein provide these data; in this work sensitive experimental
techniques are systematically applied to the same polymers to collect specific volume (or
volume) and enthalpy data for glassy polymers.
1.2 The Glass Transition Temperature
The glass transition occurs over a temperature interval for which no single
temperature is unique, but merely representative. A temperature called the glass
transition temperature, Tg, represents the transition, which is not a typical phase
transition. The Tg distinguishes an amorphous, polymeric solid from its melt, rubbery or
liquid state. At Tg, a large number of physical properties change. These include but are
not restricted to the specific heat capacity, expansitivity, compressibility, and dielectric
permittivity which change abruptly, and entropy, specific volume and enthalpy which
show gradual changes. Only the latter two properties will be discussed in this work.
Specific volume may be continuously measured in a mercury dilatometer. Figure
1-1 illustrates the relationship between specific volume and temperature for a glassy
polymer. If the polymer, in its liquid state, could be cooled infinitely slowly through the
glass transition, the dotted line would be followed, as all modes of molecular relaxation

4
would have enough time to completely relax. In practice however, finite cooling rates
cause the specific volume decrease to become retarded and the solid line is followed. The
point at which the retardation occurs is the (conventional) Tg.
Since the transition to the glassy state is a continuous curve, and the Tg is not well
defined, it is often more convenient to use the Active temperature, Tf, concept. 6’13,14 The
Active temperature is defined as a (hypothetical) temperature at which the glass would be
in metastable equilibrium if it could be brought to Tf instantaneously. It is located at the
Figure 1-1 Illustration of the relationship between specific volume and temperature for a
glassy polymer.

5
intersection of the extrapolated liquid and glass lines as shown in Figure 1-1, and is in
fact the same as the conventional Tg of the material. Although it appears that Tg and Tf
are precise temperatures, this is not the case as they both depend on the rate of cooling.
Each value shifts to a higher temperature if the cooling rate is faster (Figure 1-2);
experimental work has shown that Tg is changed by approximately 3 °C per factor of ten
change in the cooling rate. 1516 At higher cooling rates, the time for molecular
rearrangement is shorter than at the slower cooling rates, and the curve begins to deviate
from the equilibrium line at a higher temperature.
Figure 1-2 The cooling-rate dependence of the specific volume of a glass-forming
amorphous polymer.

6
Differential scanning calorimetry, DSC, is an easier and more convenient
technique for locating Tg. The technique is used to determine the enthalpy of a glassy
polymer and is analogous to the specific volume determined by dilatometry. Only a few
milligrams (~ 10 mg) of material is required. Consequently, faster rates of temperature
change are used in DSC experiments. Unlike dilatometery where samples are
characterized by cooling from the liquid to the glassy state, DSC characterizes samples
most commonly by heating up from the glassy state. When heating an amorphous
polymer, the glass transition phenomenon is observed as an abrupt change in the heat
capacity of the material. Integration of the heat capacity-temperature curve yields
enthalpy. An enthalpy-temperature plot is similar to the plot shown in Figure 1-1 except
that the curvature on both sides of the glass transition is slightly more developed. The
temperature at which the liquid and glass enthalpy curves intersect is the fictive
temperature and is similar to the temperature at which the specific volume of the glass
and liquid intersect. For any material at enthalpic or volumetric equilibrium at some
temperature, the Tf will simply be equal to that temperature.
Enthalpy is not the measured variable in DSC (the power is). Accordingly, the
method of determination of both the Tg and the Tf is not immediately obvious, as it is in
volume dilatometry (refer to Figure 1-1). There is considerable confusion in the literature
regarding these determinations. Adding to the confusion are frequently used terms such
as “onset Tg”, “mid-point Tg” and “end Tg”, which are determined at the step change in
heat capacity, but at best are only approximations to the conventional Tg. The problem,
however, is easily identified. The term Tg is an operational definition of a temperature
obtained when cooling occurs from the liquid to the glassy state, whereas the DSC uses a

7
heating scan from the glassy to the liquid state. The path by which the glass is formed
(i.e. its thermal history) will have an influence on the heating scan. In fact, Richardson
and Saville 23 have demonstrated that it is incorrect to determine Tg directly from DSC
curves because of the kinetic effects associated with aged glasses. Therefore, instead of
referring to a “glass transition temperature” of a material characterized by a heating scan,
it is more relevant and meaningful to use the fictive temperature (Tf). Values of Tf and
Tg are identical for unaged glasses, but for aged glasses the two move in opposite
directions as the amount of aging increases: Tf decreases, but the heat capacity curve
measured during heating moves to higher temperatures, thus higher Tg values.
1.3 The Basic Features of Structural Recovery
Volume recovery of polymers has been extensively studied by Kovacs, ' Endo
et al.,19 Hozumi et al.,20 and Adachi et al.21,22 Their works show three qualitative features
of the recovery process: non-linearity, asymmetry and memory effect. The first two
features result from single temperature jumps. The memory effects are observed after
two or more successive temperature jumps.
The non-linearity is shown in Figure 1-3. After equilibration at different
temperatures above a new equilibration temperature (98.6 °C), amorphous atactic
polystyrene is quenched to that temperature. Different temperature steps result in
different response rates as initially excessive volume states approach the same
equilibrium volume in a non-linear way. The asymmetry is observed when the
contraction and expansion curves with the same temperature step are compared, as
demonstrated in Figure 1-4. The contracting polymer is always closer to the equilibrium

8
than the expanding polymer. The rate of structural recovery depends on the magnitude
and the sign of the initial departure from the equilibrium state.
Figure 1-3 Nonlinear effect of volume recovery of atactic polystyrene. Samples were
equilibrated at various temperatures (and 1 atm.) as shown adjacent to each recovery
curve and then quenched to the aging temperature, Ta = 98.6 °C. The equilibrium volume
at 98.6 °C is denoted by v»,.

9
log (t - tn) (S)
Figure 1-4 Asymmetric effect of isothermal volume recovery of atactic polystyrene.
Samples were annealed above Tg, quenched to 95.8 °C and 101.4 °C, equilibrated at those
temperatures and reheated to 98.6 °C. The equilibrium volume at 98.6 °C is denoted by

10
The memory effect, illustrated by Figure 1-5, is the response from a glassy system
as it ‘remembers’ its previous thermal history. It is a more complex behavior than the
other two features and is the result of two successive temperature jumps of opposite
signs. The observed volume maximum appears only in samples that have not reached
Figure 1-5 Memory effects of the volume recovery of poly(vinyl acetate) after double
temperature jumps. Samples were quenched from 40 °C to different temperatures and
then aged for different amounts of time before reheating to 30 °C: (1) direct quenching
from 40 °C to 30 °C; (2) 40 °C to 10 °C, aging time = 160 hrs; (3) 40 °C to 15 °C, aging
time = 140 hrs; (4) 40 °C to 25 °C, aging time = 90 hrs. The equilibrium volume at 30 °C
is denoted by v„ (reprinted from ref. 18 with permission of publisher).

11
equilibrium at the lower temperature. Past the volume peaks, all of the curves
interestingly decrease to the same equilibrium volume.
Enthalpy recovery curves that are measured in situ 22'24 show the same features as
volume recovery. In DSC, however, the scan of an aged polymer usually shows the
presence of an endothermic peak (Figure 1 -6) whose position and intensity depend on the
aging conditions, both temperature and time. An amorphous polymer quenched from the
melt has excess enthalpy. During isothermal aging below the Tg, the excess enthalpy
decreases with aging time. On reheating the polymer above the Tg, the absorption of heat
results in the recovery of this enthalpy, also called the “Tg overshoot”. This recovery to
establish equilibrium generates the endothermic peak which appears superposed on the Tg
in the DSC scan. Pioneering studies of this phenomenon were made by Foltz and
McKinney 2" and Petrie,26 who all demonstrated that the magnitude of the endotherm
was a quantitative measure of the enthalpy relaxation that had occurred during aging.
These and other published results on amorphous polymers systems 27'37 have shown that
an endothermic peak is a general feature of structural recovery of glassy polymers and
that the peak area is a measure of the amount of enthalpy recovery or physical aging.
Thermal histories that combine high cooling rates and low aging temperatures
may produce endothermic peaks on the lower temperature side of the Tg. These
endotherms are called sub-Tg peaks. They have been observed in a number of polymers
systems including poly(vinyl chloride) (PVC), 34,38,39 polystyrene (PS),40'42 and
poly(methyl methacrylate) (PMMA).43 “46 Sub-Tg peaks increase in height and shift to
higher temperatures as aging time increases.34,47 Their formation can also be explained

12
in terms of the evolution of the enthalpy during the heating scan due to the structural
recovery of the polymer.
Figure 1-6 DSC traces of polystyrene showing the endothermic peak associated with
aging.

13
The generic response of the specific volume (v) or enthalpy (H) of a glassy
polymer following a quench from an equilibrium state at Ti to a lower temperature T2 is
shown schematically in Figure 1-7. The quench begins at time t = 0 and initially the
liquid polymer displays a “fast” or glass-like change in v and H associated primarily with
time
Figure 1-7 Schematic plot of specific volume or enthalpy as a function of time during
isothermal structural recovery in response to a quench from a one temperature to a lower
temperature.

14
the vibrational degrees of freedom. This is further followed by a “slow” or kinetically
impeded change in v or H associated with the structural recovery process, and continues
until equilibrium is reached at the new temperature.
1.4 Theoretical Treatments of Physical Aging
A complete theoretical understanding of the physical aging phenomenon is not yet
available. The existing theories can be divided into three main groups: free volume
theories, kinetic theories and thermodynamic theories. Although these theories may at
first appear to be very different, they really examine three aspects of the same basic
phenomenon and can be unified in a qualitative way. However, their degree of success in
quantitatively describing the phenomenon varies greatly.
1.4.1 Free Volume Theory
The bulk state of an amorphous polymer contains many voids or empty spaces.
The presence of these empty spaces can be inferred from a simple demonstration of
dissolving a polystyrene glass in benzene. One observes a contraction in the total volume
of the polymer when dissolved in the solvent. This observation indicates that a polymer
can occupy less volume and that there must have been some unused space in the glassy
matrix, which allowed for greater packing of the polymer chains. Collectively, the empty
or unused spaces are referred to as the free volume, Vf, which is more accurately defined
as the unoccupied space in a material, arising from the inefficient packing of disordered
chains in the amorphous regions of the material. Mathematically, Vf is defined by the
relationship:

15
v
f ~
V - V
o
(1-1)
where v is the observed specific volume of the sample and v0 is the specific volume
actually occupied by the polymer molecules. Each volume term is temperature
dependent. Figure 1-8 shows schematically the temperature dependence of free volume.
Figure 1-8 Schematic specific volume - temperature plot of a glassy polymer showing the
temperature dependence of the free volume.

16
The free volume is a measure of the space available for the polymer to adjust from one
conformational state to another. When the polymer is in the liquid or rubbery state the
amount of free volume will increase with temperature due to faster molecular motions.
The dependence of free volume on temperature above Tg can be expressed in terms of a
fractional free volume, f, as:
fT = fg + <*f(T-Tg) (1-2)
where fx is the fractional free volume at a temperature, T, above Tg, fg is the fractional
free volume at Tg, (f = Vf / v), and ctf is the expansion coefficient of the fractional free
volume above Tg.
The concept of free volume was first developed to explain the variation of the
viscosity, r|, of liquids above Tg.48 57 The starting point of the theory is the relationship
between viscosity and free volume, which is expressed by the empirical Doolittle 49'52
equation:
B
f] — A exp {v,,Vo) (1-3)
where A and B are constants with B being close to unity. According to this equation, if
v0 is greater than Vf, (i.e., the polymer chain is larger than the average hole size) the
viscosity will be high, whereas if v0 is smaller than Vf, the viscosity will be low. This
means that the viscosity is intimately linked to internal mobility, which in turn is closely

17
related to free volume. Hence, as free volume increases, the viscosity rapidly decreases.
Equation 1-3 has been found to be highly accurate in describing the viscosity dependence
of simple liquids. Moreover, because the mobility of a system is reflected by its viscosity
and there is an inverse relationship between free volume and viscosity, many researchers
have adopted the free volume theory to describe the volume recovery process that occurs
in glassy polymers.
Another important empirically derived relationship is the William, Landel and
Ferry (WLF) equation.15 It was developed to describe the change in viscoelastic
properties of polymers above Tg and is often employed to describe the time - temperature
dependence of physical aging. The WLF equation expressed in general terms, is:
log aT - -
C, (T-Tr)
C2 + T-Tr
(1-4)
where the temperature shift factor, ay = T|t / flTr = Xj / Txr (x is a characteristic segmental
relaxation time at temperatures T and Tr (reference temperature)), Ci and C2 are
constants. When Tr is set equal to Tg, Q and C2 are 17.44 and 51.6 K, respectively.
These values were once thought to be universal but variations have been shown from
polymer to polymer. Substitution of these values into equation 1-4 results in the relation:
log aT = -
17.44 (T-Tg)
51.6 + T-Tg
d-5)

18
This empirical expression is valid in the temperature range Tg < T < (Tg + 100 °C) and is
applicable to many linear amorphous polymers independent of chemical structure. Since
ax = Tt / Xte in equation 1-5, the WLF equation can be used to determine the relaxation
time of polymer melt behavior at one temperature in reference to another such as Tg. If
applied to the phenomenon of physical aging, this equation restricts molecular relaxation
times to a small temperature interval Tg to Tg - 51.6 K, and predicts that at T < Tg - 51.6
K molecular relaxation times are infinite, i.e., x = °° This suggests that for a quenched
amorphous polymer, physical aging effects will not be observed 52 K below Tg since
relaxation times far exceed experimental times. Despite this prediction, there is strong
evidence that aging occurs well below Tg - 51.6 K and involves molecular relaxations
associated with localized segmental motions (rotations of side groups and restricted main-
chain motions) and cooperative motions of the polymer chains. The connection between
the WLF equation and free volume is found in the mathematical definitions of the
“universal” constants Q and C2. The relationship is demonstrated in the following
paragraph.
Expressing the shift factor, ax in terms of the Doolittle equation and the fractional
free volume, f, the following is obtained:
n, _ exp[ B (1// - 1)]
nTr exp[B(l//r - 1)]
exp
(1-6)
If the reference temperature is set to Tg and then equation 1-2 inserted into equation 1-6,
the expression becomes:

19
aT =
Vt_
JIt
= exp
f
B
L V
1
/* + ccf(T -T)
4
= exp
B
( ocf(J-Tg) j
[fg + afcr-Tt) )
= exp
l 1
CQ V40
1
i i
(T-Tg)
[/.]
_af_
+ T~Tt
d-7)
The following equation is obtained by taking the logarithm of equation 1-7:
log aT
-B
(T-Tg)
[2.303/?
+
T-T
. laf\
(1-8)
This equation predicts a rapid increase in viscosity as the Tg is approached and free
volume decreases. By comparing equation 1-8 with equation 1-5, fg and otf can be
evaluated from:

20
= C, =-17.44 => /„ = 0.025 (when B = 1) (1-9)
2.3034
i = 51.6£ => af = —= 4.8 x 10 “4 (1-10)
af f 51.6 K 51.6 K
These expressions show the dependence of the “universal” constants, Ci and C2 on free
volume. The outcome of the fact that the WLF equation exhibits these constants is that
the fractional free volume at the glass transition temperature and the thermal expansion
coefficient of free volume also have “universal” values. These values are valid for a
wide range of materials, although by no means for all glass formers. The development of
the above ideas forms the core of the free volume theory which suggests that free volume
at Tg is of the order of 2.5 % for most materials.
The concept of free volume can describe quite well the mobility of many simple
and polymeric fluids. Two remarkable strengths of the free volume theory are its
conceptual appeal and relative simplicity, and the fact that the famous WLF equation can
be derived from it leading to “universal” parameters that have physically reasonable
values. Nevertheless, the free volume theory has a number of drawbacks. One drawback
is the free volume and occupied volume are not very clearly defined thus quantitative
interpretations of both are not obvious. Another drawback is the theory does not provide
insight into the molecular processes associated with physical aging and provides very
little information about the molecular motion itself. For more detailed information on the
free volume concept in glassy polymers, the reader is referred to the literature. 4'56,57'59,60

21
1.4.2 Kinetic Theory
The WLF equation was derived from free volume considerations in the previous
section. This equation can also serve to introduce some kinetic aspects of physical aging.
For example, if the time frame of an experiment is decreased by a factor of ten near Tg,
use of various forms of equation 1-5 indicate that Tg should be raised by ~ 3 °C:
lim
T->Tg
( 1 >
log aT
= lim
Í -17.44 ^
T-T
51.6 + T- T,
\ g 7
K g /
-0.338
T-
-1.0
-0.338
+ 3.0
(1-11)
For larger changes in time, values of 6 - 7 °C are obtained from equation 1-5, in
agreement with many experiments.
The kinetic theory to be developed in the next two subsections considers the
single-parameter model based on the free volume concept, and multi-parameter models
based on non-linearity and non-exponentiality (or distribution of retardation times), two
aspects of physical aging. Single parameter models are the simplest models and are
useful for qualitative descriptions of many of the features of aging. The model
summarized by Kovacs 61 is among the best and will be the one discussed here. Multi¬
parameter models are extensions of single parameter models and are more useful for
quantitative descriptions of aging behavior. Only the descriptions provided by the Tool-
Narayanaswamy-Moynihan-KAHR5 "7'18'62,63 models will be considered.

22
1.4.2.1 Single-parameter approach
In general, the properties of a pure substance in its equilibrium state can be
completely specified by its temperature (T) and pressure (p). However, in a non¬
equilibrium glassy state, additional parameters are required to specify the state of the
system. In the single-parameter model it is assumed that in addition to T and p, one
ordering parameter (free volume) is required to fully describe the non-equilibrium state of
a polymer glass. Early theories for the structural recovery of glasses were proposed by
Tool5’6 and Davies and Jones.1 These researchers assumed that the departure of glasses
from equilibrium depended upon a single ordering parameter and used a single
retardation time, T, to describe the process. Using this single retardation time and the
presumption that the rate of specific volume change is proportional to its deviation from
the equilibrium value, v», Kovacs9-18'64'6S proposed the following equation for isobaric
volume recovery:
dv
dt
asv~ V(t) - V,
r
d-12)
in which otg = (l/v instantaneous specific volume, v«, is the equilibrium specific volume and q = (dT/dt) is
the experimental rate of cooling (q < 0) or heating (q > 0).
At this point two new variables are introduced: 5, a dimensionless parameter that
represents the volume departure from equilibrium, and 8h (in J g _l), the enthalpy
departure from equilibrium or excess enthalpy. Both variables are defined as follows:

23
8 =
v(t) - v,
(1-13)
8h = H (/) - H
(1-14)
where H is the actual enthalpy, H» is the equilibrium enthalpy and the other terms are as
previously defined. Either variable can be used as the ordering parameter. For volume
changes, equation 1-12 becomes:
rd8^
= q A O' +
(1-15)
where Aa is the difference between the liquid and glass expansion coefficients, t is time
and xv is the isobaric volume retardation time. A similar expression for isobaric enthalpy
recovery is:
dt
qAcp +
(1-16)
in which Acp is the difference between the liquid and glass specific heat capacities and Th
is the enthalpy retardation time. Tool5’6'61 used the Active temperature (Tf) to define the
structure of a glass and proposed a general form of equation 1-15 in terms of Tf, i.e.,

24
dTfldt = -(:Tf-T)/rv (1-17)
where Tf = T + 8Aa and Tf = T + 5 h Acp are for volume and enthalpy recovery,
respectively. The solution to this expression determines how well actual glassy behavior
is described by the model.
Under isothermal conditions, equation 1-15 becomes:
dS_ = S_
dt tv
which has the solution
(1-18)
f
S = S0 exp
d-19)
where 8o characterizes the volumetric state of the polymer at time, t = 0. Equation 1-19
cannot, however, be fitted to experimental isothermal volume recovery data. To
overcome this shortcoming of the model, Tool5,6 assumed that xv was not a constant, but
that in addition to depending on T and p, it was also dependent on the instantaneous state
of the glass, i.e. on 5 or Tf. Utilizing the Doolittle viscosity equation in a form analogous
to equation 1-6, one can write the relationship between xv and xvg as:

25
r,
(1-20)
where Tv is the volume relaxation time at temperature T, xvg is the volume relaxation time
at equilibrium at a reference temperature Tg, B is a constant, and f and fg are the fractional
free volume at T and the equilibrium fractional free volume at Tg, respectively. Inserting
equation 1-20 into equation 1-15 leads to:
(dS\
(1-21)
A similar expression can be derived for enthalpy changes. It turns out that this
modification to give the retardation time a free volume dependence provides a qualitative
description of the isothermal physical aging of polymer glasses after a single temperature
jump and under constant rate of cooling or heating. In particular, the isotherms and the
asymmetry of approach towards equilibrium (see Figures 1-3 and 1-4) are reasonably well
described by this model. Despite these successes, however, single-parameter models fail
completely in describing memory effects (see Figure 1-5). This is because they predict
that d5/dt would be 0 at the start when 8 = 0.

26
1.4.2.2 Multi-parameter approach
Multi-parameter models were developed in an attempt to separate the effects of
temperature and structure during physical aging of materials. Kovacs et al. attributed
memory effects to the contributions of at least two independent relaxation mechanisms
involving two or more retardation times. These authors proposed a multi-parameter
approach called the KAHR 63 (Kovacs-Aklonis-Hutchinson-Ramos) model. In this
model, the aging process is divided into N sub-processes, which in the case of volume
recovery may be represented as:
dS 8
L = qba, + (1 < i < N) (1-22)
dt t¡
in which Aa¡ = g¡AoCi is the weighted contribution of the i-th parameter to Aa (= oíl -
Og) with
2><=1 0-23)
i = 1
Each ordering parameter, i, contributes an amount to the departure of the fractional free
volume from equilibrium and is directly associated with a unique retardation time, T¡.
Further, the KAHR model assumes that the 8¡’s do not affect each other. Although it is
unlikely this assumption is true, it does simplify the mathematics involved greatly. The
total departure from equilibrium is then given by the sum of all the individual 5¡, i.e.

27
(1-24)
i = 1
Similar equations can be written for the enthalpy.
Assuming that the retardation time depends on both temperature and structure, the
solution to equation 1-22, is:
r,(7\ S) = Tir exp[d(Tr - T)]exp[-(1 - x)6S/Aa] (1-25)
where T¡, r is the value of in equilibrium at the reference temperature, Tr, 0 is a structure
parameter which, within a limited temperature interval around Tg, is approximately equal
to Ah*/RTg (Ah* is activation energy), and x (0 < x < l)isa partitioning parameter (or
the non-linearity term) that determines the relative contributions of temperature and
structure to x¡: x = 0 expresses a pure structure dependence whereas x = 1 expresses a pure
temperature dependence. The corresponding equation for enthalpy recovery is:
T¡(T, 8h) = Tir exp[0(Tr - r)]exp[-(l - x)0SH /Acp] (1-26)
Both equations account for the non-linear aspect of the aging process. The distribution of
retardation times is non-continuous and is seen in equations 1-25 and 1-26 where the
subscript i refers to the i-th sub-process of a discrete distribution of N sub-processes.

