Phase equilibrium in systems containing fluorocarbons

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Title:
Phase equilibrium in systems containing fluorocarbons
Physical Description:
ix, 186 l. : ill. ; 28 cm.
Language:
English
Creator:
Kyle, B. G ( Benjamin Gayle ), 1927-
Publisher:
s.n.
Place of Publication:
Gainesville
Publication Date:

Subjects

Subjects / Keywords:
Fluorocarbons   ( lcsh )
Hydrocarbons   ( lcsh )
Genre:
bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

Notes

Thesis:
Thesis - University of Florida.
Bibliography:
Bibliography: l. 183-185.
Statement of Responsibility:
by Benjamin G. Kyle.
General Note:
Manuscript copy.
General Note:
Vita.

Record Information

Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 000423957
notis - ACH2362
oclc - 11045679
System ID:
AA00003985:00001

Full Text









PHASE EQUILIBRIUM IN SYSTEMS

CONTAINING FLUOROCARBONS









By
BENJAMIN G. KYLE


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


UNIVERSITY OF FLORIDA
FEBRUARY, 1958
















ACXXOVL19DGNKII


The author wishes to thank Dr. T. N. Reed
for his advice and guidance throughout this investigation.

Appreciation is expressed to the supervisory comiLttee

members, Dr. Iack Tyner, Dr. W. S. Brey, Dr. E. X. mschlitz,

and Dr. R. B. Bennett for their aid and cooperation.














TABLE OF CONTENTS




LIST OF TABL . . iv

LIST OF ILLUSTRATIONS . vi

CHAPTER
I PURPOSE . . 1

II NOMENCLATURE . .. 2

III INTRODUCTION . 5

IV BINARY SYSTEMS FORMING TWO LIQUID PHASES 9

V TOTAL VAPOR PRESSURE OF BINARY MIXTURES 18

VI VOLUME CHANGES IN MIXING FLUOROCARBONS AND
HyROCABOS . 30
VII ESTIMATION OF THERMODYNAMIC PROPERTIES 45

VIII TERNARY LIQUID-LIQUID SOLUBILITY STUDIES 55

IX EXTRACTIVE DISTILLATION STUDIES 67

X EVALUATION OF METHODS OF SEPARATING FLUORO-
CARBON MIXTURES . 79

XI CONCLUSIONS . . 82
APPENDIX . . 85

TABLES . . 91

FIGURES . . 129

REFERENCES . . 183

BIOGRAPHICAL ITEMS . 186


iii













LIST OF TABLES


TABLE Page


I TEST OF THE CONSOLUTE TEMPERATURE CRITERION
II CHECK RUN IN TWO LIQUID PHASE STILL .
III ISOTHERMAL COMPRESSIBILITIES FOR USE IN
EQUATION 34 . .
IV O8LVENT SELECTIVITIES .
V COMPARISON OF DIFFERENCE .

VI CALCULATION OF d3 FROM EQUATION 64 .

VII PHYSICAL PROPERTIES OF HYDROCARBONS USED
IN THIS WORK . .

VIII PHYSICAL PROPERTIES OF FLUOROCARBONS USED
IN THIS WORK . .

IX THERMOCOUPLE AND THERMOMETER CALIBRATIONS

X PYCNOMETER CALIBRATIONS . .

XI VAPOR PRESSURES OF PURE FLUOROCARBONS .

XII SOLUBILITY DATA . 1

XIII COMPARISON OF CALCULATED AND OBSERVED
CONSOLUTE TEMPERATURES AND COMPOSITIONS 1


XIV TOTAL VAPOR PRESSURE-TEMPERATURE DATA
XV COMPARISON OF VAN LAAR ACTIVITIES WITH
ACTIVITY RANGE CALCULATED FROM
EQUATION 15a . .

XVI VOLUME OF MIXTURES OF PERFLUOROHEPTANE
AND CARBON TETRACHLORIDE; PERFLUORO-
CYCLIC OXIDE AND CARBON TETRACHLORIDE;
PERFLUOROCYCLIC OXIDE AND n-HEPTANE;
AND PERFLUOROHEPTANE AND nEPANE .
iv


1


1




1


16
19

41
59
63

75

91


92

93

95

96

.01

.07

.08


09




11










TABLE Page

XVII TOTAL VOLUME CHANGE AND PARTIAL MOLAL
VOLUME CHANGE ON MIXING . 114
XVI11 CALIBRATION DATA FOR ANALYSIS OF SYSTEMS:
C7716-C.1s60F-CC14; Cr716-'CgF16o-C7H 16s
AND C6Hs5C.-C6H11CH3-C7F15COOCCa 118

XIX TIE LINE DATA . 120
XX ACTIVITIES CALCULATED FROM EQUATION 59 122
XXI ACTIVITIES CALCULATED FROM EQUATION 61 123
XXII CHARACTERISTICS OF CHROMATOGRAPHY COLUMNS
USED IN EXTRACTIVE DISTILLATION STUDIES 124
XXIII APPEARANCE TIME OF C7F16, C8F160, -C7H16
AND C6HlCH3 IN THE VARIOUS PARTITIONING
LIQUIDS . 124

XXIV RELATIVE VOLATILITY OF THE C7F16-C8F160
SOLVET AND n-C7H16-C6H11CH3 SOLVENT
STSTSs .. . s25

XXV ACTIVITY COEFFICIENT RATIOS BASED ON
AVERAGE RELATIVE VOLATILITY FOR ALL
SOLVNTS................ 125
XXVI PROPERTIES OF PURE COMPOUNDS FOR USE IN
EQUATION 684 . 126
XXVII DATA FOR USE IN EQUATIONS 37, 40, AND 46 127
XXVIII DATA USED IN ESTABLISHING EMPIRICAL COR-
RELATION FOR EXCESS FREE ENERGY 128













LIST OF FIGURES


Figure Page
1. Vapor Pressure Data for Fluorocarbons 129

2. Solubility Cell .. .. 130

3. Binary Solubility Curves Systems Containing
CyF16 . . 131
4. Binary Solubility Curves Systems Containing
C8F160 . 132

5. Binary Solubility Curves Systems Containing
(C4F9)3N . . 133
6. Binary Solubility Curves Systems Containing
C7F15C000C3 . 134

7. Binary Solubility Curves Systems Containing
C7F5l H . 135

8. Activity Isotherms . 136

9. Two Liquid Phase Still . 137

10. Van Laar Constants Versus Temperature 138

11. Total Vapor Pressure Plot System: Per-
fluorocyclic OKide-n-Beptane 139

12. Total Vapor Pressure Plot System: Per-
fluorocyclic Oxide-Toluene 140

13. Total Vapor Pressure Plot System: Per-
fluorocyclic Oxide-Methylcyclohexane 141

14. Total Vapor Pressure Plot System: Per-
fluorocyclic Oxide-Carbon Tetrachloride 142

15. Total Vapor Pressure Plot System: Per-
fluoroheptane-Carbon Tetrachloride 143










Figure Page

16. Total Vapor Pressure Plot System: Per-
fluorobeptane-n-Heptane . 144
17. Activity Coefficients System: C5H12-C5F12
T = 262.40 K. . 145
18. Excess Free Energy of Mixing System:
CS3FI2C.12H .. 146
19. Excess Free Energy of Mixing System:
C4F10-C4HlO a & 147
20. Excess Free Znergy of Mixing System:
C7F16-._C8H18 at 300 C. . 148

21. Van Laar Activity Coefficients 149

22. Van Laar Activity Coefficients Temperature
Dependence . . 150
23. Pycnometer Filling Arrangement 151

24. Volume Change on Mixing System:
C8F160-CCI4 at 50 C. . .. 152

25. Volume Change on Mixing System:
C7Fl6-C7H16 at 50 C. . 153
26. Volume Change on Mixing System:
C7FI6-CC14 at 60 C. . 154
27. Volume Change on Mixing System:
C8F160-a-C71H6 at 50 C. . 155

28. Partial Molal Volume Change System:
CF 160-n e at 500 C. . i6

29. Partial Nolal Volumg Change System:
C8F160-CC14 at 50 C. . .. 157
30. Partial Molal Volume Change System:
C7Fl6-CC14 at 60 C. . 158

31. Partial Molal Volume Change System:
C7F16-n-C7H16 at 50 C. .. 159


vii











Figure Page

32. Partial Molal Volume Change . 160
33. Thermal Coefficient of Expansion System:
C7F16-CC14 . . 161

34. Thermal Coefficient of Expansion System:
C7F16-n-C716 . 161

35. Thermal Coefficient of Expansion System:
C8F160-CC14 . 162
36. Thermal Coefficient of Expansion System:
C8F160-n-C7H16 ... . 162
37. Volume of Mixing System: C7F16-CC14 163

38. Volume of Mixing System: C7F16-C7H16 164

39. Volume of Mixing System: C7F16.--CH 18 165
40. Calibration of System C8F160-C 716 166

41. Calibration for System CC14-C8F160 167

42. Calibration for System C8F160-n-CH16 168

43. Calibration for System C6H~E3-C6H5CH3 169

44. Calibration for System C6H 11C3-CF C150OCH3 170

45. Phase Diagram System C7F16-C8F160-CC14
at 30 C. . . 171
46. Phase Diagram System: C7F16-CsF160-n-C7H16
at 30 C. . . 172
47. Phase Diagram System: C6H5CH3-C6H11CH3-
C7F1]COOC% at 25 C. . 173
48. Phase Diagram System: C6H5C%-C6H11CH3-
C7Fl5COOCH3 at 10 C. . 1. 74


viii











Figure Page

49. Heat of Mixing System: C7F16-an-C7H16
at 500 C. . . 175

50. Heat of Mixing System: C7F16-CC14 at 600 C. 176

51. Heat of Mixing System: C F -i-C H
7 16 8 18
at 300 C. . . 177

52. Heat of Mixing System: CF 10-C H10 178

53. Heat of Mixing System: C5F12-C5H12 179

54. Excess Free Energy of Mixing system;,
C7F16-CC14 . . 180

55. Free Energy Correlation for Fluorocarbons
and Paraffin Hydrocarbons . 181
56. Excess Entropy of Mixing System:
C F 6--C8 H18 at 300 C. 182














CHAPTER I


PURPOSE

The purpose of this work is twofold:
1. The determination of the necessary phase equili-
brium data for the evaluation of various methods of separat-

ing fluorocarbon mixtures and hydrocarbon mixtures, partic-

ular emphasis being given to the methods of liquid extrac-

tion, extractive distillation, and aseotropic distillation.

2. The calculation of the thermodynamic properties

of some flurocarbon-hydrocarbon mixtures and the comparison

of these calculated properties with properties predicted from

various theories of solutions.














CHAPTER II


NOMENCLATURE

a Activity, standard state taken as pure substance
A Van Laar constant

B Van Laar constant
d Distance between centers of nearest-neighbor mole-

cules
H Partition coefficient, defined as the ratio of

solute per unit volume of solvent to solute per

unit volume of gas phase
I Ionization potential
N Number of theoretical plates
pi Inlet pressure in chromatography column

po Outlet pressure in chromatography column
P0 Vapor pressure of pure compound

R Gas constant
T Absolute temperature, oK.
V Nolal volume, cc
Vg Volume occupied by vapor phase in chromatography
column

Vr Retention volume, defined as the volume of carrier
gas passed through chromatography column when solute
peak appears











3
Vs Volume occupied by stationary solvent phase in
chromatography column
Vs Molar volume of stationary solvent phase, cc
v Weight fraction
x Mole traction

y Mole fraction of a component in vapor phase
z Correction factor
AA Change in Helmholtz Free Energy

As Change in Internal Energy

A F Change in Gibbs Free Energy
A H Change in Enthalpy

AS Change in Entropy
Xo Coefficient of thermal expansion
0( Relative volatility

Isothermal compressibility
3 Solvent selectivity
Y Activity coefficient, standard state taken as pure

substance
0C Solubility parameter, ( V/y)1/2 (calories/cc)1/2
TT Total vapor pressure

Volume fraction
6 Retention time, defined as time for appearance of
solute peak













Subscripts

1

2 Refer to components

3
C Refers to consolute properties
D Refers to distillate composition

9 Refers to mixture properties

0 Refers to ideal solution properties

P Refers to constant pressure process

V Refers to constant volume process

W Refers to composition of material in distillation

pot


Superscripts
* Refers to excess properties

M Refers to mixing process

V Refers to vaporization process
I Refers to hydrocarbon-rich phase














CHAPTER III


INTRODUCTION

Before any e equipment affecting physical separation

of two or more components can be designed, phase equilibrium

data must be available. Since the majority of the unit

operations involve the contacting of two phases under condi-

tions approaching equilibrium, the determination, correla-

tion, and prediction of phase equilibrium data play an im-

portant role in the field of chemical engineering.

