Theoretical estimation of density profile of semiflexible polymers adsorbed on a surface and thermodynamic glass transition scenario by means of the Bethe-Peierls approximation

TL;DR

This paper presents a theoretical framework combining Bethe-Peierls and self-consistent field theories to analyze the density profile of semi-flexible polymers adsorbed on surfaces and explores implications for the glass transition temperature.

Contribution

It extends existing lattice theories to include semi-flexibility and nonhomogeneous systems, linking density profiles to thermodynamic glass transition scenarios.

Findings

Density profiles depend on chain flexibility and surface interaction strength.

Configurational entropy variations suggest changes in glass transition temperature near surfaces.

The model reduces to known theories in specific limits.

Abstract

We develop a theory describing density profile of the semi-flexible polymers absorbed onto a planar surface. The theoretical analysis consists of two parts. As a first part, we calculate a density profile of the adsorbed polymers by developing an extension of the Bethe-Peierls approximation to the case of nonhomogeneous systems. This approach relies on the combination of the single chain adsorption theory and the lattice version of the self-consistent field theory. Semi-flexibility of a chain is described by incorporating a finite coordination number of the lattice into the consideration, in the spirit of the previous Silberberg approach. The developed lattice theory incorporates the interaction between nearest-neighbor pairs of segments and finite chain length. The theory is completely mapped into the Scheutjens-Fleer theory in the limit of infinite coordination number. As a second part of the developed approach, we calculate the configurational entropy to investigate how the density structure of the semi-flexible polymers near the surface relates to possible reduction of glass transition temperature near nonabsorbing surface and enhancement near the strongly attractive surface.