1：Experimental Design and Method Selection:

The study uses vibrational sum-frequency generation (SFG) spectroscopy and thin-film pressure balance (TFPB) techniques to measure and validate double-layer potentials at liquid?gas interfaces. SFG is employed to probe interfacial water molecules, and TFPB is used for disjoining pressure isotherms analyzed with DLVO theory.

2：Sample Selection and Data Sources:

Mixed solutions of nonionic C10E4 and cationic C16TAB surfactants with total concentration Csurf = 0.7 mM and varying molar ratios, at ionic strengths of 0.7 mM and 500 mM adjusted with NaCl.

3：7 mM and varying molar ratios, at ionic strengths of 7 mM and 500 mM adjusted with NaCl. List of Experimental Equipment and Materials:

3. List of Experimental Equipment and Materials: SFG spectrometer (MUSIC), TFPB setup, surfactants (C10E4 and C16TAB), NaCl, glassware, and optical components.

4：Experimental Procedures and Operational Workflow:

SFG spectra were recorded in ssp polarization configuration; TFPB measurements involved creating foam films and measuring disjoining pressure isotherms; data were analyzed using fitting procedures and DLVO theory.

5：Data Analysis Methods:

SFG spectra were fitted with Lorentzian and Voigt functions; TFPB data were analyzed using DLVO theory to extract double-layer potentials.