Dynamics of polymer adsorption

Abstract

In this work a mean field, continuum model has been developed to predict dynamics of polymer adsorption from solution, on solid surface. Diffusion of a polymer molecule is described in two steps i.e. formulation of "free" (unconnected) segment diffusion, and imposition of the segmental connectivity constraint. Diffusion of a free segment, in a time variant Self-Consistent Field (SCF), is described by the Fokker-Planck equation, while the segmental connectivity is described by the random-flight model. The adsorbing surface is treated as a singular phase having zero thickness, but a finite capacity to hold the adsorbed species. A boundary condition, which accounts for interfacial equilibrium as well as configurational constraint imposed by the impenetrable surface, has been formulated. Flory-Huggins theory has been used to estimate the mean field potential. The model equations have been solved to obtain segmental concentration distribution as a function of time, from which other relevant quantities like rate of adsorption, volume fraction etc., are estimated. Steady state adsorption characteristics can also be obtained as a special case of the model.