Tetrahedratic mesophases, chiral order, and helical domains induced by quadrupolar and octupolar interactions.

We present an exhaustive account of phases and phase transitions that can be stabilized in the recently introduced generalized Lebwohl-Lasher model with quadrupolar and octupolar microscopic interactions [L. Longa, G. Pajak, and T. Wydro, Phys. Rev. E 79, 040701(R) (2009)]. A complete mean-field analysis of the model, along with Monte Carlo simulations allows us to identify four distinct classes of the phase diagrams with a number of multicritical points where, in addition to the standard uniaxial and biaxial nematic phases, the other nematic like phases are stabilized. These involve, among the others, tetrahedratic (T), nematic tetrahedratic (N(T)), and chiral nematic tetrahedratic (N(T)(*)) phases of global T(d), D(2d), and D(2) symmetry, respectively. Molecular order parameters and correlation functions in these phases are determined. We conclude with generalizations of the model that give a simple molecular interpretation of macroscopic regions with opposite optical activity (ambidextrous chirality), observed, e.g., in bent-core systems. An estimate of the helical pitch in the N(T)(*) phase is also given.

Chiral symmetry breaking in bent-core liquid crystals.

By molecular modeling we demonstrate that the nematic long-range order discovered in bent-core liquid-crystal systems should reveal further spatially homogeneous phases. Two of them are identified as a tetrahedratic nematic (N_{T}) phase with D_{2d} symmetry and a chiral tetrahedratic nematic (N_{T};{ *}) phase with D2 symmetry. These phases were found for a lattice model with quadrupolar and octupolar anisotropic interactions using mean-field theory and Monte Carlo simulations. The phase diagrams exhibit tetrahedratic (T) , N_{T} , and N_{T};{ *} phases, in addition to ordinary isotropic (I) , uniaxial nematic (N_{U}) , and biaxial nematic (N_{B}) phases.

Stability of biaxial nematic phase for systems with variable molecular shape anisotropy.

We study the influence of fluctuations in molecular shape on the stability of the biaxial nematic phase by generalizing the mean-field model of Mulder and Ruijgrok [Physica A 113, 145 (1982)]. We limit ourselves to the case when the molecular shape anisotropy, represented by the alignment tensor, is a random variable of an annealed type. A prototype of such behavior can be found in lyotropic systems--a mixture of potassium laurate, 1-decanol, and D2O , where distribution of the micellar shape adjusts to actual equilibrium conditions. Further examples of materials with the biaxial nematic phase, where molecular shape is subject to fluctuations, are thermotropic materials composed of flexible trimericlike or tetrapodlike molecular units. Our calculations show that the Gaussian equilibrium distribution of the variables describing molecular shape (dispersion force) anisotropy gives rise to new classes of the phase diagrams, absent in the original model. Depending on properties of the shape fluctuations, the stability of the biaxial nematic phase can be either enhanced or depressed, relative to the uniaxial nematic phases. In the former case the splitting of the Landau point into two triple points with a direct phase transition line from isotropic to biaxial phase is observed.