Charge regulation: A generalized boundary condition?

¹ Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University Ramat Aviv, Tel Aviv 69978, Israel
² Department of Theoretical Physics, J. Stefan Institute, and Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana - 1000 Ljubljana, Slovenia

^(a) andelman@post.tau.ac.il

Received: 19 October 2015
Accepted: 29 January 2016

Abstract

The three most commonly used boundary conditions for charged colloidal systems are constant charge (insulator), constant potential (conducting electrode) and charge regulation (ionizable groups at the surface). It is usually believed that the charge regulation is a generalized boundary condition that reduces in some specific limits to either constant-charge or constant-potential boundary conditions. By computing the disjoining pressure between two symmetric planes for these three boundary conditions, both numerically (for all inter-plate separations) and analytically (for small inter-plate separations), we show that this is not, in general, the case. In fact, the limit of charge regulation is a separate boundary condition, yielding a disjoining pressure with a different characteristic separation scaling. Our findings are supported by several examples demonstrating that the disjoining pressure at small separations for the charge regulation boundary condition depends on the details of the dissociation/association process.