Hetero-interaction between Gouy-Stern double layers: charge and potential regulation

This issue of Advances is devoted to the memory of Hans-Joachim Schulze who, before his untimely death, made substantial contributions in the domains of flotation, wetting and particle interaction, often under adverse working conditions. Many of his publications involve hetero-interaction between different oxides or between solids and air bubbles. In the present paper, the theory for the electric interaction between charged interfaces is reviewed and extended by considering regulation on the Gouy-Stern level, including hetero-interaction. We start from a generalization of the phenomenon of regulation, distinguishing electrostatic, chemical and entropic contributions to the regulation capacity. The analysis is carried out in the mean field approximation for flat double layers. Against this background we review and discuss the existing literature. It is shown that for an appropriate account it is mandatory to include Stern layers, to which not only electrical but also chemical and entropic contributions to the regulation capacity can be attributed. It is demonstrated that interaction at constant diffuse double layer potential or -charge works only at rather large distance of separation. At shorter distance, substantial deviations from this behaviour are found, with a trend that interaction at (about) constant potential is the better obeyed the higher the corresponding regulation capacities are. A lattice model is elaborated to visualize the profiles of the (surface, Stern and diffuse) charges and the corresponding potential changes upon overlap, including the cases where strong induction leads to charge-inversion of the layer with the larger regulation capacity. A number of elaborations is presented, but the potentialities of the model are virtually unlimited.