LATTICE CLUSTER THEORY FOR THE PACKING OF RODS ON A LATTICE - EXTENSION TO TREAT ANISOTROPIC ORIENTATIONAL DISTRIBUTIONS

The lattice cluster theory for the free energy of a set of mutually av oiding rigid rod polymers is extended to treat anisotropic orientation al distributions. The theory permits the systematic evaluation of corr ections to the isotropic Flory mean field approximation for arbitrary rod orientational distributions, with the Flory theory being the zerot h order isotropic limit of the full theory. The corrections to the zer oth order mean field entropy are represented as a cluster expansion an d may be evaluated as a series expansion in the polymer volume fractio n phi. We compute all corrections through order phi3 that survive in t he thermodynamic limit for the general anisotropic case, along with ne w fourth order results, which also extend the isotropic limit theory. The anisotropic rod lattice cluster theory represents an improvement o ver the DiMarzio theory for the packing entropy of rod polymers. This improvement first emerges at fourth order in phi and arises in the lat tice cluster theory from inclusion of correlations between four rods l ying along distinct lattice directions, four-rod correlations that are absent in DiMarzio's theory.