Interaction between charged bodies under the influence of charge regulation

Abstract

The surface charge of most mineral and biological surfaces is rendered in water by ionization of their surface groups to a degree determined by a balance between the growing electrostatic energy as more groups gain charge and the reduced chemical free energy that accompany that process. Formally, the equilibrium charge can be calculated by solving the coupled electro-chemical equations requiring a fixed electro-chemical potential of all species across the system. The same principle holds for more than one body, except the electrostatic potential, and hence the extent of local ionization depend now on the distance between these bodies. The change in surface ionization with distance is coined “charge regulation”. It is accentuated at short inter-body distances and is hence central to short-range phenomena including molecular recognition and the stability of mineral and biological suspensions, to name a few. As such, charge regulation deserves the comprehensive overview presented below - from early developments to most recent ones. The review elaborates on the fundamental physics and chemistry that lead to charge regulation, present recent thermodynamic results, and discuss the important role of surface entropy as a governing regulation force, particularly near surface neutrality. It discusses in detail the subject of inner and diffuse layer capacitances and how they serve to quantify charge regulation using a quantity called regulation parameter. We show that the power-law regime of the double layer force is governed by charge regulation and derive its relation to the regulation parameter. Finally, we briefly discuss out-of-equilibrium charge regulation and introduce a Langmuir-type of time dependent model, which demonstrates asymmetries in the interaction as two bodies approach or retract.