Due to the intrinsic nonlinearity of the tip-sample interaction forces that are utilized in atomic force microscopy, nonlinear behavior can be observed even under the most ‘ideal’ conditions. While the standard operating modes of the atomic force microscope (AFM) have been developed to minimize this nonlinear behavior, the authors’ work focuses on utilizing a nonlinear response of the AFM probe associated with off-resonance excitation in order to measure local material properties of the sample. Previously, period-doubling bifurcations were identified and studied for an off-resonance excitation condition of two-and-a-half times the fundamental frequency. A relationship was identified between the characteristics of the qualitative response transition and the properties of the probe and sample. For a given probe, the critical separation distance where the period-doubling bifurcation occurs is influenced by the local modulus properties of the sample. This paper details the current effort studying this relationship with the goal of developing a new AFM operation mode for obtaining localized material properties by scanning the sample. The influence of different system parameters on this relationship is studied and preliminary simulation results are presented for a simple scanning process.

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