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Application of the group-contribution lattice-fluid equation of state to random copolymer-solvent systems
ELSEVIER
Fluid Phase Equilibria 117 (1996) 33-39
Application of the Group-Contribution Lattice-Fluid Equation of State to Random Copolymer-Solvent Systems Byung-Chul Lee and Ronald P. Danner" Center for the Study of Polymer-Solvent Systems, Department of Chemical Engineering, The Pennsylvania State University, University Park, PA 16802
ABSTRACT A group-contribution lattice-fluid equation of state (GCLF-EOS), which is capable of predicting the equilibrium properties of polymer-solvent solutions, has been developed. Group contributions for the interaction energy and reference volume have been developed, based only on the saturated vapor pressures and liquid densities of low molecular weight compounds. For a mixture, group contributions of the binary parameter have been developed from the binary vapor-liquid equilibria of low molecular weight compounds. The model can be applied to the prediction of activity coettieients of solvents in random copolymers. The only input required for the model is the structure of the molecules in terms of their functional groups. No other pure component or mixture properties of the polymer or solvent are needed.
1. INTRODUCTION Calculations involving phase equilibria behavior are required in the design and operation of many polymer processes. A typical problem in polymer processing involves determining the thermodynarnic properties of polymers and solvents. The most important of these thermodynamic properties is how a solvent will distribute itself between the polymer and solvent phases. We describe a group-contribution lattice-fluid equation of state (GCLF-EOS), which is capable of predicting pure component and mixture properties of low and high molecular weight compounds. The GCLF-EOS, originally developed by High and Danner [1-3], is based on the equation of state of Panayiotou and Vera [4,5]. Several modificationson the original GCLF-EOS were made to improve the predictability of the model. New groups were added thus expanding the applicability of the model. More accurate temperature dependencies for the interaction energy and reference volume parameters were developed. All the group contribution values were revised. For a mixture, the group-conlribution mixing rule for the binary parameter was developed. All the group parameters were determined from only pure component and binary mixture equilibrium properties of low molecular weight compounds. In this work, activity coefficients of solvents in random copolymers were predicted using the modified GCLF-EOS.
2. EQUATIONOF STATE Panayiotou and Vera [4,5] have developed a lattice-fluid equation of state which corrects for the nonrandom mixing arising from the interaction energies between molecules. The density of the mixture is allowed to vary by increasing the fraction of holes in the lattice. The development of the equation of state is based on the Guggenheim's
* Author to whom all correspondence should be addressed. 0378-3812/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0378-3812(95)02933-8
34
B.-C. Lee, R.P Danner / Fluid Phase Equilibria 117 (1996)33-39
lattice statistics [6]. A detailed derivation of the equation of state is given elsewhere [1,4,5]. The equation of state for a pure component and a binary mixture in terms of reduced variables is
p_
P _ ~,'h P*
f_
ze*
r T*
_~
~--~ ge*
(2) v"
where ~ ° is the molecular interaction energy of a mixture, v" is the molecular reference volume of a mixture, z is the coordination number which is fixed at 10 and vh is the volume of a lattice site (9.7 5x 10.3 m~/kmol). v" -- E x,v,"
, = Ex,,,
q -- E x , q,
e -- E o ,
¢3)
xi is the mole fraction of component i in a mixture, r i [= vi'/vh] is the number of lattice sites occupied by a molec~e of type i, zoa [= (z-2)ri + 2] is the number of interaction sites available to molecules of type i, and 0 i is the surface area fraction of component i including holes.
zqtNt
qtNt
N h [= rN(¢ - 1)] is the number of holes in the lattice, and N i is the number of molecules of type i in the system. The interaction energy e" for a binary mixture is given by
(s) where t i is the molecular interaction energy of component i and ~t is the molecular surface fraction of component i on a hole-fi'ee basis, given by
"Or =
zq~t
-
xtqt
In Eq. 5, A e is the interchange energy and is defined as : ae
= t u + e~
- 2¢,2
(7)
where t t2 is the cross interaction energy and is expressed by the following mixing rule.
