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 i s 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, respec tively and lambda(phi) is a free parameter to be determined. This equation is then used to analyze the recent experimental data for equilibrium colloi dal suspensions with small polydispersity. Analyses show that no divergence of the a-and the a-relaxation times is found in the experimental data, alt hough the dynamic properties of the colloidal liquid exhibit a drastic slow ing down in the so-called supercooled region.