Upper and Lower Critical Solution Temperatures in the 3- Polystyrene(3) Cosolvent System Acetone( 1) + Diethyl Ether(2) BY JOHN M. G. COWE* AND IAIN J. MCEWEN Chemistry Department, University of Stirling, Stirling, Scotland Received 1 1 th July, 1973 Phase diagrams for different molecular weight fractions of polystyrene in the mixed solvent system acetone+ diethyl ether have been obtained. The system shows a variation of upper and lower critical solution temperatures with solvent composition which indicates the cosolvent nature of the mixed solvent. No solvent composition is found which can dissolve high molecular weight poly- styrene (M> lo6). The separation of critical solution temperatures can be predicted by the Prigogine theory of polymer solution thermodynamics, but not the absolute values.Phase separation, which occurs when a polymer solution is cooled below the well known upper critical solution temperature (UCST), has been the subject of extensive study; UCST phenomena being widely employed as the basis of polymer fraction- ation. The opposite effect, that of phase separation on heating a polymer solution, has received much less attention. This second separation of a polymer solution into two liquid phases is associated with the large difference in thermal expansions of polymer and solvent and should, in principle, be observed for all non-polar polymer +solvent systems near the critical temperature of the solvent. The minimum in the coexistence curve occurring at these temperatures is termed the lower critical solution temperature (LCST).The polymer + solvent systems polystyrene + acetone and polystyrene + diethyl ether have been studied by Patterson and coworkers.2 Both solvents are compara- tively " poor " in that they dissolve only low molecular weight polystyrene fractions. The effect of this is to cause the UCST and LCST to be separated by a relatively small temperature range. As the molecular weight of the polymer is increased, the range of complete polymer-solvent miscibility decreases, i.e., the UCST is raised and the LCST is lowered. At a certain molecular weight the UCST and LCST coalesce, so that the two regions of immiscibility merge, giving an " hour-glass " shaped phase diagram. Mixtures of relatively poor solvents can, in some cases, produce enhanced solvent power.When this happens the mixed solvent is said to exhibit a synergistic effect. The enhancement of solubility may be detected by a study of the limiting viscosity number or the second virial coefficient measured as a function of solvent composition at a particular ternperat~re.~ Alternatively, a more extensive study of the solubility of a polymer in the mixed solvent may be carried out which illustrates more fully the behaviour as a function of both temperature and solvent composition. In this paper we have examined the phase equilibria for several polystyrene fractions (component 3) in the mixed solvent acetone (component l)+diethyl ether (component 2). The variation of UCST and LCST with solvent composition reflects the cosolvent behav- iour of acetone +ether mixtures and establishes the limits of solution in the system.171172 CRITICAL SOLUTION TEMPERATURE An attempt to predict both UCST and LCST using the Prigogine-Flory theory of polymer solution^,^ as developed by Patterson and coworker^,^ has been made and the results assessed. EXPERIMENTAL The polystyrene samples used were obtained from the Pressure Chemical Co. who quote M,/M, ratios of less than 1-06. The solvents used were best grade and were fractionally distilled before use. UCST and LCST were estimated from cloud-point curves. These were determined optically in thick-walled Pyrex tubes (i.d. = 5 mm) essentially as described previously.6 For a true monodisperse sample the maxima and minima of the cloud point curves can be taken to represent, respectively, the UCST and LCST for the polymer.It is known that polydispersity displaces the critical point to higher polymer concentration ’ ; however, no indication of displacement, which would result in a point of inflexion in the cloud-point curve, was observed throughout this study. Accordingly we have taken the CST as the turning points