J. Phys. Chem. 1995,99, 10261- 10266
10261
Equation of State of Hydrogen-Bonded Polymer Solutions: Poly(4-hydroxystyrene) Ethanol and Tetrahydrofuran
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Aurora Compostizo,* Susana M. Cancho, Ramon G. Rubio, and Amalia Crespo Colin Departamento de Quimica Fisica, Facultad de Ciencias Quimicas, Universidad Complutense, 28040 Madrid, Spain Received: August 8, 1994; In Final Form: April 5, 1995@
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We have measured the equation of state surface for the mixtures poly(4-hydroxystyrene) ethanol, and tetrahydrofuran below 40 MPa. The results obey a superposition principle that makes it possible to build a master curve once the p-V-T surface is known at a given pressure. The master curve depends on a single system-dependent parameter that, for the two systems studied, takes almost the same value. The results have been analyzed with a lattice fluid model that includes the existence of hydrogen bonds. Even though the model describes the composition dependence of the excess volume, it underestimates the pressure dependence of the density. While the inclusion of hydrogen bonds in the model has a negligible influence on the predictions for the system with tetrahydrofuran, it improves significantly the predictions for the system with ethanol.
I. Introduction The phase behavior of polymer-solvent systems is distinctly different from that of ordinary liquid mixtures.’ The existence of a lower critical solution temperature (LCST) even for nonpolar systems underlines the importance of the so-called equation of state or free volume effects in this type of system.2 The existence of strong or oriented interactions from hydrogenbonding or other specific interactions can lead to more complex phase diagrams in which miscibility loops or hourglass coexistence curves can arise. The interest in this type of systems has increased in recent years due to the importance of polymer blends and the fact that in most blends miscibility is obtained only when specific interactions are present. For ordinary mixtures there exist theoretical tools that allow one to deal with specific interactions in a rather satisfactory ~ a y . ~In . polymer ~ systems, the chain character of the components linked by hydrogen bonds leads to association complexes that are three dimensional in character, and the degree of theoretical development is less satisfactory. In general, two main approaches have been followed: the use of association models or combinatorial methods. Within the first approach Coleman and Painter’s group5 has developed a semiempirical extension of Flory’s rigid lattice approach of consecutive linear association. Hu et and Panayiotou and Sanchez7 have developed combinatorial models in which the specific interactions and the spherical symmetric van der Waals interactions make well-differentiated contributions to the partition function, as well as to the equation of state. Painter et aL8 have shown that their association model leads to identical results identical with the combinatorial results of Panayiotou and Sanchez.’ In a recent paper vapor-liquid equilibrium data for poly(4hydroxystyrene) (P4HS) poly(viny1 acetate) (PVAc) acetone, and for p-V-T data for P4HS and a 5050 P4HS f PVAc blend have been pre~ented.~ It was found that the model of Panayiotou and Sanchez7 gave a quantitative description of the vapor-liquid equilibrium data, leading to a significant improvement with respect to the bare lattice model without specific interactions.I0 However, the improvement was not so evident with respect for the p-V-T surface of the blend. The
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@Abstract published in Advance ACS Abstracts, June 1, 1995.
0022-365419512099- 10261$09.00/0
same conclusion has been reached for the p-V-T surface of P4HS acetone.” Moreover, the analysis of vapor-liquid equilibrium and heat of mixing data of an extensive set of nonpolymeric mixtures points out that the inclusion of the specific interactions does not always improve the agreement between experimental and calculated results,’* compared to the bare lattice model.l0 Within both theoretical approaches there are two kinds of parameters: some of them are related to the physical interactions and others to the “chemical” or specific ones, the latter defining the equilibrium constants of the specific interactions. In general, the different parameters are correlated, and therefore it is difficult to choose a set of parameters unless experimental data for a wide set of properties are available. This has been already known for years for nonpolymeric systems.I3 Moreover, the equilibrium constants obtained from the best fit of thermodynamic properties usually differ from the values obtained from spectroscopic data.’* In the case of polymeric systems the distribution of hydrogen bonds is very different from that in systems with their low molecular weight analogue^.^ The approximate character of the theoretical models is at the origin of the above discrepancies. As it was pointed out by Stokes’ groupI3 in a study of nonpolymeric fluids, the use of experimental data for different thermophysical and spectroscopic properties, and for systems with similar specific interactions can help in assessing a set of reliable physical and “chemical” interaction parameters for a given set of chemical species. In the present paper we will present an experimental study of the equation of state of P4HS with ethanol (EtOH) and with tetrahydrofuran (THF). The p-V-T data are fundamental to obtain the characteristic parameters of the physical interactions of pure components, as well as to test the mixing rules for the mixtures. For the iystem P4HS EtOH it should, in principle, be possible to characterize the system by some of the interactions that were used in P4HS acetone, the main difference being that now the solvent self associates. The rest of this paper is organized as follows: section I1 briefly describes the experimental part. Section I11 contains the experimental results, which are also discussed in terms of a universal master curve recently proposed; also the effect of pressure upon several excess properties is calculated. In section IV the experimental data are used to assess the capability of a
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0 1995 American Chemical Society
Compostizo et al.
10262 J. Phys. Chem., Vol. 99,No. 25, 1995 TABLE 1: Characteristics of the Fittings of the Experimental Data to Eq 1 W B , x lO-Vkg m-3 Bzkg m-3 K-' B3 x 103kgm-3 K-2 B4 x 10
BS x
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0.70005 0.74083 0.797 13 0.89815 0.97003 1.o
1.1009 1.1351 1.0924 1.0631 1.0106 1.0371
0.693 13 0.74866 0.77397 0.79769 0.85693 1.
0.9805 1 0.96136 0.95322 0.94655 0.92908 1.21153
-0.5824 -0.8828 -0.7348 -0.7600 -0.5710 -0.7983
wEtOH (1 - w)P4HS -3.7116 0.7658 0.8149 -0.6885 - 1.8545 0.7925 -1.7199 0.7920 -4.8404 0.7986 -1.2641 0.8428 wTHF
- 1.0794
theoretical model to describe the results. Finally, section V summarizes the main conclusions. 11. Experimental Section
The p-e-T data have been measured using a modified Anton-Paar model DMA 5 12 high-pressure vibrating tube densitometer. The whole apparatus has been described in detail in a previous work.I4 The strain gauge pressure transducers were calibrated against a dead weight gauge, and the calibration was checked after the experiments on each substance were completed; this allowed the pressure to be known within fO.O1 MPa. The temperature of the U-tube was kept constant within f 0 . 5 mK and monitored with a thermistor placed beside the vibrating tube. The temperature was measured with a quartz thermometer placed in the water bath whose calibration was checked weekly against a Ga melting point standard. The temperature of the whole apparatus (except the electronics) was kept constant to fO.01 K of that of the sample. The densitometer is calibrated with eight pure subtances according to the procedure described elsewhere.', It was also necessary to account for the dependence of the period of vibration upon the viscosity of the sample. Ashcroft et a1.I6 have discussed such a dependence for a low-pressure vibrating tube densimeter; we have followed a similar procedure to cover the viscosity range of our samples using also glycerol as reference. The calibration curve was tested after the experiments on each pure substance were carried out. No hysteresis was found within f 5 x in t, the period of vibration, when measuring at low pressure after the vibrating tube was subjected to a high pressure. Under the conditions described, can be obtained within g cmP3 for the 0.1 5 plMPa 5 40.0 range. EtOH was purchased from Carlo Erba (WE quality) and THF was Fluka (HPLC quality). EtOH was dried over 0.4 nm molecular sieves, and both were used without further purification. The purity of the substances used, estimated by GLC, was better than 99.9%. The agreement of the values of the densities at 0.1 MPa with others reported in the literature is an indirect indication of the purity of both substances. Manipulation of the samples was done under N2 atmosphere. For the mixtures with THF it was necessary to use Teflon O-rings in all the parts in contact with the samples. P4HS was obtained from Polyscience (Mw = 30000). HPLC experiments on dioxane revealed a polydispersity MwIM,, 2. 111. Results and Discussion
More than 486 p-e-T-w experimental data have been obtained for P4HS EtOH over the intervals 298.15 5 T/K 5
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0.4740 0.5521 0.5667 0.5833 0.5681 0.6103
+ (1 - w)P4HS
-0.6425
MPa
0.1032 0.1025 0.1099 0.0880 0.1070 1.0652
0.6995 0.7627 0.8161 0.6901 0.8588 0.8176
B6
x loz/ K-'
a(@)/kgm-3
0.5375 0.5803 0.6241 0.6747 0.6920 0.7028
0.1 0.1 0.08 0.07 0.07 0.09
0.8540
0.08 0.1 0.1 0.1 0.08 0.09
328.15, 0 5 plMPa 5 40, and 0.70 5 w 5 0.97, w being the weight fraction of the solvent. For the system P4HS THF we have obtained over 126 points for T = 298.15 K, 0.69 5 w 5 0.86 and the same pressure range quoted above. We have not made measurements at other temperatures since for w = 0.856 93 the temperature dependence was found to be almost negligible for the interval 298-328 K. The results at each composition were fitted to a generalized Tait equation of the form
