MULTICOMPONENT POLYMER ADSORPTION - A USEFUL APPROXIMATION BASED UPONGROUND-STATE SOLUTIONS

A simple ground-state approximation (GSA) is used to calculate the com position of an adsorbed layer in a multicomponent mixture of homopolym ers. The model uses two basic assumptions. The first is that the volum e fraction at position z of a component with chain length N can be wri tten as the product of the square of an eigenfunction g(z) and the Nth power of an eigenvalue Lambda. The second is that only segments in co ntact with the surface experience a field which is different from that in the bulk solution: only for these segments the segmental weighting factor G differs from unity. With these assumptions, a simple relatio n between G and Lambda is derived. For a given adsorbed amount, Lambda can then be computed directly from an implicit equation, and the cont ribution of each chain length in a mixed adsorbed layer is obtained by weighting with Lambda(N). This approximate model gives results which are in excellent agreement with numerical self-consistent field calcul ations. Several examples are given to illustrate the applicability of the model to experimental systems: adsorption fractionation in polydis perse polymers, polymer-polymer displacement, and adsorption and desor ption isotherms in polydisperse systems. Simple expressions are obtain ed for the chain length characterising the transition between (long) a dsorbed and (short) non-adsorbed chains and for the width of the trans ition zone.