Structure and stability of isotropic states of hard platelet fluids

Abstract

We study the thermodynamics and the pair structure of hard, infinitely thin, circular platelets in the isotropic phase. Monte Carlo simulation results indicate a rich spatial structure of the spherical expansion components of the direct correlation function, including nonmonotonical variation of some of the components with density. Integral equation theory is shown to reproduce the main features observed in simulations. The hypernetted chain closure, as well as its extended versions that include the bridge function up to second and third order in density, perform better than both the Percus-Yevick closure and Verlet bridge function approximation. Using a recent fundamental measure density functional theory, an analytic expression for the direct correlation function is obtained as the sum of the Mayer bond and a term proportional to the density and the intersection length of two platelets. This is shown to give a reasonable estimate of the structure found in simulations, but to fail to capture the nonmonotonic variation with density. We also carry out a density functional stability analysis of the isotropic phase with respect to nematic ordering and show that the limiting density is consistent with that where the Kerr coefficient vanishes. As a reference system, we compare to simulation results for hard oblate spheroids with small, but nonzero elongations, demonstrating that the case of vanishingly thin platelets is approached smoothly.

Relaxation dynamics in the columnar liquid crystal phase of hard platelets

“…[48][49][50][51][52][53][54][55][56][57][58] In fact, discotic mesogens are rather complex organic molecules and many of them are required to properly simulate the phase and aggregation behavior as well as the dynamics in the Col mesophase. Atomistic models provide a worthwhile tool to access the details of liquid crystals at the molecular level, but they are too computationally demanding to handle more than some tens of mesogens during an appropriate time interval.…”

Phase diagram of hard colloidal platelets: a theoretical account

“…6 for a recent overview). These approaches usually involve integral equation or geometric density functional methods whose applicability is often restricted to isotropic fluids [7,8], models with parallel or restricted orientations [9] or particles with vanishing thickness [10,11]. A recent generalisation of the fundamental measure approach towards arbitrarily shaped hard convex bodies provides a potentially promising avenue to address more realistic models for liquid crystal ordering [12].…”

Simulation of scattering and phase behavior around the isotropic–nematic transition of discotic particles

“…Esztermann et al [20] apply DFT and fundamental measure theory (FMT) to study the I-N transition of infinitely thin disks and determine the coexistence properties at the transition, in particular the densities and the value of the nematic order parameter in the nematic phase, in good agreement with simulation results from Frenkel and Eppenga [15]. In a more recent work, using simulation, FMT DFT and IET, Cheung et al [21,22] study the isotropic phase of a variety of hard-particle liquids, with emphasis on hard platelets. Although these methods are successful in describing the equation of state at lower densities, they are found to be less successful for platelet based systems at higher densities.…”