Methods for determining the intrinsic and effective charges on spherical macroions

The intrinsic number of charges per particle, Z, on particles in a suspension of monodisperse sulfonated polystyrene latex is found by measuring steady-state voltammetric transport-limited currents for the reduction of hydrogen counterion at a Pt disk microelectrode in a suspension containing excess supporting electrolyte. Limiting currents measured in deionized latex suspensions yield a corresponding effective charge, Z*. Electrostatic binding of an inner layer of counterions to the particle renders Z* < Z. Voltammetrically determined charges agree with the intrinsic and effective Stokes charges as determined by titration and electrophoresis, respectively. ζ- Potentials calculated from the measured electrophoretic mobility of the particles yield the Loeb charge number, which agrees more closely with Z than with Z*. For existing data on spherically charged macroions, Z*/Z decreases with increasing ratio of intrinsic charge to macroion radius, Z/a. This finding is supported by effective charge values calculated from the cell model using the nonlinear Poisson-Boltzmann equation with the convention that Z* is the charge found between the c(r)/ 〈c〉 = 1 boundary and the cell wall.