Statistical mechanics of a cross-linked polymer blend

TL;DR

This paper develops a microscopic statistical mechanical model for a cross-linked polymer blend, revealing microphase structures and domain sizes consistent with experimental data and scaling theories.

Contribution

It introduces a detailed microscopic derivation of the effective Hamiltonian for a polymer blend with cross-links, predicting microphase structures and domain sizes.

Findings

Domain size is of the order of the mesh size.

Inverse scattering function is derived from the model.

Results agree with experimental data and scaling arguments.

Abstract

We study a blend of two kinds of homopolymers with tendency for segragation. Cross-links between the chains of different kinds do not allow macrophase separation. Instead microphase structure appears. Starting from a microscopic model we derive the effective Hamiltonian and calculate the form of the inverse scattering function and the domain size. The latter is found to be of the order of the mesh size. We show agreement of the results obtained by this microscopic statistical mechanical theory with experimental data and the existing scaling arguments.