A most desirable method of obtaining necessary phase
equilibrium data would involve the calculation of the pro-

perties of the mixture from those of the pure components;

however, to be used with confidence, any such method should

have some sound theoretical basis. At present there are

several approaches to the theory of solutions, most of which

have a statistical mechanical basis and require many assump-

tions and approximations and yield equations which are com-

plex and cumbersome.

A simple theory that has achieved considerable suc-

cess in the treatment of solutions of nonelectrolytes is one
developed independently by Scatchard and by Hildebrand (11).

By making four simple assumptions, Scatchard and Bildebrand










6
arrived at the following expression for the energy of mix-
ing in a binary system:*

X : (x *1 xV2) ( Q :2 2 2 (1)

The four assumptions were:

1. The energy of a system can be expressed by sum-
mation of the interaction energies of all possible pairs of
molecules. This interaction energy was assumed to depend
only on the distance between the two molecules.

2. The distribution of molecules is random with
respect to position and orientation.

3. There is no volume change on mixing at constant
pressure.

4. The interaction energy between 1-2 pairs of mole-
cules is the geometric mean of the interaction energy between
1-1 and 2-2 pairs. Strictly speaking this theory applies
only to systems containing nonpolar molecules between which
only dispersion forces are operating.

By further assuming that the entropy of mixing has
the same value as that of an ideal solution (a solution obey-
ing Raoult's law) it is possible to write for the free
energy of mixing


*A tabulation of the nomenclature used in this work
is given in Chapter II.












AP x (11 x2V2)( 2l ) { 1 2 + RT(xln x1 X2 inx2)

(2)
and for the activity coefficients

RT InY = VI(C1 i 2) 2 + ) 2

RT laY2 V2 ) 2 ) >i, 2 (3)
From its inception in 1932 until about 1950 the
success of the Scatchard-Hildebrand theory had been measured
by its prediction of the properties of hydrocarbon systems.
Since 1950 much work has appeared concerning fluorocarbon-
hydrocarbon systems which were not adequately accounted for
by the theory. These systems have such larger positive de-
viations from aoult's law than are predicted. For some
systems these positive deviations are large enough so that
at room temperature two liquid phases exist.
Because of their nonconformity to the existing
theory, fluorocarbon-hydrocarbon systems have stimulated the
interest of many investigators. The first comprehensive
study of fluorocarbon-hydrocarbon systems was made by Simons
and Dunlap (39) followed later by Simons and Mausteller (40);
these investigators determined the thermodynamic properties
of CSF2I-C5H12 and C4110-C4H10 systems respectively.
Simons and Dunlap found the Scatchard-Hildebrand
theory to be inadequate in predicting the thermodynamic











8
properties of their system, and improved the agreement by

rederiving equation 1 omitting the assumption of no volume

change on mixing. Later Reed (32) showed that for fluoro-

carbon-hydrocarbon mixtures the interaction energy between

unlike pairs of molecules is not the geometric mean of

like pairs as was also assumed in the derivation of equation

1. Reed also rederived equation 1 omitting the assumptions

of the geometric mean and no volume change. Be was alle to

calculate values of the heat of mixing which agreed very well

with the experimental data of Simons and Dunlap, and Simons

and Mausteller.

Since most fluorocarbon-hydrocarbon mixtures do not
conform to the present theory, their study should prove use*

ful toward further development and evolution of the theory

and the understanding of solution processes.












CHAPTER IV


BINARY SYSTEMS FORMING TWO LIQUID PHASES


The study of binary systems forming two liquid

phases was undertaken for two reasons:

1. To determine solubility relationships which

might be useful in selecting a solvent for separating

fluorocarbon-fluorocarbon mixtures and hydrocarbon-hydro-

carbon mixtures.

2. To obtain a measure of the positive deviations

from Raoult's law exhibited by binary mixtures of two par-

tially miscible liquids.

Experimental.--The properties of the pure compounds

used in this study are tabulated in the appendix under

Tables VII and VIII.

The unmixing temperature of a known binary mixture

was determined by heating the mixture until the two liquids

were completely miscible, then cooling the solution slowly

and observing the temperature at which the second liquid

phase appeared. The appearance of the second phase on cool-

ing is marked by cloudiness; this cloudiness is sometimes

masked by an opalescence which occurs about 2 or 3 degrees

above the consolute temperature. Due to this opalescence,

the determination of the unmixing temperature depends to some










10
extent on the judgment of the observer.

The solubility apparatus shown in Figure 2 consisted
of a heavy-walled glass test tube clamped between two staen-

less steel flanges by means of four brwas bolts. A Teflon

gasket placed between the open end of the tube and the top

flange was used to seal the tube. A thermaocouple, which

passed through the top flange, was used to measure the tem-

perature of the mixture. The whole tube assembly was ia-
mersed in an oil or water bath, which provided the necessary

temperature control.

The solubility data are tabulated in Table XII and
the solubility curves, which were obtained by plotting the

unmixing temperature-composition data, are shown on Figures
3-7. Published data are available for the two perfluorohep-

tane systems (17); these points are plotted on Figure 3

along with the present data. The agreement between the two

sets of data is satisfactory.

Due to the presence of air in the solubility tube,
the values of the unaixing temperatures so determined per-

tain to the mixture saturated with air and at a pressure in
excess of the equilibrium vapor pressure of the mixture. The

difference between these values and those of the mixture under

its own equilibrium vapor pressure is generally assumed to be
negligible, but in order to justify this assumption the un-












sixing temperature was determined for a degassed ixture
of toluee and perfluorocyclic oxide* in a sealed glass
tube under its own equilibrium vapor pressure. This value
of the unmixing temperature is plotted on Figure 4 along with
those obtained in the presence of air and it can be seen that
there is no significant difference.

Theoretical Calculation of Consolute Temperature and
Composition.--The thermodynamic conditions necessary to de-
fine the consolute temperature are

da1 ag
"Ia 0 da io
W or \(4)
dls 421a i 1
-- 0 00"


This requirement can be seen from examination of Figure 8,
where three isothermal curves of activity are plotted versus
composition. For illustrative purposes the activity is cal.
culated from the following equation
n a1 = In X BK2 (5)

At T1, a temperature below Tc (conaslute temperature), there
exist two liquid phases having the same activity. These

*A description of this material is given in the
appendix.










12
phases correspond to points A and B. The dashed portion
of the curve has no physical significance and corresponds
to the Van der Waals isotherm in the two phase region on a
pressure-volume diagram of a pure substance. As the tem-
perature is increased, the length of the line AD decreases
until the consolute temperature Tc is reached and a point
of inflection, C, is observed in the activity curve. At
this point the first and second derivatives of the activity
are equal to zero. At a temperature T2, above Tc, the
deviations from Raoult's law become smaller and the activity
is a single valued function of composition.
The value of the activity as predicted by the Scatch.
ard Hildebrand theory is

In a1 = In x1 4 (C1 d 2 422 (6)

Using equation 6 for the activity and applying the condi-
tions of equation 4, the following expressions result for
the consolute temperature and composition.

RTc xSaa2V22 (fl )2 (7)
R TC ....(.. + ...

XI a (Vi 2 2 2 '2 V ), 1/2. V
V2 m 1

By using the entropy of nixing for molecules of different


I










13
sisMe as calculated from a lattice model along with the
energy of aixing as given by equation 1, Hildebrand (18)
derived expressions for the consolute temperature and com-
position somewhat different from equations 7 and 8

OTN 2jlV2 2>2/ -/2 1 V/22 (9)

2 1/2/2 1/2 V1/2
9i : 2V1Y2(dj 4) / (VS -- ) (9)
1/2



The consolute temperatures and compositions have
been calculated from equations 7 aud 8, and 9 and 10 for the
Systems rcreted in this work and are tabulated in Table XIII.
The values of the consolute composition in Table XIII are
given only to two figures because of the uncertainty in locat-
iag the composition corresponding to the maxima temperature.
From Table XIII it is obvious that equations 8 and 10 predict
the consolute composition quite well while equations 7 and 9
provide poor estimates of the consolute temperature. Only
for the system perfluorocyclic oxide-toluene was the consolute
temperature correctly predicted by equation 7.

The fact that equations 8 and 10 predict the consolute
composition would indicate that the volume fraction is a use-
ful variable in correlating solution behavior. This is borne
out by the successful correlation of experimental activity












coefficients by the Van LUar equation, which 18 similar in
form to equation 3, but contains two adjustable parameters
instead of constants which are fixed by the physical proper-
ties of the pure components.
The failure of equations 7 and 9 to predict the
consolute temperature is probably due partly to the failure
of fluoroearbon-hydrocarbon mixtures to eofomer to the
geometric easn aseeaption which is implicit in these equa.
tions. Equation 9 predicts lower temperatures than equau-
tion 7 because the exeoss entropy of nixing due to different
volumes is always positive and therefore the deviatonas
from aoult's law due to this correction are always negative.
Sioe f luorocarbonahydrocarbon mixtures show auch larger
positive deviations than predicted, the entropy correction
Iapairs the agreement between the observed and predicted
temperatures. It can not be stated, however, that the use of
the entropy term for unequal volumes is incorrect since the
small effect it contributes is ovoershadoed by the larger
effect probably duo to the geometric mesa assumption.
It should be mentioned that, although often used in
the literature, couparlson of the calculated and observed
conaolate temperature is not a good criterion for testing
the applicability of the Scatchard-Hldebrand theory. It










15
equations 7 and 8 predict the correct temperature and com-
position, this means that the first and second derivatives
of the true activity coefficient with respect to composition
are equal to the corresponding derivatives of the activity
coefficient as given by equation 3. This is a necessary,
but not a sufficient condition which must be fulfilled by
equation 3, for it is conceivable that two different func-
tions could have equal first and second derivatives at a

given composition. This reasoning can be substantiated by
comparing activity coefficients calculated by equation 3
with experimental values for some systems which conform to
the consolute temperature criterion. This is done below.

In a two liquid phase system the activity of a comm
ponent is equal in both phases and we can write

xi 1 a Y a(1)

In many fluorocarbon-hydrocarbon systems which form two
liquid phases the mole fraction of hydrocarbon in the hydro.
carbon-rich phase approaches unity at low temperatures and
the activity coefficient also approaches unity. Thus by set-
ting Y1' equal to unity, the activity coefficient of the

hydrocarbon in the fluorocarbon-rich phase ( TY) is equal to

the ratio xl'/xl. Values of In Y 1 so calculated are com-
pared in Table I with values predicted by equation 3 for










16
three systems in which the observed and calculated conso-

lute temperatures are in good agreement.


