Bending Moduli of Charged Membranes Immersed in Polyelectrolyte Solutions

TL;DR

This study investigates how polyelectrolytes influence the bending rigidity of charged membranes, revealing significant effects under certain conditions like strong short-range interactions and low salt concentrations.

Contribution

It provides a theoretical analysis of the dependence of membrane bending moduli on electrostatics and short-range interactions using mean-field theory and the Helfrich free energy.

Findings

Polyelectrolytes can increase membrane bending moduli by about 1 k_BT under specific conditions.

Short-range repulsive membranes show smaller polyelectrolyte effects, around 0.1 to 1 k_BT.

Bending moduli follow simple scaling laws in some cases.

Abstract

We study the contribution of polyelectrolytes in solution to the bending moduli of charged membranes. Using the Helfrich free energy, and within the mean-field theory, we calculate the dependence of the bending moduli on the electrostatics and short-range interactions between the membrane and the polyelectrolyte chains. The most significant effect is seen for strong short-range interactions and low amounts of added salt where a substantial increase in the bending moduli of order $1 k_BT$ is obtained. From short-range repulsive membranes, the polyelectrolyte contribution to the bending moduli is small, of order $0.1 k_BT$ up to at most $1 k_BT$. For weak short-range attraction, the increase in membrane rigidity is smaller and of less significance. It may even become negative for large enough amounts of added salt. Our numerical results are obtained by solving the adsorption problem in spherical and cylindrical geometries. In some cases the bending moduli are shown to follow simple scaling laws.