Adhesion Kinetics between a Membrane and a Flat Substrate. An Ideal Upper Bound to the Spreading Rate of an Adhesive Patch

Abstract

A semiquantitative theory to describe the adhesion mechanism between an elastic membrane and a solid substrate (or another membrane) was developed. Since the membrane bending deformation requires a relatively small energy cost, thermally excited fluctuations may give rise to a local protrusion connecting the membrane to the substrate. This transient adhesion site is stabilized by short-range adhesion forces and it is destabilized by repulsion and elastic deformation energy. Above a critical radius of the contact site, adhesion forces prevail, enabling the contact site to expand until complete membrane-substrate adhesion is attained. This represents a typical nucleation mechanism involving both growth and dissolution processes. However, here we prove that also in the barrierless region, well beyond the critical radius, the spreading rate of a membrane still remains rather small, even under the favorable assumption of strong, sudden, and irreversible membrane-substrate adhesion. A detailed analysis of the membrane vibrational behavior near the adhesion patch rim suggests a reasonable mechanism for the spreading rate that has been analyzed by nonequilibrium statistical mechanics approaches. In relevant limiting cases, the model yields simple analytical formulas. Approximate relationships between the spreading rate and parameters like membrane elastic bending modulus, membrane-substrate interaction, temperature, and solvent viscosity have been found.