Characterizations of sharp solute-solvent interfaces in hydrophobic environments via cylindrical coordinates

This paper characterizes sharp solute-solvent interfaces in hydrophobic environments, and there are three major ingredients. The first is the variational implicit solvent model (VISM) which establishes the free energy functional of arbitrary solvation states. The minimization of this functional yields a PDE which characterizes both the stable and saddle solute-solvent interfaces. The second is a solute system consisting of two Gay-Berne ellipsoidal hydrophobic molecules. The cylindrical coordinates reduce the corresponding PDE to an ODE which is more traceable, increasing the computability of the solute-solvent interfaces under solvation effects. The third, which is the innovative part of this paper, transforms the computation of sharp solute-solvent interfaces into an ODE boundary value problem. We introduce an effective method for numerically computing saddle interfaces. This remains a hard problem in previous research. Besides, we address some qualitative results and study how the interface varies with respect to the distance between the two Gay-Berne ellipsoidal hydrophobic molecules.