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where
eo= B, + B,T + B3? B = B, exp(-B67J
(3)
Bi (i = 1-6) being independent of T and p. Table 1 collects the values of Bi for the different isopleths of the two systems, and the standard deviations of the fits which in general is within the experimental uncertainty. The system P4HS THF has been studied at only one temperature due to the almost negligible temperature effect observed for the mixture in P4HS. Figure 1 shows the effect of pressure upon the specific volume for some isopleths of the system with ethanol. The results for the system with THF are similar. As expected, the effect of pressure is larger as the concentration of solvent increases, reflecting the difference in free volume between polymer and solvent. When compared with the results of P4HS f acetone, one can conclude that, for a given value of w ,the influence of p upon Vis slightly larger in the system with acetone than for those with EtOH or THF which are rather similar. Sanchez et al.17318 have indicated that by choosing adequate variables, it is possible to merge all the p-V-T-w data onto a single curve. This is shown in Figure 2, K T , ~being the isothermal compressibility at zero pressure. The master curve can be described by
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(4)
where 6 is a parameter characteristic of each system. In our systems 6 = 11.44 for P4HS EtOH and 6 = 11.70 for P4HS -t THF, which are slightly different from the values 6 = 10.32 found for P4HS acetone and 6 = 10.09 for P4HS f poly(vinyl acetate)." Equation 4 indicates that once the temperature dependence of e and KT,O at p w 0 are known, the influence of p upon the volume can be characterized by 6. When an average 6 = 11.48 is used for the two mixtures, the residuals (eexp -
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Hydrogen-Bonded Polymer Solutions
J. Phys. Chem., Vol. 99, No. 25, 1995 10263
1.oo
0.99 h
m
a S 0.98 F 0 II
Q
v
>"
+ 0.97
-
>*
298.15
-0
308.15 318.15 328.15
......
m
----
4
A 4
0
OA
A*. A 4 A
4
0
' 4 '
:'A
A
0.96 -
=.
8
A
A
-
w=079713
0
o w=089815
0
w=097003
-
w=l
A
1
0.95
1
1
1
I
p I MPa Figure 1. Pressure dependence of the specific volume for different concentrations and temperatures P4HS for pure P4HS taken from ref 9.
I 0.04
0.03
u"
1
1
I
w TIK A 0 70005 298 15 WEtOH + (l-w)P4HS 097003 29815 0 1 298 15 0 0 69314 298 15 WTHf + (I-w)P~HS 0 085693 29815 X I 298 15
-
I
I
00 V* V0
v
-
+ EtOH. The lines represent the results
P
19
0.02 -
Q
0.01
Q
0.00 1.oo
1.01
1.02
1.03
1.04
PIP0 Figure 2. Master curve for the two systems studied according to Sanchez et al.17,'8Notice that the same characteristic parameter 6 has been used for both mixtures.
gcd)are comparable to those obtained with the full Tait equation
(a figure with the detailed residuals is included in the supplementary material). A similar p-w-T superposition principle can be obtained from the pemrbation theory applied to simple molecular fluids.Ig Huang and O'Connel120have proposed for the bulk modulus B ( = @ K T k B T ) of the system the following expression:
3
(1 - B)/C* =
2
CCa,(Q)'(fY
(5)
i=oj=o
where Q = gV* and P =T*/T, C*, V*, and P are integrals of the direct correlation function, and the a, are universal constants. For binary mixtures there exists one adjustable parameter. The results obtained using eq 5 are completely equivalent to those
10264 J. Phys. Chem., Vol. 99, No. 25, 1995
t
Compostizo et al. 1
1
1
I
1
I
1
1
I
I
0
10
20
30
40
50
0.0-
-
-0.5
-
-1.0
-
-1.5
-
1
I
I
P)
Y c9
E
v)
0 7
X
w
>
-2.0-
I
p / MPa
Figure 3. Effect of pressure upon the excess volume for P4HS
+ EtOH.