TABLE I
TEST OF THE CONSOLUTE TEMPERATURE CRITERION



Tc0 InY
SYSTEM obe. eq.7 C) x x'1 eq. eq. 2J2.
(C) 11 3

I 323.5 325 26.3 0.306 0.960 1.14 0.913 19
II 358.5 360 61.1 0.320 0.956 1.09 0.900 19
III 386 377 69.0 0.256 0.981 1.34 0.977 this
work

I. perfluoromethylcyclohexane and chloroform

II. perfluoromethylcyclohexane and benzene
III. perfluorocyclicoxide and toluene


One would expect the same percentage difference be-
tween the logarithm of the activity coefficients as between
the two temperatures in Table I since both Tc and In V are

directly proportional to the (1 6 )2 term. Inspection of
Table I reveals that the percentage difference between the
logarithms of the activity coefficients is much greater than
between the consolute temperatures. Since the values of InYl










17
and To in Table I are compared at different toperaturea.,
the possibility arises that the activity coefficients pre-
dicted by equation 3 are equal to the true activity coof-
ficients at the consolute temperature only, and not at other

temperatures. From consideration of the consolute tempera-

ture alone one would erroneously aassme that the three systems
in Table I closely conformed to the theory.












CHAPTER V
TOTAL VAPOR PRESSURE OF BINARY MIXTURES

ExperWiental.--Total vapor pressure versus temperam
ture data were obtained for six binary fluorocarbon-.hydro-
carbon fixtures. The physical properties of these compounds
are listed in Tables VII and VIII.
The measurements were made in the two liquid phase
region since liquid compositions could be determined from
the temperature and the experimentally established soli.-
bility curve.
A dynamic boiling still was used for these measure*
eants, the design details of which should be obvious from
examination of Figure 9. The still was designed so that
vigorous boiling and low liquid level would prevent super-
heating while the insulating vapor space would prevent any
heat lose by the vapor in the inside tube. Daurinag operation
of the still undor equilibrium conditions no condensation was
observed inside the ianer tube. A calibrated thermocouple
was used to measure the vapor temperature; the calibration
data for this thermocouple is reported in Table IX. The still
was connected to a vacuum system contain a mercury mnaome-
ter which could be read to the nearest tenth of a millimeter













by use of a cathetometer.

As a check on the performance of the still the total
pressure of the system 2 butanone-water was determined at

two temperatures. These values compare favorably with the
reported literature values (29) as shown in Table II.

TABLU II

CHUCK RUN IN TWO LIQUID PHASE STILL

System: 2 butanone-wvater reference 29


Literature This Work

Pressure Temperature Pressure Temperature
M oC m OC

760 73.3 768 73.6

500 62.0 503 62.0

The experimental total vapor pressure versus temperature

data are reported in Table XIV.

Calculation of Activity Coefficients from Liquid.
Liquid Solubility Data.-The following method for calculat-
ing activity coefficients has been described by Carlson and

Colburn (6). In a two liquid phase system the activity of a
component is equal in both liquid phases and we can write

xI 1 x' 1' (11)
z21 : z2' 2'










20
The mole fractions are known from the solubility data and
we have two equations containing four unknown quantities.
The number of unknowns can be reduced to two if it is an-
sumed that a twomcoustant equation can be found vhich correct-

ly expresses the activity coefficients as a function of
composition. One such equation which has proved useful in
correlating experimental activity coefficients is the Van
Lear equation.

Y "2 113)



la Y 8 (14)



Ift equations 13 and 14 are substituted into equations 11 and
12 written in logarithamic form, values of the constants A
and B can be found. This procedure can be repeated at several
temperatures so that the temperature dependence of A and B
can be determined. The Van Lear A and B have been calculated
for several of the fluorocarbon-hydrocarbon systems for which

the solubility curves were determined and it was found that
the constants were always linear functions of temperature.
Figure 10 shows several of these linear plots.
In order to have confidence in values of the activity











21
coefficient as calculated from equations 13 and 14, some
method should be available for determining whether the Van
Laar equation accurately predicts the activity coefficients.
One method of accomplishing this is to compare experimentally
determined total vapor pressures with thost calculated from
equation 15 using the vapor pressures of the pure compounds,
solubility data, and the Van Laar equation to determine the
activity coefficients.

TT : x1 TIPl + x2 2po (15)
A graphical comparison of calculated and experimental total
vapor pressures is given in Figures 11-16, where it is re-
vealed that the agreement is quite good at lower tempera-
tures, but becomes poorer as the temperature increases. The
fact that calculated and experimental values of the total
vapor pressure agree should not be taken as conclusive proof
that the activity coefficients predicted by equations 13 and
14 are correct, however, since there is an infinite number of
combinations of Y1 and T2 which will satisfy equation 15.

By rearranging equation 15 we see that the activity
of component two is a linear function of the activity of
component one.

a2 T/P2o alPlo/p20 (15a)










22
By using equation 15a we can establish limits for the ac-

tivity of the fluorocarbon (component 2) from the limits of

the hydrocarbon activity. The upper limit for the ac-

tivity of the hydrocarbon will be set at unity and since

these mixtures all exhibit positive deviations from Raoult's

law, the lower limit will be set at the mole fraction of

hydrocarbon in the hydrocarbon-rich phase. Table XV shows

the activity limits of the fluorocarbon as determined from

equation 15a along with the values calculated from the Van

Laar equation for all six systems for which the total vapor

pressure was determined. Table XV reveals that for most

systems the calculated activities fall within the range cal-

culated by equation 15a at the low temperatures, but deviate

at higher temperatures following a pattern similar to the

observed and calculated total vapor pressures.

The Van Laar activity coefficients determined from

the solubility data of Simons and Dunlap (39) are plotted

on Figure 17 along with their activity coefficients determined

from partial pressure data for the system perfluoropentane-

n-pentane. The value of the total vapor pressure in the two

liquid phase region for this system at 262.4K., calculated

from the Van Laar equation, is 214 ma. as compared to the

reported value of 216 am., and the Van Laar activity of

0.766 falls within the 0.718 to 0.855 range calculated from

equation 15a. It can be seen from Fig. 17 that the Van Laar










23
equation with constants determined from solubility data

predicts values of the activity coefficients which agree

very well with the experimental ones. The Van Laar equa-

tion with constants determined from solubility data has

successfully predicted excess free energies of mixing in

other fluorocarbon-hydrocarbon systems for which the ther-

modynamic properties have been determined. Figures 18-20

show that the calculated and experimental excess free

energies of mixing for the systems n-perfluoropentane and

n-pentane (39), n-perfluorobutane and n-butane (40) and

perfluoroheptane and iso-octane (26) are in good agreement.

These experimental values of the excess free energy of

mixing were determined from partial pressure data.

The solubility data for the system perfluorohep-

tane and isooctane were taken from reference (17); calcu-

lated values of A Fe for this system were made from the

solubility data and the Van Laar equation at 170 a while

the reported data are at 30 C. The excess free energy

data of Simons and Dunlap and Simons and Mausteller are

the averages of several temperatures in the ranges 262 to

293 K. and 233 to 260 K., respectively, while those cal-

culated from solubility data are at 262.4 and 220 K. re-

spectively. The small difference in temperature between

calculated and observed free energies is negligible since










24
the temperature derivative of the excess free energy of

mixing is the excess entropy of mixing at constant pressure.

Values of excess entropy of mixing are tabulated below for

several systems.



System at x 2 0.5, cal./mole OK Reference

C4'1O C410 1.00 40

CS12 CSH12 0.43 39

C716 i-CS.18 0.24 26

This entropy term does not usually exceed one entropy unit

and a change of ten degrees would result in less than a

10 calories per mole change in the free energy term.
The partial molal heat of mixing can also be cal

culated from the Van Laar equation and the temperature deriva-

tives of its constants

ANL -L A (16)
T -T Ax1l 12
Lk.B2










25
Beats of mixing calculated from the Van Laar equation are

approximately twice as large as those determined experi-
mentally in the three fluorocarbon-hydrocarbon systems

cited above. Wood (48) has calculated the thermodynamic
properties for the system cyclohexane-methanol from solu-

bility data alone, but using a two-constant Scatchard equa-

tion instead of the Van Lear equation to represent activity

coefficients. He found that his calculated excess free

energies of mixing were in line with those reported for the
methanol-benzene and methanol-carbon tetrachloride systems,

but his calculated heat of mixing values were about twice as

large as those for the two reported methanol systems.

Besides the Van Laar equation, two-constant Margules

and Scatchard equations were used in this work for substi-

tution into equations 11 and 12, but these equations pre-

dicted total vapor pressures that did not agree with the ob.

served vapor pressures as well as did those predicted from

the Van Laar equation. These two types of equation also

predicted heats of mixing which were in poorer agreement with

the experimental values than those predicted by the Van Lear
equation.

Since the temperature derivative of the free energy

is needed for calculation of the heat of mixing, mall errors

in the free energy will produce larger errors in the heat of












mixing. The disagreement between experimental heats of
mixing and those calculated from the Van Laar equation could
be attributed to small errors in the free energy as predicted
by the Van Laar equation. However, these errors are not of
a random nature since the calculated value is always about
two times as large as the experimental values.
In order to determine why the Van Laar equation fails
we should consider in detail the process by which the Van
Laar constants are determined. Figure 21 illustrates
graphically the conditions required to obtain the Van Laar
constants. Equations 11 and 12 can be rearranged to

In YI In Tl' : In x1'/x1 (lla)

In Y2 In Y2' lan x2'/x2 (12a)

The differences In1 In YT' and In 2 In Y2' are rep-
resented on Figure 21 by ab and cd respectively. Using equa-
tions 11, 12, 13, and 14 is equivalent to finding the con-
stants A and B such that at x1 and xl* the differences
In Y 1 In Y I' and In 2 In 2' given by the Van Laar

equation are equal to the corresponding differences between
the true activity coefficients. This does not mean that the
actual values of the Van Laar activity coefficients are cor-
rect or that the Van Laar curve is identical with the true











27
activity coefficient versus composition curve.

At lower temperatures the composition of the con-
jugate phases approaches that of the pure compounds and the

true activity coefficient and Van Laar activity coefficient

both approach unity. This means that at lower temperatures

the activity coefficients Y1' and Y2 corresponding to

points a and c on Figure 21 can be predicted by the Van Lar

equation. Since the Van Lear activity coefficients and true

activity coefficients approach each other at a and c, and

since ab and cd as given by the Van Laar equation are equal

to ab and cd corresponding to the true values of In Y^
In Y 1' and In Y 2 In Y2', the Van Lar and true ac-

tivity coefficients also approach each other at b and d.

This is manifested by the very good agreement between ob-
served and calculated total vapor pressures at lover tempera-

tures. As the temperature increases the concentration of

the major component in each phase decreases causing the ac.

tivity coefficients to differ from unity and it is possible

that differences occur between the Van Laar and true ac-
tivity coefficients at a and c. This would result in dif-
ferences at b and d and would cause the values of the observed

and calculated total vapor pressures to diverge,

One reason why the Van Laar equation does not correct-
ly predict heats of mixing can be seen from examination of










28
Figure S22. Curves 1 and 2 on Figure 22 represent the Van

Lear equation at two temperatures, curve 1 being at the
lower temperature. Curves 3 and 4 represent the true ac-

tivity coefficient curves, where curves 3 and 1, and 2 and 4

are at the same temperatures. Only the curves for one

component are shown for the sake of simplicity. The shape

of the two types of curves is greatly exaggerated for

illustrative purposes. At the temperature T1, the Van Lear
equation (1) predicts correct values of the activity coef-

ficient at a and b even though its form is different from

the true activity coefficient curve (3) at that temperature.

Increasing the temperature to T2 causes only a slight change

in the true activity coefficient curve (4), but due to the

difference in form the Van Lear curve (2) must change by a

greater amount in order that it may predict the activity

coefficients at c and d. Since the heat of mixing is de-

termined from the temperature derivative of the logarithm of

the activity coefficient at constant composition, it can be

seen that larger heats of mixing would be obtained by the Van

Lear equation. We see that the inability of the Van Lear
equation to predict heats of mixing could be due to a dif-

ference in form between the calculated and true activity coef-

ficient curve. This difference is undoubtedly small since the










29
excess free energy of mixing curves calculated from the

solubility data using the Van Lear equation agree in aag-

nitude and in shape with experimentally determined excess

free energy.curves.

