Chester A. Vause

Effects of orientational degrees of freedom in closed-loop solubility phase diagrams

Abstract It is shown, within a lattice-gas model calculation, how fluctuating orientational degrees of freedom are responsible for closed-loop phase diagrams observed in many binary liquid mixtures. Quantitative agreement with experiment is obtained, and qualitative features, such as the shape of the closed-loops, are related to molecular properties of the liquids in the mixture.

Connection between the isotropic-nematic Landau point and the paranematic-nematic critical point

Abstract It is shown, within the context of Landau theory, that in uniaxial liquid crystal systems the isotropic-nematic Landau point lies at the intersection of three coexistence curves and a line of paranematic-nematic critical points. The global phase diagram in external magnetic (or electric) field, temperature, and concentration is discussed in terms of lyotropic micellar nematics with positive magnetic (dielectric) anisotropy.

Multilattice microcanonical simulation

Abstract A numerical lattice simulation technique is presented that is efficient for use on general purpose computers. This algorithm is a combination of the microcanonical simulation introduced by Creutz, and the multilattice coding technique demonstrated by Bhanot et al. The algorithm is tested with the two-dimensional Ising model. We achieve a maximum speed of 660000 Ising spin flips per second (without measurements) on a VAX 11 780 . Satisfactory agreement with exact results is found.

EVIDENCE FOR UNIVERSALITY OF THE POTTS MODEL ON THE TWO-DIMENSIONAL. PENROSE LATTICE

Abstract A microcanonical simulation of the four-state ferromagnetic Potts model on the two-dimensional Penrose lattice indicates that the phase transition is second order and is in the same universality class as the periodic system. The five-state ferromagnetic Potts model on the two-dimensional Penrose lattice is found to be first order, as in the periodic system.

q=5 Potts model on the quenched isotropically site-diluted square and Penrose lattices

Abstract A microcanonical simulation of the q =5 Potts model on the quenched isotropically site-diluted square and Penrose lattices is performed. Analysis of the simulation data show a first-order phase transition which terminates at a critical point for dilutions in the range p c ⩽ p ⩽1 ( p =1, pure system). The critical dilutions are p c =0.974(2) for the N =32 2 square lattice, and p c =0.986(2) for the N =988 Penrose lattice. The critical point is conjectured to be in a new universality class.

Scaling theory of the paranematic nematic critical point

Abstract A thermodymanic scaling analysis of the paranematic-nematic critical point is presented. Although presumed to be in the Ising universality class, general arguments suggest that the order parameter approaches the critical point in an asymmetrical manner in contrast to mean-field predictions.

Critical point in a random side-chain nematic copolymer: Mean-field theory

Abstract A model for anisotropic phases in a random side-chain nematic copolymer is proposed and solved in the mean-field approximation. The main results of the calculation are the appearance of paranematic and nematic phases and a critical point, without the application of external electric or magnetic fields.

Lattice Theory for Helix-Coil Induced Reentrant Isotropic-Nematic Transitions

Abstract A lattice model is proposed to study reentrant isotropic-nematic phase transitions mediated by helix-coil transformations within individual liquid crystal molecules. The system consists of a racemic mixture of molecules in solution with a solvent capable of hydrogen bonding. We first introduce a model to describe helix-coil transformations in the presence of such a solvent. This model displays not only normal helix-coil transformations, but also inverted transformations (i.e. reentrant), as well as reversion to the coiled state at high temperatures. Secondly, we develop a model for the isotropic-nematic phase transition which incorporates intermolecular interactions on the same footing with the intramolecular interactions. Reentrance of the isotropic phase is driven by the inverted helix-coil transformation. Within the nematic phase the effect of induced rigidity is observed. In addition, when solvent-solvent bonding is important in the system, doubly reentrant phase diagrams are predicted. We st...

Director Fluctuations and Ising Universality at the Paranematic-Nematic Critical Point

A statistical mechanical calculation using renormalization group analysis is carried out which shows that the paranematic-nematic critical point (PNCP) is in the same university class as the liquid-gas critical point, namely that of the Ising model. The calculation explicitly shows how the non-critical director fluctuations play an important role in providing features in the phase diagram, not present in mean-field theories, such as a non-analytic order parameter diameter (two-phase average dielectric (or magnetic) anisotropy on the coexistence curve), and confirms the predictions of the scaling theory of the PNCP.

A phenomenological renormalization group approach to electric conductivity with application to high-Tc superconductors

Abstract Phenomenological renormalization group (RG) equations are introduced to describe the temperature scaling of the dc electrical conductivity with application to high- T c superconductors. The linearized phenomenological RG theory provides a closed-form expression for the temperature-dependent resistivity which is then compared with measurements on polycrystalline Er 1 Ba 2 Cu 3 O 7−δ . In the presence of an external magnetic field, the phenomenological RG theory predicts a critical field phase diagram with a square-root singularity near T c which has been observed experimentally.