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.

Study of nonequilibrium work distributions from a fluctuating lattice Boltzmann model.

A system of ideal gas is switched from an initial equilibrium state to a final state not necessarily in equilibrium, by varying a macroscopic control variable according to a well-defined protocol. The distribution of work performed during the switching process is obtained. The equilibrium free energy difference, ΔF, is determined from the work fluctuation relation. Some of the work values in the ensemble shall be less than ΔF. We term these as ones that "violate" the second law of thermodynamics. A fluctuating lattice Boltzmann model has been employed to carry out the simulation of the switching experiment. Our results show that the probability of violation of the second law increases with the increase of switching time (τ) and tends to one-half in the reversible limit of τ→∞.

A growth walk model for estimating the canonical partition function of interacting self-avoiding walk.

We have explained in detail why the canonical partition function of interacting self-avoiding walk (ISAW) is exactly equivalent to the configurational average of the weights associated with growth walks, such as the interacting growth walk (IGW), if the average is taken over the entire genealogical tree of the walk. In this context, we have shown that it is not always possible to factor the density of states out of the canonical partition function if the local growth rule is temperature dependent. We have presented Monte Carlo results for IGWs on a diamond lattice in order to demonstrate that the actual set of IGW configurations available for study is temperature dependent even though the weighted averages lead to the expected thermodynamic behavior of ISAW.

Coil-globule transition of a single short polymer chain: an exact enumeration study.

The authors present an exact enumeration study of short self-avoiding walks in two as well as in three dimensions that addresses the question, "what is the shortest walk for which the existence of all the three scaling regimes--coil, globule, and the theta--could be demonstrated." Even though they could easily demonstrate the coil and the globule phase from free energy considerations, they could demonstrate the existence of a theta temperature only by using a scaling form for the distribution of gyration radius. That even such short walks have a scaling behavior is an unexpected result of this work.

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.

Interacting growth walk: a model for hyperquenched homopolymer glass?

We show that the compact self-avoiding walk configurations, kinetically generated by the recently introduced interacting growth walk (IGW) model, can be considered as members of a canonical ensemble if they are assigned random values of energy. Such a mapping is necessary for studying the thermodynamic behavior of this system. We have presented the specific heat data for the IGW, obtained from extensive simulations on a square lattice; we observe a broad hump in the specific heat above the theta point, contrary to expectation.

Diffusion in a periodically driven damped and undamped pendulum.

We study the diffusion process in a periodically driven damped and undamped pendulum. The effect of angular frequency omega of the external periodic force on the diffusion process is investigated. We show the occurrence of normal and anomalous diffusions in the undamped system. In the presence of damping, normal chaotic diffusion is found. Near certain bifurcation points, the phase velocity is found to be intermittent and the diffusion coefficient is found to exhibit power-law divergence. We argue that the divergence of the diffusion coefficient near the bifurcation points is similar to that of the average laminar lengths near them. The effect of bias on the dynamics is also discussed.

Interacting growth walk: a model for generating compact self-avoiding walks.

We propose an algorithm based on local growth rules for kinetically generating self-avoiding walk configurations at any given temperature. This algorithm, called the interacting growth walk (IGW) model, does not suffer from attrition on a square lattice at zero temperature, in contrast to the existing algorithms. More importantly, the IGW model facilitates growing compact configurations at lower temperatures--a feature that makes it attractive for studying a variety of processes such as the folding of proteins. We demonstrate that our model correctly describes the collapse transition of a homopolymer in two dimensions.

Sticky spheres, entropy barriers, and nonequilibrium phase transitions.

A sticky spheres model to describe slow dynamics of a nonequilibrium system is proposed. The dynamical slowing down is due to the presence of entropy barriers. An exact steady state analysis of the representative mean field equations, in the case when the clusters are chosen with the same a priori probability, demonstrates a nonequilibrium phase transition from an exponential cluster size distribution to a power law.