Based on the preceding considerations it is con-

cluded that the Van Lear equation can be used to estimate
free energies in systems which form two liquid phases if

the constants are determined at temperatures where the com-

positions of the two coexisting phases approach the pure

compounds. Of course more confidence can be placed in the

Van iLar equation if total pressure data are available.
Since the temperature derivative of the free energy is small,

these estimated free energies can be used without appreciable

error at other temperatures within 20 or 30 C. of the tem-

perature at which the estimate was made. It is further con-

cluded that the heats of mixing predicted by the Van Laar

equation are unreliable.













CHAPTER VI


VOLUME CHANGES IN MIXING FLUOROCARBONS AND HYDROCARBONS

Experimental.-The molal volumes as a function of

composition were determined for four fluorocarbon-hydro-

carbon systems. The physical properties of the pure com-

pounds are given in Tables VII and VIII. Pycnometers de-

scribed by Lipkin (22) and having a nominal capacity of

5 milliliters were used to measure the volumes of mix.

tures of known composition. These pycnometers were cali-

brated with distilled mercury at 40, 450, 50, and 600 C.;

the calibration data are given in Table X.

The molal volumes of the fluorocarbon-hydrocarbon

solutions were measured over the entire composition range

at a temperature slightly above the consolute temperature

of each system. The molal volumes were also measured over

the limited composition range at two other temperatures

5 and 10 C. below the complete isotherm. For the systems

perfluorocyclic oxide-n-heptane, perfluorocyclic oxide-

carbon tetrachloride, and perfluoroheptane-n-heptane the

isothermal volume measurements were made at 400, 450, and

50o C. while for the system perfluoroheptane-carbon tetra-











31
chloride they were made at 50, 55, and 600 C. The thermal

coefficient of expansion of the materials limited the teon-

perature range to ten degrees for one filling of the pyonom-
eter.

Since some of the mixtures were two liquid phases
at room temperature it was necessary to fill the pycnonoeter

at a temperature above the consolute temperature. Figure 23
shows the arrangement for filling the pycnometer. The de-

sired mixture was weighed out into the transfer tube,

which was then closed off by means of a ground glass stopper

and placed in the water bath at a temperature above the

consolute temperature of the system. After remaining in

the water bath several minutes the tube was shaken until

mixing was complete and the ground glass stopper was replaced
by the syphon tube, which had been heated to the bath tem-

perature. The pycnometer was connected to the transfer

tube by a small section of Tygon tubing and was filled by

applying auction to the other arm. The pycnometer was al-

ways filled at the highest temperature of each series. The

pycnometer reading was taken after approximately fifteen min-
utes at the bath temperature, then the bath temperature was

lowered five degrees to the next temperature.

The water bath temperature was controlled manually











32
by meaas of an electrical heating element connected through

a Variac. The mercury-in-glass thermometer measuring the

bath temperature could be read to + 0.02 C. and was checked

against a thermocouple calibrated by the National Bureau of

Standards. The temperature of the bath never varied more

than 0.05 C. from the desired temperature while the pyc-

nometer was approaching thermal equilibrium. After the pyc-

nometer reading was made at the three temperatures the pyc-

noaeter was removed from the bath and allowed to cool to

room temperature. The pycnometer was then weighed, emptied,

and weighed empty; all weights were corrected to weights

in vacuo, Knowing the weight of material in the pycnometer,

the composition of the material, and the pycnometer read*

ingas it is a simple matter to find the molal volumes of the

mixture at the three temperatures.

The molal volume-composition data is tabulated in
Table XVI. The volume change on mixing was calculated by
equation 17

AV*= V IM x" LV 22 T (17)

The partial molal volume change on mixing was determined

by plotting the total volume change versus mole fraction
of hydrocarbon, graphically taking the tangent to the curve

at the desired composition, and determining the value of the











33

intercepts of the tangent line at x, : 0 and x, : 1.

These values of the intercepts are the partial molal volume

changes of mixing of components 2 and 1 respectively.

Plots of the total volume change on mixing ( AVM) versus

mole fraction of hydrocarbon are shown on Figures 24-27,

Values of the partial molal volume changes on mixing are

tabulated in Table XVII and plotted versus composition on

Figures 28-31.

Figure 32 shows the plots of partial molal volume

changes versus composition for the systems perfluorocyclie

oxide-n-heptane and perfluoroheptane-n-heptane superimposed,

One can see from Figure 32 that the partial molal volume

changes are practically identical for each type of compound

in both solutions and since the systems are almost symme-

trical the partial molal volume changes are nearly equal for

all three components. Since the two systems involving

carbon-tetrachloride were not determined at the same tem-

perature one would not expect the two partial molal volume

change curves to be superimposed.

It was found for these four systems that the total

volume change on mixing increased with increasing tempera-

ture; this type of behavior was also found in the C5F12.-CsEH

C4F10-C4H10 and C6F14-C6H14 systems (2).










34
The coefficient of thermal expansion (ot) as de-
fined by equation 18 was determined from the temperature-
volume data of the pure compounds and the binary mixtures.

o( : 1 fy (18)
v V T/P

Figures 33-36 show that plots of d0 versus composition for
some of the systems exhibit maxim a. The thermal coeffi-
eient of expansion for an ideal mixture (a(o) is a linear
function of the volume fraction as shown below.


0 1V1 l* a2V \1V14 x*V2/ p

0o = XLVl & xi2 l-1f
S XV1 x2V2


Equation 19 is also plotted on Figures 33-36 for
comparative purposes. In order for the total volume change
to increase with temperature it is necessary that the thermal
coefficient of expansion for the mixture be greater than the
coefficient for an ideal solution. This can be shown by dif-
ferentiating equation 17 with respect to temperature

d AM sdV dVo 2 Vo< V VO <
dT _W y 0 0












Since V t Vo

d AVN .

In order for -dAY to be positive Qo( must be greater than
3a?-
(oo; this is in accord with the experimental values of AVN
and (

Since the values of o( plotted on Figures 33-36
were determined in the region of the consolute temperature

the large values of o( might be due to the breaking up of
clusters in the liquid as the temperature increases. The
formation of clusters in systems exhibiting partial misci-
bility has been generally recognized (50). The opalescence
observed Just above the consolute temperature is believed

due to the scattering of light by clusters of molecules.

A molecule in a cluster would have more like-mole-
cules as nearest neighbors than it would have if the mixture
were homogeneous; as the temperature is raised thermal mo-
tion combats the tendency to cluster and the mixture approach-
es homogeneity. If we consider the case where one 1-1 and
one 2.2 pair rearrange to form two 1-2 pairs we find that
the interaction energy of the system containing 1.2 pairs is
2 E12 while the interaction energy of the system containing

1-1 and 2-2 pairs is E -C22 or twice the arithmetic











aean of E11 and E Since E-12 Is approximately the

geometric mean of 6 il and 22 where only dispersion
forces are acting, and since the geometric mean is always
less than the arithmetic mean, the interaction energy of
the system is less when 1-2 pairs are present. These weaker
attractive forces result in a volume expansion and an in-
crease in the enthalpy of the system.

The dispersion of clusters due to thermal agitation
would explain the fact that the volume change on mixing in-
creases with temperature and thus one would also expect the
heat of mixing to increase with temperature. The heats of
mixing in the system perfluoroheptane-iso-octane (26) were
found to increase with temperature as shown by the follow-
ing values; at a mole fraction of one-half, the heats of
fixing were 402, 468, and 616 calories per mole at 300, 50,
and 709 C. respectively. The volume change on nixing for
this system was reported only at 300 C. However, the data
of Taylor and Beed (42) show that the volume change on aix-
ing for this system also increases with temperature.

The volume change on mixing is an important property
in the study of solutions and for this reason it would be
desirable to have a theoretical expression which would pre-
dict this property. Scatchard (38) and Hildebrand (13) have










37
shown that the Gibbs free energy at constant pressure ( AFp)
is related to the Helaholtz free energy at constant volume
( A A) by the following equation

AFp AA I ( AY")2 (20)
2/pV
The correction term involving AV amounts to less than
10 calories per mole as compared to about 350 calories per
mole for AFp, and for this reason it is usually neglected.
Hildebrand used this approximation in deriving an expression
for the volume change on nixing. He started with the ther-
modynamic relation


AV : \ ) T

and by substituting A A for AFp he obtained

Ay Z T
Av ) T 4 'w ( T
By further assuming that the pressure derivative of the
entropy was zero he arrived at

S- p /T "-T Z(Vo T Ti T


(21)



(22)


(23)


His final assumption was that
1 1/z n TV
VDT )T as -V-


(24)


and that n = 1.










38
This assumption is based on the fact that for several non-
polar liquids the internal pressure )T as calculated
from the thermodynamic relation

(1 ), TA ( )z P (25)

can be represented by equation 24 where the coefficient
n varies from 0.9 to 1.1. After making this assumption,
Hildebrand arrived at the following equation for ATV


AVN /a o aW


(26)


Using equation 1 for ABl yields

go22 =(c1 )j 2 41 2 (27)

An alternate theoretical expression for AVM can be obtained
using Reed's (32) correction instead of the geometric mean
assumption, but retaining the condition of constant volume.
Under these conditions NEVN is given by
: (xl1 4 12S2) .l () 2 d'61 S2(lff)12

(28)


311 & 12
: 2(do22/doll)1/2 (34
1 d 2/doll

The ratio d22/d011 can be evaluated from the cube root of


0)










39
the solar volume ratio. Substituting equation 28 into
equation 26 results in

AV /3o(iLVl 4 xa2V2) [(I 2)2 + 2 61S 62(1

fID] +1 2 (31)
Still another expression can be obtained for DVM if it is
assumed that the entropy of mixing at constant volume is the
ideal value, then 4A B in equation 26 can be replaced by
AFIp according to the following:
AFp sAAy AtyV1 TS y
and
Ap ,es A&M TASe

If A y is assumed to have the ideal value then


and

thus
/ Av" : A re (32)

In order to calculate AYV from equations 27, 31,
and 32, it is necessary to know /o, the compressibility
of a solution showing no volume change on mixing. The com-
pressibility is defined by equation 33
/3 : 1 a V) (33)
SV i Pi T

and it can be shown that 3O is a linear function of the











volume fraction as van oo.

1o3 4A + 2 2 (34)
Isothermal compressibility data needed for equations 34,
27, 31, and 32 are available in the literature for per.
fluoroheptane, and carbon tetrachlorlde (20) and n-heptane
(46). Pressure-volume-temperature data for liquid lso-
octane are also available in the literature (3) from which
the isothermal compressibility was determined by graphical

differentiation. eostwater, Frantz, and Hildebrand (46)

have shown that for a pure liquid the quantity a as
defined by equation 35 tois independent of temperature

a = V2T0/3 (35)

Equation 35 can be used to extrapolate compressibility
data from one temperature to another if volume and coef-

ficient of thermal expansion data are also available. The

values of /3 used in equation 34 are tabulated below in

Table III.









41
TABLE III

ISOTHREMAL COMPRESSIBILITIES FOR USE IN EQUATION 34


Compound Temperature OC. /3 Atam1

Cyr7l 30 2.65(10-4)

Cy7Fi 50 3.03(10-4)

C716 60 3.42 (10-4)

n-C7yI6 50 1.82 (10"4)

CCl4 60 1.55(10"4)

1-CsS18 30 1.21(10-4)


Values of 11~v as calculated from equations 27,
31, and 32 are plotted on Figures 37-39 along with the ex-
perimental values for the systems perfluoroheptane-carbon
tetrachloride, perfluoroheptane-n-heptane, and perfluoro.
heptane-iso-octane. Figure 37 reveals that for the
C7F16-CC14 system the agreement between experimental values
of AV* and those calculated from the experimental AFpe is

quite good; the theoretical equation 31 also gives a fair-
ly good estimate of AVY. For the systems C7F16-u-C7H16

and C7F16-i-C8H18, however, all these relations prove to be











42
poor estimates of AVM. It should also be noted that
the theoretical equations 27 and 31 predict values of VIE

which are symmetrical with respect to volume fraction and

therefore should have their maximum values at a volume frac-

tion of 0.5 (about 0.3 0.4 mole fraction of fluorocarbon).

