Nanoscale Rheology: Dynamic Mechanical Analysis over a Broad and Continuous Frequency Range Using Photothermal Actuation Atomic Force Microscopy.

Polymeric materials are widely used in industries ranging from automotive to biomedical. Their mechanical properties play a crucial role in their application and function and arise from the nanoscale structures and interactions of their constitutive polymer molecules. Polymeric materials behave viscoelastically, i.e., their mechanical responses depend on the time scale of the measurements; quantifying these time-dependent rheological properties at the nanoscale is relevant to develop, for example, accurate models and simulations of those materials, which are needed for advanced industrial applications. In this paper, an atomic force microscopy (AFM) method based on the photothermal actuation of an AFM cantilever is developed to quantify the nanoscale loss tangent, storage modulus, and loss modulus of polymeric materials. The method is then validated on styrene-butadiene rubber (SBR), demonstrating the method's ability to quantify nanoscale viscoelasticity over a continuous frequency range up to 5 orders of magnitude (0.2-20,200 Hz). Furthermore, this method is combined with AFM viscoelastic mapping obtained with amplitude modulation-frequency modulation (AM-FM) AFM, enabling the extension of viscoelastic quantification over an even broader frequency range and demonstrating that the novel technique synergizes with preexisting AFM techniques for quantitative measurement of viscoelastic properties. The method presented here introduces a way to characterize the viscoelasticity of polymeric materials and soft and biological matter in general at the nanoscale for any application.

Discrimination of adhesion and viscoelasticity from nanoscale maps of polymer surfaces using bimodal atomic force microscopy.

The simultaneous excitation and measurement of two eigenmodes in bimodal atomic force microscopy (AFM) during sub-micron scale surface imaging augments the number of observables at each pixel of the image compared to the normal tapping mode. However, a comprehensive connection between the bimodal AFM observables and the surface adhesive and viscoelastic properties of polymer samples remains elusive. To address this gap, we first propose an algorithm that systematically accommodates surface forces and linearly viscoelastic three-dimensional deformation computed via Attard's model into the bimodal AFM framework. The proposed algorithm simultaneously satisfies the amplitude reduction formulas for both resonant eigenmodes and enables the rigorous prediction and interpretation of bimodal AFM observables with a first-principles approach. We used the proposed algorithm to predict the dependence of bimodal AFM observables on local adhesion and standard linear solid (SLS) constitutive parameters as well as operating conditions. Secondly, we present an inverse method to quantitatively predict the local adhesion and SLS viscoelastic parameters from bimodal AFM data acquired on a heterogeneous sample. We demonstrate the method experimentally using bimodal AFM on polystyrene-low density polyethylene (PS-LDPE) polymer blend. This inverse method enables the quantitative discrimination of adhesion and viscoelastic properties from bimodal AFM maps of such samples and opens the door for advanced computational interaction models to be used to quantify local nanomechanical properties of adhesive, viscoelastic materials using bimodal AFM.

Disentangling Ferroelectric Wall Dynamics and Identification of Pinning Mechanisms via Deep Learning.

Field-induced domain-wall dynamics in ferroelectric materials underpins multiple applications ranging from actuators to information technology devices and necessitates a quantitative description of the associated mechanisms including giant electromechanical couplings, controlled nonlinearities, or low coercive voltages. While the advances in dynamic piezoresponse force microscopy measurements over the last two decades have rendered visualization of polarization dynamics relatively straightforward, the associated insights into the local mechanisms have been elusive. This work explores the domain dynamics in model polycrystalline materials using a workflow combining deep-learning-based segmentation of the domain structures with nonlinear dimensionality reduction using multilayer rotationally invariant autoencoders (rVAE). The former allows unambiguous identification and classification of the ferroelectric and ferroelastic domain walls. The rVAE discovers the latent representations of the domain wall geometries and their dynamics, thus providing insight into the intrinsic mechanisms of polarization switching, that can further be compared to simple physical models. The rVAE disentangles the factors affecting the pinning efficiency of ferroelectric walls, offering insights into the correlation of ferroelastic wall distribution and ferroelectric wall pinning.

