A continuum model for polymer adsorption at the solid-liquid interface

A continuum version of self-consistent field model for polymer adsorption a t the solid-liquid interface has been formulated and solved to obtain confi gurational statistics of an adsorbed polymer chain. The solid surface is vi ewed as a singular phase (having zero thickness but finite adsorption capac ity) in equilibrium with the solution. Chain configuration is described by the random flight model. The surface boundary condition accounts for both t he configurational constraint and the adsorption equilibrium. The potential field is described by a modified form of the Flory-Huggins theory, which i ncorporates the effect of unequal partial volumes of the species (chain seg ment and solvent molecule) in the solution and their unequal partial areas in the surface phase. The model predictions are in qualitative agreement wi th the Scheutjens and Fleer model, except that the model predicts a negativ e value of chi(c)*, the critical adsorption energy parameter. The model has been validated using experimental data reported in the literature. The pre sent model has advantages over the Scheutjens and Fleer model both in terms of ease of computation and the ability of the model to account for the dif ference in the packing densities between the solution and the surface.