where N w is the number of water molecules adsorbed on the surface of gold with surface area A, N A is Avogadro's number, M w the molar mass of water, ρ w (r) is the radial mass density of water at radius r, and ρ w (z) is the mass density of water along the direction perpendicular to the planar surface, z. The upper limits of the integrals, r max and z max , were taken as the profile position corresponding to the minimum following the peak of the adsorption band (for example, see Figure ). The integrals were estimated using numerical quadrature.