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Mesophase behaviour of polyhedral particles


Translational and orientational excluded-volume fields encoded in particles with anisotropic shapes can lead to purely entropy-driven assembly of morphologies with specific order and symmetry. To elucidate this complex correlation, we carried out detailed Monte Carlo simulations of six convex space-filling polyhedrons, namely, truncated octahedrons, rhombic dodecahedrons, hexagonal prisms, cubes, gyrobifastigiums and triangular prisms. Simulations predict the formation of various new liquid-crystalline and plastic-crystalline phases at intermediate volume fractions. By correlating these findings with particle anisotropy and rotational symmetry, simple guidelines for predicting phase behaviour of polyhedral particles are proposed: high rotational symmetry is in general conducive to mesophase formation, with low anisotropy favouring plastic-solid behaviour and intermediate anisotropy (or high uniaxial anisotropy) favouring liquid-crystalline behaviour. It is also found that dynamical disorder is crucial in defining mesophase behaviour, and that the apparent kinetic barrier for the liquid–mesophase transition is much lower for liquid crystals (orientational order) than for plastic solids (translational order).

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Figure 1: Effect of shape anisotropy on hard-particle mesophase order.
Figure 2: Summary of equilibrium structures for different SFPs.
Figure 3: Phase behaviour of shapes with low anisotropy and high symmetry.
Figure 4: Phase and structural behaviour of hexagonal prisms.
Figure 5: Phase and structural behaviour of cubes.
Figure 6: Phase behaviour for shapes with high anisotropy and low symmetry.


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This work was supported by a Department of Energy Basic Energy Science Grant ER46517. This publication is based on work supported in part by award no. KUS-C1-018-02, made by King Abdullah University of Science and Technology (KAUST).

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U.A. and F.A.E. planned the research, analysed the data and wrote/revised the manuscript. U.A. carried out the simulations. F.A.E. outlined the initial project.

Corresponding author

Correspondence to Fernando A. Escobedo.

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The authors declare no competing financial interests.

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Agarwal, U., Escobedo, F. Mesophase behaviour of polyhedral particles. Nature Mater 10, 230–235 (2011).

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