Density-functional theory and Monte Carlo simulations of the phase behavior of a simple model liquid crystal

Phase Transitions and Hysteresis for a Simple Model Liquid Crystal by Replica-Exchange Monte Carlo Simulations

In this work, the advantages of applying the temperature and pressure replica-exchange method to investigate the phase transitions and the hysteresis for liquid-crystal fluids were demonstrated. In applying this method to the commonly used Hess-Su liquid-crystal model, heat capacity peaks and points of phase co-existence were observed. The absence of a smectic phase at higher densities and a narrow range of the nematic phase were reported. The identity of the crystalline phase of this system was found to a hexagonal close-packed solid. Since the nematic-solid phase transition is strongly first order, care must be taken when using this model not to inadvertently simulate meta-stable nematic states at higher densities. In further analysis, the Weighted Histogram Analysis Method was applied to verify the precise locations of the phase transition points.

Perturbation Theory versus Thermodynamic Integration. Beyond a Mean-Field Treatment of Pair Correlations in a Nematic Model Liquid Crystal

The phase behavior and structure of a simple square-well bulk fluid with anisotropic interactions is described in detail. The orientation dependence of the intermolecular interactions allows for the formation of a nematic liquid-crystalline phase in addition to the more conventional isotropic gas and liquid phases. A version of classical density functional theory (DFT) is employed to determine the properties of the model, and comparisons are made with the corresponding data from Monte Carlo (MC) computer simulations in both the grand canonical and canonical ensembles, providing a benchmark to assess the adequacy of the DFT results. A novel element of the DFT approach is the assumption that the structure of the fluid is dominated by intermolecular interactions in the isotropic fluid. A so-called augmented modified mean-field (AMMF) approximation is employed accounting for the influence of anisotropic interactions. The AMMF approximation becomes exact in the limit of vanishing density. We discuss advantages and disadvantages of the AMMF approximation with respect to an accurate description of isotropic and nematic branches of the phase diagram, the degree of orientational order, and orientation-dependent pair correlations. The performance of the AMMF approximations is found to be good in comparison with the MC data; the AMMF approximation has clear advantages with respect to an accurate and more detailed description of the fluid structure. Possible strategies to improve the DFT are discussed.

The Impact of Colloidal Surface-Anchoring on the Smectic A Phase

Liquid-crystalline phases are known for their unique properties, i.e., the combination of fluidity and long-range orientational and/or positional order. The presence of a colloidal particle gives rise to perturbations of this order locally. These perturbations are the origin of intercolloidal forces driving the colloidal self-assembly in a directed manner. Hence, the understanding of these perturbations is the first step in understanding and controlling the self-assembly process. Here, we perform Monte Carlo simulations to investigate the perturbations of orientational and positional order in a smectic A phase caused by a spherical colloid. We model the host phase via an interaction potential that reproduces characteristic features of phase behavior, structure, dynamics, and elasticity [S. Püschel-Schlotthauer et al. J. Chem. Phys. 2016, 145, 164903]. For strong homeotropic anchoring conditions, we find a Saturn ring defect and an onion structure in the smectic A phase; the latter has never been reported for colloids so far. For strong planar anchoring conditions, we find Boojum defects that become elongated at low temperature, similar to what is observed in experiments. However, for weak planar anchoring conditions, a double surface ring defect is exhibited in the smectic A phase.

A novel model for smectic liquid crystals: Elastic anisotropy and response to a steady-state flow

By means of a combination of equilibrium Monte Carlo and molecular dynamics simulations and nonequilibrium molecular dynamics we investigate the ordered, uniaxial phases (i.e., nematic and smectic A) of a model liquid crystal. We characterize equilibrium behavior through their diffusive behavior and elastic properties. As one approaches the equilibrium isotropic-nematic phase transition, diffusion becomes anisotropic in that self-diffusion D_⊥ in the direction orthogonal to a molecule's long axis is more hindered than self-diffusion D_∥ in the direction parallel to that axis. Close to nematic-smectic A phase transition the opposite is true, D_∥ < D_⊥. The Frank elastic constants K₁, K₂, and K₃ for the respective splay, twist, and bend deformations of the director field n̂ are no longer equal and exhibit a temperature dependence observed experimentally for cyanobiphenyls. Under nonequilibrium conditions, a pressure gradient applied to the smectic A phase generates Poiseuille-like or plug flow depending on whether the convective velocity is parallel or orthogonal to the plane of smectic layers. We find that in Poiseuille-like flow the viscosity of the smectic A phase is higher than in plug flow. This can be rationalized via the velocity-field component in the direction of the flow. In a sufficiently strong flow these smectic layers are not destroyed but significantly bent.

Mean-field density functional theory of a nanoconfined classical, three-dimensional Heisenberg fluid. I. The role of molecular anchoring

In this work, we employ classical density functional theory (DFT) to investigate for the first time equilibrium properties of a Heisenberg fluid confined to nanoscopic slit pores of variable width. Within DFT pair correlations are treated at modified mean-field level. We consider three types of walls: hard ones, where the fluid-wall potential becomes infinite upon molecular contact but vanishes otherwise, and hard walls with superimposed short-range attraction with and without explicit orientation dependence. To model the distance dependence of the attractions, we employ a Yukawa potential. The orientation dependence is realized through anchoring of molecules at the substrates, i.e., an energetic discrimination of specific molecular orientations. If the walls are hard or attractive without specific anchoring, the results are "quasi-bulk"-like in that they can be linked to a confinement-induced reduction of the bulk mean field. In these cases, the precise nature of the walls is completely irrelevant at coexistence. Only for specific anchoring nontrivial features arise, because then the fluid-wall interaction potential affects the orientation distribution function in a nontrivial way and thus appears explicitly in the Euler-Lagrange equations to be solved for minima of the grand potential of coexisting phases.

Coarse-grained treatment of the self-assembly of colloids suspended in a nematic host phase

The complex interplay of molecular scale effects, nonlinearities in the orientational field and long-range elastic forces makes liquid-crystal physics very challenging. A consistent way to extract information from the microscopic, molecular scale up to the meso- and macroscopic scale is still missing. Here, we develop a hybrid procedure that bridges this gap by combining extensive Monte Carlo (MC) simulations, a local Landau-de Gennes theory, classical density functional theory, and finite-size scaling theory. As a test case to demonstrate the power and validity of our novel approach we study the effective interaction among colloids with Boojum defect topology immersed in a nematic liquid crystal. In particular, at sufficiently small separations colloids attract each other if the angle between their center-of-mass distance vector and the far-field nematic director is about 30°. Using the effective potential in coarse-grained two-dimensional MC simulations we show that self-assembled structures formed by the colloids are in excellent agreement with experimental data.

Condensation, demixing, and orientational ordering of magnetic colloidal suspensions

In this work we study the phase behavior of magnetic particles suspended in a simple nonmagnetic solvent. Magnetic particles are modelled as spherical particles carrying a three-dimensional, classical Heisenberg spin, whereas solvent molecules are treated as spherically symmetric Lennard-Jones particles. The binary mixture of magnetic particles and solvent is studied within the framework of classical density functional theory (DFT). Within DFT pair correlations are treated at the modified mean-field level at which they are approximated by orientation dependent Mayer f functions. In the absence of an external magnetic field four generic types of phase diagrams are observed depending on the concentration of magnetic particles. In this case we observe liquid-liquid phase coexistence between an orientationally ordered (polarized) and a disordered phase characterized by slightly different concentrations of magnetic particles. Liquid-liquid phase coexistence is suppressed by an external field and vanishes completely if the strength of the field is sufficiently large.