Lattice cluster theory for the packing of rods on a lattice: Extension to treat anisotropic orientational distributions
- 1 August 1993
- journal article
- research article
- Published by AIP Publishing in The Journal of Chemical Physics
- Vol. 99 (3), 2149-2166
- https://doi.org/10.1063/1.466178
Abstract
The lattice cluster theory for the free energy of a set of mutually avoiding rigid rod polymers is extended to treat anisotropic orientational distributions. The theory permits the systematic evaluation of corrections to the isotropic Flory mean field approximation for arbitrary rod orientational distributions, with the Flory theory being the zeroth order isotropic limit of the full theory. The corrections to the zeroth order mean field entropy are represented as a cluster expansion and may be evaluated as a series expansion in the polymer volume fraction φ. We compute all corrections through order φ3 that survive in the thermodynamic limit for the general anisotropic case, along with new fourth order results, which also extend the isotropic limit theory. The anisotropic rod lattice cluster theory represents an improvement over the DiMarzio theory for the packing entropy of rod polymers. This improvement first emerges at fourth order in φ and arises in the lattice cluster theory from inclusion of correlations between four rods lying along distinct lattice directions, four‐rod correlations that are absent in DiMarzio’s theory.Keywords
This publication has 16 references indexed in Scilit:
- Marriage of exact enumeration and 1/d expansion methods: Lattice model of dilute polymersJournal of Statistical Physics, 1992
- Effect of monomer structure and compressibility on the properties of multicomponent polymer blends and solutions: 1. Lattice cluster theory of compressible systemsMacromolecules, 1991
- Lattice theories of polymeric fluidsThe Journal of Physical Chemistry, 1989
- Lattice models of polymer solutions: Monomers occupying several lattice sitesThe Journal of Chemical Physics, 1987
- Statistical mechanics of the packing of rods on a lattice: Cluster expansion for systematic corrections to mean fieldThe Journal of Chemical Physics, 1986
- Statistical Mechanics of Dimers on a Plane LatticePhysical Review B, 1961
- The statistics of dimers on a latticePhysica, 1961
- Statistics of Orientation Effects in Linear Polymer MoleculesThe Journal of Chemical Physics, 1961
- Statistical thermodynamics of semi-flexible chain moleculesProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1956
- Phase equilibria in solutions of rod-like particlesProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1956