Unexpected Effects of Surfactant Adsorption Upon Water/Vapor Surface Geometry and Fluctuations

As described by capillary wave theory, adsorbates at a water/vapor interface change surface geometry and fluctuations through altered surface tension. Detailed theoretical studies of surface geometry in the presence of adsorbates, specifically amphiphilic surfactants are relatively sparse and many applications have focused upon ensemble average surface geometric characteristics. In this work we demonstrate that different interpretations of surface geometry emerge when considering the distributions of the geometric descriptors of surface curvature and orientation as a function of adsorbed surfactant concentration and sterics. Molecular dynamics simulations of tributyl phosphate (TBP) adsorbed to the water/vapor surface indicate that increased surface coverage homogeneously enhances symmetric sharp surface waves until a critical concentration is reached that is concomitant with TBP self-assembly. Thereafter, the convexity and concavity of the surface stop cancelling one another and skewing of the surface geometry metric distributions is increased. We define this as a homogeneous $\rightarrow$ inhomogenous surface geometry transition. Examining the surface geometry as a function of alkyl chain length reveals that smaller surfactants at surface coverages below that needed for surfactant-surfactant interactions \textit{inhomogenously} enhance surface curvature on the surface and that adsorbed alkyl tails to the surface can stabilize and increase homogeneous distributed surface geometric metrics. We label this an inhomogenous $\rightarrow$ homogeneous geometric transition. These results reflect the opportunity to incorporate more realistic distributions of surface geometry within the collective understanding of capillary wave theory and the relationship between surface geometry and macroscopic properties like surface tension.