STATISTICAL-THEORY OF THE ADSORPTION OF INTERACTING CHAIN MOLECULES .1. PARTITION-FUNCTION, SEGMENT DENSITY DISTRIBUTION, AND ADSORPTION-ISOTHERMS

We present a general theory for polymer adsorption using a quasi-crystalline lattice model The partition function for a mixture of polymer chains and solvent molecules near an interface is evaluated by adopting the Bragg-Williams approximation of random mixing within each layer parallel to the surface. The interaction between segments and solvent molecules is taken into account by use of the Flory-Huggins parameter χ; that between segments and the interface is described in terms of the differential adsorption energy parameter χs. No approximation was made about an equal contribution of all the segments of a chain to the segment density in each layer. By differentiating the partition function with respect to the number of chains having a particular conformation an expression is obtained that gives the numbers of chains in each conformation in equilibrium. Thus also the train, loop, and tail size distribution can be computed. Calculations are carried out numerically by a modified matrix procedure as introduced by DiMarzio and Rubin. Computations for chains containing up to 1000 segments are possible. Data for the adsorbed amount T, the surface coverage θ, and the bound fraction p = θ/T are given as a function of χs, the bulk solution volume fraction φ*, and the chain length r for two χ values. The results are in broad agreement with earlier theories, although typical differences occur. Close to the surface the segment density decays roughly exponentially with increasing distance from the surface, but at larger distances the decay is much slower. This is related to the fact that a considerable fraction of the adsorbed segments is present in the form of long dangling tails, even for chains as long as r = 1000. In previous theories the effect of tails was usually neglected. Yet the occurrence of tails is important for many practical applications. Our theory can be easily extended to polymer in a gap between two plates (relevant for colloidal stability) and to copolymers. © 1979 American Chemical Society.