of the coexistence curves. RESULTS Typical cloud-point curves for the system are shown in fig. 1. In pure acetone, polystyrene fraction M, = 20 400 gives an hour-glass phase diagram which is almost identical to that obtained by Patterson and coworkers for a 19 800 fraction (fig. lA, curve a). At temperatures and compositions inside the hour-glass a two phase region exists where acetone and polystyrene are immiscible. On addition of ether to solutions of polystyrene in acetone ($1 = 0.95) the phase diagram opens out to form two regions of immiscibility separated by a continuous one phase region; both UCST and LCST can now be identified.The effect of increasing the ether content of the mixed solvent in the range 41 = 0.91 to 41 = 0.67 leads to further separation of the UCST and LCST as shown by curves c and din fig. 1A and 1B. This behaviour is also observed in the single solvent acetone but by using polymer fractions of decreasing molecular weight. At compositions beyond $1 -0.67 there is a tendency for the critical temperatures to begin converging once again. The cloud-point curves for polystyrene M, = 20 400 in pure ether and at 41 = 0.05 are shown in fig. lB, curves e and$ With the next fraction in the series, polystyrene M, = 37 0o0, the UCST and LCST are separated by a single phase region when the solvent composition lies between C#I~ = 0.82 and 0.05.Fig. 1C shows the acetone-rich end of the composition range. At 41 = 0.82 the UCST and LCST have just separated while at 41 = 0.83 the regions of immiscibility have merged to give an hour-glass diagram. The dashed line in this diagram represents an estimate. The two phase nature of this region was established by heating a solution of composition 43 = 0.13 to 320 K ; a homogeneous solution was not obtained. With increasing ether content the cloud-point curves for fraction M,,, = 37 O00 are further separated as can be seen from ourves c and d of fig. 1C whose corresponding UCST have decreased to 250 and 203 K respectively.As fractions of higher molecular weight are used the solvent composition range over which solution can be effected is further decreased. Cloud point curves for polystyrene fraction Mw = 860 000 are shown in fig. 1D. The highest fraction studied (Mw = 2 x lo6) could not be dissolved under any of the possible conditions suggested by fig. 2 in which the CST for all the polystyrene fractions are plotted as a function of solvent composition. (It should be noted that this is not a true phase diagram as the volume fraction of the polymer at the critical temperatures is a functionJ . M. G . COWIE AND I . J . MCEWEN 173 I- l , l 3 I 1 L 43 (C) 0.0 0. I 0.2 0.3 FIG. 1.-A-D. Typical cloud-point curves for the system acetone+ether+polystyrene.+1 =volume fraction acetone in the solvent mixture, 43 = volume fraction polymer in solution. A & B : fraction 20 400; (a) dl = 1.00, (6) 41 = 0.95, (c) +1 = 0.91, (d) +1 = 0.67, (e) 41 = 0.00, (f) +1 = 0.05. C : fraction 37 000; (a) = 0.83, (b) = 0.82, (c) +1 = 0.71, (d) +l = 0.50. D : fraction 860000; (a) (bl = 0.30, (6) 41 == 0.33, (c) $1 = 0.38.174 CRITICAL SOLUTION TEMPERATURE of both M, and solvent composition.) The resulting set of contours represents the variation of CST with solvent composition and defines the regions of solubility of polystyrene in the liquid mixtures. It can be seen that high molecular weights will not dissolve in any composition of the mixed solvent. 0 0.5 I #2 FIG. 2.-Plots of UCST and LCST against 42 for all fractions.d2 = volume fraction ether in solvent mixture. (a) Fraction 20 400, (6) fraction 37 OOO, (c) fraction 110 OOO, ( d ) fraction 267 000, (e) estimated curve for fraction 411 000, (f) fraction 860 000. FIG. 3.-UCST and LCST, taken from sections on fig. 2, as a function of r-*. (a) q51 = 0.35, (b) #1 = 0.50, (c) #1 = 0.20. Dashed lines calculated and fitted as described in text. This molecular weight dependence of the polymer solubility in the mixed solvent is illustrated more clearly in fig. 3, where cross-sections at constant solvent composition are plotted as a function of polymer chain length. Table 1 contains the values of UCST and LCST for all the fractions studied, the fraction molecular weights and the solvent compositions.J . M . G. COWIE AND I . J .MCEWEN 175 TABLE 1.