Extracting local surface charges and charge regulation behavior from atomic force microscopy measurements at heterogeneous solid-electrolyte interfaces.

We present a method to determine the local surface charge of solid-liquid interfaces from Atomic Force Microscopy (AFM) measurements that takes into account shifts of the adsorption/desorption equilibria of protons and ions as the cantilever tip approaches the sample. We recorded AFM force distance curves in dynamic mode with sharp tips on heterogeneous silica surfaces partially covered by gibbsite nano-particles immersed in an aqueous electrolyte with variable concentrations of dissolved NaCl and KCl at pH 5.8. Forces are analyzed in the framework of Derjaguin-Landau-Verwey-Overbeek (DLVO) theory in combination with a charge regulation boundary that describes adsorption and desorption reactions of protons and ions. A systematic method to extract the equilibrium constants of these reactions by simultaneous least-squared fitting to experimental data for various salt concentrations is developed and is shown to yield highly consistent results for silica-electrolyte interfaces. For gibbsite-electrolyte interfaces, the surface charge can be determined, yet, an unambiguous identification of the relevant surface speciation reactions is not possible, presumably due to a combination of intrinsic chemical complexity and heterogeneity of the nano-particle surfaces.