CONTRIBUTION TO THE STATISTICAL-THEORY OF SOLUTIONS OF POLYMERS IN A CRITICAL SOLVENT

The thermodynamics of high polymers in equilibrium with a low-molecula r solvent with a large correlation radius (super- and near-critical so lvent) is studied. Special attention is devoted to the analysis of typ ical phase diagrams describing the conditions of solubility of a polym er in such a solvent. The nature of these diagrams is determined by th e existence of long-range multiparticle attraction between the monomer s, which increases as the critical point of the solvent is approached. At the critical point the contribution of this attraction to the free energy of the system is nonanalytic with respect to the polymer conce ntration. It is shown that the nontrivial dependences of the polymer-p olymer and polymer-solvent coupling constants, which appear in the phe nomenological analysis, on the pressure and temperature of the solvent play an important role in the quantitative analysis of the phase diag rams of the solubility of the polymer. These dependences are found in explicit form under the assumption that in the absence of intermonomer bonds the system can be described as a compressible two-component lat tice alloy. The partition function of the system under study is repres ented as a functional integral over two coupled, strongly fluctuating fields, one of which, describing the fluctuations of the polymer densi ty, is the 0 component. By virtue of the specific nature of the proble m, the effective temperature corresponding to the 0-component of the f ield cannot be specified independently, but can be determined by minim izing the total free energy of the system. (C) 1998 American Institute of Physics. [S1063-7761(98)01109-3].