8 n is the binary parameter and i"n is a factor which takes into account the nonrandom mixing between components i andj [7]. i,l~ ffi
2
1 + i l - 401~(1-O-~
(9)
B. C. Lee, R.P. Danner / Fluid Phase Equilibria I 17 (I 996) 33 - 39 -
35
(10)
In the derivation of Eq. 1, it was assumed that the holes mixed randomly, while the molecules mixed nonrandomly. The weight fraction activity coefficient of component i in a mixture, fit [= ai/w.,], is
h,',, = ~ , , - ~ ,
+ ~
+ q,~
~-~ t ~ ,o,- I 1 + q,
r,"
-
T
(11) "
where ~ and wl are the volume and weight fractions of component i in the mixture, respectively, and 0tp is the surface area fraction of pure component i at the same temperature and pressure as the mixture.
3. GROUP-CONTRIBUTION MIXING RULES The equation of state has two adjustable parameters, ei and vs', for each component, and one adjustable parameter, gn, for a binary mixture. To make the model predictive, the group-contribution mixing rules for these three parameters have been developed. The molecular interaction energy between like molecules, ca, is determined from the group interaction energies using the following mixing rule.
• .
= E E e:oe. k
s
.e_r
(12)
where e~ is the group interaction energy between like groups k. The group surface area fractions, Ok¢°, are expressed by
n(OQn
(13)
where r~c° is the number of group k in component i and Qk is the dimensionless surface area parameter of group k, as used in the UNIFAC melhod [8]. The molecular reference volume, vi', is calculated from the group reference volume parameter, IL,, using the following mixing rule.
at'= '~t nPRk
(14)
The two characteristic parameters are functions of temperature. A quadratic form with respect to temperature was found to be adequate to account for the temperature dependencies of the parameters. Thus, e~
=
e~
+
el,t
+
'[-.
R,. = i 7
e~
R,~ T, + ~
(15)
g
where T is the system temperature in kelvins and To was arbitrarily set to 273.15 K.
(16)
B.- C. Lee, R.P. Danner / Fluid Phase Equilibria l 17 (1996) 33-39
36
The binary parameter, 5 n, in Eq. 8 is calculated from the group binary parameter between groups m and n, g.m, from
-- E E
,,..
(17)
where O,,°'° is the surface area fraction of group m in the mixture.
El ,.c*o. - E E .I e, k
(t:
(Is)
s
All the group parameters were determined only from low molecular weight compounds. The group parameters, e~, and R~, were determined in three steps. First, two molecular parameters (ca and vi") for each pure compound were determined by fitting the experimental vapor pressure and liquid density data to the equation of state. The parameters at various temperatures were calculated for a series of alkanes, cycloalkanes, arenes, alkenes, ethers, ketones, and so on. Secondly, the group parameters (ekkand Ro at each temperature were regressed from the molecular parameters, using F_.xlS.12 and 14. Finally, the constants, e~, and Rij,, were determined by fitting the group parameters obtained at the various temperatures to Eqs. 15 and 16. Similarly, the group binary parameters (am) were estimated from experimental binary VLE data of low molecular weight binary mixtures. In this work/J 12was considered to be independent of temperature. The pure component properties were obtained from Daubert and Danner [9] and the binary VLE data were obtained from Gmehling et al. [10]. Tables of the group parameters are given by Lee and Danner [11] and also are available by request. 4. RESULTS A N D DISCUSSION