0.0
-0.2
-0.4
-0.6
I
I
1
1
1
1
J
0
10
20
30
40
50
p / MPa Figure 4. Effect of pressure upon excess enthalpy and excess Gibbs energy for the system P4HS
shown in Figure 2. Moreover, the results for the present systems and those of P4HS acetone' collapse on the same (1 - B)/ c* vs @V*curve. More recently, Garcia Baonza et aL2' have shown that the combination of h z a n ' s equation22for the thermal expansion coefficient a,,and of Furth's for the spinodal leads to master curve equivalent to eq 4. This model was shown to describe quite accurately the p - V-T results of simple Since it was based in the existence of a high-pressure point at which all the a, vs p curves cross over, the good results of Figure 2 might suggest that such a crosspoint must also exist
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for polymer systems. Unfortunately the restricted upper limit of our experimental setup does not allow us to test this point for our systems. From the experimental point, the results obtained with eq 4 are interesting since they mean that once the temperature dependence of and KT are well characterized at zero pressure, a small set of parameters (one in Sanchez approach, four in Garcia Baonza's one) allows us to describe the pressure dependence of the volumetric properties. Furthermore, Caceres et al.25have shown that derivatives of thep-V-T surface such as C,, can be determined with acceptable accuracy. This would
Hydrogen-Bonded Polymer Solutions
J. Phys. Chem., Vol. 99, No. 25, 1995 10265
TABLE 2. Pure-Component Parameters Characteristic of Physical Interactions Obtained from p-V-T Data and Thermochemical Parameters of Each Type of Hydrogen-Bond Interactions pampa PK ea/g cm-' P4HS THF EtOH
415.3 509.1 365.9 385.9
U
703.4 499.4 597.0 412.3
E"M mol-' S"/J K-' mol-' OH OH (P4HS-P4HS) OH O < (P4HS-THF) OH OH (EtOH-EtOH)
-21.8 -18.4 -25.1
1.262 1.0167 0.8776 0.9013 V"/cm3mol-'
0.0 -4.0 -5.6
-26.5 -12-8 -26.5
Parameters for the case in which hydrogen bonds are considered in pure ethanol. a
be useful in reducing the high pressure experiments necessary for determining the p-V-T surface, However, the situation is far less clear for the case of mixing functions, which are small differences between large numbers, and thus a high precision in p-V-T-w is necessary in order to obtain meaningful excess functions. As 'an example, Figure 3 shows the temperature and pressure dependence of the excess volume for different isopleths for the system with ethanol. The largest influence of p and T is found for the highest polymer concentration and at the lowest pressure, a result similar to that found for previous systems." The large difference in free volume between polymer and solvent can explain the behavior shown. Overall, the qualitative behavior of the system P4HS EtOH is similar to that of P4HS acetone." However, for given p , T, and w the magnitude of the excess volume is rather smaller for the system with ethanol than for that with acetone. The overall sign and magnitude of p depend on the difference in free volume between the components and the difference of the interactions between molecules of the same specie and of different species. The fact that VE < 0 in our systems can be
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understood in terms of the strong hydrogen bonds formed between the hydroxyl groups of P4HS and the carbonyl group of acetone, the ether group of THF or the hydroxyl group of EtOH.5,26The facts that EtOH is already self-associated before mixing and that the mixed specific interactions with P4HS are of the same type as those already existing in P4HS and EtOH can explain that p is smaller in magnitude than in P4HS acetone. This also explains that the system with THF shows p very similar to the one with acetone. From eqs 1-3 we have calculated the effect of pressure upon the excess enthalpy HE, and the excess Gibbs energy @; the results are shown in Figure 4 only for P4HS EtOH, since the effect upon for P4HS THF is like the one previously reported for P4HS acetone.' For the system with ethanol, the influence of p upon @ and @ is rather similar to that of the other systems for very diluted mixtures. However, for mixtures more concentrated in P4HS m takes small positive values except at the highest pressures, while for P4HS acetone @ decreases continuously with increasing p and takes almost the same value as AGE. These differences reflect the different values in p in both systems, as well as the fact that the absolute value of ( a ~ / % " j pdecreases ,, with increasing p more for P4HS EtOH than for P4HS acetone.
