Entropic pressure in lattice models for polymers

TL;DR

This paper addresses discrepancies in lattice models of polymers by proposing a modified local pressure expression that aligns with continuous system physics, especially for ideal polymers near scale-invariant boundaries.

Contribution

It introduces a non-local correction to the lattice-based local pressure to ensure consistency with total force measurements and continuous system behavior.

Findings

Modified pressure expression matches continuous system results for ideal polymers.

Non-local correction accounts for long-range correlations between polymer contact points.

Addresses fundamental discrepancies in lattice models of entropic pressure.

Abstract

In lattice models local pressure on a surface is derived from the change in the free energy of the system due to the exclusion of a certain boundary site, while the total force on the surface can be obtained by a similar exclusion of all surface sites. In these definitions, while the total force on the surface of a lattice system matches the force measured in a continuous system, the local pressure does not. Moreover, in a lattice system, the sum of the local pressures is not equal to the total force as is required in a continuous system. The difference is caused by correlation between occupations of surface sites as well as finite displacement of surface elements used in the definition of the pressures and the force. This problem is particularly acute in the studies of entropic pressure of polymers represented by random or self-avoiding walks on a lattice. We propose a modified expression for the local pressure which satisfies the proper relation between the pressure and the total force, and show that for ideal polymers in the presence of scale-invariant boundaries it produces quantitatively correct values for continuous systems. The required correction to the pressure is non-local, i.e., it depends on long range correlations between contact points of the polymer and the surface.