Effects of non-equilibrium association–dissociation processes in the dynamic electrophoretic mobility and dielectric response of realistic salt-free concentrated suspensions

Abstract

Electrokinetic investigations in nanoparticle suspensions in aqueous media are most often performed assuming that the liquid medium is a strong electrolyte solution with specified concentration. The role of the ions produced by the process of charging the surfaces of the particles is often neglected or, at most, the concentrations of such ions are estimated in some way and added to the concentrations of the ions in the externally prepared solution. The situation here considered is quite different: no electrolyte is dissolved in the medium, and ideally only the counterions stemming from the particle charging are assumed to be in solution. This is the case of so-called salt-free systems. With the aim of making a model for such kind of dispersions as close to real situations as possible, it was previously found to consider the unavoidable presence of H+ and OH− coming from water dissociation, as well as the (almost unavoidable) ions stemming from the dissolution of atmospheric CO2. In this work, we extend such approach by considering that the chemical reactions involved in dissociation and recombination of the (weak) electrolytes in solution must not necessarily be in equilibrium conditions (equal rates of forward and backward reactions). To that aim, we calculate the frequency spectra of the electric permittivity and dynamic electrophoretic mobility of salt-free suspensions considering realistic non-equilibrium conditions, using literature values for the rate constants of the reactions. Four species are linked by such reactions, namely H+ (from water, from the – assumed acidic – groups on the particle surfaces, and from CO2 dissolution), OH− (from water), HCO3− and H2CO3 (again from CO2). A cell model is used for the calculations, which are extended to arbitrary values of the surface charge, the particle size, and particle volume fraction, in a wide range of the field frequency ω. Both approaches predict a high frequency relaxation of the counterion condensated layer and a Maxwell–Wagner–O'Konski electric double layer relaxation at intermediate frequencies. Also, in both cases an inertial decay of the electrophoretic mobility at high ω takes place. The most significant difference between the present model and previous results based on the equilibrium hypothesis is by no means negligible: only in non-equilibrium conditions do we find a low-frequency relaxation (mostly noticed in permittivity data, while its significance is lower in dynamic mobility spectra). This new relaxation presents all the characteristic features of the concentration polarization (or alpha) dispersion. These are: i) the average electric polarization of the system increases when the relaxation frequency is surpassed, contrary to the behavior after Maxwell–Wagner type relaxations; ii) the amplitude of the relaxation increases with surface charge, reaching a sort of saturation if the charge is too high; iii) the relaxation frequency increases with volume fraction while the relaxation amplitude decreases; iv) the characteristic frequency is reduced by the increase in particle radius. All these facts confirm that the non-equilibrium approach seems to better describe the physics of the system by giving rise to a concentration polarization kind of relaxation, only possible when ions can accumulate on both sides of the particles as dictated by the field, and not as determined by equilibrium conditions in the dissociation–recombination reactions involved.