John Melcher

Cantilever dynamics in atomic force microscopy

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.

Equivalent point-mass models of continuous atomic force microscope probes

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.

Origins of phase contrast in the atomic force microscope in liquids

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 ϕ29 virions in buffer solutions using the phase-contrast images.

Invited Article: VEDA: A web-based virtual environment for dynamic atomic force microscopy

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 nanoHUBs 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.

Multiple impact regimes in liquid environment dynamic atomic force microscopy

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.

Resolving Structure and Mechanical Properties at the Nanoscale of Viruses with Frequency Modulation Atomic Force Microscopy

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.

Drive-amplitude-modulation atomic force microscopy: from vacuum to liquids

Summary 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.

Gaining insight into the physics of dynamic atomic force microscopy in complex environments using the VEDA simulator

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.

A self-calibrating optomechanical force sensor with femtonewton resolution

We report the development of an ultrasensitive optomechanical sensor designed to improve the accuracy and precision of force measurements with atomic force microscopy. The sensors reach quality factors of 4.3 × 106 and force resolution on the femtonewton scale at room temperature. Self-calibration of the sensor is accomplished using radiation pressure to create a reference force. Self-calibration enables in situ calibration of the sensor in extreme environments, such as cryogenic ultra-high vacuum. The senor technology presents a viable route to force measurements at the atomic scale with uncertainties below the percent level.

The impacting cantilever: modal non-convergence and the importance of stiffness matching.

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