Solvation Forces Near Hydrophobic Surfaces: A Classical Density Functional Theory Study

We use classical density functional theory (DFT) to model solvation interactions between hydrophobic surfaces, which we show to be characterized by depletion attraction at small surface to surface separations and a slowly decaying bipower law interaction at large separations. The solvation interaction originates from van der Waals (vdW) and Coulombic interactions between molecules in the polar solvent, e.g., water, and from the molecules thermal motion and finite volume. We investigate model hydrophobic surfaces represented by bubbles and nonpolar solids, e.g., aliphatic particles, and calculate in a DFT fashion the distribution of molecules in the interlaying solvent between two such surfaces and the hydrophobic excess force resulting from it. The interactions are largely attractive, which is well-known in measurement, albeit vdW attraction between molecules in solids and in the solvent may cause repulsion at certain interface to interface separations. We commence our analysis by suggesting an asymptotic analytical bipower law expression for the solvation interaction at large separations. Thereafter we present a full numerical solution, which is in good agreement with the analytical prediction and further explores the interaction at small surface to surface separations. Our theoretical results yield adhesion energies which agree with previous experiments.