Slow dynamics of equilibrium density fluctuations in suspensions of hard spheres near the glass transition

A mean-field nonlinear equation for the particle mean-square displacement is derived for equilibrium suspensions of colloidal hard spheres as dM(2)(t)/dt=6D(S)(L)(phi)+6[D-S(S)(phi)-D-L(S)(phi)]e(-lambda(phi )M2(t)), where phi is a volume fraction of identical hard spheres. D-S(S)(phi) and D-S(L)(phi) are the short- and long time self-diffusion coefficients, respectively and lambda(phi) is a free parameter to be determined. This equation is then used to analyze the recent experimental data for equilibrium colloidal suspensions with small polydispersity. Analyses show that no divergence of the a-and the a-relaxation times is found in the experimental data, although the dynamic properties of the colloidal liquid exhibit a drastic slowing down in the so-called supercooled region.