Toward an Improved Method for Determining the Hamaker Constant of Solid Materials Using Atomic Force Microscopy. I. Quasi-Static Analysis for Arbitrary Surface Roughness

The initial development and preliminary validation of improvements to an existing approach-to-contact atomic force microscopy (AFM) method for determining the Hamaker constant, A, of solid materials is presented. The updated method explicitly accounts for the surface topography of the given substrate, which will lead to improved estimates of A and extend the range of the types of the surfaces to which the method can be applied. After deriving a general van der Waals (vdW) force expression between the AFM cantilever tip, treated as an effective sphere, and a surface with arbitrary roughness, the deflection of the cantilever tip at first contact with the surface, dc, is then obtained for all tip locations. Since the vdW force varies locally along the surface, a distribution of dc-values is obtained for a given value of A. For various model surfaces, we discuss the effect of surface roughness on the resulting dc-distributions, which indicates that surface roughness cannot be accounted for in an approximate way. We also present preliminary experimental validation of the updated method, whereby the predicted dc-distribution of a simplified version of an amorphous silica surface is found to compare favorably with the dc-distribution obtained from AFM experiments.