Quantitative mapping of viscoelastic properties of soft matter with a nanoscale spatial resolution is demonstrated by bimodal AFM.

Fast quantitative mapping of mechanical properties with nanoscale spatial resolution represents one of the major goals of force microscopy. This goal becomes more challenging when the characterization needs to be accomplished with subnanometer resolution in a native environment that involves liquid solutions. Here we demonstrate that bimodal atomic force microscopy enables the accurate measurement of the elastic modulus of surfaces in liquid with a spatial resolution of 3 Å. The Young's modulus can be determined with a relative error below 5% over a 5 orders of magnitude range (1 MPa to 100 GPa). This range includes a large variety of materials from proteins to metal-organic frameworks. Numerical simulations validate the accuracy of the method. About 30 s is needed for a Young's modulus map with subnanometer spatial resolution.

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Force spectroscopy is enhancing our understanding of single-biomolecule, single-cell, and nanoscale mechanics. Force spectroscopy postulates the proportionality between the interaction force and the instantaneous probe deflection. By studying the probe dynamics, we demonstrate that the total force acting on the probe has three different components: the interaction, the hydrodynamic, and the inertial. The amplitudes of those components depend on the ratio between the resonant frequency and the frequency at which the data are measured. A force–distance curve provides a faithful measurement of the interaction force between two molecules when the inertial and hydrodynamic components are negligible. Otherwise, force spectroscopy measurements will underestimate the value of unbinding forces. Neglecting the above force components requires the use of frequency ratios in the 50–500 range. These ratios will limit the use of high-speed methods in force spectroscopy. The theory is supported by numerical simulations.

Atomic force microscope based single-molecule force spectroscopy provides a description of a variety of intermolecular interactions such as those occurring between receptor molecules and their ligands. Advances in force spectroscopy have enabled performing measurements at high-speeds and sub-microsecond resolutions. We report experiments performed on a biotin-avidin system that reveal that the measured force decreases with the loading rate at high rates. This result is at odds with the established Bell-Evans theory that predicts a monotonic increase of the rupture force with the loading rate. We demonstrate that inertial and hydrodynamic forces generated during the breaking of the bond dominate the measured force at high loading rates. We develop a correction factor to incorporate those effects into the Bell-Evans theory. The correction is necessary to obtain accurate values of the intermolecular forces at high speeds.