Correlating Crystallographic Orientation and Ferroic Properties of Twin Domains in Metal Halide Perovskites.

Metal halide perovskite (MHP) solar cells have attracted worldwide research interest. Although it has been well established that grain, grain boundary, and grain facet affect MHPs optoelectronic properties, less is known about subgrain structures. Recently, MHP twin stripes, a subgrain feature, have stimulated extensive discussion due to the potential for both beneficial and detrimental effects of ferroelectricity on optoelectronic properties. Connecting the ferroic behavior of twin stripes in MHPs with crystal orientation will be a vital step to understand the ferroic nature and the effects of twin stripes. In this work, we studied the crystallographic orientation and ferroic properties of CH3NH3PbI3 twin stripes, using electron backscatter diffraction (EBSD) and advanced piezoresponse force microscopy (PFM), respectively. Using EBSD, we discovered that the orientation relationship across the twin walls in CH3NH3PbI3 is a 90° rotation about ⟨1̅1̅0⟩, with the ⟨030⟩ and ⟨111⟩ directions parallel to the direction normal to the surface. By careful inspection of CH3NH3PbI3 PFM results including in-plane and out-of-plane PFM measurements, we demonstrate some nonferroelectric contributions to the PFM responses of this CH3NH3PbI3 sample, suggesting that the PFM signal in this CH3NH3PbI3 sample is affected by nonferroelectric and nonpiezoelectric forces. If there is piezoelectric response, it is below the detection sensitivity of our interferometric displacement sensor PFM (<0.615 pm/V). Overall, this work offers an integrated picture describing the crystallographic orientations and the origin of PFM signal of MHPs twin stripes, which is critical to understanding the ferroicity in MHPs.

Epitaxial Ferroelectric Hf0.5 Zr0.5 O2 with Metallic Pyrochlore Oxide Electrodes.

The synthesis of fully epitaxial ferroelectric Hf0.5 Zr0.5 O2 (HZO) thin films through the use of a conducting pyrochlore oxide electrode that acts as a structural and chemical template is reported. Such pyrochlores, exemplified by Pb2 Ir2 O7 (PIO) and Bi2 Ru2 O7 (BRO), exhibit metallic conductivity with room-temperature resistivity of <1 mΩ cm and are closely lattice matched to yttria-stabilized zirconia substrates as well as the HZO layers grown on top of them. Evidence for epitaxy and domain formation is established with X-ray diffraction and scanning transmission electron microscopy, which show that the c-axis of the HZO film is normal to the substrate surface. The emergence of the non-polar-monoclinic phase from the polar-orthorhombic phase is observed when the HZO film thickness is ≥≈30 nm. Thermodynamic analyses reveal the role of epitaxial strain and surface energy in stabilizing the polar phase as well as its coexistence with the non-polar-monoclinic phase as a function of film thickness.

High-Speed Nanomechanical Mapping of the Early Stages of Collagen Growth by Bimodal Force Microscopy.

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.

Nanomechanical sampling of material for nanoscale mass spectrometry chemical analysis.

The ability to spatially resolve the chemical distribution of compounds on a surface is important in many applications ranging from biological to material science. To this extent, we have recently introduced a hybrid atomic force microscopy (AFM)-mass spectrometry (MS) system for direct thermal desorption and pyrolysis of material with nanoscale chemical resolution. However, spatially resolved direct surface heating using local thermal desorption becomes challenging on material surfaces with low melting points, because the material will undergo a melting phase transition due to heat dissipation prior to onset of thermal desorption. Therefore, we developed an approach using mechanical sampling and collection of surface materials on an AFM cantilever probe tip for real-time analysis directly from the AFM tip. This approach allows for material to be concentrated directly onto the probe for subsequent MS analysis. We evaluate the performance metrics of the technique and demonstrate localized MS sampling from a candelilla wax matrix containing UV stabilizers avobenzone and oxinoxate from areas down to 250 nm × 250 nm. Overall, this approach removes heat dissipation into the bulk material allowing for a faster desorption and concentration of the gas phase analyte from a single heating pulse enabling higher signal levels from a given amount of material in a single sampling spot.Graphical abstract.

