We measured the splay (K11) and bend (K33) elastic constants in the nematic phase of a bent-core liquid crystal. In the vicinity of the nematic-isotropic transition temperature K33 is proportional to the square of the order parameter. In the nematic range K11 increases monotonically with decreasing temperature, whereas K33 is practically independent of temperature and is smaller than K11 . K33 exhibits a pretransitional slow divergence toward the transition temperature to the smectic phase and becomes slightly larger than K11. The small K33 is explained on the basis of strong coupling of the bent shape of the molecules with the bend distortion.
Heisenberg spin exchange (HE) studies of translational diffusion of the nitroxide radicals PD-tempone and P probe in two liquid crystalline solvents 60CB-80CB and 40,6 are described. It is shown that while PD-tempone undergoes strong exchange in the two solvents, the more anisotropic P-probe exhibits a tendency toward weak exchange which becomes more prominent in the low temperature mesophases. The molecular diffusion rates measured from our HE studies are compared with rates measured over larger distances using electron-spin resonance (ESR) imaging methods; we find that, in similar thermotropic liquid crystals, the former are somewhat faster. Also, while diffusion rates for PD-tempone (using HE) in the ordered phases of 60CB-80CB are consistent with a single activation energy, those in 40,6 show variations; suggesting that probe expulsion from core to chain regions in the former most likely occurs prior to SA formation, whereas in the latter it occurs in the SA phase. The absence of discontinuities in our diffusion data at the N-S A -RN transitions supports the belief that these transitions are subtle, with nothing dramatic occurring as the reentrant nematic (RN) phase is formed. The effect of including a potential of mean force U(r) between colliding radicals due to the liquid-crystal structure, is also considered. Our analyses indicate that the potential is of a repulsive nature [i.e., U( d) > 0] suggesting the possibility of solvent molecules inhibiting collisions of radicals at distances shorter than the sum of their solvated radii. The influence of orientational ordering on HE involving nonspherical radicals is considered, but changes from strong to weak exchange in the ordered phases appear to depend on how 'T the lifetime of the interacting radical pair is influenced by U(r). A careful effort is made to 1 separate the HE effects from the intermolecular electron-electron dipolar (EED) interactions. It is suggested that anomalies in D obtained from HE vs EED in this and earlier studies may also be rationalized in terms of the effects of U(r).
Wang and Landau proposed recently, a simple and flexible non-Boltzmann Monte Carlo method for estimating the density of states, from which the macroscopic properties of a closed system can be calculated. They demonstrated their algorithm by considering systems with discrete energy spectrum. We find that the Wang-Landau algorithm does not perform well when the system has continuous energy spectrum. We propose in this paper modifications to the algorithm and demonstrate their performance on a lattice model of liquid crystalline system (with Lebwohl-Lasher interaction having continuously varying energy), exhibiting transition from high temperature isotropic to low temperature nematic phase.
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