Theories of Order and Dynamics in Soft Materials

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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.***