Multicomponent polymer adsorption a useful approximation based upon ground-state solutions

Abstract

Abstract A simple ground-state approximation (GSA) is used to calculate the composition of an adsorbed layer in a multicomponent mixture of homopolymers. The model uses two basic assumptions. The first is that the volume fraction at position z of a component with chain length N can be written as the product of the square of an eigenfunction g(z) and the Nth power of an eigenvalue Λ. The second is that only segments in contact 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 relation between G and Λ is derived. For a given adsorbed amount, Λ can then be computed directly from an implicit equation, and the contribution of each chain length in a mixed adsorbed layer is obtained by weighting with ΛN. This approximate model gives results which are in excellent agreement with numerical self-consistent field calculations. Several examples are given to illustrate the applicability of the model to experimental systems: adsorption fractionation in polydisperse polymers, polymer-polymer displacement, and adsorption and desorption isotherms in polydisperse systems. Simple expressions are obtained for the chain length characterising the transition between (long) adsorbed and (short) non-adsorbed chains and for the width of the transition zone.