-UCST AND LCST FOR POLYSTYRENE FRACTIONS IN THE MIXED SOLVENT ACETONE+ DIETHYL ETHER fraction Mw dl LCST/K UCST/K - - 1 .oo 0.95 367 310 0.91 375 292 0.83 383 261 0.67 386 219 0.20 362 187 0.09 345 197 0.05 333 210 0.00 316 230 20400 0.40 379 189 0.82 326 312 0.71 358 250 37000 0.50 364 203 0.20 341 193 0.05 297 239 fraction Ma 41 LCST/K UCST/K 0.17 295 227 0.30 322 207 llOOO0 0.40 327 213 0.50 328 230 0.60 3 14 266 0.24 290 23 1 0.30 304 222 267000 0.40 3 10 225 0.47 307 239 0.50 301 - 411000 0.31 291 233 0.30 268 248 86OOOO 0.33 275 245 0.38 274 252 DISCUSSION To date, only one publication has dealt with both UCST and LCST in a quasi- ternary system.8 The system studied was polystyrene disrolved in solvent + non- solvent mixtures and points of similarity can be seen.Hour-glass shaped phase diagrams were obtained and the separation of UCST and LCST increased with improving solvent power, The system acetone( 1) + ether(2) +polystyrene(3), although approximating to a solvent + non-solvent system at low molecular weights, is essen- tially one of two poor solvents. The behaviour of the cloud point curves bears some resemblance to that reported by Wolf et aL8 but is due to the cosolvent nature of the mixtures. The cosolvent nature and the separation of UCST and LCST with im- proving solvent power is illustrated in fig. 2. Synergism is indicated by the increase in solubility with any mixture compared with that of the pure components. The " best " solvent mixture, which we may define as the one which will dissolve the highest molecular weight fraction, appears to occur at approximately Analysis of existing vapour pressure data for the binary liquid system acetone+ ether shows that, at mole fraction 0.5 and at 303 K, AGE = 452 Jmol-l, i.e., acetone and ether are moderately incompatible as evidenced by the positive excess free energy of mixing.The cosolvent action which lowers the UCST also leads to a less easily explained raising of the LCST above that expected for a linear interpolation between the two components. The effect can be explained qualitatively if one postulates that the introduction of a polymer chain into the binary solvent environment serves to bind the acetone and ether molecules more strongly by acting as a bridge between these relatively incompatible species. This would have the effect of reducing the expected rate of expansion of the binary liquid pair relative to that of the polymer, thereby raising the LCST. This is in keeping with the nature of cosolvent systems already studied ; qualitatively, the cosolvent effect of acetone +ether mixtures can be ex- plained by a preference for (1-2-3) contacts over (1-2), (1-3) or (2-3) contacts.2 It is interesting to note that high molecular weight polystyrene is soluble, in the appropriate mixture of acetone and ether, only at temperatures well below room = 0.34.176 CRITICAL SOLUTION TEMPERATURE temperature.This somewhat surprising result indicates that use of a mixed solvent for polymer studies should be approached with some caution unless the phase rela- tions for the system have previously been determined.Since attempts to dissolve a polystyrene fraction of MW = 2 x lo6 under the conditions defined by the area inside the contour for the 860 OOO fraction (fig. 2) were not successful, it was concluded that no single mixture of acetone and ether will act as a theta solvent for polystyrene. This is confirmed by plotting, in fig. 3, UCST and LCST against r-i for three sections, each at a constant but different solvent composi- tion, from fig. 2. Here r has been taken as the degree of polymerisation and not the ratio of molar volumes. The data form a curve at each solvent composition such that at high values of r the UCST and LCST coalesce. The curves define the solubil- ity, at a particular q51, as a function of chain length.The single phase region lies within the bounds of the curve, outside this a homogeneous solution cannot form. This behaviour has already been reported for the system secondary cellulose acetate + acetone. The simpler, two parameter, theories of polymer