Isotropic ↔ anisotropic surface geometry transitions induced by adsorbed surfactants at water/vapor interfaces

Adsorbates at a water/vapor interface change the surface geometry through altered surface tension, yet detailed theoretical studies are relatively sparse, and many applications focus on ensemble average characteristics. Here, we demonstrate that different interpretations of surface geometry emerge when considering the distributions of surface curvature and orientation as a function of adsorbed surfactant concentration and sterics. At low surface densities, the tributyl phosphate (TBP) sorbed water/vapor surface has an increased presence of ridges that are defined by principal curvatures κ₁ and κ₂ of opposite signs yet close in magnitude. As the TBP surface density increases, the difference in principal curvatures slowly increases. There is a distinct transition of the surface geometry, where the ridge-like features become much more pronounced, having sides whose orientation is normal to a flat interfacial plane. Thus, as the TBP surfactant is added to the surface, the surface curvatures become anisotropic in terms of the difference in magnitude of κ₁ and κ₂. We label this an isotropic → anisotropic geometric transition. Comparing the surface geometry as a function of the carbon tail length of the alkyl phosphate surfactant reveals that smaller surfactants also anisotropically enhance surface curvatures and that adsorbed alkyl tails to the surface stabilize and increase the symmetry of surface waves along the two principal curvature axes. We label this an anisotropic → isotropic geometric transition. These results reflect the opportunity to incorporate more realistic distributions of surface geometry within the collective understanding of statistical theories of surfaces, including capillary wave theory.