Clustering theory and vapor sorption by high polymers

An interpretive theory applicable to any binary system at sorption equilibrium is given by Zimm's equation relating directly the activity-volume behavior and the molecular geometry of the system. A clustering function, G11/V 1, a monotone, increasing function of the probability of finding molecules of the same kind close to one another is given by Where Values of G11/V 1<-1 decrease with increasing tendency of like molecules to segregate one from another or to form alternate arrays with molecules of the other component of a binary system; G11/v 1=-1 for a random mixture of equal size molecules; G11/V 1 >-1 increases with increasing tendency of like molecules to cluster. Diverse sorption behavior is easily interpreted in terms of this equation. For example, in water-protein systems the range of behavior from strong-binding, site adsorption to diffuse swelling as water concentration increases can be explained. The almost athermal, Langmuir-type adsorption found for methane in hydrocarbon polymer melts, the more familiar behavior of ordinary polymer solutions, and critical solution phenomena are equally amenable to treatment.