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Photo-induced isomerization of azobenzene molecules drives mass migrations in azopolymer samples. The resulting macroscopic directional photo-deformation of the material morphology has found many applications in literature, although the fundamental mechanisms behind this mass transfer are still under debate. Hence, it is of paramount importance to find quantitative observables that could drive the community toward a better understanding of this phenomenon. In this regard, azopolymer mechanical properties have been intensively studied, but the lack of a nanoscale technique capable of quantitative viscoelastic measurements has delayed the progress in the field. Here, we use bimodal atomic force microscopy (AFM) as a powerful technique for nanomechanical characterizations of azopolymers. With this multifrequency AFM approach, we map the azopolymer local elasticity and viscosity, with high resolution, after irradiation. We find that, while in the (previously) illuminated region, a general photo-softening is measured; locally, the Young modulus and the viscosity depend upon the inner structuring of the illuminating light spot. We then propose a possible interpretation based on a light-induced expansion plus a local alignment of the polymer chains (directional hole-burning effect), which explains the experimental observations. The possibility to access, in a reliable and quantitative way, both Young modulus and viscosity could trigger new theoretical–numerical investigations on the azopolymer mass migration dynamics since, as we show, both parameters can be considered measurable. Furthermore, our results provide a route for engineering the nanomechanical properties of azopolymers, which could find interesting applications in cell mechanobiology research.

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.

The physical performance of an epoxy-based material is largely influenced by the formation of heterogeneous nanostructures (HNSs) in the glassy three-dimensional epoxy network. Thus, understanding the connectivity and local mechanical properties of HNSs formed in cured epoxy networks is of critical importance in the development of advanced epoxy-based materials for innovative adhesion technology. Here, we use bimodal atomic force microscopy (AFM) to map the local mechanical responses of HNSs evolved in an epoxy–amine system during curing. Both modulus and dissipated energy quantities describing the elastic and adhesive responses, respectively, were simultaneously obtained at different harmonic vibrations in each bimodal AFM measurement. HNSs exhibiting different elastic and adhesive responses were clearly visualized for all epoxy networks at different levels of curing. The architecture and local mechanical responses of HNSs were visibly altered with increasing degree of conversion. Soft domains representing network regions with relatively lower elastic moduli and weaker adhesive interactions were dominant and continuously connected at initial stages of curing up to conversion degrees of ∼91%. However, hard domains became increasingly connected upon approaching the fully cured stage. In combination with previously reported results obtained using the particle tracking technique to study the network heterogeneity at lower conversion degrees of the same epoxy system, we were able to provide a full picture describing the generation and development of mechanical heterogeneities in the network during curing in which the length scale of the heterogeneities decreased from several hundred nanometers at the pregelation stage to ∼10 nm at the fully cured stage. [ABSTRACT FROM AUTHOR]

During the past years, different theoretical and experimental works are done to enhance the observables (mostly higher eigenmode's phase contrast) in multifrequency atomic force microscopy methods. In this study, the geometry of rectangular cantilevers is studied and an optimum dimension that can provide maximum phase contrast for a given set of samples is found. The analysis is done both numerically and experimentally. A sensitivity analysis is provided to demonstrate which dimension (length, width, thickness, tip‐radius, and cantilever and sample angle) of the cantilever has a higher effect on the results. The effects of geometrical dimensions are categorized into to: (a) effect on dynamics of the cantilever (b) effects on cantilever's specifications (i.e., spring constant and quality factor). Length and width of the cantilever dominates the static behavior of the cantilever. While thickness (for lower values), tip radius, and approach angle mostly affect the dynamic behavior of the cantilever. Theoretically, it is found as the length increases the phase contrast increase. This relationship is opposite for width. It was also observed that the effect of thickness for a specific range on the phase contrast depends on the 1st eigenmode amplitude setpoint. This study shows for having higher contrast, lower tip‐radius is needed. The optimum angle between cantilever and sample to enhance bimodal atomic force microscopy imaging is also found. Based on the commercially available cantilevers, the optimum cantilever dimension is provided. Three different cantilevers with similar dimensions are experimentally tested and theoretical results are verified. [ABSTRACT FROM AUTHOR]

