Quantitative mapping of magnetic properties at the nanoscale with bimodal AFM.

We demonstrate that a force microscope operated in a bimodal configuration enables the mapping of magnetic interactions with high quantitative accuracy and high-spatial resolution (∼30 nm). Bimodal AFM operation doubles the number of observables with respect to conventional magnetic force microscopy methods which enables to determine quantitatively in a single processing step several magnetic properties. The theory of bimodal AFM provides analytical expressions for different magnetic force models, in particular those characterized by power-law and exponential distance dependences. Bimodal AFM provides a self-evaluation protocol to test the accuracy of the measurements. The agreement obtained between the experiments and theory for two different magnetic samples support the application of bimodal AFM to map quantitatively long-range magnetic interactions.

Fast, quantitative and high resolution mapping of viscoelastic properties with bimodal AFM.

Quantitative mapping of viscoelastic properties of soft matter with a nanoscale spatial resolution is an active and relevant research topic in atomic force microscopy (AFM) and nanoscale science characterization. The AFM has demonstrated its accuracy to measure the energy dissipated on a sample surface with an atomic-scale resolution. However, the transformation of energy dissipation values associated with viscoelastic interactions to a material property remains very challenging. A key issue is to establish the relationship between the AFM observables and some material properties such as viscosity coefficient or relaxation time. Another relevant issue is to determine the accuracy of the measurements. We demonstrate that bimodal atomic force microscopy enables the accurate measurement of several viscoelastic parameters such as the Young's modulus, viscosity coefficient, retardation time or loss tangent. The parameters mentioned above are measured at the same time that the true topography. We demonstrate that the loss tangent is proportional to the viscosity coefficient. We show that the mapping of viscoelastic properties neither degrades the spatial resolution nor the imaging speed of AFM. The results are presented for homogeneous polymer and block co-polymer samples with Young's modulus, viscosity and retardation times ranging from 100 MPa to 3 GPa, 10 to 400 Pa s and 50 to 400 ns, respectively. Numerical simulations validate the accuracy of bimodal AFM to determine the viscoelastic parameters.

Fast and high-resolution mapping of elastic properties of biomolecules and polymers with bimodal AFM.

Fast, high-resolution mapping of heterogeneous interfaces with a wide elastic modulus range is a major goal of atomic force microscopy (AFM). This goal becomes more challenging when the nanomechanical mapping involves biomolecules in their native environment. Over the years, several AFM-based methods have been developed to address this goal. However, none of these methods combine sub-nanometer spatial resolution, quantitative accuracy, fast data acquisition speed, wide elastic modulus range and operation in physiological solutions. Here, we present detailed procedures for generating high-resolution maps of the elastic properties of biomolecules and polymers using bimodal AFM. This requires the simultaneous excitation of the first two eigenmodes of the cantilever. An amplitude modulation (AM) feedback acting on the first mode controls the tip-sample distance, and a frequency modulation (FM) feedback acts on the second mode. The method is fast because the elastic modulus, deformation and topography images are obtained simultaneously. The method is efficient because only a single data point per pixel is needed to generate the aforementioned images. The main stages of the bimodal imaging are sample preparation, calibration of the instrument, tuning of the microscope and generation of the nanomechanical maps. In addition, with knowledge of the deformation, bimodal AFM enables reconstruction of the true topography of the surface. It takes ~9 h to complete the whole procedure.

Dynamics of breaking intermolecular bonds in high-speed force spectroscopy.

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.

Mapping Elastic Properties of Heterogeneous Materials in Liquid with Angstrom-Scale Resolution.

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.

Fundamental High-Speed Limits in Single-Molecule, Single-Cell, and Nanoscale Force Spectroscopies.

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.