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

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 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.