Comparison of dynamic light scattering measurements and mode-coupling theory for the tagged particle dynamics of a hard-sphere suspension

The mean-squared displacement, velocity autocorrelation function, and the non-Gaussian parameter, obtained by dynamic light scattering on suspensions of particles with hard-sphere interactions, are compared with the results of the idealized version of mode-coupling theory. Both leading order asymptotic and full numerical solutions of the mode-coupling equations are considered. Experiment and the full numerical results of the theory expose similar qualitative changes at the volume fraction of the first order freezing transition. In particular, the emergence of negative algebraic decays in the velocity autocorrelation function of the under-cooled suspension suggest the emergence of clusters in which particles are trapped. Consistency of experiment, computer simulation, and theory in this regard suggests that, at particular strengths of the delayed, nonlinear feedback, contained in mode coupling theory, the latter predicts not only structural arrest which, as already established, is symptomatic of a glass transition, but also a more subtle change in dynamics that signals the onset of the first order transition