Determination of Surface Potential and Electrical Double-Layer Structure at the Aqueous Electrolyte-Nanoparticle Interface

The structure of the electrical double layer has been debated for well over a century, since it mediates colloidal interactions, regulates surface structure, controls reactivity, sets capacitance, and represents the central element of electrochemical supercapacitors. The surface potential of such surfaces generally exceeds the electrokinetic potential, often substantially. Traditionally, a Stern layer of nonspecifically adsorbed ions has been invoked to rationalize the difference between these two potentials; however, the inability to directly measure the surface potential of dispersed systems has rendered quantitative measurements of the Stern layer potential, and other quantities associated with the outer Helmholtz plane, impossible. Here, we use x-ray photoelectron spectroscopy from a liquid microjet to measure the absolute surface potentials of silica nanoparticles dispersed in aqueous electrolytes. We quantitatively determine the impact of specific cations (Li^{+}, Na^{+}, K^{+}, and Cs^{+}) in chloride electrolytes on the surface potential, the location of the shear plane, and the capacitance of the Stern layer. We find that the magnitude of the surface potential increases linearly with the hydrated-cation radius. Interpreting our data using the simplest assumptions and most straightforward understanding of Gouy-Chapman-Stern theory reveals a Stern layer whose thickness corresponds to a single layer of water molecules hydrating the silica surface, plus the radius of the hydrated cation. These results subject electrical double-layer theories to direct and falsifiable tests to reveal a physically intuitive and quantitatively verified picture of the Stern layer that is consistent across multiple electrolytes and solution conditions