The further development of an existing
approach-to-contact atomic
force microscopy (AFM) method for determining the Hamaker constant, A, of a solid nondeformable material is presented. Upon
explicitly accounting for the surface roughness of the given substrate,
an estimate of A is directly obtained from the resulting
distribution of deflections of the AFM cantilever tip at first contact
with the surface, d
c. We explore the effects
of surface roughness on the resulting d
c distributions for several model surfaces. We also analyze the dynamic
behavior of the cantilever tip for a range of cantilever approach
speeds. At sufficiently slow approach speeds, the dynamic d
c distributions are nearly identical to those
obtained in the quasi-static limit. Consequently, a method is proposed
whereby the relative entropy between the dynamic and quasi-static
distributions is used to estimate the value of A.
Finally, an experimental test of the method is performed in which
the self-Hamaker constant of an amorphous silica surface is determined
to be in excellent agreement with the literature established value.
Because the surface topography is directly included in the method,
the uncertainty in the estimation of the self-Hamaker constant is
also significantly reduced, compared to other similar approaches.