Brownian and fractional polymers with self-repulsion

TL;DR

This paper develops a formalism for modeling polymers as Brownian or fractional processes, incorporating solvent interactions and polymer-polymer potentials, with applications to calculating average polymer lengths.

Contribution

It introduces a new formalism that accounts for both solvent interactions and arbitrary potentials in polymer modeling using Brownian and fractional processes.

Findings

Computed average squared length for a Gaussian Gibbs factor.

Compared results with Edwards' and step factors.

Demonstrated the formalism's applicability to complex potentials.

Abstract

Brownian and fractional processes are useful computational tools for the modelling of physical phenomena. Here, modelling linear homopolymers in solution as Brownian or fractional processes, we develop a formalism to take into account both the interactions of the polymer with the solvent as well as the effect of arbitrary polymer-polymer potentials and Gibbs factors. As an example the average squared length is computed for a non-trivial Gaussian Gibbs factor, which is also compared with the Edwards' and a step factor.