Lee and Danner [ 11] have shown that the GCLF-EOS can be reliably applied to homopolymer-solvent systems covering a wide range of polymer and solvent types. In this work application of the model to random copolymer-solvent systems has been investigated. The weight fraction activity coefficients (WFAC) at finite concentrations of solvents have been predicted for a number of random copolymer-solvent systems. Copolymer was assumed to be one pseudocomponent and hence molecular parameters for a copolymer were determined by taking the average with respect to the weight fractions of two homopolymers in the copolymer. In these calculations no pure component or mixture properties of the solvent or copolymer are used other than the molecular structures of the solvent and polymer repeating unit. The experimental data were obtained from Danner and High [ 12] and Gupta and Prausnitz [ 13]. Figures 1 and 2 show the predictions of the WFACs for poly(styrene-co-butadiene)-ethylbenzene and poly(styrene-co-butadiene)-cyclohexane systems. The content (weight fraction) of each homopolymer in the copolymer was observed to have an effect on the activity coefficient. Ethylbenzene and cyelohexane were less soluble in polystyrene than in polybutadiene. The WFACs increased as the styrene content in the copolymer increased. In other words, the solubilities of solvents decreased with increasing styrene content of the copolymer. The model gave excellent predictions. Moreover, the model predicted well the effect of homopolymer contents on the activity coefficients. The predictions of the WFACs for poly(ethylene-co-vinyl acetate)-cyclohexane system are shown in Figure 3. The WFACs increased with increasing the content of vinyl acetate in the copolymer. Figure 4 shows the WFAC predictions for three copolymer-solvent systems. The model showed good agreements with the experimental data. Most systems in these eases, however, are nonpolar. The experimental and prediction WFACs of the copolymer were found to lie between those of two homopolymers in the copolymer. Figures 5 and 6 show the predictions of WFACs of chloroform and acetone in poly(styrene-co-butadiene). The WFACs for the homopolymer systems are also included. The styrene content did not affect the experimental activity coefficients in either of these systems. The model predicted reasonable behavior with styrene content in the case of chloroform, but underpredieted the WFACs for the acetone system.
37
B.-C. Lee, R.P. Danner / Fluid Phase Equilibria 117 (1996) 33-39
5
~,
0
30% styrene
- O-
45% styrene
E
•~ - -
o
0 - oc-
77% styrene
0 ¢n
> 0 U)
o
0
0 ,¢,
0 <: LL
U.
.
1
.
.
0.0
.
.
.
0.2 Weight
.
0.4
0.6
Fraction
0.8
~\
N
"X[I~
0.2 Weight
Figure 2.
&
e-
>
5
0
¢/) "0" 0 <: 14.
4
'~Z~
25% vinyl acetate
- ®-
50% vinyl acetate
E
0.2 Weight
Figure 3.
0.4 Fraction
0.6
of Solvent
Prediction of WFAC of cyclohexane in poly(ethylene-co-vinyl acetate). Experimental data are from [13].
1.0
of Solvent
P(VAc&VC) [10% VAc, 1.0E5] Methanol, 353.15K
- A - P(E&VAc) [3.6% VAc, 3.0E4]
~1
"-"
224-Trimethylpentane, 383.15K
0 0 < LL
;.oE,
0.8
0.8
> 0 O3
3
1 0.0
Fraction
0.6
G)
. .w.
7
0.4
Prediction of WFAC of cyclohexane in poly(styrene-co-butadiene). Experimental dAtAare from [13].
I-I
. ~ - - 70% vinyl acetate
;"g
T - 333.15K
3
of Solvent
1"1
23% styrene
-~.-- 45% styrene
1 0.0
1.0
Prediction of WFAC of ethylbenzene in poly(styrene-co-butadiene). Experimental data are from [12].
Figure 1.
5% styrene
1.0
1 0.0
0.2 Weight
Figure 4.
0.4 Fraction
0.6
0.8
1.0
of Solvent
Prediction of WFAC of solvents in copolymers. P(E&VAc)/224-trimethylpentane data are from [12] and the other data from [13].
38
B.-C. Lee, R.P. Danner / Fluid Phase Equilibria 117 (1996)33-39
A
- - E l - -- polybutadiene - -(3- - 23% styrene
•
=
polystyrene
"6
o<
..6
\
..w.
--,~---
A 0
O
03 •"O
/:
45% styrene
polystyrene
(1.57E4, 323.15K)
5
O < It.
1.0Es
polybutadieno
- - 0 - - 23% styrene
A
•,-. r- 7 ID >
- - ~ - - - - 45% styrene
3
....
O e
N~/~/9
T - 333.15K .w-
lees
0.6
0.8
3
1
0.0
0.2
0.4
0.6
0.8
1.0
W e i g h t F r a c t i o n of S o l v e n t Figure 5.
