Abstract
DiMarzio’s lattice model is used to calculate the configurational entropy of a population of rigid rectangular parallelepipeds which is arbitrarily heterogeneous in both lengths and widths. An analytical expression is obtained which is a product of a small number of terms and is readily applicable to statistical thermodynamic calculations. The limit of infinitesimal lattice cell size is considered as an approximation of a continuum description. In this continuum limit, the alignment transition for monodisperse nematogen is found to occur at a lower density, and with a smaller density discontinuity, than is predicted by the lattice model in its original form. Although, at a given density, the alignment and the pressure are generally greater in the continuum description than in the discrete description, the alignment and pressure are less at the transition in the continuum case than they are at the transition in the discrete case. Whereas the original lattice model predicts that no transition occurs for particles of axial ratio less than 3.65, in the continuum limit the transition disappears only when the axial ratio is less than 3.06. Alternative approaches for treating solvents are discussed.