Capillary waves interfacial roughness

Interface between two liquid solvents — Two liquid solvents can be miscible (e.g., water and ethanol) partially miscible (e.g., water and propylene carbonate), or immiscible (e.g., water and nitrobenzene). Mutual miscibility of the two solvents is connected with the energy of interaction between the solvent molecules, which also determines the width of the phase boundary where the composition varies (Figure) [i]. Molecular dynamic simulation [ii], neutron reflection [iii], vibrational sum frequency spectroscopy [iv], and synchrotron X-ray reflectivity [v] studies have demonstrated that the width of the boundary between two immiscible solvents comprises a contribution from thermally excited capillary waves and intrinsic interfacial structure. Computer calculations and experimental data support the view that the interface between two solvents of very low miscibility is molecularly sharp but with rough protrusions of one solvent into the other (capillary waves), while increasing solvent miscibility leads to the formation of a mixed solvent layer (Figure). In the presence of an electrolyte in both solvent phases, an electrical potential difference can be established at the interface. In the case of two electrolytes with different but constant composition and dissolved in the same solvent, a liquid junction potential is temporarily formed. Equilibrium partition of ions at the - interface between two immiscible electrolyte solutions gives rise to the ion transfer potential, or to the distribution potential, which can be described by the equivalent two-phase Nernst relationship. See also - ion transfer at liquid-liquid interfaces. 

The concept of capillary waves can be used to explain how the surface roughness increases the interfacial capacity beyond the Verwey-Niessen value. For this purpose, Pedna and Badiali [82] have solved the linear Poisson-Boltzmann equation across the interface between two solutions vyith different dielectric constants and Debye lengths separated by a corrugated surface. A major difficulty is the boundary condition at the rough interface. 

The concept of capillary wave explains the increase of the interfacial capacity beyond the Verwey-Niessen limit, and thus helps in understanding the structure of the interface. A quantitative interpretation of experimental data within this model is, however, difficult since there are other causes for the deviations from Verwey-Niessen theory besides the surface roughness. 

---