Prediction of WFAC of chloroform in poly(styrene-co-butadiene). Experimental d~ta are from [13].
0.0
0.2
0.4
1.0
W e i g h t F r a c t i o n of S o l v e n t Figure 6.
Prediction of WFAC of acetone in poly(styrene-co-butadiene). Experimental data are from [13].
5. CONCLUSIONS A modified GCLF-EOS has been developed which is capable of predicting accurately the activity coefficients of solvents in polymers. Group contribution parameters have been determined only from the saturated vapor pressures and liquid densities and the binary VLE data of low molecular weight compounds. The model can be applied to the prediction of activity coefficients of solvents in random copolymers. For many systems (certainly for nonpolar ones), the model can predict well the effect of the homopolymer content on the activity coefficients. The only information required for the GCLF-EOS is the structure of the molecules in the polymer and solvent in terms of their functional groups. No other pure component or mixture properties of polymer and solvent are needed. ACKNOWLEDGMENT Authors are grateful to Dr. R.B. Gupta and Professor J.M. Prausnitz for providing their experimental data. This material is based upon work supported by the National Science Foundation under Grant No. CTS-9015427. REFERENCES I.
2. 3.
lV[ S. High, Prediction of Polymer-Solvent Equilibria with a Group Contribution Lattice-Fluid Equation of State, Ph.D. Thesis, The Pennsylvania State University, University Park, PA (1990). M. S. High and R. P. Dauner, Fluid Phase Equilibria, 53,323 (1989). M. S. High and R. P. Danner, AIChE J., 36, 1625 (1990).
B.- C. Lee, R.P. Danner / Fluid Phase Equilibria I 17 (1996) 33-39
.
5. 6. 7. 8. 9. 10. 11. 12. 13.
39
C. Panayiotou and J. H. Vera, Polym. Eng. Sci., 22, 345 (1982). C. Panayiotou and J. H. Vera, Polym. J., 14, 681 (1982). E. A. Guggenheim, Mixtures, Clarendon Press, Oxford (1952). C. Panayiotou and J. H. Vera, Can. J. Chem. Eng., 59, 501 (1981). Aa. FroderLsluad,R. L. Jones and J. M. Prausuitz, AIChE J., 21, 1086 (1975). T. E. Daubert and R. P. Danner, Physical and Thermodynamic Properties of Pure Compounds : Data Compilation, Taylor and Francis, New York (extent 1993). J. Gmehling, et al., Vapor-Liquid Equilibrium Data Collection, DECHEMA Chemistry Data Series, DECHEMA, Frankfurt, Vol. I, (1977-1993). B. -C. Le¢ and R. P. Danner, AIChE J., accepted, March (1995). R. P. Danncr and M. S. High, Handbook of Polymer-Solution Thermodynamics, Design Institute for Physical Property Data, American Institute of Chemical Engineers, New York (1993). R. B. Gupta and J. M. Prauanitz, J. Chem. Eng. Data, submitted, February (1995).
Fluid Phase Equilibria 117 (1996) 33-39
Application of the Group-Contribution Lattice-Fluid Equation of State to Random Copolymer-Solvent Systems Byung-Chul Lee and Ronald P. Danner" Center for the Study of Polymer-Solvent Systems, Department of Chemical Engineering, The Pennsylvania State University, University Park, PA 16802
ABSTRACT A group-contribution lattice-fluid equation of state (GCLF-EOS), which is capable of predicting the equilibrium properties of polymer-solvent solutions, has been developed. Group contributions for the interaction energy and reference volume have been developed, based only on the saturated vapor pressures and liquid densities of low molecular weight compounds. For a mixture, group contributions of the binary parameter have been developed from the binary vapor-liquid equilibria of low molecular weight compounds. The model can be applied to the prediction of activity coettieients of solvents in random copolymers. The only input required for the model is the structure of the molecules in terms of their functional groups. No other pure component or mixture properties of the polymer or solvent are needed.
