Excluded area computations for non-convex molecules

Rosso, Riccardo

doi:10.1080/00268970802575556

Cited by 5 publications

(2 citation statements)

References 23 publications

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“…41 Finally the Fourier coefficient of the excluded area for i Ͼ 0 can be obtained from To evaluate the excluded area in the range of / 2 Ͻ Ͻ we use the following symmetry property of the excluded area: A exc ͑͒ = A exc ͑ − ͒.…”

Section: Appendix A: Excluded Area For Zigzag Needles and A I Fouriermentioning

confidence: 99%

Nematic and smectic ordering in a system of two-dimensional hard zigzag particles

Varga

Gurin

Armas-Pérez

et al. 2009

The Journal of Chemical Physics

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The orientational and positional ordering of the two-dimensional system of hard zigzag particles has been investigated by means of Onsager theory. Analytical results are obtained for the transition densities of the isotropic-nematic and the nematic-smectic phase transitions. It is shown that the stability of the nematic and smectic phases is very sensitive to the molecular shape. In the hard needle limit, only the isotropic-nematic phase transition takes place, while increasing the tail length and the bent angle between the central core and the tails destabilizes the nematic phase. On the other hand the stability of the smectic phase is due to the increasing excluded area cost with bent angle and the tail length. The zigzag particles pack in a layered structure such that they are tilted and form semi-ideal gas in the layers to push the high cost excluded area regions into the interstitial regions. The predictions of Onsager theory are in good agreement with MC simulation data.

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Section: Appendix A: Excluded Area For Zigzag Needles and A I Fouriermentioning

confidence: 99%

Nematic and smectic ordering in a system of two-dimensional hard zigzag particles

Varga

Gurin

Armas-Pérez

et al. 2009

The Journal of Chemical Physics

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“…Since Onsager's well known paper [11], there has been a long quest for explicit expressions of the excluded volume for nematogenic molecules and, as a result, analytic formulae are known mostly for convex molecules with D 1h symmetry-ellipsoids of revolution, spherocylinders-D 2h symmetry-biaxial ellipsoids, speheroplateles [12], spherocuboids [13]-and a few other cases embraced by the family of sphero-zonotopes [13]. For non-convex molecules, the excluded area has been computed explicitly for two-dimensional V-shaped molecules whose shape is obtained through a kinematic construction [14].…”

Section: Introductionmentioning

confidence: 99%

Excluded-Volume Short-Range Repulsive Potential for Tetrahedral Molecules

Bisi

Longa

̧k

et al. 2010

Molecular Crystals and Liquid Crystals

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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 D 2h 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).

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Excluded-volume potential for rigid molecules endowed with C_2v symmetry

Bisi

Rosso

2011

Eur. J. Appl. Math

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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 C2v 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].

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Excluded area computations for non-convex molecules

Cited by 5 publications

References 23 publications

Nematic and smectic ordering in a system of two-dimensional hard zigzag particles

Nematic and smectic ordering in a system of two-dimensional hard zigzag particles

Excluded-Volume Short-Range Repulsive Potential for Tetrahedral Molecules

Excluded-volume potential for rigid molecules endowed with C_2v symmetry

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Excluded area computations for non-convex molecules

Cited by 5 publications

References 23 publications

Nematic and smectic ordering in a system of two-dimensional hard zigzag particles

Nematic and smectic ordering in a system of two-dimensional hard zigzag particles

Excluded-Volume Short-Range Repulsive Potential for Tetrahedral Molecules

Excluded-volume potential for rigid molecules endowed with C2v symmetry

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Excluded-volume potential for rigid molecules endowed with C_2v symmetry