Determination of Diffusion Coefficient and Rheological Properties of Surface Layers from Surface Trough Diffusion

Abstract

A theoretical analysis of the surface trough diffusion problem is used in this paper to interpret the diffusion coefficient, the dilational elasticity, and the viscosity of a surface layer from experimental measurements of the surface diffusion motion. A simple Kelvin-Voight model, in which the elastic and viscous stresses are additive, is assumed for the material behavior of the surface layer in dilational deformation. The surface flow problem is solved based on the analytical solution of the surface diffusion equation. The surface distribution at any time and the time course at any surface position of dynamic quantities such as concentration, concentration gradient, displacement, velocity, velocity gradient, area strain, and area strain rate are all deduced in explicit form and graphically studied in detail. An interpretation is proposed to obtain the kinetic and rheological properties of the surface layer from experimental measurement of the displacements at the central position of the trough surface at different times, or from the record of the time when the diffusion front passed through a specified surface position. The idea of accessing the diffusivity and dilational viscoelasticity of lipid monolayers by mechanical measurement is new, simple, and feasible. The experiment deserves to be realized in the study of monolayers and bilayers of chemical and biological molecules.