Constant-pressure molecular-dynamics simulations of the crystal-smectic transition in systems of soft parallel spherocylinders

In order to investigate thermodynamic properties and microscopic structure around the crystal-smectic transition, we present constant-pressure molecular-dynamics simulations for soft parallel spherocylinders as a model for liquid crystals. The method of Andersen [J. Chem. Phys. 72, 2384 (1980)] as well as the method of Parrinello and Rahman [Phys. Rev. Lett. 45, 1196 (1980)] are applied to a right parallelepiped simulation box, and the equation of state for this model is evaluated. Thermodynamic properties such as enthalpy and volume as functions of reduced density ${\mathrm{\rho }}^{\mathrm{*}}$ or of temperature show a clear first-order transition. The dependence of ${\mathit{l}}_{\mathrm{\perp }}$ the square root of the specific area of the plane perpendicular to the molecular axis, on ${\mathrm{\rho }}^{\mathrm{*}}$ shows a feature characteristic of two-dimensional melting. We calculate the specific length ${\mathit{l}}_{\mathit{z}}$ in the direction of the molecular axis, which corresponds to the thickness of a smectic layer in the liquid-crystal region. From the ${\mathrm{\rho }}^{\mathrm{*}}$ dependence of ${\mathit{l}}_{\mathit{z}}$ and ${\mathit{l}}_{\mathit{z}}$/${\mathit{l}}_{\mathrm{\perp }}$, we show that the anisotropy of the molecular volume plays an important role in the crystal-smectic transition. We also observe a clear change in both diffusion and structural properties before and after this transition. The mean-square displacements in directions perpendicular to the alignment show that in the smectic phase the moleules diffuse freely within the layers, although the density wave in the direction perpendicular to layers does exist even after the transition.