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.
A study of the liquid crystalline phase transitions in a system of hard-sphere chains is presented. The chains comprise m=7 tangentially bonded hard-sphere segments in a linear conformation (LHSC). The isothermal–isobaric Monte Carlo simulation technique is used to obtain the equation of state of the system both by compressing the isotropic (I) liquid and by expanding the solid (K). As well as the usual isotropic and solid phases, nematic and smectic-A liquid crystalline states are seen. A large degree of hysteresis is found in the neighborhood of the I–N transition. The results for the rigid LHSC system were compared with existing data for the corresponding semiflexible hard-sphere chains (FHSC): the flexibility has a large destabilizing effect on the nematic phase and consequently it postpones the I–N transition. The results of the simulations are also compared with rescaled Onsager theories for the I–N transition. It is rather surprising to find that the Parsons approach, which has been so successful for other hard-core models such as spherocylinders and ellipsoids, gives very poor results. The related approach of Vega and Lago gives a good description of the I–N phase transition. The procedure of Vega and Lago, as with all two-body resummations of the Onsager theory, only gives a qualitative description of the nematic order.
The isotropic–nematic phase transition in a fluid of hard spherocylinders with a spherocylindrical square-well attraction is examined using Monte Carlo simulations and two theoretical approaches. The first theory is a first-order perturbation theory which incorporates the Parsons decoupling approximation for the pair distribution function. The second theory is a simple resummation of the virial coefficients in the nematic phase which maps the thermodynamics of the nematic phase to those of the isotropic phase. In general both the theoretical approaches and the simulation results show a destabilization of the nematic phase with respect to the isotropic phase as the temperature is decreased. However, close comparison between the simulation results and the theories reveals that the Parsons approach is quantitatively deficient. On the other hand, the results for the resummation procedure are in good agreement with the simulation results over the full isotropic range and for the isotropic–nematic phase transition. The comparison of the nematic phase close to the phase transition shows reasonable agreement between theory and simulation, however, the theoretical results become much poorer deep in the nematic phase. The reason for this is attributed to the crude manner in which the orientational dependence is included into the attractive contribution to the free energy.
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