Webinar

Properly capturing fluctuations is crucial in understanding heterogeneous cooperative dynamics of a diverse class of physical systems from colloidal (and polymer) glasses to biopolymers as well as in understanding the thermodynamic phase behavior of polymers around a mean-field solution in polymer field theory. In this presentation, I will talk about two of such systems where fluctuations (activated dynamics or fluctuation free energy) are crucial. (I) Understanding the nature of glass transition and kinetic arrest remains a multifaceted grand challenge in non-equilibrium statistical mechanics, condensed matter physics, and materials science. In the first part of the talk, formulation of a microscopic force-based theory to understand the dynamical and mechanical properties of dense suspensions of colloidal materials with strong short-ranges attractive forces will be discussed. The classic theoretical “projection” approximation of replacing all microscopic forces by a single effective force determined by equilibrium pair correlations in ideal Mode Coupling Theory (MCT) is reformulated based on a “projectionless” approach. The observed theoretical predictions of non-monotonic changes of alpha relaxation related to re-entrant transition are in good agreements with experiments and simulations. (II) Enhanced alignment of polymers in their nematic state are responsible for crucial mechanical and material properties of fibers found in both biological systems and chemical physics. In this second part, building on the exact single-chain statistics of semiflexible polymers and mean-field solutions for both isotropic and nematic states, I will talk about extending an analytical theory for the free energy functional of semiflexible polymer solution with alignment interaction up to quadratic order to specifically understand the three Frank elastic (FE) constants of long wavelength splay, bend, and twist modes of deformation. These deformations characterize the normal modes of the deviation of local nematic director field of liquid crystalline behavior. The theoretical picture suggests the three FE constants can be exactly mapped to correlation functions involving real spherical harmonics.