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

Lattice Monte Carlo study of orientational order in a confined system of biaxial particles: Effect of an external electric field

In this work we have used lattice Monte Carlo to determine the orientational order of a system of biaxial particles confined between two walls inducing perfect order and subjected to an electric field perpendicular to the walls. The particles are set to interact with their nearest neighbors through a biaxial version of the Lebwohl-Lasher potential. A particular set of values for the molecular reduced polarizabilities defining the potential used was considered; the Metropolis sampling algorithm was used in the Monte Carlo simulations. The relevant order parameters were determined in the middle plane of the sample and for some cases across the whole thickness of the sample. We have determined the temperature-electric field phase diagram for this system and found, as expected, five different system configurations corresponding to three different mesophases. At low temperatures and low fields the system finds itself in an undistorted biaxial phase. On increasing the field at low temperatures, a Freedericksz transition takes place and the secondary directors reorient towards the field while the primary director stays undistorted and parallel to the walls. On increasing the field further, a second Freedericksz transition occurs and the primary director orients also towards the field direction. The orientational order measured at the field strengths tested is not affected by the field. On increasing the temperature, a transition to a uniaxial phase occurs and within the range of this phase a field increase leads also to a Freedericksz transition where the main director reorients towards the field. At higher temperature a transition to a disordered phase is found. We have performed finite size scaling analysis for the Freedericksz critical fields and found that they scale with the distance L between the walls as L^{-1} as expected from continuum theory. From these fields we have also determined the temperature dependence of two elastic constant ratios. Critical exponents and critical temperatures for the order parameter and the correlation length for the biaxial-uniaxial phase transition and the uniaxial to disordered phase transition were also determined by finite size scaling and are discussed.

Complex free-energy landscapes in biaxial nematic liquid crystals and the role of repulsive interactions: A Wang-Landau study

General quadratic Hamiltonian models, describing the interaction between liquid-crystal molecules (typically with D_{2h} symmetry), take into account couplings between their uniaxial and biaxial tensors. While the attractive contributions arising from interactions between similar tensors of the participating molecules provide for eventual condensation of the respective orders at suitably low temperatures, the role of cross coupling between unlike tensors is not fully appreciated. Our recent study with an advanced Monte Carlo technique (entropic sampling) showed clearly the increasing relevance of this cross term in determining the phase diagram (contravening in some regions of model parameter space), the predictions of mean-field theory, and standard Monte Carlo simulation results. In this context, we investigated the phase diagrams and the nature of the phases therein on two trajectories in the parameter space: one is a line in the interior region of biaxial stability believed to be representative of the real systems, and the second is the extensively investigated parabolic path resulting from the London dispersion approximation. In both cases, we find the destabilizing effect of increased cross-coupling interactions, which invariably result in the formation of local biaxial organizations inhomogeneously distributed. This manifests as a small, but unmistakable, contribution of biaxial order in the uniaxial phase. The free-energy profiles computed in the present study as a function of the two dominant order parameters indicate complex landscapes. On the one hand, these profiles account for the unusual thermal behavior of the biaxial order parameter under significant destabilizing influence from the cross terms. On the other, they also allude to the possibility that in real systems, these complexities might indeed be inhibiting the formation of a low-temperature biaxial order itself-perhaps reflecting the difficulties in their ready realization in the laboratory.

Hierarchy of orientational phases and axial anisotropies in the gauge theoretical description of generalized nematic liquid crystals

The paradigm of spontaneous symmetry breaking encompasses the breaking of the rotational symmetries O(3) of isotropic space to a discrete subgroup, i.e., a three-dimensional point group. The subgroups form a rich hierarchy and allow for many different phases of matter with orientational order. Such spontaneous symmetry breaking occurs in nematic liquid crystals, and a highlight of such anisotropic liquids is the uniaxial and biaxial nematics. Generalizing the familiar uniaxial and biaxial nematics to phases characterized by an arbitrary point-group symmetry, referred to as generalized nematics, leads to a large hierarchy of phases and possible orientational phase transitions. We discuss how a particular class of nematic phase transitions related to axial point groups can be efficiently captured within a recently proposed gauge theoretical formulation of generalized nematics [K. Liu, J. Nissinen, R.-J. Slager, K. Wu, and J. Zaanen, Phys. Rev. X 6, 041025 (2016)2160-330810.1103/PhysRevX.6.041025]. These transitions can be introduced in the model by considering anisotropic couplings that do not break any additional symmetries. By and large this generalizes the well-known uniaxial-biaxial nematic phase transition to any arbitrary axial point group in three dimensions. We find in particular that the generalized axial transitions are distinguished by two types of phase diagrams with intermediate vestigial orientational phases and that the window of the vestigial phase is intimately related to the amount of symmetry of the defining point group due to inherently growing fluctuations of the order parameter. This might explain the stability of the observed uniaxial-biaxial phases as compared to the yet to be observed other possible forms of generalized nematic order with higher point-group symmetries.