Abstract Nanoscale Young's modulus mapping of the cross-section of electrode composite films used in lithium ion batteries was carried out using bimodal atomic force microscopy. Clear difference in Young's modulus was observed between the particles of active materials and matrix of conductive additives/binders in the composites of LiCoO 2 -based positive and graphite-based negative electrodes. Interestingly, there were a few particles showing significantly reduced Young's modulus in the 100% state-of-charge positive electrode although such particles were not present in the pristine electrode. Graphical abstract Image 1 Highlights • A coin cell was fabricated from a LiCoO 2 positive and graphite negative electrode. • Bimodal AFM was applied for the electrodes after the charge-discharge cycle. • Nano-mechanical mappings of their cross-sections were successfully demonstrated. [ABSTRACT FROM AUTHOR]

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.

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 non-experts in simulations. Finally, the accuracy of dForce has been tested against numerical simulations performed during the last 18 years.

A new electromechanical coupling model was built to quantitatively analyze the tuning fork probes, especially the complex ones. A special feature of a novel, soft tuning fork probe, that the second eigenfrequency of the probe was insensitive to the effective force gradient, was found and used in a homemade bimodal atomic force microscopy to measure power dissipation quantitatively. By transforming the mechanical parameters to the electrical parameters, a monotonous and concise method without using phase to calculate the power dissipation was proposed. [ABSTRACT FROM AUTHOR]

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 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.

Highlights: [•] Review of bimodal AFM applications in soft matter. [•] Quantitative mapping of nanomechanical properties. [•] Examples on how to relate the observables with the Young modulus. [•] Three-dimensional images of protein–liquid interfaces. [•] Protein flexibility map of an isolated protein with a 2nm resolution. [ABSTRACT FROM AUTHOR]

The addition of a small fraction of solid nanoparticles to thermosetting polymers can substantially improve their fracture toughness, while maintaining various intrinsic thermomechanical properties. The underlying mechanism is largely related to the debonding process and subsequent formation of nanovoids at a nanoscale nanoparticle/epoxy interface, which is thought to be associated with a change in the structural and mechanical properties of the formed epoxy network at the interface compared with the matrix region. However, a direct characterization of the local physical properties at this nanoscale interface remains significantly challenging. Here, we employ a recently developed bimodal atomic force microscopy technique for the direct mapping of nanoscale elastic and adhesive responses of an amine-cured epoxy resin filled with ∼50 nm diameter silica nanoparticles. The obtained elastic modulus and dissipated energy maps with high spatial resolution evidence the existence of a ∼20-nm-thick interfacial epoxy layer surrounding the nanoparticles, which exhibits a reduced modulus and weaker adhesive response in comparison with the matrix properties. While the presence of such a soft and weak-adhesive interfacial layer is found not to affect the architecture of structural heterogeneities in the epoxy matrix, it conceivably supports the toughening mechanism related to the debonding and plastic nanovoid growth at the silica/epoxy interface. The incorporation of this soft interfacial layer into the Halpin-Tsai model also provides a good explanation for the effect of the silica fraction on the tensile modulus of cured epoxy nanocomposites.

Abstract: The cantilever is mechanically driven at two resonant frequencies in a bimodal atomic force microscope (AFM). To generate the feedback signal for topography measurement the deflection signal is demodulated at one frequency and for compositional surface mapping at the other. In particular, the second mode amplitude and phase signals are used to map surface forces such as the van der Waals interaction. On electrically charged surfaces both, van der Waals forces and electrostatic forces contribute to the second eigenmode signal. The higher eigenmode signal in bimodal AFM reflects the local distribution of electrical charges. Mechanically driven bimodal AFM thus also provides a valuable tool for compositional mapping based on surface charges. [Copyright &y& Elsevier]

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.

