GROUND-STATE DESCRIPTION OF THE ADSORPTION OF HOMODISPERSE AND POLYDISPERSE POLYMERS

A ground-state approximation (GSA) is employed to model the structure of an adsorbed layer of homodisperse and polydisperse polymer. The mod el uses the basic assumption that the volume fraction at a distance z from the surface of a component with chain length N can be written as the product of the square of an eigenfunction g(z) and the N-th power of an eigenvalue e(epsilon). This approximation implies the neglect of end effects (tails): only loops are considered. For a homodisperse po lymer, the eigenvalue is defined through epsilon N = In(1/phi(b)), whe re phi(b) is the bulk solution concentration. The eigenfunction can be written in terms of two parameters: a ''proximal'' length D which thr ough the boundary condition may be related to the adsorption energy, a nd a ''distal'' length which is inversely proportional to root epsilon . For a polydisperse polymer, D is the same as for a homodisperse poly mer, but e has to be computed from an implicit equation which involves a summation over all chain lengths present. The contribution of each chain length N in a mixed adsorbed layer is obtained by weighting with e(epsilon N). This approximate analytical model gives results which a re in good agreement with numerical self-consistent-field calculations . Examples are given to illustrate the applicability of the model to p olydisperse systems. These include adsorption preference of long chain s in polymer mixtures and the difference between adsorption and desorp tion isotherms in polydisperse systems. Simple expressions are obtaine d for the chain length characterising the transition between (long) ad sorbed and (short) non-adsorbed chains and for the width of the transi tion zone.