Non-exponential relaxation of density fluctuations in strongly interacting colloidal suspensions

Abstract

The relaxation of density fluctuations is characterized by the experimentally accessible dynamic structure factor S( k, t). Whereas the short-time behaviour of this quantity is well understood, its long-time characteristics are more difficult to determine since memory effects become important giving rise to non-exponential relaxation. Formally, exact results for these memory effects can be derived on the basis of the many-body Smoluchowski equation, but for their evaluation one has to introduce approximations. Previous results, obtained by a mode-coupling approximation, were used to calculate a mean relaxation time τ (k) of S(k,t) and a reduced memory function Δ( k), which characterizes the deviation of S ( k, t) from a simple exponential decay in time. A comparison with experimental results showed only partial agreement. Whereas theory predicts Δ( k → 0) = 0, the experiments found that Δ( k) approaches a finite value in this limit. It will be shown that this discrepancy is due to polydispersity effects. We have improved the mode-coupling approximation and have extended the theory to polydisperse systems. It is remarkable that fairly small amounts of polydispersity give indeed rise to a finite value of Δ( k → 0) for the dynamic structure factor of the polydisperse system in contrast to a vanishing Δ( k → 0) for monodisperse suspensions.