An experimental/theoretical method to measure the capacitive compactness of an aqueous electrolyte surrounding a spherical charged colloid

The capacitive compactness has been introduced very recently [G. I. Guerrero-García et al., Phys. Chem. Chem. Phys. 20, 262–275 (2018)] as a robust and accurate measure to quantify the thickness, or spatial extension, of the electrical double layer next to either an infinite charged electrode or a spherical macroion. We propose here an experimental/theoretical scheme to determine the capacitive compactness of a spherical electrical double layer that relies on the calculation of the electrokinetic charge and the associated mean electrostatic potential at the macroparticle’s surface. This is achieved by numerically solving the non-linear Poisson-Boltzmann equation of point ions around a colloidal sphere and matching the corresponding theoretical mobility, predicted by the O’Brien and White theory [J. Chem. Soc., Faraday Trans. 2 74, 1607–1626 (1978)], with experimental measurements of the electrophoretic mobility under the same conditions. This novel method is used to calculate the capacitive compactness of NaCl and CaCl₂ electrolytes surrounding a negatively charged polystyrene particle as a function of the salt concentration.