A re-examination of the phase diagram of hard spherocylinders

Abstract

The phase transitions exhibited by systems of hard spherocylinders, with a diameter D and cylinder length L, are re-examined with the isothermal–isobaric Monte Carlo (MC-NPT) simulation technique. For sufficiently large aspect ratios (L/D) the system is known to form liquid crystalline phases: isotropic (I), nematic (N), smectic-A (Sm A), and solid (K) phases are observed with increasing density. There has been some debate about the first stable liquid crystalline phase to appear as the aspect ratio is increased from the hard-sphere limit. We show that the smectic-A phase becomes stable before the nematic phase as the anisotropy is increased. There is a transition directly from the isotropic to the smectic-A phase for the system with L/D=3.2. For larger aspect ratios, e.g., L/D=4, the smectic-A phase is preceded by a nematic phase. This means that the hard spherocylinder system exhibits I–Sm A–K and I–N–Sm A triple points, the latter occurring at a larger aspect ratio. We also confirm the simulation results of Frenkel [J. Phys. Chem. 92, 3280 (1988)] for the system with L/D=5, which exhibits isotropic, nematic, smectic-A, and solid phases. All of the phase transitions are accompanied by a discontinuous jump in the density, and are, therefore, first order. In the light of these new simulation results, we re-examine the adequacy of the Parsons [Phys. Rev. A 19, 1225 (1979)] scaling approach to the theory of Onsager for the I–N phase transition. It is gratifying to note that this simple approach gives an excellent representation of both the isotropic and nematic branches, and gives accurate densities and pressures for the I–N phase transition. As expected for such a theory, the corresponding orientational distribution function is not accurately reproduced at the phase transition. The results of the recent Onsager/DFT theory of Esposito and Evans [Mol. Phys. 83, 835 (1994)] for the N–Sm A bifurcation point are also in agreement with the simulation data. It is hoped that our simulation results will be used for comparisons with systems with more complex interactions, e.g., dipolar hard spherocylinders and hard spherocylinders with attractive sites.

The phase behavior of a binary mixture of rodlike and disclike mesogens: Monte Carlo simulation, theory, and experiment

“…In a fluid of pure hard spherocylinders of (L/D) HSC ϭ5 the isotropic-nematic transition is observed for packing fractions I ϭ0.407Ϫ N ϭ0.415, and the nematic-smectic A transition for packing fractions N ϭ0.472 Ϫ SmA ϭ0.487. [27][28][29][30] Similarly, in a fluid of pure hard cut spheres of (L/D CS ϭ0.12) an isotropic-columnar phase transition is observed for packing fractions I ϭ0.395-Col ϭ0.436. 31,32 However, the simulated equimolar mixture presents a stable mixed isotropic phase for packing fractions up to 0.44 at least.…”

“…A small destabilization with respect to the transition densities of the pure components is again seen; a pure fluid of hard-spherocylinders of (L/D) HSC ϭ5 exhibits a nematicsmectic A phase transition at packing fractions of N ϭ0.472 and SmA ϭ0.487. 29 In this configuration, the interface lies normal to the layers of the rod-rich smectic phase, so that the density profile of the rodlike molecules is homogeneous in the direction z normal to the interface. On the other hand, the columns of the disc-rich columnar phase lie parallel to the interface, and hence the density profile of the disclike molecules provides an indication of the structure of this phase ͓see Fig.…”

Global fluid phase behavior in binary mixtures of rodlike and platelike molecules

“…It has been known for some time that the fluid phases of anisotropic hard particles such as ellipsoids, 49,50 spherocylinders, [51][52][53][54] and cylinders, 8 can exhibit varying degrees of orientational and translational order which give rise to liquid crystalline phase behavior including nematic, smectic, and columnar phases. It is also known that these phases are stabilized by the reduction of the excluded volume in the aligned configurations.…”

Understanding and Describing the Liquid-Crystalline States of Polypeptide Solutions: A Coarse-Grained Model of PBLG in DMF

“…22,23,27,28,33,36,39 An essential requirement for the stabilization of a LC phase is that the molecules be highly anisotropic in shape, such as long rigid rods or thin flat discs. For this reason, rodlike [41][42][43][44][45][46][47] particles are often employed as prototype models for prolate LC molecules (see reference 48 for a relatively recent review). Hard non-spherical particles are often taken as 'zeroth-order' models for lyotropic or colloidal LCs in which the appearance of anisotropic phases is controlled by the solute concentration.…”