[Show abstract][Hide abstract] ABSTRACT: The problem of an Euler-Bernoulli cantilever beam whose free end impacts with a point constraint is revisited from the point of view of modal analysis. It is shown that there is non-uniqueness of consistent impact laws for a given modal truncation. Moreover, taking an N-mode compliant, bilinear formulation and passing to the rigid limit leads to a sequence of impact models that does not converge as . The dynamics of such truncated models are studied numerically and found to give rise to quite different dynamics depending on the number of degrees of freedom taken. The simulations are compared with results from simple experiments that show a propensity for multiple-tap dynamics, in which higher-order modes lead to rapidly cycling intermittent contact. The conclusion reached is that, to derive an accurate model, one needs to avoid the impact limit altogether, and take sufficiently many modes in the formulation to match the actual stiffness of the constraining stop. mechanical engineering, applied mathematics.
Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences 05/2013; 371(1993):20120434. DOI:10.1098/rsta.2012.0434 · 2.15 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The recent achievement of atomic resolution with dynamic atomic force microscopy (dAFM) [Fukuma et al., Appl. Phys. Lett. 2005, 87, 034101], where quality factors of the oscillating probe are inherently low, challenges some accepted beliefs concerning sensitivity and resolution in dAFM imaging modes. Through analysis and experiment we study the performance metrics for high-resolution imaging with dAFM in liquid media with amplitude modulation (AM), frequency modulation (FM) and drive-amplitude modulation (DAM) imaging modes. We find that while the quality factors of dAFM probes may deviate by several orders of magnitude between vacuum and liquid media, their sensitivity to tip-sample forces can be remarkable similar. Furthermore, the reduction in noncontact forces and quality factors in liquids diminishes the role of feedback control in achieving high-resolution images. The theoretical findings are supported by atomic-resolution images of mica in water acquired with AM, FM and DAM under similar operating conditions.
[Show abstract][Hide abstract] ABSTRACT: We introduce drive-amplitude-modulation atomic force microscopy as a dynamic mode with outstanding performance in all environments from vacuum to liquids. As with frequency modulation, the new mode follows a feedback scheme with two nested loops: The first keeps the cantilever oscillation amplitude constant by regulating the driving force, and the second uses the driving force as the feedback variable for topography. Additionally, a phase-locked loop can be used as a parallel feedback allowing separation of the conservative and nonconservative interactions. We describe the basis of this mode and present some examples of its performance in three different environments. Drive-amplutide modulation is a very stable, intuitive and easy to use mode that is free of the feedback instability associated with the noncontact-to-contact transition that occurs in the frequency-modulation mode.
[Show abstract][Hide abstract] ABSTRACT: Structural Biology (SB) techniques are particularly successful in solving virus structures. Taking advantage of the symmetries, a heavy averaging on the data of a large number of specimens, results in an accurate determination of the structure of the sample. However, these techniques do not provide true single molecule information of viruses in physiological conditions. To answer many fundamental questions about the quickly expanding physical virology it is important to develop techniques with the capability to reach nanometer scale resolution on both structure and physical properties of individual molecules in physiological conditions. Atomic force microscopy (AFM) fulfills these requirements providing images of individual virus particles under physiological conditions, along with the characterization of a variety of properties including local adhesion and elasticity. Using conventional AFM modes is easy to obtain molecular resolved images on flat samples, such as the purple membrane, or large viruses as the Giant Mimivirus. On the contrary, small virus particles (25-50 nm) cannot be easily imaged. In this work we present Frequency Modulation atomic force microscopy (FM-AFM) working in physiological conditions as an accurate and powerful technique to study virus particles. Our interpretation of the so called "dissipation channel" in terms of mechanical properties allows us to provide maps where the local stiffness of the virus particles are resolved with nanometer resolution. FM-AFM can be considered as a non invasive technique since, as we demonstrate in our experiments, we are able to sense forces down to 20 pN. The methodology reported here is of general interest since it can be applied to a large number of biological samples. In particular, the importance of mechanical interactions is a hot topic in different aspects of biotechnology ranging from protein folding to stem cells differentiation where conventional AFM modes are already being used.
