Topological phase transitions in two-dimensional bent-core liquid crystal models.

Two-dimensional liquid crystal (LC) models of interacting V-shaped bent-core molecules with two rigid rodlike identical segments connected at a fixed angle (θ=112^{∘}) are investigated. The model assigns equal biquadratic tensor coupling among constituents of the interacting neighboring molecules on a square lattice, allowing for reorientations in three dimensions (d=2, n=3). We find evidence of two temperature-driven topological transitions mediated by point disclinations associated with the three ordering directors, condensing the LC medium successively into uniaxial and biaxial phases. With Monte Carlo simulations, temperature dependencies of the system energy, specific heat, orientational order parameters, topological order parameters, and densities of unbound topological defects of the different ordering directors are computed. The high-temperature transition results in topological ordering of disclinations of the primary director, imparting uniaxial symmetry to the phase. The low-temperature transition precipitates simultaneous topological ordering of defects of the remaining directors, resulting in biaxial symmetry. The correlation functions, quantifying spatial variations of the orientational correlations of the molecular axes show exponential decays in the high-temperature (disordered) phase, and power-law decays in the low-temperature (biaxial) phase. Differing temperature dependencies of the topological parameters point to a significant degree of cross coupling among the uniaxial and biaxial tensors of interacting molecules. This simplified Hamiltonian leaves θ as the only free model parameter, and the system traces a θ-dependent trajectory in a plane of the phenomenological parameter space.

Topological transition in a two-dimensional three-vector model: A non-Boltzmann Monte Carlo study.

Two-dimensional three-vector (d=2,n=3) lattice model of a liquid crystal (LC) system with order parameter space (R) described by the fundamental group Π_{1}(R)=Z_{2} was recently investigated based on non-Boltzmann Monte Carlo simulations. Its results indicated that the system did not undergo a topological transition condensing to a low temperature critical state as was reported earlier. Instead, a crossover to a nematic phase was observed, induced by the onset of a competing relevant length scale. This mechanism is further probed here by assigning a more restrictive R symmetry with Π_{1}(R)=Q (the discrete and non-Abelian group of quaternions), thus engaging the three spin degrees in the formation of point topological defects (disclinations). The results reported here indicate that such a choice of symmetry of the Hamiltonian with suitable model parameters leads to a defect-mediated transition to a low-temperature phase with topological order. It is characterized by a line of critical points with quasi-long-range order of its three spin degrees. The associated temperature-dependent power-law exponent decreases progressively and vanishes linearly as temperature tends to zero. The high-temperature disordered phase shows exponential spin correlations and their temperature-dependent lengths exhibit an essential singular divergence as the system approaches the topological transition point. Biaxial LC models have the required R symmetry owing to their tensor orientational orders and are suggested to serve as prototype examples to exhibit topological transition in (d=2,n=3) lattice models.

Two Phase Transitions in the Two-Dimensional Nematic Three-Vector Model with No Quasi-Long-Range Order: Monte Carlo Simulation of the Density of States.

The presence of stable topological defects in a two-dimensional (d=2) liquid crystal model allowing molecular reorientations in three dimensions (n=3) was largely believed to induce a defect-mediated Berzenskii-Kosterlitz-Thouless-type transition to a low temperature phase with quasi-long-range order. However, earlier Monte Carlo (MC) simulations could not establish certain essential signatures of the transition, suggesting further investigations. We study this model by computing its equilibrium properties through MC simulations, based on the determination of the density of states of the system. Our results show that, on cooling, the high temperature disordered phase deviates from its initial progression towards the topological transition, crossing over to a new fixed point, condensing into a nematic phase with exponential correlations of its director fluctuations. The thermally induced topological kinetic processes continue, however, limited to the length scales set by the nematic director fluctuations, and lead to a second topological transition at a lower temperature. It is argued that in the (d=2, n=3) system with an attractive biquadratic Hamiltonian, the presence of additional molecular degrees of freedom and local Z_{2} symmetry associated with lattice sites together promote the onset of an additional relevant scaling field at matching length scales in the high temperature region, leading to a crossover.

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.

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.

Colloidal nanoparticles trapped by liquid-crystal defect lines: a lattice Monte Carlo simulation.

