Study of the phase separation in polymer solutions using the pair approximation of the CVM: analytical solution of the problem

Abstract

The phase diagrams of polymer solutions are studied 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, 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 is investigated. The critical temperature and the critical concentration are also studied. 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). A novel technique to solve the set of equations derived from the CVM is presented, and an analytical solution of the problem is given