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Liquid-Liquid Equilibrium Calculations for Polymer Solutions using the GC-Flory Equation of State

SUMMARY During the last years, the GC-Flory EOS has been used to calculate activity coefficients in polymer-solvent mixture (1,2). Using parameters based on vapor-liquid equilibrium (VLE) the GC-Flory EOS was also applied to the prediction of the miscibility/immiscibility phenomena of monodisperse polymer-solvent systems. It was shown (3) that the model was capable to predict only qualitatively the phase behavior of such systems. Recently the GC-Flory EOS was developed for liquid-liquid equilibrium (LLE) calculations (4). The model parameters have been estimated from the experimental LLE data. The prediction of LLE phase behavior of polymer solutions with the new LLE parameter table is significantly improved over the ones obtained using the VLE parameter tables. The comparison of the accuracy of the prediction was carried out, and it was shown that the model was capable to predict quantitatively the most relevant types of phase diagrams typical of LLE of polymer solutions. INTRODUCTION Since many polymeric materials are produced in a solution, reliable estimates of liquid-liquid equilibrium are necessary for prediction and optimization of the process performances. In principle, LLE compositions may be calculated using any model for Gibbs energy. Models relying on a group contribution approach, such as the UNIFAC model (5,6), have been applied to low molar mass compound mixtures, but they require a special set of parameters (7). Such models have been extended recently to LLE calculations for polymer solutions using parameters based on vapor-liquid equilibrium (8,9,2,10), but they yielded only qualitative predictions. Instead, a group contribution lattice fluid equation of state (10) gave better results. In order to predict LLE as well as possible with the presently available models for the excess Gibbs energy, it is necessary to base the model parameters on LLE data. The purpose of this work is to present the GC-Flory EOS parameter table especially suited for the prediction of LLE. LLE experimental data (11) were used to calculate group-interaction parameters. These may be used to predict LLE compositions in mixtures for which no data are available, as long as the mixture in question can be constructed from groups for which parameters are available. The GC-Flory EOS used in this work is that revised and further simplified by Bogdanić and Fredenslund (1), only the parameter values differ. RESULTS AND DISCUSSION The GC-Flory EOS was used to predict liquid-liquid equilibrium in binary polymer-solvent systems. The detailed description of the model with the fundamental equation is given in reference (1), and will not be repeated here. The parameters needed are group sizes and surface areas Rn and Qn, and EOS parameters. The GC-Flory EOS parameters are related to pure component properties, Ci and εii0, and to a mixture energy of interaction, εij0. The values attributed to Rn and Qn are those derived from the van der Waals group volumes and surface areas, while EOS parameters are estimated from experimental data. Those parameters are defined in terms of the group parameters CT0,n, CT,n and Cn0, the interaction energies between like groups n, εnn, and Δεnm, i.e. interaction energies between unlike groups n and m. Values for Rm, Qm, CT0,n, CT,n and Cn0 are given for eleven different groups in Table 1, and in the first approximation they are the same as in the ref. 1. The problem of fitting the GC-Flory EOS to experimental LLE data was reduced to finding the values of parameters εnn and Δεnm that will predict LLE composition as close as possible to the experimental values. For all examined cases in this work, the overall mean absolute deviation between experimental and calculated LLE compositions was no more than 1.5 wt.