1,721,041 research outputs found
Biaxial and uniaxial phases produced by partly repulsive mesogenic models involving D2h molecular symmetries
No full textThe present paper considers biaxial nematogenic lattice models, involving particles of D2h symmetry, whose centers of mass are associated with a three-dimensional simple-cubic lattice. The pair potential is isotropic in orientation space and restricted to nearest neighbors. Let two orthonormal triads define orientations of a pair of interacting particles. The investigated potential models are quadratic with respect to the nine scalar products between the two sets of unit vectors. Actually, based on available geometric identities, these expressions can be reduced to diagonal form containing only the scalar products between corresponding unit vectors and depending on three parameters. Over the years, this comparatively simple functional form has also proven to be rather versatile. By now, various sets of potential parameters capable of producing mesogenic behavior of some kind have been proposed and studied in the literature. A new and simplified form was recently proposed and investigated by Sonnet, Virga, Durand, and De Matteis [ A. M. Sonnet, E. G. Virga and G. E. Durand Phys. Rev. E 67 061701 (2003); G. De Matteis and E. G. Virga Phys. Rev. E 71 061703 (2005)] and is known to support a biaxial phase at sufficiently low temperature. Following the idea of the above authors, we have studied a more extended range of parameters, including cases where biaxiality cannot be sustained in the pair ground state. In cases where a biaxial phase survives, an appropriate mean-field analysis may predict the existence of a direct second-order transition to the isotropic phase as well as a second-order sequence isotropic-to-uniaxial-to-biaxial. A second-order phase transition is also predicted, which involves isotropic and uniaxial phases only. Monte Carlo simulations have been carried out as well, for a few points in the parameter space, and found to produce results which partly confirm mean-field predictions
Mesogenic lattice models with partly antinematic interactions producing uniaxial nematic phases.
No full textTricritical points in biaxial liquid crystal phases
No full textWe further pursue the analysis of a mean-field model recently proposed by Sonnet et al. [Phys. Rev. E 67,
061701 (2003)] to describe nematic biaxial phases. This model, which is based on a simplified version of
Straley’s pair potential, is characterized by the prediction of a tricritical point along the transition line between
uniaxial and biaxial phases. We show that the same model predicts another tricritical point, but along the line
of the direct isotropic-to-biaxial transition. Our prediction is quantitative, as it stems from an analytical
criterion for tricriticality
Calamitic and antinematic orientational order produced by the generalized Straley lattice model
No full textWe consider here a classical model, consisting of D2h-symmetric particles in a three-dimensional simple-cubic lattice; the pair potential is isotropic in orientation space, and restricted to nearest neighbors. The simplest potential model is written in terms of the squares of the scalar products between unit vectors describing the three interacting arms of the molecules, as proposed in previous literature. Two predominant antinematic couplings of equal strength (+1) are perturbed by a comparatively weaker calamitic one, parameterized by a coupling constant −z ranging in [−1,0]. This choice rules out thermodynamically stable phases endowed with macroscopic biaxiality. The antinematic terms favor states with the corresponding molecular axes mutually orthogonal. Although the low-temperature phase of the special case with null calamitic term (PP0) is uniaxial and antinematically ordered, in the general case presented here both Monte Carlo and molecular-field approaches show that, for z close to zero, the models exhibit a low-temperature uniaxial nematic phase, followed by an antinematic one, and finally by the orientationally disordered one. On the other hand, for sufficiently large values of z, we only find evidence of uniaxial calamitic behavior, as expected by following the limiting cases
Orientationally ordered phases produced by fully antinematic interactions: a simulation study.
No full textWe consider here a classical model, consisting of D2h symmetric particles, whose centers of mass are associated with a three-dimensional simple-cubic lattice; the pair potential is isotropic in orientation space, and restricted to nearest neighbors. Two orthonormal triads define orientations of a pair of interacting particles; the simplest potential models proposed in the literature can be written as a linear combination involving the squares of the scalar products between corresponding unit vectors only, thus depending on three parameters, and making the interaction model rather versatile. A coupling constant with negative sign tends to keep the two interacting unit vectors parallel to each other, whereas a positive sign tends to keep them mutually orthogonal (antinematic coupling). We address here a special, extreme case of the above family, involving only antinematic couplings: more precisely, three antinematic terms whose coefficients are set to a common positive value (hence the name PPP model). The model under investigation produces a doubly degenerate pair ground state; the nearest-neighbor range of the interaction and the bipartite character of the lattice can propagate the pair ground state and increase the overall degeneracy, but without producing frustration. The model was investigated by a simplified molecular field treatment as well as by Monte Carlo simulation, whose results suggested a second-order transition to a low-temperature biaxially ordered phase; ground-state configurations producing orientational order have been selected by thermal fluctuations. The molecular field treatment also predicted a continuous transition, and was found to overestimate the transition temperature by a factor 2
Constrained stability for biaxial nematic phases
No full textWe study the invariance properties of the molecular Hamiltonian interaction put forward by Straley to describe biaxial nematic phases. We show that the reduction to two out of four scalar order parameters, which was accidently remarked upon in the literature, is indeed a rigorous consequence of the Hamiltonian invariance for specific values of the interaction parameters. The stability analysis of the mean-field free energy in the reduction classes for the order parameters reveals a sequence of Landau triple points
Director libration in nematoacoustics
No full textWe extended the analysis of a variational theory for nematoacoustics recently proposed by Virga [Phys. Rev. E 80, 031705 (2009)] by allowing the nematic director to vibrate about an average orientation at the frequency of a propagating wave, a periodic motion that we call the director libration. The acoustic susceptibilities, two phenomenological parameters that, in this theory, express the coupling between director and acoustic fields, are estimated along with an extra viscosity coefficient by using available experimental data
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