Phase diagrams polymer-solvent

Figure 2.33 Polymer-solvent phase diagram showing binodal, spinodal, and miscibility gap. Reprinted, by permission, from J. M. G. Cowie, Polymers Chemistry Physics of Modem Materials, 2nd ed., P. 167. Copyright 1991 by Chapman Hall.

The model of Marchetti et al. is based on the compressible lattice theory which Sanchez and Lacombe developed to apply to polymer-solvent systems which have variable levels of free volume [138-141], This theory is a ternary version of classic Flory-Huggins theory, with the third component in the polymer-solvent system being vacant lattice sites or holes . The key parameters in this theory which affect the polymer-solvent phase diagram are ... 

The main features of the polymer - solvent phase diagram can be obtained at the simple Flory - Huggins level [11,73] In effect, this theory leads to the following predictions for the dependence of the position of the critical point on the molecular mass (M —> oo) ... 

Fig. 1.9 Calculated polymer-solvent phase diagram. The bimodal (continuous line) is the coexistence curve the points below it correspond to thermodynamically unstable states, which undergo phase separation. However, the pints between the bimodal and the spinodal (dashed line) are ki-netically stable, since there is a free-energy barrier to phase separation. C indicates the critical point the collapse temperature. The deviation of the low-concentration branch of the spinodal from the vertical axis below T is an artifact of the mean-field approximation. (From ref. [62])...

Figure 1. Schematic plots of polymer/polymer/solvent phase diagrams for (a) two miscible polymers plus a solvent Inducing phase separation, (b) two immiscible polymers. The lines AB and CD show evaporation pathways.

Figure 2, Polymer/solvent phase equilibrium diagram...

Dubault, A., Casagrande, C., and Veyesie, M., Flexible polymers in nematic solvents phase diagrams in dilute regime. Mol. Cryst. Liq. Cryst., 72,189-194 (1982). 

Figure 7. (a) Schematic illustrating the increase in concentration and expulsion of solvent as surfaces are compressed in the simulations, (b) Pressure-polymer concentration phase diagram. Flocculation of surfaces occurs at the upper critical solution density when the concentration between the surfaces reaches an unstable value (the critical concentration). 

Keywords Modeling Mixed solvents Phase diagrams Polymer solutions Ternary mixtures Thermodynamics... 

More importantly, the crystalline-solvent phase diagrams, thus solved in the context of the Flory-Huggins theory alone, cannot account for the existence of the solidus line, because the crystal phase always coincides with the pure crystalline polymer axis due to the inherent assumption, adopted from Prigogine theory, of the complete rejection of solvent molecules from the crystaHine phase [66,67]. Thus,... 

Fig. 123.—(a) Phase diagram calculated for three-component systems consisting of nonsolvent [1], solvent [2], and polymer [3] taking Xi==X2=l and Xz equal to 10 (dashed curve), 100 (solid curve), and °° (dotted curve) xi2 = xi3 = 1.5 and X23 =0. All critical points (O) are shown and tie lines are included for the xs = 100 curve. (Curves calculated by Tompa. ) (b) The binodial curve for a 3 = 100 and three solvent ratio lines. The precipitation threshold is indicated by the point of tangency X for the threshold solvent mixture. 

The physical reason for the inherent lack of incentive for mixing in a polymer-polymer system is related to that already cited in explanation of the dissymmetry of the phase diagram for a polymer-solvent binary system. The entropy to be gained by intermixing of the polymer molecules is very small owing to the small numbers of molecules involved. Hence an almost trivial positive free energy of interaction suffices to counteract this small entropy of mixing. 

If there are included among the diluents mixed with the crystalline polymer some which are sufficiently poor solvents, the phase diagram may then exhibit liquid-liquid phase separation, in addition to the liquid-crystal boundary curve. Examples are shown in Figs. 133... 

Calculation of the Binodial in the Phase Diagram for the Two-Component System Comprising a Solvent and a Single Polymer Species. —... 

Based on the analogy between polymer solutions and magnetic systems [4,101], static scaling considerations were also applied to develop a phase diagram, where the reduced temperature x = (T — 0)/0 (0 0-temperature) and the monomer concentration c enter as variables [102,103]. This phase diagram covers 0- and good solvent conditions for dilute and semi-dilute solutions. The latter will be treated in detail below. 

Binder, K., Muller, M., Virnau, P. and Gonzalez MacDowell, L. Polymer+Solvent Systems Phase Diagrams, Interface Free Energies, and Nucleation. Vol. 173, pp. 1-104. 

Interactions of such glassy polymeric particles should resemble the collisions of hard spheres. Phase diagrams of the type shown in Fig. 36 have been obtained for various polymer-organic solvent mixtures [85,94,345-353]. 

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