Lattice-based Monte Carlo simulations are performed to study a confined liquid crystal system with a topological disclination line entangling a colloidal nanoparticle. In our microscopic study the disclination line is stretched by moving the colloid, as in laser tweezing experiments, which results in a restoring force attempting to minimize the disclination length. From constant-force simulations we extract the corresponding disclination line tension, estimated as ∼50 pN, and observe its decrease with increasing temperature.

Rheological properties of a reentrant nematic liquid crystal.

We report experimental studies on small angle light scattering (SALS), and rheodielectric and electrorheological properties of a binary mixture of octyloxy cyanobiphenyl and hexyloxy cyanobiphenyl liquid crystals. The mixture exhibits nematic (N) to smectic-A (SmA) phase transitions, and then again to a reentrant nematic (N(R)) phase transition. Rapid shear thinning in the quenched samples in the low shear rate region in the N and SmA phases observed from SALS experiments is attributed to the realignment of the director within the domains. The domains are elongated along the shear direction at higher shear rates. The temperature variation of the effective viscosity and static dielectric constant reveals the changes in the director orientation across N-SmA-N(R) phase transitions. At a steady shear rate the effective viscosity increases with the electric field in all the phases and saturates at much higher fields. It also exhibits two anomalous peaks across N-SmA-N(R) phase transitions beyond a particular field. The shear modulus of the SmA phase in an intermediate field is significantly larger than that measured at both low and high fields. This enhanced viscoelasticity of the SmA phase is argued to originate from the increased dislocation density.

Effect of electric field on the rheological and dielectric properties of a liquid crystal exhibiting nematic-to-smectic-A phase transition.

We report simultaneous measurements of shear viscosity (η) and dielectric constant (ε) of octyloxy cyanobiphenyl (8OCB) in the nematic (N) and smectic-A (SmA) phases as functions of temperature and electric field. With increasing electric field η increases in the N phase whereas it decreases in the SmA phase and saturates beyond a particular field in both the phases. The flow curves in the intermediate-field range show two Newtonian regimes in the N phase. The temperature-dependent behavior of η and ε at zero or at small electric field suggests the occurrence of several structures that results from precessional motion of the director along the neutral direction as reported in similar other system. We show that the precessional motions are gradually suppressed with increasing electric field and the effective viscosity resembles with the Miesowicz viscosity η1 at high enough electric field. In the intermediate field range the temperature-dependent η exhibits anomalous behavior across the N-SmA phase transition which is attributed to the large contribution of Leslie coefficient α1.

Slow dynamics in a liquid crystal: 1H and 19F NMR relaxometry.

Spin-lattice relaxation rates (R(1H) and R(1F)) of two nuclear species ((1)H and (19)F) are measured at different temperatures in the isotropic phase of a liquid crystal (4(')-butoxy-3(')-fluoro-4-isothiocyanatotolane-4OFTOL), over a wide range of Larmor frequency (10 kHz-50 MHz). Their dispersion profiles are found to be qualitatively very different, and the R(1F) in particular shows significant dispersion (varying over two orders of magnitude) in the entire isotropic range, unlike R(1H). The proton spin-lattice relaxation, as has been established, is mediated by time modulation of magnetic dipolar interactions with other protons (case of like spins), and the discernable dispersion in the mid-frequency range, observed as the isotropic to nematic transition is approached on cooling, is indicative of the critical slowing of the time fluctuations of the nematic order. Significant dispersion seen in the R(1F) extending to very low frequencies suggests a distinctly different relaxation path which is exclusively sensitive to the ultra slow modes apparently present in the system. We find that under the conditions of our experiment at low Zeeman fields, spin-rotation coupling of the fluorine with the molecular angular momentum is the dominant mechanism, and the observed dispersion is thus attributed to the presence of slow torques experienced by the molecules, arising clearly from collective modes. Following the arguments advanced to explain similar slow processes inferred from earlier detailed ESR measurements in liquid crystals, we propose that slowly relaxing local structures representing such dynamic processes could be the likely underlying mechanism providing the necessary slow molecular angular momentum correlations to manifest as the observed low frequency dispersion. We also find that the effects of the onset of cross-relaxation between the two nuclear species when their resonance lines start overlapping at very low Larmor frequencies (below ~400 kHz), provide an additional relaxation contribution.

