Direct Quantification of Water Surface Charge by Phase-Sensitive Second Harmonic Spectroscopy

We develop and verify a phase-sensitive second harmonic generation spectroscopic scheme that allows for direct determination of the absolute surface charge density and surface potential of a water interface without need of prior interfacial information. The method relies on selective probing of surface-field-induced reorientation order of water molecules in the electrical double layer and is, hence, independent of the interfacial molecular bonding structure. Application of this technique to a mixed surfactant monolayer on water suggests the manifest effect of the chain-chain interactions among the monolayer on adsorption of soluble ionic surfactants. We also deduce the third-order nonlinear susceptibility of bulk water and prove its applicability to analysis of charges of various water interfaces. In addition, we show that the Debye-H\"uckle theory should be avoided in the spectroscopic analysis for its potential significant error, as evidenced experimentally and theoretically.