44689-G7
Liquid Crystalline Elastomers: Elasticity, Fluctuations, and Defects
We have studied the isotropic-cholesteric transition of a weakly chiral liquid crystalline elastomer sample. When such a system is brought to low temperature cholesteric phase, the locally preferred helical nematic order is incompatible with global geometry. The system is therefore frustrated and appropriate compromise has to be achieved between the nematic ordering and the elastic deformation. In the weak chirality limit, we compare two possible solutions: a helical state as well as a double twist state. We find that the double twist state very efficiently minimizes both the elastic free energy and the chiral nematic free energy. On the other hand, the pitch of the helical state is strongly affected by the nemato-elastic coupling. As a result this state is not efficient in minimizing the chiral nematic free energy.
We have studied long-wave-length elastic fluctuations rubber materials. We found that, due to the subtle interplay with the incompressibility constraint, these fluctuations qualitatively modify the large-deformation stress-strain relation as predicted by classical rubber elasticity. To leading order, this mechanism provides a simple and generic explanation for the universally observed peak structure of Mooney-Rivlin stress-strain relation, which has been a mystery for more than half century. Our work discovers the internal inconsistency of the classical theory of rubber elasticity and points out thermal fluctuations as the generic mechanism leading to the breakdown of molecular level theories. It is likely to produce far-reaching impact on the field of soft matter physics and polymer science in the future. This work is featured by Physical Review Focus on February 20, 2008.
The physics of translational order on curved substrates has received increasing attention recently. We have studied smectic order on arbitrary curved substrate using the methods of modern differential geometry and topology. We systematically classify and characterize all low energy smectic states on torus as well as on sphere. Two dimensional smectic systems confined on either manifold exhibit many topologically distinct low energy states. Different states are not accessible from each other by local fluctuations. The total number of low energy states scales as the square root of the substrate area. We also address the energetics of 2D smectics on curved substrate and calculate the mean field phase diagram of smectics on a thin torus. Finally, we also discuss the motion of disclinations for spherical smectics, and illustrate the interesting connection between spherical smectics and the theory of elliptic functions.
We have studied the organization of topological defects in a system of nematogens confined to the two-dimensional sphere. We first perform Monte Carlo simulations of a fluid system of hard rods (spherocylinders) living in the tangent plane. The sphere is adiabatically compressed until we reach a jammed nematic state with maximum packing density. The nematic state exhibits four +1/2 disclinations arrayed on a great circle rather than at the vertices of a regular tetrahedron. This arises from the high elastic anisotropy of the system in which splay is far softer than bending. We also introduce and study a lattice nematic model on sphere with tunable elastic constants and map out the preferred defect locations as a function of elastic anisotropy. We establish the existence of a one-parameter family of degenerate ground states in the extreme splay-dominated limit. Our work shows how to control the global defect geometry of spherical nematic by tuning relevant elastic moduli.
We have studied vacancy diffusion on the classical triangular lattice dimer model, subject to the kinetic constraint that dimers can only translate, but not rotate. A single vacancy, i.e. a monomer, in an otherwise fully packed lattice, is always localized in a tree-like structure. The distribution of tree sizes is asymptotically exponential and has an average of 8.16 sites. A connected pair of monomers has a finite probability of being delocalized. When delocalized, the diffusion of monomers is anomalous. Our work is relevant to understanding the diffusion of particles in structure glasses near the glass transition.
