Colloidal cuboids have the potential to self-assemble into biaxial liquid crystal phases, which exhibit two independent optical axes. Over the last few decades, several theoretical works have predicted the existence of a wide region of the phase diagram where the biaxial nematic phase would be stable, but imposed rather strong constraints on the particle rotational degrees of freedom. In this work, we use molecular simulation to investigate the impact of size dispersity on the phase behaviour of freely-rotating hard cuboids, here modelled as self-dual-shaped nanoboards. This peculiar anisotropy, exactly in between the oblate and prolate geometry, has been proposed as the most appropriate to promote phase biaxiality. We observe that size dispersity radically changes the phase behaviour of monodisperse systems and leads to the formation of an elusive biaxial nematic phase, being found in a large region of the packing fraction vs. polydispersity phase diagram. Although our results confirm the tendencies reported in past experimental observations on colloidal dispersions of slightly prolate goethite particles, they cannot reproduce the direct isotropic-to-biaxial nematic phase transition observed in these experiments.

中文翻译：

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自由旋转的多分散长方体的自组装：揭示了双轴向列相的边界。

胶体长方体具有自组装成双轴液晶相的潜力，双相液晶相具有两个独立的光轴。在过去的几十年中，一些理论工作已经预测了相图的较宽区域的存在，在该区域中双轴向列相将是稳定的，但是对粒子旋转自由度施加了相当强的约束。在这项工作中，我们使用分子模拟研究了尺寸分散度对自由旋转的硬长方体（在此建模为自双形状纳米板）的相行为的影响。恰好在扁圆形和扁圆形之间的这种奇异各向异性被认为是最适合促进相双轴性的。与多分散相图。尽管我们的结果证实了过去实验观察到的关于略呈扁长针状针铁矿颗粒的胶态分散体的趋势，但它们无法再现在这些实验中观察到的直接的各向同性向双轴向列相变。