Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel.
Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.
Soft Matter. 2018 Dec 19;15(1):116-126. doi: 10.1039/c8sm01290c.
Symmetry considerations preclude the possibility of twist or continuous helical symmetry in bulk crystalline structures. However, as has been shown nearly a century ago, twisted molecular crystals are ubiquitous and can be formed by about 1/4 of organic substances. Despite its ubiquity, this phenomenon has so far not been satisfactorily explained. In this work we study twisted molecular crystals as geometrically frustrated assemblies. We model the molecular constituents as uniaxially twisted cubes and examine their crystalline assembly. We exploit a renormalization group (RG) approach to follow the growth of the rod-like twisted crystals these constituents produce, inquiring in every step into the evolution of their morphology, response functions and residual energy. The gradual untwisting of the rod-like frustrated crystals predicted by the RG approach is verified experimentally using silicone rubber models of similar geometry. Our theory provides a mechanism for the conveyance of twist across length-scales observed experimentally and reconciles the apparent paradox of a twisted single crystal as a finite size effect.
对称性考虑排除了体心晶体结构中扭曲或连续螺旋对称性的可能性。然而，正如近一个世纪前所表明的那样，扭曲的分子晶体无处不在，大约有 1/4 的有机物质可以形成。尽管这种现象无处不在，但到目前为止，还没有令人满意的解释。在这项工作中，我们将扭曲的分子晶体作为具有几何各向异性的组装体进行研究。我们将分子成分建模为单轴扭曲的立方体，并研究它们的晶体组装。我们利用重整化群（RG）方法来跟踪这些组成部分产生的棒状扭曲晶体的生长，在每个步骤中都研究它们的形态、响应函数和残余能量的演化。RG 方法预测的棒状各向异性晶体的逐渐解扭在实验中通过使用类似几何形状的硅橡胶模型得到了验证。我们的理论为实验观察到的扭曲跨尺度传递提供了一种机制，并调和了扭曲单晶作为有限尺寸效应的明显悖论。
