Daniel Kiracofe

On eigenmodes, stiffness, and sensitivity of atomic force microscope cantilevers in air versus liquids

The effect of hydrodynamic loading on the eigenmode shapes, modal stiffnesses, and optical lever sensitivities of atomic force microscope (AFM) microcantilevers is investigated by measuring the vibrations of such microcantilevers in air and water using a scanning laser Doppler vibrometer. It is found that for rectangular tipless microcantilevers, the measured fundamental and higher eigenmodes and their equivalent stiffnesses are nearly identical in air and in water. However, for microcantilevers with a tip mass or for picket shaped cantilevers, there is a marked difference in the second (and higher) eigenmode shapes between air and water that leads to a large decrease in their modal stiffness in water as compared to air as well as a decrease in their optical lever sensitivity. These results are explained in terms of hydrodynamic interactions of microcantilevers with nonuniform mass distribution. The results clearly demonstrate that tip mass and hydrodynamic loading must be taken into account in stiffness ...

Comparison of photothermal and piezoacoustic excitation methods for frequency and phase modulation atomic force microscopy in liquid environments

In attempting to perform frequency modulation atomic force microscopy (FM-AFM) in liquids, a non-flat phase transfer function in the self-excitation system prevents proper tracking of the cantilever natural frequency. This results in frequency-and-phase modulation atomic force microscopy (FPM-AFM) which lies in between phase modulation atomic force microscopy (PM-AFM) and FM-AFM. We derive the theory necessary to recover the conservative force and damping in such a situation, where standard FM-AFM theory no longer applies. Although our recovery procedure applies to all cantilever excitation methods in principle, its practical implementation may be difficult, or even impossible, if the cantilever is driven piezoacoustically. Specifically, we contrast the piezoacoustic excitation method to the photothermal method in the context of force spectroscopy of hydration structures at the mica-water interface. The results clearly demonstrate that photothermal excitation is superior to piezoacoustic excitation, as it...

High efficiency laser photothermal excitation of microcantilever vibrations in air and liquids

Photothermal excitation is a promising means of actuating microscale structures. It is gaining increased interest for its capability to excite atomic force microscopy (AFM) microcantilevers with wide frequency bandwidth in liquid environments yielding clean resonance peaks without spurious resonances. These capabilities are particularly relevant for high speed and high resolution, quantitative AFM. However, photothermal efficiency is low, which means a large amount of laser power is required for a given mechanical response. The high laser power may cause local heating effects, or spill over the cantilever and damage sensitive samples. In this work, it is shown that by simply changing from a probe with a rectangular cross-section to one with a trapezoidal cross-section, the photothermal efficiency of an uncoated silicon cantilever can be increased by more than a order of magnitude, and the efficiency of a coated cantilever can be increased by a factor of 2. This effect is demonstrated experimentally and explained theoretically using thermomechanical analysis. Results are shown for both air and water, and for normal bending and torsional oscillations.

Quantitative force and dissipation measurements in liquids using piezo-excited atomic force microscopy: a unifying theory.

The use of a piezoelectric element (acoustic excitation) to vibrate the base of microcantilevers is a popular method for dynamic atomic force microscopy. In air or vacuum, the base motion is so small (relative to tip motion) that it can be neglected. However, in liquid environments the base motion can be large and cannot be neglected. Yet it cannot be directly observed in most AFMs. Therefore, in liquids, quantitative force and energy dissipation spectroscopy with acoustic AFM relies on theoretical formulae and models to estimate the magnitude of the base motion. However, such formulae can be inaccurate due to several effects. For example, a significant component of the piezo excitation does not mechanically excite the cantilever but rather transmits acoustic waves through the surrounding liquid, which in turn indirectly excites the cantilever. Moreover, resonances of the piezo, chip and holder can obscure the true cantilever dynamics even in well-designed liquid cells. Although some groups have tried to overcome these limitations (either by theory modification or better design of piezos and liquid cells), it is generally accepted that acoustic excitation is unsuitable for quantitative force and dissipation spectroscopy in liquids. In this paper the authors present a careful study of the base motion and excitation forces and propose a method by which quantitative analysis is in fact possible, thus opening this popular method for quantitative force and dissipation spectroscopy using dynamic AFM in liquids. This method is validated by experiments in water on mica using a scanning laser Doppler vibrometer, which can measure the actual base motion. Finally, the method is demonstrated by using small-amplitude dynamic AFM to extract the force gradients and dissipation on solvation shells of octamethylcyclotetrasiloxane (OMCTS) molecules on mica.

Multiple regimes of operation in bimodal AFM: understanding the energy of cantilever eigenmodes

Summary 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.

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.

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.

Microcantilever dynamics in liquid environment dynamic atomic force microscopy when using higher-order cantilever eigenmodes

Dynamic atomic force microscopy is currently evolving from a single to a multifrequency instrument for nanoscale imaging often employing higher-order microcantilever eigenmodes for improved resolution and force spectroscopy. In this work the authors study the fundamentals of cantilever dynamics and energy dissipation when soft cantilevers are driven at their second flexural eigenmode and interact with samples in liquid environments. Contrary to the conventional first eigenmode operation, second eigenmode operation in liquids is often dominated by a subharmonic response (e.g., one tap every four drive cycles) and there is an energy transfer to the first eigenmode creating a new channel of energy dissipation and compositional contrast.

Non-Linear Frequency Response of Atomic Force Microscope Cantilevers at the Solid-Liquid Interface

One significant advantage of atomic force microscopy (AFM) over other microscopy methods is its ability to characterize surfaces in liquid environments. However, operation in liquid is complicated by the large hydrodynamic loading, which leads to low quality factors, and in turn leads to many changes in the dynamics as opposed to air/vacuum environments. A thorough understanding of the dynamics is necessary for properly interpreting data from experiments. In this work, we study the non-linear dynamics of AFM micro-cantilevers interacting with hard surfaces in liquids. In comparison to prior works that have mostly examined the dynamics at a single drive frequency, we examine the full nonlinear frequency response. Two important results are highlighted. First, in addition to the primary resonance, there are also superharmonic resonances, which can distort tapping mode approach curves. Secondly, we point out that the layering (hydration forces) of liquid molecules at the solid-liquid interface, traditionally detected using small amplitude (linear) AFM, in fact has a significant effect on the nonlinear response. These results are shown by experiments and examined analytically. The effects of parameters such as cantilever stiffness and quality factors are studied using numerical simulation.Copyright

Unifying Theory of Quantitative Atomic Force Microscopy Using Piezo Excitation in Liquids

Base-excitation of microcantilevers using a dither piezoelectric element, also known as acoustic excitation, is one of the most popular methods for dynamic atomic force microscopy (AFM) because it is inexpensive, easy to use and does not require special cantilevers. However, in liquid environments there are problems using this method for quantitative force spectroscopy. The problems arise due spurious peaks in the driving spectrum (also known as “forest of peaks”) caused by piezo and fluid cell resonances, as well as a large base motion, which make it very hard to quantify the exciting forces. Although some groups have tried to overcome these limitations, it is has generally been accepted that acoustic excitation is unsuitable for quantitative force spectroscopy in liquids. In this work the authors show that a thorough understanding of the excitation forces and base motions reveals a method by which quantitative analysis is in fact possible with acoustic excitation in liquid environments, thus opening this popular method for quantitative dynamic AFM in liquids. This method is validated by experiments using a scanning laser Doppler vibrometer, which can measure the actual base motion. Finally, the method is demonstrated by performing force spectroscopy on solvation shells of octamethylcyclotetrasiloxane (OMCTS) molecules on mica.Copyright