Osmotic Pressure of Confined Square Lattice Self-Avoiding Walks

TL;DR

This paper models the osmotic pressure of confined square lattice self-avoiding walks using Flory-Huggins theory, estimating the interaction parameter and validating the theory's applicability to dense two-dimensional polymer-like systems.

Contribution

It applies Flory-Huggins mean field theory to a 2D self-avoiding walk confined in a square lattice, providing an estimated interaction parameter.

Findings

Flory-Huggins theory describes the free energy well.

Estimated Flory interaction parameter is 0.32(1).

The model effectively captures the behavior of dense 2D self-avoiding walks.

Abstract

Flory-Huggins theory is a mean field theory for modelling the free energy of dense polymer solutions and polymer melts. In this paper we use Flory-Huggins theory as a model of a dense two dimensional self-avoiding walk confined to a square in the square lattice. The theory describes the free energy of the walk well, and we estimate the Flory interaction parameter of the walk to be $\chi_{saw} = 0.32(1)$.