Understanding and Describing the Liquid-Crystalline States of Polypeptide Solutions: A Coarse-Grained Model of PBLG in DMF

A perturbation theory is employed to construct a free-energy functional capable of describing the isotropic and nematic phases of attractive rod-like particles. An algebraic van der Waals-Onsager equation of state is then developed to determine the global phase behavior of prolate particles for various aspect ratios and strengths of the attractive potential. Compared with the phase diagram of athermal systems, the incorporation of an attractive potential is seen to stabilize the nematic state, leading to an increase in the degree of orientational order of the system at high densities. The most salient feature for systems with large aspect ratios is the existence of regions of nematic-nematic phase separation. A simple attractive-rod model is used to describe the phase behavior of solutions of a relatively rigid polypeptide, poly(gamma-benzyl-L-glutamate) (PBLG), in dimethylformamide (DMF); this system exhibits a unique phase separation between two liquid-crystalline states. The coarse-grained representation of the mesogen employed here is a hard spherocylinder decorated with an attractive square-well potential which acts at the center of mass of the particle. A quantitative description of the experimental isotropic-nematic phase behavior of the PBLG solutions can be achieved with the proposed model using just two temperature-dependent parameters.