Temperature- and electric-field-induced inverse Freedericksz transition in a nematogen with weak surface anchoring.

We report electric field dependence of the anchoring transition in a mesogen on cooling in a cell with perfluoropolymer treated surfaces. Below a crossover voltage V(co) the transition is discontinuous between planar and homeotropic alignments, and as the temperature is lowered, the transition temperature decreases quadratically with the field. Above V(co) the transition is continuous between planar and tilted alignments, the transition temperature decreasing essentially linearly with the rms field. We develop a simple model to account for these results and argue that the higher field regime corresponds to a temperature driven inverse Freedericksz transition in which the director orientation starts tilting at the weakly anchored surfaces while the tilt angle remains zero at the midplane of the cell.

Splay bend elasticity of a bent-core nematic liquid crystal.

We measured the splay (K11) and bend (K33) elastic constants in the nematic phase of a bent-core liquid crystal. In the vicinity of the nematic-isotropic transition temperature K33 is proportional to the square of the order parameter. In the nematic range K11 increases monotonically with decreasing temperature, whereas K33 is practically independent of temperature and is smaller than K11 . K33 exhibits a pretransitional slow divergence toward the transition temperature to the smectic phase and becomes slightly larger than K11. The small K33 is explained on the basis of strong coupling of the bent shape of the molecules with the bend distortion.

Splay-bend elasticity of a nematic liquid crystal with T-shaped molecules.

We measured the splay (K11) and bend (K33) elastic constants in the nematic phase of a liquid crystal with T-shaped molecules. We find that the ratio, K33/K11 ≃1 in the entire nematic range except very close to the nematic to Sm-A (SN) transition. Both K33 and K11 show pretransitional divergence as the SN transition is approached from higher temperature. The ratio, K33/K11 suggests that the length (L) to effective width (D) ratio (i.e., L/D ) is significantly smaller due to the presence of long and flexible lateral group, compared to that of rigid rodlike molecules. It is argued that apart from the extra contribution to the elasticity the long and flexible lateral group also has a significant contribution to the suppression of the splay fluctuations in the onset of smectic short-range fluctuation. The structure of the Sm-A phase is investigated by using small angle x-ray diffraction, and a possible arrangement of the molecules in the Sm-A layer is proposed.

Nonlinear effect of GdnHCl on hydration dynamics of proteins: a 1H magnetic relaxation dispersion study.

Proton magnetic relaxation dispersion investigations with aqueous solutions of lysozyme and bovine serum albumin (BSA) in the 0-5 M range of guanidine hydrochloride (GdnHCl), pH 4.4, 27 degrees C, were taken up with the objective of examining the hydration dynamics of internal cavity waters as the protein is held under increasingly destabilizing conditions. Field cycling NMR and conventional pulsed NMR techniques were employed to cover a frequency range of 100 kHz to 50 MHz. Analyses of dispersion profiles at different concentrations of GdnHCl were carried out considering the contributions from internal and surface waters. The denaturant-dependent variation of internal water contribution indicates that the reorientational disorder of internal waters decreases with increments of the denaturant up to its subdenaturing limit. For both proteins, the variation of effective correlation time with GdnHCl apparently shows a marginal shrink in hydrodynamic volumes under the subdenaturing condition. These results suggest that subdenaturing amounts of GdnHCl restrict the motional freedom of the internal waters, and can have considerable influence on the surface hydration. On increasing the denaturant concentration further, the dispersion amplitude drops sharply, indicating that the chaotropic action of the denaturant now runs over its own cavity water-ordering effect operative in the subdenaturing limit. The results are fundamentally important for the understanding of the susceptibility of protein structure and hydration to denaturants.

Wang-Landau Monte Carlo simulation of isotropic-nematic transition in liquid crystals.

Wang and Landau proposed recently, a simple and flexible non-Boltzmann Monte Carlo method for estimating the density of states, from which the macroscopic properties of a closed system can be calculated. They demonstrated their algorithm by considering systems with discrete energy spectrum. We find that the Wang-Landau algorithm does not perform well when the system has continuous energy spectrum. We propose in this paper modifications to the algorithm and demonstrate their performance on a lattice model of liquid crystalline system (with Lebwohl-Lasher interaction having continuously varying energy), exhibiting transition from high temperature isotropic to low temperature nematic phase.