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The formal description of penetrant clustering in polymers given by Zimm and Lundberg is applied to systems obeying Flory-Huggins thermodynamics. Several equivalent procedures for evaluation of the cluster function are suggested including circumstances in which the interaction parameter χ1 varies with composition. An analysis of the cluster function for penetrant and the companion expression for clustering of the polymeric solute is presented for some familiar, special cases of Flory-Huggins' behavior. The utility of the analyses is illustrated by application of these analytical techniques to data taken from the literature.
Orofino et al. (1969) studied this question.