Computation of Lifshitz−van der Waals Forces between Alkylthiol Monolayers on Gold Films

Abstract

The van der Waals interactions between gold films modified with self-assembled monolayers of alkylthiols have been calculated from Lifshitz theory over the range of 1−100 nm, using a detailed multilayer structure to model the surfaces. The Hamaker functions describing the interactions vary with separation in a manner that cannot be approximated with any of the Hamaker constants of the materials constituting the system. The effects of small changes in thickness of various layers have been investigated; the total interaction is very sensitive to the thickness of the adsorbed hydrocarbon layers, and accurate measures of this thickness in real systems is essential for quantitative comparisons with the calculations. For thin gold films on silica supports, the interaction is also very sensitive to the gold thickness, whereas for gold thicknesses greater than 25 nm, the error in assuming the gold layer to be infinite is less than a few percent. Some simplified models have been considered, and in the case of thick gold films, a five-layer model with hydrocarbon-coated gold half-spaces in a medium is sufficient to model the system. Comparison of the calculated results with experiments confirms the qualitative features of the calculated Hamaker functions and in some cases also shows good quantitative agreement. However, the quality of available data is not sufficient to enable a detailed quantitative assessment of the conformity. In addition, Hamaker constants for gold and titanium have been calculated using tabulated optical data, and the results are compared with figures based on previously used models for the optical properties.