The celebrated work of Onsager on hard particle systems, based on the truncated second order virial expansion, is valid at relatively low volume fractions for large aspect ratio particles. While it predicts the isotropic-nematic phase transition, it does not provide a realistic equation of state in that the pressure remains finite for arbitrarily high densities. In this work, we derive a mean field density functional form of the Helmholtz free energy for nematics with hard core repulsion. In addition to predicting the isotropic-nematic transition, the model provides a more realistic equation of state. The energy landscape is much richer, and the orientational probability distribution function in the nematic phase possesses a unique feature—it vanishes on a nonzero measure set in orientation space.

In this paper, we present a simple one tensor mean field model of biaxial nematic liquid crystals. The salient feature of our approach is that material parameters appear explicitly in the order parameter tensor. We construct the free energy from a mean field potential based on anisotropic dispersion interactions, identify the order parameter tensor and its elements, and obtain self-consistent equations, which are then solved numerically. The results are illustrated in a 3D ternary phase diagram. The phase behavior can be simply related to molecular parameters. The results may be useful for designing molecules that show a thermotropic biaxial phase.

Photomechanical materials perform mechanical work in response to illumination. Photoisomerization-based photomechanical materials may operate in different regimes depending on the intensity of the illuminating light. We examine the photoresponse of liquid crystalline azo-acrylate networks and show that a material property, the characteristic intensity of the material, defines the boundaries between different regimes. Asymptotic analysis indicates that whereas at low relative light levels, photostress is proportional to intensity, at high levels, it is proportional to fluence. Model predictions are in good agreement with the experimental results.

Much is known about the Freedericksz transition induced by uniform electric and magnetic fields in nematic liquid crystals. In this work, we are interested in the effects of a spatially varying field on the transition. Specifically, we study the director configuration in a homeotropic nematic cell in a spatially varying magnetic field with cylindrical symmetry. The experiment is conducted with a ring magnet which provides a radial magnetic field with magnitude monotonically decreasing to zero at the center. The nematic cell is positioned in the central plane of the ring, with the cell normal parallel to the ring normal. Interference patterns of the nematic cell between crossed polarizers were observed. The director configuration in the nematic cell is modeled with Frank–Oseen theory, and the computed interference pattern from the simulated director field are compared with experiment. We conclude that if the magnetic field strength varies with position in the plane of the cell, there is no Freedericksz transition.

In this paper, we propose a suitable surface energy expression for cholesteric liquid crystals. We show that there exists a symmetry allowed term for chiral nematics that doesn’t appear in the traditional Rapini-Papoular surface energy form. We discuss some consequences of this new surface anchoring term.