Analysis of the electrophoretic mobility and viscosity of dilute Ludox solutions in terms of a spherical gel layer model

Abstract

A spherical gel layer model of colloidal particles is used to analyze the electrophoretic mobility and viscosity of a dilute suspension of the silica sol, Ludox, reported previously by Laven and Stein (J. Laven, H.N. Stein, J. Colloid Interface Sci. 238 (2001) 8–15). The colloid is modeled as a sphere with a solid inner core surrounded by a diffuse gel layer of uniform thickness and comprising a specific fraction, f, of the colloidal particle's mass. The gel layer is accessible to solvent and ions, but the gel layer retards the flow of solvent, which is assumed to obey the Brinkman equation. The colloidal charge is assumed to be spherically symmetric, but its disposition on the surface of the core particle and gel layer (α=fraction of charge in the gel layer) is left as an adjustable parameter. Experiments at pH 5.7 and 8.7 over a KCl concentration range of 0.3 to 80 mM are examined. At high salt and/or low pH, the thickness of the gel layer is estimated to be 1.0 to 1.6 nm depending on the assumed fraction of silica present in the gel layer. At low salt (0.3 mM) and high pH, where the net absolute charge of Ludox is large, the thickness of the gel layer is estimated to be 3.7 to 4.1 nm. Thus, the thickness of the gel layer appears to increase with decreasing salt at high pH. The net charge required to simultaneously match experimental and model mobilities and viscosities is sensitive to the choice of f and α. Nonetheless, for reasonable choices of these parameters (f=0.13 and α≅1.0), the estimated net absolute charges of Ludox from present modeling are in good agreement with the titration charges of Bolt (G.H. Bolt, J. Phys. Chem. 61 (1957) 1166–1169), and Milonjic (S.K. Milonjic, Colloids Surf. 23 (1987) 301–311) over the entire salt concentration range at pH 8.7. At pH 5.7, however, the estimated net absolute charge from current modeling exceeds the Bolt values by about 50%.