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

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

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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.