Colloidal charge determination in concentrated liquid dispersions using torsional resonance oscillation

The high-frequency rheology of concentrated liquid charge-stabilized dispersions has been measured using a surface-loaded torsional resonator. The high-frequency shear moduli are extracted from the measurement as a function of ionic strength and surface acid content. A theory which enables the determination of the effective surface charge of the concentrated dispersions is presented. At high ionic strengths the theory simplifies to an analytic formula relating the effective surface charge to the high-frequency limiting shear modulus in terms of an effective hard-sphere diameter. The effective hard-sphere diameter is obtained experimentally from the high concentration asymptote of the zero-shear viscosity. The resulting effective surface charge increases with added electrolyte content in agreement with charge renormalization theory. The effective charge also increases with added weak and strong surface acid content. The method, which operates on concentrated dispersions, is found to yield effective charges that agree with dilute measurements of the electrophoretic mobility. Moreover, the effective hard-sphere scaling reduces the high-frequency viscosity to a master curve independent of salt content.