Aleksander Labuda

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...

Atomic force microscopy in viscous ionic liquids.

Extracting quantitative information from amplitude-modulation atomic force microscopy (AM-AFM) in viscous ionic liquids is difficult because existing theory requires knowledge of the cantilever natural frequency, which cannot be measured in the absence of a resonance peak. We present a new model that describes cantilever dynamics in an overdamped medium (Q < 0.5) and derive the theory necessary to extract the stiffness and damping in highly viscous liquids. The proposed methodology is used to measure the solvation layers of an ionic liquid at a gold electrode.

Quantitative measurements of electromechanical response with a combined optical beam and interferometric atomic force microscope

An ongoing challenge in atomic force microscope (AFM) experiments is the quantitative measurement of cantilever motion. The vast majority of AFMs use the optical beam deflection (OBD) method to infer the deflection of the cantilever. The OBD method is easy to implement, has impressive noise performance, and tends to be mechanically robust. However, it represents an indirect measurement of the cantilever displacement, since it is fundamentally an angular rather than a displacement measurement. Here, we demonstrate a metrological AFM that combines an OBD sensor with a laser Doppler vibrometer (LDV) to enable accurate measurements of the cantilever velocity and displacement. The OBD/LDV AFM allows a host of quantitative measurements to be performed, including in-situ measurements of cantilever oscillation modes in piezoresponse force microscopy. As an example application, we demonstrate how this instrument can be used for accurate quantification of piezoelectric sensitivity—a longstanding goal in the electromechanical community.

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.

Switching Atomic Friction by Electrochemical Oxidation

Friction between the sliding tip of an atomic force microscope and a gold surface changes dramatically upon electrochemical oxidation of the gold surface. Atomic-scale variations of the lateral force reveal details of the friction mechanisms. Stick-slip motion with atomic periodicity on perfect Au(111) terraces exhibits extremely low friction and almost no dependence on load. Significant friction is observed only above a load threshold at which wear of the surface is initiated. In contrast, irregular stick-slip motion and a linear increase of friction with load are observed on electrochemically oxidized surfaces. The observations are discussed with reference to the amorphous structure of the oxo-hydroxide surface and atomic place exchange mechanisms upon oxidation. Reversible, fast switching between the two states of friction has been achieved in both perchloric and sulfuric acid solutions.

High-resolution friction force microscopy under electrochemical control

We report the design and development of a friction force microscope for high-resolution studies in electrochemical environments. The design choices are motivated by the experimental requirements of atomic-scale friction measurements in liquids. The noise of the system is analyzed based on a methodology for the quantification of all the noise sources. The quantitative contribution of each noise source is analyzed in a series of lateral force measurements. Normal force detection is demonstrated in a study of the solvation potential in a confined liquid, octamethylcyclotetrasiloxane. The limitations of the timing resolution of the instrument are discussed in the context of an atomic stick-slip measurement. The instrument is capable of studying the atomic friction contrast between a bare Au(111) surface and a copper monolayer deposited at underpotential conditions in perchloric acid.

The noise of coated cantilevers

In atomic force microscopy, cantilevers with a reflective coating are often used to reduce optical shot noise for deflection detection. However, static AFM experiments can be limited by classical noise and therefore may not benefit from a reduction in shot noise. Furthermore, the cantilever coating has the detrimental side-effect of coupling light power fluctuations into true cantilever bending caused by time-varying thermal stresses. Here, we distinguish three classes of noise: detection, force, and displacement noise. We discuss these noises with respect to cantilever coating in the context of both static and dynamic AFM experiments. Finally, we present a patterned cantilever coating which reduces the impact of these noises.

Optical detection system for probing cantilever deflections parallel to a sample surface

To date, commercial atomic force microscopes have been optimized for measurements of forces perpendicular to the sample surface. In many applications, sensitive parallel force measurements are desirable. These can be obtained by positioning the cantilever with its long axis perpendicular to the sample: the so-called pendulum geometry. We present a compact optical beam deflection system which solves the geometrical constraint problems involved in focusing a light beam onto a cantilever in the pendulum geometry. We demonstrate the performance of the system on measurements of forces imparted by a muscle myofibril, which is in-plane to a high-magnification objective of an optical microscope.

Generalized Hertz model for bimodal nanomechanical mapping

Summary Bimodal atomic force microscopy uses a cantilever that is simultaneously driven at two of its eigenmodes (resonant modes). Parameters associated with both resonances can be measured and used to extract quantitative nanomechanical information about the sample surface. Driving the first eigenmode at a large amplitude and a higher eigenmode at a small amplitude simultaneously provides four independent observables that are sensitive to the tip–sample nanomechanical interaction parameters. To demonstrate this, a generalized theoretical framework for extracting nanomechanical sample properties from bimodal experiments is presented based on Hertzian contact mechanics. Three modes of operation for measuring cantilever parameters are considered: amplitude, phase, and frequency modulation. The experimental equivalence of all three modes is demonstrated on measurements of the second eigenmode parameters. The contact mechanics theory is then extended to power-law tip shape geometries, which is applied to analyze the experimental data and extract a shape and size of the tip interacting with a polystyrene surface.

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.