Density functional theory for dense nematic liquid crystals with steric interactions

Abstract

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

Dynamic Mechanochemical feedback between curved membranes and BAR protein self-organization

“…This theory accounts for protein area coverage , orientational order as given by a nematic order parameter S, and membrane curvature. This is presented in detail in an accompanying paper 21 .…”

“…This theory accounted for protein diffusion and for membrane elasticity and hydrodynamics. Here, we extend it to include the sorption dynamics of proteins 39 and their orientational order 21 . Indeed, some curved proteins such as those containing BAR domains are elongated objects interacting anisotropically with the curvature of the membrane.…”

Contributions of repulsive and attractive interactions to nematic order

“…where, as shown in [4], λ has the role of a dimensionless phenomenological parameter. 2 The free energy then becomes…”

“…After having established on a rigorous basis the limit of dilution under which the Onsager theory is justifiable [3], we continue our inquiries by considering dense systems where hard ellipsoids interact via purely steric excluded volume effects. Using a mean-field approach, we have been able to describe the behavior, and calculate the order parameter as function of density [4]. An unusual result of our model is that the single particle orientational distribution function has compact support; that is, the probability of some range of particle orientations is strictly zero.…”

Modelos microscópicos para cristais líquidos nemáticos

“…Nesta seção iremos apresentar uma formulação alternativa do problema, discutida no trabalho de Nascimento et al [62], com o objetivo de estudar a transição nemáticaisotrópica em situações que vão além do regime da teoria de Onsager, queé mais apropriada para baixas densidades. Além disso, também mudaremos o foco para um sistema de esferóides prolatos, que são formas mais sugestivas para descrever moléculas líquidocristalinas.…”