solutions l o do not predict LCST nor do they allow curvature in (CST, r-3) plots. The three parameter Prigogine theory,4* which considers changes in free volume of the Components, has been applied to systems showing LCST. As yet no refinement is available which takes account of quasi-ternary systems. We have made the assumption that the theory, as it stands, can be applied to the liquid mixtures if these are treated as single liquids and have derived the required " average " parameters using the ideal mixing rule.Patterson and Delmas have shown," using the Prigogine theory, that at the point of critical miscibility Here 3c, is the number of external degrees of freedom of the solvent molecule, z is a measure of the difference in free volume of the components of the mixture and is obtained from expansion data, while v2 represents the difference in the chemical nature of the components. v17 the reduced volume of the solvent, may also be ob- tained from expansion data. By solving eqn (1) the variation of CST with molecular weight may be predicted. Values of c1 and T~ for both acetone and ether have been calculated by Patterson et aZ.* from the equation of state data of Flory and Eichinger.12 These values, and those of the temperature reduction parameters, TT, are shown in table 2.We define an average parameter for the solvent as where xi is the parameter for the pure solvent and 4i is the volume fraction. Values of c1v2 are obtained by a fitting technique ; the value of v2 is adjusted SO that the coalescence point of UCST and LCST, predicted by (I), is the same as that indicated by the experimental curves in fig. 3. These procedures are fully described elsewhere. The results of the theoretical calculation are shown by the dashed curves in fig. 3. In each case, the theory has successfully predicted the general shape of the experi- mental curves and has almost exactly reproduced the separation of UCST and LCST. The major weakness is that the theory fails to predict the absolute values of the CST correctly. In order to match the theoretical and experimental curves it is necessary to displace the temperature axes.This procedure has been adopted for other systems.2* Eqn (1) applies at zero or negligible pressure. The cloud point j i = 41x1 +42x2 (2)J. M. G . COWIE AND I . J. MCEWEN 177 curves obtained here are at the vapour pressure of the solvent which may be as high as 10 atm in some cases. However the effect of pressure, which raises LCST and lowers UCST,13 cannot account for the discrepancies between theory and experiment. It may be that some improvement in the absolute predictive power of the theory for the critical temperatures could be obtained if accurate solvent expansion factors at high temperatures were known. No such data are presently available. TABLE 2.-PARAMETERS USED IN THE CALCULATION OF CST system Tf /K C1T2 clY2 x 103 polystyrene+ acetone 7 4349 0.156 17.74 polystyrene+ acetone+ ether, polystyrene+ ether t 4056 0.229 5.55 41 = 0.50 4203 0.190 8.51 5 41 = 0.35 4155 0.202 6.73 5 41 = 0.20 4113 0.21 3 6.06 3 t taken from ref.(2) ; fitted as described in text and in ref. (6). The authors wish to thank S.R.C. for financial support to one of us (I. J. McE.). D. Patterson, Macromolecules, 1969, 2, 672. K. S. Siow, G. Delmas and D. Patterson, Macromolecules, 1972, 5,29. J. M. G. Code and J. T. McCrindle, European Polymer J., 1972,8,1185. (a) I. Prigogine (with the collaboration of V. Mathot and A. Bellman$), The Molecular Theory of Solutions (North-Holland, Amsterdam, 1957) ; (b) P. J. Flow, Disc. F'uduy Soc., 1970,49, 7.D. Patterson, J. Polymer Sci. C, 1969, 16, 3379. J. M. G. Cowie, A. Maconnachie and R. J. Ramon, Macromolecules, 1971, 4, 57. B. A. Wolf, J. W. Breitenbach and H. Senftl, J. Polymer Sci. C, 1970, 31, 345. J. Sameshita, J. Amer. Chem. Soc., 1918, 40, 1482. 