Slow dynamics of equilibrium density fluctuations in a supercooled colloidal liquid

On the basis of the recent theory for nonequilibrium suspensions of colloidal hard spheres, the nonlinear equation for the particle mean-square displacement M2(t) is derived for equilibrium suspensions of colloidal hard spheres asdM2(t)/dt=6DSL(φ)+6[DSS(φ)−DSL(φ)]exp[−λ(φ)M2(t)],where φ is a volume fraction of identical hard spheres, DSS(φ) and DSL(φ) are the short- and long-time self-diffusion coefficients, respectively, and λ(φ) is a free parameter to be determined. This equation is used to analyze the recent experimental data for equilibrium colloidal suspensions with small polydispersity. By treating φ and λ as free fitting parameters, a simple transformation from the theoretical volume fraction φ to the experimental volume fraction φexp is obtained. The long-known phenomena similar to those in glass-forming materials, such as the α and β relaxation processes, are also found. With increasing volume fraction φexp, we then observe a progression from normal liquid, to supercooled liquid, and to glass without any sharp transitions in λ and DSL. Thus, analyses show that no divergence of the α- and β-relaxation times take place although the dynamic properties of the colloidal liquid show a drastic slowing down in a supercooled region.