Elastic Modulus at High Frequency of Polymerically Stabilized Suspensions

Abstract

The elastic moduli of polymerically stabilized suspensions consisting of colloidal silica particles coated with endgrafted PDMS (M n = 80 000) in heptane, were measured as a function of concentration. And the elastic modulus at high frequency was quantitatively described by model calculations with microscopic parameters. In the modeling of 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 with the magnitude of their parameters obtained from (elaborate) characterizations of the particles. Both models result in a quantitative description of the experimental and thickness of the polymer layer.

Interaction between Polymer-Grafted Particles

“…The most accurate approach 4,23 uses the free energy per chain, f(l; R), from a single particle of radius, R, with its brush compressed to a thickness of l. The Appendix provides a simple analytical estimate for f(l; R) calculated with SST. In SCFT, f(l; R) has to be evaluated numerically, but this is nevertheless a trivial one-dimensional calculation of an isolated particle with a reflecting boundary placed at r ) R + l. Once the free energy of the uniformly compressed brush is known, the interaction energy of nonuniform compression is approximated as…”

Dynamics and structure of complex fluids from high frequency mechanical and optical rheometry

“…Based on a theory for simple liquids theoretical expressions including hydrodynamic interactions have been derived relating the limiting high frequency modulus G′ ∞ of concentrated dispersions to the colloidal interaction potential Ψ [55,56]. For aqueous colloidal dispersions the high frequency limit is typically reached beyond f = 1 kHz.…”

Rheological properties of silica dispersions stabilized by stereoregular poly(methyl methacrylate)

“…4 shows the evolution of shear stress versus shear rate for suspensions at φ = 0.23, which is equivalent to 0.06 g PMMA/g SiO 2 in benzyl alcohol. Suspensions with either i-PMMA or s-PMMA exhibit a yield stress τ 0 , frequently observed with structured suspensions [16][17][18][19]. Although attempts to fit experimental data with Casson and HerschelBulkley models were made, the best results were obtained with the simple Bingham model.…”

“…Various rheological behaviors have been correlated with colloidal characteristics such as adsorption density, adsorbed layer thickness, and polymer conformation [16][17][18][19][20][21]. To our knowledge, the effect of the PMMA tacticity on the rheology of dispersions has never been investigated.…”