Fulvio Bisi

Excluded-Volume Short-Range Repulsive Potential for Tetrahedral Molecules

Tetrahedral symmetry in nematic liquid crystals has been studied for several years, since the seminal paper by Fel [1]. Amongst statistical theories of nematic liquid crystals, a molecular mean-field model has proven to be quite effective in predicting phase sequences for thermotropic biaxial nematic molecules endowed with D2h symmetry, as a function of the parameters entering their interaction potential [2,3]. This model has highlighted the role of a partially repulsive quadrupolar potential of mean torque in promoting condensed phases. It has been shown that the quadrupolar approximation to the excluded-volume interaction between hard spherocuboids can be written precisely as the superposition of two London interactions: one repulsive and one attractive [4]; furthermore, polar steric interactions have been shown to be capable of inducing orientationally ordered states possibly unexpected [5]. By adapting a numerical code available to the scientific community, we evaluate the analytical excluded volume function for non-convex tetrahedral molecules, modelled as chains of tangent hard spheres. Since this function is overly complicated, we expand it over a suitable set of Symmetry Adapted Wigner Functions (SAWFs).

Excluded-volume potential for rigid molecules endowed with C 2 v symmetry

The excluded volume of a pair of molecules is proportional to the second virial coefficient in hard-core models that represent, for instance, the reference model in perturbation approaches to statistical theories of fluids [see, e.g. Chap. 5 of Kalikmanov, V. (2001), Statistical Physics of Fluids . Texts and Monograph in Physics, Springer, Berlin]. In three space dimensions, there exist exact results for convex molecules and in fact lack of convexity has been a major obstacle in applying the mathematical techniques employed in the convex case. In this paper, we illustrate how a mixed—analytical and numerical—method can be used to obtain exact expressions of the excluded volume for a pair of non-convex molecules conceived as aggregates of hard spheres; these can model van der Waals regions associated to the atoms forming each molecule. To compute the excluded volume for molecules endowed with C 2 v symmetry, modelled as chains of tangent hard spheres, we adapt a numerical code available to the scientific community. Because the result is a rather cumbersome expression in term of the relative orientation of the interacting molecules, we expand it over a suitable set of symmetry adapted Wigner functions to build up approximate, but faithful expressions, and we also prove analytical results announced elsewhere [Bisi, F., Durand, G., Rosso, R. & Virga, E. (2008), Polar steric interactions for v-shaped molecules. Phys. Rev . E, 78 , 011705].

Bifurcation Analysis of a Mean-Field Model for Biaxial Nematics

The interest for macroscopic biaxiality has been recently revived by the experimental evidence of thermally driven transitions to biaxial phases, promoted by newly synthesized nematogenic molecules. In particular, the interaction model proposed by Straley for molecules endowed with D2h symmetry has been widely reconsidered. We elaborated a mean-field model based on a quadrupolar approximation to the mean torque potential has proven capable of capturing the universal features characterizing all phase diagrams compatible with the interaction model. Moreover, the phase sequences and the order of the transitions are weakly influenced by one of the interaction parameters. Here we show how to we derive the analytical bifurcation equations underlying our numerical analysis, and, subsequently, how these equations are instrumental to the correct resolution of the mean-field model. These bifurcation equations are integrated in a numerical code based on MATCONT, used for bifurcation analysis, which will be made available to the scientific community.

Surface Order Forces in Nematic Liquid Crystals

The notion of surface order force in nematic liquid crystals is presented and contrasted with the notions of similar forces already introduced in the literature. We illustrate how a surface order force could in principle be measured and how it would convey the mechanical signature of an intrinsically nanoscopic phenomenon, often referred to as order reconstruction. The relationship between this force and the occurrence of biaxial states of the nematic order tensor is further illuminated.

Determination of the symmetry classes of orientational ordering tensors

The orientational order of nematic liquid crystals is traditionally studied by means of the second-rank ordering tensor

Steric Effects in Polar Nematic Liquid Crystals

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Universal Features in the Nematic Uniaxial-to-Biaxial Transition

. When this is calculated through experiments or simulations, the symmetry group of the phase is not known \emph{a-priori}, but needs to be deduced from the numerical realisation of

Universal Mean-Field Phase Diagram for Biaxial Nematics

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Universal mean-field phase diagram for biaxial nematics obtained from a minimax principle.

, which is affected by numerical errors. There is no generally accepted procedure to perform this analysis. Here, we provide a new algorithm suited to identifying the symmetry group of the phase. As a by product, we prove that there are only five phase-symmetry classes of the second-rank ordering tensor and give a canonical representation of

Order reconstruction in frustrated nematic twist cells

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