Viscoelasticity and generalized Stokes-Einstein relations of colloidal dispersions

The linear viscoelastic and diffusional properties of colloidal model dispe rsions are investigated and possible relations between the (dynamic) shear viscosity and various diffusion coefficients are analyzed. Results are pres ented for hard sphere and charge-stabilized dispersions with long-range scr eened Coulomb interactions. Calculations of the dynamic long-time propertie s are based on a (rescaled) mode coupling theory (MCT). For hard sphere sus pensions a simple hydrodynamic rescaling of the MCT results is proposed whi ch leads to good agreement between the theory and experimental data and Bro wnian dynamics simulation results. The rescaled MCT predicts that the zero- shear limiting viscosity of hard sphere dispersions obeys nearly quantitati ve generalized Stokes-Einstein (GSE) relations both with regard to the long -time self-diffusion coefficient and the long-time collective diffusion coe fficient measured at the principal peak of the static structure factor. In contrast, the MCT predicts that the same GSEs are violated in the case of d ispersions of highly charged particles. The corresponding short-time GSEs a re found to be partially violated both for charged and uncharged colloidal spheres. A frequency dependent GSE, relating the elastic storage and viscou s loss moduli to the particle mean squared displacement, is also investigat ed, According to MCT, this GSE holds fairly well for concentrated hard sphe res, but not for charge-stabilized systems. Remarkably good agreement is ob tained, however, with regard to the frequency dependence of the Laplace-tra nsformed reduced shear stress relaxation function and the Laplace-transform ed reduced time-dependent self-diffusion coefficient for both charged and u ncharged particle dispersions. (C) 1999 American Institute of Physics. [S00 21-9606(99)50541-2].