Polymer-solvent interaction parameter phase equilibria

Problem 3.15 A polymer solution was cooled very slowly until phase separation took place to give two phases in equilibrium. Analysis of the phases showed that the volume fractions of polymer in the two phases were 2 = 0.01 and < 2 = 0.89, respectively. Using the Flory-Huggins equation for A/ri [cf. Eq. (3.53)], together with the equilibrium condition = A/i", calculate an estimate of the polymer-solvent interaction parameter for the conditions of phase separation. 

The equilibrium theory predicts that phase separation is promoted by increasing concentration of the divinyl monomer and reactivity of its vinyls, by increasing dilution, molar volume of the diluentj and polymer-solvent interaction parameters. The critical conversion at phase separation is usually located close to the gel point and the volume of the network phase first decrease and may in certain cases increase again... 

Miscibility in polymer blends is controlled by thermodynamic factors such as the polymer-polymer interaction parameter [8,9], the combinatorial entropy [10,11], polymer-solvent interactions [12,13] and the "free volume effect [14,15] in addition to kinetic factors such as the blending protocol, including the evaporation rate of the solvent and the drying conditions of the samples. If the blends appear to be miscible under the given preparation conditions, as is the ca.se for the blends dcscibcd here, it is important to investigate the reversibility of phase separation since the apparent one-phase state may be only metastable. To obtain reliable information about miscibility in these blends, the miscibility behavior was studied in the presence and absence of solvents under conditions which included a reversibility of pha.se separation. An equilibrium phase boundary was then obtained for the binary blend systems by extrapolating to zero solvent concentration. 

From the discussion of swelling equilibrium follows that a volume phase transition of a gel needs further contributions to free energy, resulting, for example, in specific polymer-solvent interactions. The high-temperature collapse of a nonionic single chain and gels in water has been described by using the concentration-dependent interaction parameters x"-... 

The algorithm we used for solvent/polydisperse polymer equilibria calls for only one solvent/polymer interaction parameter. The interaction parameter (pto) i ed in the algorithm can be determined from essentially any type of ethylene/polyethylene phase equilibrium data. Cloud-point data have been used (18). while Cheng (16) and Harmony ( ) have done so from gas sorption data. 

FIGURE 3.14 Liquid-liquid equilihrium for HDPE with n-alkanols. Lines are simplified PC-SAFT correlations for each of the five solvents (pentanol highest, nonanol lowest). Polymer molecular weight is 20,000. Binary interaction parameters are as follows pentanol 0.0006 hexanol 0.003 heptanol 0.0025 octanol 0.0033 and nonanol 0.0029. (From Fluid Phase Equilib., 222-223, von Sohns, N., Kouskoumvekaki, LA., Lindvig, T., Michelsen, M.L., and Kontogeorgis, G.M., A novel approach to liquid-liquid equilibrium in polymer systems with application to simplified PC-SAFT, 87-93, Copyright 2004, with permission from Elsevier.)... 

Both SAFT and PC-SAFT contain pure component parameters the energy parameter or u, the hard-sphere diameter a, or the hard-sphere volume and the number of segments m per molecule. For small (solvent) molecules these parameters are obtained from a fit of vapor pressure data and saturated liquid volume data. Since they do not have a vapor pressure, this fit is not possible for polymers, and the pure component polymer parameters are obtained from a fit to PVT data of the molten polymer or from a fit to PVT data and binary phase equilibrium data. For the description of a mixture one needs one binary interaction parameter ky per binary, which has to be fitted to phase equilibrium data. If necessary, ky can be made temperature-dependent. In general, phase equilibria are very sensitive to the kij value. 

Binodials calculated by Tompa are shown in Fig. 123,a for the special case of a nonsolvent [l], a solvent [2], and a polymer [3] with Vi = V2, X23 = 0, and xi2 = Xi3 = 1.5. Otherwise stated, the nonsolvent-solvent and the nonsolvent-polymer segment free energies of interaction are taken to be equal, while that for the solvent and polymer is assumed to be zero. It is permissible, then, to take Xi = X2 = l and o 3 = V3/vi. The number of parameters is thus reduced for this special case from five to two. Binodial curves are shown in Fig. 123,a for 0 3 = 10, 100, and 00 tie lines are shown for the intermediate curve only. The critical points for each curve, shown by circles, represent the points at which the tie lines vanish, i.e., where the compositions of the two phases in equilibrium become identical. 

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