6. Delmas and D. Patterson, IUPAC Symposium Macromolecular Chemistry, Toronto, 1968. ' R. Koningsveld, L. A. KIeintjens and A. R. Shultz, J. Polymer Sci. A-2, 1970, 8, 1261. lo H. Tompa, Polymer Solutions (Butterworths, London, 1956). l 2 B. E. Eichinger and P. J. Flory, Trans. Furaday SOC., 1968,68,2035. l3 D. Patterson, Pure Appl. Chem., 1972, 31, 133. Upper and Lower Critical Solution Temperatures in the 3- Polystyrene(3) Cosolvent System Acetone( 1) + Diethyl Ether(2) BY JOHN M. G. COWE* AND IAIN J.MCEWEN Chemistry Department, University of Stirling, Stirling, Scotland Received 1 1 th July, 1973 Phase diagrams for different molecular weight fractions of polystyrene in the mixed solvent system acetone+ diethyl ether have been obtained. The system shows a variation of upper and lower critical solution temperatures with solvent composition which indicates the cosolvent nature of the mixed solvent. No solvent composition is found which can dissolve high molecular weight poly- styrene (M> lo6). The separation of critical solution temperatures can be predicted by the Prigogine theory of polymer solution thermodynamics, but not the absolute values. Phase separation, which occurs when a polymer solution is cooled below the well known upper critical solution temperature (UCST), has been the subject of extensive study; UCST phenomena being widely employed as the basis of polymer fraction- ation.The opposite effect, that of phase separation on heating a polymer solution, has received much less attention. This second separation of a polymer solution into two liquid phases is associated with the large difference in thermal expansions of polymer and solvent and should, in principle, be observed for all non-polar polymer +solvent systems near the critical temperature of the solvent. The minimum in the coexistence curve occurring at these temperatures is termed the lower critical solution temperature (LCST). The polymer + solvent systems polystyrene + acetone and polystyrene + diethyl ether have been studied by Patterson and coworkers.2 Both solvents are compara- tively " poor " in that they dissolve only low molecular weight polystyrene fractions.The effect of this is to cause the UCST and LCST to be separated by a relatively small temperature range. As the molecular weight of the polymer is increased, the range of complete polymer-solvent miscibility decreases, i.e., the UCST is raised and the LCST is lowered. At a certain molecular weight the UCST and LCST coalesce, so that the two regions of immiscibility merge, giving an " hour-glass " shaped phase diagram. Mixtures of relatively poor solvents can, in some cases, produce enhanced solvent power. When this happens the mixed solvent is said to exhibit a synergistic effect. The enhancement of solubility may be detected by a study of the limiting viscosity number or the second virial coefficient measured as a function of solvent composition at a particular ternperat~re.~ Alternatively, a more extensive study of the solubility of a polymer in the mixed solvent may be carried out which illustrates more fully the behaviour as a function of both temperature and solvent composition.In this paper we have examined the phase equilibria for several polystyrene fractions (component 3) in the mixed solvent acetone (component l)+diethyl ether (component 2). The variation of UCST and LCST with solvent composition reflects the cosolvent behav- iour of acetone +ether mixtures and establishes the limits of solution in the system. 171172 CRITICAL SOLUTION TEMPERATURE An attempt to predict both UCST and LCST using the Prigogine-Flory theory of polymer solution^,^ as developed by Patterson and coworker^,^ has been made and the results assessed.EXPERIMENTAL The polystyrene samples used were obtained from the Pressure Chemical Co. who quote M,/M, ratios of less than 1-06. The solvents used were best grade and were fractionally distilled before use. UCST and LCST were estimated from cloud-point curves. These were determined optically in thick-walled Pyrex tubes (i.d. = 5 mm) essentially as described previously.6 For a true monodisperse sample the maxima and minima of the cloud point curves can be taken to represent, respectively, the UCST and LCST for the polymer. It is known that polydispersity displaces the critical point to higher polymer concentration ’ ; however, no indication of displacement, which would result in a point of inflexion in the cloud-point curve, was observed throughout this study.Accordingly we have taken the CST as the turning points