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Advances in the Computer Simulatons of Liquid Crystals by Michael P. Allen (auth.), Paolo Pasini, Claudio Zannoni

By Michael P. Allen (auth.), Paolo Pasini, Claudio Zannoni (eds.)

Computer simulations supply an important set of instruments for knowing the macroscopic houses of liquid crystals and in their section transitions by way of molecular versions. whereas simulations of liquid crystals are according to a similar common Monte Carlo and molecular dynamics innovations as are used for different fluids, they current a few particular difficulties and peculiarities attached to the intrinsic houses of those mesophases.
the sphere of computing device simulations of anisotropic fluids is interdisciplinary and is evolving very quickly. the current quantity covers quite a few suggestions and version platforms, from lattices to demanding particle and Gay-Berne to atomistic, for thermotropics, lyotropics, and a few biologically attention-grabbing liquid crystals. Contributions are written by means of a very good panel of foreign academics and offers a well timed account of the strategies and difficulties within the field.

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STONE EXPANSION OF THE PAIR DISTRIBUTION We have seen earlier on, when discussing the calculation of (P2 ) from Me simulations, the advantages of using a rotational invariant description when calculating order parameters for a sample where no field is applied and the director can fluctuate from a configuration to the next. Here we wish to discuss the calculation of suitable rotationally invariant pair properties. The pair distribution can depend on orientations of the two molecules WI, W2 and on the intermolecular vector orientation (Le.

The minimum set of order parameters required to describe biaxial molecules in a biaxial phase is [20,21, 12] (P2 ), (R~2)' (R~o), (R~2). :an symmetryadapted for the D2h group of the particles and phase [4]. Their explicit expressions, for the even terms, are: _ 1 L L = 2'Re(Dmn + Dm _ n ) = (52) ~ [cos(ma) cos(n'Y)[d~mn(f3) + d~n(f3)] + sin (ma) sin(n'Y)[d~mn(f3) - d~n(f3)]]. (53) 29 Experimentally one would try to select a sufficiently high number of molecular properties AijOL and measure their average values (A~lB).

5 we show a set of order parameters obtained from Me simulation of the simple second rank 31 attractive pair potential [19, 22]: U(Wij) + -fij{P2(COS,6ij) + 2A[R~2(Wij) + R~o(Wij)] (64) 4A2 R~2(Wij)} with the biaxial molecules, or "spins", fixed at the sites of a three dimensional cubic lattice. The coupling parameter, fij, is taken to be a positive constant, f when particles i and j are nearest neighbors and zero otherwise. Wij is the relative orientation of the molecular pair. The biaxiality parameter A accounts for the deviation from cylindrical molecular symmetry: when A is zero, the potential reduces to the Lebwohl-Lasher P2 potential, while for A different from zero the particles tend to align not only their major axis, but also their faces.

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