The flow-phase diagram of Doi-Hess theory for sheared nematic polymers II: finite shear rates

Abstract

The purpose of this paper is to extend the rheological predictions of the Doi-Hess kinetic theory for sheared nematic polymers from the anomalous weak shear regime (Forest et al. 2004a) to arbitrary shear rates, and to associate salient rheological and optical properties with the solution space of kinetic theory. Using numerical bifurcation software (AUTO), we provide the phase diagram of all stable monodomain orientational probability distribution functions (PDFs) and their phase transitions (bifurcations) vs nematic concentration (N) and normalized shear rate (Peclet number, Pe) for Pe≥1. Shear stresses, normal stress differences, the peak direction of the orientational distribution, and birefringence order parameters are calculated and illustrated for each type of PDF attractor: steady flow-aligning, both in and out of the flow deformation plane and along the vorticity axis; unsteady limit cycles, where the peak orientation direction rotates in-plane or around the vorticity axis or in bi-stable orbits tilted between them; and chaotic attractors first observed in kinetic simulations by Grosso et al. (2001). We pay particular attention to correlations between rheological features and the variety of monodomain phase transitions. Together with the weak flow regime, these results provide a nearly complete picture of the rheological consequences of the Doi-Hess kinetic theory for sheared monodomains of rigid, extreme aspect ratio, nematic rods or platelets.