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As the application of atomic force microscopy (AFM) in soft matter characterization has expanded, the use of different types of cantilevers for these studies have also increased. One of the most common types of cantilevers used in soft matter imaging is V-shaped cantilevers due to their low normal spring constant. These types of cantilevers are also suitable for nanomanipulation due to their high lateral spring constants. The combination of low normal spring constant and high lateral spring constants makes V-shaped cantilevers promising candidates for imaging soft matter. Although these cantilevers are widely used in the field, there are no studies on the static and dynamic behavior of V-shaped cantilevers in multifrequency AFM due to their complex geometry. In this work, the static and dynamic properties of V-shaped cantilevers are studied while investigating their performance in multifrequency AFM (specifically bimodal AFM). By modeling the cantilevers based on Timoshenko beam theory, the geometrical dimensions such as length, base width, leg width and thickness are studied. By finding the static properties (mass, spring constants) and dynamic properties (resonance frequencies and quality factors) for different geometrical dimensions, the optimum V-shaped cantilever that can provide the maximum phase contrast in bimodal AFM between gold (Au) and polystyrene (PS) is found. Based on this study, it is found that as the length of the cantilever increases the 2nd eigenmode phase contrast decreases. However, the base width exhibits the opposite relationship. It is also found that the leg width does not have a monotone relationship similar to length and base width. The phase contrast increases for the range of 14 to 32 µm but decreases afterwards. The thickness of a V-shaped cantilever does not play a major role in defining the dynamics of the cantilever compared to other parameters. This work shows that in order to maximize the phase contrast, the ratio of second to first eigenmode frequencies should be minimized and be close to a whole number. Additionally, since V-shaped cantilevers are mostly used for soft matter imaging, lower frequency ratios dictate lower spring constant ratios, which can be advantageous due to lower forces applied to the surface by the tip given a sufficiently high first eigenmode frequency. Finally, two commercially available V-shaped cantilevers are theoretically and experimentally benchmarked with an optimum rectangular cantilever. Two sets of bimodal AFM experiments are carried out on Au-PS and PS-LDPE (polystyrene and low-density polyethylene) samples to verify the simulation results.

[EN] The nanoscale determination of the mechanical properties of interfaces is of paramount relevance in materials science and cell biology. Bimodal atomic force microscopy (AFM) is arguably the most advanced nanoscale method for mapping the elastic modulus of interfaces. Simulations, theory, and experiments have validated bimodal AFM measurements on thick samples (from micrometer to millimeter). However, the bottom-effect artifact, this is, the influence of the rigid support on the determination of the Young’s modulus, questions its accuracy for ultrathin materials and interfaces (1–15 nm). Here we develop a bottom-effect correction method that yields the intrinsic Young’s modulus value of a material independent of its thickness. Experiments and numerical simulations validate the accuracy of the method for a wide range of materials (1 MPa to 100 GPa). Otherwise, the Young’s modulus of an ultrathin material might be overestimated by a 10-fold factor., Financial support from the Ministerio de Ciencia e Innovación (PID2019-106801GB-I00), CSIC 202050E013, and Comunidad de Madrid S2018/NMT-4443 (Tec4Bio-CM) is acknowledged.

[EN] High-speed atomic force microscopy (AFM) enabled the imaging of protein interactions with millisecond time resolutions (10 fps). However, the acquisition of nanomechanical maps of proteins is about 100 times slower. Here, we developed a high-speed bimodal AFM that provided high-spatial resolution maps of the elastic modulus, the loss tangent, and the topography at imaging rates of 5 fps. The microscope was applied to identify the initial stages of the self-assembly of the collagen structures. By following the changes in the physical properties, we identified four stages, nucleation and growth of collagen precursors, formation of tropocollagen molecules, assembly of tropocollagens into microfibrils, and alignment of microfibrils to generate microribbons. Some emerging collagen structures never matured, and after an existence of several seconds, they disappeared into the solution. The elastic modulus of a microfibril (∼4 MPa) implied very small stiffness (∼3 × 10–6 N/m). Those values amplified the amplitude of the collagen thermal fluctuations on the mica plane, which facilitated microribbon build-up., Financial support from the Ministerio de Ciencia e Innovación (PID2019-106801GB-I00; MAT2016-76507-R), Comunidad de Madrid S2018/NMT-4443 (Tec4Bio-CM), and European Commission Marie Sklodowska-Curie grant agreement No.721874 are acknowledged.

