Slow dynamics of equilibrium density fluctuations in a supercooled colloidal liquid

Abstract

On the basis of the recent theory for nonequilibrium suspensions of colloidal hard spheres, the nonlinear equation for the particle mean-square displacement M 2( t) is derived for equilibrium suspensions of colloidal hard spheres as dM 2(t)/ dt=6D S L(φ)+6[D S S(φ)−D S L(φ)] exp[−λ(φ)M 2(t)] , where φ is a volume fraction of identical hard spheres, D S S ( φ) and D S L ( 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 φ exp 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 φ exp, we then observe a progression from normal liquid, to supercooled liquid, and to glass without any sharp transitions in λ and D S L . 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.