HIGH-FREQUENCY MODULUS OF HARD-SPHERE COLLOIDS

The singular nature of the hard sphere potential combined with lubrica tion stresses near contact poses interesting issues with respect to th e high frequency viscoelastic behavior. Dilute theories demonstrate cl early that soft potentials and/or lubrication stresses that reduce the relative mobility to zero at contact lead to a well defined plateau i n G' as omega --> infinity, whereas a hard sphere potential without hy drodynamic interaction produces G' approximate to omega(1/2) in this l imit. The former follows from a small deformation of the equilibrium s tructure due solely to the oscillatory convection and the latter from a diffusional boundary layer near contact required to satisfy the no-f lux boundary condition. Two sets of data that delineate the high frequ ency response for colloidal hard spheres at high volume fraction appea r to differ in this regime, suggesting different physics for the inter actions at small separations. Here we apply our nonequilibrium theory to extend the existing treatments to high volume fractions to predict both limits quantitatively and provide a possible interpretation for t he experimental results. The two experimental systems only differ in t he surface modification of the particles and the high frequency modulu s is the only theological property sensitive to this difference. The p redictions of our theory with varying extent of hydrodynamic interacti on illustrate the link between the behavior of the high frequency modu lus and the hydrodynamic properties very near the particle surface.