28
A discrete distribution is advantageous as it allows examination of 5¡ (or 5h. 0 at any point
during the aging process.
The temperature dependence of x¡ at constant 5 is given by the temperature shift
function, at:
TjiT, 8)
Tt exp[0(T, - T)]
(1-27)
while the structural dependence is given by the structural shift function a§:
S)
T,(T, 0)
exp[-(l - x )65 / A a]
(1-28)
where 5 = 0 denotes equilibrium. A combination of equations 1-27 and 1-28 leads to the
following expression:
r, (7\ S) = ri raTas
(1-29)
The retardation time spectrum, G(t¡, r) is obtained from the parameters g¡ and r.
The spectrum has a constant shape, assured by assuming that the gj’s are independent of T
and 5, whereas x¡ (at the same T and 5) is given by equation 1-29. A change in
temperature from Tr to T or a change in 5 will thus shift the spectrum along the log x axis
by amounts log aj or log a¿, respectively. This fundamental assumption of the spectrum

29
of retardation times shifting its position with respect to the internal structure but not
changing its shape, is referred to as the thermorheological simplicity of physical aging.
For any thermal history of the type
T(t) = T0 + \'oqdt (1-30)
where To, is the temperature at which an equilibrium state (all 8¡s = 0) is initially
established, the thermal history dependence of 5 can be written in a compact form using a
reduced time variable z:
Z = j'o(aTasy'dt (1-31)
which reduces the instantaneous rates of change of structure (8¡) at any temperature and 8
to those obtained in equilibrium at T. The relevant expression for 5(t) (which depends on
the thermal history and material properties) is then given by:
£(z) = -Aaf R(z - z)—dz
J0 dz
(1-32)
where R(z), the normalized retardation (recovery) function of the system, is determined
from:

30
N
R(z) = -exp(-z/r,.ir)
d-33)
i = 1
This function describes the non-exponential behavior of the recovery process. The value
of R(z) changes from unity to zero as z (or t) increases from zero to infinity and must be
determined from experiment. All other material functions (aj, a$, Aa) must also be
determined experimentally.
The KAHR model is capable of predicting the experimental data obtained at
different cooling rates (Figure 1-2), isothermal recovery following a single “down”
temperature jump (Figure 1-3 and 1-4 ) and a single “up” temperature jump (Figure 1-4 ).
The KAHR model is also quite successful in describing asymmetry of isothermal
approach curves (Figure 1-4). It reproduces all of the features of the memory effects
(Figure 1-5) which can only be explained by the multiplicity of retardation times.
Reliable fits to peaks obtained on constant heating through the transition range (Figure
1-6) have also been performed with the KAHR model.
Common descriptions of the kinetics of structural recovery are found in the multi¬
parameter models of Tool5, Narayanaswamy 63 and Moynihan 66 (TNM). These models
show the required dependence of T on both temperature and structure and are generally
represented by the equation:
t(T, Tf) = t0 exp
xAh
~RT
(1-34)

31
This non-linear equation is applicable at temperatures close to Tg; it clearly separates the
temperature and structure dependences of T. The characteristic retardation time, To, is the
retardation time in equilibrium (Tf = T) at an infinitely high temperature, x has the same
definition as in the KAHR model, and R is the molar gas constant. In the limit of small
departures from equilibrium (Tf —> T), this equation becomes an Arrhenius type equation
(x = Xoexp[Ah*/RT]) with an activation energy, Ah*.
The second requirement for physical aging is non-exponential character or a
distribution of retardation times. This is introduced into the TNM model by use of the
stretched exponential response function:
O = exp[-(r/r)^] (1-35)
known as the Kohlrausch67 -Williams-Watts 68 (KWW) function. The non-exponential
parameter P (0 < P < 1) is inversely proportional to the width of a corresponding
distribution of retardation times, whereas x is given by equation 1-34.
When equations 1-34 and 1-35 are combined with a constitutive kinetic equation,
in which the isothermal rate of approach to equilibrium is proportional to the departure
from equilibrium, equation 1-17 is generated. The TNM model can then describe the
response of the glass to any thermal history.
The TNM model has been remarkably successful in describing isothermal
enthalpy recovery and DSC endotherms on heating at constant rate.32 “35- 43, u’69
However, there has only been partial success in evaluating the parameters defining the
kinetics (x, P, Ah*) for different polymer glasses as there is quite a wide variation in these

32
values. A possible explanation 70 of these discrepancies might be that the KWW type
continuous distribution used is not appropriate for such recovery in all polymers.
1.4.3 Thermodynamic Theory
The thermodynamic theory of glasses was formulated by both Gibbs and
DiMarzio (G-D) who argued that, even though the observed glass transition is
indeed a kinetic phenomenon, the underlying true transition can possess equilibrium
properties, even if it is difficult to realize. At infinitely long times, they predict a true
second-order transition, when the material finally reaches equilibrium. The
thermodynamic theory attempted to explain the Kauzmann 74 paradox, which can be
stated as follows. If the equilibrium thermodynamic quantities of a material, e.g. entropy
(S), volume (V), and enthalpy (H), are extrapolated through the glass transition, the
values of S, V and H for the glass will be lower than for the corresponding crystals. The
G-D theory resolves the problem by predicting a thermodynamic glass transition when the
conformational entropy, Sc, goes to zero.
The G-D theory of the glass transition is based on an application of the Flory-
Huggins75,76 lattice model for polymer solutions. One of these scientists, DiMarzio,77
has argued that the use of a lattice model is more promising for the study of polymers
rather than for simple liquids, because in polymers it is possible to form glasses from
systems with no underlying crystalline phase. Atactic polymers are such systems because
their irregular structures do not, in general, permit them to crystallize.
The G-D theory employs a lattice of coordination number z filled with polymer
molecules (nx) each with a degree of polymerization x, and vacant sites (n0). Each

33
polymer chain has a lowest energy shape, and the more the shape deviates from it, the
greater the internal energy of the molecule. This energy is expressed as two energies,
intramolecular energy and intermolecular energy. The intramolecular energy is given by
xfAe, where f is the number of bonds in the high-energy state (state 2) and Ae = £2 - £1 is
the energy difference between high- and low-energy conformational states. The
intermolecular energy is proportional to the number of vacant sites (nc) and the non-
bonded interaction energy, AEh. The partition function is calculated by the same method
used by Flory and Huggins78 and Sc which describes the location of vacant sites and
polymer molecules, is derived from it.
A second-order transition is included in the partition function in the Ehrenfest
sense. The Ehrenfest equation for a second-order transition is:
dp _ A a
dT Ak
(1-36)
where p is the pressure, T is the transition temperature, Aa and Ak are the changes in
volumetric thermal expansion and compressibility, respectively, associated with the
transition. The lattice model predicts the existence of a true second-order transition at a
temperature T2. The transition occurs at Sc = 0, and the Kauzmann 74 paradox is resolved
for thermodynamic reasons rather than kinetic ones. Thus, extrapolation of high
temperature behavior through the glass transition is not allowed, for as the material is
cooled, a break in the S - T (or V - T or H - T) curves occurs because of a second-order
transition. As a glass-forming material is cooled down, at a given pressure, the number of

34
possible arrangements (i.e. the conformational entropy) of the molecules decreases with
decreasing temperature. This is due to a decrease in the number of holes (a volume
decrease), a decrease in the permutation of holes and chain segments, and the gradual
approach of the chains towards populating the low-energy state (state 1). Finally when
Sc = 0 the temperature T2 is reached. The G-D theory also allows the glassy state as a
metastable state of energy greater than that of the low-energy crystalline state for
crystallizable materials.
The temperature T2 is not of course an experimentally measurable quantity but
lies below the experimental Tg and can be related to Tg on this basis. Evidently, Gibbs
and DiMarzio were making comparisons with experimental data and used the
experimental (kinetic) Tg in their equations. Nevertheless, the theory is capable of
describing a whole range of experimentally established phenomena such as the molecular
weight dependence of Tg 7I'79, the variation of Tg with the molecular weight of
crosslinked polymers 80'81, the change in specific heat capacity associated with the glass
transition ’ (typical values for amorphous polymers are 0.3 - 0.6 J g K ), the
change in Tg due to plasticization84 and deformation 80 and the dependence of Tg on the
compositions of copolymers 85 and polymer blends.71,86'87
Adam and Gibbs 84 attempted to unify the theories relating the rate effect of the
observed glass transition and the equilibrium behavior of the hypothetical second-order
transition. They proposed the concept of “co-operatively rearranging regions,” defined
as regions in which conformational changes can take place without influencing their
surroundings. At T2, this region becomes equal to the size of the sample, since only one
conformation is available to each molecule.

35
Adam and Gibbs derived the following expression for viscosity:
In n = B + —
TS
(1-37)
C
where B and C are constants. By assigning a temperature dependence to Sc, it is possible
to derive the WLF equation (equation 1-4) from equation 1-37. The temperature (T2) at
which the second-order transition would occur may then be calculated from the WLF
equation as follows: To shift an experiment from a finite time-scale to an infinite one
requires a value of log aj approaching infinity. Clearly, this will be the case (at Tr = Tg) if
the denominator on the right hand side of equation 1-4 goes to zero while the numerator
remains finite, i.e.,
C2 + T2-Tg = 0
(1-38)
Since C2 is relatively constant for most polymers, then
(1-39)
Thus, T2 would be observed about 50 °C below Tg for an experiment carried out infinitely
slowly. Equation 1-39 holds for a wide range of glass-forming systems, both polymeric
and low molecular weight. Thus, the incorporation of co-operativity into the G-D theory

36
appears to resolve most of the differences between the kinetic and thermodynamic
interpretations of the glass transition.
1.5 Summary of Theoretical Aspects
From the discussion above, it is clear that the phenomenon of physical aging is
very complex and that no single theory, as yet, is capable of accounting for all the aspects
of it. The current theories can be divided into three main groups: free volume, kinetic and
thermodynamic theories. The free volume theory introduces free volume in the form of
segment-size voids as a requirement for the onset of co-ordinated molecular motion, and
provides relationships between coefficients of thermal expansion below and above Tg. It
treats the glass transition as a temperature at which the polymer has a certain universal
free volume (i.e. as an iso-free volume state) and yields equations relating viscoelastic
motion to variables of temperature and time. According to the kinetic theory, there is no
thermodynamic glass transition; the phenomenon is purely kinetic. The transition
temperature (Tg) is defined as the temperature at which the retardation time for the
segmental motions in the main polymer chain is of the same order of magnitude as the
time scale of the experiment. The kinetic theory is concerned with the rate of approach to
equilibrium of the system, taking the respective motions of holes and molecules into
account. It provides quantitative information about the heat capacities below and above
Tg, and the material parameters defining the kinetics of the system. The 3 °C and
sometimes 6 - 7 °C shift in the glass transition per decade of time scale of the experiment
is also explained by the kinetic theory. The thermodynamic theory introduces the notion
of equilibrium and the requirements for a true second-order transition, albeit at infinitely

37
long time scales. The equilibrium properties of the true second-order transition are
described by the Ehrenfest equation. The theory postulates the existence of a true second-
order transition, which the glass transition approaches as a limit when measurements are
carried out more and more slowly. This limit is the hypothetical thermodynamic
transition temperature (T2) at which the theory postulates the conformational entropy is
zero. The thermodynamic theory successfully predicts the variation of Tg with molecular
weight and cross-link density, composition, and other variables. Adam and Gibbs
incorporated the idea of co-operativity into the theory and rederived the WLF equation
from which the relationship (Tg - T2) = 50 °C is obtained.
All the models discussed above incorporate the two aspects of non-linearity and
non-exponentiality (or distribution of retardation times) which have long been recognized
as essential. In this way they all provide a qualitatively good description of many aging
phenomena. The details of the ways in which these aspects are introduced are obviously
different between models, for example free volume versus conformational entropy, or
discrete distribution functions versus continuous KWW functions. Nevertheless, these
differences are of little importance in comparison with the common features of the
models.
1.6 Comparison of Volume and Enthalpy Studies
There are numerous reports in the literature on enthalpy recovery in polymers
and fewer on volume recovery in polymers. Even less than these are the number of
studies in which comparable volume and enthalpy recovery data are obtained. Only a few

38
of these studies have been performed on identical samples of materials and there is yet to
be a clear conclusion about volume and enthalpy.
Weitz and Wunderlich 88 prepared densified glasses of polymers by slowly
cooling them from the liquid state under elevated pressures. These researchers then
measured the enthalpy and volume recovery of the densified polymers by DSC and
volume dilatometry, respectively, at atmospheric pressure. Their findings for volume and
enthalpy showed a difference in the times to reach a specific percent recovery. Volume
was faster than enthalpy in reaching this specified percentage in PS whereas in PMMA it
was slower.
on
Sasabe and Moynihan used DSC at constant atmospheric pressure to investigate
enthalpy recovery in poly(vinyl acetate) (PVAc) at different constant heating rates and
then compared their results with volume data from the work of McKinney and
Goldstein. After performing curve-fitting with their mathematical model, they found
that the average equilibrium volume recovery time was smaller by a factor of two than the
corresponding enthalpy recovery time.
Roe privately communicated to Prest et al.91 that enthalpy changed more rapidly
than volume in PVC. The supporting data, however, were not published. Prest et al. 91
reported volume and enthalpy data on an anionically polymerized PS sample. The
enthalpy changes were collected at 5, 10 and 20 °C min _1 and corrected to zero heating
rate. Volume recovery data on the same sample were obtained in the laboratory of A. J.
Kovacs. From different representations of the data, Prest et al. 91 concluded that in this
particular PS sample, volume equilibrium was reached long before the enthalpy had fully
recovered, and that the two processes had significantly different temperature

39
dependences. Cowie et al.92 also used volume data from A. J. Kovacs to compare with
their enthalpy measurements on PVAc. DSC was used to obtain the excess enthalpy data
for PVAc aged at 10 K below its Tg. From a plot of effective retardation times versus
aging times, these authors were able to show that the enthalpy recovery was faster than
the volume recovery in the PVAc glass.
In another study, Adachi and Kotaka 22 investigated the enthalpy recovery of PS
by isothermal microcalorimetry and the volume recovery of the same sample by volume
dilatometry. Following a double-step temperature jump (as in Kovacs memory
i o
experiments ), they observed that the time to reach maximum volume for PS near its Tg
was 0.4 decades longer than that for reaching maximum enthalpy. Adachi and Kotaka 22
also found that, for a broad and narrow molecular weight distribution PS, volume and
enthalpy recovery were very similar, but not the same. They calculated that it required
2.0 kJ cm' of enthalpy to create free volumes in PS.
Using a Calvet-type calorimeter with a precision mercury dilatometer in the
calorimeter cell, Oleinik 93 simultaneously measured enthalpy and volume recovery on
atactic PS, following simple up-and down- temperature jumps. He found a one-to-one
correspondence between volume and enthalpy and related their rates of approach to
equilibrium by a constant. In a similar recent study, Takahara et al. 94 simultaneously
measured volume and enthalpy recovery in a PS sample near Tg and demonstrated that the
times for both processes to reach equilibrium were the same within experimental error.
As part of their investigation, Perez et al. 95 used length dilatometry and DSC to
study the aging of PMMA at various temperatures below its Tg. From the corresponding
volume and enthalpy measurements on the same material, they concluded that the time

40
scales for volume recovery were shorter than those for enthalpy recovery. The authors
used a defect theory to explain their findings.
More recently, Simon et al. reported on the time scales of recovery for volume and
enthalpy in polyetherimide % (PEI) and PS 97 at various aging temperatures. Analysis of
the data led to the findings that the times required to reach equilibrium for both properties
were the same within experimental error, for both polymers. These researchers also
observed differences in the approach to equilibrium for volume and enthalpy. In both
polymers, volume approach to equilibrium was faster than enthalpy approach at short
times.
Finally, in the only relevant study this author has seen on miscible polymer
blends, Robertson and Wilkes 98 examined the physical aging in different compositions of
blends of poly(2,6-dimethyl-1,4-phenylene oxide) (PPO) and atactic PS, by measuring
volume and enthalpy changes. Using DSC and dilatometry, they collected aging data at
30 °C below the Tgs of the blends. They found that the dependence of the enthalpy and
volume recovery rates on PPO content were similar in all of the blends.
1.7 Objectives of This Research
The overall objectives of this investigation are to compare volume and enthalpy
recovery behavior in the same amorphous glassy polymer and across glassy polymers,
from isothermal physical aging experiments. Volume dilatometry and differential
scanning calorimetry are used as tools to investigate the structural recovery at different
aging temperatures following a quench from the equilibrium liquid state.

41
Physical aging was monitored at several temperatures for times ranging up to
several days. The large quantities of comparable volume and enthalpy recovery data
generated were analyzed in detail to gain insight into the structural recovery process that
occurs in glassy polymers as they age. Comparisons between volume and enthalpy data
included times to reach equilibrium, relative approaches to equilibrium, evolution of
effective retardation times, and aging parameters.
Two polymer systems were studied: a homopolymer of polystyrene (PS) and
miscible blend of polystyrene/poly(2,6-dimethyl-1,4-phenylene oxide). Both systems are
well known, as over the years, they have been subjected to numerous and extensive
studies. The choice of these two systems were based on five important points:
1. the measurement range of the automated dilatometer.
2. both polymer systems are completely amorphous.
3. availability of each homopolymer and ease of preparation of the blend from the
component homopolymers.
4. compatibility of the components in all blend ratios.
5. the glass transition temperatures and experimental conditions for aging
are in an easily accessible temperature range for both homopolymer and blend.
The blend composition selected was one in which one component was highly
dilute. Specifically, a blend composition of 90 % by mass of atactic PS and 10 % by
mass of PPO (90/10 PS/PPO) was chosen. The homopolymer and binary system were
prepared in accordance with accepted procedures, aged, and their volume and enthalpy
recovery data evaluated.

CHAPTER 2
AUTOMATED VOLUME DILATOMETRY
Chapter Overview
The data in this dissertation were collected with two pieces of analytical
instrumentation. This chapter describes one of them, a custom-built automated
dilatometer, and its performance capabilities. The section that immediately follows this
overview provides background information on the conventional technique of volume
dilatometry and discusses previous successful attempts at automation of this technique.
The remainder of the chapter gives a detailed description of the instrument, its operational
procedures, test measurements on polystyrene and a discussion and analysis of possible
errors associated with its measurements.
2.1 Background
The determination of the change in length or volume of a sample as a function of
temperature constitutes the technique termed dilatometry. When this change is a
variation in length the term length dilatometry is used; volume dilatometry is the term
applied to volume changes. Over the years, volume changes in materials have been
measured with various forms of capillary type dilatometers.18, ^ 99 “111 In its simplest
form , a volume dilatometer consists of a capillary attached to a sample reservoir;
temperature is controlled by immersing the dilatometer (without the capillary) in a
42

43
heating or cooling liquid. In general, a column of mercury surrounds the material and
any change in its dimensions is observed as a change in the mercury height. The height
of the mercury column is usually measured with a cathetometer and then multiplied by
the cross-sectional area of the capillary (calibrated separately) to give the volume change
of the sample and confining liquid. In all volume dilatometry experiments, only the
volume changes are measured directly. To convert these volume changes to actual
volumes, the volume of the sample at some convenient temperature must be determined
by measuring its specific volume. Manual measurements with this type of dilatometer are
very slow, quite laborious, and require constant attention by the observer. Therefore,
many attempts have been made to automate the data collection process by using various
automatic techniques to follow the height of the mercury in the capillary. One such
attempt involves a device called a linear variable differential transformer (LVDT).
An LVDT is an electromechanical transducer that is commonly used in
Thermomechanical Analysis (TMA) and produces an electrical output proportional to the
displacement of a moveable core. Tung 112 was the first to fit an LVDT to a dilatometer.
He measured polymer crystallization rates and found excellent reproducibility between
measurements on different specimens of the same polymer. He also measured
crystallization rates with a conventional dilatometer and found very good agreement
between the measurements from both instruments. Hbjfors and Flodin 113 extended
Tung’s design in what they referred to as “differential dilatometry” to measure polymer
crystallization rates and melting temperatures. In their set-up, two dilatometers—one
with sample and one without-were fitted with LVDTs whose differential electrical

44
outputs were registered by a recorder. Very reproducible results were obtained with this
instrument.
Recently, LVDTs have been used to monitor volume changes of polymers held at
various temperatures. In 1990, Duran and McKenna 114 floated an LVDT on the mercury
surface of a dilatometer and measured volume changes of a polymer subjected to
torsional deformations. The computer to which the LVDT was interfaced automatically
recorded the volume changes. Sobieski et al.115 employed a modified version of the
Zoller designed bellows dilatometer to automatically measure volume changes of a
polymer during physical aging experiments. Similar measurements were made with a
conventional capillary dilatometer ; the results demonstrated that the automated
dilatometer was just as reliable as the proven technique of capillary dilatometry.
In this work, a fully automated dilatometer with some features of both the
McKenna and Zoller designs, was used to measure volumes and volume changes. This
instrument was originally conceived by Drs. Gregory B. McKenna and Randy Duran but
was designed by and constructed under the direction of Drs. Randy Duran and Pedro
Bernal at the University of Florida. Automation and the design of the instrument afforded
a number of advantages : (i) data collection over several days or even weeks without
constant attention by the researcher, (ii) the instrument is a complete measuring system
(no external calibration necessary for volume measurements) and (iii) high precision and
good accuracy of measurements.

45
2.2 Instrument Description
2.2.1 Dilatometer Design
All the dilatometers used in the experiments reported herein are U-shaped in
design (Figure 2-1) and are constructed entirely from clear fused quartz using routine
glassblowing skills. Each has two main components: the specimen compartment which
has walls of ca. 1 mm thickness and a capillary column which is made of precision bore
quartz tubing (Wilmad Glass, Buena, N.J., Catalog Number 902) of internal diameter
5.0190 ± 0.00051mm. The main advantage of this dilatometer design is it minimizes the
length of capillary extending above the bath.
2.2.2 Dilatometer Confining Liquid
Mercury was chosen for the confining liquid to be used in the dilatometer because
it offered many advantages. These included: (1) total insolubility and nonreactivity with
the polymer, (2) stability, nonvolatility, and very accurately known expansion over the
temperature range of interest, and (3) a large density that enhances precision of the
dilatometer calibration. Clean mercury that was thrice distilled (three repeated vacuum
distillations were necessary to remove all the visible particulate matter from the mercury)
was stored in the distilling flask of a cleaned one-piece glass distillation apparatus
situated in a fume hood. The dilatometer was filled by directly attaching it to the
receiving end of the distillation apparatus and further distilling the cleaned distillate into
it.

46
Repeated distillation of the mercury was necessary because the expansion of any
impurities can contribute to noise in the measured signal and lead to erroneous volume
results for the specimen. However, the repeatability of data collected with the dilatometer
(see Figures 2-4, 5, 7, 8 and 9) demonstrated the negligible effect of any noise in the
signal.
2.2.3 Measurement System
Figure 2-1 shows a simplified schematic diagram of the automated measuring
system. An LVDT and an extension rod-core-float assembly measure the mercury height
in the capillary column. The LVDT consists of a primary coil, two secondary coils that
give opposing outputs, and a free moving rod-shaped ferro magnetic core. The core is
floated on the mercury surface by a threaded stainless steel extension rod and float. The
rod makes contact with the mercury via a flat cylindrical stainless steel float of 5 mm
diameter that is screwed onto one end. The purpose of the float is to increase the volume
of the mercury displaced due to the weight of the rod and core which is attached to the
extension rod that extends out of the capillary to the LVDT transformer. The LVDT is
attached to a device which is fastened to a micrometer, which in turn is supported by a
metal rod. The device permits lateral and vertical movements of the core to align the hole
in the transformer with the capillary due to variations in temperature of the experiments
and in the amount of mercury used to fill the dilatometer. An auto-calibrated digital
readout/controller (Lucas Schaevitz Microprocessor (MP) Series 1000) provides the
excitation voltage across the LVDT and reads the output voltage. This real time output is
linearly proportional to the LVDT core displacement. Data is communicated to a

47
Figure 2-1 Schematic illustration of the dilatometer and its measuring system: (A) LVDT
coil, (B) LVDT core, (C) wire lead to LVDT readout/controller, (D) micrometer,
(E) sample, (F) stainless steel connecting rod, (G) stainless steel cylindrical float, (H)
glass dilatometer, (I) metal rod support.

48
personal computer through an RS-232 interface on the digital readout/controller using
two personally modified QuickBasic programs. The entire data collection system is
therefore automated making it possible to collect data in real time over very long periods.
The LVDT (model 100 MHR, Lucas Schaevitz, Inc., Pennsauken, N.J.) is a
miniature highly reliable (MHR) device that has a measurement range of ± 0.100 in.
(± 0.254 cm) and can operate from - 55 °C to 150 °C. The small mass of the core and its
freedom of movement enhance the response capabilities for dynamic measurements and
gives the LVDT infinite resolution. However, because the LVDT is connected to the
analog to digital board on the digital readout/controller, a more realistic resolution is
about 1 x 10 '5 in. (0.254 pm). For the capillary of internal diameter 5.0190 mm, the
volume resolution is 5.03 x 10 6 cm 3.
2.2.4 Constant Temperature Baths
Three constant temperature oil baths—a Neslab TMV-40DD, an EX-251 HT, and a
Hart Scientific High Precision Bath (Model 6035)—were all part of the fully automated
set-up depicted in Figure 2-2. Silicon oils (Dow Coming 510 & 710) were the heat
transfer media used in these baths. All baths were equipped with stirrers so as to
maintain uniform temperature throughout the baths. The temperature of the TMV-40DD
and the Hart Bath were internally controlled to within ± 0.005 °C and the EX-251 HT to
within ± 0.05 °C. Calibrated high precision digital platinum resistance thermometers
(Hart Scientific Micro-Therm Thermometer, Models 1006 & 1506) with resolutions of
0.001°C were used to externally monitor the temperatures of the baths and the indicated
temperatures were the ones recorded in all experiments. The EX-251 HT bath was

49
A B C d
Figure 2-2 Schematic diagram of the components of the automated dilatometer :
(A) & (D) analog to digital converters; (B) & (C) personal computers; (E) & (G) high
precision digital thermometers; (F) LVDT readout/controller; (H) automated dilatometer;
(I) TMV-40DD/aging bath; (J) & (N) platinum resistance temperature probes; (K), (M) &
(P) silicon oils; (L) EX-251 HT/annealing bath; (O) Hart Scientific High Precision bath.

50
maintained at a high temperature to anneal the specimen to equilibrium volume and the
TMV-40DD was maintained at the desired temperature for aging experiments.
Measurements of volume change as a function of temperature were conducted in the Hart
Bath. This bath, a digital thermometer, and a digital readout/controller were all interfaced
to a personal computer, which commanded them using the constant temperature scan
program in Appendix B. Temperature, time and LVDT voltage were simultaneously
recorded so that measurements of volume versus temperature at constant scan rates were
easily obtained.
2.3 Data Manipulation
All data were collected and stored on the dilatometer computers in ASCII file
format and then transferred via floppy disks to other computers in the lab. Microcal’s
software Origin 5.0 was used to construct graphs for analysis of the data.
2.4 Preparation of a Specimen Dilatometer
The dilatometer was first cleaned with Nochromix solution, rinsed repeatedly with
Millipore water (18.0 MQ'm), and dried in a vacuum oven. Approximately 1 g of dried
polymer was weighed out on a microbalance and placed in the dilatometer. To avoid
heating the specimen during sealing, the dilatometer was placed upright in a container
filled with ice so that the sample was about 4 cm below the ice level. The specimen
compartment was then rapidly sealed a few centimeters above the ice level using a
hydrogen flame. The sealed dilatometer was degassed at a temperature above the glass
transition of the specimen for 24 h under a vacuum of ~1.3 x 10'2 N m 2 (-10 ^ torr).

