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

The\natomic force microscope (AFM), as it is able to characterize\nsurface topography as well determine the AFM cantilever tip–surface\nforce, proves effective at estimating the value of the Hamaker constant, <i>A</i>, for a given solid material. Two main AFM-based methods\nhave been proposed for estimating values of <i>A</i>. In\nthe approach-to-contact (AtC) method, Hamaker constants are inferred\nfrom the deflections at which the AFM tip first jumps into contact\nwith the substrate. In the pull-off (PO) method, the deflections that\narise when the AFM tip is finally pulled away from the substrate are\nused to estimate values of <i>A</i>. In prior applications\nof these two methods, the short-range intermolecular repulsive forces\nthat are known to arise between the AFM tip and the substrate were,\nhowever, ignored. Upon invoking a physically relevant description\nof these short-range and steeply repulsive forces, we investigate\nthe effects of repulsive interactions on the values of <i>A</i> estimated from the existing AtC and PO methods when applied to neutrally\ncharged systems under low humidity or vacuum conditions. For experimentally\nrelevant surfaces, we find that repulsive forces have a modest effect\non the AtC method, although they still need to be accounted for in\norder to generate improved estimates of the Hamaker constant. On the\nother hand, repulsive forces have a significant effect on the Hamaker\nconstants inferred from the PO method, and must be properly accounted\nfor when using this approach. Our analysis also includes an explicit\nincorporation of surface roughness into the PO method, which is not\ntypically done in most prior applications of the PO method.