Derivation of Hamaker Dispersion Energy of Amorphous Carbon Surfaces in Contact with Liquids Using Photoelectron Energy-Loss Spectra

Abstract

Hamaker interaction energies and cutoff distances have been calculated for disordered carbon films, in contact with purely dispersive (diiodomethane) or polar (water) liquids, using their experimental dielectric functions e (q, ω) obtained over a broad energy range. In contrast with previous works, a q-averaged q is derived from photoelectron energy-loss spectroscopy (XPS-PEELS) where the energy loss function (ELF) q is a weighted average over allowed transferred wave vector values, q, given by the physics of bulk plasmon excitation. For microcrystalline diamond and amorphous carbon films with a wide range of (sp3/sp2 + sp3) hybridization, non-retarded Hamaker energies, A 132 (L < 1 nm), were calculated in several configurations, and distance and wavenumber cutoff values were then calculated based on A 132 and the dispersive work of adhesion obtained from contact angles. A geometric average approximation, H 0 CVL = (H 0 CVC H 0 LVL )1/2, holds for the cutoff separation distances obtained for carbon-vacuum-liquid (CVL), carbon-vacuum-carbon (CVC) and liquid-vacuum-liquid (LVL) equilibrium configurations. The linear dependence found for A CVL, A CLC and A CLV values as a function of A CVC, for each liquid, allows predictive relationships for Hamaker energies (in any configuration) using experimental determination of the dispersive component of the surface tension, $$ {\gamma}_{CV}^d $$ , and a guess value of the cutoff distance H 0 CVC of the solid.