Figures 24-27 reveal that the volume changes for the four

systems of this work and the C7F16-1-CgH18 system are mor-

nearly symmetrical with respect to mole fraction, having

their maxima at a sole fraction of approximately 0.5.

Since equations 27, 31, and 32 failed to predict

reasonable values for &V it might be instructive to ex.
amine critically some of the assumptions and approximations

involved In obtaining equation 26.

The first approximation involved the neglect of the

pressure derivative of the correction term (a V)2 when sub-

stituting for AFpe in equation 21. Although this term is

small and can be neglected in equation 20 its pressure deriv-

ative may not be small enough to be neglected in equation 22.

Another source of error in equation 2# might result from
the assumption that the pressure derivative of the entropy

term in equation 22 is zero. It should be mentioned, how-
ever, that unless these two assumptions are made the ex-

pression for AV* becomes extremely complicated.










43
Another assumption, the effects of which can be
clearly seen, is the assumption that the internal pressure

can be represented by equation 24, where a is equal to
unity. The data are available with which to calculate the
internal pressure of perfluorobeptane (20) from equation

25. This calculation was made and it was found that a

value of n equal to 1.40 was necessary to satisfy equation
24.

If the coefficient n is not assumed equal to unity,
equation 26 would be written

AV a noaIyN (36)

Since n for a fluorocarbon-hydrocarbon mixture would pro.
bably lie between 1.0 and 1.4, equation 36 would predict
values of &VU larger than those predicted by equations

27, 31, and 32, which implicitly assume a value of n equal
to unity. A value of n between 1.0 and 1.4, however,
would still predict low values of aVT for the C7F16-n-C7y16

and C7F16-i-C8H8 systems since a value of n between 2.0

and 3.0 would be required for these systems. Since equa-
tions 31 and 32 closely predict &yV for the C7F16-CC14

system the inclusion of n in equation 36 would impair the
agreement in this case.











44
It is possible that equation 26 is reasonably

correct and that the expressions for AE are in error.

This possibility will be discussed in more detail in

Chapter VII.

It is concluded that there are many assumptions

and approximations involved in the derivation of equation

26 which prevent the accurate prediction of volume changes.













CHAPZU VII


NBTINATICK OF THUF ODYAMIC PROPEBTI B


Heat of Mixing.-It was previously mentioned that
Reed rederived the equations of Scatchard and Hildebrand
omitting the assumptions of no volume change and the geooe-
trio mean, and obtained an expression which predicted heats
of mixing in agreement with experimental values. Reed's
expression for the heat of mixing in a binary mixture is
given below:

AM: = (z 1V xgaV) ( + 22) 2 <1 (1

A I D) 2 1(1 I ) + X2(1 ) (37)
*j VlV2
Where (1/) 2 (38)


The terms fI and tD were defined previously by equations 29

and 30. Although equation 37 predicts values of AZp it can
be shown that the difference between ApRp and AHp is neg.
eligible. In order to use equation 37 it is necessary to know
the ionization potentials and partial molal volumes of coa-
ponents 1 and 2. Reed (34) has presented a method of pre-
dicting the ionization potential of a compound from its po-
larisability and structure which yields good results and can
be used in the absence of experimental data.
Hildebrand (14) has shown that by considering the vol-
45











46
ume change on mixing that the heat of mixing can be calcu-
lated from the following expression.

AHP: &ay (1. OLT) (39)
If the entropy change at constant volume is assumed ideal,
then &I*N can be replaced by AFpe and
&Hp = A p(1. O c T) (40)

Equation 40 can be used to calculate heats of mixing in
fluorocarbon-hydrocarbon systems for which the thermal coef-
ficient of expansion (o ) is known and where AFpe can be
calculated from the binary solubility data as outlined in
Chapter V.
Still another method of estimating the heat of mix-
ing involves the use of the following thermodynamics relation
AHp = arp TASp (41)
In terms of the excess properties, equation 41 can be written

AdRp p A fe TSA S (42)
Since a method of estimating A Fp is available it is only nec-
essary to estimate 6 Sp. The entropy change due to the vol-
ume change on mixing can be determined from the following
Maxwell relation
1-681 = (43)

For a volume change at constant pressure A 8 is given by
/-Vo AM
AS : ( ) dV (44)










47
By assuming that ( .P ) is constant over the small volume
\(T/ V
change, equation 44 results in

A~sf =Y
The 68 in equation 45 represents the change in entropy be.
tween a constant pressure and a constant volume process.
Equation 45 can then be used in equation 42 giving

AHp 1 AFpe 4 TZP ) AV)v T ASYe (46)

If A e is again assumed equal to zero, equation 46 can
be used to calculate heats of mixing where binary solubility
data, volume change on mixing data, and the value of/ Pl

for the pure compounds are available.
Westwater, Frants, and Hildebrand have measured the
quantity (4P) for several pure compounds and equiaolar bins.

ry mixtures and have found that the( Z P term for mixtures
\VT )T V
can be calculated from those of the pure compounds through
the following relation
1/2 1/2 2
amix : (xlal x2a2 ) (47)
where a is defined by equation 35.
The heats of mixing have been calculated from equa-
tions 37, 40, and 46 for the systems C7F16-n-C7118 6 C7F-16-

CC14, 1F6-~IClHi8, CS12-*C5O1I and C4710-C41R0, and are
plotted versus composition on Figures 49-53. The data neces-
sary for these calculations is tabulated in Table XXVII.
The necessary (~P data are not available for the
The nece sary V











48
C512-C5H12 and C4F10-C4H10 systems and therefore equation 46
cannot be used. Figures 51-53 reveal that equations 37 and
40 predict values of the heat of mixing in good agreement
with the reported literature values. The agreement between
equations 37, 40, and 46 is very good in the case of the
C7F16-CC14 system although no experimental values of ABp are
available for comparison. Agreement between equations 37, 40,
and 46 is not too good, however, in the C7yF6-n-C7HI6 system

where again no experimental values of AH are available for
comparison.
Free Energy of Mixing.-.As was mentioned in Chapter
V the excess free energy of mixing can be estimated quite
well from binary solubility data. Equation 28 can also be
used to estimate excess free energy of mixing if it is as-
sumed that the entropy of mixing at constant volume has the
same value as for an ideal system. Figures 18-20 show a com-
parison of AFpe calculated from equation 28 and from binary
solubility data. Reported literature values of AFp are
available for comparison in the CsF12-C5H12, C4F10-C4H10L
and C7F16--C8H18 systems. In the case of C7716-CCI4 no
literature values are available, but agreement between AFp9
calculated from equation 28 and A Fpe calculated from solubil-
ity dr :a is good. In the remaining systems equation 28 always
predicts values of AFdy which are too low.
The excess free energy of nixing can be estimated in
an empirical manner. If it is assumed that equation 28 is










49
the correct expression for A( y* and that the excess entropy
of mixing at constant volume can be represented by equation
48, then it is possible to write equation 49 for ApF .

OSe xiV i 1 1 x2V) *1 ZO 2) 2 t 2 4S 62(1
DI 1 42 (48)
AFpL (1 + zT) (xzl1 V xgV2) (( 1 12)2

2d1JC2(1 f ID) 2 (49)
The term z in equation 49 is merely a correction factor and
can be determined from an empirical correlation of z versus

2)1 e) 2 6l (l fifD)] shown on Figure 58.
Values of z used in establishing this correlation
were obtained from free energy and consolute temperature data
reported in the literature for fifteen fluorocarbon-hydro-
carbon systems. For all these systems the equations of
Scatchard and Hildebrand predict values of the free energy
or consolute temperature which are too low.
The Scatchard-Hildebrand equations for the excess
free energy and consolute temperature can be written
AFe (xIVI x2V2)K 1 2 (50)

RC (i X2V2)3 (51)
where K = (1 + zT) [(d1 d)2 .2& d4(f fD1f (52)
The parameter K represents the effective value of
(1 & 2 )2 d d"2d ( I. f o)]
necessary to fit the Scatchard-Hildebrand equations to the











50
experimental data. The value of z was determined from the
reported free energy and consolute temperature data by
using equations 50, 51, and 52. Values of K and z for the
fifteen systems are tabulated in Table XXVIII along with
the literature reference and the method of obtaining K.

This correlation is only applicable to mixtures
of fluorocarbons and paraffin hydrocarbons. Systems con-
taining benzene, carbon tetrachloride and chloroform could
not be so correlated. A glance at Figure 55 reveals that
the points are widely scattered about the correlation
line and suggests that values of AFpe calculated from

z and equation 49 would be subject to quite a bit of error.
This is not the case because z is a correction factor and
large differences in s result in smaller differences in
the factor 1 + sT. This correlation fits the excess free
energy data with an average deviation of 7 per cent and a
maximum deviation of 20 per cent.

Entropy of Mixing.-The entropy of mixing at con-
stant pressure can be given by equation 45

ASoP an to) o+ the (45)

or in terms of the excess properties

Ap AB (le + Va (45)











51
For the CyF1-i"-CaH18 system values of ASp' and AVf
have been reported (26) and the necessary ( p P data

are available in the literature (20) (3). Values of

TA5Be and TeZl A4 are plotted versus composition

on Figure 56 where it can be seen that the T z Aym

teom is much larger than T ASpW indicating negative

values for A Sye. Negative values of A8e would also

explain the fact that lFe as calculated from equation 28

Are lower than experimental values, since in using equa-
tion 28g ASye was assumed equal to zero, These negative

values of A Sye would also explain the large difference

between experimental values of AH and those calculated by
by equation 46 as shown on Figure 51. The same conclusion
concerning A 8 in the Cjl6en. CH16 system could also be

drawn from Figure 49,
The C7F16-CC14 system however, appears to have a
value of d SyW equal to zero since from Figure 54 it can

be seen that F4 7 calculated from equation 28 is in agree-
sent with AF determined from solubility data. Also values
of AH calculated from equations 37, 40, and 46 are in good
agreement as shown on Figure 50.
Another argument in favor of negative values of
A~ is the fact that the empirical correlation involving










52
z and equation 49 predicts free energies of nixing. This
correlation is based on the assumption that A Sy can be
predicted by equation 483 Since a is a positive number
then ASy* as given by equation 48 will be negative.

