Results and Discussion. Fig. shows an example of nonlinear optical interference fringes recorded while flowing ultrapure water first, then an aqueous pH4 solution at MgCl2 concentrations ranging from 1 µM to 1 mM, and finally a pH 2.5 0.5 M salt solution across a fused silica hemisphere. Clear shifts in the fringe amplitude and phase are evident in the data and quantified using a simple cosine fit function of the form y0 + E . cos(k . x + j). This equation accounts for the signal offset, y0, the SHG amplitude, E, and its phase, j. The constant k =3.14° mm -1 arises from the group velocity dispersion and the 100-millimeter-long time delay stage we use to record the nonlinear optical fringes. Like in our earlier work, we reference the SHG phase to the one we obtain at the high ionic strength and the pH of zero charge (500 mM, pH 2.5), where we expect the surface potential to be minimized and where the SHG response is therefore purely real-valued (E∝e i𝜙 , where 𝜙=0°), and the total surface potential, Ftot, and the nonlinear second order susceptibility, c , as detailed earlier. Fig. shows Ftot and c as a function of cation concentration for the three chloride salts we surveyed. When the salts are added with 10 mM screening electrolyte present (Fig. ), we find negligible changes in Ftot and c . We find that even the trivalent Al 3+ cation does not possess a sufficiently large enough driving force to adsorb to the interface when the negative surface charges from the deprotonated silanol groups are screened by 10 mM electrolyte concentration. In other words, surface charge screening from the 10 mM background electrolyte requires too much work for specific adsorption to occur. This situation is quite different when we perform the adsorption isotherm measurement without any added screening electrolyte (Fig. ). Here, we find that the magnitudes of the total potential and the second order nonlinear susceptibility both decrease with increasing metal cation concentration. The decrease is more pronounced for Al 3+ when compared to Mg 2+ or Na + . Among all three cations, the sodium cation requires the largest concentration to reduce the magnitude of the total surface potential to a given level, as anticipated given it has the lowest charge density in the series. The nonlinear susceptibility, at a given ion concentration, is smallest for the hardest cation and highest for the softest cation, as perhaps expected from a cation polarizability argument. In Fig. we show the total number of absorbed cations per square centimeter, Nads, which we compute by first multiplying the difference of the total potential, Ftot, relative to the lowest metal cation concentration, Φ !"!,$ , with the Faraday constant, F, and the cation valency, n, then dividing by the thermal energy, RT, and then employing this value as the argument in a Boltzmann term that we multiply into the bulk cation concentration, Cbulk with units of mol L -1 . Raising this product to the power of 2/3 yields the number of cations per unit area, and a factor of 1/100 converts from decimeters squared to centimeters squared, as shown in the following equation: