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Ind. Eng. Chem. Res. 1999, 38, 1172-1173
Comments on the Paper “Empirical Method To Correlate and To Predict the Vapor-Liquid Equilibrium and Liquid-Liquid Equilibrium of Binary Amorphous Polymer Solutions” Attila Imre* and W. Alexander Van Hook Department of Chemistry, University of Tennessee, Knoxville, Tennessee 37996
Sir: In a recent paper1 Vetere proposed empirical equations to predict equilibrium properties of polymer/ small-molecule solutions including the location of the upper critical solution temperature (UCST) for liquidliquid demixing in the (T, r) projection (presumably at the equilibrium vapor pressure of the solution). Here r is the effective polymerization number, r ) V2/V1, where V2 is the molar volume of the polymer and V1 that of the solvent and T is the temperature. Three separate equations were proposed:
(i) for nonpolar polymers in nonpolar noncyclic solvents, T (K) ) 75.0 + 2.53M1 (1 - r-0.5)4
(1)
(ii) for nonpolar polymers in nonpolar cyclic solvents, T (K) ) 162 + 1.77M1(1 - r-0.5)3
(2)
(iii) for mixtures containing both polar and nonpolar compounds T (K) ) 20 + 320.6(1 - r-0.5)/(F2)2
(3)
M1 is the molecular weight of the solvent (g‚mol-1) and r2 the polymer density (g‚cm-3) at 298 K. The validity of the proposed correlating equations was checked with UCST data for 14 different systems selected from the book of Danner and High.2 Although the agreement is satisfactory for these 14 cases, we believe this to be accidental and conclude the Vetere method is not reliable for the prediction of UCSTs of polymer/smallmolecule mixtures. For a wider test of Vetere’s method, we employed UCST data on 43 different polystyrene solutions taken from the paper of van Opstal, Koningsveld, and Kleintjens3 and the review of Imre and Van Hook.4 Polystyrene was chosen for this test because it is the most commonly studied nonpolar polymer solute. As such, it enjoys the most nearly complete liquid-liquid solubility data bank.4 Many fewer data are available for demixing at LCST, and for that reason, we have not checked Vetere’s predictions for LCST demixing. Because that method is also unable to predict the correct M2 dependence,1 we consistently compared eqs 1-3 with experiment using reliable UCST demixing data on solutions * To whom correspondence should be addressed. Permanent address: KFKI Atomic Energy Research Institute, P.O. Box 49, Budapest H1525, Hungary. E-mail:
[email protected].
Figure 1. Experimental and predicted UCST values for polystyrene solutions. The solid line corresponds to full agreement. Symbols: filled circle, polar solvent; empty circle, nonpolar noncyclic solvent; triangle, nonpolar cyclic solvent.
of the highest available M2. Solvent densities (298 K) and molecular weights, r1 and M1, were from CS ChemFinder,5 and r2 ) 1.05 g/cm3 was used as the density of polystyrene. UCSTs calculated from eqs 1-3 are compared with experiment in Table 1 and Figure 1. As is clearly seen in either the table or figure, the differences between experimental and predicted UCSTs are too large to permit the Vetere method to be employed as a predictive tool with any degree of confidence. In most cases the difference is bigger than 100 K, and for only 7 of the 43 solutions is ∆T < 10 K. We conclude that eqs 1-3 cannot be used reliably to predict liquid-liquid equilibrium in polymer solutions. Acknowledgment This work was supported by the U.S. Department of Energy, Division of Material Sciences. Literature Cited (1) Vetere, A. Empirical Method To Correlate and To Predict the Vapor-Liquid Equilibrium and Liquid-Liquid Equilibrium of Binary Amorphous Polymer Solutions. Ind. Eng. Chem. Res. 1998, 37, 2864. (2) Danner, R. P.; High, M. S. Handbook of Polymer Solution Thermodynamics; DIPPR, American Institute of Chemical Engineers: New York, 1993. (3) van Opstal, L.; Koningsveld, R.; Kleintjens, L. A. Description of Partial Miscibility in Chain Molecule Mixtures. Macromolecules 1991, 24, 161.
10.1021/ie980834e CCC: $18.00 © 1999 American Chemical Society Published on Web 12/29/1998
Ind. Eng. Chem. Res., Vol. 38, No. 3, 1999 1173 Table 1. Experimental and Predicted UCST Values for Polystyrene Solutions: ∆T (K) ) UCSTPred (K) - UCSTExptl (K) UCST (K) solvent
M2 × 10-3
M1F1
2700 2700 2700 2700 2700 2700 9 9 9 9 9 9 4 4 4 5500 2700 600 3450 19.8 2050 37 10.3 22 48
77.1 88.1 102.1 102.1 116.2 116.2 74.1 88.2 102.2 130.2 158.3 186.3 214.4 242.4 270.5 100.2 160.2 146.1 116.2 74.1 390.6 74.1 50.1 55.1 75.1
expt
0.932 0.902 0.888 0.872 0.868 0.862 0.810 0.815 0.819 0.826 0.829 0.833 0.823 0.818 0.812 0.963 1.055 1.076 0.878 0.713 0.973 0.917 0.786 0.782 1.045
311 227 191 240 223 281 408 398 398 395 398 402 383 386 391 358 302 310 181 236 285 316 271 364 303
309 309 309 309 309 309 281 278 276 271 267 264 235 230 225 309 309 306 309 289 307 297 287 294 299
-2 83 118 69 86 28 -127 -119 -122 -124 -131 -138 -149 -157 -166 -48 7 -4 128 54 22 -19 16 -70 -4
Nonpolar Noncyclic 72.2 0.626 86.2 0.655 100.2 0.684 114.2 0.703 142.3 0.730 170.3 0.749 212.4 0.768 254.5 0.782
292 318 359 353 361 369 385 404
111 140 190 200 204 216 228 237
-181 -178 -169 -153 -157 -153 -157 -167
Nonpolar Cyclic 70.1 0.745 84.2 0.779 98.2 0.811 112.2 0.836 140.3 0.858 84.2 0.749 98.2 0.769 112.2 0.788 138.3 0.896 218.4 0.856
290 304 289 286 288 342 336 335 291 296
284 308 334 358 407 308 332 351 401 525
-6 4 45 73 119 -34 -4 16 110 229
{∑|∆T|}/n [{∑[∆T]2/n]1/2
92 112
pred
Polar methyl acetate ethyl acetate n-propyl acetate i-propyl acetate i-butyl acetate tert-butyl acetate n-butanol n-pentanol n-hexanol n-octanol n-decanol n-dodecanol n-tetradecanol n-hexadecanol n-octadecanol cyclohexanol diethyl malonate diethyl oxalate ethyl n-butyrate diethyl ether dioctyl phthalate ethyl formate acetone propionitrile nitroethane n-pentane n-hexane n-heptane n-octane n-decane n-dodecane n-pentadecane n-octadecane cyclopentane cyclohexane cycloheptane cyclooctane cyclodecane methyl cyclopentane methyl cyclohexane ethyl cyclohexane tert-decalin 1-phenyldecane
1.1 2.03 4.8 4.8 4 4 4 4 2700 2700 10000 10000 10000 2000 1971 569 2700 600
∆T (K)
(g/cm3)
(4) Imre, A.; Van Hook, W. A. Liquid-Liquid Demixing from Solutions of Polystyrene. 1. A Review. 2. Improved Correlation with Solvent Properties. J. Phys. Chem. Ref. Data 1996, 25, 637; 1996, 25, 1277.
(5) CS ChemFinder, a public and free database of the Cambridge Soft Corp. (http://chemfinder.camsoft. com/).
IE980834E