51
Following this evacuation, the dilatometer and its contents were allowed to cool to room
temperature under vacuum and then weighed to correct for any mass loss from the
specimen. Afterwards, the dilatometer was again attached to the distillation apparatus
and evacuated for 24 h. With the vacuum still applied, clean mercury (section 2.1.2.2)
was then distilled into the dilatometer. The mass of mercury was determined after
weighing the filled dilatometer.
The vacuum quality has to be quite good during degassing and filling of the
dilatometer because air has to be removed from the confining spaces of the dilatometer
and also from the specimen. Gases should be removed as quantitatively as possible
because their expansitivities are much different from that of the specimen and can lead to
very noisy signals and inflated volume data for the specimen. Quantification of the total
gas volume in the dilatometer is addressed in the following section. In some instances
after filling, microbubbles of air were present in the capillary arm of the dilatometer. A
procedure, which required gentle tapping of the arm and dipping the dilatometer
alternately in warm and cold water a few times, was quite adequate for dislodging the air
bubbles.
2.5 Volume Measurements
To perform a measurement, the dilatometer was suspended from a support rod and
immersed in the oil baths such that the mercury meniscus was always below the oil level.
A stem correction, similar to that used for thermometers 116, is usually applied to most
capillary dilatometers because part of the capillary emerges from the bath. This
correction term is dependent on the capillary diameter and the differential thermal

52
expansions of the glass dilatometer and the mercury and can be on the order of a few
millimeters. However, in the present instrument no stem correction is necessary since the
mercury never rises above oil level. Consequently, the mercury in the dilatometer is
always uniformly heated.
Measurements of volume as a function temperature were performed on all
specimen dilatometers and a dilatometer filled only with mercury. Before and between
measurements, the dilatometer was always allowed to sit at room temperature and the
core position was set to give a stable negative voltage reading. Setting of the core
position was achieved by adjustment of the connecting rod such that it floated on the
mercury surface. With the variation of the temperature in the room, the signal was usually
stable after 40 - 50 min. For consistency and measurement comparison, the dilatometer
was always allowed to sit for the same amount of time before each run. Once the voltage
signal (displayed by the digital readout/controller) was stable, the initial voltage was
recorded. The dilatometer was carefully raised from its position in a stand away from the
baths, and suspended in the Hart Bath. The computer was then instructed to collect data
at a constant rate of 0.100 °C min _1.
Reference specific volumes of the polymer specimens were also determined by
measurements conducted in the high precision Hart Bath. The specific volume of each
polymer was determined at a reference temperature above its Tg (see Appendix C, Part I
for a specimen calculation), which was necessary to obtain absolute and reproducible
values. The specimen and dilatometer were prepared as described earlier. Afterwards,
the dilatometer was supported in a vertical position by a clamp and leveled with a
leveling device. A thin strip of graph paper (used as a guide) was attached to the mercury

53
column. A reference mark was placed on the graph paper a few millimeters below the
mercury meniscus and the position of the meniscus was also marked. With the aid of a
set of vernier calipers (accuracy 0.001 in.; resolution 0.0005 in.), the distance between the
two marks was measured. The initial voltage was stabilized as before and the computer
was instructed (through the QuickBasic program in Appendix A) to record all signals.
Eight measurements were performed on the specimen at the reference temperature. The
mercury was removed from the dilatometer and the specimen was extracted with
chloroform. After rinsing four times with chloroform, the dilatometer was cleaned as
described in section 2.4 and refilled with mercury. Adjustment and recording of the
mercury column height were repeated as before and voltage measurements were again
taken. Any contribution to volume change from the glassware is cancelled out by this
procedure.
In the preparation of mercury-only dilatometers, it was often observed that a
gaseous void—the result of poor vacuum quality—existed in the bulb of the dilatometers.
The vacuum produced at the pump vacuum inlet was earlier stated as ~10 torn
However, this value was never realized at the dilatometer due to many factors including
the narrow bore imposed by the dilatometer capillary. By the technique shown in part II
of Appendix C, it was estimated that a gas void of volume 0.01265 cm 3, which is ~ 2 %
of the total sample volume, consistently remained in the dilatometer. Inevitably, due to
equipment design, these voids added some uncertainty (~ 2 %) to the reference specific
volume calculation, but are not expected to significantly affect the aging results presented
in Chapters 4 and 5.

54
2.6 Quantitative Aspects
The volume change of the specimen, A Vs (in cm ) in volume dilatometry is
generally corrected according to the following equation:
AVS = AVlo! - AVHg - AVq (2-1)
where AVtot, AVHg, and AVq are the total volume change, the volume change of mercury,
and the volume change of quartz, respectively. However, it is more useful to express
volume change of the specimen as specific volume change of the specimen (Avs).
Dividing through by the mass of the specimen and keeping the terms in the same order,
equation 2-1 can be rewritten to show how Avs (in cm g' ) is calculated:
A^s =
< 1 '
\msJ
[{(Ivdt- (Ivdt),} • (V')] - [ocHgmHKvHg{T,-T2)]
— [aQ (mQ jpQ)(T, - T2)]
(2-2)
V'= n
v2z
W
(2-3)
Both equations are valid over the linear measurement range of the LVDT (or, in terms of
temperature, from ~ 145- to ~ 45-°C). The various quantities are defined as follows: ms
(in g) is the mass of the specimen; (lvdt),0 (in mV) is the LVDT voltage at time, t = 0 at
Ti; (lvdt)t (in mV) is the LVDT voltage after time, t, during the quench and subsequent

55
specimen recovery at T2; T| and T2 (in °C) were previously defined (see Figure 1-7);
V' is 5.046 x 10 4 cm 3 mV the volume sensitivity of the LVDT; d (0.50190 cm) is the
measured internal diameter of the precision capillary column; h' (in cm mV 1 ) is the
displacement per unit voltage of the LVDT core; Vng (0.073556 cm 3 g ') is the mercury
specific volume at 0 °C 117; mng (in g) is the mass of mercury in the dilatometer; ctHg is
1.8145 x 10 4 °C the mercury volume coefficient of thermal expansion at 0 °C 118; oíq
is 1.65 x 10 6 °C the volume coefficient of thermal expansion of quartz 119; mQ (in g)
is the mass of the quartz; Pq is 2.20 g em ”3, the volume density of the quartz.
Once the specific volume change at some temperature, (AVs)t, and the reference
specific volume, vTr, are known, the total specific volume at the same temperature,
(Vs) t, can then be determined from the relationship:
(in cm3 • g~') = {(A)r + vT } (2-4)
2.7 Calibration of the LVDT
Two calibrations were performed on the LVDT. The first was done to calibrate
the LVDT core for displacement per unit voltage, h'. With the LVDT connected to a
digital readout/controller, the connecting rod was placed on a micrometer calibration
stand. The micrometer wheel was turned in both clockwise and counterclockwise
directions in increments of 0.01 in. and the voltages due to the new core positions were
recorded from the digital readout/controller. During the calibration, the temperature of
the room varied between 27.5- and 29.5-°C. However, even though an LVDT is very

56
sensitive to temperature variations, no significant drifts were observed in the voltage
signals for up to 20 min after the core was displaced, indicating very good control of the
signal by the digital readout/controller.
The calibration curve is displayed in Figure 2-3. Using linear regression, a slope
of 2.5504 x 10 ~3 cm mV '' with an uncertainty of ± 2.2464 x 10 cm mV _1 was
obtained, which indicates that the LVDT signal has excellent repeatability and linearity
throughout its measurement range.
For the second calibration, the LVDT was fitted to the mercury-only dilatometer
and both cooling and heating temperature scans were performed . This calibration
provided information on the effect of temperature on the LVDT signal. The curves in
Figure 2-4 show that the LVDT produces a stable highly linear output over a wide
temperature range.
2.8 Test Measurements on Polystyrene
Atactic PS was chosen to test the performance of the dilatometer. Two
dilatometers containing PS specimens were prepared following the procedure outlined in
section 2.4.
2.8.1 Reference Specific Volume
As mentioned earlier, the specific volume of the material is required to convert
volume changes into actual volumes. Measurements were performed on each of the
two specimens at 115.000 ± 0.005 °C and 1 atm. pressure following the procedure
described in section 2.5. The average reference specific volumes for the two specimens

57
were calculated as 0.95857 ± 0.00017 cm3 g 1 (see Appendix C, Part I) and 0.95412
±0.00017 cm g . This difference in specific volume for the two PS specimens from
the same sample was somewhat surprising because at the reference temperature, PS is in
LVDT Voltage (mV)
Figure 2-3 Plot of core displacement vs. LVDT voltage. The connecting rod was turned
in both clockwise (O) and counterclockwise (+) directions by a micrometer-type gage
head calibrator. The slope is 2.5504 x 10 ~3 ± 2.2464 x 10 ^ cm mV Calibration
temperature was 28.5 ± 1.0 °C.

58
190
the equilibrium liquid state. However, such differences have been reported before.
Therefore, it was necessary to determine the specific volume of each specimen for
comparison of their results.
Temperature (°C)
Figure 2-4 LVDT voltage as a function of temperature for a mercury-only dilatometer.
Data collected at a constant scan rate of 0.100 °C min (A = heating data; O = cooling
data).

59
2.8.2 Volume Change Measurements
In order to test the precision of volume measurements, a number of experiments
were performed on the PS. Three different procedures were followed: (i) the dilatometer
was subjected to repeated scans in the oil bath, (ii) the dilatometer was removed from the
oil bath, allowed to cool at room temperature, placed back in the oil bath and then re¬
scanned, and (iii) a second specimen was scanned.
Figure 2-5 displays the raw data obtained using procedures (i) and (ii). Different
initial voltages were used in both cases and the scans were made at a rate of 0.100 °C
min -1. The two curves at (a) are quite repeatable and are virtually parallel to curve (b);
a simple vertical shift will superpose the curves. The data from 140 °C to 105 °C and
90 °C to 50 °C on all the curves were fitted with best-fit straight lines using the method of
least squares. The deviations from the straight lines are plotted as functions of
temperature in Figure 2-6. The deviations of the data are all within ± 0.8 mV, which
corresponds to ± 0.8 % of the maximum voltage (100 mV) meaning that the overall
precision in the LVDT measurements is better than 1 %.
The ± 0.8 mV deviation also corresponds to a maximum uncertainty of
± 4.0 x 10 ^ cm3 in the volume change measurements. However, in reality, the volume
uncertainty is less than this, because below the transition region, the curves are not
necessarily straight lines. This portion of the curves may be slightly curved due to the
decreasing rate of structural recovery that occurs in the polymer as it is slowly cooled
well into its non-equilibrium glassy state.

60
The LVDT signals in Figure 2-5 were converted to specific volumes using
equations (2-2, 3, 4). The curves of specific volumes against temperature (Figure 2-7) are
typical of a glassy polymer. Linear regression was used to draw straight lines from 140 °C
to 120 °C and from 50 °C to 65 °C. The intersection of these lines is generally assigned
as Tg of the polymer, and at a constant cooling rate of 0.100 °C min -1, the average Tg is
97.1 ± 1.5 °C.
Temperature (°C)
Figure 2-5 Temperature dependence of the LVDT voltage in the volume measurements
of polystyrene for (a) three scans (a cooling-heating-cooling sequence) (b) a cooling scan
after the dilatometer w Temperature scans performed at a rate of 0.100 °C min

Residual voltages (mV)
61
Figure 2-6 Deviations of experimental values from best-fit straight lines drawn through
the linear portions of the voltage versus temperature curves (symbols correspond to those
in Figure 2-5).

62
Temperature (°C)
Figure 2-7 Specific volume as a function of temperature for PS. The averaged Tg,
calculated from the intersections of the glassy and liquid lines of four curves obtained at a
scan rate of 0.100 °C min was 97.1 ± 1.5 °C. (Some data points have been excluded
for clarity).

63
Figure 2-8 Specific volume as a function of temperature for two different PS specimens.
(Six curves representing three heating and three cooling scans are superimposed).

64
Results from the second specimen are displayed in Figure 2-8 along with the
curves from Figure 2-7 for comparison. The curves have similar slopes above Tg, but
slightly different slopes below Tg due to the instability of the glassy state. Volume
coefficients of thermal expansion were determined from the six curves, by the method of
least squares using the formula a = d (In V)/dT. Table 2-1 shows the calculated glass
(Og) and liquid (aO expansion coefficients and their literature values ’ for PS. The
calculated values fall within the literature ranges indicating that the accuracy of the
experimental data is quite good.
Table 2-1 Volume thermal expansion coefficients for PS.
Expansion coefficients
rc1)
Literature*
Calculated
Oc (X 10-4)
1.7-2.5
2.28 ± 0.22
aL (x 10â– 4)
5.7 - 6.0
5.97 ± 0.09
* values obtained from references 120 and 121.
2.8.3 Aging Experiments
When a polymer is cooled from an equilibrium state above its Tg to some
temperature below Tg, its specific volume (or volume) decreases until it can establish a
new equilibrium. This recovery phenomenon is referred to as physical aging and was
investigated in PS at a number of different temperatures. Only part of the results is
presented here to demonstrate the capability of the instrument. Details and discussion of
this study will be given in Chapter 4.

65
The specific volume changes due to structural recovery at 95.6- and 98.6-°C are displayed
in Figure 2-9. The abscissa of the graph is log (t - ti) where t is the elapsed time from the
start of the quench and ti is the thermal equilibration time (~ 137 s) of the sample after
transfer to the aging bath. The ordinate is 5 (the normalized volume departure from
equilibrium) and the horizontal line from the origin of the ordinate
Figure 2-9 Specific volume change showing the structural recovery of two specimens of
glassy PS at 95.6 °C and 98.6 °C. Experiments performed at normal atmospheric
pressure. ( •, = specimen 1, A = specimen 2).

66
represents equilibrium values. The two curves at 95.6 °C show aging of two different
specimens. Two aging runs on the same specimen are shown at 98.6 °C. By observation,
the precision of the data is quite good, as in general the curves at both temperatures are
superimposable.
The curves also show that PS achieves an equilibrium structure in the time frame
of the experiment. At the lower temperature, the aging of one of the specimens was
carried out for more than three days. Figure 2-10 displays the relative specific volume as
Figure 2-10 Relative specific volume change as a function of time showing the long time
stability of the LVDT. The time interval is from the initial attainment of equilibrium
until the end of the experiment. Measurement temperature was 95.6 °C.

67
a function of time after equilibrium is initially established. The specific volume and
hence, the LVDT signal remained stable for more than 45 h. Therefore, the electronics
of the instrument are very stable and consequently the dilatometer can be used to collect
data over long periods of time.
2.9 Error Considerations and Analysis
In any measurement, there is always a degree of uncertainty resulting from
measurement error. A combination of the errors from all possible sources results in the
overall measurement error. Static errors, introduced by the components of the measuring
system in the automated dilatometer are usually the major contributors to overall
measurement error. Static errors result from the physical nature of the various
components of the measuring system as that system responds to a stimulus that is time-
invariant during measurement. Three types of errors combine to give the static error:
reading errors, characteristic (instrumental) errors and environmental errors. In the
present measuring system, reading errors which apply exclusively to the readout or
display device, are eliminated by use of the digital readout/display; characteristic errors
are minimized or eliminated by the signal conditioning electronics of the LVDT
readout/controller, calibration, and the LVDT design. 122
Environmental errors, on the other hand, affect not only the measuring system but
also the physical quantity to be measured. Such errors are usually due to temperature,
pressure, humidity and moisture, magnetic or electric fields, vibration or shock, and
periodic or random motion. The design of the LVDT 122, the careful handling of the
measurement system during measurements, the thermostated room temperature and

68
constant external pressure (atmospheric pressure), either minimized or eliminated most of
these errors in the output signals for our measurements.
The output signal from the LVDT is a measure of volume changes occurring in
the dilatometer. The error associated with the volume changes can be assessed through
two procedures: (i) a propagation of errors calculation, and (ii) the error in our reference
specific volume measurements.
The propagation of errors calculation is performed by taking the total differential
of equation 2-2:
in which
V' = 5.0459 x 10“‘cm 3 mV'1 ,
3 V' = ±4.4444 x 10 "7 cm 3 mV *'
[(lvdt),o - (lvdt),] = 200.00 mV ,
[3(lvdt)t0 - 3(1 vdt),] = 0.01 mV
mHg = 45.4652 g ,
3mHg = 3mQ = 3ms = 0.00001 g
ms = 0.69227 g, mQ = 29.72601 g
T, = 115.000 °C, T2 = 28.5 °C.
Substitution of the experimental numbers above, into the differential equation gives a
maximum specific volume change error of approximately ± 1.35 x 10 4 cm 3 g

69
Our unique approach to reference specific volume determination resulted in good
agreement between the specific volume of PS under ordinary temperature conditions and
that found in the literature obtained under similar conditions. ’ ’ ' ’ For example,
the extrapolation of the lower (glassy) region of Figure 2-7 to a temperature of 23 °C,
gives a specific volume of 0.93253 cm 3 g _1 for PS. The value deduced at the same
temperature from literature data is ~ 0.955 cm3 g _l. Thus, the difference of -0.022
cm 3 g 1 results in an error of - 2.3 % (most probably caused by the trapped gas in the
mercury-only dilatometer) in our specific volume measurements.
Based on equation 2-4, the measured specific volume depends on both the specific
volume change and the reference specific volume. Accordingly, any error in the
measured specific volume is related to errors in the other two quantities by the equation:
ÁMt) = y¡s2((Avs\) + s2(vTr) (2-5)
where s represents the uncertainty or error in each term. Substitution of the two
calculated uncertainties above into this equation yields a maximum overall error of
± 0.022 cm g or ± 2.2 % error in specific volume measurements of the PS specimen.
The absolute accuracy of the specific volume is, of course, limited by the accuracy
of the previously mentioned dilatometric determination of Vrr. In the work to be
presented later, however, the absolute accuracy of vTr is not very critical. The interest,
for example, is not in the general level of specific volume; the only requirement is that the
volume recovery curves measured with different dilatometers, or repeatedly with one

70
dilatometer coincide. By definition, however, all dilatometers give the same specific
volume, that is Vxr, at the reference temperature, Tr. Therefore, it is the (absolute) error in
the specific volume change, vT - vTr, that is of primary interest, because it is this error
which determines the deviations and scatter in recovery data such as is observed in
Figures 2-9 and 5-9. This error, which is dependent on the measuring temperature, was
earlier estimated by error propagation to be 1.35 x 10 4 cm3 g “* over the temperature
range 28.5 to 115.000 °C.
Finally, the automated dilatometer has several advantages: it is very reliable (high
precision and good accuracy), simple to build, records voltages due to very slow changes
in mercury height, and the linear relationship between the LVDT signal and displacement
of the core simplifies the use of results. Perhaps the most significant advantage of this
instrument is that volume change measurements are completely automated thus
eliminating the need for constant attention. With a volume sensitivity of 5.046 x 10
cm 3 mV 1 and resolution of 5.03 x 10 “6 cm3, the automated dilatometer is an ideal
instrument for accurately following the small volume changes induced in a polymer by
variations in its thermal environment.

CHAPTER 3
DIFFERENTIAL SCANNING CALORIMETRY
Chapter Overview
The other analytical instrument used in this study is a differential scanning
calorimeter (DSC). The chapter begins with the basis for thermal measurements by DSC
and then provides a brief treatment of the features of the instrument. The DSC must be
properly calibrated before measurements are made and therefore emphasis has to be
placed on the calibration procedures. Accordingly, in section 3.3 calibrant data are
presented in order to determine the characteristics of the DSC. Enthalpy data on PS are
presented to demonstrate instrument capability, and methods of data analysis are
discussed. Procedures for ensuring the collection of highly reliable data are also
mentioned. The chapter ends with an evaluation of the experimental uncertainty
associated with the enthalpy measurements.
3.1 Introduction
The first DSC was introduced in 1964 by Watson et al.124 at Perkin-Elmer. Since
then, there have been a number of improvements to the instrument; temperature scanning,
and data collection and analysis are now computer-controlled. These improvements,
71

72
along with the speed of experimentation, ease of operation, and the high reproducibility
of the technique, have made DSC very popular.
In today’s laboratories, DSC is a widely used method for the study of thermal
events in materials. Thermal events are the result of stored thermal energy in materials.
In simple substances thermal energy arises mainly from translational motion of
molecules, while in polymers it comes from motions of polymer segments. The stored
energy changes whenever the state of the system changes and every change is
accompanied by an input or output of energy in the form of heat. The ability of the
material to absorb or release this heat is expressed as heat capacity (Cp), the magnitude of
which depends on the type of molecular motion in a material and, in general, increases
with temperature. In DSC, the temperature of a material is usually varied through a
region of transition or reaction by means of a programmed heating or cooling rate, and the
power which is a measure of the material’s heat capacity, recorded as a function of
temperature. In the case of an amorphous material being heated, when its temperature
reaches Tg its heat capacity changes abruptly (no change in enthalpy). At this
temperature, the material absorbs more heat because it has a higher heat capacity, and the
thermal event appears as a deviation from the DSC baseline. The deviations are either in
the endothermic (positive) direction for heating or in the exothermic (negative) direction
on cooling.
A very frequent application of DSC is to the glass transition region of amorphous
polymers. The goals of such efforts are to characterize and to model structural recovery
in glasses. The usual approach is to first anneal the specimen to equilibrium at a
temperature above Tg, to cool it at a constant rate, then to age it for a fixed period of time

73
at a temperature below Tg, and finally to heat it through the transition region. The DSC
output is proportional to the specimen’s specific heat capacity (cp), which typically
produces a peak on heating, going from a value characteristic of the glass, cpg, to one
characteristic of the liquid, cpi. The area under the peak, found by integration, is the
amount of enthalpy recovered. Petrie’s pioneering work laid the foundations for this
kind of study by DSC. She established the equivalence between energy absorbed through
the glass transition region during heating and the enthalpy released during the preceding
aging period. Some years later, Lagasse 125 took a possible thermal lag into account and
suggested a modified experimental procedure. His work greatly expanded the feasibility
of enthalpy recovery measurements by DSC.
The DSC typically ramps the temperature in a linear fashion and requires the input
of an initial temperature, a final temperature, and a rate to achieve the final temperature.
Additionally, it has the capability of maintaining the sample at the initial or final
temperature for a specified amount of time. Many types of commercial DSCs exist;
however, since the measurements presented here were made on a Perkin-Elmer
instrument, only the key features of this instrument will be discussed.
3.2 Instrumental Features
In this work, a Perkin Elmer Differential Scanning Calorimeter 7 Series (DSC 7)
was used to make calorimetry measurements and to characterize polymer specimens.
Figure 3-1 shows the diagrams of the DSC 7. The measuring system consists of two
microfumaces ( a sample holder and a reference holder) of the same type made of a
platinum-iridium alloy, each of which contains a temperature sensor (platinum resistance

74
Sample Holder A
B
Sample Reference
Fig 3-1 (A) Block diagram and (B) schematic diagram of a power compensated DSC
system (reprinted from ref. 126 with permission of publisher).

75
thermometer) and a heating resistor (made of platinum wire). Both microfumaces are
separately heated and are positioned in an aluminum block whose base is surrounded by
coolant. The (DEC) computer controls the DSC via a temperature controller (TAC 7 /
DX). Under the control of the computer, the DSC 7 can be operated in both the normal
temperature scanning mode and the isothermal mode. Data is analyzed by the Perkin
Elmer 7 Series / UNIX Thermal Analysis System software installed in the computer.
The DSC 7 operates on the power compensated “null-balance” principle, in which
energy absorbed or liberated by the specimen is exactly compensated by adding or
subtracting an equivalent amount of electrical energy to a heater located in the sample
holder. The power (energy per unit time) to the furnaces is continuously and
automatically adjusted in response to any thermal effects in the sample, so as to maintain
sample and reference holders at identical temperatures. The differential power, AP,
required to achieve this condition is recorded as the ordinate with the temperature or time
as the abscissa.
3.3 Calibration of the DSC
A calibration procedure provides a vital check of the reproducibility and accuracy
of the DSC measurements as it the only way of checking the many varying
experimental parameters and their interaction. A DSC measures the differential power
output as a function of the programmed temperature and not the true specimen
temperature. Therefore, it is imperative that the proportionality factors, Kq (the heat
calibration factor) and KP (the heat flow rate calibration factor), that relate the indicated
signal to the true heat and heat flow rate, be determined through calibration.

76
The DSC 7 was calibrated according to the guidelines of E. Gmelin and St. M.
Sarge. 130 Three calibrations were performed: (i) temperature calibration, (ii) heat (energy
output) calibration, and (iii) heat flow rate (power output) calibration.
Temperature and heat calibrations were carried out using high purity (> 99.99 %)
indium, tin, and lead as calibration standards. Two different masses of each “fresh”
(oxide layer removed) metal were weighed in aluminum pans that were then hermetically
sealed. With each calibration sample, the thermal effect was recorded at heating rates of
0.1-, 0.5-, 1.0-, 2.5-, 5.0-, and 10.0-°C min -1. The experiments for each heating rate were
performed twice. The first experiments were never used to compute calibration
parameters usually, because of insufficient contact between sample and pan. After the
first melting, the contact area increases causing better heat transfer thus second runs were
used. Using a two standard calibration procedure, average values of the extrapolated
peak onset temperature for indium (156.57 ± 0.10 °C) and tin (231.30 ± 0.15 °C) at 10.0
°C min 1 were entered into the DSC 7 calibration set for the temperature scale
calibration. The literature value of the true transition heat (the area in J g -1 under a
transition peak) of indium (28.45 J g ') was also entered to calibrate the energy output
scale of the instrument. For each metal, the area under the melt transition was obtained
by integration using the DSC software. The heat calibration factor, Kq, was calculated
from
4
(3-1)

77
where Qtnie is the true transition heat and A is the measured peak area. Figure 3-2
displays Kq values as a function of both the heating rate and mass of the calibrant.
Because there are no significant differences between the values of Kq for each mass or
the different heating rates (most obvious at the higher heating rates), the mean calibration
curve in Figure 3-3 was calculated. The scatter observed in Figure 3-3 data is typical for
a power compensated DSC.130'131 An average value of Kq = 1.04 ± 0.02 was calculated
and used to correct all measured peak areas prior to data analysis. This value was
determined from the data obtained at 10 °C min _1 on the larger mass of each calibrant.
(The same heating rate, and similar masses of polymer specimens will be employed in the
enthalpy recovery experiments).
The heat flow rate of the DSC 7 was checked with synthetic sapphire ((X-AI2O3,
corundum) over the range 25 to 180 °C using a heating rate of 10.0 °C min -1. Runs were
performed on two sapphire samples of different masses and an empty aluminum pan.
Each calibration, which consisted of measuring the calibrant and measurement with the
empty pan, was repeated three times. Values of KP which are necessary to determine the
actual heat flow rate of the sample, were calculated from the data using the relation:
KP(T)
Cp.Sapp(T) 0.060-[/^(T) - P0(T)]
(3-2)
where: Cp, sapp = heat capacity of sapphire (in J K1)
q = heating rate (in K min-1)
Pm = measured heat flow rate of the sapphire (in mW)

Heat calibration factor,
78
Heating rate, q (°C min '1)
Figure 3-2 Dependence of the heat calibration factor, Kq, on heating rate and mass of
indium, tin, and lead (• = sample mass 11.6 mg, □ = sample mass 3.5 mg).

Heat calibration factor,
79
*°
T,rs <°C)
Figure 3-3 Heat calibration curve determined with indium, tin, and lead for the DSC 7
(□, A, o = sample mass 3.5 mg; ■,▲,• = sample mass 11.6 mg)

80
Po = measured heat flow rate of the empty pan (in mW).
T = temperature (in Kelvin (K))
The heat capacity of sapphire was determined by multiplying the mass of the sapphire by
its specific heat capacity which was calculated from the equation:
cp,Sapp = - 5.81126x10"' + 8.25981 x 10"3T - 1.76767 x 10"5 T2
+ 2.17663 x 10"8T3 - 1.60541 x 10 " T4 + 7.01732 x 10 “15 T 5
- 1.67621 x 10 "18T 6 + 1.68486 x 10 “22T7,
(3-3)
290 K < T(K) < 2250 K
Figure 3-4 shows only part of KP(T) as a function of both temperature and mass
for the DSC 7. There is very little dependence of KP(T) on temperature or mass;
therefore, an average calibration curve (the solid line) can be calculated. Average values
of Kp are fairly constant for this instrument. The values at various temperatures were
used to adjust measured power outputs to actual sample power outputs (PtrUe) using the
relation:
(3-4)
All adjustments were made prior to data analyses.

