Density–Nematic Coupling in Isotropic Linear Polymers: Acoustic and Osmotic Birefringence

Abstract

AbstractLinear polymers and other connected “line liquids” exhibit a geometrical coupling between density and equilibrium orientational order on the macroscopic level that gives rise to a Meyer‐de Gennes vectorial conservation law for polar orientational order, or its amended version for apolar nematic order when described as “recovered” polar order. They generally exhibit fluctuations of orientational order, starting with its lowest moment, the polar order, which in the isotropic phase is geometrically decoupled from density. As a contrast, quadrupolar (nematic) orientational fluctuations are inherently coupled to density fluctuations already in the isotropic system and not subject to the existence of an orientational phase transition. To capture this, it takes the tensorial description of the nematic order, leading to a geometrical coupling between density and orientational order in the form of a tensorial conservation law. This coupling implies that a spatial density variation will induce nematic order and thereby an acoustic or osmotic optical birefringence even in isotropic phase. The theory is validated by performing detailed Monte Carlo simulations of isotropic melts and comparing the results with macroscopic predictions. This also exposits a means of determining the macroscopic parameters by microscopic simulations to yield realistic continuum models of specific polymeric materials.