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Results are presented from molecular dynamics simulations of binary liquid crystal mixtures using a generalisation of a well established Gay-Berne intermolecular potential. The simulations are undertaken in both the microcanonical (NVE) and the isoenthalpic-isobaric (NPH) ensembles. Firstly a 50:50 mixed system is simulated in the NVE ensemble containing generalised Gay-Berne (GGB) rod-like molecules with length to breadth axial ratios of 3.5:1 (molecules A) and 3:1 (molecules B). The molecules in this system differs only slightly from the well-characterised Gay-Berne (GB) potential with length to breadth ratio of 3:1. It is shown that the system exhibits isotropic (/), nematic (N) and smectic-B (SmB) phases with both the I-N and N-SmB phase boundaries not clearly defined. Competition between two density waves parallel to the director of the same wavelength but different phase lead to a pre-smectic ordering preceding the N-SmB phase transition. The longer molecules are shown to have a consistently higher order parameter the difference being greatest in the nematic phase and decrease with lowering temperature. Although a degree of local ordering is shown within each smectic layer the smectic phase is fully commensurate. Secondly, phase behaviour diagrams are presented from a series of constant-NPH simulations over a range of pressures and concentrations. The binary mixtures exhibit a rich phase behaviour, displaying isotropic, nematic, smectic-A (SmA), induced smectic-A and smectic-B phases depending on the choice of pressure and concentration. It is shown that the temperature range over which the nematic phase is stable can be extended greater than either homogeneous system by elevating the system pressure and/or by choice of concentration, agreeing with experimental results. The mixture exhibits a stable SmA island at a mole fraction of xa = 0.50 depending on the choice of pressure and a narrow induced SmA phase at xa = 0.25.

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Liquid crystals (LCs) are anisotropic fluids that exhibit numerous thermodynamically stable phases in between an isotropic liquid and a three-dimensionally ordered solid. In their simplest ordered phase, the nematic, LCs show orientational order due to molecular self assembly and at the same time maintaining fluid flow properties. In the smectic phase, they show both orientational and partial translational order characterized by a 1-d density wave. Liquid crystalline substances have been extensively studied due to their applications and as important physical models of self-assembly. The effect of the disorder and impurities on LC systems is an important and challenging problem to the fundamental understanding of phases ordering or self-assembly and continually attracts the attention of researchers. The disordered systems often display complex and rich phenomena, being the generalization of the pure (ideal) systems. Disorder can dramatically alter the physical properties of multi-component, composite systems. In particular, the effect of disorder on phase transitions is important as the disorder typically couples to the order parameter, which can be usefully described as a random local field that is conjugate to the order parameter. This is usually realized in systems with random inclusions in a phase ordering media, e.g., a colloidal dispersion of solids in a complex fluid. Another form of disorder is presented by dilution effects, which imposes instead the random breaking or weakening of intermolecular bonds or interactions responsible for the phase ordering. Exploring a good physical system representing random dilution effects in a controlled manner offers a physical probe to unresolved problems in the understanding of mesophasic order. This Dissertation presents a series of studies of dilution and different form of disorder effect on liquid crystal phase transitions. We have used high-resolution AC-calorimetry, dielectric spectroscopy as well as polarizing microscopy to characterize the effects of solvent such as hexane, acetone, decane, and nanomaterials such as multiwall carbon nanotubes and ferroelectric nanoparticles on the phase transitions of several liquid crystals. The liquid crystals of interest are: pentylcyanobiphenyl (5CB), octylcyanobiphenyl (8CB), and decylcyanobiphenyl (10CB). Studies have been carried out as a function of solvent, nanotube, and nanoparticles concentration and temperature spanning the isotropic to nematic (I-N), nematic to smectic-A (N-SmA), and isotropic to smectic-A (I-SmA) phase transitions.

Abstract In this study, we employed the Monte Carlo simulation method to investigate the q-state coupled XY model based on the Landau free energy of couple hexatic order and herringbone order proposed by Bruinsma and Aeppli. On two-dimensional triangular lattices simulation results reveal that the q-state coupled XY model will generate a q-state clock phase transition and a XY transition. The unique generated q-state clock phase transition and XY transition will couple in some coupling parameter domain. The novel coupled transitions behavior agree with the phase transition of some kinds of liquid crystal. For example, the three-state Potts phase transition generated by a 3-state coupled XY model and the Sm-A ¡÷Hex-B transition of free ¡V standing two layers liquid crystal are matched. Their heat capacity anomaly is similar and the heat capacity exponent is both closed to £\¡Ü0.3. We also investigated the system of coupled ferromagnetic order and antiferromagnetic order. Adapted the positive coupling parameter on the Hamiltonian of 3-state coupled XY model, the simulation results reveal that the system generate an antiferromagnetic three-state Potts transition. In some parameter domain the antiferromagnetic three-state Potts transition and XY transition are coupled, and become a novel transition. The novel transition may explain the Sm-A ¡÷Hex-B transition of some kinds of liquid crystal which lack herringbone order.