We present a simulation environment, dForce, which can be used for a better understanding of dynamic force microscopy experiments. The simulator presents the cantilever-tip dynamics for two dynamic AFM methods, tapping mode AFM and bimodal AFM. It can be applied for a wide variety of experimental situations in air or liquid. The code provides all the variables and parameters relevant in those modes, for example, the instantaneous deflection and tip-surface force, velocity, virial, dissipated energy, sample deformation and peak force as a function of time or distance. The simulator includes a variety of interactions and contact mechanics models to describe AFM experiments including: van der Waals, Hertz, DMT, JKR, bottom effect cone correction, linear viscoelastic forces or the standard linear solid viscoelastic model. We have compared two numerical integration methods to select the one that offers optimal accuracy and speed. The graphical user interface has been designed to facilitate the navigation of nonexperts in simulations. Finally, the accuracy of dForce has been tested against numerical simulations performed during the last 18 years., This work was funded by the European Research Council ERC-AdG-340177 (3DNanoMech) and the Spanish Ministry of Economy (MINECO) through grant CSD2010-00024.

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., We thank the financial support from the European Research Council ERC-AdG-340177 (3DNanoMech), the Ministerio of Educación, Cultura y Deporte for grant FPU15/04622, and the Ministerio de Economía y Competitividad for grants CSD2010-00024 and MAT2016-76507-R.

Bimodal force microscopy is a dynamic force-based method with the capability of mapping simultaneously the topography and the nanomechanical properties of soft-matter surfaces and interfaces. The operating principle involves the excitation and detection of two cantilever eigenmodes. The method enables the simultaneous measurement of several material properties. A distinctive feature of bimodal force microscopy is the capability to obtain quantitative information with a minimum amount of data points. Furthermore, under some conditions the method facilitates the separation of the topography data from other mechanical and/or electromagnetic interactions carried by the cantilever response. Here we provide a succinct review of the principles and some applications of the method to map with nanoscale spatial resolution mechanical properties of polymers and biomolecules in air and liquid., R.G. thanks the financial support from the Ministerio de Economía y Competitividad (Consolider Force-For-Future, CSD2010-00024, MAT2009-08650) and the Comunidad de Madrid S2009/MAT-1467.

One of the key goals in atomic force microscopy (AFM) imaging is to enhance material property contrast with high resolution. Bimodal AFM, where two eigenmodes are simultaneously excited, confers significant advantages over conventional single-frequency tapping mode AFM due to its ability to provide contrast between regions with different material properties under gentle imaging conditions. Bimodal AFM traditionally uses the first two eigenmodes of the AFM cantilever. In this work, the authors explore the use of higher eigenmodes in bimodal AFM (e.g., exciting the first and fourth eigenmodes). It is found that such operation leads to interesting contrast reversals compared to traditional bimodal AFM. A series of experiments and numerical simulations shows that the primary cause of the contrast reversals is not the choice of eigenmode itself (e.g., second versus fourth), but rather the relative kinetic energy between the higher eigenmode and the first eigenmode. This leads to the identification of three distinct imaging regimes in bimodal AFM. This result, which is applicable even to traditional bimodal AFM, should allow researchers to choose cantilever and operating parameters in a more rational manner in order to optimize resolution and contrast during nanoscale imaging of materials.

Bimodal force microscopy has expanded the capabilities of atomic force microscopy (AFM) by providing high spatial resolution images, compositional contrast and quantitative mapping of material properties without compromising the data acquisition speed. In the first bimodal AFM configuration, an amplitude feedback loop keeps constant the amplitude of the first mode while the observables of the second mode have not feedback restrictions (bimodal AM). Here we study the conditions to enhance the compositional contrast in bimodal AM while imaging heterogeneous materials. The contrast has a maximum by decreasing the amplitude of the second mode. We demonstrate that the roles of the excited modes are asymmetric. The operational range of bimodal AM is maximized when the second mode is free to follow changes in the force. We also study the contrast in trimodal AFM by analyzing the kinetic energy ratios. The phase contrast improves by decreasing the energy of second mode relative to those of the first and third modes., This work was funded by the Spanish Ministry of Economy (MINECO) through grant CSD2010-00024.

This article is part of the Thematic Series "Noncontact atomic force microscopy"., Bimodal atomic force microscopy is a force-microscopy method that requires the simultaneous excitation of two eigenmodes of the cantilever. This method enables the simultaneous recording of several material properties and, at the same time, it also increases the sensitivity of the microscope. Here we apply fractional calculus to express the frequency shift of the second eigenmode in terms of the fractional derivative of the interaction force. We show that this approximation is valid for situations in which the amplitude of the first mode is larger than the length of scale of the force, corresponding to the most common experimental case. We also show that this approximation is valid for very different types of tip–surface forces such as the Lennard-Jones and Derjaguin–Muller–Toporov forces., This work was funded by the Spanish Ministry of Science (MICINN) (CSD2010-00024;MAT2009-08650), and the Comunidad de Madrid (S2009/MAT-1467).