Surface Polymer Network Model and Effective Membrane Curvature Elasticity

TL;DR

This paper introduces a microscopic model for surface polymer networks on membranes, analyzing how polymer interactions and sliplinks influence membrane curvature elasticity through a surface scattering method.

Contribution

It presents a novel microscopic model linking polymer surface interactions and sliplink density to membrane curvature elasticity using a multiple surface scattering approach.

Findings

Derived expressions for curvature elastic modulus and Gaussian modulus.

Showed dependence of membrane spontaneous curvature on polymer separation and sliplink density.

Quantified how surface interactions affect membrane elasticity parameters.

Abstract

A microscopic model of a surface polymer network - membrane system is introduced, with contact polymer surface interactions that can be either repulsive or attractive and sliplinks of functionality four randomly distributed over the supporting membrane surface anchoring the polymers to it. For the supporting surface perturbed from a planar configuration and a small relative number of surface sliplinks, we investigate an expansion of the free energy in terms of the local curvatures of the surface and the surface density of sliplinks, obtained through the application of the Balian - Bloch - Duplantier multiple surface scattering method. As a result, the dependence of the curvature elastic modulus, the Gaussian modulus as well as of the spontaneous curvature of the "dressed" membrane, ~{\sl i.e.} polymer network plus membrane matrix, is obtained on the mean polymer bulk end to end separation and the surface density of sliplinks.