Polynomial force approximations and multifrequency atomic force microscopy

Bulk chemical composition contrast from attractive forces in AFM force spectroscopy

A key application of atomic force microscopy (AFM) is the measurement of physical properties at sub-micrometer resolution. Methods such as force-distance curves (FDCs) or dynamic variants (such as intermodulation AFM (ImAFM)) are able to measure mechanical properties (such as the local stiffness, k r) of nanoscopic heterogeneous materials. For a complete structure-property correlation, these mechanical measurements are considered to lack the ability to identify the chemical structure of the materials. In this study, the measured attractive force, F attr, acting between the AFM tip and the sample is shown to be an independent measurement for the local chemical composition and hence a complete structure-property correlation can be obtained. A proof of concept is provided by two model samples comprised of (1) epoxy/polycarbonate and (2) epoxy/boehmite. The preparation of the model samples allowed for the assignment of material phases based on AFM topography. Additional chemical characterization on the nanoscale is performed by an AFM/infrared-spectroscopy hybrid method. Mechanical properties (k r) and attractive forces (F attr) are calculated and a structure-property correlation is obtained by a manual principle component analysis (mPCA) from a k r/F attr diagram. A third sample comprised of (3) epoxy/polycarbonate/boehmite is measured by ImAFM. The measurement of a 2 × 2 µm cross section yields 128 × 128 force curves which are successfully evaluated by a k r/F attr diagram and the nanoscopic heterogeneity of the sample is determined.

Force reconstruction from tapping mode force microscopy experiments

Fast, accurate, and robust nanomechanical measurements are intensely studied in materials science, applied physics, and molecular biology. Amplitude modulation force microscopy (tapping mode) is the most established nanoscale characterization technique of surfaces for air and liquid environments. However, its quantitative capabilities lag behind its high spatial resolution and robustness. We develop a general method to transform the observables into quantitative force measurements. The force reconstruction algorithm has been deduced on the assumption that the observables (amplitude and phase shift) are slowly varying functions of the tip-surface separation. The accuracy and applicability of the method is validated by numerical simulations and experiments. The method is valid for liquid and air environments, small and large free amplitudes, compliant and rigid materials, and conservative and non-conservative forces.

Dynamic calibration of higher eigenmode parameters of a cantilever in atomic force microscopy by using tip-surface interactions

We present a theoretical framework for the dynamic calibration of the higher eigenmode parameters (stiffness and optical lever inverse responsivity) of a cantilever. The method is based on the tip-surface force reconstruction technique and does not require any prior knowledge of the eigenmode shape or the particular form of the tip-surface interaction. The calibration method proposed requires a single-point force measurement by using a multimodal drive and its accuracy is independent of the unknown physical amplitude of a higher eigenmode.