Orientational order in binary mixtures of hard Gaussian overlap molecules

Binary mixtures of rod-like colloids under shear: microscopically-based equilibrium theory and order-parameter dynamics

This paper is concerned with the dynamics of a binary mixture of rod-like, repulsive colloidal particles driven out of equilibrium by means of a steady shear flow (Couette geometry). To this end we first derive, starting from a microscopic density functional in Parsons-Lee approximation, a mesoscopic free energy functional whose main variables are the orientational order parameter tensors. Based on this mesoscopic functional we then explore the stability of isotropic and nematic equilibrium phases in terms of composition and rod lengths. Second, by combining the equilibrium theory with the Doi-Hess approach for the order parameter dynamics under shear, we investigate the orientational dynamics of binary mixtures for a range of shear rates and coupling parameters. We find a variety of dynamical states, including synchronized oscillatory states of the two components, but also symmetry breaking behavior where the components display different in-plane oscillatory states.

Induced stabilization of columnar phases in binary mixtures of discotic liquid crystals

Three discotic liquid-crystalline binary mixtures, characterized by their extent of bidispersity in molecular thickness, were investigated with molecular dynamics simulations. Each equimolar mixture contained A-type (thin) and B-type (thick) discogens. The temperature-dependence of the orientational order parameter reveals that A-type liquid samples produce ordered phases more readily, with the (hexagonal) columnar phase being the most structured variant. Moderately and strongly bidisperse mixtures produce globally-segregated samples for temperatures corresponding to ordered phases; the weakly bidisperse mixture displays microheterogeneities. Ordered phases in the B-type liquid are induced partially by the presence of the A-type fluid. In the moderately bidisperse mixture, order is induced through orientational frustration: a mixed prenematic-like phase precedes global segregation to yield nematic and columnar mesophases upon further cooling. In the strongly bidisperse mixture, order is induced less efficiently through a paranematic-like mechanism: a highly-ordered A-type fluid imparts order to B-type discogens found at the interface of a fully-segregated sample. This ordering effect permeates into the disordered B-type domain until nematic and columnar phases emerge upon further cooling. At sufficiently low temperatures, all samples investigated exhibit the (hexagonal) columnar mesophase.

Structure of molecular liquids: hard rod-disk mixtures

The structure of hard rod-disk mixtures is studied using Monte Carlo simulations and integral equation theory, for a range of densities in the isotropic phase. By extension of methods used in single component fluids, the pair correlation functions of the molecules are calculated and comparisons between simulation and integral equation theory, using a number of different closure relations, are made. Comparison is also made for thermodynamic data and phase behavior.

Fractionation in Gay-Berne liquid crystal mixtures

We present a constant-pressure molecular dynamics simulation study of the phase behavior of binary (50:50) Gay-Berne liquid crystal mixtures consisting of elongated particles with different lengths (LA>LB) and equal diameters. We focus on systems at dense liquid-state conditions. Considering three mixtures characterized by different values of LA(B) and different length ratios q=LB/LA<1, we find complex fluid-fluid phase behavior resulting from the interplay between nematic, smectic-A-type, or smectic-B-type orientational ordering, on the one hand, and demixing into two phases of different composition (fractionation), on the other hand. The driving "forces" of demixing transitions are the temperature and the length ratio. Indeed, in the system characterized by the largest value of q (q=0.86) orientational order occurs already in mixed states, whereas full fractionation is found at q=0.71. The two resulting states are either of type smectic-B-nematic (intermediate temperatures) or smectic-B-smectic-B (low temperatures). In the intermediate case q=0.80 we observe a stepwise ordering and demixing behavior on cooling the system from high temperatures. Moreover, our results show that the stability range of (partially) nematic structures in mixtures of sufficiently small q can be significantly larger than in the pure counterparts, in qualitative agreement with experimental observations.

Direct correlation functions of binary mixtures of hard Gaussian overlap molecules

We study the direct correlation function (DCF) of a classical fluid mixture of nonspherical molecules. The components of the mixture are two types of hard ellipsoidal molecules with different elongations, interacting through the hard Gaussian overlap (HGO) model. Two different approaches are used to calculate the DCFs of this fluid, and the results are compared. Here, the Pynn approximation [J. Chem. Phys. 60, 4579 (1974)] is extended to calculate the DCF of the binary mixtures of HGO molecules, then we use a formalism based on the weighted density functional theory introduced by Chamoux and Perera [J. Chem. Phys. 104, 1493 (1996)]. These results are fairly in agreement with each other. The pressure of this system is also calculated using the Fourier zero components of the DCF. The results are in agreement with the Monte Carlo molecular simulation.

Nematic-nematic phase separation in binary mixtures of thick and thin hard rods: results from Onsager-like theories

The fundamental nature of the nematic-nematic phase separation in binary mixtures of rigid hard rods is analyzed within the Onsager second-virial theory and the extension of Parsons and Lee which includes a treatment of the higher-body contributions. The particles of each component are modeled as hard spherocylinders of different diameter , but equal length . In the case of a system which is restricted to be fully aligned (parallel rods), we provide an analytical solution for the spinodal boundary for the limit of stability of demixing; only a single region of coexistence bounded at lower pressures (densities) by a critical point is possible for such a system. The full numerical solution with the Parsons-Lee extension also indicates that, depending on the length of the particles, there is a range of values of the diameter ratio where the phase coexistence is closed off by a critical point at lower pressure. A second region of coexistence can be found at even lower pressures for certain values of the parameters; this region is bounded by an "upper" critical point. The two coexistence regions can also merge to give a single region of coexistence extending to very high pressure without a critical point. By including the higher-order contributions to the excluded volume (end effects) in the Onsager theory, we prove analytically that the existence of the lower critical point is a direct consequence of the finite size of the particles. A new analytical equation of state is derived for the nematic phase using the Gaussian approximation. In the case of Onsager limit (infinite aspect ratio), we show that the phase behavior obtained using the Parsons-Lee approach substantially deviates from that with the Onsager theory for the transition due to the nonvanishing third and higher order virial coefficients. We also provide a detailed discussion of the phase behavior of recent experimental results for mixtures of thin and thick rods of the same length, for which the Onsager and Parsons-Lee theories can provide a qualitative description.

Orientational orders of small anisotropic molecules confined in slit pores

Based on a constant-pressure Monte Carlo molecular simulation, we have studied orientationally ordered transitions of small anisotropic molecules confined in two parallel hard walls. These molecules are modeled by the hard Gaussian overlap model. The molecular elongations of the chosen molecules are so small that the molecules cannot form stable liquid-crystal (LC) phases in the bulk. But in the slit pores, we found, while the distance between two walls of the pores decreases to the molecular scale, an orientationally ordered phase can form. It shows that even hard confining surfaces favor the alignment of the small anisotropic molecules. Thus we conclude that the required molecular elongation for forming LC phases will decrease in confinement. Our results indicate that some non-LC small molecules may form stable LC phases due to the inducement of confining surfaces.