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IV. Comparison with a Lattice-Fluid Model The complete formulation for the lattice-fluid model incorporating hydrogen bonds has been given by Panayiotou and Sanchez.' We will only repeat here the equation of state and the equations that allow to incorporate the hydrogen bonds into it. The equation of state reads
p
+ p 2 + ?jln(l
- p ) + p ( 1 - IF)]
=o
(6)
where the reduced variables are defined by p =p/p*, = T P ,
1 .oo
1.02
0.99
1.01
0.98
1.oo
0.97
0.99
0.96
0.98
h
m n Y
0 II
Q
W
>a \
>a
0.95
0.97 0
10
20
30
40
p / MPa Figure 5. Comparison of the experimental pressure dependence of the specific volume with the predictions of the lattice-fluid model. LF refers to the model without hydrogen bonds, and HB to the case in which they are included.
Compostizo et al.
10266 J. Phys. Chem., Vol. 99, No. 25, 1995
and @ = @V*, p*, P,and V* being substance-dependent parameters that define the van der Waals-type interactions between molecules. The average number of segments per molecule, 7, is defined by 1Tr = l/r - vH
(7)
where V H is the fraction of hydrogen bonds in the system, and r has the same meaning as in the original lattice-fluid model of Lacombe and Sanchez.Io For the self-associated P4HS homopolymer
rvH = 1 - { [A(A
+ 4)]"2 - A}/2
(8)
with
A = r/Q exp(G",,/RT)
(9)
S022, and VO22 being characteristic of the -OH-OH hydrogen bonds in the P4HS homopolymer. For the case of pure ethanol similar equations hold, the difference being the number of proton-acceptor groups per molecule: a for P4HS and 1 for ethanol. For the binary mixture P4HS(2) THF(1)
E022,
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+ ax2 4-A[@, + ax2 -I-A)2 - 4 a x , ~ ~ ] l ' ~ ] /(12 1) In the case of P4HS + EtOH the situation is slightly more
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of other properties such as the chemical potential of P4HS acetone was highly improved when the hydrogen bonds were incl~ded.~
V. Conclusions Thep-V-T-w surfaces of P4HS EtOH and THF have been obtained for pressures below 40 MPa. The results follow a master curve recently proposed by Sanchez et al.'7~'8Moreover, once the temperature and composition dependence of the density is known at one pressure, it is possible to describe its pressure dependence using a single parameter for both systems. The excess volumes have been successfully correlated using a lattice-fluid model. The binary parameter characteristic of the van der Waals-like interactions seems to be more meaningful when hydrogen bonds are included in the model. Even though for the system with THF the predictions of the model are almost identical irrespective of the inclusion of hydrogen bonds or not, for the system with EtOH the hydrogen-bond contributions improve significantly the prediction of the compressibility of the system. Nevertheless, the model, in any of the two versions, underestimates the influence of the pressure upon the specific volume.
