The competition between Brownian motion and adhesion in soft materials

The phenomenon considered is the potential for adhesion between a membrane and a nearby substrate through bonding of receptor molecules in the membrane to ligand molecules on the substrate. The membrane is immersed in a thermal reservoir and, consequently, experiences thermal undulations. The undulations must be suppressed in order to effect bonding, and this competition is the focus of the present discussion. A simple physical model is introduced which incorporates thermal motion of a one-dimensional membrane, and its tendency for bonding is represented by an interaction potential with the substrate. The model is analyzed within the framework of classical statistical mechanics, based on a description of adhesion in terms of the standard deviation of the membrane at the potential bonding points. The principal result is in the form of a quantitative relationship between the membrane span and the depth of the bonding potential that must be satisfied in order for bonding to be completed. (c) 2007 Elsevier Ltd. All rights reserved.