Orientational Wetting and Topological Transitions in Confined Solutions of Semiflexible Polymers

Abstract

Despite their considerable practical and biological applications, the link between molecular properties, assembly conditions and self-organized structure in confined polymer solutions remains elusive. Here, we explore the lyotropic nematic ordering of semi-flexible chains in spherical confinement for multiple contour lengths across a wide regime of concentrations. We uncover an original crossover from two distinct quadrupolar states, both characterized by regular tetrahedral patterns of surface topological defects, to either longitudinal, latitudinal or spontaneously-twisted bipolar structures with increasing densities. These transitions, along with the intermediary arrangements that they involve, are attributed to the combination of orientational wetting with subtle variations in their liquid-crystal (LC) elastic anisotropies. Our molecular simulations are corroborated by density functional calculations, and are quantified through the introduction of several order parameters as well as an unsupervised learning scheme for the localization of topological defects. Our results agree quantitatively with the predictions of continuum nematic elasticity theories, and evidence the extent to which the folding of macromolecules and the self-assembly of low-molecular-weight LCs may be guided by the same, universal principles.