of the coexistence curves. RESULTS Typical cloud-point curves for the system are shown in fig. 1. In pure acetone, polystyrene fraction M, = 20 400 gives an hour-glass phase diagram which is almost identical to that obtained by Patterson and coworkers for a 19 800 fraction (fig. lA, curve a). At temperatures and compositions inside the hour-glass a two phase region exists where acetone and polystyrene are immiscible. On addition of ether to solutions of polystyrene in acetone ($1 = 0.95) the phase diagram opens out to form two regions of immiscibility separated by a continuous one phase region; both UCST and LCST can now be identified.The effect of increasing the ether content of the mixed solvent in the range 41 = 0.91 to 41 = 0.67 leads to further separation of the UCST and LCST as shown by curves c and din fig. 1A and 1B. This behaviour is also observed in the single solvent acetone but by using polymer fractions of decreasing molecular weight. At compositions beyond $1 -0.67 there is a tendency for the critical temperatures to begin converging once again. The cloud-point curves for polystyrene M, = 20 400 in pure ether and at 41 = 0.05 are shown in fig. lB, curves e and$ With the next fraction in the series, polystyrene M, = 37 0o0, the UCST and LCST are separated by a single phase region when the solvent composition lies between C#I~ = 0.82 and 0.05.Fig. 1C shows the acetone-rich end of the composition range. At 41 = 0.82 the UCST and LCST have just separated while at 41 = 0.83 the regions of immiscibility have merged to give an hour-glass diagram. The dashed line in this diagram represents an estimate. The two phase nature of this region was established by heating a solution of composition 43 = 0.13 to 320 K ; a homogeneous solution was not obtained. With increasing ether content the cloud-point curves for fraction M,,, = 37 O00 are further separated as can be seen from ourves c and d of fig. 1C whose corresponding UCST have decreased to 250 and 203 K respectively. As fractions of higher molecular weight are used the solvent composition range over which solution can be effected is further decreased.Cloud point curves for polystyrene fraction Mw = 860 000 are shown in fig. 1D. The highest fraction studied (Mw = 2 x lo6) could not be dissolved under any of the possible conditions suggested by fig. 2 in which the CST for all the polystyrene fractions are plotted as a function of solvent composition. (It should be noted that this is not a true phase diagram as the volume fraction of the polymer at the critical temperatures is a functionJ . M. G . COWIE AND I . J . MCEWEN 173 I- l , l 3 I 1 L 43 (C) 0.0 0. I 0.2 0.3 FIG. 1.-A-D. Typical cloud-point curves for the system acetone+ether+polystyrene. +1 =volume fraction acetone in the solvent mixture, 43 = volume fraction polymer in solution. A & B : fraction 20 400; (a) dl = 1.00, (6) 41 = 0.95, (c) +1 = 0.91, (d) +1 = 0.67, (e) 41 = 0.00, (f) +1 = 0.05.C : fraction 37 000; (a) = 0.83, (b) = 0.82, (c) +1 = 0.71, (d) +l = 0.50. D : fraction 860000; (a) (bl = 0.30, (6) 41 == 0.33, (c) $1 = 0.38.174 CRITICAL SOLUTION TEMPERATURE of both M, and solvent composition.) The resulting set of contours represents the variation of CST with solvent composition and defines the regions of solubility of polystyrene in the liquid mixtures. It can be seen that high molecular weights will not dissolve in any composition of the mixed solvent. 0 0.5 I #2 FIG. 2.-Plots of UCST and LCST against 42 for all fractions. d2 = volume fraction ether in solvent mixture. (a) Fraction 20 400, (6) fraction 37 OOO, (c) fraction 110 OOO, ( d ) fraction 267 000, (e) estimated curve for fraction 411 000, (f) fraction 860 000. FIG.3.-UCST and LCST, taken from sections on fig. 2, as a function of r-*. (a) q51 = 0.35, (b) #1 = 0.50, (c) #1 = 0.20. Dashed lines calculated and fitted as described in text. This molecular weight dependence of the polymer solubility in the mixed solvent is illustrated more clearly in fig. 3, where cross-sections at constant solvent composition are plotted as a function of polymer chain length. Table 1 contains the values of UCST and LCST for all the fractions studied, the fraction molecular weights and the solvent compositions.J . M . G. COWIE AND I . J . MCEWEN 175 TABLE 1.