Hamaker constants of inorganic materials

Abstract

Calculations of Hamaker constants using Lifshitz theory require the availability of accurate dielectric data, especially in the ultraviolet spectral region, and the use of a convenient and appropriate mathematical representation. In this review, a multiple oscillator model — the so-called Ninham-Parsegian (N-P) representation — has been used and spectral parameters for 31 different inorganic materials (including diamond) have been generated from critically evaluated optical data or collected from the literature. For most materials, a two-oscillator model (one UV and one IR term) was used but more detailed representations were included when available. The spectral parameters presented here can be combined with previous data, mainly focused on hydrocarbon and organic systems, to yield an extensive spectral data base for both solids and liquids enabling Lifshitz calculations of Hamaker constants for many materials combinations. Non-retarded Hamaker constants for symmetric material combinations across vacuum ( A 1v1) and water ( A 1w1) have been calculated for the different materials; these calculations were performed using the full Lifshitz theory. Asymmetric combinations, A 1v3 and A 1w3, against four commonly used materials in atomic force microscopy studies: silica, amorphous silicon nitride, sapphire, and muscovite mica, have also been covered. The use of a new dielectric representation for water resulted in significantly lower values of A 1w1 compared to previous calculations. Analytical approximations to the full Lifshitz theory were evaluated and found to give surprisingly accurate results (the Tabor-Winterton approximation) for A 1v1 when the IR contribution is of minor importance. An attempt to make the TW approximation more general by establishing some scaling relationship between n 0 and ω UV was met with little success; only the UV spectral parameters of the covalent oxides, sulphides and nitrides may be fitted to a simple power law relation. The Lifshitz calculations in this study were compared with an alternative method where a more detailed dielectric representation in the visible-ultraviolet spectral range was obtained through Kramers-Kronig (K-K) transformation of reflectivity data over a broad frequency range. Despite the difference in dielectric information, the two methods generally yield non-retarded Hamaker constants which do not differ significantly. This is not true for all materials, e.g. water, where a more detailed representation using either an N-P representation with several oscillators or the K-K representation must be used. It was shown that the omission of the static and low frequency contribution in the latter method may result in a significant underestimation of the value for A 1w1 when the dispersive contribution becomes very small.