Publications

Justine Laurent, Audrey Steinberger and Ludovic Bellon,  Nanotechnology 24, 225504 (2013)

doi: 10.1088/0957-4484/24/22/225504

The functionalization of an atomic force microscope (AFM) cantilever with a colloidal bead is a widely used technique when the geometry between the probe and the sample must be controlled, particularly in force spectroscopy. But some questions remain: how does a bead glued at the end of a cantilever influence its mechanical response? And more importantly for quantitative measurements, can we still determine the stiffness of the AFM probe with traditional techniques? In this paper, the influence of the colloidal mass loading on the eigenmode shape and resonant frequency is investigated by measuring the thermal noise on rectangular AFM microcantilevers with and without beads attached at their extremities. The experiments are performed with a home-made ultra-sensitive AFM, based on differential interferometry. The focused beam from the interferometer probes the cantilever at different positions and the spatial shapes of the modes are determined up to the fifth resonance, without external excitation. The results clearly demonstrate that the first eigenmode is almost unchanged by mass loading. However the oscillation behavior of higher resonances presents a marked difference: with a particle glued at its extremity, the nodes of the modes are displaced towards the free end of the cantilever. These results are compared to an analytical model taking into account the mass and inertial moment of the load in an Euler–Bernoulli framework, where the normalization of the eigenmodes is explicitly worked out in order to allow a quantitative prediction of the thermal noise amplitude of each mode. A good agreement between the experimental results and the analytical model is demonstrated, allowing a clean calibration of the probe stiffness.

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Tianjun Li, Ludovic Bellon,  EPL 98, 14004 (2012)

doi: 10.1209/0295-5075/98/14004

In this letter, we characterize the internal dissipation of coated micro-cantilevers through their mechanical thermal noise. Using a home-made interferometric setup, we achieve a resolution down to 10-14 m/rtHz in the measurement of their deflection. With the use of the fluctuation dissipation theorem and of the Kramers-Kronig relations, we rebuilt the full mechanical response function from the measured noise spectrum, and investigate frequency dependent dissipation as a function of the air pressure and of the nature of the metallic coatings. Using different thicknesses of gold coatings, we demonstrate that the internal viscoelastic damping is solely due to the dissipation in the bulk of the coating.

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Julien Buchoux, Ludovic Bellon, Sophie Marsaudon, Jean-Pierre Aimé, European Journal of Physics B 84, 69–77 (2011)

doi: 10.1140/epjb/e2011-20204-1

Applications based on Single Walled Carbon Nanotube (SWNT) are good example of the great need to continuously develop metrology methods in the field of nanotechnology. Contact and interface properties are key parameters that determine the efficiency of SWNT functionalized nanomaterials and nanodevices. In this work we have taken advantage of a good control of the SWNT growth processes at an atomic force microscope (AFM) tip apex and the use of a low noise (10-13 m/rtHz) AFM to investigate the mechanical behavior of a SWNT touching a surface. By simultaneously recording static and dynamic properties of SWNT, we show that the contact corresponds to a peeling geometry, and extract quantities such as adhesion energy per unit length, curvature and bending rigidity of the nanotube. A complete picture of the local shape of the SWNT and its mechanical behavior is provided.

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J.R. Gomez-Solano, L. Bellon, A. Petrosyan and S. Ciliberto, Europhysics Letters 89, 60003 (2010)

doi: 10.1209/0295-5075/89/60003

We experimentally study the fluctuations of the work done by an external Gaussian random force on two different stochastic systems coupled to a thermal bath: a colloidal particle in an optical trap and an atomic force microscopy cantilever. We determine the corresponding probability density functions for different random forcing amplitudes ranging from a small fraction to several times the amplitude of the thermal noise. In both systems for sufficiently weak forcing amplitudes the work fluctuations satisfy the usual steady state fluctuation theorem. As the forcing amplitude drives the system far from equilibrium, deviations of the fluctuation theorem increase monotonically. The deviations can be recasted to a single master curve which only depends on the kind of stochastic external force.

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P. Paolino, B. Tiribilli and L. Bellon, Journal of Applied Physics 106, 094313 (2009)

doi: 10.1063/1.3245394

Measurements of the deflection induced by thermal noise have been performed on a rectangular atomic force microscope cantilever in air. The detection method, based on polarization interferometry, can achieve a resolution of 10-14 m/Hz1/2 in the frequency range 1 kHz – 800 kHz. The focused beam from the interferometer probes the cantilever at different positions along its length and the spatial modes’ shapes are determined up to the fourth resonance, without external excitation. Results are in good agreement with theoretically expected behavior. From this analysis accurate determination of the elastic constant of the cantilever is also achieved.

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P. Paolino and L. Bellon, Nanotechnology 20, 405705 (2009)

doi: 10.1088/0957-4484/20/40/405705

We measure the mechanical thermal noise of soft silicon atomic force microscopy cantilevers. Using an interferometric setup, we obtain a resolution down to 10-14 m/Hz1/2 on a wide spectral range (3 Hz to 105 Hz). The low frequency behavior depends dramatically on the presence of a reflective coating: almost flat spectrums for uncoated cantilevers versus 1/f like trend for coated ones. The addition of a viscoelastic term in models of the mechanical system can account for this observation. Use of Kramers-Kronig relations validate this approach with a complete determination of the response of the cantilever: a power law with a small coefficient is found for the frequency dependence of viscoelasticity due to the coating, whereas the viscous damping due to the surrounding atmosphere is accurately described by the Sader model. 

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L. Bellon, Journal of Applied Physics 104, 104906 (2008)

doi: 10.1063/1.3021102

We present a simple theoretical framework to describe the thermal noise of a microscopic mechanical beam in a viscous fluid: we use the Sader approach to describe the effect of thesurrounding fluid (added mass and viscous drag) and the fluctuation dissipation theorem for each flexural modes of the system to derive a general expression for the power spectrum density offluctuations. This prediction is compared with an experimental measurement on a commercial atomic force microscopy cantilever in a frequency range covering the two first resonances. A very good agreement is found on the whole spectrum, with no adjustable parameters but the thickness of the cantilever.

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