Parametric tip model and force-distance relation for Hamaker constant determination from atomic force microscopy

A new parametric tip force-distance relation (PT/FDR) is shown for describing the probe-sample system in atomic force microscopy (AFM). A surface integration technique is designed to calculate the interactions between arbitrarily shaped bodies. The technique is based on the Hamaker pairwise in integration in a continuous fashion, reducing the six-dimensional integration to a four-dimensional procedure. The PT/FDR is derived and a nonlinear fitting process is utilized to extract the model parameters and the Hamaker constant from AFM force-distance data.