Relative Permittivity in the Electrical Double Layer from Nonlinear Optics
Second harmonic generation (SHG) spectroscopy has been applied to probe the fused silica/water interface at pH 7 and the uncharged 11bar02 sapphire/water interface at pH 5.2 in contact with aqueous solutions of NaCl, NaBr, NaI, KCl, RbCl, and CsCl as low as several 10 microM. For ionic strengths up to about 0.1 mM, the SHG responses were observed to increase, reversibly for all salts surveyed, when compared to the condition of zero salt added. Further increases in the salt concentration led to monotonic decreases in the SHG response. The SHG increases followed by decreases are found to be consistent with recent reports of phase interference and phase matching in nonlinear optics. By varying the relative permittivity employed in common mean field theories used to describe electrical double layers, and by comparing our results to available literature data, we find that models recapitulating the experimental observations are ones in which 1) the relative permittivity of the diffuse layer is that of bulk water, with other possible values as low as 30, 2) the surface charge density varies with salt concentration, and 3) the charge in the Stern layer or its thickness vary with salt concentration. We also note that the experimental data exhibit sensitivity depending on whether the salt concentration is increased from low to high values or decreased from high to low values, which, however, is not borne out in the fits, at least within the current uncertainties associated with the model point estimates.