Reexamination of the mean-field phase diagram of biaxial nematic liquid crystals: Insights from Monte Carlo studies

Investigations of the phase diagram of biaxial liquid-crystal systems through analyses of general Hamiltonian models within the simplifications of mean-field theory (MFT), as well as by computer simulations based on microscopic models, are directed toward an appreciation of the role of the underlying molecular-level interactions to facilitate its spontaneous condensation into a nematic phase with biaxial symmetry. Continuing experimental challenges in realizing such a system unambiguously, despite encouraging predictions from MFT, for example, are requiring more versatile simulational methodologies capable of providing insights into possible hindering barriers within the system, typically gleaned through its free-energy dependences on relevant observables as the system is driven through the transitions. The recent paper from this group [Kamala Latha et al., Phys. Rev. E 89, 050501(R) (2014)], summarizing the outcome of detailed Monte Carlo simulations carried out employing an entropic sampling technique, suggested a qualitative modification of the MFT phase diagram as the Hamiltonian is asymptotically driven toward the so-called partly repulsive regions. It was argued that the degree of (cross) coupling between the uniaxial and biaxial tensor components of neighboring molecules plays a crucial role in facilitating a ready condensation of the biaxial phase, suggesting that this could be a plausible factor in explaining the experimental difficulties. In this paper, we elaborate this point further, providing additional evidence from curious variations of free-energy profiles with respect to the relevant orientational order parameters, at different temperatures bracketing the phase transitions.

Detection of an intermediate biaxial phase in the phase diagram of biaxial liquid crystals: entropic sampling study

We investigate the phase sequence of biaxial liquid crystals, based on a general quadratic model Hamiltonian over the relevant parameter space, with a Monte Carlo simulation which constructs equilibrium ensembles of microstates, overcoming possible (free) energy barriers (combining entropic and frontier sampling techniques). The resulting phase diagram qualitatively differs from the universal phase diagram predicted earlier from mean-field theory (MFT), as well as the Monte Carlo simulations with the Metropolis algorithm. The direct isotropic-to-biaxial transition predicted by the MFT is replaced in certain regions of the space by the onset of an additional intermediate biaxial phase of very low order, leading to the sequence N(B)-N(B1)-I. This is due to inherent barriers to fluctuations of the components comprising the total energy, and may explain the difficulties in the experimental realization of these phases.

Calamitic and antinematic orientational order produced by the generalized Straley lattice model

We consider here a classical model, consisting of D_{2h}-symmetric particles in a three-dimensional simple-cubic lattice; the pair potential is isotropic in orientation space, and restricted to nearest neighbors. The simplest potential model is written in terms of the squares of the scalar products between unit vectors describing the three interacting arms of the molecules, as proposed in previous literature. Two predominant antinematic couplings of equal strength (+1) are perturbed by a comparatively weaker calamitic one, parameterized by a coupling constant -z ranging in [-1,0]. This choice rules out thermodynamically stable phases endowed with macroscopic biaxiality. The antinematic terms favor states with the corresponding molecular axes mutually orthogonal. Although the low-temperature phase of the special case with null calamitic term (PP0) is uniaxial and antinematically ordered, in the general case presented here both Monte Carlo and molecular-field approaches show that, for z close to zero, the models exhibit a low-temperature uniaxial nematic phase, followed by an antinematic one, and finally by the orientationally disordered one. On the other hand, for sufficiently large values of z, we only find evidence of uniaxial calamitic behavior, as expected by following the limiting cases.

Antinematic orientational order produced by an extreme case of the generalized Straley lattice model

We address here a special, extreme case of the quadratic pair interaction potential between classical, D(2h)-symmetric particles (the generalized Straley model) on a three-dimensional simple cubic lattice. The model involves predominant antinematic couplings and it has been studied by Monte Carlo simulation and a molecular field treatment. The obtained results show a second-order transition between the isotropic phase and the low-temperature one, exhibiting uniaxial antinematic order.

Orientationally ordered phase produced by fully antinematic interactions: a simulation study

We consider here a classical model, consisting of D(2h) symmetric particles, 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. Two orthonormal triads define orientations of a pair of interacting particles; the simplest potential models proposed in the literature can be written as a linear combination involving the squares of the scalar products between corresponding unit vectors only, thus depending on three parameters, and making the interaction model rather versatile. A coupling constant with negative sign tends to keep the two interacting unit vectors parallel to each other, whereas a positive sign tends to keep them mutually orthogonal (antinematic coupling). We address here a special, extreme case of the above family, involving only antinematic couplings: more precisely, three antinematic terms whose coefficients are set to a common positive value (hence the name PPP model). The model under investigation produces a doubly degenerate pair ground state; the nearest-neighbor range of the interaction and the bipartite character of the lattice can propagate the pair ground state and increase the overall degeneracy, but without producing frustration. The model was investigated by a simplified molecular field treatment as well as by Monte Carlo simulation, whose results suggested a second-order transition to a low-temperature biaxially ordered phase; ground-state configurations producing orientational order have been selected by thermal fluctuations. The molecular field treatment also predicted a continuous transition, and was found to overestimate the transition temperature by a factor 2.

Mesogenic lattice models with partly antinematic interactions producing uniaxial nematic phases

The present paper considers nematogenic lattice models, involving particles of D_{2h} 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 simplest potential models proposed in the literature can be reduced to a linear combination involving the squares of the scalar products between corresponding unit vectors only and depending on three parameters. By now, various sets of potential parameters have been proposed and studied in the literature, some of which capable of producing biaxial orientational order at sufficiently low temperature. On the other hand, in experimental terms, mesogenic biaxial molecules mostly produce uniaxial mesophases; thus we address here two very simple cases, involving a nematic (calamitic) term as well as one (model P0M) or two (model PPM) antinematic ones, whose coefficients are set equal in magnitude; when only one antinematic coefficient is used, the third one is set to zero. The calamitic term favors the alignment of two corresponding molecular axes, whereas antinematic terms or geometric constraints tend to keep two other pairs of axes mutually orthogonal. The models were investigated by molecular-field treatments and Monte Carlo simulation and found to predict a first- or second-order transitions between uniaxial nematic and isotropic phases; the molecular-field treatments yielded results in reasonable agreement with simulation.