Density--nematic coupling in isotropic linear polymers
Linear polymers and other connected "line liquids" exhibit a coupling between density and equilibrium nematic order on the macroscopic level that gives rise to a Meyer-de Gennes vectorial conservation law. Nevertheless, isotropic linear polymer melts/solutions exhibit fluctuations of the density and of the nematic order that are not coupled by this vectorial constraint, just like for isotropic liquids composed of disconnected non-spherical particles. It takes the proper tensorial description of the nematic order in linear polymer liquids, leading to a tensorial conservation law connecting density and orientational order, that finally implicates coupled density and nematic order fluctuations, already in the isotropic system and not subject to the existence of an orientational phase transition. This coupling implies that a spatial variation of density or a local concentration gradient will induce nematic order and thereby an acoustic or osmotic optical birefringence even in an otherwise isotropic polymer melt/solution. We validate the theoretical conceptions by performing detailed Monte Carlo simulations of isotropic melts of "soft" worm-like chains with variable length and flexibility, and comparing the numerically determined orientation correlation functions with predictions of the macroscopic theory. The methodology drawn sets forth a means of determining the macroscopic parameters by microscopic simulations to yield realistic continuum models of specific polymeric materials.