Biharmonic versus bimodal AFM: Numerical and experimental study on soft matter

Bimodal atomic force microscopy (AFM) provides both topographical and material composition of a material with a single-pass experiment. Based on the rectangular beam theory, the cantilever's second to first eigenmode frequency is 6.27. Due to the fact that they are not multiple integers, there are irregular taps over the surface during an experiment. This can cause nonlinear vibrations in the cantilever in addition to the fact that the probe does not interact with each pixel similarly. Therefore, exciting the cantilever with higher harmonics instead of the eigenmodes in multifrequency AFM mechanisms and its advantages are discussed. Based on this theoretical discussion, this study provides the guideline to select the correct harmonic. It is found that the ratio of second to first eigenmode frequency heavily depends on the geometry of the cantilever. Additionally, it is found that cantilevers with lower eigenmode frequency ratios, excited with the first eigenmode frequency and higher harmonic, can provide higher phase contrasts. Numerical studies are done on a polystyrene (PS) and gold (Au) sample system. Based on this study, first one needs to minimize f 2 / f 1. Second, the second excitation frequency should be the closest n-th harmonic to f 2 / f 1 (i.e., one needs to minimize | n − f 2 f 1 |). Experimentally, a bimodal AFM scheme with an external function generator is used to image PS and low-density polyethylene polymer blend. The highest 2nd eigenmode phase contrast is observed with a cantilever that has a lower f 2 / f 1 and is excited with its first eigenmode frequency and 6th harmonic (i.e., the nearest harmonic to the second eigenmode).