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Acknowledgment. This work was supported in part by DGICYT under Grant PB92-0200-C. References and Notes
rvH = {xl
complex since there is self-association in both pure components and also cross-association. This leads to a system of coupled equations:
with Nd(l)= Na(l) = N I , and N,$2) = N J 2 ) = dN2, d being the number of hydroxyl groups per polymer molecule. In eq 12 i, j , m, n = 1-2, and the Au are defined in a manner similar to that for A in eq 8, with GO12 = G021. As in the system P4HS THF the system of eq 12 has to be solved coupled to the equation of state. Table 2 shows the pure-component parameters used for characterizing both the physical and the hydrogenbond interactions. The binary parameter of the model 4 has been fitted in order to reproduce the composition dependence of the excess volume at p = 0.1 MPa. We have performed the calculations both with the full model and with the lattice model without hydrogen bonds ( V H = 0). Figure 5 shows that despite both models understimating the effect of pressure upon specific volume, the inclusion of hydrogen bond contributions led to better predictions for the mixture with self-associating solvent. The same conclusions are reached at with respect to the composition dependence of the excess volume. Moreover, it must be remarked that in order to obtain the fits shown in Figure 5, the bare lattice model leads to a binary adjustable parameter that differs from unity significantly more than the model that includes the chemical contribution. Since this means that for the simplest version of the model the binary parameter that characterizes the physical interactions is absorbing part of the effects of hydrogen bonds, this may explain why the prediction
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(1) Kleintjens, L. A. Fluid Phase Equilib. 1989, 33, 289. (2) Siow, V. S.; Delmas, G.; Patterson, D. Macromolecules 1972, 5, 29. (3) Chapman, W. G.; Gubbins, K. E.; Jackson, G.; Radosz, M. Ind. Eng. Chem. Res. 1990, 29, 1709. (4) Huang, S. H.; Radosz, M. lnd. Eng. Chem. Res. 1991, 30, 1994. ( 5 ) Coleman, M. M.; Graf, J. F.; Painter, P. C. Specific Interactions and the Miscibility of Polymer Blends; Technomic: Lancaster, PA, 1991. (6) Hu, Y.; Ying, X.; Wu, D. T.; Prausnitz, J. M. Fluid Phase Equilibria 1993, 83, 289. (7) Panayiotou, C.; Sanchez, I. C. J. Phys. Chem. 1991, 95, 10090. (8) Painter, P. C.; Veytsman, B.; Coleman, M. M. J. Polym. Sci., Part A: Polym. Chem. 1994, 32, 1189. (9) Luengo, G.; Rubio, R. G.; Sanchez, I. C.; Panayiotou, C. Makromol. Chem. 1994, 145, 104. (10) Lacombe, R.; Sanchez, I. C. Macromolecules 1978, I I , 1145. ( 1 1 ) Compostizo, A.; Cancho, S. M.; Crespo Colin, A,; Rubio, R. G. Macromolecules 1994, 27, 3478. (12) Coto, B. Ph.D. Thesis; Universidad Complutense, Madrid, 1994. (13) Stokes, R. H.; Adamson, M. J. Chem. Sac., Faraday Trans. I1977, 73, 1232. Stokes, R. H.; Adamson, M. J. Chem. Thermodyn. 1976,8, 683. Stokes, R. H.; Marsh, K. N. J. Chem. Thermodyn. 1976, 8, 709. (14) Compostizo, A.; Crespo Colin, A,; Vigil, M. R.; Rubio, R. G.; Diaz Peiia, M. J. Phys. Chem. 1988, 92, 3998. (15) Crespo Colin, A.; Cancho, S. M.; Rubio, R. G.; Compostizo, A. J. Phys. Chem. 1993, 97, 10796. (16) Ashcroft, S. J.; Booker, D. R.; Turner, J. C. R. J. Chem. SOC., Faraday Trans. 1990, 86, 145. (17) Sanchez, I. C.; Cho, J.; Chen, W. J. J. Phys. Chem. 1993,97,6120. (18) Sanchez, I. C.; Cho, J.; Chen, W. J. Macromolecules 1993, 26, 4234. (19) Gubbins, K. E.; O'Connell, J. P. J. Chem. Phys. 1974, 60, 3449. (20) Huang, Y. H.; O'Connell, J. P. Fluid Phase Equilib. 1987, 37, 75. (21) Garcia Baonza, V.; Caceres Alonso, M.; Nuiiez Delgado, J. J. Phys. Chem. 1994, 98, 4955. (22) Pruzan, Ph. J. Phys. Lett. 1984, 45, 273. (23) Skripov, V. P. Metastable Liquids; Wiley: London. 1984. (24) Rubio, R. G.; Calado, J. C. G.; Clancy, J. C. G.; Streett, W. B. J. Phys. Chem. 1985, 89, 4637. (25) Caceres, M.; Garcia Baonza, V.; Rubio, J. E. F.; Arsuaga, J. M.; Nuiiez, J. Ber. Bunsen-Ges. Phys. Chem. 1994, 98, 563. (26) Sanchis, A,; Prolongo, M. G.; Rubio, R. G.; Masegosa, R. M. Polym. J. 1995, 27, 10. JP942093A