-UCST AND LCST FOR POLYSTYRENE FRACTIONS IN THE MIXED SOLVENT ACETONE+ DIETHYL ETHER fraction Mw dl LCST/K UCST/K - - 1 .oo 0.95 367 310 0.91 375 292 0.83 383 261 0.67 386 219 0.20 362 187 0.09 345 197 0.05 333 210 0.00 316 230 20400 0.40 379 189 0.82 326 312 0.71 358 250 37000 0.50 364 203 0.20 341 193 0.05 297 239 fraction Ma 41 LCST/K UCST/K 0.17 295 227 0.30 322 207 llOOO0 0.40 327 213 0.50 328 230 0.60 3 14 266 0.24 290 23 1 0.30 304 222 267000 0.40 3 10 225 0.47 307 239 0.50 301 - 411000 0.31 291 233 0.30 268 248 86OOOO 0.33 275 245 0.38 274 252 DISCUSSION To date, only one publication has dealt with both UCST and LCST in a quasi- ternary system.8 The system studied was polystyrene disrolved in solvent + non- solvent mixtures and points of similarity can be seen.Hour-glass shaped phase diagrams were obtained and the separation of UCST and LCST increased with improving solvent power, The system acetone( 1) + ether(2) +polystyrene(3), although approximating to a solvent + non-solvent system at low molecular weights, is essen- tially one of two poor solvents.The behaviour of the cloud point curves bears some resemblance to that reported by Wolf et aL8 but is due to the cosolvent nature of the mixtures. The cosolvent nature and the separation of UCST and LCST with im- proving solvent power is illustrated in fig. 2. Synergism is indicated by the increase in solubility with any mixture compared with that of the pure components. The " best " solvent mixture, which we may define as the one which will dissolve the highest molecular weight fraction, appears to occur at approximately Analysis of existing vapour pressure data for the binary liquid system acetone+ ether shows that, at mole fraction 0.5 and at 303 K, AGE = 452 Jmol-l, i.e., acetone and ether are moderately incompatible as evidenced by the positive excess free energy of mixing.The cosolvent action which lowers the UCST also leads to a less easily explained raising of the LCST above that expected for a linear interpolation between the two components. The effect can be explained qualitatively if one postulates that the introduction of a polymer chain into the binary solvent environment serves to bind the acetone and ether molecules more strongly by acting as a bridge between these relatively incompatible species. This would have the effect of reducing the expected rate of expansion of the binary liquid pair relative to that of the polymer, thereby raising the LCST.This is in keeping with the nature of cosolvent systems already studied ; qualitatively, the cosolvent effect of acetone +ether mixtures can be ex- plained by a preference for (1-2-3) contacts over (1-2), (1-3) or (2-3) contacts.2 It is interesting to note that high molecular weight polystyrene is soluble, in the appropriate mixture of acetone and ether, only at temperatures well below room = 0.34.176 CRITICAL SOLUTION TEMPERATURE temperature. This somewhat surprising result indicates that use of a mixed solvent for polymer studies should be approached with some caution unless the phase rela- tions for the system have previously been determined. Since attempts to dissolve a polystyrene fraction of MW = 2 x lo6 under the conditions defined by the area inside the contour for the 860 OOO fraction (fig.2) were not successful, it was concluded that no single mixture of acetone and ether will act as a theta solvent for polystyrene. This is confirmed by plotting, in fig. 3, UCST and LCST against r-i for three sections, each at a constant but different solvent composi- tion, from fig. 2. Here r has been taken as the degree of polymerisation and not the ratio of molar volumes. The data form a curve at each solvent composition such that at high values of r the UCST and LCST coalesce. The curves define the solubil- ity, at a particular q51, as a function of chain length. The single phase region lies within the bounds of the curve, outside this a homogeneous solution cannot form. This behaviour has already been reported for the system secondary cellulose acetate + acetone.The simpler, two parameter, theories of polymer solutions