If negative values of A8Sy are common to most
fluorocarbon-hydrocarbon solutions, it is surprising that
equation 40 predicts values of AH in agreement with experi-
mental values in the C7116-i-C8H18, C51-Cg512, and

C4o10-C410 systems. In order to understand why equation
40 is successful in this respect it would be well to ex-
amine its derivation. This is done in the following parao,
graphs6
In order to determine the effect of small volume
changes on A By as given by equation I, Hildebrand ex-

panded A Ey about Vo using a Taylor series and obtained

IT "
(53)
By negle,'ting second order and higher terms in AV and
using the thermodynamic relation



he obtained
4Z a & BYv q T7;)V A'V1 T P 'AT1 (54)











53
The relation between AEpO and 4Hp is

aHp s 4XI PaVM (55)

Substituting equation 55 into equation 54 gives

A Up 4- ay \T/ V
We have already seen from equation 26 that the volume change
on mixing is related to the energy of mixing at constant
volume (26)

By substituting equation 26 into equation 56 Hildebrand
obtained
AHS: a E T /3, AyM (57)

If /3 and 30 are assmed equal then equation 39 results
A Hp = A (1 oT) (39)

A possible reason why equation 40 predicts reason-
able values of A H in spite of negative values of ASe is
apparent from equation 56. The substitution of A F for
ARv in equation 56 would result in values of AH which
were too high. This effect is compensated by expressing
AT by equation 26, which we have seen generally predicts
values of AYV which are too low. Thus equation 40 provides
a good estimate of AH, probably due to a fortuitous cancel-
lation of errors.
The fact that it is possible for equation 40 to pre-
dict reasonable values for A H even though A W is not zero










54

and the fact that AFe as calculated by equation 28 is less

than the observed values leads to the conclusion that &8Ve

could also be negative in the C5F12-CH12 and C4F10-C4Hlo

systems.
Negative values of ASVe for fluorocarbon-hydrocarbon

systems are not unreasonable and are consistent with the con-
cept of clustering. In a mixture containing clusters, the

distribution of molecules would not be random and one would

expect the entropy of mixing to be less than the ideal value.
The effect of raising the temperature would be to increase

the random thermal motion of the molecules and decrease the
clustering tendency. Thus the value of A tye should be-
come less negative as the temperature is increased, causing

the value of LSpe to increase with temperature. This effect

was found in the C7H16-i-C8H18 system where the following
values of A8pe were reported for an equimolar mixture.

t AlSpe (cal./mole OK)

30 oC. 0.24
50 OC. 0.46
70 oC. 0.89













CNAP!'U VIII


TERNARY LIQUID-LIQUID O8LUBILITY STUDIES

The ternary liquid-liquid solubility studies were
undertaken to determine whether fluorocarbon mixtures could
be separated by solvent extraction, and whether fluorocarbons
would be good solvents for mixtures of other types of coa-
pounds. Various types of organic compounds were tested as
possible solvents for separating a mixture of perfluoro-
heptane (C7Fi6) and perfluorocyclic oxide (CsFL60).

Mperimental,.-These preliminary studies were per-
formed by vigorously shaking an approximately equiaolar
mixture of the two fluorocarbons with the prospective sol-
vent in a small screv-cap vial and using a Perkin-Klaer
"Vapor Practometer" to analyse the two coexisting liquid
phases. The criterion of a good prospective solvent was tak-
en to be the difference in the C71F6 and C8130O peak height

fractions in the two liquid phases. Of all the organic sol-
vents tested, carbon tetrachloride (CC14) and a-heptane

(n-C7uH16) were found to be the most promising. The ternary

liquid-liquid phase diagrams were determined for the systems

C7Fl6-CSF60-nyHi16 and C7F11-C8Q160-CCl4 at 300 C.
55












56
The methyl ester of perfluoro-octanoic acid
(C7F15COOCH) was tested as a possible solvent for mixtures

of toluene (CgHNCH3) and methyl cyclohexane (COH1ICH3)oince

the consolute temperatures for these two binary systems

containing the eater were quite different. Toluene and

the eater are completely miscible at room temperature where-

as the consolute temperature of the methyloyalohexane-ester

system ts 45 C. The ternary liquid phase diagram was deo

termined for this system at 253 and 100 C.

The isothermal ternary liquid phase diagrams were
determined from chromatographic analysis of the two coex-
isting liquid phases. The liquid mixture was contained in

a screw-cap vial and was vigorously shaken while immersed
in a water bath. After being shaken for some time, samples

of each phase consisting of approximately 0.04 ml. were with-

drawn for analysis by a hypodermic syringe and the mixture

was again shaken. Two or three successive samples were taken

with shaking in between sampling. The hypodermic syringe

was warmed to approximately 100 C. above the temperature of
the mixture prior to sampling in order to prevent any con-

centration changes due to cooling the saturated phases. The
sample was injected into the chromatograph immediately after

sampling so as to prevent formation of a second phase in the
syringe upon cooling.












The water bath used in these determinations was deo
scribed in Chapter VI. The vial was shaken by hand during
the determination et the toluene-methylcyclohexane-ester
system, but it was found that considerable shaking was neces-
sary to effect equilibrium between phases in the two perfluo-
robeptane-perfluorocyclic oxide systems. Therefore, the vial
was shaken by an air-driven mechanism for approximately
thirty minutes before and between sampling. The agreement
between the analyses for successive samples was taken as
the criterion of equilibrium.
Since analyses were performed chromatographically,
it was first necessary to find a suitable partitioning liquid
that would resolve the ternary mixture into three separate
peaks on the chromatograph with no overlapping. After the
proper partitioning liquid had been found, it was then neces-
sary to prepare calibration curves of peak height fraction
against weight fraction for two of the three possible binary
mixtures, since it was found that a ternary mixture could be
analysed from calibration data for only two of the three
possible binary mixtures. This is due to the fact that the
solutes are in very low concentration in the partitioning
liquid and therefore act independently of each other. The
calibration data and curves used for analyses are given in
Tables XVIII and Figures 40-44.










58
The peak height traction for aucoessive samples of
one phase were usually in good agreement and the compoel-
tion was determined from the average peak height fractions.
Where significant differences occurred between peak height
fractions of Successive samples, the compositions of each
sample wer also calculated and are tabulated. The tie l11e
data necessary for construction of the phase diagcrms is taba
lAted in Table XIX sad the phase diagrams are ahown on Figures
45.45'
Conjugate curves are drawn on the phase diagrams
for the purpose of interpolating tie lines; the plait points
for two of the systems were outlasted by extrapolating the
conjugate curve to its intersection with the binodal eurve.
ohese conjugate curves were constructed from points located
by drawing lines through each end of the tie line parallel
to the side of the diagram in such a manner that these two
lines iater eoted inside the diagrams.
Varteressian and renake (44) found that ternary sol m
ability data could be represented by the following relationship

/3 Wl j ,
VI 2 3' X2
The tern /1 is known as the selectivity of the solvent aad
gives a measure of the ease with which a binary mixture can
be separated with a give solvent by solvent extraetion










59
methods. A /3 value of unity would indicate no selectivity
while solvents having higher values of /3 we mare selective.
The seleetivity is amnlogous to the relative volatility
vhi h is need as a measure of the ease with whibh a binary
mixture can be separated by distillation.
Values of the selectivity have been calculated tfro
the tie lie data sad equation 88 tor the four system
studied in this work. inse these values of the selectivity
vary only slightly with composition, their average values
are tabulated below in Table IV.

TABL IV

SOLVUTT LaCTIVITTI8


Mixture to be solvent t c. Average


C1eIo-C77r1 ccI4 so3 1.20

Ce5ru-ce3ls ,C7Ne i300 1.09

C6e5Ca3PC1c4xC3 C71PcscOc3 3sI0 .a16

eaeaCs.Nclncsa ir77cooc3 1o 1.s23


Table IT
tetrashloride is


ahows that neither a-eptaae nor carbon
a good solvent for the fluorocarbon miature











60
but that carbon tetrachloride is the better of the two.
It is also obvious that the ester is not a good solvent

for the hydrocarbon mixture.

From consideration of the Scatchard-Hildebrand the-
ory one would not expect a nonpolar solvent to be very se-

lective for either C7F16 or C87160 since their solubility

parameters (C) are almost equal, being 5.93 and 6.05 re-
spectively. The difference is a measure of the deviation

of a binary system from Raoultt* law as shown by equation 3.

One can see that for a given solvent the S difference be-
tween C7F16 and solvent is practically the same as the Cr

difference between C8F160 and solvent. The high solvent

selectivity found in some reported systems can be attributed

to specific effects such as association, solvation, or hy-
drogen bonding, which are not present in nonpolar systems.
Since the solubility parameters of the fluorocarbons are
almost equal, and since they are nonpolar they cannot exhibit

specific interaction effects with the solvent, It is con-

sidered unlikely that a separation can be effected by sol-
vent extraction.

Theoretical Calculation of Activities in Ternary
Systems.-Hildebrand (15) has extended the treatment of solu-

tions of nonelectrolytes to ternary systems and has arrived










61
at equations 59 for the activity coefficients in terms of
the properties of the pure compounds.

Rt In Y< 1 3 Vi 2 d 2) ( 1 63) 3] 2

(59)
T ]A Vg 2 Z 2
RTlnY3 V3 (3 1S)s f (3- 2) ] 2

Using equations59 the activities in the two conu-.
gate liquid phases can be calculated from the tie line
data. If equations 59 correctly predict activity coeffi-
cients, the calculated activities must satisfy the condition
that the activity of each component be equal in both phases.

Z1 YL x YI

x2) 2 x2'Y2' (60)

3 3 s3 3
Squations 59 were used along with the tie line data
to calculate activities in the coexisting phases for the
systems CF71.-C816O-CCL4 and C716-C810.Oa-CC716. The

solubility parameters were evaluated froa the properties of
the pure components. These calculated activity values are
tabulated in Table XX. From Table XX it is obvious that the
results of equations 59 do not satisfy the conditions of
equations 60. If, however, equations 59 are used with the











solubility parameters evaluated from the binary solubility
data, the activities are found to satisfy equations 60, s
can be sees trom Table XX.
The "etteetive" solubility parameters eaa be found
from the binary solubility data by substituting equations
3 into equations 11 and 12. Two empirical values of each
difference are obtained trom this procedure sinoe there are
two equations (11 and 12) sad only one uaknown (the X ditf
tmenoae) It was found that there was only a slight dif-
ferenee between the two f difference terms sad therefore
aa average value vwa used for substitution into equation 59o
Since the following relation holds
&1 only the difference for two of the binary systems is
needed to evaluate all possible c difterenaes required by
equations g9. Valuea of the O dffttreace evaluated ftro the
binary solubility data are compared with these evaluated
from properties of the pure compounds n Table V.











TAME V

COUPARIS0N OF S DMFFRENCE


S e Difference
System .
Pure Compounds Solubility

C716.-n-CAH16 1.43 2.87

CgF60i-n-C7H16 1.31 2.78

C7r16-cc14 2.52 3.10

C1r6O0-CC14 2.40 2.94


8ince the Van Laar equation has proved useful in

treating binary systems it would be interesting to see if
ternary systems are also amenable to this treatment.
White (47) has applied the Van Laar equation to calculate
equilibrium vapor-liquid compositions in ternary systems
from data obtained from the binary systems. He compared
the calculated results with experimental data for three
ternary systems and found the agreement to be good enough
for engineering purposes. Robinson and Gilliland (36)
have shown that the Van Laar treatment can be extended to
ternary systems where the Van Laar constants for only two
binary systems are needed to calculate activity coefficients
in the ternary system. The ternary Van Laar relations are












'A2 x3A32 vAW/%s


in Y_2 x2A12 All *_ xA_32_ 32
21/12 *, 2 + zx3A32B32]

in Y3 1 | 12 rA31/B12 1' 32
[ /lA Bl: 4+ 2 + Ax3A32/SS
In evaluating the constants in equations 61 the
relations are used


2
(61)

2


following


A12 B21
812 A21
and
A21 B12
Since the square roots of the binary Van Laar con-
stants are needed for equations 61 the question arises as to
whether the positive or negative root should be used. In
This case the binary Van Laar equation is considered similar
in form to equations 3, where the constants can be written

A12 V1 (1 d2) 2
1,f 2 3 ( &2 2)2

22 T
and A12 V1


The square root of A12 is taken to be positive if 6 is


In Y1 =












greater than C2 and negative if the reverse is true. The

relation existing between the constants which allows the
evaluation of all constants from the constants of two bi-

nary systems is

\A \/ ra3X 0

The necessary constants for use in equations 81 were
determined from the binary Van Lar constants by the pro-
cedure described above. The activities for each component
in the two coexisting phases were calculated for the systems
CyF16-C8gF10-CC14 and C7F6CgsF1r60-W-C718.6 These activities

are tabulated in Table ZXX and it can be seen that equations
61 satisfy the conditions of equations 60. Thus we see that
equations 59 or 61 can be used to predict activities in
ternary systems when the constants are evaluated experimen-
tally from two binary systems.
It is also possible to use equations 59 or 61 to
construct the ternary phase diagram from the binary solu-
bility data. This can be done graphically by using equation
59 or 61 to plot contours of constant activity for each com-
ponent on a triangular diagram. The composition of the two
phases in equilibrium can be found by locating two points
at which the activity of each component is equal. An at-
tempt was made to use this method to calculate the phase











66
diagram for the C7716-CF160-CC14 system, but location of

the phase compositions proved very difficult since it was
necessary to interpolate between three sets of activity

contours.













