Microscopic theory of gelation and elasticity in polymer-particle suspensions

A simplified mode-coupling theory (MCT) of ergodic-nonergodic transitions, in conjunction with an accurate two-component polymer reference interaction site model (PRISM) theory for equilibrium structural correlations, has been systematically applied to investigate gelation, localization, and elasticity of flexible polymer-hard particle suspensions. The particle volume fraction at the fluid-gel transition is predicted to depend exponentially on reduced polymer concentration and size asymmetry ratio at relatively high colloid concentrations. In contrast, at lower particle volume fractions, a power-law dependence on polymer concentration is found with effective exponents and prefactors that depend systematically on the polymer/particle size ratio. Remarkable power-law and near universal scaling behavior is found for the localization length and elastic shear modulus. Multiple experiments for gel boundaries and shear moduli are in good agreement with the no adjustable parameter theory. The one exception is the absolute magnitude of the shear modulus which is strongly overpredicted, apparently due to nonequilibrium dense cluster formation. The simplified MCT-PRISM theory also captures the qualitative aspects of the weak depletion-driven "glass melting" phenomenon at high particle volume fractions. Calculations based on an effective one-component model of structure within a low particle volume fraction framework yield qualitatively different features than the two-component approach and are apparently all in disagreement with experiments. This suggests that volume fraction and size asymmetry dependent many-body screening of polymer-mediated depletion attractions at finite particle concentrations are important.