l o do not predict LCST nor do they allow curvature in (CST, r-3) plots. The three parameter Prigogine theory,4* which considers changes in free volume of the Components, has been applied to systems showing LCST. As yet no refinement is available which takes account of quasi-ternary systems. We have made the assumption that the theory, as it stands, can be applied to the liquid mixtures if these are treated as single liquids and have derived the required " average " parameters using the ideal mixing rule. Patterson and Delmas have shown," using the Prigogine theory, that at the point of critical miscibility Here 3c, is the number of external degrees of freedom of the solvent molecule, z is a measure of the difference in free volume of the components of the mixture and is obtained from expansion data, while v2 represents the difference in the chemical nature of the components.v17 the reduced volume of the solvent, may also be ob- tained from expansion data. By solving eqn (1) the variation of CST with molecular weight may be predicted. Values of c1 and T~ for both acetone and ether have been calculated by Patterson et aZ.* from the equation of state data of Flory and Eichinger.12 These values, and those of the temperature reduction parameters, TT, are shown in table 2. We define an average parameter for the solvent as where xi is the parameter for the pure solvent and 4i is the volume fraction.Values of c1v2 are obtained by a fitting technique ; the value of v2 is adjusted SO that the coalescence point of UCST and LCST, predicted by (I), is the same as that indicated by the experimental curves in fig. 3. These procedures are fully described elsewhere. The results of the theoretical calculation are shown by the dashed curves in fig. 3. In each case, the theory has successfully predicted the general shape of the experi- mental curves and has almost exactly reproduced the separation of UCST and LCST. The major weakness is that the theory fails to predict the absolute values of the CST correctly. In order to match the theoretical and experimental curves it is necessary to displace the temperature axes. This procedure has been adopted for other systems.2* Eqn (1) applies at zero or negligible pressure.The cloud point j i = 41x1 +42x2 (2)J. M. G . COWIE AND I . J. MCEWEN 177 curves obtained here are at the vapour pressure of the solvent which may be as high as 10 atm in some cases. However the effect of pressure, which raises LCST and lowers UCST,13 cannot account for the discrepancies between theory and experiment. It may be that some improvement in the absolute predictive power of the theory for the critical temperatures could be obtained if accurate solvent expansion factors at high temperatures were known. No such data are presently available. TABLE 2.-PARAMETERS USED IN THE CALCULATION OF CST system Tf /K C1T2 clY2 x 103 polystyrene+ acetone 7 4349 0.156 17.74 polystyrene+ acetone+ ether, polystyrene+ ether t 4056 0.229 5.55 41 = 0.50 4203 0.190 8.51 5 41 = 0.35 4155 0.202 6.73 5 41 = 0.20 4113 0.21 3 6.06 3 t taken from ref. (2) ; fitted as described in text and in ref. (6). The authors wish to thank S.R.C. for financial support to one of us (I. J. McE.). D. Patterson, Macromolecules, 1969, 2, 672. K. S. Siow, G. Delmas and D. Patterson, Macromolecules, 1972, 5,29. J. M. G. Code and J. T. McCrindle, European Polymer J., 1972,8,1185. (a) I. Prigogine (with the collaboration of V. Mathot and A. Bellman$), The Molecular Theory of Solutions (North-Holland, Amsterdam, 1957) ; (b) P. J. Flow, Disc. F'uduy Soc., 1970,49, 7. D. Patterson, J. Polymer Sci. C, 1969, 16, 3379. J. M. G. Cowie, A. Maconnachie and R. J. Ramon, Macromolecules, 1971, 4, 57. B. A. Wolf, J. W. Breitenbach and H. Senftl, J. Polymer Sci. C, 1970, 31, 345. J. Sameshita, J. Amer. Chem. Soc., 1918, 40, 1482. 6. Delmas and D. Patterson, IUPAC Symposium Macromolecular Chemistry, Toronto, 1968. ' R. Koningsveld, L. A. KIeintjens and A. R. Shultz, J. Polymer Sci. A-2, 1970, 8, 1261. lo H. Tompa, Polymer Solutions (Butterworths, London, 1956). l 2 B. E. Eichinger and P. J. Flory, Trans. Furaday SOC., 1968,68,2035. l3 D. Patterson, Pure Appl. Chem., 1972, 31, 133.