STUDY OF THE PHASE-SEPARATION IN POLYMER-SOLUTIONS USING THE PAIR APPROXIMATION OF THE CVM - ANALYTICAL SOLUTION OF THE PROBLEM

We study the phase diagrams of polymer solutions using the pair approximation of the Cluster Variational Method (CVM). In this model the solvent (oligomers) and the solute (polymers) are chains with different lengths. In particular, we study the dependence of the phase diagram on the lengths of the components of the mixture, on the lattice, and on the relative size of the components of the mixture. We also study the critical temperature and the critical concentration. Some comparison of our results with the Flory and Guggenheim approximations are done for the symmetric case (when oligomer chains and polymer chains have the same length) and the asymmetric case (when oligomer chains and polymer chains have different length). We present a novel technique to solve the set of equations derived froin the CVM, and an analytical solution of the problem is given.