Lattice model for thermotropic liquid crystals. II. Results and conclusions

Abstract

The fcc lattice model presented in the preceding paper [Phys. Rev. A 40, 6021 (1989)] is used to study smectic-A and nematic mesophases formed by molecules with a central rigid core and two symmetric semiflexible pendent tails. The method used to solve the complex nonlinear equations for the density and the orientational, positional, and conformational order parameters of the model system at a particular temperature and pressure is described, as is the procedure used to find smectic-nematic (Sm-N), nematic-isotropic (N-I), and smectic-isotropic (Sm-I) phase-transition temperatures. Calculated mesophase diagrams, i.e., plots of transition temperatures versus tail length f/2, are presented for 12 model homologous series with various values of the tail-bending energy \ensuremath{\xi} and the segmental interaction energies.For small values of \ensuremath{\xi}, the model systems exhibit no stable nematic phase and the Sm-I transition temperature ${T}_{\mathrm{Sm}\mathrm{\ensuremath{-}}\mathit{I}}$ decreases with increasing tail length f/2. For moderate values of \ensuremath{\xi}, behavior qualitatively very similar to that exhibited by many homologous series of real mesogens is obtained, i.e., ${T}_{N\mathrm{\ensuremath{-}}I}$ decreases and ${T}_{\mathrm{Sm}\mathrm{\ensuremath{-}}\mathit{N}}$ increases with increasing f/2 until the two curves meet to form a falling ${T}_{\mathrm{Sm}\mathrm{\ensuremath{-}}\mathit{I}}$ curve. For very large values of \ensuremath{\xi}, the ${T}_{\mathrm{Sm}\mathrm{\ensuremath{-}}\mathit{N}}$ curve is nearly flat and the ${T}_{N\mathrm{\ensuremath{-}}I}$ curve rises sharply as f/2 increases. Over a narrow range of moderately large \ensuremath{\xi} values, reentrant behavior is exhibited by the homologs with longer tails. A detailed analysis of this model behavior leads to a coherent physical explanation of the behavior of the Sm-N, N-I, and Sm-I transition temperatures as a function of tail length for many real homologous series. Our results indicate that tail flexibility plays a major role in determining the nature and stability of smectic-A, nematic, and isotropic liquid phases of rodlike mesogens with alkyl or alkoxy tails. In particular, it is strongly suggested that conformational entropic stabilization of the smectic relative to the nematic mesophase is at least as important as energetic stabilization of the smectic phase by strong attractions between molecular cores.