Nanoscale Mass Spectrometry Multimodal Imaging via Tip-Enhanced Photothermal Desorption.

Materials ranging from adhesives, pharmaceuticals, lubricants, and personal care products are traditionally studied using macroscopic characterization techniques. However, their functionality is in reality defined by details of chemical organization on often noncrystalline matter with characteristic length scales on the order of microns to nanometers. Additionally, these materials are traditionally difficult to analyze using standard vacuum-based approaches that provide nanoscale chemical characterization due to their volatile and beam-sensitive nature. Therefore, approaches that operate under ambient conditions need to be developed that allow probing of nanoscale chemical phenomena and correlated functionality. Here, we demonstrate a tool for probing and visualizing local chemical environments and correlating them to material structure and functionality using advanced multimodal chemical imaging on a combined atomic force microscopy (AFM) and mass spectrometry (MS) system using tip-enhanced photothermal desorption with atmospheric pressure chemical ionization (APCI). We demonstrate enhanced performance metrics of the technique for correlated imaging and point sampling and illustrate the applicability for the analysis of trace chemicals on a human hair, additives in adhesives on paper, and pharmaceuticals samples notoriously difficult to analyze in a vacuum environment. Overall, this approach of correlating local chemical environments to structure and functionality is key to advancing research in many fields ranging from biology, to medicine, to material science.

Publisher Correction: Enhanced ferroelectricity in ultrathin films grown directly on silicon.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Enhanced ferroelectricity in ultrathin films grown directly on silicon.

Ultrathin ferroelectric materials could potentially enable low-power perovskite ferroelectric tetragonality logic and nonvolatile memories1,2. As ferroelectric materials are made thinner, however, the ferroelectricity is usually suppressed. Size effects in ferroelectrics have been thoroughly investigated in perovskite oxides-the archetypal ferroelectric system3. Perovskites, however, have so far proved unsuitable for thickness scaling and integration with modern semiconductor processes4. Here we report ferroelectricity in ultrathin doped hafnium oxide (HfO2), a fluorite-structure oxide grown by atomic layer deposition on silicon. We demonstrate the persistence of inversion symmetry breaking and spontaneous, switchable polarization down to a thickness of one nanometre. Our results indicate not only the absence of a ferroelectric critical thickness but also enhanced polar distortions as film thickness is reduced, unlike in perovskite ferroelectrics. This approach to enhancing ferroelectricity in ultrathin layers could provide a route towards polarization-driven memories and ferroelectric-based advanced transistors. This work shifts the search for the fundamental limits of ferroelectricity to simpler transition-metal oxide systems-that is, from perovskite-derived complex oxides to fluorite-structure binary oxides-in which 'reverse' size effects counterintuitively stabilize polar symmetry in the ultrathin regime.

Publisher Correction: Reply to: On the ferroelectricity of CH3NH3PbI3 perovskites.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Quantitative Electromechanical Atomic Force Microscopy.

The ability to probe a material's electromechanical functionality on the nanoscale is critical to applications from energy storage and computing to biology and medicine. Voltage-modulated atomic force microscopy (VM-AFM) has become a mainstay characterization tool for investigating these materials due to its ability to locally probe electromechanically responsive materials with spatial resolution from micrometers to nanometers. However, with the wide popularity of VM-AFM techniques such as piezoresponse force microscopy and electrochemical strain microscopy there has been a rise in reports of nanoscale electromechanical functionality, including hysteresis, in materials that should be incapable of exhibiting piezo- or ferroelectricity. Explanations for the origins of unexpected nanoscale phenomena have included new material properties, surface-mediated polarization changes, and/or spatially resolved behavior that is not present in bulk measurements. At the same time, it is well known that VM-AFM measurements are susceptible to numerous forms of crosstalk, and, despite efforts within the AFM community, a global approach for eliminating this has remained elusive. In this work, we develop a method for easily demonstrating the presence of hysteretic (i.e., "false ferroelectric") long-range interactions between the sample and cantilever body. This method should be easy to implement in any VM-AFM measurement. We then go on to demonstrate fully quantitative and repeatable nanoelectromechanical characterization using an interferometer. These quantitative measurements are critical for a wide range of devices including MEMS actuators and sensors, memristor, energy storage, and memory.

