Elastic Modulus at High Frequency of Polymerically Stabilized Suspensions

The elastic moduli of polymerically stabilized suspensions consisting of colloidal silica particles coated with endgrafted PDMS (Mn = 80 000) in heptane, were measured as a function of concentration. And the elastic modulus at high frequency G'.. was quantitatively described by model calculations with microscopic parameters. In the modeling of G'.. we essentially followed the method of Elliott and Russel [Elliott, S. L.; Russel, W. B. J. Rheology 1998, 42, 361]. To suit our case of strongly curved polymer layers, we made adaptations in the description of both the pair potential and hydrodynamic interactions. Anticipating that the predicted is sensitive to the modeling of the polymer brush, we explored two different models to predict the pair potential and the polymer layer thickness: a numerical self-consistent field lattice model [Wijmans, C. M.; Zhulina, E. B. Macromolecules 1993, 26, 7214] and an analytical method based on the approach of Li and Witten [Li, H.; Witten, T. A. Macromolecules 1994, 27, 449]. The polymer models were used separately in the model calculations for G'.. with the magnitude of their parameters obtained from (elaborate) characterizations of the particles. Both models result in a quantitative description of the experimental G'.. and thickness of the polymer layer.