(591e) Frank Elastic Constants of Semi-Flexible Polymer Nematic Solutions

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. Polymers with sufficient backbone bending rigidity, or so called semiflexible polymers, are particularly prone to forming nematic liquid crystalline phases with strong alignment at low temperatures and/or high concentrations. The strongly aligned phases are an excellent candidate for synthesis of conducting polymers for flexible electronics, where chain alignment promotes efficient charge transport. Semiflexible polymers are also particularly prevalent in biophysics since DNA effectively acts like a rigid polymer on short length scales but behaves as a flexible polymer on large lengths. DNA forms lyotropic crystalline phases in solutions in presence of crowding or presence of ions and induces supercoiling in plasmid DNA. The nematic phases also help in packing DNA into viral capsids. Hence understanding liquid crystalline polymer nematic behavior is of fundamental interest from both materials science and biophysics perspective.

Phase behavior and single-chain statistics of semiflexible polymers with alignment interactions have been previously studied using self-consistent field theory. Exact mean-field equations for both isotropic and nematic states and solutions using spheroidal functions have also been achieved. A plethora of interesting phase behavior arises from the interplay of isotropic Flory-Huggins interactions and anisotropic Maier-Saupe interactions. Here, we extend the analytical theory for the free-energy functional of semiflexible polymer blends with alignment interactions up to quadratic order in 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. While the extension of semiflexible polymer field theory to understand FE constants have been long proposed, our approach is based on a quadratic expansion around an isotropic-nematic mean field solution that uses exact chain statistics. The theoretical picture suggests the three FE constants can be mapped to correlation functions involving real spherical harmonics. We show results based on a wide range of polymer length, polymer rigidity traversing flexible to rigid rod limit as well as various strengths of local alignment field. To aid theoretical analysis, numerical simulations are also performed that shows excellent agreement with theory predictions. Taken together, this provides a concrete picture of a molecular statistical mechanics derivation and calculation of FE constants for polymers with arbitrary rigidity.