Frequency equation and semi-empirical mechanical coupling strength of microcantilevers in an array.

A characteristic equation for the frequencies of the T-shaped and overhang-shaped cantilevers is derived for the first time. We show that there are optimum values of the overhang lengths and widths that maximize the frequency and the number of maxima is corresponding to the mode number. The frequency of higher-order modes could be tuned by changing the overhang dimensions. Especially, a semi-empirical formula for the coupling strength κ between cantilevers in an array is proposed where the strength presents a cubic decrease with the overhang width ξ and a linear increase with the overhang length η , κ = η / ξ 3 . There is a very good agreement between the proposed formula and the values obtained in recent experiments by other researchers.

Development of a flexure-based nano-actuator for high-frequency high-resolution directional sensing with atomic force microscopy.

Scanning probe microscopies typically rely on the high-precision positioning of a nanoscale probe in order to gain local information about the properties of a sample. At a given location, the probe is used to interrogate a minute region of the sample, often relying on dynamical sensing for improved accuracy. This is the case for most force-based measurements in atomic force microscopy (AFM) where sensing occurs with a tip oscillating vertically, typically in the kHz to MHz frequency regime. While this approach is ideal for many applications, restricting dynamical sensing to only one direction (vertical) can become a serious limitation when aiming to quantify the properties of inherently three-dimensional systems, such as a liquid near a wall. Here, we present the design, fabrication, and calibration of a miniature high-speed scanner able to apply controlled fast and directional in-plane vibrations with sub-nanometer precision. The scanner has a resonance frequency of ∼35 kHz and is used in conjunction with a traditional AFM to augment the measurement capabilities. We illustrate its capabilities at a solid-liquid interface where we use it to quantify the preferred lateral flow direction of the liquid around every sample location. The AFM can simultaneously acquire high-resolution images of the interface, which can be superimposed with the directional measurements. Examples of sub-nanometer measurements conducted with the new scanner are also presented.

Dynamic analysis of flexural vibration mode of an atomic force microscope cantilever with a sidewall probe in liquid.

In this paper, dynamic behavior and the resonance frequencies of flexural vibration modes of an atomic force microscope cantilever with sidewall probe immersed in liquid to surface stiffness variations have been investigated and a closed-form expression is derived. Using numerical analysis, the flexural resonance frequencies of microcantilever immersed in liquid are calculated and the results are compared with the air environment. Then, the effect of sidewall length and normal stiffness on the frequency is investigated. Moreover, the surface-coupled effect between the cantilever and simple surface when the cantilever is close to the surface is considered and its effect on the quality factors of the first to fourth modes is studied.

Mapping Elastic Properties of Heterogeneous Materials in Liquid with Angstrom-Scale Resolution.

Fast quantitative mapping of mechanical properties with nanoscale spatial resolution represents one of the major goals of force microscopy. This goal becomes more challenging when the characterization needs to be accomplished with subnanometer resolution in a native environment that involves liquid solutions. Here we demonstrate that bimodal atomic force microscopy enables the accurate measurement of the elastic modulus of surfaces in liquid with a spatial resolution of 3 Å. The Young's modulus can be determined with a relative error below 5% over a 5 orders of magnitude range (1 MPa to 100 GPa). This range includes a large variety of materials from proteins to metal-organic frameworks. Numerical simulations validate the accuracy of the method. About 30 s is needed for a Young's modulus map with subnanometer spatial resolution.

Optimization of phase contrast in bimodal amplitude modulation AFM.

Bimodal force microscopy has expanded the capabilities of atomic force microscopy (AFM) by providing high spatial resolution images, compositional contrast and quantitative mapping of material properties without compromising the data acquisition speed. In the first bimodal AFM configuration, an amplitude feedback loop keeps constant the amplitude of the first mode while the observables of the second mode have not feedback restrictions (bimodal AM). Here we study the conditions to enhance the compositional contrast in bimodal AM while imaging heterogeneous materials. The contrast has a maximum by decreasing the amplitude of the second mode. We demonstrate that the roles of the excited modes are asymmetric. The operational range of bimodal AM is maximized when the second mode is free to follow changes in the force. We also study the contrast in trimodal AFM by analyzing the kinetic energy ratios. The phase contrast improves by decreasing the energy of second mode relative to those of the first and third modes.

Force reconstruction from tapping mode force microscopy experiments.

Fast, accurate, and robust nanomechanical measurements are intensely studied in materials science, applied physics, and molecular biology. Amplitude modulation force microscopy (tapping mode) is the most established nanoscale characterization technique of surfaces for air and liquid environments. However, its quantitative capabilities lag behind its high spatial resolution and robustness. We develop a general method to transform the observables into quantitative force measurements. The force reconstruction algorithm has been deduced on the assumption that the observables (amplitude and phase shift) are slowly varying functions of the tip-surface separation. The accuracy and applicability of the method is validated by numerical simulations and experiments. The method is valid for liquid and air environments, small and large free amplitudes, compliant and rigid materials, and conservative and non-conservative forces.

Molecular and nanoscale compositional contrast of soft matter in liquid: interplay between elastic and dissipative interactions.

We demonstrate that the phase contrast observed with an amplitude modulation atomic force microscope depends on two factors, the generation of higher harmonics components and the energy dissipated on the sample surface. Those factors are ultimately related to the chemical composition and structure of the surface. Our findings are general, but they specifically describe the results obtained while imaging soft materials in liquid. Molecular resolution experiments performed on a protein membrane surface in liquid confirm the theory.