A generalized Gaussian overlap model for fluids of anisotropic particles

The heat conductivity of liquid crystal phases of a soft ellipsoid string-fluid evaluated by molecular dynamics simulation

We have applied a nonequilibrium molecular dynamics heat flow algorithm to calculate the heat conductivity of a molecular model system, which forms uniaxial and biaxial nematic liquid crystals. The model system consists of a soft ellipsoid string-fluid where the ellipsoids interact according to a repulsive version of the Gay-Berne potential. On compression, this system forms discotic or calamitic uniaxial nematic phases depending on the dimensions of the molecules, and on further compression a biaxial nematic phase is formed. In the discotic nematic phase, the heat conductivity has two components, one parallel and one perpendicular to the director, where the last mentioned component is the largest one. This order of magnitudes is reversed in the calamitic nematic phase. In the biaxial nematic phase there are three components of the heat conductivity, one in the direction around which the long axes of the molecules are oriented, this is the largest component, another one in the direction around which the normals of the broadsides of the molecules are oriented, this is the smallest component, and one in the direction perpendicular to these two directions with a magnitude in between those of the first mentioned components. The relative magnitudes of the components of the heat conductivity span a fairly wide interval so it should be possible to use the model to parameterise experimental data.

Computer simulations of biaxial nematics

Biaxial nematic (N(b)) liquid crystals are a fascinating condensed matter phase that has baffled, for more than thirty years, scientists engaged in the challenge of demonstrating its actual existence, and which has only recently been experimentally found. During this period computer simulations of model N(b) have played an important role, both in providing the basic physical properties to be expected from these systems, and in giving clues about the molecular features essential for the thermodynamic stability of N(b) phases. However, simulation studies are expected to be even more crucial in the future for unravelling the structural features of biaxial mesogens at the molecular level, and for helping in the design and optimization of devices towards the technological deployment of N(b) materials. This review article gives an overview of the simulation work performed so far, and relying on the recent experimental findings, focuses on the still unanswered questions which will determine the future challenges in the field.

Biaxial and uniaxial phases produced by partly repulsive mesogenic models involving D2h molecular symmetries

The present paper considers biaxial nematogenic lattice models, involving particles of D2h symmetry, whose centers of mass are associated with a three-dimensional simple-cubic lattice. The pair potential is isotropic in orientation space and restricted to nearest neighbors. Let two orthonormal triads define orientations of a pair of interacting particles. The investigated potential models are quadratic with respect to the nine scalar products between the two sets of unit vectors. Actually, based on available geometric identities, these expressions can be reduced to diagonal form containing only the scalar products between corresponding unit vectors and depending on three parameters. Over the years, this comparatively simple functional form has also proven to be rather versatile. By now, various sets of potential parameters capable of producing mesogenic behavior of some kind have been proposed and studied in the literature. A new and simplified form was recently proposed and investigated by Sonnet, Virga, Durand, and De Matteis [A. M. Sonnet, E. G. Virga, and G. E. Durand, Phys. Rev. E 67, 061701 (2003); G. De Matteis and E. G. Virga, Phys. Rev. E 71, 061703 (2005)] and is known to support a biaxial phase at sufficiently low temperature. Following the idea of the above authors, we have studied a more extended range of parameters, including cases where biaxiality cannot be sustained in the pair ground state. In cases where a biaxial phase survives, an appropriate mean-field analysis may predict the existence of a direct second-order transition to the isotropic phase as well as a second-order sequence isotropic-to-uniaxial-to-biaxial. A second-order phase transition is also predicted, which involves isotropic and uniaxial phases only. Monte Carlo simulations have been carried out as well, for a few points in the parameter space, and found to produce results which partly confirm mean-field predictions.

Minimal coupling model of the biaxial nematic phase

A minimal coupling model exhibiting isotropic, uniaxial, and biaxial nematic phases is analyzed in detail and its relation to existing models known in the literature is clarified. Its intrinsic symmetry properties are exploited to restrict the relevant ranges of coupling constants. Further on, properties of the model are thoroughly investigated by means of bifurcation theory as proposed by Kayser and Raveché [Phys. Rev. A 17, 2067 (1978)] and Mulder [Phys. Rev. A 39, 360 (1989)]. As a first step toward this goal, the bifurcation theory is applied to a general formulation of density functional theory in terms of direct correlation functions. On a general formal level, the theory is then analyzed to show that the bifurcation points from the reference, high-symmetry equilibrium phase to a low-symmetry structure depend only on the properties of the one-particle distribution function and the direct pair correlation function of the reference phase. The character of the bifurcation (whether spinodal, critical, tricritical, isolated Landau point, etc.) depends, in addition, on a few higher-order direct correlation functions. Explicit analytical results are derived for the case when only the leading L=2 terms of the potential (mean-field analysis) or of the direct pair correlation function expansion in the symmetry-adapted basis are retained. Formulas are compared with the numerical calculations for the mean-field, momentum L=2 potential model, in which case they are exact. In particular, bifurcations from the isotropic and uniaxial nematic to the biaxial nematic phases are discussed. The possibility of the recently reported nematic uniaxial-nematic biaxial tricritical point [A. M. Sonnet, E. G. Virga, and G. E. Durand, Phys. Rev. E 67, 061701 (2003)] is analyzed as well.