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Theory of small amplitude bimodal atomic force microscopy in ambient conditions

Small oscillation amplitudes in dynamic atomic force microscopy can lead to invasive and high resolution imaging. Here we discuss small oscillation amplitude imaging in the context of ambient conditions and simultaneously excite the second flexural mode to access contrast channels sensitive to variations in sample's properties. Two physically distinct regimes of operation are discussed, one where the tip oscillates above the hydration layer and another where the tip oscillates in perpetual contact with it. It is shown that the user can control the region to be probed via standard operational parameters. The fundamental theory controlling the sensitivity of the second mode phase shift to compositional variations is then developed. The second mode phase shift is controlled by an interplay between conservative tip-sample interactions, energy transfer between modes and irreversible loss of energy in the tip sample junction.