Title: How Thick is the Air-Water Interface? -- A Direct Experimental Measurement of the Decay Length of the Interfacial Structural Anisotropy

Abstract: The air-water interface is a highly prevalent phase boundary with a far-reaching impact on natural and industrial processes. Water molecules behave differently at the interface compared to the bulk, exhibiting anisotropic orientational distributions, reduced intermolecular connectivity in the hydrogen bond network, and significantly slower dynamics. Despite many decades of research, the thickness of the structural anisotropy in the interfacial layer remains controversial, with a direct experimental measurement being absent. In this study, we utilise an advancement in non-linear vibrational spectroscopy to gain access to this important parameter. Combining phase-resolved sum- and difference-frequency generation (SFG and DFG) responses, we directly measure the decay in structural anisotropy of the air-water interface. We find a decay length of ~6-8\r{A}, in excellent agreement with depth-resolved SFG spectra calculated from ab initio parameterised molecular dynamics (MD) simulations. The result reveals surprisingly short anisotropic orientational correlations from the interfacial layer that are even shorter than in the bulk. Furthermore, the recorded SFG and DFG responses are decomposed into a vibrationally resonant and non-resonant contribution through isotopic exchange measurements. Through their separate analysis, we show that the resonant response is a sensitive probe of the structural anisotropy at the interface whereas the non-resonant contribution contains a significant isotropic contribution from the bulk and therefore only partially reports on the interfacial structure. This finding places stringent restrictions on the insight available through both purely non-resonant and second-order intensity studies.