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.