Frequency domain identification of tip-sample van der Waals interactions in resonant atomic force microcantilevers

Hamaker constants are characteristic material properties that determine the magnitude of the nonlinear van der Waals force between atoms, molecules and nanoscale aggregates of atoms. This paper explores the novel possibility of using Harmonic Balance based nonlinear system identification methods to extract from the nonlinear vibration spectrum of resonant atomic force silicon microcantilevers, the Hamaker constants between a few atoms at the tip of the microcantilever and graphite, gold and silicon carbide samples. First, the nonlinear dynamics of a diving board microcantilever coupled to the samples through van der Waals force potentials are investigated through a discretized model of the system. Next, the feasibility of using Harmonic Balance based nonlinear system identification techniques are demonstrated using simulations of the discretized model. Finally the method is implemented on an AFM system. The results indicate that the proposed method provides a novel alternative way to measure Hamaker constants and the measured results are within the range of known experimental data.