Heat flow rate calibration factor,
81
Figure 3-4 Heat flow rate calibration curve determined from several runs with two
different masses of sapphire for the DSC 7. The solid line is the average heat calibration
factor.

82
Data from a DSC can be very reliable and reproducible if certain necessary
procedures are followed. To ensure these aspects in the DSC data presented in this
dissertation, careful attention was given to the following parameters: (i) flat, thin
specimens were used in all situations, (ii) flat aluminum DSC pans were matched to
within 0.01 mg, (iii) the specimen and reference pans were always placed in the center of
the DSC furnaces, (iv) the vented platinum lids used to cover both furnaces were always
oriented in the same position, (v) the furnaces were purged with dry helium gas at a rate
of 25 mL min -1, (vi) the DSC outer enclosure (the dry box) was constantly purged with
dry nitrogen gas, (vii) the ice and water coolant was always kept at the same level in the
reservoir, (viii) identical scanning rates were employed on all polymer specimens, and
(ix) the mass of the polymer specimen was selected to be as close as possible or equal to
that of the sapphire standard.
3.4 Thermal Treatments
Following the calibration, thermal effects in PS were investigated. The PS
specimen was cut from the same atactic PS sample as the dilatometer specimens. The
study is discussed in greater detail in Chapter 4. Below, however, the approach taken is
discussed and analyses are shown using a representative data set from the PS study. Note
that key results on all polymer samples used in this research were obtained by following
similar methods and analyses.

83
3.4.1 Specimen Characterization
Before initiating enthalpy recovery experiments, the PS specimen has to be
characterized. The previously dried and weighed specimen was hermetically sealed in an
aluminum pan and placed in the DSC furnace. This single specimen of PS was used
throughout and left untouched in the instrument furnace in an attempt to reduce
experimental scatter due to differences in heat transfer effects. A check of the structural
thermal stability of the specimen was made by cycling the instrument between 35- and
180-°C several times. Structural equilibrium was achieved in the specimen when the
heating and cooling curves were superimposed. After the third set of scans this was the
case for the PS specimen.
The glass transition temperature of PS was measured next. The specimen was
first annealed at a high temperature for some time to ensure it was in equilibrium and to
erase the effects of previous thermal histories, was quenched at a cooling rate of 100 °C
min ', and then was immediately reheated at 10 °C min '. The mid-point of the
inflection on the power output curve in the glass transition region was calculated as Tg
(Figure 3-5). The enthalpic glass transition temperature (or the fictive temperature), Tf, h ,
was also calculated. Both calculations were performed by the UNIX software on the DSC
computer.

Power (mW)
84
Temperature (°C)
Figure 3-5 DSC curve for PS obtained at a heating rate of 10 °C min _1 following a
quench at 100 °C min

85
3.4.2 Enthalpy Change Measurements
The procedure employed involves repeated cooling-heating-isothermal stage
sequences and is depicted in Figure 3-6. Moving from left to right on the diagram,
thermal and structural equilibrium at a high temperature (T0), above Tg of the specimen,
is a necessary first step. This is followed by a quench, at a constant rate, to the desired
aging temperature, Ta, where the specimen is aged for a period of ta minutes. After aging,
the specimen is quenched again at the same rate to a temperature, T|0W, selected as the
start of the measuring scan. The specimen is held there for a few minutes (long enough
for thermal equilibrium) and is then immediately heated, at a constant rate, up to T0 where
there is another isothermal period of a few minutes. The specimen is then cooled to T|0W
again, and the identical heating sequence is repeated immediately. The last heating run is
thus on an unaged specimen and, in general, it serves to eliminate errors due to
instrumental baseline and calibration drift, and differences in the location of the specimen
within the DSC furnace. The cooling legs to T|0W, prior to the heating scans, are
necessary so as to avoid significant departures between the DSC traces of the aged and
unaged material.
The DSC traces resulting from the previous procedure contain thermal
contributions from the specimen, the aluminum pans, and the DSC sample holders. The
latter two contributions must be subtracted out. A baseline scan (with empty pans in the
DSC) is usually performed prior to enthalpy change measurements, using the same
isothermal—heating—isothermal sequence above and is stored into the DSC control
software. As part of the analysis, the scan is subtracted from the power outputs of both

86
the aged and unaged specimens, which are recorded as a function of time during the
heating stages.
£
3
(Ü
&
E
.o
Figure 3-6 Dlustration of procedural steps for measuring enthalpy changes in DSC.
Figure 3-7 shows thermograms of the aged and unaged PS specimen, baseline
already subtracted, superimposed on each other. The net area enclosed by the two curves
is the enthalpy change 26, l32,133 during physical aging, commonly referred to as the
recovered enthalpy (AH (ta, Ta)). A typical enthalpy - temperature (H - T) diagram that
describes the physical aging process is schematically shown in Figure 3-8. The following

87
t (min)
Figure 3-7 Output power (P) of the aged and unaged PS specimen, and the difference
between the two output signals (AP). Aging condition is 98.6 °C for 6 h.
parameters are required for the calculations of AH (ta, Ta): H4Th), the enthalpy of the
polymer at a reference temperature, Th, located high in the equilibrium state; H4Ta), the
equilibrium enthalpy at the aging temperature, Ta; HB(0, Ta), the enthalpy of the unaged
state at Ta; and Hc(ta, Ta), the enthalpy of the polymer aged for a time ta at Ta.
AP (mW)

Enthalpy
88
Temperature
Figure 3-8 Schematic diagram describing the pathway of enthalpy evolution during DSC
measurements. Path ABCO'CA represents the physical aging process and path ABOBA
is without aging.

89
Referring to Figures 3-7 and 3-8, and assuming that the heating rate of the
specimen in the DSC is the same as the heating rate in the DSC furnace (a good
assumption since the specimen is very thin and flat), then AH (ta, Ta) may be calculated
according to the following:
AH(tmJa) = H B(0,Ta) - Hc(ta,Ta)
= [H„(Th) - Hc(ta,Ta)] - [HATh)~ Hg(0,Ta)]
(3-5)
m a m
= -f" [*>_(»)-*>_*«)]<*
where Paged and Punaged are the output powers for the aged and unaged specimen,
respectively, and th is the time that corresponds to the reference temperature, Th.
For each Ta, there is a limiting equilibrium enthalpy, AH„,(ta, Ta), whose value
decreases as aging temperature increases. The value of AHoo(ta, Ta) can only be measured
experimentally when the Ta is close to Tg. 95,134,135
&H„(ta,Ta) = lim A//(
= HB(0,Ta) - HATa)
(3-6)
When the Ta is not close to Tg and the time scale examined is not long enough, the
equilibrium enthalpy has to be estimated. This can be done (from Figures 3-7 and 3-8) by
evaluating the integral:

90
(3-7)
where P” represents the extrapolated liquid state output power deduced from a linear
function obtained from averaging liquid state output powers of the unaged polymer
specimen.
From Figure 3-8, the enthalpy differences of interest are [Hb - Hoo(Ta)] and
[He - H„o(Ta)]. These two quantities are derived from the experimentally obtained
quantities described above as follows:
(3-8)
(3-9)
Subtraction of these two quantities, provides the enthalpy change (Hb - He), the lost
enthalpy on aging that is recoverable in the DSC heating scan. Also, the quantity
[He - H<*,(Ta)] which is the departure from equilibrium is commonly represented by the
parameter, 8h (from equation 1-14), often called the excess enthalpy.

91
3.4.3 Calculations on Test Data Set
Data from isothermal aging studies on PS is presented in Table 3-1. Recovered
enthalpies (AH (ta, Ta)), their standard deviations (s(AH(ta, Ta)), and 5h values were
calculated from three measurements for aging times less than two days, and from two
measurements for aging times longer than two days. For example, the enthalpy recovered
on heating PS, following six hours (21600 s) of aging at 98.6 °C, has an average value of
0.939 J g 1 and a standard deviation of ± 0.015 J g '. The equilibrium enthalpy (AH.*,) is
determined from a plot of AH(ta, Ta) versus log ta» as depicted in Figure 3-9. The
leveling off of AH(ta, Ta) is an indication that equilibrium has been reached The value of
AH», determined experimentally was 0.940 ± 0.006 J g -l.
3.4.4 Methods of Reducing Experimental Uncertainty
The most crucial aspect of an isothermal enthalpy recovery experiment is the
accuracy of the enthalpy measurement. The key considerations in improving the accuracy
of the measurements are: (1) to choose a conveniently achievable and reproducible
reference state, (2) to reduce uncertainties in both measured and derived quantities, and
(3) to assess possible errors associated with data manipulation. In view of these critical
factors, the measures taken to obtain the most accurate results are briefly described.
Quenching a specimen from a temperature greater than Tg to the aging
temperature is the first step in studies of structural recovery in the glassy state. For a
given set of experimental conditions, there is always a maximum attainable cooling

92
Table 3-1 Aging data for the enthalpy recovery of PS at 98.6 °C.
Time (s)
10gta
(ta in s)
AH(ta, Ta)
(Jg_1)
s(AH(ta, Ta))
(J g "')
5h
(J g ')
300
2.48
0.554
±0.014
0.386
600
2.78
0.652
±0.022
0.288
1200
3.08
0.754
±0.019
0.186
1800
3.26
0.815
±0.006
0.125
3600
3.56
0.909
±0.014
0.031
5700
3.76
0.926
±0.012
0.014
10800
4.03
0.942
±0.014
-0.002
21600
4.33
0.939
±0.015
0.0006
32400
4.51
0.945
±0.011
-0.005
54000
4.73
0.940
±0.016
-0.0004
64800
4.81
0.943
±0.004
-0.003
86400
4.94
0.928
±0.006
0.012

93
Figure 3-9 The change in enthalpy versus log ta for isothermal aging of PS at 98.6 °
The data level off when equilibrium is reached.

94
(quenching) rate, which depends on the nature, shape, and size of the specimen. The
effect of cooling rate on the Tg of PS in DSC was measured employing a procedure
similar to that used by Richardson and Saville. The specimen was cooled at rates from
10 to 300 °C min _1 and then immediately reheated at 10 °C min From an analysis of
the results, a rate of 100 °C min _l was considered to be a sufficiently accurate
approximation of the maximum attainable cooling rate, and is the rate used for this study.
Consequently, in the isothermal enthalpy recovery experiments, the state attained
immediately after cooling at 100 °C min -1 was considered as the initial state of the aging
process at that temperature.
At the end of the aging period, the PS specimen was cooled to Tiow = 38.6 °C
before starting the heating sequence, for the following reason. When heating is initiated
from an isothermal stage (here, from 38.6 °C at 10 °C min “') there is always a short
signal lag before the constant heating rate is attained, which varied from one DSC run to
another. This fact, if not accounted for, could cause additional uncertainty in the
calculated enthalpy. To avoid it, the lower limit of integration was chosen as indicated by
the line at ta in Figure 3-7; rather than in the level region of the curve 125 which represents
the isothermal period at T|0W. The implicit assumption here is that during the cooling of
the aged sample to T|0W, a temperature deep into the glassy state, there is no appreciable
process of recovery. 125 Thus, the cooling to T|0W and the brief period there, does not
cause any significant reduction in the recovered enthalpy.

95
3.4.5 Error Analysis
Every measurement contains some kind of error, either systematic or random.
Systematic errors are usually the result of operator error. They are one-sided errors in that
they always make a measurement either too small or too large. For example, a 50 mL
burette may only deliver 49.95 mL, or a thermocouple may read the temperature
consistently high by a certain amount. These errors are isolatable and correctable. In this
dissertation it is safe to assume that systematic errors have been minimized. Random
errors, on the other hand, cause a measurement to fluctuate about a central value; they
cannot be avoided. They are easier to quantify and are the ultimate limitation on the
precision or reproducibility of a set of measurements.
Random errors in the DSC enthalpy measurements are assessed by propagating
the errors from measurements and calculations. By taking the total differential of
equation 3-7 and then substituting for some terms, the error analysis equation for 5h
values is determined as:
(3-10)
where s is the uncertainty in each term expressed as its standard deviation. The
maximum uncertainty in 8h for the PS specimen at 98.6 °C was calculated to be ± 0.023.
This value represents a ± 6 % error. In actuality, however, the integrants involved in the
calculation of a particular enthalpy difference, i.e. Punaged, P" for HB - H„ (Equations 3-5,
3-7, 3-8) and Paged, P" for He - H» (Equations 3-5, 3-7, 3-9), are obtained from the same

96
thermogram, and the errors associated with the data, although preserved in the
integrations, tend to cancel out each other in the subtraction. As a result, the uncertainty
in 8h is actually much smaller than that indicated above.
A DSC can accurately monitor the process of physical aging through
measurements of enthalpy recovery. Once the instrument has been properly calibrated,
and procedures followed that take into account the thermal lag, the actual "quenching"
rate, and a possible hardware system bias, highly reliable results can be obtained. In the
next chapter, many of these results for PS are compared with corresponding volume data
from the dilatometer.

CHAPTER 4
THE TIME-DEPENDENT BEHAVIOR OF VOLUME AND ENTHALPY IN
POLYSTYRENE
4.1 Introduction
All amorphous polymers undergo physical aging below Tg. As an amorphous
polymer is cooled from an initial state of thermodynamic equilibrium, its free volume and
molecular mobility decreases. At Tg, the change in mobility is so drastic that the polymer
structure cannot attain equilibrium with the rate of cooling l8'56'81 and a glass is formed.
Glass formation is a kinetic event. It depends on the cooling rate since the molecular
mobility required to maintain equilibrium increases with increasing cooling rate. If a
glass, which is an inherently unstable material, is kept at constant environmental
conditions it undergoes a process whereby it evolves towards a temporally distant
equilibrium. *'2 This process, which was first described in detail by Struik 8, is called
physical aging.
Physical aging is a gradual continuation of the glass formation at temperatures
below Tg (see Figure 1-1). It affects all those temperature-dependent properties which
change drastically and abruptly at Tg. During aging the material becomes stiffer and more
brittle as its specific volume, enthalpy, entropy, creep- and stress-relaxation rates,
dielectric constant, refractive index, etc. decrease. Physical aging can have a significant
impact on the use of polymers, and any applications of these materials require that careful
97

98
consideration be given to the variation of their properties with time. In order to better
characterize this behavior, it is of interest to investigate the time dependence of material
properties and to determine any correlations between them.
Specific volume and enthalpy are two material properties that may show different
rates of physical aging because of their different sensitivities to structural recovery. One
can conclude, however, that only when the material establishes equilibrium will structural
changes cease to occur and properties cease to evolve. Then, theoretically, the time to
reach equilibrium will be independent of the property being measured. However, the fact
that equilibrium is approached asymptotically complicates matters. Therefore,
experimentally obtained times to reach equilibrium will depend on the sensitivity of the
measured property to structural changes, as well as the working definition of the time to
reach equilibrium and the resolution of the data.
The literature contains a number of reports on the time scales of recovery for
specific volume and enthalpy. These results were reviewed in Chapter 1 and show no
universal behavior. For example, in some investigations, the specific volume changed
more rapidly than enthalpy in PS, 88 91 PVAc,89 and PMMA, 9? but in others, it changed
more slowly than enthalpy in PS,22 PVAc, 92 and PMMA 88. The times to reach
equilibrium for specific volume and enthalpy in PS 94,97 and PEI,96 were also found to be
the same (within experimental error) in some studies.
Results for the same materials are contradictory and the reasons for this are
unclear. On the other hand, there is no a priori reason why different polymer structures
should show the same relative responses in their material properties. Nevertheless, what
is clear, is there is a need for further analysis. In this study, the physical aging behavior of

99
PS specimens from the same polymer sample, after temperature down-jumps to various
temperatures, is characterized by following the specific volume and enthalpy changes,
which are measured by two sensitive instruments, an automated dilatometer and a
differential scanning calorimeter (DSC). Different representations of the data will be
shown to compare the results from both techniques. It is the intention in this study to
be as direct as possible in making the comparisons between volume and enthalpy and
also to examine a wider temperature range than was previously reported for parallel
measurements of both properties on the same polymer.88-91-94'97
4,2 Experimental
4.2.1 Preparation of Polystyrene Specimens
The pellet form of atactic poly(styrene) (PS) was purchased from Aldrich
Chemical Company, Inc. The average molecular weights of this polymer, determined by
gel permeation chromatography (GPC) analysis relative to polystyrene standards using
chloroform as a solvent, were Mw = 315,500 gmol_l and Mn = 140,000 gmol 1 (Mw/Mn =
2.25). The structure of PS is shown in Figure 3-1.
Before use, the PS pellets were placed in a Teflon dish and dried to a constant
weight under vacuum for two days at 180 °C. During this time they flowed into each
other forming a large piece of polymer. The dried polymer was placed in a Carver
Laboratory Hot Press and molded at 200 °C into a thin flat sheet of less than 1 mm
thickness. A razor blade was used to cut portions of the flat sheet into strips for volume
measurements. The other portions were cut into disks with a cork borer for enthalpy

100
measurements. The thin strips and disks were then stored in a sealed dessicator to
prevent any moisture uptake before experiments.
4.2.2 Dilatometrv
Three types of experiments were conducted on the PS specimen. Two types,
namely volume versus temperature and reference specific volume determinations have
already been described in Chapter 2. In the third type of experiments, isothermal physical
aging studies were performed. The volume evolution for this process is shown
schematically in Figure 4-2: The dilatometer and specimen were initially annealed at a
Figure 4-1 Molecular structure of polystyrene.
temperature, Teq = 116.6 °C (for volume T ' = Teq; for enthalpy T 1 = Th) for 1 h in the
EX-251 HT bath so as to allow the system to reach to complete thermal and volumetric
equilibrium, Voo(Teq). Then the data acquisition program (Appendix A) was started, and
the dilatometer was immediately quenched (path AB) by transfer to the aging bath and

101
allowed to age (path BC) at the aging temperature (Ta). The isothermal aging time was
assumed to start after thermal equilibrium was reached. The time to reach thermal
equilibrium (ti) was about 137 s (determined as indicated in Chapter 2). The recovered
volume, Av, was calculated as the difference between the specific volume at this time, Vi,
and the specific volume after time t, at the aging temperature, vt. If equilibrium was
reached in the time interval for aging, the recovered volume was given by Av(t) = Vi - v»;
if it was not, then by Av(t) = V] - vt. The Ta’s used were 100.6-, 98.6-, 97.6-, 95.6-, 93.6-,
Figure 4-2 Schematic diagram of volume and enthalpy evolution during physical aging.
The material is annealed above the Tg ( = Tf) for a period of time and then cooled to and
aged at Ta (path ABC). Path CD represents the excess enthalpy or specific volume.

102
91.6-, and 81.6-°C. At Ta’s where equilibrium was not attained (Ta = 91.6- and 81.6-°C),
equilibrium specific volumes were determined by extrapolation of the liquid line of the
PS cooling curve (see Figure 4-2 above). Each recovery curve in the following pages is
an average of at least three runs at the same temperature.
4.2.3 Calorimetry
The general procedure is outlined in Chapter 3 (sections 3.4.1 - 3.4.2). The mass
of the PS specimen was 12.12 mg. The other conditions (Figure 3-6) were T0 = 138.6 °C,
Tl0w = 38.6 °C, and each isothermal period at T0 and Tiow was 3.5 min. Aging was carried
out at the same temperatures used for dilatometry. The measurements were performed in
triplicate at short aging times and duplicate at aging times longer than two days. The
average values of these results were used in data analyses.
4.2.4 Excess Specific Volume and Enthalpy Quantities
A direct comparison between volume and enthalpy recovery during physical aging
is shown schematically in Figure 4-2. The path CD is the excess enthalpy (8h) in an H vs.
T plot and similarly, the excess volume, 5y, in a v vs. T plot. Both parameters are
determined as follows:
Sv = K ~ v„(Ta) = [v, - v„{Ta)] - [v, - v,]
= &v~(Ta) - Av(t)
(4-1)

103
SH = Hc - Hm(Ta) = [Hb - Hm = AHJTa) - AH(t)
(4-2)
The recovery curves presented in section 4.3.2 (and 5.3.2) were calculated from these
expressions.
4.3 Results and Discussion
4.3.1 Glass Transition Temperatures of Specimens
In a simple cooling experiment (see Figure 1-1 and curve AB in Figure 3-8) the Tg
is equal to Tf which is the temperature at the intersection of the extrapolated liquid and
glassy lines. Figure 4-3 shows the results of a cooling experiment (re-plotted from Figure
2-7) on PS made with the dilatometer. At a cooling rate of 0.100 °C min the volume
fictive temperature, Tf,v is 97.1 ± 1.5 °C.
Accurate values of the measured quantities are difficult to obtain from DSC
curves by cooling.136 Therefore, a heating scan rather than a cooling scan is most often
used to obtain DSC data. Nevertheless, the Tg of the specimen is expected to be close to
its Tg obtained on cooling, if heating follows immediately after cooling from an
equilibrium state above Tg. 66-l36-137 Figure 4-4 shows the real output power versus time
and temperature for the unaged PS specimen obtained at a heating rate of 10 °C min 1
following a rapid quench (-100 °C min '). The plots were calculated from a DSC trace
such as is displayed in Figure 4-5.

104
Temperature (°C)
Figure 4-3 Specific volume - temperature curve for PS obtained with the volume
dilatometer at a cooling rate of 0.100 °C min The discontinuity at ~ 70 °C is an
experimental artifact. (Not all data points are included; linear fit ranges were indicated in
Chapter 2 where data first appeared).

P/m (W g1)
105
Time (min)
7 8 9 10 11 12 13 14 15
Temperature (°C)
Figure 4-4 The mass normalized output power (P/m) (symbol O) and calculated specific
heat capacity (symbol A) of PS as functions of temperature and time. Curve obtained at a
heating rate of 10 °C min 1 following a rapid quench at 100 °C min
t b r)

106
Figure 4-5 Determination of the Active and glass transition temperatures of PS by the
DSC.
Figure 4-5 illustrates application of the DSC method in calculating Tg and Tf, H.
The uppermost lines are integral or enthalpy curves integrated over the area between 60 to
141°C. The intersection of these lines is Tf H, represented on the plot by the longest
vertical line. To the immediate right of this line, where the PS curve is marked, is the
(mid-point) Tg. The Tf, h calculated from three PS curves was found to have an average

107
value of 102.6 ± 1.0 °C. This value is consistent with the established fact that the glass
transition temperature increases with scan rate. The approximately 6 °C difference
between this value and that for Tf, v agrees with experimental work l5'56 that has shown
that Tg changes by approximately 2 - 3 °C per decade of time.
Another method for determination of the TfS is to plot the specific volume change
to equilibrium, Av<„ = Vi - v„,, and AH„ as functions of Ta for those isotherms that have
reached equilibrium. This approach not only eliminates the thermal lag involved in any
finite scan but it also provides a value for the Tf of PS in the quenched dilatometer.
Figure 4-6 shows the respective plots from which values of Tf, v = 101.0 °C and Tf,n =
103.3 °C were determined.
Fictive temperatures for the same state assessed from different properties are
expected to be different. ' This is observed for the Tf values determined for volume
and enthalpy. The temperature difference of 2.3 °C can be explained as follows. In the
volume experiments, temperature jumps (Teq - Ta) of 23.0-, 21.0-, 19.0-, 18.0-, and
16.0-°C were made and the estimated time for thermal equilibrium before aging was
137 s (2.28 min). The cooling rate in each case was therefore 10.1-, 9.2-, 8.3-, 7.9-, and
7.0-°C min which gives an average of 8.5 °C min'1. The cooling rate in the enthalpy
measurements (100 °C min '), which results in a higher Tf, h, is about 12 times faster
than this rate. Previous studies on the logarithmic relationship between Tg and the
cooling rate have shown that a rate twelve times faster will shift the Tg by 2 - 3 °C.
Therefore, the different cooling rates experienced by the specimens account for the
different values of Tf, v and Tf, H.

108
By measuring the specific volume at (137 s) for a number of different Ta’s, an
isochronal specific volume - temperature curve can be constructed to show the
dependence of Tf on cooling rates. The v-T curve plotted for PS is shown in Figure 4-7.
The Ta’s used include those previously indicated as well as 55.6-, 60.6-, 66.6-, 71.6-, and
85.6-°C. The cooling curve of PS at 0.100 °C min and experimentally obtained
Figure 4-6 Av„ (circles) and AH„ (squares) as a function of aging temperature for PS.
(t.B r) ~hv

109
equilibrium specific volumes are also included in the plot. As expected, the faster
cooling rate of the quench increases the Tf of PS (from 97.1 °C to 101.0 °C). The
diagram also illustrates that an aged glass, at least at high Ta’s, relaxes to the extrapolated
equilibrium line. This behavior is assumed in most theories regarding polymer glasses,
though we have not yet seen such a comparison in the literature.
Temperature (°C)
Figure 4-7 Isochronal (time = 137 s) specific volume (squares) and equilibrium specific
volume (triangles) versus temperature for the quenched PS, compared with data (circles)
on the same polymer from slow cooling (rate = 0.100 °C min _1) experiments. (Observed
peak at about 70 °C is an experimental artifact).

