Chemo-mechanical interactions between adsorbed molecules and thin elastic films

A general mechanics framework is presented to describe the interaction of molecular groups adsorbed on deformable thin films. Equations describing film deformation are expressed in terms of the pair potential that governs the interaction between adsorbed groups and large-deflection deformation descriptions. We illustrate that the pair potential can be used to define two-dimensional constitutive parameters for the adsorbed groups that describe their energetic contribution during arbitrary deformations. The framework is applicable to a wide range of interactions, including electrochemical interactions between a solution and film surface, interactions between neighboring adsorbed biopolymers and interactions between living cells. Key dimensionless parameters involving molecular interaction, surface coverage, film dimensions, and elastic properties are highlighted, and simplified governing equations for small deflections are identified. Solutions are presented that describe the influence of adsorbed groups on bending of cantilevers, pinned films and built-in (clamped) films. For clamped films, the critical molecular interaction parameters required to induce buckling are identified, and post-buckling behavior discussed in terms of the implications for making biological sensors.