Interpenetration and segregation of interacting polymer chains in a solution: exact results on fractal lattices

Abstract

A model of two interacting self-attracting, self-avoiding walks is proposed to study the critical behavior of two interacting chemically different linear polymers in a solution that may have different qualities for different chains. We solve the model exactly on truncated n-simplex lattices for 4≤n≤6 using the real-space renormalization-group transformation. Depending upon the solvent quality, the temperature, and the attractive interactions between interchain and intrachain monomers, the configuration of either segregation or interpenetration or zipping of chains may arise. It is shown that these configurations correspond to different fixed points of the renormalized-group transformation. The value of the contact exponent is calculated exactly at the tricritical points corresponding to the segregation-interpenetration and the interpenetration-zipped-state chain transitions. The phase boundaries of these states are shown on a plane of fugacity weight attached with a zipped step (i.e., a step in which both walks move side by side) and the Boltzmann factor associated with the attraction between unlike monomers. The phase diagram is shown to have different universality domains of critical behavior.