Swelling of particle-encapsulating random manifolds

TL;DR

This paper develops a unified scaling theory for the swelling behavior of particle-encapsulating random manifolds, revealing conditions under which swelling due to particles differs from pressure-induced swelling, supported by Monte Carlo simulations.

Contribution

It introduces a scaling framework for swollen manifolds with encapsulated particles and distinguishes thermodynamic equivalence from pressure-induced swelling, validated by simulations.

Findings

Mean volume increases with particle number following a universal scaling law.

Swelling due to particles can be thermodynamically inequivalent to pressure-induced swelling.

Monte Carlo simulations confirm the theoretical predictions in specific models.

Abstract

We study the statistical mechanics of a closed random manifold of fixed area and fluctuating volume, encapsulating a fixed number of noninteracting particles. Scaling analysis yields a unified description of such swollen manifolds, according to which the mean volume gradually increases with particle number, following a single scaling law. This is markedly different from the swelling under fixed pressure difference, where certain models exhibit criticality. We thereby indicate when the swelling due to encapsulated particles is thermodynamically inequivalent to that caused by fixed pressure. The general predictions are supported by Monte Carlo simulations of two particle-encapsulating model systems -- a two-dimensional self-avoiding ring and a three-dimensional self-avoiding fluid vesicle. In the former the particle-induced swelling is thermodynamically equivalent to the pressure-induced one whereas in the latter it is not.