110
It is worth noting that, although the glass transition is the predominant transition
detected in PS, it is not the only transition shown by this polymer. Apart from the glass
transition (labeled as a), PS exhibits four other transitions, 120 referred to as liquid-liquid
(1,1), (3, y, and 8 in order of decreasing temperature. From dilatometry data, 120 the liquid-
liquid transition occurs in the rubbery phase of the polymer near 170 °C, the y-process
around 140 °C, the [3-process in the range 30 - 70 °C, and the 5-process at temperatures
less than -200 °C. These transitions, which are normally weak, occur outside the
temperature range for our aging experiments and therefore are not expected to affect the
aging results.
4.3.2 Isothermal Recovery at Various Aging Temperatures
The volume recovery curves for PS aged at various temperatures are depicted in
Figures 4-8 and 4-9. The isotherms in Figure 4-8 can generally be separated into three
regions: an initial delay region, a linear inflectional region, and a plateau region where
8y = 0. The plateau occurs when the volume levels off and is an indication that
equilibrium has been reached.
The 81.6 and 91.6 °C isotherms in Figure 4.9 resemble one another. Values of 8y
for these isotherms were determined from extrapolated equilibrium specific volumes (v)
based on the calculated liquid state volume thermal expansion coefficient (oíl) for PS,
5.97 x 10 4 °C ■’ (see Table 2-1). A large temperature difference, from the annealing to
aging temperature, does not necessarily vary the volume contraction rates of
these isotherms. This implies that the molecular motions responsible for structural

Ill
rearrangements towards equilibrium are independent of aging temperature when the
material is far from equilibrium. Within the experimental time interval shown,
equilibrium is not reached at any of the temperatures.
The contraction non-linearity at the tails of the isotherms in Figure 4-8 is not seen
in the isotherms at 91.6 and 81.6 °C in Figure 4-9, because the departure from the
postulated equilibrium line is still quite large. In sharp contrast to Figure 4-8, the volume
logft-g (S)
Figure 4-8 Isothermal volume contraction of PS at various aging temperatures after a
quench from Teq = 116.6 °C.

112
change at both temperatures is proportional to temperature difference. Thus, there is no
secondary transition in the PS specimen over this 10 °C temperature range. This
conclusion holds regardless of the length of the experimental aging time. Both Figures
4-8 and 4-9 show a commonly known fact about physical aging, that is, as the aging
temperature decreases, the time required to reach equilibrium increases.
Figure 4-9 Isothermal volume contraction of PS at 81.6 °C and 91.6 °C following a
quench from Tgq = 116.6 °C (calculation of 5y is described in the text). Data at 93.6 °C
are included for comparison.

113
The enthalpies recovered after aging PS at several temperatures for different
lengths of time are shown in Figures 4-10 and 4-11. Simple visual inspection reveals that
equilibrium is reached at 100.6-, 98.6-, 97.6-, and 95.6-°C, that is when the change in
enthalpy levels off. The maximum aging time the DSC could accommodate without
removing the specimen was 10000 minutes. Therefore, the specimen at 93.6 °C either
iogta (s)
Figure 4-10 The change in enthalpy versus log aging time for PS at various temperatures.
Each curve, except the bottom curve, is shifted vertically by 0.5 J gfor clarity.

114
reaches equilibrium or is close to it, after aging for this amount of time. In Figure 4-11
equilibrium is not reached at 91.6- and 81.6-°C within the length of time investigated. As
with volume data, the specimen takes longer to reach equilibrium as the aging
temperature decreases.
0.0
3.0
+
+
2.5
+
*
+
2.0
+
+
*
*
81.6 °C
91.6 °C
4_
1.5
i
*
+
+
*
1.0
+
+
*
*
0.5
i
. i
i
i
. i . i
. i . i
2.0
2.5
3.0
3.5
4.0
4.5 5.0
5.5 6.0
i°gta (s)
Figure 4-11 The change in enthalpy versus log aging time for PS at 81.6 °C and 91.6 °C.
For clarity, the curve at 91.6 °C is shifted vertically by 0.5 J g

115
Figures 4-12 and 4-13 depict the excess enthalpies as a function of log aging time.
The features in the former plot are similar to those observed for volume in Figure 4-8.
The estimated equilibrium enthalpies at 81.6 °C and 91.6 °C were determined from the
average linear equation of six power versus time curves of the unaged specimen, as:
(P'/m) = 0.05901 + 0.210 W/g (4-3)
log ta (s)
Figure 4-12 Isothermal enthalpy contraction of PS aged at the indicated temperatures
following a quench from T0 = 138.6 °C.

116
By integrating equation 4-3 from ta’s = 7.8 min and 8.8 min to th = 13 min, AfL,(ta, Ta)
values of 4.283 J g _l and 3.583 J g _1 were calculated for the Tas of 81.6 °C and 91.6 °C,
respectively. The 5h values determined from these enthalpies are shown in Figure 4-13.
Similar to the data in Figure 4-11, the enthalpy recovery curves at 91.6- and 81.6-°C
Figure 4-13 Isothermal enthalpy contraction of PS aged at 81.6 °C and 91.6 °C following
a quench from T0 = 138.6 °C (calculation of 8h is described in the text). The isotherm
from the 93.6 °C data is also added for comparison.

117
one another. Also, the excess enthalpy retained at the two temperatures is proportional to
temperature difference. Furthermore, irrespective of the length of the experimental aging
interval, there is no secondary transition for PS between 91.6- and 81.6-°C. Thus, as with
volume, the slope of the enthalpy isotherms is independent of aging temperature when the
material is far from equilibrium.
4.3.3 Comparison of Volumetric and Enthalpic Recovery Rates
A commonly utilized parameter8’l8, ll9'139'140 for comparing volume and enthalpy
recovery is the physical aging rate, r. It is defined as the inflectional slope of a recovery
isotherm in the time interval where the specific volume or enthalpy varies linearly with
the logarithm of the aging time. Normally, it is expressed as:
r dS '
aiog a-*,) \
y
A
dv(t)
a log(r-fj)
\
A
(4-4)
for volume measurements and
^log ta
X
A
(4-5)
for enthalpy measurements. However, 8 and 8h are not fully comparable quantities (see
equations 1-13 and 1-14). For a more direct comparison with the calculated enthalpy
recovery rates, equation 4-4 was replaced with the following equation for the calculation

118
of volume recovery rates:
rv = ~
as.
3log(r-/,)
A
(4-6)
In Figure 4-14, the volume rates so determined are displayed along with enthalpy rates as
functions of aging temperature. The data show qualitatively similar curvature for both
rates. There is a steep increase just below the respective Tf’s followed by a less rapid
increase, as both rates appear to approach a maximum value.
Volume recovery rate data have been found to pass through a maximum at around
15 - 20 °C below the Tf for many polymers. 11 To determine if this was the case, an
aging run was carried out at 66.6 °C and the recovery rate determined. The value is
included in Table 4-1 along with all the other rate data. It appears that the PS specimen
has a maximum rate close to or in the temperature range given above. Whether or not the
value at 81.6 °C is indeed a maximum requires additional rate data for other temperatures
between 66.6 and 81.6 °C. The decrease in rate from 81.6 to 66.6 °C can be ascribed to
the increasing effect of the self-retardation of volume contraction as the temperature
decreases. Greiner and Schwarzl 120 used the normalized parameter 8 (as opposed to the
unnormalized 8y) to calculate volume recovery rates for a PS specimen and found a rate
trend similar to ours.
Enthalpy (H) and volume (V) are related by the thermodynamic equation that
defines enthalpy, i.e., AHP = AU + pAV where p is constant pressure. Thus, it is expected
that enthalpy changes will be larger than volume changes (which are fairly small) under

119
the same conditions, the difference being partially attributed to internal energy changes,
AU, that occur in the material. In Figure 4-14 and Table 4-1, the larger enthalpy recovery
rates reflect the larger changes in enthalpy over the same time interval at each
temperature. This also implies that enthalpy recovery curves have a steeper approach to
equilibrium than do volume recovery curves (see section 3.4.7).
1.0
0.9
0.8
0)
T3
(0
o
0)
â– o
0.7
To>
0.6
CO
E
0.5
CO
o
X
0.4
^ >
0.3
0.2
0.1
90
Temperature (°C)
105
Figure 4-14 Physical aging rate, r, as a function of temperature, for PS (o = r'v and
• = rH), over the same time interval.

120
Table 4-1 Physical aging rate data for PS at various aging temperatures.
Temperature
(°C)
r'v
(cm 1 g 1 decade 1)
rH
(J g 1 decade -1)
100.6
1.92 x 1 O'4
0.150
98.6
2.88 x 10'4
0.336
97.6
3.93 x 10'4
0.469
95.6
4.99 x 10 4
0.551
93.6
6.32 x 10-4
0.624
91.6
6.36 x 10 4
0.656
81.6
7.34 x 10-4
0.667
66.6
7.30 x 10-4
4.3.4 Comparison of Times to Reach Equilibrium for Volume and Enthalpy
Another interesting way to look at volume and enthalpy data is to examine their
times to reach equilibrium. Figure 4-15 depicts a comparison between these times at
various temperatures. The time to reach equilibrium is taken as the time at which the
change in the property measured becomes zero within the scatter of the data. As
mentioned earlier, equilibrium is approached asymptotically, which makes it difficult to
pinpoint exactly the time to reach equilibrium. Therefore, the experimental error
associated with each time is also included in the plot. Times to reach equilibrium (t*,)
increase with decreasing temperature and, within the experimental error, it is apparent
that these times are identical for both volume and enthalpy.

121
Figure 4-15 Time necessary for the attainment of thermodynamic equilibrium, U, for
volume (open circles) and enthalpy (solid circles) recovery at different temperatures for
PS.

122
4.3.5 Effective Retardation Times of Volume and Enthalpy
While actual structural recovery is best described by a distribution of retardation
times, it is often analyzed in terms of a single effective retardation time, xeff, '8'81,141,142
defined as:
MO = -[*/('.)]
dSP+(ta)
dt„
\-i
1
(d In Sp+ (ta)/dta)
(4-7)
where ta is the same as before and 8p+ is the normalized property, P, (volume or enthalpy)
of the material, whereby 8/ = 8v / AVoo and Sh+ = 8v / AHoo. The effective retardation
time depends both on the aging temperature and 8p+(ta), whose value depends on the
structure of the glass at each given aging time. Its reciprocal (l/xeff) is a measure of the
rate of recovery of the system as it approaches thermodynamic equilibrium.
Typically, following a down quench, xeff increases with aging time. This is
evident in Figure 4-16 which compares the enthalpy retardation times (xeff, h) with the
volume retardation times (xeff, v)- A number of features are observed.
First of all, in general, the data points lie below the solid line whose slope is equal
to one, i.e. where xeff, h = Xeff. v Therefore, at any instant the effective retardation time for
enthalpy change is smaller than that for volume change. Consequently, following a down
quench with PS, enthalpy recovers faster than volume. Secondly, as time increases, xeff, h
and teff, v increase but with xeff, v increasing more rapidly than xeff, h- This is evidenced by
the curvature of the data away from the equal-retardation-time line.

123
Figure 4-16 The effective retardation time of enthalpy recovery versus the effective
retardation time of volume recovery for PS aged at various temperatures.

(s) c_CHXhmi (s) e.(HX
124
Figure 4-16—continued

125
Thirdly, xeff. v, xeff, h and the difference between them, increase as the aging temperature
decreases. Increasingly long times at these low temperatures lead to rates of volume and
enthalpy change that may become quite similar. Conversely, recovery rates are dissimilar
at the higher aging temperatures. For example, after 3 h of aging at 98.6 °C, xeff, v is
approximately twice xeff, h which indicates that the excess enthalpy is approaching zero at
a rate ~ 2 times faster than the excess volume.
An exception to the above observations is the data at 95.6 °C. This data indicate
that enthalpy recovery is faster than volume recovery at first, but then volume recovery
overtakes it and eventually approaches equilibrium at the faster rate. This result is not
readily explainable and is not observed at any other temperature. Nevertheless, it does
illustrate the very complex nature of the glassy state and the processes involved in
physical aging.
Another possible way of comparing the effective retardation times of volume and
enthalpy is to plot logarithm of xeff versus some instantaneous state of the glass. In
general, at any particular time during structural recovery, the amount of excess enthalpy is
not the same as the amount of excess volume (see Figures 4-22 - 4-25). However, by
plotting Xeff.v and xeff, h against the single parameter, 5y, (or 8h), a direct comparison of the
relative rates of the volume and enthalpy recovery can be made at the same one time
evolving macroscopic property, v(t). (Recall that 5y = v(t) - v„,). Figures 4-17 shows the
dependence of the calculated values of In xeff, P (P = v or H) on 8y (The same dependence
will be found if xeff. v and xeff, h are in turn plotted against 8h). The increasing values of
Xeff’s for each isotherm indicate that the recovery rate of the material is decreasing as it
approaches equilibrium and as the excess volume decreases. This is consistent with the

126
self-retarding nature of the aging process. At all temperatures, xeff, v values are longer
than Xeff, h values indicating that enthalpy is recovering faster. For example, when 8v ~
2 x 10 4 cm3 g 1 enthalpy is recovering ~1.6 times faster than volume at 98.6 and 93.6 °C.
Figure 4-17 Plots of In xeff for volume recovery (P = v, open symbols) and enthalpy
recovery (P = H, filled symbols) as a function of the excess specific volume of PS at
different aging temperatures.

eff, P
127
8vx103 (cm3 g1)
8.0
Figure 4-17—continued

128
and ~1.2 times faster at 95.6 °C. Retardation times become longer and, in general, quite
similar as the aging temperature decreases which suggests that at lower temperatures in
the glassy state, the recovery rates may become identical.
Figure 4-18 Plots of In xeff, h as a function of the distance of the PS polymer from
enthalpy equilibrium.

eff, H
129
W
c
Figure 4-18--continued.

130
4.3.6 Temperature Dependence of Effective Retardation Times
Over a relatively narrow temperature interval close to Tg, the temperature
dependence of the recovery process may be described approximately by a single effective
retardation time. 143"150 This approach uses an Arrhenius type equation from which the
activation energy of the process can be determined:
Teff (ta’Ta) = A eXPt Eapp ^TJ* exp[- CSp ] (4-8)
where Eapp is an apparent activation energy, A is a pre-exponential factor, and C is a
constant that gives the dependence of x on structure.
Equation 4-8 can be rewritten as:
^effOaJa) = ^ A'(7fl ) ~ CSp
= In A + EappIRTa - C8P
(4-9)
The best-fit values of In A'(Ta) and C at each aging temperature can be obtained from the
intercept and slope of the plot of In xeff versus 5y or 8h- The slope and intercept of a plot
of In A'(Ta) against 1/Ta then provides the apparent activation energy, Eapp, and In A,
respectively, for the recovery process. Cowie and Ferguson l43,144 used similar plots in
their analysis of polymer recovery data.

131
Plots of In Teff, v versus 8v and In xeff, h versus 6h are drawn in Figures 4-17 and
4-18, respectively. The intercepts of these plots are In A'(Ta). Plots of In A'(Ta) versus
1/Ta, over the narrow temperature range 100.6 °C to 91.6 °C, are shown in Figures 4-19
and 4-20. Values of Eapp, In A, and C calculated from these plots are 1232 ± 171 kJ
mol -391 ± 56, and 2454 ± 135 gem 3 for volume versus 1218 ± 165 kJ mol_1, -387 ±
54, and 2.89 ± 0.40 g J _l for enthalpy. Volume and enthalpy recovery are known to be
quite similar and this is indicated by the pre-exponential factors (A) and apparent
activation energies (Eapp) which are essentially the same for both processes.
Petrie 26 145 and Marshall145 studied the physical aging in a PS sample by DSC
and found the following the aging parameters for enthalpy recovery: Eapp = 1192 kJ
mol ', In A = 371 (when x is in seconds), and C = 2.92 g J Within measurement error,
the enthalpy results calculated here agree with their results. Our value of Eapp for
enthalpy is also comparable to that of other linear polymers calculated by this method:
polyethylene terephthalate) (860 kJ mol ‘), 133 poly(vinyl methyl ether) (407.4 kJ mol '),
143 polycarbonate (1731 kJmol '*), 144 poly(methyl methacrylate) (507 kJmol '),149 and
poly(vinyl chloride) (1409 kJ mol '). 149
The parameters obtained from equation 4-8 can be related to those from equations
1-25 and 1-26 where the retardation time also involves separate temperature and structure
dependence. The material parameters 0 and x may be determined from the following
1 ’
RTr2
relationships:

132
1000 / Ta (1C1)
Figure 4-19 Arrhenius plot of In A (Ta) versus 1/Ta for volume recovery in PS.

133
Figure 4-20 Arrhenius plot of In A’(Ta) versus 1/Ta for enthalpy recovery in PS.

134
and x = 1 (for enthalpy Acp is used).
0
Taking Tr = Tf, v = 374.0 K and AoCsP = 3.73 x 10 4 cm 3 g 1 K'1 (AOsP = otsP. l
- 0Csp,G where otsP = dv/dT), the parameters 0 and x for volume are 1.06 K'1 and 0.136,
respectively. The same parameters for enthalpy, with Tr = Tf, h = 376.3 K and the
calculated average Acp for PS = 0.295 J g ''K'1, arel.03 K 1 and 0.172, respectively.
These parameters are similar to those found for other polymer glasses. 145-149,151 In
addition, while both processes can be described by the same 0, the larger partition factor
(x) for enthalpy reflects the higher temperature dependence of enthalpy changes.
A minimum of four parameters (e.g., A, Ah* (= Eapp), P, x) is required to describe
structural recovery kinetics. If Tf determined from different macroscopic properties (e.g.,
v and H) of a material, for the same cooling rate are not the same, then one or more of the
above parameters are different for the two properties. As shown in Table 4-2, the kinetic
parameters have different values. However, the cooling rate was not the same in the
volume and enthalpy measurements and this probably has a greater effect on the
difference in Tf values than do the small differences in the kinetic parameters.
Table 4-2 Aging parameters for PS
Parameters
Volume
Enthalpy
In A (s)
-391 ±56
-387 ± 54
Eapp (kJ mol )
1232±171
1218 ± 165
c
2454 ± 135 g em 3
2.89 ± 0.40 g J -1
0 (K1)
1.06
1.03
X
0.136
0.172

135
4.3.7 Enthalpy Change Per Unit Volume Change
The PS data can be examined by looking at the behavior of the ratio between the
enthalpy change and the volume change with time. Figure 4-21 shows plots of this ratio,
8h / 5v, as a function of aging time. It is obvious from this figure that the value of the
ratio is not constant. It decreases as time increases implying that 8h is changing at a more
Figure 4-21 The enthalpy change per unit volume change with time at (a) 98.6- and
97.6-°C, (b) 95.6- and 93.6-°C, and (c) 91.6- and 81.6-°C (lines are included only as
visual aids).

136
rapid rate than 8y. Furthermore, at increasing times, the volume recovery appears to slow
down while the enthalpy continues to recover at an increased rate. This suggests that
enthalpy is more sensitive to the underlying structural changes at long times and that it
approaches equilibrium more steeply than does volume. This is shown more succinctly in
Figure 4-21--continued

137
Figure 4-21—continued
Figures 4-22 through 4-25 where volume and enthalpy recovery curves are plotted against
log aging time. The curves at 81.6- and 91.6-°C are very far from equilibrium. Error bars
are shown on the enthalpy data because the relative scatter in these data is much greater
than that in the volume data. Within the scatter of the data, volume and enthalpy curves
at 100.6 °C through 93.6 °C appear to reach equilibrium at the same time.

8 x103 (cm3g1) 8vx103 (cm3g1)
138
•°gta (s)
iogta (s)
Figure 4-22 Comparison of volume (empty shapes) and enthalpy (filled shapes)
isotherms at 100.6 °C and 98.6 °C as a function of aging time.
(J g )

8v x 103 (cm3 g1) 8v x 103 (cm3 g1)
139
log ta (s)
iogta (s)
Figure 4-23 Comparison of volume (empty shapes) and enthalpy (filled shapes)
isotherms at 97.6 °C and 95.6 °C as a function of aging time.

8v x 103 (cm3 g'1) 6vx103 (cm3g1)
140
log ta (s)
Figure 4-24 Comparison of volume (empty shapes) and enthalpy (shapes with error bars)
isotherms at 93.6 °C and 91.6 °C as a function of aging time.

141
Figure 4-25 Comparison of volume (dotted shapes) and enthalpy (shapes with error bars)
isotherms at 81.6 °C as a function of aging time.
As time approaches zero, the curvature of the data in Figure 4-21 indicates that the
ratio may be approaching an asymptotic or constant value. It is in these shorter times that
structural changes occur most rapidly, and 5y and 8h may be changing rapidly at the same
rate. However, the small increases in the 8h / 5v ratio as time becomes increasingly
smaller suggests that aging in PS, volume recovers faster than enthalpy. In general, larger values of 5h/ 8y are
observed at the higher temperatures and at short times. The magnitude of the ratio at
these times is proportional to the size of the temperature difference between the annealing
and aging temperatures, and it implies that temperature has a greater effect on enthalpy
changes than it does on volume changes.

142
All the plots in Figure 4-21 show the same general behavior, approaching an
asymptotic value at short times but decreasing as time increases. This nonlinear
relationship between the two properties lends to the credibility of the observations and
indicates that different mechanisms are operating at different stages as equilibrium is
approached. It also accounts for the different approaches to equilibrium observed for
both properties in Figures 4-22 - 4-25, caused by their different sensitivities to the
structural change that occurs during physical aging.
The relative change in enthalpy with volume is the energy for creating a unit free
volume. This ratio has been quantified by the parameter (dH /dV)T in the work by
Oleinik on PS.24 In that work, it was found to equal 1 - 2 x 10 9 J m'3 for down-jump
experiments over the entire measurement time interval and for all aging temperatures.
For up-jump experiments, the parameter was 30 % larger but still independent of
measurement conditions. In this work, (dH/dV)T can be determined from the slope of
an excess enthalpy versus excess volume plot, i.e.,:
rdH_'
dS„
JT
(4-10)
The value of (dH /dV)T calculated at each temperature is shown in Table 4-3. The
values are in agreement with the measurements of Oleinik. However, as shown in Figure
4-21, 5h/8v is not constant over the entire time range of measurements for our
experiments and therefore neither are (dSH /dSv )T nor (dH/dV)T; rather, as 5y

143
approaches zero, (dH/dV)T increases such that the enthalpy and volume reach
equilibrium at the same time.
Table 4-3 Quantification of the energy per unit free volume for PS.
Ta
(dSH I^SV)T
Range for 5y
O H/dV)T
(°C)
(Jem3)
(cm 3 g 1)
(Jin3)
100.6
1439
5v> 1.5 x 10 5
1.44 x 10 9
98.6
1299
6v> 1.5x 10*4
1.30 x 10 9
97.6
1174
5v> 1.5 x 10 4
1.17 x 109
95.6
1133
5v> 1.5 x 10 ^
1.13 x 10 9
93.6
1015
5v > 6.5 x 10 4
1.02 x 10 9
91.6
1227
5v> 1.7 x 10'3
1.23 x 10 9
81.6
1229
8v > 4.7 x 10 3
1.23 x 10 9
Finally, the analysis presented here is based on the assumption that the same
nonequilibrium state was realized in both the dilatometer and DSC specimens following
the down-quench to the aging temperature. Since two very different specimen sizes are
used in the two techniques, this can never be achieved. Struik 152 recently addressed the
effect of nonideal down quenching and suggested that the effect of nonideal cooling may
persist for long periods after thermal equilibration. The data here (and in the next
chapter) have not been corrected for this effect as the form of the correction does not
appear to be straightforward. Accepting this caveat, we are able to make a direct
comparison, in the sense that the data come from the same polymer sample. Moreover,
part of our results are corroborated by the experimental results of Takahara et al. 94
These researchers reported probably the first data for simultaneous measurements of

144
enthalpy and volume recovery in one PS specimen near Tg, and demonstrated that the
time scales for volume and enthalpy recovery functions to attain equilibrium are the same
within the experimental errors—findings that are the same as ours using two different
specimen sizes. Additionally, we have presented evidence to show that in general,
enthalpy recovers faster than volume, but that both properties reach equilibrium at the
same time. It appears that volume initially recovers faster but is eventually overtaken by
enthalpy which has a faster recovery rate for the major part of the recovery process. The
measurements were performed over a wider range of temperatures than was previously
investigated by others on the same material. Our approach of using directly comparable
excess quantities and different representations of the data to gain insights, have also not
been used by others in studying PS. Nevertheless, it is not clear whether our results are
due only to the model chosen for data analysis or to the material studied. It is clear that
more work is definitely required on other materials and/or using other models to fully
understand the relationship between various properties in the glassy state.

