Pseudo-Casimir stresses and elasticity of a confined elastomer film

TL;DR

This paper explores how thermal fluctuations of cross-links in confined elastomer films influence their elastic free energy and stresses, revealing deviations from classical rubber elasticity and drawing parallels with Casimir effects.

Contribution

It introduces a model accounting for cross-link fluctuations in elastomer films and compares different boundary conditions, highlighting their impact on elastic behavior and fluctuation-induced stresses.

Findings

Significant deviations from classical rubber elasticity when including cross-link fluctuations.

Identification of power law decay in pseudo-Casimir stress under rigid pinning conditions.

Inverse decay of correction to fluctuation stress with substrate separation under soft gluing potentials.

Abstract

Investigations of the elastic behavior of bulk elastomers have traditionally proceeded on the basis of classical rubber elasticity, which regards chains as thermally fluctuating but disregards the thermal fluctuations of the cross-links. Here, we consider an incompressible and flat elastomer film of an axisymmetric shape confined between two large hard co-planar substrates, with the axis of the film perpendicular to the substrates. We address the impact that thermal fluctuations of the cross-links have on the free energy of elastic deformation of the system, subject to the requirement that the fluctuating elastomer cannot detach from the substrates. We examine the behavior of the deformation free energy for one case where a rigid pinning boundary condition is applied to a class of elastic fluctuations at the confining surfaces, and another case where the same elastic fluctuations are subjected to soft "gluing" potentials. We find that there can be significant departures (both quantitative and qualitative) from the prediction of classical rubber elasticity theory when elastic fluctuations are included. Finally, we compare the character of the attractive part of the elastic fluctuation-induced, or pseudo-Casimir, stress with the standard thermal Casimir stress in confined but non-elastomeric systems, finding the same power law decay behavior when a rigid pinning boundary condition is applied, for the case of the gluing potential, we find that the leading order correction to the attractive part of the fluctuation stress decays inversely with the inter-substrate separation.