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

A continuum version of self-consistent field model for polymer adsorption at the solid-liquid interface has been formulated and solved to obtain configurational statistics of an adsorbed polymer chain. The solid surface is viewed as a singular phase (having zero thickness but finite adsorption capacity) in equilibrium with the solution. Chain configuration is described by the random flight model. The surface boundary condition accounts for both the configurational constraint and the adsorption equilibrium. The potential field is described by a modified form of the Flory-Huggins theory, which incorporates the effect of unequal partial volumes of the species (chain segment and solvent molecule) in the solution and their unequal partial areas in the surface phase. The model predictions are in qualitative agreement with the Scheutjens and Fleer model, except that the model predicts a negative value of chi(c)*, the critical adsorption energy parameter. The model has been validated using experimental data reported in the literature. The present 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 difference in the packing densities between the solution and the surface