1. INTRODUCTION Calculations involving phase equilibria behavior are required in the design and operation of many polymer processes. A typical problem in polymer processing involves determining the thermodynarnic properties of polymers and solvents. The most important of these thermodynamic properties is how a solvent will distribute itself between the polymer and solvent phases. We describe a group-contribution lattice-fluid equation of state (GCLF-EOS), which is capable of predicting pure component and mixture properties of low and high molecular weight compounds. The GCLF-EOS, originally developed by High and Danner [1-3], is based on the equation of state of Panayiotou and Vera [4,5]. Several modificationson the original GCLF-EOS were made to improve the predictability of the model. New groups were added thus expanding the applicability of the model. More accurate temperature dependencies for the interaction energy and reference volume parameters were developed. All the group contribution values were revised. For a mixture, the group-conlribution mixing rule for the binary parameter was developed. All the group parameters were determined from only pure component and binary mixture equilibrium properties of low molecular weight compounds. In this work, activity coefficients of solvents in random copolymers were predicted using the modified GCLF-EOS.
2. EQUATIONOF STATE Panayiotou and Vera [4,5] have developed a lattice-fluid equation of state which corrects for the nonrandom mixing arising from the interaction energies between molecules. The density of the mixture is allowed to vary by increasing the fraction of holes in the lattice. The development of the equation of state is based on the Guggenheim's
* Author to whom all correspondence should be addressed. 0378-3812/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0378-3812(95)02933-8
34
B.-C. Lee, R.P Danner / Fluid Phase Equilibria 117 (1996)33-39
lattice statistics [6]. A detailed derivation of the equation of state is given elsewhere [1,4,5]. The equation of state for a pure component and a binary mixture in terms of reduced variables is
p_
P _ ~,'h P*
f_
ze*
r T*
_~
~--~ ge*
(2) v"
where ~ ° is the molecular interaction energy of a mixture, v" is the molecular reference volume of a mixture, z is the coordination number which is fixed at 10 and vh is the volume of a lattice site (9.7 5x 10.3 m~/kmol). v" -- E x,v,"
, = Ex,,,
q -- E x , q,
e -- E o ,
¢3)
xi is the mole fraction of component i in a mixture, r i [= vi'/vh] is the number of lattice sites occupied by a molec~e of type i, zoa [= (z-2)ri + 2] is the number of interaction sites available to molecules of type i, and 0 i is the surface area fraction of component i including holes.
zqtNt
qtNt
N h [= rN(¢ - 1)] is the number of holes in the lattice, and N i is the number of molecules of type i in the system. The interaction energy e" for a binary mixture is given by
(s) where t i is the molecular interaction energy of component i and ~t is the molecular surface fraction of component i on a hole-fi'ee basis, given by
"Or =
zq~t
-
xtqt
In Eq. 5, A e is the interchange energy and is defined as : ae
= t u + e~
- 2¢,2
(7)
where t t2 is the cross interaction energy and is expressed by the following mixing rule.
8 n is the binary parameter and i"n is a factor which takes into account the nonrandom mixing between components i andj [7]. i,l~ ffi
2
1 + i l - 401~(1-O-~
(9)
B. C. Lee, R.P. Danner / Fluid Phase Equilibria I 17 (I 996) 33 - 39 -
35
(10)
In the derivation of Eq. 1, it was assumed that the holes mixed randomly, while the molecules mixed nonrandomly. The weight fraction activity coefficient of component i in a mixture, fit [= ai/w.,], is
h,',, = ~ , , - ~ ,
+ ~
+ q,~
~-~ t ~ ,o,- I 1 + q,
r,"
-
T
(11) "
where ~ and wl are the volume and weight fractions of component i in the mixture, respectively, and 0tp is the surface area fraction of pure component i at the same temperature and pressure as the mixture.
3. GROUP-CONTRIBUTION MIXING RULES The equation of state has two adjustable parameters, ei and vs', for each component, and one adjustable parameter, gn, for a binary mixture. To make the model predictive, the group-contribution mixing rules for these three parameters have been developed. The molecular interaction energy between like molecules, ca, is determined from the group interaction energies using the following mixing rule.
• .