Static and dynamic calibration of torsional spring constants of cantilevers.

A method for calibrating the dynamic torsional spring constant of cantilevers by directly measuring the thermally driven motion of the cantilever with an interferometer is presented. Random errors in calibration were made negligible (<1%) by averaging over multiple measurements. The errors in accuracy of ±5% or ±10% for both of the cantilevers calibrated in this study were limited only by the accuracy of the laser Doppler vibrometer (LDV) used to measure thermal fluctuations. This is a significant improvement over commonly used methods that result in large and untraceable errors resulting from assumptions made about the cantilever geometry, material properties, and/or hydrodynamic physics of the surroundings. Subsequently, the static torsional spring constant is determined from its dynamic counterpart after careful LDV measurements of the torsional mode shape, backed by finite element analysis simulations. A meticulously calibrated cantilever is used in a friction force microscopy experiment that measures the friction difference and interfacial shear strength (ISS) between graphene and a silicon dioxide AFM probe. Accurate calibration can resolve discrepancies between different experimental methods, which have contributed to a large scatter in the reported friction and ISS values in the literature to date.

Chemical nature of ferroelastic twin domains in CH3NH3PbI3 perovskite.

The extraordinary optoelectronic performance of hybrid organic-inorganic perovskites has resulted in extensive efforts to unravel their properties. Recently, observations of ferroic twin domains in methylammonium lead triiodide drew significant attention as a possible explanation for the current-voltage hysteretic behaviour in these materials. However, the properties of the twin domains, their local chemistry and the chemical impact on optoelectronic performance remain unclear. Here, using multimodal chemical and functional imaging methods, we unveil the mechanical origin of the twin domain contrast observed with piezoresponse force microscopy in methylammonium lead triiodide. By combining experimental results with first principles simulations we reveal an inherent coupling between ferroelastic twin domains and chemical segregation. These results reveal an interplay of ferroic properties and chemical segregation on the optoelectronic performance of hybrid organic-inorganic perovskites, and offer an exploratory path to improving functional devices.

Fast, High Resolution, and Wide Modulus Range Nanomechanical Mapping with Bimodal Tapping Mode.

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.

Big, Deep, and Smart Data in Scanning Probe Microscopy.

Scanning probe microscopy (SPM) techniques have opened the door to nanoscience and nanotechnology by enabling imaging and manipulation of the structure and functionality of matter at nanometer and atomic scales. Here, we analyze the scientific discovery process in SPM by following the information flow from the tip-surface junction, to knowledge adoption by the wider scientific community. We further discuss the challenges and opportunities offered by merging SPM with advanced data mining, visual analytics, and knowledge discovery technologies.

Calibration of higher eigenmodes of cantilevers.

A method is presented for calibrating the higher eigenmodes (resonant modes) of atomic force microscopy cantilevers that can be performed prior to any tip-sample interaction. The method leverages recent efforts in accurately calibrating the first eigenmode by providing the higher-mode stiffness as a ratio to the first mode stiffness. A one-time calibration routine must be performed for every cantilever type to determine a power-law relationship between stiffness and frequency, which is then stored for future use on similar cantilevers. Then, future calibrations only require a measurement of the ratio of resonant frequencies and the stiffness of the first mode. This method is verified through stiffness measurements using three independent approaches: interferometric measurement, AC approach-curve calibration, and finite element analysis simulation. Power-law values for calibrating higher-mode stiffnesses are reported for several cantilever models. Once the higher-mode stiffnesses are known, the amplitude of each mode can also be calibrated from the thermal spectrum by application of the equipartition theorem.