Probing Charged Aqueous Interfaces Near Critical Angles: Effect of Varying Coherence Length

Angle-resolved vibrational sum frequency generation experiments have been used to study the silica–water interface as a function of ionic strength. Well below the critical angle, the sum frequency intensity increases up to 10^–4 M NaCl and then drops. However, near the critical angle, a plateau may be observed up to 10^–4 M. We first demonstrate that this is a result of the interaction of a long Debye length at low ionic strength with a long coherence length near the critical angles. In order to account for the behavior at the lowest concentrations where surface potentials are typically large, it is necessary to consider an electrostatic potential that extends into the bulk aqueous phase beyond the Debye–Hückel approximation. Because the extent of second- and third-order contributions to the nonlinear polarization can vary with ionic strength, but not with the angle of incidence, we perform a global fit to the experimental data using our proposed model to extract the relative magnitude of the two susceptibilities. The ionic strength dependence of this ratio points to the critical nature of the silanol deprotonation and the development of surface charge and illustrates how surface water molecules respond. These results highlight the importance of varying the coherence length in order to probe the water structure at charged interfaces.