= E E e:oe. k
s
.e_r
(12)
where e~ is the group interaction energy between like groups k. The group surface area fractions, Ok¢°, are expressed by
n(OQn
(13)
where r~c° is the number of group k in component i and Qk is the dimensionless surface area parameter of group k, as used in the UNIFAC melhod [8]. The molecular reference volume, vi', is calculated from the group reference volume parameter, IL,, using the following mixing rule.
at'= '~t nPRk
(14)
The two characteristic parameters are functions of temperature. A quadratic form with respect to temperature was found to be adequate to account for the temperature dependencies of the parameters. Thus, e~
=
e~
+
el,t
+
'[-.
R,. = i 7
e~
R,~ T, + ~
(15)
g
where T is the system temperature in kelvins and To was arbitrarily set to 273.15 K.
(16)
B.- C. Lee, R.P. Danner / Fluid Phase Equilibria l 17 (1996) 33-39
36
The binary parameter, 5 n, in Eq. 8 is calculated from the group binary parameter between groups m and n, g.m, from
-- E E
,,..
(17)
where O,,°'° is the surface area fraction of group m in the mixture.
El ,.c*o. - E E .I e, k
(t:
(Is)
s
All the group parameters were determined only from low molecular weight compounds. The group parameters, e~, and R~, were determined in three steps. First, two molecular parameters (ca and vi") for each pure compound were determined by fitting the experimental vapor pressure and liquid density data to the equation of state. The parameters at various temperatures were calculated for a series of alkanes, cycloalkanes, arenes, alkenes, ethers, ketones, and so on. Secondly, the group parameters (ekkand Ro at each temperature were regressed from the molecular parameters, using F_.xlS.12 and 14. Finally, the constants, e~, and Rij,, were determined by fitting the group parameters obtained at the various temperatures to Eqs. 15 and 16. Similarly, the group binary parameters (am) were estimated from experimental binary VLE data of low molecular weight binary mixtures. In this work/J 12was considered to be independent of temperature. The pure component properties were obtained from Daubert and Danner [9] and the binary VLE data were obtained from Gmehling et al. [10]. Tables of the group parameters are given by Lee and Danner [11] and also are available by request. 4. RESULTS A N D DISCUSSION
Lee and Danner [ 11] have shown that the GCLF-EOS can be reliably applied to homopolymer-solvent systems covering a wide range of polymer and solvent types. In this work application of the model to random copolymer-solvent systems has been investigated. The weight fraction activity coefficients (WFAC) at finite concentrations of solvents have been predicted for a number of random copolymer-solvent systems. Copolymer was assumed to be one pseudocomponent and hence molecular parameters for a copolymer were determined by taking the average with respect to the weight fractions of two homopolymers in the copolymer. In these calculations no pure component or mixture properties of the solvent or copolymer are used other than the molecular structures of the solvent and polymer repeating unit. The experimental data were obtained from Danner and High [ 12] and Gupta and Prausnitz [ 13]. Figures 1 and 2 show the predictions of the WFACs for poly(styrene-co-butadiene)-ethylbenzene and poly(styrene-co-butadiene)-cyclohexane systems. The content (weight fraction) of each homopolymer in the copolymer was observed to have an effect on the activity coefficient. Ethylbenzene and cyelohexane were less soluble in polystyrene than in polybutadiene. The WFACs increased as the styrene content in the copolymer increased. In other words, the solubilities of solvents decreased with increasing styrene content of the copolymer. The model gave excellent predictions. Moreover, the model predicted well the effect of homopolymer contents on the activity coefficients. The predictions of the WFACs for poly(ethylene-co-vinyl acetate)-cyclohexane system are shown in Figure 3. The WFACs increased with increasing the content of vinyl acetate in the copolymer. Figure 4 shows the WFAC predictions for three copolymer-solvent systems. The model showed good agreements with the experimental data. Most systems in these eases, however, are nonpolar. The experimental and prediction WFACs of the copolymer were found to lie between those of two homopolymers in the copolymer. Figures 5 and 6 show the predictions of WFACs of chloroform and acetone in poly(styrene-co-butadiene). The WFACs for the homopolymer systems are also included. The styrene content did not affect the experimental activity coefficients in either of these systems. The model predicted reasonable behavior with styrene content in the case of chloroform, but underpredieted the WFACs for the acetone system.
37
B.-C. Lee, R.P. Danner / Fluid Phase Equilibria 117 (1996) 33-39
5
~,
0
30% styrene
- O-
45% styrene
E
•~ - -
o
0 - oc-
77% styrene
0 ¢n
> 0 U)
o
0
0 ,¢,
0 <: LL
U.
.
1
.
.
0.0
.
.
.
0.2 Weight
.
0.4
0.6
Fraction
0.8
~\
N
"X[I~
0.2 Weight
Figure 2.
&
e-
>
5
0
¢/) "0" 0 <: 14.
4
'~Z~
25% vinyl acetate
- ®-
50% vinyl acetate
E
0.2 Weight
Figure 3.
0.4 Fraction
0.6
of Solvent
Prediction of WFAC of cyclohexane in poly(ethylene-co-vinyl acetate). Experimental data are from [13].
1.0
of Solvent
P(VAc&VC) [10% VAc, 1.0E5] Methanol, 353.15K
- A - P(E&VAc) [3.6% VAc, 3.0E4]
~1
"-"
224-Trimethylpentane, 383.15K
0 0 < LL
;.oE,
0.8
0.8
> 0 O3
3
1 0.0
Fraction
0.6
G)
. .w.
7
0.4
Prediction of WFAC of cyclohexane in poly(styrene-co-butadiene). Experimental dAtAare from [13].
I-I
. ~ - - 70% vinyl acetate
;"g
T - 333.15K
3
of Solvent
1"1
23% styrene
-~.-- 45% styrene
1 0.0
1.0
Prediction of WFAC of ethylbenzene in poly(styrene-co-butadiene). Experimental data are from [12].
Figure 1.
5% styrene
1.0
1 0.0
0.2 Weight
Figure 4.
0.4 Fraction
0.6
0.8
1.0
of Solvent
Prediction of WFAC of solvents in copolymers. P(E&VAc)/224-trimethylpentane data are from [12] and the other data from [13].
38
B.-C. Lee, R.P. Danner / Fluid Phase Equilibria 117 (1996)33-39
A
- - E l - -- polybutadiene - -(3- - 23% styrene
•
=
polystyrene
"6
o<
..6
\
..w.
--,~---
A 0
O
03 •"O
/:
45% styrene
polystyrene
(1.57E4, 323.15K)
5
O < It.
1.0Es
polybutadieno
- - 0 - - 23% styrene
A
•,-. r- 7 ID >
- - ~ - - - - 45% styrene
3
....
O e
N~/~/9
T - 333.15K .w-
lees
0.6
0.8
3
1
0.0
0.2
0.4
0.6
0.8
1.0
W e i g h t F r a c t i o n of S o l v e n t Figure 5.
Prediction of WFAC of chloroform in poly(styrene-co-butadiene). Experimental d~ta are from [13].
0.0
0.2
0.4
1.0
W e i g h t F r a c t i o n of S o l v e n t Figure 6.
Prediction of WFAC of acetone in poly(styrene-co-butadiene). Experimental data are from [13].
5. CONCLUSIONS A modified GCLF-EOS has been developed which is capable of predicting accurately the activity coefficients of solvents in polymers. Group contribution parameters have been determined only from the saturated vapor pressures and liquid densities and the binary VLE data of low molecular weight compounds. The model can be applied to the prediction of activity coefficients of solvents in random copolymers. For many systems (certainly for nonpolar ones), the model can predict well the effect of the homopolymer content on the activity coefficients. The only information required for the GCLF-EOS is the structure of the molecules in the polymer and solvent in terms of their functional groups. No other pure component or mixture properties of polymer and solvent are needed. ACKNOWLEDGMENT Authors are grateful to Dr. R.B. Gupta and Professor J.M. Prausnitz for providing their experimental data. This material is based upon work supported by the National Science Foundation under Grant No. CTS-9015427. REFERENCES I.
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