Electrostatic and chemical interactions of ions in electrolytes and in ionic-point-charge double layers

Abstract

By the application of the Madelung constant, the Debye - Hückel radius is deduced directly from the definition of the average edge length of a cube which contains one ion of a 1-1 electrolyte. The theoretical function of activity coefficient with concentration m γm = 1/[γms + F+(mE+ - 1) +F-(mE- - 1)] is deduced assuming that the ion interactions are, along with the electrostatic free-energy change, also under the influence of the chemical potential of cations and anions. The constant parameters, γms, E+, F+, E- and F- can be estimated by fitting the function to experimental sets of points of any electrolyte. The theoretical function of the electrokinetic quotient, q, is proposed. This is measured as the electrophoretic mobility, or electroosmotic transport across membranes, or streaming current, or streaming potential on ionic strength or concentration, Ic, which reads q = qm - s|log(Icm/Ic)| . The theoretical function is defined by three constant parameters: qm = maximum electrokinetic quotient, s = slope of the lines, Icm = ionic strength defining qm, one independent variable, m = molality, and one dependent variable q = electrokinetic quotient. Constant parameters can be estimated by fitting the theoretical function to experimental sets of electrokinetic points. Electrostatic potentials kp and kpm replacing the classical Smoluchowki and Henry ζ potentials can be calculated from s, qm and q, which are obtained by fitting, using kp/kpm = 10|(qm-q)/(2s)|. © Springer-Verlag 1999.