Lubensky T C, Mukhopadhyay Ranjan, Radzihovsky Leo, Xing Xiangjun
Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania 19174, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Jul;66(1 Pt 1):011702. doi: 10.1103/PhysRevE.66.011702. Epub 2002 Jul 19.
A nematic liquid-crystal gel is a macroscopically homogeneous elastic medium with the rotational symmetry of a nematic liquid crystal. In this paper, we develop a general approach to the study of these gels that incorporates all underlying symmetries. After reviewing traditional elasticity and clarifying the role of broken rotational symmetries in both the reference space of points in the undistorted medium and the target space into which these points are mapped, we explore the unusual properties of nematic gels from a number of perspectives. We show how symmetries of nematic gels formed via spontaneous symmetry breaking from an isotropic gel enforce soft elastic response characterized by the vanishing of a shear modulus and the vanishing of stress up to a critical value of strain along certain directions. We also study the phase transition from isotropic to nematic gels. In addition to being fully consistent with approaches to nematic gels based on rubber elasticity, our description has the important advantages of being independent of a microscopic model, of emphasizing and clarifying the role of broken symmetries in determining elastic response, and of permitting easy incorporation of spatial variations, thermal fluctuations, and gel heterogeneity, thereby allowing a full statistical-mechanical treatment of these materials.
向列型液晶凝胶是一种具有向列型液晶旋转对称性的宏观均匀弹性介质。在本文中,我们开发了一种研究这些凝胶的通用方法,该方法纳入了所有潜在的对称性。在回顾了传统弹性力学并阐明了未变形介质中点的参考空间和这些点映射到的目标空间中旋转对称性破缺的作用之后,我们从多个角度探讨了向列型凝胶的异常特性。我们展示了从各向同性凝胶通过自发对称性破缺形成的向列型凝胶的对称性如何强制产生软弹性响应,其特征是剪切模量消失以及在沿某些方向的应变临界值之前应力消失。我们还研究了从各向同性凝胶到向列型凝胶的相变。除了与基于橡胶弹性的向列型凝胶方法完全一致外,我们的描述还具有重要优点,即独立于微观模型、强调并阐明对称性破缺在确定弹性响应中的作用,以及允许轻松纳入空间变化、热涨落和凝胶不均匀性,从而能够对这些材料进行完整的统计力学处理。