The Effects of Short-Range Intermolecular Repulsive Forces on Hamaker Constant Estimation Using Atomic Force Microscopy

Abstract

The atomic force microscope (AFM), as it is able to characterize surface topography as well determine the AFM cantilever tip–surface force, proves effective at estimating the value of the Hamaker constant, A, for a given solid material. Two main AFM-based methods have been proposed for estimating values of A. In the approach-to-contact (AtC) method, Hamaker constants are inferred from the deflections at which the AFM tip first jumps into contact with the substrate. In the pull-off (PO) method, the deflections that arise when the AFM tip is finally pulled away from the substrate are used to estimate values of A. In prior applications of these two methods, the short-range intermolecular repulsive forces that are known to arise between the AFM tip and the substrate were, however, ignored. Upon invoking a physically relevant description of these short-range and steeply repulsive forces, we investigate the effects of repulsive interactions on the values of A estimated from the existing AtC and PO methods when applied to neutrally charged systems under low humidity or vacuum conditions. For experimentally relevant surfaces, we find that repulsive forces have a modest effect on the AtC method, although they still need to be accounted for in order to generate improved estimates of the Hamaker constant. On the other hand, repulsive forces have a significant effect on the Hamaker constants inferred from the PO method, and must be properly accounted for when using this approach. Our analysis also includes an explicit incorporation of surface roughness into the PO method, which is not typically done in most prior applications of the PO method.