CHAPTER 5
PHYSICAL AGING IN A P0LYSTYRENE/P0LY(2,6-DIMETHYL-1,4-PHENYLENE
OXIDE) BLEND
5.1 Introduction
In this chapter physical aging in an amorphous polymer blend is examined. Many
of the analyses applied to PS in the previous chapter are also applied here in order to
compare for the blend volume and enthalpy recovery. Following this, aging in the blend
is compared with aging in its major component homopolymer, PS.
5.1.1 Polymer Blends 153'157
Since the introduction of Noryl, a commercial thermoplastic blend by General
Electric Company in the mid-sixties, 158 the interest in polymer blends has grown rapidly
in both industry and academia. From a practical point of view, the mixing of polymers is
an easy and economical way to create materials with desired properties, thereby making
blends candidates for novel applications. Consequently, at present there are a significant
number of commercial blends available, and high levels of effort are still being expended
to create more materials with desired property advantages.
Polymer blends may be defined as intimate mixtures of two or more kinds of
polymers, with no covalent bonds between them. They can also be classified by their
phase behavior as either miscible or immiscible. Miscible blends contain components
145

146
that are mutually soluble in one another and exhibit a single amorphous phase.
Immiscible blends contain components that are not intimately mixed and thus show
multiple amorphous or semi-crystalline phases. In a completely immiscible blend, each
phase contains a pure blend component whereas the phases of partially immiscible blends
may contain some of each material in the blend.
Among all the possible combinations of existing polymers, miscible blends are a
rather small group. 153 157 That is because the most likely result when two polymers are
combined is a two-phase mixture. The reason that two polymers are not usually miscible
is best understood in a thermodynamic context through the Gibbs free energy change
upon mixing, AGm.
A necessary condition for materials to be miscible is that AGm has to be negative;
it may be expressed at any given temperature, T, as:
AGm = AHm - TASm (5-1)
When small molecules are mixed, the entropy change upon mixing, ASm, is large and
AGm becomes favorable (negative). However, when the molecules consists of long
chains, this is not the case. Instead ASm is generally very small and the enthalpy change
upon mixing, AHm, decides the sign and magnitude of AGm:
AG = AHm
(5-2)

147
For most polymer pairs, AHm is normally positive and only if AHm < TASm, or in some
cases if AHm is negative, will the two polymers mix to form a single phase. The other
principle criterion for miscibility involves the second derivative of the free energy change
with respect to composition, i.e.,
a2AG,„
> o
(5-3)
where <))¡ is the volume fraction of the ith component. It follows then that miscibility
within a polymer mixture should only occur under the following circumstances: (i)
mixing polymers of low molecular weight (oligomers): the ASm term becomes more
appreciable (larger than that for high molecular weight polymers) and overwhelms the
unfavorable (positive) AHm; (ii) mixing of two polymers that are chemically and
physically similar (e.g. copolymers): the small ASm involved may be sufficient to
overcome the very small positive AHm; (iii) mixing of two polymers in which there are
favorable interactions such as hydrogen bonding or charge transfer between the functional
groups: AHm is expected to be negative in this case.
Miscible polymer blends were once considered to be very rare. However, since
the introduction of the trademark blend Noryl, which is a mixture of polystyrene (PS) and
poly(2,6-dimethyl-1,4-phenylene oxide) (PPO), continuous research has led to an increase
in the number of known miscible pairs, many of which have practical applications.
Along with PS/PPO, the list includes well investigated binary systems such as nitrile
rubber/ poly(vinyl chloride) (PVC), polystyrene/ poly(vinyl methyl ether) (PS/PVME),

148
poly(methyl methacrylate)/ poly(vinylidene fluoride) (PMMA/PVDF), and poly(methyl
methacrylate)/ poly(vinylidene chloride) (PMMA/PVDC). A detailed review of miscible
polymer blends can be found in several texts. 153'157
Miscibility in polymer blends is commonly assessed from the determination of Tg.
A single composition-dependent Tg (often broadened) that lies between the Tgs of the
pure components indicates miscibilty of the polymer blend, whereas two separates Tgs
indicate immiscibility. Experimental techniques that have been commonly used to assess
the miscibility include dynamic mechanical analysis, dielectric methods, dilatometry, and
differential scanning calorimetry.
For the preparation of polymer blends, the method most widely practiced in
industries is mechanical mixing; this method is simple with low costs. In the laboratory,
polymer blends are often prepared with a third component (a solvent) using such methods
as solution-casting or freeze drying from a common solvent. Such methods normally
require only small amounts of materials and very simple lab equipment. Another method
used in blend preparation is in-situ polymerization, where a blend is prepared by
polymerization of one component in the presence of the other. This method often
produces an interpenetrating networks (IPNs) or simultaneous interpenetrating networks
(SINs) of blended polymers. Considerable care must be exercised in the preparation stage
of polymer blends as the method of blend preparation can affect the compatibility of the
polymers. 139 Each preparation technique has its own advantages and disadvantages and
these are adequately discussed in the literature. 153'157

149
5.1.2 Blends of Polystyrene and Poly(2,6-dimethyl-l,4-phenvlene oxide)
The PS/PPO polymer blend is the most widely studied compatible system of
polymers. The molecular structures of both component polymers are shown in Figure
5-1. PS possesses phenyl rings and has vinyl links in the backbone whereas PPO contains
(b)
Figure 5-1 Molecular structures of (a) polystyrene and (b) poly(2,6-dimethyl-1,4-
phenylene oxide).

150
phenylene rings with ether links. PS is an extremely brittle substance while PPO is a
highly ductile polymer with excellent tensile strength, modulus, and chemical resistance.
The Tg of PPO is exceptionally high (more than a 100 °C greater than that of PS) and can
be attributed to the presence of the stiff phenylene groups in the backbone, which lower
the overall flexibility of the polymer chain. PPO also has poor processability but
blending it with PS provides a tough material which can then be easily processed. PS and
PPO are thermodynamically compatible in all proportions over a considerable range of
molecular weights. 160 "162 Their blends can be heated up to 350 °C, well above the usual
experimental range, without phase separating. ~ It is generally accepted that this
phenomenon is related to the strength of the interactions between PS and PPO. Films of
PS/PPO blends are clear and the refractive index has been reported to increase linearly
with PPO content. 164
Many studies have used various techniques to investigate the PS/PPO blends.
Differential scanning calorimetry and thermo-optical analysis of PS/PPO blends 165'171
found a single Tg transition as well as did dielectric relaxation ’ and dynamic
mechanical thermal analysis. 160,165,167 Small angle neutron scattering (SANS)
measurement 174 found a large and positive second virial coefficient (A2), indicating that
PS is a good solvent for PPO. Further, A2 decreases linearly when the temperature of the
blend is raised, consistent with the large temperature (> 350 °C) normally required to
cause PS/PPO blends to phase separate.
Blends of PS/PPO display a negative AHm across the entire composition range as
measured by calorimetry. 175 l8“ The negative AHm has been attributed to specific
interactions between the phenyl and phenylene rings 161 and between the methyl groups

151
and the phenyl rings. 183-185 The consequence of this interchain interaction is a volume
contraction which produces blends with higher densities than the weighted average of the
densities of the pure components. Densification or free volume contraction in PS/PPO
blends is further corroborated by volume measurements which show a negative excess
QR 197 io¿
volume of mixing across the blend composition range. ’
The reasons for choosing a mixture of PS and PPO for this study are as follows:
(i) blends of PS/PPO are known to be compatible and amorphous over the entire range of
compositions; (ii) the large difference between the Tgs of PS and PPO. The Tg of PS is
around 100 °C and that of PPO is about 210 °C; (iii) as stated earlier, PPO is highly
ductile whereas PS is extremely brittle. The mixtures should therefore possess interesting
intermediate properties. Compared to pure PS, discussed in chapter 4, on the one hand,
one can systematically change the overall local chain rigidity (PPO more rigid), but at the
same time increase the density and perhaps the free volume.
The number of studies in the literature on volume and enthalpy recovery in
miscible polymer blends is limited. Most of the studies involve enthalpy measurements.
Two of them came from the laboratories of Cowie and his coworkers. In the first study,
Cowie and Ferguson 144 investigated enthalpy recoveries in a miscible blend of
PS/PVME, with components of very dissimilar Tgs, and found that the total amount of
recovery was much lower for the blend than for the corresponding homopolymers. They
concluded that the observed aging effects were primarily contributed by the PVME
component. In a more recent study, Cowie et al.187 were able to reproduce the structural
relaxation behavior of PS/PPO blends using a model based on the calculation of the
configurational entropy of the samples during different thermal histories. Very good fits

152
were obtained and led to material parameters which indicated that the blends were
stronger, and had smaller correlation lengths at their various Tgs than the pure polymers.
Oudhuis and ten Brinke investigated the conclusions of Cowie and Ferguson in the
study above by performing enthalpy recovery measurements in PS/PPO, a blend also with
a large difference between the Tgs of its components. They found a similar disparity
between the enthalpy recovery of the blends and the pure components. However, unlike
the previous investigators, they attributed the difference to concentration fluctuations in
the blend. Mijovic et al. monitored enthalpy recovery in a series of miscible blends of
PMMA and poly(styrene-co-acrylonitrile) (SAN) at different temperatures below their
Tgs. PMMA and SAN have very similar Tgs and at the higher aging temperatures those
blends rich in SAN showed faster rates of recovery. All blend compositions displayed
similar recovery rates at the lowest aging temperature. Mijovic and Ho were also able
to successfully (within the margins of experimental error) simulate the enthalpy
recoveries of their blends using the four-parameter Moynihan model,7 a model known to
describe the kinetics of the glass transition and aging of pure polymers quite well.
In another investigation, and the only one this author has seen involving a parallel
study, Robertson and Wilkes 9S examined isothermal physical aging in miscible blends of
PS/PPO. They reported only recovery rate data at one temperature; similar volume and
enthalpy recovery rates were found for blends of various PPO content.
The study described in the following pages investigates the physical aging
process, as followed by volume and enthalpy changes, in a miscible blend of PS and PPO.
This research effort will aid in obtaining a further understanding of the aging process in

153
miscible blends, a research area previously investigated in only a limited number of
studies. 144-,87-“34
5.2 Experimental
5.2.1 Preparation of Polystyrene / Polv(2,6-dimethvl-1.4-phenvlene oxide) Blend
Powdered PPO (Mw = 50,000 g mol '*, Mn = 20,000 g mol ’) from Polysciences
Inc. and the sample of atactic PS (Mw = 315,500 gmolMn = 140,000 gmol"’) used in
the previous study, were used in this study. The polymers were used without further
purification.
To prepare a blend of 90/10 % (by mass) PS/PPO, the two polymers were
dissolved in chloroform (boiling point 61 °C) to make a 5 % (w/v) solution. The polymer
mixture solution was continuously stirred for one day. The resulting clear solution was
cast into films on glass plates and dried in a hood at room temperature for 24 h. The
solvent cast films, which were homogeneous, were further dried in a vacuum oven at
room temperature for 24 h, followed by 72 h at 65 °C. The dried films were then molded
at 200 °C in a Carver Laboratory Hot Press into a thin flat sheet of thickness 0.5-0.8 mm.
Finally, the sheet of polymers was cut into thin strips and disks and stored in a sealed
dessicator prior to volume and enthalpy measurements.
Prior to performing dilatometry and calorimetry measurements, it was necessary
to determine if the blend was indeed thermally stable within the planned measurement
range for our aging experiments. The thermal stability was checked by
thermogravimetric analysis (TGA), and Figure 5-2 shows the TGA curve obtained under

154
an atmosphere of air. Phase separation of the blend, which eventually decomposes, does
not begin to occur until about 355 °C (indicated by arrow), consistent with the literature
value. This temperature is much higher than our measurement range, therefore, the
data to be presented in the following sections are not affected by phase separation or
thermal decomposition of the blend.
Figure 5-2 TGA curve of 90/10 PS/PPO blend showing the range over which the blend
thermally decomposes. The arrow indicates where phase separation begins (~ 355 °C).
The specimen was purged with air while varying the temperature rate at 30 °Cmin

155
5.2.2. Dilatometry
The same types of volume measurements performed on the PS sample were also
conducted on the PS/PPO blend. Details of the procedures were reported in Chapter 2
and section 4.2.2. The following conditions were used for the physical aging
experiments: three PS/PPO specimens of masses 0.57354-, 0.70910-, and 1.00520-g;
annealing temperature, Teq = 130.8 °C and aging temperatures, Ta’s = 115.8-, 112.8-,
109.8-, 107.8-, 106.8-, 104.8-, 102.8-, 100.8-, 95.8-, and 90.8-°C. The recovery
isotherms presented are averages of multiple runs of one specimen or runs of multiple
specimens. No volume measurements were performed on pure PPO for two reasons: (i)
its literature Tg was outside the measurement range of the automated dilatometer, (ii) the
polymer was found to be quite thermally unstable above 215 °C and could not be
annealed above its Tg for the length of time necessary to produce a reproducible
equilibrium state of the polymer.
5.2.3 Calorimetry
The procedures were the same as those reported for PS in sections 3.4.1, 3.4.2 and
4.2.3. The mass of the PS/PPO (90/10 %) blend was 13.90 mg. The conditions used for
the aging studies were: an annealing temperature, T0 = 150.0 °C, a low temperature, T|0W
= 50.0 °C and aging temperatures, Ta’s = 115.8-, 112.8-, 109.8-, 106.8-, and 100.8-°C. It
was possible to perform a few DSC scans on PPO, but aging measurements could not be
conducted for the same reason given above.

156
5.3 Results and Discussion
5.3.1 Glass Transition Temperatures of Specimens
Figure 5-3 shows the specific volume-temperature curve of PS/PPO blend
obtained from the dilatometer at a rate of 0.100 °C min Specific volumes were
calculated from a reference specific volume of 0.94894 cm 3 g'' determined at 130.000
± 0.005 °C. There is an approximate 4 % difference between our room temperature value
(obtained by extrapolation of the glass line) and the literature value 98,177 at the same
temperature.
The blend exhibits a single inflection at the glass transition, which is the primary
evidence for miscibility 153'157 of the system. The glass transition temperature was
determined by the intersection of the extrapolated liquid and glassy lines, and an average
value of 105.8 ± 2.0 °C was found from the three PS/PPO specimens. As expected, this
Tg value lies between the dilatometric Tgs of PS (97.1 °C) and PPO (literature value ~
205 °C 195). The thermal expansivity for PS/PPO, determined from three cooling curves
(not shown), was found to be 7.05 x 10 4 °C 1 and 2.66 x 10 4 °C in the liquid and
glassy regions, respectively, the difference between these two values at Tg, Aa, being 4.39
x 10 "4 °C '. These values compare very favorably with similar data reported for different
blend compositions by Zoller and Hoehn. 195 They lie between the values given for PPO
(0Cl = 7.91 x 10 °C _l, Og = 2.09 x 10 ~4 °C -1) and those previously calculated for our
PS sample (see Table 2-1). The PS data is also compared with PS/PPO blend data in
Figure 5-2. Smaller specific volumes and a higher Tg are observed for the blend. High

157
Tg’s normally indicate low free volumes. However, results of positron annihilation
lifetime (PAL) studies 196 on a PS/PPO blend of the same composition and similar
molecular weights of pure components as used in our blend, have shown an increase in
free volume when the two homopolymers, PS and PPO, are mixed. It will be discussed
later why we believe that this has also occurred in our 90/10 PS/PPO blend.
Temperature (°C)
Figure 5-3 Specific volume-temperature curve for the PS/PPO (90/10) blend and the PS
homopolymer obtained at a cooling rate of 0.100 °C min _l in the volume dilatometer.
Peaks at ~ 70 °C on each curve are experimental artifacts. (Linear fits were from 45 to 65
°C and 120 to 136 °C for PS/PPO; fits for PS have been previously indicated in the text).

158
10
Time (min)
11 12
13 14
15
1.8
1.7
1.6
1.5
- 1.3
1.2
Figure 5-4 The mass normalized output power and calculated specific heat capacity as
functions of temperature and time for PS/PPO (90/10) and PS. Curves obtained at a
heating rate of 10 °C min 1 following a rapid quench at 100 °C min (Triangles =
specific heat capacity; circles and squares = power; linear ranges for Tf determination
were 65 to 80 °C and 133 to 143 °C for PS/PPO and for PS, as previously indicated in the
text).
r)

159
The DSC curves for the PS/PPO blend and PS homopolymer are shown in Figure
5-4. Both data sets were obtained at a heating rate of 10.0 °C min '* after quenching from
the melt. The Tf’s for the blend and PS homopolymer are 115.1 ± 2.4°C and 102.6 ± 1.0
°C, respectively, and are consistent with literature values. I56,163,165'168'169,191 The single
(midpoint) Tg observed for the blend (see Figure 5-5) is an indication of the compatibility
Temperature (°C)
Figure 5-5 DSC trace of the 90/10 PS/PPO blend showing the single Tg, compared with
DSC traces of PPO and PS. Data was obtained at a heating rate of 10.0 °C min

160
of PS and PPO. The change in specific heat capacity at the midpoint Tg. Acp, for the
blend is 0.343 ± 0.028 J g'' K _1 and lies within the range 0.24 to 0.60 J g'' K *' for
many pure polymers. 197
As stated previously, the Tg is affected by the scan rate. The faster cooling rate
applied to the PS/PPO blend prior to physical aging, changes the dilatometric Tg (Tf, v) to
a value different than that above. One way of determining the Tf, v of the quenched blend
is to plot the change in specific volume to equilibrium, Av» (= Vi - v»»), against the aging
temperature. Similarly, the same can be done for the change in enthalpy to equilibrium,
AHoo. Both quantities are shown in Figure 5-5 as a function of aging temperature. A Tf, v
of 117.2 °C and Tf, h of 116.9 °C were obtained at Av» and AFL equal to zero,
respectively, in Figure 5-6.
An isochronal specific volume - temperature curve can be constructed for the
blend by measuring the specific volume at the thermal equilibration time (ti = 137 s) for a
number of different Ta’s. The Ta’s used were those previously given in the experimental
section, as well as 55.8-, 60.8-, 70.8-, and 80.8-°C. The v-T curve plotted for the blend is
shown in Figure 5-7. Included in this diagram are the cooling curve of PS/PPO at 0.100
°C min and the experimentally obtained equilibrium specific volumes at the higher
Ta’s. As expected, the higher quench rate increases the Tf of the blend (from 105.8 °C to
117.2 °C). Except for the two highest Ta’s ( 112.8- and 115.8-°C), it appears that the
blend equilibrium specific volumes do not follow the extrapolated liquidus line. It was
not practical, within the set of experiments performed, to run lower Ta’s to equilibrium.
Thus, it is difficult to determine whether the apparent deviation from the liquidus line is
real. Further experiments should be attempted to clarify this point.

161
The PS/PPO blend shows a broader glass transition region than PS. This is
observed in both Figures 5-3,-4 and -7, but is more clearly seen in Figure 5-4. The
broadening of the glass transition region due to mixing can be seen in other miscible
polymer blends. 198 - 200 This behavior suggests that the mixing of PS and PPO extends to
very small volumes. Using the widely accepted definitions of the onset and end of the
glass transition region, the breadth of the glass transition from the DSC thermograms was
15.4 °C for the 90/10 PS/PPO blend compared to 8.6 °C for PS.
Figure 5-6 Av» (circles) and AFL (squares) as a function of aging temperature for
PS/PPO blend.

162
Broadening of the Tg range of compatible polymer blends is well known and is
generally attributed to a distribution of molecular segmental environments generated by
local concentration fluctuations. 172,201'205 In the latter part of this section, this concept
will be employed to interpret discrepancies between volume and enthalpy recovery of the
blend and the pure component, PS, from physical aging experiments
Temperature (°C)
Figure 5-7 Isochronal (time = 137 s) specific volume (circles) and equilibrium specific
volume (triangles) versus temperature for the quenched PS/PPO, compared with data
(squares) on the same polymer from slow cooling (rate = 0.100 °C min _1) experiments
(observed peak at about 70 °C is an experimental artifact).

163
5.3.2 Isothermal Recovery at Various Aging Temperatures
Volume and enthalpy recovery are shown in Figures 5-8 and 5-9 for 90/10 % (by
mass) PS/PPO blend aged at temperatures ranging from 115.8 °C to 80.8 °C for times up
to several days. In order to directly compare volume and enthalpy recovery data at the
same aging temperatures, 5y and 8h were determined from equations 4-1 and 4-2.
Where 8y and 8h are equal to zero, the blend has reached structural equilibrium. At
Figure 5-8 Isothermal volume contraction of PS/PPO blend at various aging
temperatures after a quench from Teq =130.8 °C.

8V x 103 (cm3 g1)
164
Figure 5-8—continued.

8v,x103 (cm3 g‘1)
165
log (t -t,) (s)
Figure 5-8—continued

166
Figure 5-9 Isothermal enthalpy contraction of PS/PPO blend aged at the indicated
temperatures following a quench from Tc = 150.0 °C.
temperatures where equilibrium is not reached (e.g., at 95.8- and 90.8-°C in the volume
data), equilibrium volume was estimated by extrapolation of liquid state quantities using
0Cl. ps/ppo = 7.05 x 10 4 °C _1. The same features observed in the structural recovery data
for PS are generally observed in the PS/PPO recovery data. As the aging temperature
decreases, the time required to reach a state of volume equilibrium in the material
increases.

167
In contrast to chemical aging or degradation, physical aging is a thermo-reversible
process.8 This means that the original state of thermodynamic equilibrium can be
recovered by re-heating the aged material above its Tg thereby erasing the previous aging
history. Re-quenching to the same aging temperature should introduce the same aging
log (t -(s)
Figure 5-10 Volume recovery data for two specimens of 90/10 PS/PPO during isothermal
aging at Ta = 106.8 °C following a quench from 130.8 °C. Tests for thermo-reversibility
are represented by "+" symbols; solid circles and diamonds are first runs for the two
specimens.

168
effects as before. Figure 5-10 depicts the thermo-reversibility of the volume data for the
PS/PPO blend. Physical aging data were collected at 106.8 °C from two blend specimens
upon being quenched from the equilibrium liquid state. The first run of the first specimen
is displayed as solid circles in Figure 5-10. In the repeated run (the "+" symbols), the
blend specimen was re-heated to 130.8 °C, held there for one hour, and re-quenched to
106.8 °C. The data from both quenches are almost identical. This fact confirms that the
PS/PPO blend does not degrade chemically during the aging process and that the effect of
thermal history on the recovery is repeatable on the same specimen. The thermo¬
reversibility shown in Figure 5-10 clearly establishes the physical character of the aging
process. The second specimen was also quenched and aged (diamond-shaped open
symbols) once. This data illustrates the reproducible nature of the effects of thermal
history on specimens taken from the same blend sample.
5.3.3 Comparison of Times to Reach Equilibrium for Volume and Enthalpy
The temperature dependence of the times for structural recovery in the PS/PPO
blend to reach equilibrium is plotted in Figure 5-11. The time at which the change in the
property becomes zero is the time to reach equilibrium. Because recovery data levels off
asymptotically, it is often difficult to pinpoint exactly when equilibrium is reached.
However, we believe that the data points in Figure 5-11 are accurate to the experimental
errors reported. Within the margins of experimental error, the time to reach a state of
structural equilibrium for both properties, volume and enthalpy, appears to be identical.

169
Figure 5-11 Time necessary for the attainment of thermodynamic equilibrium, U, for
volume (open circles) and enthalpy (solid circles) recovery at different temperatures for
PS/PPO.

170
5.3.4 Effective Retardation Times of Volume and Enthalpy
An interesting way of examining the processes of volume and enthalpy recovery
in PS/PPO is to analyze the data in terms of the effective retardation time, xeff. 18,81-14'•142
A simple observation of Figures 5-8 and 5-9 shows that the position of the isotherms on
the logarithmic time scale shifts to longer times with increasing aging time and
decreasing aging temperature. This affects the retardation times of the recovery
isotherms, which become longer as the aging time and aging temperature continue to
increase and decrease, respectively. Longer ieff’s imply slower rates of recovery as the
system approaches equilibrium while shorter xeff’s imply faster rates of approach.
Rather than show the variation of volume effective retardation times (xeff, v) and
enthalpy retardation times (xeff, h) with aging time, it is perhaps more relevant to relate
these parameters to some instantaneous state of the glass. Values of xeff, p’s were
calculated from equation 4-7 and are plotted in Figure 5-12 as a function of the excess
volume (8v), which is the difference, v(t) - Voo. The rapidly increasing values of xeff’s,
characteristic of the self-retarding nature of the aging process, are evident as the 90/10 %
(by mass) PS/PPO blend approaches equilibrium. Although at any particular instant
during structural recovery, 5y and 8h, are generally not the same, Figure 5-12 allows the
comparison of xeff. v and xeff, h and also illustrates the relative rates of volume and enthalpy
aging at the same condition of a one time evolving thermodynamic variable, v(t).
The difference between the xeff, v and xeff, h values decreases with aging time at
each temperature. At 100.8 °C, the values are almost identical for the most of the aging
in the PS/PPO blend, implying that the rate of volume change is equal to the rate of

171
enthalpy change at the same values of v(t). (Plotting xeff, v and xeff, h alternatively against
5h will show the same coincidence of aging rates.) The feature observed at 100.8 °C,
however, is not seen at the other temperatures; xeff, v’s are longer than xeff, h’s. For
example, the data indicates that when 5y ~ 4.2 x 10 "4 cm3 g enthalpy recovery is ~ 2.0
and ~ 1.5 times faster than volume recovery at 109.8- and 106.8-°C, respectively.
Figure 5-12 Plots of In xeff for volume recovery (P = v, open symbols) and enthalpy
recovery (P = H, closed symbols) as a function of the excess specific volume of PS/PPO
at five aging temperatures.

172
5.3.5 Temperature Dependence of Effective Retardation Times
The volume data in Figure 5-12 and the enthalpy data in Figure 5-13 can be
described approximately by a single xeff. 143 “150 Equation 4-8 (and its rewritten form in
equation 4-9), which involves separate temperature and structure dependence, is used for
this purpose. This equation was first applied in the pioneering work of Petrie,26 and is
often referred to as the Petrie model.
Figure 5-13 Plots of In Teff, H as a function of the distance of the PS/PPO system from
enthalpy equilibrium for five aging temperatures.

173
Use of the Petrie model first requires the determination of the best-fit values of In
A'(Ta) and C at each aging temperature. Linear regression was applied to the plots of In
Xeff,v versus 8v and In xeff, h versus 8h, and the slopes and intercepts calculated provided
the values for C and In A'(Ta), respectively. Average values of C were determined from
the volume and enthalpy data at four aging temperatures. Values of In A'(Ta) for each Ta
were then plotted versus 1/Ta, and using linear regression the apparent activation energy,
Eapp, and In A were obtained from the slope and the interceptl43,144 of the plot,
respectively. Figures 5-14 shows the Arrhenius plots from which these two parameters
were determined.
The above method of analysis gave the following values for the blend parameters
from four aging temperatures: C = 1.80 g J ‘, Eapp = 417 ± 0.03 kJ moland In A =
-134 ± 20 for enthalpy recovery and C = 1663 g em "3, Eapp = 449 ± 9 kJ moland In A =
-124 ± 1 for volume recovery. The differences in the parameters Eapp and A support the
earlier conclusion that enthalpy recovers at a faster rate than volume.
The pre-exponential factor (A) from the enthalpy results can be compared with the
weighted average of the In A values for the PS homopolymer and a PPO homopolymer 188
of similar molecular weight as ours. The calculated average is In A = -381 which differs
greatly from that of the blend. Although only one aging parameter is compared (none of
the other parameters for PPO have been found in the literature), the result may suggest
that enthalpy aging parameters (or aging parameters in general) for the blend cannot be
obtained by taking an average of the two sets of homopolymer parameters.

174
Figure 5-14 Arrhenius plots of In A’(Ta) versus 1/Ta for (a) volume recovery and (b)
enthalpy recovery in 90/10 PS/PPO.

175
5.3.6 Enthalpy Change Per Unit Volume Change
Another interesting way of examining the blend data is to look at the behavior of
the ratio 8h / 5y with aging time. To this end, plots of this parameter versus aging time at
two selected aging temperatures are shown in Figure 5-15. For these aging temperatures,
Figure 5-15 The enthalpy change per unit volume change of the 90/10 PS/PPO blend as a
function of aging time at 100.8- and 106.8-°C.