CHAPTER IX


ETRACTIVE DISTILLATION STUDIES

The term extractive distillation refers to the
process of adding a solvent to a Mixture to be separated

by distillation in order to improve the relative volatility.
The solvent is able to improve the relative volatility by
altering the activity coefficients of the various compo-
nents. The relative volatility (0() is defined for a bi-
nary mixture by equation 62

( = y- (62)
i Y2

(In equation 62 the subscript 1 refers to the more volaw
tile compound.) For systems obeying Dalton's law of par-
tial pressures and where deviations from ideal gas behavior
can be neglected the ratio yl/x1 is given by


yl/xI -a

Substituting into equation 62 gives

o1 A1f (63)


From equation 63 it can be seen that by selecting a solvent











63
which increases the ratio of activity coefficients the rela-
tive volatility is increased.
In practice the solvent used is essentially non-
volatile or of a low volatility compared to the original
components and the quantity used is such that the original
components are in low concentrations in the liquid phase and
dc not interact with each other appreciably. This being the
case, the ternary mixture can be treated approximately as
two binary mixtures involving each original component with
the solvent. Since the solvent is essentially nonvolatile
the vapor phase is assumed to consist only of the original
components.
The Scatchard-Hildebrand theory can be used to pre-
dict some properties of a good solvent for extractive
distillation. Assuming two independent binary systems, the
expression for the logarithm of the activity coefficient
ratio as given by equation 3 is

RT lan Y1/ Y2 00 V1 4 3 V2 4 <) 32

(64)
(In equation 64 the subscript 3 refers to the solvent.)
If the molal volumes of components 1 and 2 are ap-
proximately equal then equation 64 becomes


S in [Y/ 2) (,

(65)











69
From equation 65 we see that the logarithm of the activity

coefficient ratio depends upon the square of the volume

fraction of solvent and upon the solubility parameter of the

solvent. From the standpoint of separating power the

properties of a good solvent will be those which increase

the right hand side of equation 64 or 65. This indicates

that the molal volume and the solubility parameter are im-

portant factors in selecting a solvent. It is difficult to

predict the effect of temperature upon the activity coeffi-

cient ratio as given by equation 65 since the molal volume

changes in the same direction as the temperature, and the

difference term is more or less independent of temperature.

One would therefore not expect the activity coefficient ratio

to be a strong function of temperature.

In this work several compounds will be evaluated as
extractive distillation solvents for mixtures of perfluoro.

heptane (CyFl6) and porfluorocyclic oxide (C8F160); also

n-heptane (n-C7H16) and methylcyclohexane (C6gl11C%).

A convenient method of evaluating prospective ex-
tractive distillation solvents is by means of gas-liquid par-

tition chroaatography. Porter, Dual, and Stross (30) have
shown that the activity coefficient of a solute in an in-

finitely dilute solution in the partitioning liquid can be

obtained from the appearance time of the solute peak. The












activity coefficient ratio in equation 63 can be found from
the appearance times of components 1 and 2 when the prospec-
tive solvent is used as the partitioning liquid. The follow-
ing relations were given by Porter et al for determining the
activity coefficient in the infinitely dilute solution.

V R 0 VO+ B av (66)

S : aT/YOpVs (67)

V 0 V (p/ ) ) (68)
R L,3(Pi/ Po)2

The volume occupied by the vapor phase in the column (V0)
is usually mall compared to V0 and can be neglected.
Neglecting V0 and combining equations 66 and 67 we get
o VgRT
VR O (69)
P Vg
If the appearance times, for components 1 and 2 are de-
termined under the same conditions of constant flow rate and
constant pressure drop through the partitioning column then
we can write

S02 R2 02 (70)
.- .- (0

From equitiun 69 the ratio VR2/ v1i can be written

vT = 91 (71)
YR 2 oP










71
Equating equations 70 and 71 gives


(72)
Y20 GlPlO
Substituting equation 72 into equation 63 yields the follow-
ing expression for the relative volatility of components 1
and 2 at infinite dilution in the partitioning liquid.

o0 : e0/ 0e (73)

Since the value of the relative volatility as given by equa-
tion 73 is for an infinitely dilute solution, the ratio of
the appearance times gives the maximum separation that can be
obtained when using the partitioning liquid as an extractive
distillation solvent.

Experimental. -The chromatography columns used in
this work were made from one meter lengths of one-fourth inch
copper tubing; these columns were used in a Perkin-Blmer
"Vapor Fractometer,' model 154.

The stationary phase was Celite C44857 (Johns-
Manville), a diatomaceous earth having rather uniform parti-
cle sime. Before this celite was used the very small parti-
cles were removed by allowing the material to settle in water

and decanting the water containing the suspended fines. After
this the celite was washed several times with concentrated
hydrochloric acid, then washed with distilled water and dried













in an oven.

The prospective solvents were perfluorokerosene,
and three Kel-F oils having the general structure

Cl(CF2CFCl1)Cl. These oils are products of the N. W.
Kellogg Company and were designated Kel-F oils 1, 3, and

10. The N. W. Kellogg Company reports the following vapor
pressures for these oils at 1000 C.

Kel-F Oil 1...17 mm

Kel-F Oil 2... 1 Ma

Kel-F Oil 10..0.1 ma
These four liquids were chosen as partitioning
liquids since their vapor pressures were low enough to

prevent their removal from the packing during operation of

the column at adequate gas flow rates and temperatures.
The ratio of partitioning liquid to Celite used in the
preparation of the partitioning columns was 0.5 to 0.7 ml

of liquid per gram of Celite. The weight of packing required
to fill the column was measured so that the void volume and

the volume of the stationary phase could be computed. The
properties of these columns are tabulated in Table XXII.

The four above mentioned par' zoningg liquids were
evaluated as possible extractive distillation solvents for
the binary systems C7F16 with C8F160, and C7H16 with C6HICE3*.











73
Table XXIII gives the appearance times of C71F8, C8160,

CyH16 and COH11C3 in the partitioning liquids and Table
XXIV gives the values of the relative volatility as cal-
culated from equation 73.

From Table XXIV it can be seen that all four sol.
vents can be rated equally as extractive distillation sol.

vents frr both binary systems. The pronounced effect of team
perature upon the relative volatility is also noted from
Table XXIV.

The C7F16-CsF160 system was investigated by Yen (49)
and was found to obey Raoult's law. Since this system is
ideal the relative volatility is merely the ratio of vapor
pressures. Using the vapor pressures listed in the appendix

for C7716 and C8g160, the calculated relative volatilities

for this system at 350 and 80 C. are 2.34 and 1.96 rela-
tively. Using an average value of the relative volatility
for these compounds in the four solvents it can be seen that
the addition of the solvent changed the relative volatility
from 2.34 to 2.62 at 350 C. and from 1.96 to 2.16 at 800 C.
This change corresponds to a change in Y*/ Y2 from 1.00 to

1.11 at 35 C. and from 1.00 to 1.10 at 800 C. The effect
of temperature upon the activity coefficient ratio is very
slight as was previously suggested.











74
The n-heptane-aethylcyclohexane system was investi-

gated by Bromiley and Quiggle (4), who found the average value

of the relative volatility to be 1.074 in the temperature

range 900 to 101 C. The system obeys Raoult's law and the

relative volatility can be expressed as the ratio of vapor
pressures. Using the vapor pressures calculated from the

Antoine equation given by reference 1 the calculated relative
volatilities for this system are 1.003 and 1.057 at 35 and

800 C. respectively.

Again using the average value of the relative vola-

tility for all solvents it is seen that the relative vola-
tility for these hydrocarbons changed from 1.003 to 1.11 at

350 and from 1.057 to 1.21 at 800 C. The addition of the sol-
vent caused the activity coefficient ratio to change from
1.00 to 1.11 at 35 C. and from 1.00 to 1.14 at 800 C. Again

the effect of temperature on the activity coefficient ratio
is seen to be slight.
Since the physical properties necessary for evalua-

tion of the solubility parameters of the solvents (Cf3) are

not available it is not possible to predict the expected

value of the activity coefficient ratio as given by equation

64 or 65. Equation 64 can be used, however, to evaluate the
solvent solubility parameter ( 63) by using the experimentally

determined activity coefficient ratio and the necessary phys-











75
leal properties of the solutes given in Table XXVI. Values
of S3 were calculated from data for the C7F16-C68018 -
solvent, and C7I16-C6H11CR3 solvent systems at the tem-
peratures of 3U C. sad 80 C. These values of f3 are
tabulated below and it can be seen that 63 ea oentially
the me value when evaluated from experimental data f ra
two different systems.

TABLE VI

CALCULATION OF d0 3 GM EQUATION 64



t (C.) C716-CSgF1O-Solvent C7Hlg-CgNlCC1-solvent

35 7.88 8.05
so8 7.80 7.52


The results in Table VI indicate that the equations
of Seatahard and Nildebrand are applicable to prediction of
solvent properties. From the results of Table VI the average
solvent solubility parameters are 7.98 at 380 C. and 7.51 at
80 C.
These values of the solubility parameter nay seem
somewhat high for chlorofluerocarbon compounds since chloro-.
flueorocarbons for which data are available have solubility

parameters between these of fluorocarbons and hydrocarbons









76
kaviag the Sme boiling points. It should be acted, how..
ever, that the solubility parameter iaereasem with lacreso-
Lag molecular weight within a homologous series a is ob-
vious from the following table of solubility parameters for
the paraffin series as reported by Hildebrand (16).

compound a at 2s c.

!- A%" 7.05

W-C. 14 7.30


_n yCa 7.,.


0% 4 8.0

It right be argued that the large olubility parsme-

ter of the solvets would le4d to imiastellity in the case

of the fluoremarbons, but since the molal volumes of these

solvents are undoubtedly large the entropy effect due to vol-

ame disparity should be considered. The effect of differences

in moIal volumes to to decrease the positive deviatloas from

Raoult'a law and it is possible that the volume disparity is

large *ough to permit miscibility in spite of the large
difference.

In the light of the volume disparity it would be










77
interesting to determine the effect of this factor upon the
activity ooeffieieat ratio of solutes in an extractive
distillation solvent Instead of using equation 3, the
folloviag equatioea as give by Hildebrand (12) will be used
far the activity oeeefieiont since a corretion term for
volume disparity is ieclu4ded
Ia Y11 (c 6) xa 4 i/2 (I ) (74)
T2
If ve again ask the assumption that the volume fraction of
solvent is large enough that component 1 and 2 act ainde
pendeatly of seah other v oea write for the activity 0oef-.
ftlient ratio

In I/ Cs )2 +:2 '12 S2 CF3&2 02s
xL';: Vl/ "" (7$)


V2
When the nolal volumes of the solutes are apprxiaately
equal the last two teras in equation 76 awe eligible and
equation 7T reduces to equation 64. Thus while the volume
eorreetion does affect the ladividmal activity sooefileents,
the relative volatility of the solutes is unaffected. The
success of the Scatehard4ild ebrmad Theory is predicting rel-
ative volatilitte for extractive distillation As then due to
the eamoellation of errors in the individual activity coeffl-
eient expressions when the ratio of activity ooefflieeata are











78
used. hies tact wM rwcogaiad by meed (3s) sad vwa ued by
bin to explala the uneosm of the Scateard "b-il-d raad the-
ory in prediCting asetropes (33) sad relative velatil.tis
in hydrocarbon system.














