Recent vibrational sum frequency generation spectroscopic experiments [Sengupta et al., J. Phys. Chem. Lett. 13, 11391-11397 (2022)] demonstrated synergistic interfacial adsorption effects between the anionic dodecyl sulfate (DS-) and the polar, but charge-neutral hexaethylene glycol monododecyl ether (C12E6), surfactants. In this study, the interfacial adsorption thermodynamics underlying these synergistic effects are analyzed through free energy decompositions. A general decomposition method utilizing alchemical intermediate states is outlined. Combining free energy decompositions with the potential distribution theorem illuminates the statistical interpretations of correlated effects between different system components. This approach allows for the identification of the physical effects leading to synergistic adsorption thermodynamics of DS- binding to the air-C12E6-water interface. The binding properties are found to result from a combination of effects predominantly including energetic van der Waals stabilization between DS- and C12E6, as well as competing energetic and entropic effects due to changes in the interfacial water structure as a result of introducing a C12E6 monolayer into the bare air-water interface.
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