Quantification of van der Waals forces in bimodal and trimodal AFM

The multifrequency formalism is generalized and exploited to quantify attractive forces, i.e., van der Waals interactions, with small amplitudes or gentle forces in bimodal and trimodal atomic force microscopy (AFM). The multifrequency force spectroscopy formalism with higher modes, including trimodal AFM, can outperform bimodal AFM for material property quantification. Bimodal AFM with the second mode is valid when the drive amplitude of the first mode is approximately an order of magnitude larger than that of the second mode. The error increases in the second mode but decreases in the third mode with a decreasing drive amplitude ratio. Externally driving with higher modes provides a means to extract information from higher force derivatives while enhancing the range of parameter space where the multifrequency formalism holds. Thus, the present approach is compatible with robustly quantifying weak long range forces while extending the number of channels available for high resolution.