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Simulations of model biaxial particles

Wednesday 20th March 2013 - 09:50 to 10:40
INI Seminar Room 1
The behaviour of axially symmetric particles has been well-investigated by both theory and computer simulation. Colloidal particles with such shapes have also been studied experimentally. For one component systems, nematic and smectic phases have been observed for rod-like particles, while discotic nematic and columnar phases have been noted for discs. If, however, one considers less symmetrical particles, then other phases become possible. Freiser (1970) showed theoretically that such a system might form a biaxial nematic phase, in which all particle axes are partially aligned, as opposed to a normal, uniaxial nematic where only one axis is ordered. Experimentally, a biaxial nematic phase has been reported for lyotropic systems (Yu & Saupe, 1980) and for suspensions of board-like goethite particles (van den Pol et al., 2009). There also exist reports of thermotropic biaxial nematic phases, though debate still continues as to whether these really exist for these systems. I would like to present simulation results (and hopefully some simple theory) on two types of model particle which might show biaxial behaviour. The first model is of V-shaped particles (also called boomerangs, bananas and bent-cores), while the second is closely related to the board-like shapes of goethite mentioned above. In both cases the particles interact via repulsive interactions only. Both models have received previous theoretical and simulation attention, but hopefully a little extra investigation will not come amiss.

In both cases we used constant pressure, and sometimes constant stress, molecular dynamics simulations, compressing the system from an initial isotropic phase. For relatively straight V-shped particles, the simulations are straightforward and result in uniaxial nematic and biaxial smectic phases. For a bond angle of less than ca. 130 degrees, however, the system tends to jam on compression and equilibration becomes problematic. We therefore investigated mixtures of V-shapes to see whether mixing suppressed the smectic phases, giving room for a biaxial nematic phase to form. While, at least to date, this hope was not fulfilled, we still observed some effects that we believe are of interest.

The other system studied is of fused hexagons – a model related to hard boards. The phase behaviour observed here was rather rich. Depending on geometry we found rod-like, discotic and biaxial nematic phases. Rod-like particles formed both uniaxial and biaxial smectic A and C phases. Disc-like particles formed not only columnar phases but also lamellar phases. Hopefully we will be able to rationalise the presence of at least some of these structures using simple-minded stability analysis.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons