Dynamic free energies, cage escape trajectories, and glassy relaxation in dense fluids of uniaxial hard particles

We extend the nave mode coupling theory and nonlinear Langevin equation theory of coupled translational-rotational activated dynamics in dense fluids of uniaxial hard particles to more anisotropic rods, and mechanistically analyze in depth the dynamic free-energy surface, hopping process, kinetic vitrification, and fragility. Universal behavior is predicted for the transient center-of-mass (CM) localization length and angle based on a differential volume fraction that quantifies the distance from the dynamic crossover and proper geometric nondimensionalization of the localization quantities. The thermally activated real space cage escape process is increasingly controlled by the CM translation relative to the rotational motion as the particle aspect ratio grows. The mean first passage or structural relaxation time grows faster than exponentially with volume fraction, and is a nonmonotonic function of aspect ratio. The latter results in a kinetic vitrification volume fraction and dynamic fragility that vary nonmonotonically with shape anisotropy. The barrier hopping time based on the simplified CM theory where particle rotation is dynamically frozen is massively reduced by ∼2-3.5 orders of magnitude if the cooperative rotation-translation paths are exploited to escape local cage constraints.