Theory of slow dynamics in highly charged colloidal suspensions

A systematic theory for the dynamics of charge-stabilized colloidal suspensions of interacting Brownian particles with both Coulomb and hydrodynamic interactions is presented. A nonlinear deterministic diffusion equation for the average local volume fraction of macroions $\Phi \mathrm{}(x,t)\mathrm{}$ and a linear stochastic diffusion equation for the nonequilibrium density fluctuations around Φ, both of which contain an anomalous self-diffusion coefficient $D_S\sim \left[1-\Phi \mathrm{}\right(x,t)/{\phi }_g{]}^{\gamma },$ are derived, where $\gamma =1\mathrm{}$ here. The glass transition volume fraction ${\phi }_g$ is found to be small as ${\phi }_g\sim {(Zql}_B{/a)}^{-3}$ for highly charged colloidal suspensions with $Z\gg q,$ where Ze is the charge of the macroions, $-\mathrm{qe}$ is the charge of counterions, $l_B$ is the Bjerrum length, and a is the radius of the macroions. The dynamic anomaly of $D_S\left(\Phi \right),$ which results from the correlations among macroions and counterions, due to long-range Coulomb interactions, is shown to cause slow dynamical behavior near ${\phi }_g.$ This situation is exactly the same as that of the hard sphere suspensions previously discussed by the present author, where $\gamma =2.\mathrm{}$