%. The obtained mm and mn parameter values are listed in Table 2. It should be underlined that all of these parameters were estimated from pure component and mixtures properties involving only low-molar mass components. Table 1. Group Rn, Qn and C Values of the GC-Flory EOS Main no. Group name Subgroup no. name Rn Qn CT0,n CT,n Cn0 1 CH2 1 CH3 0.9011 0.848 -0.0738 -3.570 0 2 CH2 0.6744 0.540 0.1080 -3.570 0 3 CH 0.4469 0.228 0.3442 -3.570 0 4 C 0.2195 0.000 0.4779 -3.570 0 5 cy-CH2 0.6744 0.540 0.0070 -3.570 0 2 ACH 6 ACH 0.5313 0.400 0.0152 -2.900 -0.013 7 AC 0.3652 0.120 0.2640 -2.900 -0.013 ... ... ... ... ... ... ... ... ... 7 C=C 16 CH2=CH 1.3454 1.176 0.1503 -15.010 0 17 CH=CH 1.1167 0.867 0.1762 -15.010 0 18 CH2=C 1.1173 0.988 0.4961 -15.010 0 19 CH=C 0.8886 0.676 0.5010 -15.010 0 Table 2. Group-Interaction Parameters mm and mn, J/q-unit CH2 ACH C=C CH2 -2970 50 -101 ACH -4000 -310 C=C -2900 Figures 1 and 2 illustrate the capability of the GC-Flory EOS to predict LLE for binary polymer solutions, comparing experimental and predicted phase equilibrium data. Figure 1 refers to the HDPE/n-hexane system, for which the LCST is predicted under 10C Figure 1. Coexistence curves for HDPE/n-hexane systems as predicted by GC-Flory EOS (). Experimental data (,) are taken from reference (12) and () from reference (13) Figure 2. Coexistence curves for PIB/n-hexane systems as predicted by GC-Flory EOS (). Experimental data are taken from reference (14) Figure 2 refers to the PIB/n-hexane system, which shows phase diagrams of combined type. For this system the difference between the calculated and the experimental critical points is again within 20C. The comparison of the accuracy of the prediction of LLE was carried out many examples, and it was found that the model is capable to predict quantitatively the most relevant types of phase diagrams typical of LLE of polymer solutions (i.e. phase diagrams of the UCST, LCST, combined UCST and LCST, and "hourglass" types), and provides a thermodynamic framework to describe the LLE phase behavior of polymer solutions. REFERENCES [1] Bogdanić, G.; Fredenslund, Aa. Ind.Eng.Chem.Res., 1994, 33, 1331. [2] Bogdanić, G.; Fredenslund, Aa. Eng.Chem.Res., 1995, 34, 324. [3] Saraiva, A.; Bogdanić, G.; Fredenslund, Aa. Ind.Eng.Chem.Res., 1995, 34, 1835. [4] Bogdanić, G. 18th European Seminar on Applied Thermodynamics, Hutna Hora, Conference Book, pp. 51, 2000. [5] Fredenslund, Aa.; Gmehling, J.; Rasmussen, P. Vapor-Liquid Equilibria Using UNIFAC, Elsevier Scientific, New York, 1977. [6] Fredenslund, Aa. Fluid Phase Equil., 1989, 52, 135. [7] Magnussen, T.; Rasmussen, P.; Fredenslund, Aa. Ind. Eng. Chem., Proc. Des. Dev., 1981, 20, 331. [8] Kontogeorgis, G.M.; Fredenslund, Aa.; Tassios, D.P. Ind. Eng. Chem. Res., 1993, 32, 362. [9] Kontogeorgis, G.M.; Saraiva, A.; Fredenslund, Aa.; Tassios, D.P. Ind. Eng. Chem. Res., 1995, 34, 1823. [10] Lee, B.C.; Danner, R.P. AIChE J., 1996, 42, 3223. [11] Sørensen, J.M.; Arlt, W. “Liquid-Liquid Equilibrium Data Collection”, DECHEMA Chemistry Data Series, Vol.V, Frankfurt, Part 1, 1979; Parts 2 and 3, 1980. [12] Kodama, Y.; Swinton, F.L. Brit.Polym.J., 1978, 10, 191. [13] Orwol, R.A.; Flory, P.J. J.Am.Chem.Soc., 1967, 89, 6822. [14] Delmas, G.; Saint-Romain, P. Eur.Polym.J., 1974, 10, 1133.

liquid-liquid equilibria; prediction; estimation; GC-Flory EOS; polymer solutions

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