Pressure exerted by a grafted polymer: Bethe lattice solution

TL;DR

This paper analytically investigates the pressure exerted by a grafted self-avoiding walk polymer on a wall within a Bethe lattice framework, revealing exponential decay of pressure and analyzing the effects of a discontinuous adsorption transition.

Contribution

It provides an exact solution for the pressure exerted by a grafted polymer on a Bethe lattice, highlighting differences from regular lattice behaviors and examining the adsorption transition.

Findings

Pressure decays exponentially with distance from the grafting point.

Discontinuous adsorption transition influences the pressure behavior.

Pressure decay differs from regular lattice and Gaussian walk models.

Abstract

We solve the problem of a chain, modeled as a self-avoiding walk, grafted o the wall limiting a semi-infinite Bethe lattice of arbitrary coordination number q. In particular, we determine the pressure exerted by the polymer on the wall, as a function of the distance to the grafting point. The pressure, in general, decays exponentially with the distance, at variance with what is found for SAWs and directed walks on regular lattices and gaussian walks. The adsorption transition, which is discontinuous, and its influence on the pressure are also studied.