Transcending Lifshitz Theory: Reliable Prediction of Adhesion Forces between Hydrocarbon Surfaces in Condensed Phases Using Molecular Contact Thermodynamics

Abstract

Lifshitz theory is widely used to calculate interfacial interaction energies and underpins established approaches to the interpretation of measurement data from experimental methods including the surface forces apparatus and the atomic force microscope. However, a significant limitation of Lifshitz theory is that it uses the bulk dielectric properties of the medium to predict the work of adhesion. Here, we demonstrate that a different approach, in which the interactions between molecules at surfaces and in the medium are described by a set of surface site interaction points (SSIPs), yields interaction free energies that are correlated better with experimentally determined values. The work of adhesion W(Lifshitz) between hydrocarbon surfaces was calculated in 260 liquids using Lifshitz theory and compared with interaction free energies ΔΔG calculated using the SSIP model. The predictions of these models diverge in significant ways. In particular, ΔΔG values for hydrocarbon surfaces are typically small and vary little, but in contrast, W(Lifshitz) values span 4 orders of magnitude. Moreover, the SSIP model yields significantly different ΔΔG values in some liquids for which Lifshitz theory predicts similar values of W(Lifshitz). These divergent predictions were tested using atomic force microscopy. Experimentally determined works of adhesion were closer to the values predicted using the SSIP model than Lifshitz theory. In mixtures of methanol and benzyl alcohol, even greater differences were found in the interaction energies calculated using the two models: the value of ΔΔG calculated using the SSIP model declines smoothly as the benzyl alcohol concentration increases, and values are well correlated with experimental data; however, W(Lifshitz) decreases to a minimum and then increases, reaching a larger value for benzyl alcohol than for methanol. We conclude that the SSIP model provides more reliable estimates of the work of adhesion than Lifshitz theory.