ACS PRF | ACS
All e-Annual Reports
44689-G7
Liquid Crystalline Elastomers: Elasticity, Fluctuations, and Defects
We have examined the effects of thermal elastic fluctuations in the nonlinear elasticity of rubber materials. We found that, due to the subtle interplay with the incompressibility constraint, these fluctuations qualitatively modify the large-deformation stress-strain relation, compared to that of classical rubber elasticity. To leading order, this mechanism provides a simple and generic explanation for the peak structure of Mooney-Rivlin stress-strain relation, and shows a good agreement with experiments. It also leads to the prediction of a phonon correlation function that depends on the external deformation. This research 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.
We have also studied the role of spatial heterogeneity in the elastic properties of soft random via a two-pronged approach. First, we propose and explore a nonlocal phenomenological model for the elastic free energy. In the mechanically equilibrated state, the system exhibits randomness in the residual stress and Lame coefficients. Second, we investigate a semi-microscopic model network using replica statistical mechanics. We show that the Goldstone fluctuations of the semi-microscopic model reproduce the phenomenological model, and via this we establish the correspondence between the statistical properties of the residual stress and Lame coefficients. Correlations involving the residual stress are found to be long-ranged and to be governed by a universal parameter that also gives the mean shear modulus. Our research is the first attempt to derive the elastic heterogeneity of random solids from a semi-microscopic description.
We have explored a macroscopic, algebraic approach to rate independent hysteresis using semigroup theory. We use field history to describe the metastable states relevant to rate independent hysteresis and identify the semigroup structure of this history space. Using semigroup theory and related mathematical techniques, we discovered the general relation between return point memory (RPM) and partial order. We also prove a variational principle of rate independent hysteresis with RPM. Last but not least, we characterize the erasing properties of field histories using semigroup theory and discuss possible application of hysteresis phenomena as new mechanism of information storage. Our work is the first attempt to develop a macroscopic theory of hysteresis, as well as the first study of irreversible physics using semigroup theory. The exact results we obtained may play important roles in the future study of nonequilibrium physics.
We study the elasticity of one-dimensional translationally ordered system on two-dimensional curved substrate using modern differential geometry and topology. We identify a new type of global dislocation defects and clarify its relation with the topological properties of the underlying curved. The associated topological charge classifies all ground states with no local defects. We also analyze the energetics of smectic/columnar order on curved substrate. Coupling between nematic director field and extrinsic curvature, which are ignored by other studies, is shown to be important. We also compute the mean field phase diagram of smectic order on a torus is analyzed. Two phases are identified: a small/thin phase where the nematic director is locked by curvature and a large/fat phase where the director varies continuously with system parameters. Our study sheds new light on the deep connection between elasticity theory in curved space, differential geometry, and topology.
We are currently studying the properties of isotropic chiral solids. We have identified elastic interactions with chiral nature in the framework of continuous elasticity theory, and have analyzed the consequences of these novel chiral couplings on the large-scale elastic properties of the solid, as well as on the thermal fluctuations of phonon modes. To understand the origin of chirality in elasticity theory, we have analyzed the thermal fluctuations of a chiral liquid crystalline elastomer in its isotropic phase, but in the vicinity of the isotropic-nematic transition. By integrating out the fluctuations of nematic order we derive an effective model with chiral couplings. The coefficients of these chiral couplings scale inversely with the nematic correlation length, and therefore may become very large near the isotropic-nematic transition. This discovery suggests a novel mechanism for designing isotropic chiral solids by tuning the fluctuations of the nematic order. We are currently exploring the isotropic-nematic transition of a chiral solid crosslinked in the isotropic phase and the possibility of a solid blue phase.