176
the ratio is not constant; instead, it decreases with time. The decrease is due to the fact
that the excess enthalpy is decreasing toward zero at a faster rate than the excess volume.
At short times, the ratio 8h / Sv does not change rapidly and seem to be
approaching an asymptotic or constant value. Structural changes are most rapid during
these times and thus the two properties may be changing rapidly at the same rate.
However, the small increases in the 8h / 5v ratio as time becomes increasingly smaller
suggests that 8v is decreasing at the more rapid rate. Therefore, during the initial stages of
physical aging, volume recovers faster than enthalpy.
As volume changes are smaller than enthalpy changes under the same conditions,
volume data are always closer to equilibrium. However, at increasing times in Figure
5-15, volume recovery slows down while the enthalpy continues to recover at an
increased rate. This is evidenced by the sharp decrease in the ratio at longer times, which
suggests that the sensitivity of the enthalpy to the underlying structural changes is
increasing compared to that of volume at long times, resulting in an approach to
equilibrium that is steeper for enthalpy than for volume. This is illustrated more
succinctly in Figures 5-16 through 5-18 where excess volume and enthalpy curves are
plotted against log aging time. Error bars are included with the enthalpy data because the
measurement error in these data is much greater than in the volume data. It is obvious
that volume and enthalpy approach equilibrium in different ways. Thus, their sensitivities
to the underlying structural change differ. However, though volume initially recovers
faster than enthalpy, within limits of experimental error, both properties appear to reach
equilibrium at the same time in the 90/10 PS/PPO blend.

5v x 103 (cm3 g'1) 5vx103 (cm3g1)
177
log ta (s)
logta (s)
Figure 5-16 Comparison of volume (empty shapes) and enthalpy (filled shapes)
isotherms at 115.8- and 112.8-°C as a function of aging time in 90/10 PS/PPO blend.

8x103 (cm3 g'1) 8vx103 (cm3g1)
178
logt (s)
i°g ta (s)
Figure 5-17 Comparison of volume (empty shapes) and enthalpy (filled shapes)
isotherms at 109.8- and 106.8-°C as a function of aging time in 90/10 PS/PPO blend.

179
log ta (s)
Figure 5-18 Comparison of volume (empty shapes) and enthalpy (filled shapes)
isotherms at 100.8 °C as a function of aging time in 90/10 PS/PPO blend.
The curvature of both data sets in Figure 5-15 also indicates that there is no
simple one-to-one correspondence between volume and enthalpy recovery. Such a
relationship would only be possible if the approach to equilibrium for both properties
were identical. As illustrated in Figures 5-16-5-18, this is not the case; rather, the
different mechanisms operating at different stages during the recovery process leads to a
relationship between volume and enthalpy that is nonlinear.
The ratio of the differential change in enthalpy to the corresponding change in
volume, (dH/dV)T, can provide us with the energy for creating unit free volume in 90/10

180
PS/PPO. This parameter can be determined form the slope of a plot of 8h versus 5v.
Values of (3H/dV)T were previously quantified for the PS homopolymer used in
preparing the blend and these were found to be 1.02 - 1.44 x 10 J m ' which lies within
the range of 1 - 2 x 10 9 J m'3 reported by Oleinik on a PS sample.24
Table 5-1 contains the results of (dH /dV)T calculations at three temperatures for
the blend. Interestingly, for 5y > 2.2 x 10 4 cm 3 g the parameter (dH /dV)T for the
blend seems fairly constant and agrees with the measurements of Oleinik. However, over
the entire experimental time range of measurements, (dH /dV)T is not constant, since as
shown in Figure 5-15 5h/8v is not constant and therefore neither are (dSH/dSv)T nor
(dH/dV)T; rather, as 5y approaches zero, (dH/dV)T increases such that the enthalpy
and volume arrive at equilibrium in the same time. The larger values of (dH /dV)T for
the blend compared to PS are consistent with the fact that a larger amount energy would
be required to create unit free volume in the more rigid system of PS/PPO, than in the less
rigid structure of PS. As have been observed in all previous analyses, the 90/10 PS/PPO
blend behaves just as a pure polymer does with respect to structural recovery.
Table 5-1 Quantification of the energy per unit free volume for 90/10 PS/PPO.
Ta
(dSH/dSir)T
Range for 8v
(dH /dV)T
(°C)
(Jem'3)
(cm 3 g l)
(Jm'3)
109.8
1792
5v > 2.2 x 10 4
1.79 x 10 9
106.8
1653
5v > 2.2 x 10 4
1.65 x 10 9
100.8
1642
8v > 2.2 x 10 4
1.64 x 10 9

181
5.3.7 Comparison of Structural Recovery in PS/PPO and PS
It is a known fact that the molecular mobility of a material increases with the
elevation of temperature in the glassy state. When the temperature is near the glass
transition region, the molecular mobility becomes very rapid. A comparison at the same
aging temperature (T) may not therefore accurately represent any difference between the
blend and its constituent homopolymers since they have different Tgs. Instead, it is
usually more appropriate to make the comparison at equal temperature distances below a
given reference temperature, the Tg. The distance, represented by Tg - T, is based on the
presumption of an iso-free volume state at Tg. 48,206 In what is to follow, the Tf values
will be used for Tgs of both polymer systems and the comparable temperature interval
Tg - T (actually Tf,v - T) will serve as the reference point.
Volume recovery data for the PS/PPO blend collected at Ta = 112.8-, 109.8-, and
107.8-°C are shown in Figure 5-19 along with similar data for PS at Ta’s = 96.6, 93.6 and
91.6 °C. Each respective temperature lies at 4.4, 7.4 and 9.4 °C below the Tf, v’s of the
blend and the pure component and can be represented as Ta = Tg - 4.4 °C, Tg - 7.4 °C and
Tg - 9.4 °C, respectively. The volume recovery curves of the blend are very similar to
those of the PS homopolymer, an expected result since PS is the major component (90 %
by mass) in the blend. It is likely that t he PS regions in the blend are more dominant in
the overall recovery process than are the PPO regions. This implies that PS rich regions,
which are generated by concentration fluctuations, may play an important role in the
volume recovery experiments.

5v x 103 (cm3 g1)
182
Figure 5-19 Volume recovery curves of 90/10 PS/PPO (open symbols) and PS (filled
symbols) at (a) Ta = Tg - 7.4 °C (curves 1 & 2), (b) Ta = Tg - 4.4 °C (curves 3 & 4), and
(c) Ta = Tg - 9.4 °C (curves 5 & 6).

Figure 5-19—continued
00
U>

184
Effective retardation times (teff) were calculated for the six curves above and the
results are presented in Figure 5-20 as a function of the excess volume of the polymer.
The results indicate that the blend (with shorter xeff’s) recovers at a much faster rate than
the homopolymer. Consequently, the blend attains equilibrium (depicted in Figure 5-19)
5x10'3 (cm3 g'1)
Figure 5-20 Plots of In Teff versus excess volume of 90/10 PS/PPO (open symbols) and
PS (filled symbols) from volume recovery curves at (a) Ta = Tg - 7.4 °C (1 & 2), (b) Ta =
Tg - 4.4 °C (3 & 4), and (c) Ta = Tg - 9.4 °C (5 & 6).

185
Figure 5-20—continued
substantially before the homopolymer does. For example, at Ta = Tg - 7.4 °C, while it
takes 10 s for the PS/PPO blend to reach a state of volume equilibrium, it requires an
additional two decades of time for the PS homopolymer to achieve an equilibrium
structure.

186
A very striking difference between the aging data for both polymer systems is the
volume changes of the blend are much smaller than those for the homopolymer. The
smaller volume changes of the blend are always closer to equilibrium (the zero line) than
the larger volume changes for PS. It would seem likely, therefore, that at comparable
aging temperatures, the blend would achieve equilibrium before PS. The only way
volume recovery in PS could achieve equilibrium before or at the same time as that in the
blend would be for PS to have substantially greater rates of recovery than those of the
blend. As illustrated in Figure 5-20, this is not the case. A simple explanation for the
smaller values of Av(t) for the blend is the presence of concentration fluctuations which
lead to a range of Tg values, some of which are close to the aging temperatures. Further
discussion of this will given below.
As presented earlier (see Figure 5-4), the breadth of the glass transition in the
PS/PPO blend is 15.4 °C which is wider than that in PS (8.6 °C). This broader glass
transition, which is typical of blends with constituent polymers of sufficiently different
Tgs, has been interpreted as originating from the presence of concentration
fluctuations. Concentration fluctuations 172,201'205 give rise to a range of
microenvironments at which the local Tg varies depending on the blend composition. If
we assume that the 90/10 % PS/PPO blend contains domains richer in one component
than the other then the widening of the glass transition can be attributed to PS-rich
domains and PPO-rich domains. This is a valid assumption based on the fact that PS
contributes the major volume in the PS/PPO glass. Further, it is hypothesized that the
temperature scale of the PS/PPO glass transition is divided into two domains: the PS-rich
domains found in the temperature range from the onset Tg (Tg, ¡) to mid-point Tg and the

187
PPO-rich domains located between Tg and the end Tg (Tg, f). Both Tg, ¡ and Tgi f can be
treated as the apparent glass transition temperatures of the PS-rich and PPO-rich domains,
respectively. Additionally, density fluctuations will increase the breadth of the glass
transition for the component homopolymers and a Tg, ¡ and Tg, f can also be defined for
PS. With the blend having two domains, the additional hypothesis can be made that its
total volume recovery, v(t), is the sum of contributions v¡(t) from the PS-rich region and
Vf(t) from the PPO-rich region, i.e.,
v(t) = v,(t) + Vf(t) (5-1)
At any equal aging temperature distance Tg - T = Ta. the actual Ta of the 90/10
PS/PPO blend is located closer to Tg, ¡ for the blend than that for the pure components due
to the broader glass transition region. (This is obvious when we consider that Tg, ¡ is
111.7 °C and 100.6 °C for the blend and PS homopolymer, respectively, and at (say) the
temperature distance Tg - 7.4 °C, Ta is equal tol09.8 °C for the PS/PPO blend and 93.6
°C for the PS homopolymer). The free volume and molecular mobility of a polymeric
material is known to increase as the aging temperature approaches its glass transition.
Therefore, at a fixed Tg - T, the PS-rich domains of the blend have higher molecular
mobilities than the pure PS homopolymer chains since the distance between Ta and
Tg, j is shorter for the blend than that for the pure PS polymer. This shorter temperature
interval is also expected to lead to smaller volume changes for the PS/PPO glass because
it will actually be closer to the equilibrium (liquid) line than the PS glass. In contrast to
the PS-rich domains, the PPO-rich domains are expected to have lower mobilities

188
because their effective Tg is at a larger temperature distance from Ta. Consequently, the
volume recovery in PS/PPO will be determined by the more mobile domains, i.e., by v¡(t)
from equation 5-1. This is consistent with the data displayed in Figure 5-19 that show
shorter times to equilibrium and also smaller volume changes for PS/PPO than those for
pure PS at the same Tg - T. Thus, the contributions from the PS-rich domains dominate
the initial recovery process in the 90/10 PS/PPO blend.
Although there were no measurements made on the PPO homopolymer, there is
evidence in the literature, that at the same Tg - T, this polymer has a faster recovery rate
than PS. This higher mobility of pure PPO chains means that the polymer contains
greater free volume than PS, consistent with its bulkier phenylene ring requiring more
space for movement than the phenyl ring in PS. Therefore, we believe that the PPO
generates extra free volume when blended in the PS matrix, even though PPO has a much
higher Tg. In fact, there is supporting evidence by Zoller and Hoehn 195 that the free
volume in PS/PPO blends increases with increasing PPO content. The extra free volume
leads to greater chain mobility in the blend over that of pure PS. Additional support for
greater free volume in a 90/10 PS/PPO blend is also seen in PAL spectra recently
obtained by Chang et al. 196
We attempted shifting the blend cooling curve so that the intersection of its glassy
and liquid lines coincided with that of PS. The result is shown in Figure 5-21. The
observed differences are a consequence of the different specific thermal expansions of the
two polymer systems (0CsP. L and OsP, G for the 90/10 PS/PPO blend are 7.11 x 10 A - and
2.61 x 10 ^ -cm 3 g '* °C _1, respectively; a^, l and OsP, G for PS are 6.04 x 10 4 - and
2.31 x 10 ^ -cm 3 g 1 °C _1, respectively).

189
Figure 5-21 Cooling curves of PS/PPO and PS compared at Tf = 97.1 ± 1.5 °C. The
original PS/PPO curve was shifted by -7.3 °C and + 0.016350 cm 3 g 1 (peaks observed
around 70 °C on each curve are experimental artifacts).
Enthalpy aging data were not collected at the same aging temperature distances
for both polymer systems so no direct comparisons could be made. Nevertheless, the
features observed in volume and enthalpy recovery data for PS in the previous chapter are
the same as those observed in the recovery data for PS/PPO in this chapter. Therefore,

190
enthalpy data for the blend and pure PS at equal distances below Tg should show similar
behavior to the curves in Figure 5-19. Thus, it is likely that the same arguments made
above for volume recovery could also be made for enthalpy recovery in the blend and
homopolymer at comparable temperature distances.
To summarize, the behavior of the blend with respect to volume recovery (and
most probably enthalpy recovery) resembles that of a pure component except that the
presence of concentration fluctuations leads to a distribution of effective retardation times
which cover a range of apparent Tg values. The initial part of the volume recovery in the
blend is determined by the greater mobilities of the PS-rich regions, whose mobilities it
appears, are enhanced by extra free volume introduced into the blend by the PPO-rich
regions.
Unfortunately, there is no literature data that this researcher can find, with which
to compare the present recovery data for the 90/10 blend. Nevertheless, the arguments
above are consistent with both the presented data and information reported in the
literature for the blend components. Our effort appears to be the first to measure and
compare volume and enthalpy recovery in a blend in general, and in a 90/10 PS/PPO
blend in particular. The results reveal a somewhat surprising occurrence, in that the blend
which has a higher Tg, appears to possess more free volume than the lower Tg
component, PS. The presence of this greater free volume is strongly supported by the
literature data of others. 195'196 As stated at the beginning of this chapter, the analysis
performed was similar to that for PS. The results obtained were also the same in regards
to the behavior of blend volume and enthalpy in their approach to equilibrium.

CHAPTER 6
SUMMARY AND CONCLUSIONS
6.1 Introduction
Physical aging experiments often require a quench from the equilibrium state of a
material into its non-equilibrium glassy state, where its property changes are monitored
isothermally as it tries to reach a new equilibrium. In this dissertation, changes in volume
and enthalpy were assessed by monitoring changes in the thermodynamic states of a PS
homopolymer and a miscible PS/PPO blend due to the physical aging process. The
overall purpose of these measurements was to compare volume and enthalpy recovery
responses within the same polymer, and possibly between polymer systems. The thermo-
analytical techniques of dilatometry and calorimetry were used to probe the structural
changes as they occurred in the polymers held at different temperatures below their Tg’s.
6.2 Instrumentation
Changes in volume were measured by an automated mercury dilatometer; the
design and operation of which were reported in Chapter 2. Unlike more conventional
volume dilatometers, this dilatometer was automated by use of an LVDT. Any
instrument that measures volume changes in polymers due to physical aging must be able
to monitor very small changes. The LVDT was capable of detecting volume changes as
small as 5.03 x 10 6 cm 3 and specific volume changes accurate to ±1.35 x 10 4 cm 3 g
191

192
The automated set-up provided many advantages, including the ability to follow very
slow changes in mercury height over several days, and high precision (better than 1 %)
and good accuracy in measuring the small changes in volume. Probably, the most
significant advantage of the instrument is that volume and volume change measurements
are completely automated thus eliminating the constant observer attention that is
necessary for conventional dilatometers. The long time stability of the dilatometer
electronics was found to be more than 45 h at a high temperature—a very necessary
feature since aging experiments usually require a long time during which measurements
are constantly taken. The simple design and measurement characteristics of the
automated dilatometer make it an ideal instrument for carrying out measurements
isothermally, continuously, and without interruption of the aging process. Any
improvements in the technique would require improvement in the accuracy of
measurements. This can be most easily accomplished by use of better vacuum quality
(10 -5 - 10 7 torr) and larger specimen masses.
Calibration of the differential scanning calorimeter (DSC) is an important
precondition for making enthalpy change measurements. The DSC's temperature scale,
heat, and heat flow rate were calibrated with high purity standards according to
established guidelines. 129 This led to the calculations of the heat calibration factor found
to be 1.04 and the heat flow rate calibration factor, which is temperature dependent. A
DSC does not measure the true specimen temperature, therefore both calibration factors
were necessary to convert DSC measurements to actual heat and heat flow rates of the
specimen. It was found that the reliability and reproducibility of data could be improved
by keeping a number of parameters fixed. Enthalpy measurements are feasible by DSC

193
because the instrument can measure power output as a function of time. Integration of
the area under the curve followed by normalization by the specimen’s mass provides the
enthalpy of the specimen. Changes in enthalpy were calculated as the difference between
the heating curves of the aged and unaged specimen. It was demonstrated how
measurements of enthalpy changes could be used to monitor accurately the process of
physical aging. A procedure was used that took into account the thermal lag, the actual
cooling rate, and a possible hardware system bias. Considering all factors involved, the
maximum possible error calculated for enthalpy change measurements was ±6%. This
error is reasonable for the high aging temperatures used in this study. However, it was
suggested that the actual error is much smaller because of the procedure involved in the
enthalpy change determinations. The DSC is a sensitive instrument that offers the
advantage of using a thin, flat specimen of small mass (a few milligrams). Together with
the dilatometer, it allowed us to obtain aging data for two polymer systems.
6.3 Volume and Enthalpy Recovery Within PS and PS/PPO
Isothermal volume and enthalpy recovery experiments have been used to study the
physical aging behavior of PS and a miscible blend 90/10 % (by mass) PS/PPO. The data
were obtained in a wide range of aging temperatures, from 100.6 to 81.6 °C for PS and
from 115.8 to 90.8 °C for PS/PPO. The volume and enthalpy recovery curves show the
nonlinearity associated with structural recovery, and reduce with log aging time in a
similar, but not identical, way. Structural equilibrium was experimentally reached at Ta’s
from 115.8 to 100.8 °C for PS/PPO and Tas from 100.6 to 93.6 °C for PS. At Ta’s =
95.8- and 90.8-°C for the miscible blend and 81.6- and 91.6-°C for the homopolymer, the

194
experimental aging times were not long enough to achieve structural equilibrium. The
time scales for both volume and enthalpy to reach equilibrium in PS and in PS/PPO were
found to be the same within the margins of experimental error. The thermoreversible
nature of physical aging in PS/PPO and PS was verified (see Figure 2-9) through cyclic
volume recovery measurements. The difference between the volume and enthalpy fictive
temperatures reported for each polymer can be attributed to different cooling rates in the
specimens, as well as, in the case of the miscible blend, the presence of concentration
fluctuations.
The kinetics of structural recovery was analyzed in terms of effective retardation
time, Teff. It was observed that the rates of recovery (given by l/xeff) of both polymer
systems increase with the aging temperature and decrease as the polymers approach
equilibrium. In PS/PPO, the rates appear to become identical as the aging temperature
decreases. A similar behavior may occur in PS with decreasing temperature. However,
the results clearly show that enthalpy recovers faster than volume in these single down
quench experiments with PS and PS/PPO. A single parameter model involving a separate
contribution of the temperature and structure was applied. Aging parameters were
calculated and demonstrated some of the similarities and differences between volume and
enthalpy recovery.
The energy for creating unit free volume was calculated for each polymer. A
larger value was determined for the miscible blend consistent with the more rigid
structure of the blend. It was also shown that the approach to equilibrium for volume and
enthalpy recovery was different. Moreover, it appeared that volume initially recovered

195
faster but was then quickly overtaken by the faster recovering enthalpy so that both
reached equilibrium at the same time.
6.4 Aging in PS/PPO Versus Aging in PS
Volume recovery in PS/PPO and the constituent PS homopolymer have been
investigated with respect to Tg - T. Differences in the recovery process are explained by
invoking the presence of concentration fluctuations on the blend. Due to these
concentration fluctuations, a range of Tg values is present, or alternatively the glass
transition region is broader, and at any given temperature the recovery rate will vary from
place to place. The results show that aging in PS/PPO is faster than in the pure
component PS and that the total excess volume for the blend is much smaller than that for
PS. Furthermore, it is suggested that it is the more mobile lower Tg regions that are
responsible for the initial decay of the volume function in the blend. These regions are
PS-rich and are influenced by the local concentration fluctuations. The higher Tg PPO-
rich regions are also influenced by local concentration fluctuations and it is expected that
they will provide minor contributions to the total aging process. However, at the
temperatures used in this study, the volume recovery processes of the PPO-rich regions
should be much slower than those of the PS-rich regions. Finally, the results of this study
provide evidence that the recovery behavior in polymer blends can be influenced
considerably by the presence of concentration fluctuations.

APPENDIX A
CONSTANT TEMPERATURE AGING PROGRAM
This modified QuickBasic program plots the LVDT voltage versus the natural
logarithm of time in hours and was used to obtain aging data. The data is recorded at the
bottom of the plot in three columns: number of the run (NR), the LVDT signal and the
time in seconds.
******DeCLARATION of subroutines variables and functions*****
DEFINT A-Z
DIM ERSTAT%, tf%, Time!(1000), lvdt!(1000), ARRAY(IOOO)
COUNT% = 1000
MAXLVDT! =-100
MINLVDT! = 100
SCREEN 2
****************** mainprogram ***************
CLS
VIEW PRINT 10 TO 20
PRINT “ POLYMER AGING”
PRINT “ FOR CONSTANT TEMPERATURE!”
VIEW PRINT 14 TO 20
INPUT “
PRINT
INPUT “
INPUT “
INPUT “
DATA FILE NAME : ” ; FILENAMES
START STEP DURATION : ” ; STEPSIZE !
STEP NUMBER : ” ; STEPNUMBER
SECONDS UNTIL NOW : ” ; TIMEUNTILNOW!
196

197
INPUT “ TIME EXTENSION FACTOR : ” ; EXTENSION!
OPEN FILENAMES FOR APPEND AS #1
CLS
VIEW PRINT 2 TO 24
LOCATE 2, 65 : PRINT “PROGRAM:”
LOCATE 3, 65 : PRINT “ POLYMER AGING ”
LOCATE 5, 65 : PRINT “ FILE : ” ;
LOCATE 6, 65 : PRINT FILENAMES
LOCATE 8, 65 : PRINT “STOP”
VIEW (500, 1)- (638, 70), , 1
VIEW (50, 1)- (495, 120), , 1
VIEW (500, 76) - (638, 120), , 1
LOCATE 14 , 67 : PRINT “NEXT DATA : ”
LOCATE 11, 67 : PRINT “TIME (sec): ”
Start time! = TIMER
VIEW PRINT 19 TO 21
PRINT “NR. LVDT TIME (sec)”
VIEW PRINT 20 TO 25
PRINT: PRINT: PRINT: PRINT: PRINT
FOR K = 1 TO STEPNUMBER
»**He************ lvdt *********************
ReadLVDT:
LVDTHELP2! = 0
FOR o = 1 TO 4
OPEN “ COM2 : 9600 ,N, 8, 1, RS, CD, CS, DS ” FOR RANDOM AS # 4
AS = INPUTS (8, # 4)
CLOSE #4
IF LEN (AS) < > 8 THEN GO TO ReadLVDT
LVDTHelp! = VAL (LEFTS (AS, 7))
IF ABS (LVTDHelp!) > .12 THEN GOTO ReadLVDT
LVTDHELP2! = LVTDHELP2! + LVDTHelp!
NEXTo
lvdt!(K) = LVDTHELP2! / 4
ACTUALTIME! = TIMER
Time!(K) = ACTUALTIME! - Starttime! + TIMEUNTILNOW!