PLoS ONE 01/2012; 7(1):e30204. DOI:10.1371/journal.pone.0030204 · 3.23 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Dynamic atomic force microscopy (dAFM) continues to grow in popularity among scientists in many different fields, and research on new methods and operating modes continues to expand the resolution, capabilities, and types of samples that can be studied. But many promising increases in capability are accompanied by increases in complexity. Indeed, interpreting modern dAFM data can be challenging, especially on complicated material systems, or in liquid environments where the behavior is often contrary to what is known in air or vacuum environments. Mathematical simulations have proven to be an effective tool in providing physical insight into these non-intuitive systems. In this article we describe recent developments in the VEDA (virtual environment for dynamic AFM) simulator, which is a suite of freely available, open-source simulation tools that are delivered through the cloud computing cyber-infrastructure of nanoHUB (www.nanohub.org). Here we describe three major developments. First, simulations in liquid environments are improved by enhancements in the modeling of cantilever dynamics, excitation methods, and solvation shell forces. Second, VEDA is now able to simulate many new advanced modes of operation (bimodal, phase-modulation, frequency-modulation, etc.). Finally, nineteen different tip-sample models are available to simulate the surface physics of a wide variety different material systems including capillary, specific adhesion, van der Waals, electrostatic, viscoelasticity, and hydration forces. These features are demonstrated through example simulations and validated against experimental data, in order to provide insight into practical problems in dynamic AFM.
The Review of scientific instruments 01/2012; 83(1):013702. DOI:10.1063/1.3669638 · 1.61 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Standard spring constant calibration methods are compared when applied to higher eigenmodes of cantilevers used in dynamic atomic force microscopy (dAFM). Analysis shows that Sader's original method (Sader et al 1999 Rev. Sci. Instrum. 70 3967-9), which relies on a priori knowledge of the eigenmode shape, is poorly suited for the calibration of higher eigenmodes. On the other hand, the thermal noise method (Hutter and Bechhoefer 1993 Rev. Sci. Instrum. 64 1868-73) does not require knowledge of the eigenmode and remains valid for higher eigenmodes of the dAFM probe. Experimental measurements of thermal vibrations in air for three representative cantilevers are provided to support the theoretical results.
[Show abstract][Hide abstract] ABSTRACT: Existing force spectroscopy methods in tapping mode atomic force microscopy (AFM) such as higher harmonic inversion [M. Stark, R. W. Stark, W. M. Heckl, and R. Guckenberger, Proc. Natl. Acad. Sci. U. S. A. 99, 8473 (2002)] or scanning probe acceleration microscopy [J. Legleiter, M. Park, B. Cusick, and T. Kowalewski, Proc. Natl. Acad. Sci. U. S. A. 103, 4813 (2006)] or integral relations [M. Lee and W. Jhe, Phys. Rev. Lett. 97, 036104 (2006); S. Hu and A. Raman, Nanotechnology 19, 375704 (2008); H. Holscher, Appl. Phys. Lett. 89, 123109 (2006); A. J. Katan, Nanotechnology 20, 165703 (2009)] require and assume as an observable the tip dynamics in a single eigenmode of the oscillating microcantilever. We demonstrate that this assumption can distort significantly the extracted tip-sample interaction forces when applied to tapping mode AFM with soft cantilevers in liquid environments. This exception is due to the fact that under these conditions the second eigenmode is momentarily excited and the observed tip dynamics clearly contains contributions from the fundamental and second eigenmodes. To alleviate this problem, a simple experimental method is proposed to screen the second eigenmode contributions in the observed tip deflection signal to allow accurate tip-sample force reconstruction in liquids. The method is implemented experimentally to reconstruct interaction forces on polymer, bacteriorhodopsin membrane, and mica samples in buffer solutions.
[Show abstract][Hide abstract] ABSTRACT: The ability to simultaneously map variations in topography and composition (local stiffness, adhesion, charge, hydrophillicity/phobicity, viscoelasticity) of samples in ambient and liquid environments has made dynamic atomic force microscopy (dAFM) a powerful tool for nanoscale metrology. In ambient and vacuum environments, quality factors (Q-factors) of the fundamental resonance are typically large, and the contrast channels in dAFM are relatively well understood. In liquid environments, however, Q-factors are typically low due to cantilever interactions with the surrounding viscous liquid, which introduces a new class of nonlinear dynamics that is accompanied by new contrast channels, such as, higher harmonic amplitudes and phases. In particular, we find that the interpretation of the traditional contrast channels is quite different in low-Q environments compared to high-Q environments. We present a theoretical investigation of the contrast channels in dAFM in the context of frequency modulation and tapping mode dAFM with an emphasis on low-Q environments.
ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference; 01/2010
[Show abstract][Hide abstract] ABSTRACT: We study the physical origins of phase contrast in dynamic atomic force microscopy (dAFM) in liquids where low-stiffness microcantilever probes are often used for nanoscale imaging of soft biological samples with gentle forces. Under these conditions, we show that the phase contrast derives primarily from a unique energy flow channel that opens up in liquids due to the momentary excitation of higher eigenmodes. Contrary to the common assumption, phase-contrast images in liquids using soft microcantilevers are often maps of short-range conservative interactions, such as local elastic response, rather than tip-sample dissipation. The theory is used to demonstrate variations in local elasticity of purple membrane and bacteriophage phi 29 virions in buffer solutions using the phase- contrast images.
Proceedings of the National Academy of Sciences 08/2009; 106(33). DOI:10.1073/pnas.0902240106 · 9.67 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Atomic Force microscope (AFM) cantilevers commonly used for imaging soft biological samples in liquids experience a momentary excitation of the higher eigenmodes at each tap. This transient response is very sensitive to the local sample elasticity under gentle imaging conditions because the higher eigenmode time period is comparable to the tip-sample contact time. By mapping the momentary excitation response, we demonstrate a new scanning probe spectroscopy capable of resolving with high sensitivity the variations in the elasticity of soft biological materials in liquids.
[Show abstract][Hide abstract] ABSTRACT: A canonical assumption in dynamic atomic force microscopy is that the probe tip interacts with the sample once per oscillation cycle. We show this key ansatz breaks down for soft cantilevers in liquid environments. Such probes exhibit "drum roll" like dynamics with sequential bifurcations between oscillations with single, double, and triple impacts that can be clearly identified in the phase of the response. This important result is traced to a momentary excitation of the second flexural mode induced by tip-sample forces and low quality factors. Experiments performed on supported biological membranes in buffer solutions are used to demonstrate the findings. (C) 2008 American Institute of Physics.
[Show abstract][Hide abstract] ABSTRACT: We describe here the theory and applications of virtual environment dynamic atomic force microscopy (VEDA), a suite of state-of-the-art simulation tools deployed on nanoHUB (www.nanohub.org) for the accurate simulation of tip motion in dynamic atomic force microscopy (dAFM) over organic and inorganic samples. VEDA takes advantage of nanoHUB's cyberinfrastructure to run high-fidelity dAFM tip dynamics computations on local clusters and the teragrid. Consequently, these tools are freely accessible and the dAFM simulations are run using standard web-based browsers without requiring additional software. A wide range of issues in dAFM ranging from optimal probe choice, probe stability, and tip-sample interaction forces, power dissipation, to material property extraction and scanning dynamics over hetereogeneous samples can be addressed.
[Show abstract][Hide abstract] ABSTRACT: Dynamic atomic force microscopy, in essence, consists of a vibrating microcantilever with a nanoscale tip that interacts with a sample surface via short- and long-range intermolecular forces. Microcantilevers possess several distinct eigenmodes and the tip-sample interaction forces are highly nonlinear. As a consequence, cantilevers vibrate in interesting, often unanticipated ways; some are detrimental to imaging stability, while others can be exploited to enhance performance. Understanding these phenomena can offer deep insight into the physics of dynamic atomic force microscopy and provide exciting possibilities for achieving improved material contrast with gentle imaging forces in the next generation of instruments. Here we summarize recent research developments on cantilever dynamics in the atomic force microscope.
[Show abstract][Hide abstract] ABSTRACT: The theoretical foundations of dynamic atomic force microscopy (AFM) are based on point-mass models of continuous, micromechanical oscillators with nanoscale tips that probe local tip-sample interaction forces. In this letter, the authors present the conditions necessary for a continuous AFM probe to be faithfully represented as a point-mass model, and derive the equivalent point-mass model for a general eigenmode of arbitrarily shaped AFM probes based on the equivalence of kinetic, strain, and tip-sample interaction energies. They also demonstrate that common formulas in dynamic AFM change significantly when these models are used in place of the traditional ad hoc point-mass models.
[Show abstract][Hide abstract] ABSTRACT: With increasing efforts to improve resolution and material contrast in dynamic atomic force microscopy (dAFM), it has become
important to precisely understand and exploit the mechanical dynamics of the AFM probe as it interacts with samples. Here
we provide a broad overview of several topics in this area relevant to both amplitude and frequency modulated (AM and FM)
AFM. We discuss three-dimensional eigenmodes of cantilever probes and tuning forks, and summarize their nonlinear dynamical
interactions with the sample and their operation in liquids. An emphasis is placed on experimental implications of these physical
phenomena. We conclude with an outlook of the relevance of these new developments for atomic resolution dAFM and for low-force