 
Summary: Bending moduli of charged membranes immersed in polyelectrolyte
solutions
Adi Shafir and David Andelman*
Received 6th September 2006, Accepted 25th January 2007
First published as an Advance Article on the web 26th February 2007
DOI: 10.1039/b612808d
We study the contribution of polyelectrolytes in solution to the bending moduli of charged
membranes. Using the Helfrich free energy, and within the meanfield theory, we calculate the
dependence of the bending moduli on the electrostatics and shortrange interactions between the
membrane and the polyelectrolyte chains. The most significant effect is seen for strong
shortrange interactions and low amounts of added salt where a substantial increase in the
bending moduli of order 1 kBT is obtained. For shortrange repulsive membranes, the
polyelectrolyte contribution to the bending moduli is small, of the order the 0.1 kBT up to at most
1 kBT. For weak shortrange attractions, the increase in membrane rigidity is smaller and of less
significance. It may even become negative for a large enough amount 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.
1. Introduction
The study of interactions between charged and flexible
membranes and polyelectrolytes (PEs) in solution has gener
