Theories of Order and Dynamics in Soft Materials

这项资助支持一个基础广泛的理论计划，将推进我们在三个不同领域的知识：液晶弹性体，手性颗粒气体，以及依赖于动力学变量的耗散或扩散系数系统。 液晶弹性体是既具有橡胶的弹性性能又具有液晶的取向和可能的位置顺序的材料。 取向顺序，这是很容易受到外部场的影响，和弹性变形之间的强相互作用，使这些材料的候选人各种有趣的应用，从人工肌肉致动器应力可调谐激光器。 理想的弹性体是通过各向同性橡胶的破胶相变形成的单轴橡胶。 它的特征是软弹性，其中单轴固体的五个弹性常数之一为零。 实验室单域双相弹性体不是在自发对称破缺的过程中形成的;它们通常被制备成使得双相序在交联时被锁定。 这些系统表现出半软弹性，在小应变的应力-应变关系的特点是由一个单轴固体的五个弹性常数，但变得更像那些在较大的应变软弹性。 本研究的第一个主要目标是通过研究局部键方向和非线性有序之间相互作用的模型来提高我们对半软弹性的理解，并发展近晶-C弹性体的理论，其理想形式在近晶层的平面中表现出自发的对称性破缺和相关的软弹性。响尾蛇是细长的物体，其在平面上具有优选的自旋方向。面 如果它们所处的表面受到周期性的垂直振动，它们将平均沿单一方向旋转。 这提出了一种可能性，最近在哈弗福德学院的实验中实现了，创造一种不寻常的手性颗粒气体，具有均匀的自旋角动量输入。 该基金的第二个主要项目是研究导致手性气体中单个颗粒自旋的优先意义的机制以及气体本身的性质。 胶体粒子的摩擦系数取决于它与静止壁或另一个胶体粒子的距离，而二元混合物的扩散系数则取决于其组分的相对密度。 这类系统的动力学性质（而非平衡性质）与耗散系数不依赖于动力学变量的系统不同。 该基金的第三个项目是研究和发展形式主义，以描述依赖于动力学变量的耗散系数的平衡系统。这些项目的更广泛影响主要是对学生和博士后的培训和教育。这项资助支持一个基础广泛的理论计划，将推进我们在三个不同领域的知识：液晶弹性体，手性颗粒气体，以及依赖于动力学变量的耗散或扩散系数系统。 这些项目的更广泛影响主要是对学生和博士后的培训和教育。

This grant supports a broadly based theoretical program that will advance our knowledge in three distinct areas: liquid crystal elastomers, chiral granular gases, and systems with dissipative or diffusion coefficients that depend on dynamical variables. Liquid crystalline elastomers are materials that have both the elastic properties of rubber and the orientational, and possibly positional, order of liquid crystals. The strong interplay between orientational order, which is easily influenced by external fields, and elastic distortion makes these materials candidates for a variety of interesting applications from artificial muscles to actuators to stress tunable lasers. The ideal nematic elastomer is a uniaxial rubber that forms via a symmetry-breaking phase transition from an isotropic rubber. It is characterized by soft elasticity in which one of the five elastic constants of an uniaxial solid vanishes. Laboratory monodomain nematic elastomers are not formed in a process of spontaneous symmetry breaking; they typically are prepared so that nematic order is locked in at the time of crosslinking. These systems exhibit semi-soft elasticity in which stress-strain relations at small strain are characterized by the five elastic constants of a uniaxial solid but become more like those of soft elasticity at larger strains. The first major goal of this research is to improve our understanding of semi-soft elasticity through investigations of models with an interplay between local bond directions and nematic order and to develop theories for smectic-C elastomers, the ideal form of which exhibit spontaneous broken symmetry and an associated soft elasticity in the plane of the smectic layers.Rattlebacks are elongated objects that have a preferred direction of spin on a flat surface. If the surface on which they sit is subjected to a periodic vertical vibration, they will spin on average in a single direction. This raises the possibility, recently realized in experiments at Haverford College, of creating an unusual chiral granular gas with a homogeneous input of spin angular momentum. The second major project in this grant is the study of both the mechanisms leading to the preferred sense of spin of individual grains in the chiral gas and the properties of the gas itself. Of particular interest is the conversion of spin angular momentum to center-of-mass vorticity.The friction coefficient of a colloidal particle depends on its distance from a stationary wall or from another colloidal particle, and the diffusion coefficient of a binary mixture can depend on the relative density of its components. The dynamical, but not equilibrium, properties of systems such as these will differ from those of systems whose dissipative coefficients do not depend on dynamical variables. The third project of this grant is the study of and development of formalisms to describe equilibrium systems with dissipative coefficients that depend on dynamical variables. The broader impact of these projects is primarily training and education of students and postdocs.%%%This grant supports a broadly based theoretical program that will advance our knowledge in three distinct areas: liquid crystal elastomers, chiral granular gases, and systems with dissipative or diffusion coefficients that depend on dynamical variables. The broader impact of these projects is primarily training and education of students and postdocs.***