• A fully atomistic molecular dynamics model of bimodal atomic force microscopy is presented. • The double spring oscillator model can be used to represent the first two vibration modes of a cantilever beam. • It provides the possibility to observe the dynamic process of atomic interaction in bimodal AFM. Bimodal atomic force microscopy (AFM) is an important branch of multi-frequency AFM, which can simultaneously obtain the surface morphology and properties of samples. However, the atomic-scale phenomena in the vibration process of bimodal AFM have not been observed due to the absence of atomic-scale model. In this paper, the molecular dynamics (MD) simulations are used to model bimodal AFM. A double springs oscillator model is used to describe the first two vibration mode of the AFM cantilever. By applying dual-frequencies excitation, the dynamics of the model tip and the tip–substrate interactions are observed. The amplitude, phase shift and the average force change of the tip obtained in the simulation were found to be consistent with the continuum simulation results. The effect of different amplitude ratios on the vibration response of the tip is analyzed and validated by experiments. This novel model makes it possible to simulate two vibration modes of cantilever at atomic scale in bimodal AFM. [ABSTRACT FROM AUTHOR]

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.

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., (Copyright © 2020, Damircheli and Eslami; licensee Beilstein-Institut.)

The spatial resolution of atomic force microscopy (AFM) needed to resolve material interfaces is limited by the tip-sample separation ( d) dependence of the force used to record an image. Here, we present a new multiscale functional imaging technique that allows for in situ tunable spatial resolution, which can be applied to a wide range of inhomogeneous materials, devices, and interfaces. Our approach uses a multifrequency method to generate a signal whose d-dependence is controlled by mixing harmonics of the cantilever's oscillation with a modulated force. The spatial resolution of the resulting image is determined by the signal's d-dependence. Our measurements using harmonic mixing (HM) show that we can change the d-dependence of a force signal to improve spatial resolution by up to a factor of two compared to conventional methods. We demonstrate the technique with both Kelvin probe force microscopy (KPFM) and bimodal AFM to show its generality. Bimodal AFM with harmonic mixing actuation separates conservative from dissipative forces and is used to identify the regions of adhesive residue on exfoliated graphene. Our electrostatic measurements with open-loop KPFM demonstrate that multiple force modulations may be applied at once. Further, this method can be applied to any tip-sample force that can be modulated, for example, electrostatic, magnetic, and photoinduced forces, showing its universality. Because HM enables in situ switching between high sensitivity and high spatial resolution with any periodic driving force, we foresee this technique as a critical advancement for multiscale functional imaging.

Tapping mode atomic force microscopy (AFM), also known as amplitude modulated (AM) or AC mode, is a proven, reliable, and gentle imaging mode with widespread applications. Over the several decades that tapping mode has been in use, quantification of tip-sample mechanical properties such as stiffness has remained elusive. Bimodal tapping mode keeps the advantages of single-frequency tapping mode while extending the technique by driving and measuring an additional resonant mode of the cantilever. The simultaneously measured observables of this additional resonance provide the additional information necessary to extract quantitative nanomechanical information about the tip-sample mechanics. Specifically, driving the higher cantilever resonance in a frequency modulated (FM) mode allows direct measurement of the tip-sample interaction stiffness and, with appropriate modeling, the set point-independent local elastic modulus. Here we discuss the advantages of bimodal tapping, coined AM-FM imaging, for modulus mapping. Results are presented for samples over a wide modulus range, from a compliant gel (∼100 MPa) to stiff materials (∼100 GPa), with the same type of cantilever. We also show high-resolution (subnanometer) stiffness mapping of individual molecules in semicrystalline polymers and of DNA in fluid. Combined with the ability to remain quantitative even at line scan rates of nearly 40 Hz, the results demonstrate the versatility of AM-FM imaging for nanomechanical characterization in a wide range of applications.

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.

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.

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 non-experts in simulations. Finally, the accuracy of dForce has been tested against numerical simulations performed during the last 18 years.

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 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.