CHAPTER X


EVALUATION OF METHODS OF SEPARATING FLUOROCARBON MIXTURES

This discussion will deal mainly with possible pro-
cedures for separation of fluorocarbon mixtures since

separation procedures for hydrocarbon mixtures have been

covered quite thoroughly by Rossini et &1a (37).

Distillation.--Several binary systems containing
fluorocarbons have been investigated (5) (24) (49) with

ideal solution behavior reported in all cases. Since fluoro-

carbon-fluorocarbon mixtures can be expected to follow ideal

behavior, the relative volatility or the ease of separation

depends upon the ratio of vapor pressures of the compounds

to be separated.

Yen has shown that when fluorocarbon mixtures are
distilled, laboratory distillation columms are approximately

one-half as efficient as when hydrocarbon mixtures are dis-

tilled. A laboratory distillation column having 100 theoret-

ical plates in a hydrocarbon separation would have approxi-
mately 50 theoretical plates in a fluorocarbon separation.

Aseotropic Distillation.-As would be expected from
the large positive deviations exhibited by fluorocarbon-

hydrocarbon mixtures, aseotropes are formed between fluoro-
79













carbons and hydrocarbons even when differences in normal

boiling points are large. This azeotropic tendency has been

exploited by Mair (23), who used fluorocarbons as azeotrop-

ing agents in separating paraffin and cycloparaffin hydro-

carbons.

The C7F16 and CSF160 used in this work were each

purified by azeotropic distillation with n-C7H16. Since the

addition of a hydrocarbon azeotroping agent to a fluorocarbon

mixture would also increase the efficiency of the distilla-

tion column, it is possible that azeotropic distillation

holds some promise as a means of separating fluorocarbon mix-

tures.

Extractive Distillation.-*It was shown earlier that
some enhancement of the relative volatility of a fluorocarbon

mixture could be obtained by employing a chlorofluorocarbon

solvent for extractive distillation. Yen found chlorofluoro.

carbons to have column efficiencies slightly less than hydro-

carbons, but approximately twice as large as fluorocarbons,

In this case the added solvent would enhance the separation

by increasing the relative volatility and by increasing the

column efficiency.

The effect of the relative volatility and column effi-
ciency upon the separation obtainable by distillation can be

seen from an equation derived by Fenske (8).















X2) D /w (76)
Equation 76 applies for conditions of total reflux and con-
stant o0. The left hand side is a measure of the separation
attainable in a column of N plates; a large value of the
ratio on the left-hand side indicates good separation. The
effect of increasing the coluxa efficiency is to increase the
number of theoretical plates (N); thus if both the relative
volatility and the column efficiency are increased the re-
sulting change in separation can be large.
Liquid Jatraction.-We have seen earlier that separam
tion of fluorocarbons by liquid extraction is not feasible
where specific interactions between one component and the sol-
vent are absent. Where a functional group is present in a
fluorocarbon, there is the possibility that a solvent can be
found which will be selective for this compound. An example
of this type could be found in the system C81F60-C1F35H-

C2H5OH where C8gl60 and C2HsOH are practically immiscible
while C7F15H and C2H50H are miscible even at temperatures as

low as -50 C. In this case there is undoubtedly a hydrogen
bonding effect which would permit the separation of C7F15H
from C81F60 by extraction with C2Hs5O.














CHAPTER XI


COWCLUSIONS

The experimental work and discussion included in
the previous sections of this dissertation provide the

basis for the following conclusions.

1. The simple Scatchard-Rildebrand theory is in-

adequate for predicting excess free energies of mixing,

heats of mixing, and volume changes in fluorocarbon-hydro-

carbon mixtures.
2. The Scatchard-Bildebrand theory with the modi-

fications introduced by Reed provides good estimates of the

heat of mixing in fluorocarbon-hydrocarbon systems.

3. Good estimates of the excess free energy of mix-

ing can be calculated from the Van Laar equation and bi-
nary solubility data.

4. Beats of mixing calculated from the Van Laar

equation and solubility data are unreliable.

5. The excess free energy of mixing fluorocarbons
with paraffin hydrocarbons can be estimated from an empiri-

cal correlation if values of the solubility parameters,
ionization potentials, and molal volumes are available.












6. Comparison of the calculated and observed con-

solute temperature is not a good criterion for testing the

applicability of the Scatchard-Hildebrand theory.

7. Mixtures of fluorocarbons with hydrocarbons

exhibit large volume changes on mixing (in the order of 3

per cent of the total volume at 50 mole per cent). This

volume change on mixing was found to increase with increas-

ing temperature.

8. A negative excess entropy of mixing at constant

volume can be used to explain the disagreement in some

fluorocarbon-hydrocarbon systems between observed thermody-

namic properties and those calculated from the Scatchard-

Hildebrand theory.

9. The concept of clustering can be used to explain

the negative values of the excess entropy of mixing at con-

stant volume.

10. Scatchard-Hildebrand or Van Laar equations may

be used to predict activities in ternary systems if the con-

stants are determined empirically from the solubility data

for two of the binary systems.

11. The Scatchard-Hildebrand equations can be used

to predict relative volatilities in systems containing an

extractive distillation solvent.











84
12. The possibility of separating a mixture of two

fluorocarbons by liquid extraction is slight unless one

fluorocarbon contains a functional group which will permit

some sort of interaction with the solvent.

13. Future work should be directed toward the

measurement and theoretical calculation of the excess entropy

of mixing at constant volume.

14. The problem of theoretically calculating the

volume change attending mixing remains unsolved. Some light

may be shed upon this problem when a theory is developed

which will predict the entropy term.











APPENDIX


I. Purity of Compounds Used

Hydrocarbons.-Most of the hydrocarbons used in this

work were obtainable commercially in a reasonable degree of

purity and were not further purified. The physical proper-

ties of these compounds are listed in Table VII along with

the reported literature values.

Fluorocarbons.-Five fluorocarbon compounds were

used in this work. The physical properties of which are

listed in Table VIII. The physical properties of some of

these fluorocarbons have been reported in the literature;

these values are also included in Table VIII. Since the

supply of some of the fluorocarbon compounds was limited

it was necessary to recover some fluorocarbons from mixtures

with hydrocarbons and repurify then. Where this was done

the physical properties of both batches are recorded in
Table VIII.

1# Perfluorocyclic oxide, C8F160. This material

was the major constituent in "Fluorochemical 0-75"

manufactured by the Minnesota Mining and Manufacturing
Company. It is believed that this fluorocarbon is a

five or six membered, oxygen-containing ring with side
chains. This material was first fractionated in a labo-

ratory distillation column having 60 theoretical plates
85












(when tested with hydrocarbons). The center cut from

this fractionation was further purified by an aseotropic

distillation with n-heptane. The fluorocarbon was then

separated from the hydrocarbon by cooling the azeotrope

to dry ice temperature where liquid phases were found

having very low mutual solubility. The perfluorocyclic

oxide was then freed from the small amount of remaining

n-heptane by redistillation in a 30 theoretical plate

column (when tested with hydrocarbons). A chromatograph
of this purified material revealed only one peak.

2. Perfluoroheptane, C7F16. This material was a
constituent of "Fluorochemical 101" marketed by the Minn-

esota Mining and Manufacturing Company and was purified

by the same procedure as perfluorocyclic oxide. This

purified material also exhibited only one peak when sub-

jected to chromatographic analysis.

3. Perfluorotributyl amine, (C4F9)3N. This material

was the center cut obtained by fractionation of Minne-

sota Mining and Manufacturing Company's "Fluorochemical
N-43" in a 60 theoretical plate column (when tested with

hydrocarbons). Chroastographic analysis indicated that

this material was a mixture of several components, proba-

bly isomers.

4. 1-Hydroperfluoroheptane, C77F15H. This material











87
was prepared in the Fluorine Research Laboratory by

Dr. N. C. Brown by the decarboxylation of the sodium

salt of perfluorooctanoic acid. This material was puri-

fied by simple distillation in a column having 60 theoret-

ical plates (when tested with hydrocarbons).

5. Methyl perfluorooctanoate, C7F15COOCH3. This
material was also prepared by Dr. H. C. Brown from per-

fluorooctanoic acid and was purified by simple distilla-

tion in a 60 theoretical plate column (for hydrocarbons).

II. Thermocouple and Thermometer Calibration

All thermocouples used in this work were the copper-
constantan type. Thermocouple readings were made with a

Leeds and Northrup potentiometer No. 8662 which could be
read to 0.001 millivolt.

1. Thermocouple in two liquid phase still. The

calibration temperatures for this thermocouple were the

ice point and the boiling points of methylcyclohexane at

757.45 and 381.05 pressure. The boiling points of
methylcyclohexane at these pressures were determined from

the Antoine equation given in reference 1. The poten-

tiometer readings (in millivolts) at these temperatures
were used to determine the constants in a three-constant

equation. The calibration data and equation are given

in Table IX.









88
2. Thermocouple in Solubility Cell. This thermo-
couple was calibrated against a thermocouple previously

calibrated by Dr. T. K. Reed of the Fluorine Research

Laboratory having the following calibration equation.

t 0.050 + 24.91e 0.3592.2
The two thermocouples were immersed in a wator bath

and both readings were made at the same temperature.

These millivolt readings are listed in Table IX along

with the bath temperatures calculated from the above

calibration equation. Since the two thermocouple

readings were practically identical, the calibration

equation for the thermocouple in the solubility cell

was taken to be

t Z 0.050 + 24.91e 0.3592e2
3. Thermometer in Temperature Bath. This mercury-

in-glass thermometer was graduated in tenths cf degree

centigrade and could be read to 0.02 C. This ther-

mometer was calibrated against a thermocouple calibrated

by the National Bureau of Standards. The calibration

data are given in Table IX.

Pycnometer Calibration Data and Equations.--The
calibration data for five pycnoneters at several tempera-

tures are tabulated in Table X. The pycnometers were de-

signed by Lipkin (22) and w.wr: essentially U tubes with a











89

bulb in one arm. The arms were capillary tubes provided

with etched graduations.

At a constant temperature each pycnometer was cali-

brated by determining the volumes corresponding to three dif-

ferent liquid heights in the capillary arms. The volume was

related to the total liquid height by the following equation

V = Vo + ah

The constants Vo and a were determined by the method of

least squares.

The volume of a pycnometer at a particular liquid

height was determined from the weight of distilled mercury

occupying the pycnometer and the density of mercury at that

temperature. All weighing were corrected for air buoyancy.

The pycaometers were kept in a constant temperature bath for

approximately thirty minutes before the liquid heights were

read. The constant temperature bath never varied more than

0.050 C. froa the calibration temperature.

Vapor Pressure Measurements.*-The vapor pressures of

all of the pure fluorocarbons were determined over a range of

temperatures by measuring the boiling temperature under various

applied pressures. The still shown on Figure 9 and a boiling

point still similar to that described by Quiggle, Tongberg,

and Fenske (31) were used for these measurements. Calibrated

thermocouples were used for temperature readings. The stills











90

were connected to a closed system containing a mercury
manometer which could be read to 0.10 am by means of a
cathetometer. The experimental data are reported in Table

XI and log p is plotted versus 1/T in Figure 1.











11 A AF 4 A^ A* A
#-A
U A f-IQ 6r4Cf P-4C4 r4 ri) u4<
94 %woe

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M6 "4 m .
1 eg a 0 0 .
0

14 *-t tc o .
j ^' *I ." 8 ft
2 4


^*'B 8^ >^ti <(^ ~ i A
54 4 !M e g 8
+f t % a o
S. *




| 4 11043 8 2 8
^-. H .
00 i 0 "1 0 0


cc0
&r go 5 0 0. 0



m M 0. 0 0.



8 -^ i
00 0 p4 r(0 0
f I
'4"I




i~it.. 0. C'
440 0
sd Owd
i 0r 0 0 S m
i~ 00 3*4 1
j~ --- ff i -dca --- d__-'





____ a & nsa Aug



91