Comparing the Flory approach with the DiMarzio theory of the statistical mechanics of rodlike particles

Three descriptions of the rod orientation in the Flory lattice model for rods (generalized to a continuum) are compared in an athermal system with the more accurate DiMarzio model for rodlike particles in a continuum. The Flory-type rod orientation distribution functions yield distributions quite similar to the DiMarzio distribution. The Flory-type distribution function obtained from the rod orientation expression (y-1) = (x-1) sin theta can be used in the DiMarzio entropy equation at a calculational advantage to yield entropies which are virtually indistinguishable from the original. Flory-type nematic and isotropic entropies differ from the DiMarzio entropies, giving slightly different phase equilibria. A solution to the "entropy catastrophe" for rods is explained in terms of the improper use of a one-dimensional boundary condition in the third dimension. 38 ref.--AA