198
IF lvdt!(K) > MAXLVDT! THEN MAXLVDT! = lvdt!(K)
DF lvdt!(K) < MINLVDT! THEN MINLVDT! = lvdt!(K)
A$ = INKEY$
IF A$ = “S” OR A$ = “s” THEN GOSUB SAVEANDSTOP
VIEW PRINT 20 TO 25
PRINT: PRINT: PRINT: PRINT
PRINT USING “###”; K ;
PRINT USING “ #########.##### ” ; lvdt!(K); Time!(K)
PRINT
WRITE #1 , K, lvdt!(K), Time!(K)
VIEW PRINT
LOCATE 15, 67 : PRINT USING “ ##### . ; STEPSIZE! + Time!(K)
GOSUB PLOTDATA
IF TIMER > (86400-STEPSIZE!) THEN
DO
LOOP UNTIL TIMER = 0
TIMEUNTILNOW! = TIMEUNTILNOW! + 86400
DO
LOOP UNTIL (TIMER + 86400 - ACTUALTIME!) >= STEPSIZE!
GO TO MAINLOOP
END IF
DO
LOCATE 12, 67 : PRINT USING “##### . ; TIMER + TIMEUNTILNOW! -
Starttime
LOOP UNTIL (TIMER - ACTUALTIME!) >= STEPSIZE!
MAINLOOP :
STEPSIZE! = STEPSIZE! + K * EXTENSION!
NEXT K
SAVEANDSTOP:
CLOSE #1
END
PLOTDATA:

199
EF K <= 1 THEN RETURN
IF MINLVDT! = MAXLVDT! THEN RETURN
VIEW (50, 1) - (495, 120), 0, 1
VIEW PRINT
LOCATE 15, 1 : PRINT USING “ ## . #### ” ; MINLVDT!
LOCATE 1,1: PRINT USING “ ## . #### ” ; MAXLVDT!
LOCATE 17, 2 : PRINT USING “ #### . ; LOG(Time!(l) / 3600);
PRINT “ LOG (TIME) (HOURS) ” ;
PRINT USING “ #### . ; LOG (Time! (K) / 3600);
PRINT “
WINDOW (LOG (Time! (1)/3600), (MAXLVDT!)) - (LOG(Time! (K) / 3600),
(MINLVDT!))
PSET (LOG(Time!(l) / 3600), lvdt!(l))
FOR N = 2 TO K : LINE - (LOG(Time!(N) /3600), lvdt!(N)), 1 : NEXT N
RETURN

APPENDIX B
TEMPERATURE SCANNING PROGRAM
This modified QuickBasic program was used to obtain plots of specific volume
versus temperature at constant scan rates. The data is recorded in three columns as
temperature, LVDT voltage, and time in seconds.
DECLARE FUNCTION TIME! ( )
‘This program is able to read the LVDT of a LUCAS-SCHAEVITZ MP-1000
‘in dependence of the temperature.
‘The connected bath is a HART-SCIENCE Model 6035 Bath.
‘The Bath Heatrate is more or less controlled by the computer.
‘The screen will show the actual data by numbers and as a Plot.
‘The plot shows the derivative of the LVDT-signal by Temperature (8 LVDT/8T)
‘and the difference between the desired Heatrate and the actual heatrate.
‘The plot of Delta-LVDT can be re-scaled by pressing the r-key.
‘The program can be stopped by pressing the s-Key without loosing data.
‘If no filename is given, the program chooses Test.dat as filename.
‘The data-files are in the actual DOS-DIRECTORY
>************************£)ecjaratjon variables***********************
‘****************yarjabies for Bath-control********************
200

201
RBYTE = 1: COMMAND = 0
STATUS $ (0) = “OFF ” : STATUS $ (1) = “ON ”
RELY = &H30 ‘
BYTL = &H20 ‘
BYTH = &H10 ‘
CNTL = &H70 4
DSAB = &HF 4
LDLB = &H5 4
LDHB = &H6 4
LDAC = &H3 4
TMIN = 0
TMAX = 300 4
GAIN = 129.7697’
address of relay control bits
address of low 4 bits on DAC bus
address of high 4 bits on DAC bus
address of DAC control bits
DAC control word to disable all data latches
latches 8 bits on bus into DAC low byte register
latches 8 bits on bus into DAC high byte register
sets DAC with data in high and low byte registers
minimum temperature of bath
maximum temperature of bath
GAIN = (DAC1-DAC2) / (TEMP1-TEMP2)
‘ adjust GAIN for maximum accuracy of bath temperature
TO = 20.4496 4 TO is temperature of bath with DAC set to 0
‘adjust TO for maximum accuracy of bath temperature
OPEN “LTP1 : ” FOR RANDOM AS #1’ bath must be connected to LPT1 parallel port
ps for rest of the pro^Fciixi5^^^^^^^^^^^^
smooth = 0
DeltaTemp = .1
Numberpoints = 300
Deltamin = 10000: Deltamax = -10000: LowDeltaLVDT = 0: DeltaDeltaLVDT = .001
DIM TempDat(Numberpoints), LVDTDat(Numberpoints), RateDat(Numberpoints)
DIM TimeDat(Numberpoints), DeltaLVDT(Numberpoints),
SmoothLVDT(Numberpoints)
********************** ggj SCreen ********************
SCREEN 9
CLS
COLOR 9, 7
VIEW PRINT 1 TO 25
************ *******************jyjA]NPROGRAM** **********************
‘**********************Jjjpjjt Parameter*************************
LOCATE 10, 1: PRINT “ Temperature Dependence”
LOCATE 14, 1: INPUT “ Data filename : ” ; File$
INPUT “ Start temperature (0 for actual Temp.): ” , StartTemp
INPUT “ Heat rate (°C/min): ” , Heatrate

202
INPUT “ End Temperature (°C): ” , EndTemp
‘**********************0^^ filename and open fie********************
IF File$ = “ ” THEN File$ = ‘Test.dat”
Open File$ FOR APPEND AS #5
‘ ********* * *ehange Heatrate to °C/sec***********
Heatrate = Heatrate / 60
i^c**************** * Setup screen* * ****************
CLS
VIEW (1,35)-(47, 40), 0,0
VIEW (1, 260) - (470, 300), 0, 4
LOCATE 23, 2 : PRINT ‘Temperature dependence : ”
LOCATE 24, 2 : PRINT “File : ” ; File$; ” Heatrate : ” ; Heatrate * 60; “°C/min” ; ”
Endtemp. ; ” ; Endtemp; “°C”
LOCATE 20, 2 : PRINT “ Temp. : °C LVDT: 8 : ”
LOCATE 21,2: PRINT “ Actual Heatrate : °C/min Desired Temp : °C ”
VIEW (50, 1) - (600, 230), 8, 4
VIEW (480, 260) - (630, 340), 0, 4
LOCATE 20, 62 : PRINT “Program-Control: ”
LOCATE 22, 62 : PRINT “Rescale save”
LOCATE 23, 62 : PRINT “ smooth ”
LOCATE 24, 62 : PRINT “ Up Down + - ”
4******************Get starttemperature if AutoStartTemp was chosen***********
IF StartTemp = 0 THEN
GOSUB ReadTemp
GOSUB ReadTemp
Bathtemp = actualtemp
GOSUB setbath
GOTO Mainloop
END IF
‘******************^yajt for starttemperature if starttemp was chosen************
LOCATE 8, 25 : PRINT “Please wait until Start-Temperature is reached”
LOCATE 9, 25 : PRINT “After the Temperature is reached,the Program”
LOCATE 10, 25 : PRINT “will wait for 30 min!
Bathtemp = StartTemp : GOSUB setbath

203
DO
GOSUB ReadTemp : GOSUB ReadLVDT
LOCATE 20, 11 : PRINT USING “### . ## actualtemp
LOCATE 20, 34 : PRINT USING “ + #. ##### ” ; lvdt
LOCATE 21, 50 : PRINT USING “###.##”; StartTemp
LOOP UNTIL ABS(Bathtemp - actualtemp) < = DeltaTemp
Helptime = TIMER + 60 * 30
DO
LOOP WHILE TIMER < Helptime
jOOp^ 5jííjííJí5jí5jííjCí}ííjCí|Cí|CíÍC5lCíjC»ÍC5jC5|Cí|C*ÍC^Cíf»5fí»(í*JC
Mainloop :
COLOR 15, 7
VIEW (50, 1) - (600, 230), 8, 4
LOCATE 9, 25 : PRINT “The first value will be shown soon!”
4H5^h**1®^^^^^time for first
StartTemp = actualtemp
Starttime = TIMER
‘******************cbeck jf heatrate is in the right direction***********
IF SGN(Heatrate) < > SGN(EndTemp - StartTemp) THEN
VIEW PRINT 1 TO 25
CLS
LOCATE 10, 30 : PRINT “Heatrate or Endtemperature are WRONG!”
LOCATE 11, 30 : PRINT “Press Enter to Continue”
LOCATE 12, 30 : INPUT a
STOP
END IF
‘*****************£^1^1^ xime Stepsize and time of last Point***********
Deltatime = ABS(StartTemp - EndTemp) / ABS(Heatrate) / Numberpoints
i***********§et variable;, for the Graphic screen************
HighTemp = EndTemp : LowTemp = StartTemp
IF HighTemp < LowTemp THEN LowTemp = EndTemp : HighTemp = StartTemp
TempDis = (HighTemp - LowTemp) / 3

204
GOSUB ReadLVDT : LVDTDat(O) = lvdt: TimerDat(O) = Time : TempDat(O)
= StartTemp
PRINT #5, TempDat(n); “ , ”; LVDTDat(n); “ , ”; TimeDat(n)
Oldtime = Starttime
OldTemp = StartTemp
ActualTime = Time
‘*****************Reatj j-^g rest 0f points
FOR n = 1 TO Numberpoints
DO
‘**********§gt Bath read Temp and Time************
Bathtemp = StartTemp + Time * Heatrate
GOSUB setbath
GOSUB ReadTemp
ActualTime = Time
‘***********pr¿n£ BathTemp, desired Temp and rate************
LOCATE 20, 11 : PRINT USING “### . ; actualtemp
LOCATE 21, 19 : PRINT USING “## .###”; (actualtemp - Oldtemp) /
(actualTime - Oldtime) * 60
LOCATE 21, 25 : PRINT “ °C/min ”
LOCATE 21, 50 : PRINT USING “### . ; Bathtemp
‘**********reset timecounter and check Keyboard**********
Oldtime = ActualTime : OldTemp = actualtemp
IF INKEYS = “R” OR INKEYS = “r” OR n = 2 THEN GOSUB Rescale
IF INKEYS = “S” OR INKEYS = “S” THEN GOSUB SaveExit
IF INKEYS = THEN GOSUB DecreasePlot
IF INKEYS = “+” THEN GOSUB IncreasePlot
IF INKEYS = “d” OR INKEYS = “D” THEN GOSUB DownPlot
IF INKEYS = “U” OR INKEYS = “u” THEN GOSUB UpPlot
IF INKEYS = “M” OR INKEYS = “m” THEN GOSUB smooth
<************Check if it is time t0 read LVDT-data*********************
LOOP WHILE Time < = (n * Deltatime)
.***************Read LVDT print it ^ caiculate the Data for************
‘***************tije file and the screen**********************

205
GOSUB ReadLVDT
LOCATE 20, 34 : PRINT USING “+# . ##### lvdt
LVDTDat(n) = lvdt
TempDat(n) = actualtemp
TimeDat(n) = Time
RateDat(n) = (actualtemp - TempDat(n - 1 )) / (TimeDat (n) - TimeDat(n - 1))
* 60
<***********the jf statement is necessary in the case, that there***********
<***********js no change in the temperature between two points***********
IF actualtemp = TempDat(n - 1) THEN actualtemp = actualtemp + Heatrate *
(TimeDat(n) - TimeDat(n - 1))
DeltaLVDT(n) = (lvdt - LVDTDat(n - 1)) / (actualtemp - TempDat(n - 1))
LOCATE 20, 48 : PRINT USING “+# . ###### ” ; DeltaLVDT(n)
IF n >= 4 THEN : SmoothLVDT(n - 2 ) = (3 * DeltaLVDT(n - 2 ) + 2 *
(DeltaLVDT(n - 3) + DeltaLVDT (n - 1 )) + 1 * ( DeltaLVDT(n - 4 ) + DeltaLVDT(n)))
19
<******************^^6 Point on screen and on pile***********
GOSUB PlotPoint
PRINT #5, TempDat(n); “ , ” ; LVDTDat(n); “ , ” ; TimeDat(n)
NEXT n
CLOSE #5
VIEW (1, 260 ) - (630, 340 ), 0, 4
LOCATE 22, 15 : PRINT “The Measurement is finished. All data are saved.”
DO
LOOP WHILE 1
‘********************§et Bath-Temperature*****************
setbath :
‘***********Check if Bathtemp is in the allowed Range*************
IF Bathtemp < TMIN THEN Bathtemp = TMIN
IF Bathtemp > TMAX THEN Bathtemp = TMAX

206
DAC = INT ((Bathtemp - TO) * GAIN) ‘temperature is linearly proportional
‘to DAC setting
IF DAC < 0 THEN DAC = O’ 0 <= DAC <= 65535
IF DAC > 65535! THEN DAC = 65535!
‘ DAC is set four bits at a time
OUT3 = INT (DAC / &H1000): RES = DAC - OUT3 * &H1000
OUT2 = INT (RES / &H100): RES = RES - OUT2 * &H100
OUT1 = INT (RES / &10): RES = RES - OUT1 * &H10
OUTO = INT (RES)
PRINT #1, CHR$ (CNTL + DSAB);
PRINT #1, CHR$ (BYTL + OUTO);
PRINT #1, CHR$ (BYTH + OUT1);
PRINT #1, CHR$ (CNTL + DSAB);
PRINT #1, CHR$ (CNTL + LDLB);
PRINT #1, CHR$ (CNTL + DSAB);
PRINT #1, CHR$ (BYTL + OUT2);
PRINT #1, CHR$ (BYTH + OUT3);
PTINT #1, CHR$ (CNTL + DSAB);
PRINT #1, CHR$ (CNTL + LDHB);
PRINT #1, CHR$ (CNTL + DSAB);
PRINT #1, CHR$ (CNTL + LDAC);
PRINT #1, CHR$ (CNTL + DSAB);
RETURN
ReadTemp:
***************** tdnpd*2.turc ***************
OPEN “COMI: 9600, n, 8, 1, ASC, CD, CS, DS, RS” FOR INPUT AS #3
INPUT #3, actual temp
PRINT actualtemp
CLOSE #3
RETURN
ReadLVDT:
‘***************** Read LVDT* ****** ***************
lvdt = 0
FOR o = 1 TO 4
OPEN “COM2 : 9600,N,8,1,RS,CD,CS,DS” FOR RANDOM AS #4
a$ = INPUTS (8, #14)
CLOSE #4

207
IF LEN (a$) < > 8 THEN GOTO ReadLVDT
LVDTHelp = VAL (LEFTS (a$, 7))
IF ABS (LVDTHelp) > .12 THEN GOTO ReadLVDT
lvdt = lvdt + LVDTHelp
PRINT lvdt
NEXTo
lvdt = lvdt /4
RETURN
Rescale :
‘H=*********=Kj^Q^jjjg £q screen**********************
‘*****************ggt Data for the first value**************
IF n = 2 THEN DeltaLVDT(O) = DeltaLVDT(l): RateDat(O) = RateDat(l)
i***************^^^ maximum and minimum values************
IF Deltamin >= Deltamax THEN Deltamin = 0 : Deltamax = .0001
LowDeltaLVDT = Deltamin : DeltaDeltaLVDT = Deltamax - Deltamin
Drawscreen:
Chdrt frame and scales
VIEW (50, 1) - (600, 230), 8, 4
COLOR 10, 7
LOCATE 16, 1 : PRINT USING “+#. ### ” ; LowDeltaLVDT
LOCATE 1,1: PRINT USING “+# .###”; LowDeltaLVDT +
DeltaDeltaLVDT
LOCATE 7, 1: PRINT “6 LVDT ”
PRINT “• ”
PRINT “8T”
COLOR 9, 7
LOCATE 18, 7 : PRINT USING “### . ## LowTemp
LOCATE 18, 73 : PRINT USING “### . ## HighTemp
LOCATE 18, 25 : PRINT USING “### . ## LowTemp + TempDis
LOCATE 18, 35 : PRINT “Temp. (°C) ”
LOCATE 18, 50 : PRINT USING “### . ## ” ; LowTemp + 2 * TempDis
COLOR 12, 7
LOCATE 1, 77 : PRINT USING .1
LOCATE 17, 77 : PRINT USING .1
LOCATE 9, 77 : PRINT USING 0

208
LOCATE 4, 77 : PRINT “ 5 ”
LOCATE 5, 77 : PRINT “Heat”
LOCATE 6, 77 : PRINT “Rate”
COLOR 15, 7
WINDOW (LowTemp, - .1) - (HighTemp, .1)
LINE (LowTemp + TempDis, - .1) - (Lowtemp + TempDis, - .09), 4
LINE (LowTemp + 2 * TempDis, - .1) - (LowTemp + 2 * TempDis, -.09), 4
PSET (LowTemp, 0), 4
LINE (LowTemp, 0) - (HighTemp, 0), 3
‘****:)::t:*:i:******p)j.£yy Delta Heatrate*********************
PSET (TempDat (0), RateDat (0) - Heatrate), 12
FOR m = 0 TO n - 1 : LINE - (TempDat(m), RateDat(m) - 60 * Heatrate), 12 :
NEXT m
‘******************Draw j)eita LVDT*****************
WINDOW (LowTemp, LowDeltaLVDT) - (HighTemp, LowDeltaLVDT +
DeltaDeltaLVDT)
IF smooth = 0 OR n < 6 THEN
PSET (TempDat (0), DeltaLVDT (0)), 10
FOR m = 0 TO n - 1 : LINE - (TempDat(m), DeltaLVDT(m), 10 :
NEXT m
ELSE
PSET (TempDat (2), SmoothLVDT (2)), 10
FOR m = 3 TO n - 3 : LINE - (TempDat(m), SmoothLVDT(m)), 10 :
NEXT m
END IF
Keyboard
DO
LOOP WHILE INKEYS < > “ ”
RETURN
PlotPoint:
<*******************j)raw point on Screen*******************
<************Set Min and Max Delta LVDT*************

209
IF DeltaLVDT(n) < Deltamin THEN Deltamin = DeltaLVDT(n) - ABS(.l *
DeltaLVDT(n))
IF DeltaLVDT(n) > Deltamax THEN Deltamax = DeltaLVDT(n) + ABS (.1 *
DeltaLVDT (n))
i********************^ jjqj draw if there are only 2 points**********
IF n < 3 THEN RETURN
‘******************Draw Delta fieatRate******************
WINDOW (LowTemp, - .1) - (HighTemp, .1)
LINE (TempDat(n - 1), RateDat(n - 1) - 60 * Heatrate) - (TempDat(n),
RateDat(n) - 60 * Heatrate), 12
<******************j)raw Delta LVDT********************
WINDOW (LowTemp, LowDeltaLVDT) - (HighTemp, LowDeltaLVDT +
DeltaDeltaLVDT)
IF smooth = 0 OR n < 6 THEN
LINE (TempDat(n-l), DeltaLVDT(n-l)) - (TempDat(n), DeltaLVDT
(n)), 10
ELSE
LINE (TempDat(n-3), SmoothLVDT(n-3)) - (TempDat(n-2), Smooth
LVDT(n-2)), 10
END IF
RETURN
SaveExit:
Programm and Save
4**********************de^r Keyboard*****************
DO
LOOP WHILE INKEYS < > “ ”
‘******************£Qnfji-m Exit**********************
VIEW (50, 1) - (600, 230), 0, 4
LOCATE 10, 20 : INPUT “Do you really want to stop the experiment?
(Y/N): ”,
HelpS

210
IF Help$ = “Y” OR Help$ = “y” THEN
CLOSE #5
STOP
END IF
GOSUB Rescale
RETURN
IncreasePlot:
i***************!^,-^^ scaie 0f DeltaLVDT*************
<**********************Qear Keyboard ***************
DO
LOOP WHILE INKEYS < > “ ”
DeltaDeltaLVDT = DeltaDeltaLVDT * .8
GOSUB Drawscreen
RETURN
DecreasePlot:
‘***************j}ecreggg Scale of DeltaLvdt*************
* ********************* *ciear Keyboard**************5*1***
DO
LOOP WHILE INKEYS <> “ ”
DeltaDeltaLVDT = DeltaDeltaLVDT * 1.2
GOSUB Drawscreen
RETURN
DownPlot:
‘***************move scaje of DeltaLVDT ¿own*************
4*i;í!í5ií5ií5iíí!í5ií5!íífí5ií5ií5ií5ií*|ií5ií5i{5f*'ie5i:»ií5iíJCcybodrd^*5iíjic5ií5ií5ií5iííií:i;«iííií5iísiííií'i*íf*5ií
DO
LOOP WHILE INKEYS <> “ ”
LowDeltaLVDT = LowDeltaLVDT + DeltaDeltaLVDT * .2
GOSUB Drawscreen
RETURN
UpPlot:

211
‘***************jYjQyg scale of DeltaLVDT Up*************
‘******************=H=t:**uiear Keyboard********** *******
DO
LOOP WHILE INKEY$ <> “ ”
LowDeltaLVDT = LowDeltaLVDT - DeltaDeltaLVDT * .2
GOSUB Drawscreen
RETURN
smooth :
‘********Sm00th DeltaLVDT-data by using the theoretical Heatrate*******
smooth = (smooth = 0)
GOSUB Drawscreen
RETURN

APPENDIX C
CALCULATIONS OF REFERENCE SPECIFIC VOLUME AND TRAPPED GAS
VOLUME IN DILATOMETER
The calculations below are specific to one of the PS specimens. The approach,
however, is applicable to any polymer specimen measured by the automated dilatometer.
Dilatometer parameters
Diameter of dilatometer capillary
0.50190 cm
Calibration factor (h')
2.5504 x 10 “3 cm mV 1
Reference temperature (Tr)
115.000 ±0.005 °C
Room temperature (T2)
28.5 ± 1.0 °C
Density of mercury at Tr
13.3157 g em '3
Mass of dilatometer and PS before degassing
30.42027 g
Mass of PS before degassing
0.69426 g
Mass of dilatometer
29.72601 g
Mass of dilatometer and PS after degassing
30.41828 g
Corrected mass of PS (after degassing)
0.69227 g
Mass of dilatometer and PS plus mercury
75.8835 g
Mass of mercury
45.4652 g
Height of mercury above reference mark in
PS dilatometer
6.4545 mm
Height of mercury above reference mark in
mercury-only dilatometer
6.0015 mm
Mass of mercury placed in dilatometer after
removal of PS
54.4385 g
212

213
LYDT voltages measurements for PS in dilatometer
No. of Run
LVDTinitial (V)
LVDTfjnai (V)
Absolute LVDT
change(V)
1
-0.09764
0.053465
0.151105
2
-0.090645
0.059980
0.150625
3
-0.08523
0.06553
0.15076
3
-0.0866925
0.064205
0.1508975
5
-0.08912
0.0614775
0.1505975
6
-0.090205
0.0609
0.151105
7
-0.09004
0.0604475
0.1504875
8
-0.087645
0.0631520
0.150797
Average LVDT voltage change = 0.150797 V = 150.7968 mV
LVDT voltages measurements for mercury alone in dilatometer
No. of
Run
LVDT¡nit¡a| (V)
LVDTfina, (V)
Absolute LVDT
change(V)
1
-0.08768
0.065345
0.153025
2
-0.08843
0.065035
0.153465
3
-0.08792
0.066045
0.153965
3
-0.08748
0.0656975
0.1531775
5
-0.0875975
0.06601
0.1536075
Average LVDT voltage change = 0.153448 V = 153.448 mV
Part I
Calculation of Reference Specific Volume (vTr) at 115.000 ± 0.005 °C
Mercury-only dilatometer
Total distance from reference mark to top of mercury meniscus
= 0.64545 cm + (153.448 mV x 2.5504 x 10 “3 cmmV~')
= 1.03680378 cm

214
Volume of mercury in dilatometer at Tr = (54.4385 g +13.3157 g em ~3)
= 4.08829427 cm3
Volume of mercury in column above reference mark = n r 2 (height)
= 7t* [(0.50190 + 2)2 cm 2]*(1.03680378 cm)
= 0.20512606 cm3
Volume of mercury up to the reference mark
= (4.08829427-0.20512606)cm3 = 3.88316821 cm3
Specimen dilatometer
Total distance from reference mark to top of mercury meniscus
= 0.60015 cm + (150.797 mV x 2.5504 x 10 “3 cm mV _1)
= 0.98474267 cm
Volume of mercury in dilatometer at Tr = (45.4652 g + 13.3157 g em "3)
= 3.41440555 cm3
Volume of mercury in column above reference mark = nr 2 (height)
= ji* [(0.50190 + 2) 2 cm 2]*(0.98474267 cm)
= 0.19482605 cm3
•\ Volume of mercury up to the reference mark
= (3.41440555-0.19482605) cm 3 = 3.21957950 cm 3
=> Volume of PS specimen = (3.88316821 - 3.21957950) cm3 = 0.66358871 cm 3
=> Hence, the reference specific volume of PS = (0.66358871 cm 3 0.69221 g)
= 0.95857 cm 3 g-1

215
Therefore, the specific volume of PS at any temperature, (vs)t, during a volume change is
given by:
(vs)t = {(Avs)t + 0.95857} cm3 g 1
(The specific volumes from each of eight measurements on PS are 0.95880-, 0.95845-,
0.95854-, 0.95864-, 0.95843-, 0.95880-, 0.95835-, and 0.95857-cm 3 g_1, which give an
average value of 0.95857 ± 0.00017 cm3 g -1)
Part II
Quantification of Gas Void in Dilatometer
There are two methods from which the volume change in mercury can be
calculated. Both methods should provide the same value for the change in mercury
volume. Any difference in the values represents the volume of air trapped in the
dilatometer.
The first method involves the volume coefficient of thermal expansion of mercury as
follows:
(1) Change in mercury volume, AVHg = [aHg vHg mHg (Ti - T2)]
= (1.8145 x 10 ^ °C _1)*(0.073556 cm 3 g -1)*(54.4385 g)*[(l15 - 28.5) °C]
= 0.06284885 cm3

216
The second method utilizes the change in the LVDT voltage in heating the mercury from
room temperature to 115 °C:
(2) Change in mercury volume from LVDT voltages, AVHg
= total volume change - volume change of quartz
= [AVtot - AVq]
AVHg = [n r 2 h' (A lvdt)] - [otg (mQ/pQ)(Tr - T2)]
= K *[(0.50190 + 2) 2 cm2]*(2.5504 x 10 ~3 cm mV _,)*(153.448 mV)
- {(1.65 x 10 ^ °C _1)*(29.72601 g / 2.20 gem ~3)*[(115 - 28.5) °C]}
= 0.07549877 cm3
.*. The volume of gas trapped in the mercury-only dilatometer:
= (0.07549877 - 0.06284885) cm 3
- 0.01265 cm3
The actual volume of the PS specimen:
= 0.66359-0.01265 = 0.65094 cm3
meaning that the error contributed by trapped gas to the specific volume measurements is
= (0.01265 - 0.65094)* 100 %
« 1.9 %.

REFERENCES
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BIOGRAPHICAL SKETCH
Bernard Anthony Liburd was bom on the tropical island of St.Kitts, in the
Eastern Caribbean, on February 2, 1965. After graduating from the Basseterre Senior
High School in 1983 with three A levels in Maths, Physics and Chemistry, Bernard joined
the teaching profession. He taught at the secondary school level from 1983 to 1987 and
then left St. Kitts to attend the University of the Virgin Islands (UVI) in St. Thomas,
U.S.V.I. Because of his A level standing, Bernard received advanced credits and was
able to complete his studies at UVI in three years (December 1990). In May 1991, he
officially graduated summa cum laude with a B.S. degree in chemistry with physics.
Upon completion of his studies, Bernard returned to the teaching profession and
taught science and computer courses at All Saints Cathedral School in St. Thomas,
U.S.V.I., for two years. Although he enjoyed teaching, Bernard was not satisfied with
just a B.S. degree. He wanted to learn more about science and make a contribution by
performing his own research. In 1993, Bernard applied to and was accepted into the
chemistry graduate program at the University of Florida (UF). There he joined the
research group of Dr. Randolph S. Duran and undertook a project involving the thermal
analysis of polymer systems.
Currently, Bernard teaches chemistry full time to undergraduates at Guilford
College in Greensboro, North Carolina, where he also resides with his wife and two
children.
228

I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philose
Randolph SJ Duran, Chairman
Associate Professor of Chemistry
I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
¡1 Reynolds
«or of Chemistry
I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
fames D. Winefordner
fordne
\
iraduate Research Professor of
Chemistry
I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
L
Ll
\A
Vaneica Y. Young*-
Ü
Yi
I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
Dinesh O. Shah
Charles A. Stokes Professor of Chemical
Engineering

This dissertation was submitted to the Graduate Faculty of the Department of
Chemistry in the College of Liberal Arts and Sciences and to the Graduate School and
was accepted as partial fulfillment of the requirements for the degree of Doctor of
Philosophy.
December 1999
Dean, Graduate School

ID
1780
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097-
UNIVERSITY OF FLORIDA
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