Abstract
A bifurcational analysis is performed on Doi's equation of nematodynamics that describes the non‐equlibrium isotropic‐nematic phase transition of rigid rod polymers in the presence of steady biaxial stretching flow. The symmetry of the flow and of the governing order parameter equations are shown to be the source of a rich bifurcation, symmetry breaking, and multistability behavior involving two physically equivalent biaxial nematic phases, one uniaxial nematic phase and one uniaxial paranematic phase. According to the relative intensity of the nematic ordering field and stretching rate, the uniaxial isotropic‐biaxial nematic transition may be continuous (2nd order), discontinuous (1st order), or it may exhibit a tricritical non‐equilibrium phase transition point. The solutions to the Doi equations of nematodynamics are found to be consistent with those of Khokhlov and Semenov [Macromolecules 15, 1272 (1982)], which are based on a version of the Onsager theory of isotropic‐nematic phase transitions. The present simulations provide a useful guide for orientation control in biaxial stretching flows.