Glassy dynamics and mechanical response in dense fluids of soft repulsive spheres. I. Activated relaxation, kinetic vitrification, and fragility.

The microscopic nonlinear Langevin equation theory of activated glassy dynamics is applied to dense fluids of spherical particles that interact via a finite range Hertzian contact soft repulsion. The activation barrier and mean alpha relaxation time are predicted to be rich functions of volume fraction and particle stiffness, exhibiting a non-monotonic variation with concentration at high volume fractions. The latter is due to a structural "soft jamming" crossover where the real space local cage order weakens when soft particles significantly overlap. The highly variable dependences of the relaxation time on temperature and volume fraction are reasonably well collapsed onto two distinct master curves that are qualitatively consistent with a recent scaling ansatz and computer simulation study. A kinetic vitrification diagram is constructed and compared to its dynamic crossover analog. Intersection of the dynamic crossover and soft jamming threshold boundaries occurs for particles that are sufficiently soft, implying the nonexistence of a clear activated dynamics regime or kinetic arrest transition for such particles. The isothermal dynamic fragility is predicted to vary over a wide range as a function of particle stiffness, and soft particles behave as strong glasses. Qualitative comparisons with simulations and microgel experiments reveal good agreement.