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Adhesion and dissipation at nanoscale

Tianjun Li, PhD Thesis, École Normale Supérieure de Lyon & East China Normal University – Shanghai (2013)

hal: tel-00907812

In this thesis, we test some interactions involving surfaces processes at the nanometer scale. The experiments are conducted with a highly sensitive interferometric Atomic Force Microscope (AFM), achieving a resolution down to 10-28 m2/Hz for the measurement of deflection. Combined with original thermal noise analysis, this tool allows quantitative characterization of the mechanical response of micrometer and nanometer sized systems, such as microcantilevers or carbon nanotubes, on a large frequency range.The first part of my work deals with the viscoelasticity of the coating of AFM cantilevers. Evidenced by a 1/f thermal noise at low frequency, this phenomenon is present when a cantilever is coated with a metallic layer (gold, aluminium, platinium, etc…). Using the fluctuation dissipation theorem and Kramers Kronig relations, we extract the frequency dependance of this viscoelastic damping on a wide range of frequency (1 Hz to 20 kHz). We find a generic power law dependence in frequency for this dissipation process, with a small negative coefficient that depends on materials. The amplitude of this phenomenon is shown to be linear in the coating thickness, demonstrating that the damping mechanism takes its roots in the bulk of the metallic layer.The second part of my work tackles new experiments on the interaction of carbon nanotubes with flat surfaces. Using our AFM, we perform a true mechanical response measurement of the rigidity and dissipation of the contact between the nanotube and the surface, in a peeling configuration (the nanotube is partially absorbed to the substrate). The results of this protocol are in line with the dynamic stiffness deduced from the thermal noise analysis, showing an unexpected power law dependence in frequency for the contact stiffness. We suggest some possible physical origins to explain this behavior, such as an amorphous carbon layer around the nanotube.

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Interferometría de alta resolución para AFM

Felipe Aguilar Sandoval, PhD Thesis, Universidad de Santiago de Chile (2013)

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El manuscrito se compone de cinco capítulos. Después de una introducción corta al AFM y el objetivo del trabajo, el primer capítulo describe el principio de funcionamiento del dispositivo interferométrico de cuadratura de fase, su diseño y implementación. Destaca como el instrumento permite medir deflexiones importantes (hasta varias veces la longitud de onda del láser utilizado), con una sensibilidad constante.

El segundo capítulo se enfoca en la descripción del comportamiento mecánico del “microcantilever”, y el ruido térmico de éste: las fluctuaciones de deflexión debidas a la temperatura del sistema se pueden medir con buena precisión usando el interferómetro, ofreciendo un método de calibración de su rigidez. En este capitulo, Felipe vuelve a las bases de la descripción de una viga empotrada con el modelo de Euler-Bernoulli, demostrando experimentalmente la validez de este modelo para el microcantilever, y luego desarrolla una demostración del teorema de fluctuación-disipación por este sistema, partiendo de la equipartición de la energía.  Finalmente, usando el modelo de Sader para describir la amortiguación del sistema, logra tener una descripción completa del ruido térmico del “microcantilever”.

En el tercer capítulo, se explica como se puede acondicionar las salidas del interferómetro a cuadratura de fase para usar lo en un dispositivo de microscopia de sonda de barrido clásico. De hecho, el interferómetro tiene dos salidas que permite seguir la deflexión en un rango amplio con sensibilidad constante, cuando se necesita una sola señal de retroalimentación para hacer imagines en modo contacto o dinámico con un AFM. Un dispositivo analógica ha sido desarrollado para esa tarea, y Felipe lo caracteriza ampliamente, demostrando su capacitad y limitaciones.

El cuarto capitulo se enfoca en entender las varias fuentes de ruido del sistema de detección, demostrando que la mayor parte se debe al ruido de disparo o “shot noise”, que se traduce por un ruido blanco del orden de 10-14 m/√Hz en los espectros de fluctuaciones de la deflexión con el láser He-Ne inicial. Después de una derivación de la expresión de este “shot noise”, Felipe concluye que el ruido de detección del interferómetro se puede mejorar subiendo la potencia del láser y bajando su longitud de onda. Usando un láser de estado solido verde de potencia 40 veces mayor que la del He-Ne, logra bajar el ruido de fondo de un orden de magnitud, llegando a una resolución del orden del femtómetro por raíz Hertz.

En un último capítulo, Felipe Aguilar estudia como la mayor potencia de iluminación afecta la respuesta del “cantiléver”. De hecho, se detecta un corrimiento de sus frecuencias de resonancia a medida que sube la potencia del láser. Ese efecto se entiende por la subida de la temperatura del cantilever que absorbe una parte de la luz enfocada en su extremo. Para entender como ese efecto depende del modo considerado, Felipe desarrolla una análisis completo del fenómeno considerando el efecto de un perfil de temperatura sobre las ecuaciones de Euler-Bernoulli. Este modelo describe con buen éxito las observaciones experimentales.

Al final del manuscrito, una conclusión corta resuma el trabajo y abre unas perspectivas a explorar para el futuro.

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Quadrature phase interferometer for high resolution force spectroscopy

Pierdomenico Paolino, Felipe A. Aguilar Sandoval and Ludovic Bellon,  Rev. Sci. Instrum. 84, 095001 (2013)

doi: 10.1063/1.4819743

In this article, we present a deflection measurement setup for Atomic Force Microscopy (AFM). It is based on a quadrature phase differential interferometer: we measure the optical path difference between a laser beam reflecting above the cantilever tip and a reference beam reflecting on the static base of the sensor. A design with very low environmental susceptibility and another allowing cal- ibrated measurements on a wide spectral range are described. Both enable a very high resolution (down to 2.5 × 10-15 m/√Hz), illustrated by thermal noise measurements on AFM cantilevers. They present an excellent long-term stability and a constant sensitivity independent of the optical phase of the interferometer. A quick review shows that our precision is equaling or out-performing the best results reported in the literature, but for a much larger deflection range, up to a few μm.

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Functionalized AFM probes for force spectroscopy: eigenmode shapes and stiffness calibration through thermal noise measurements

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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Dissipation of micro-cantilevers as a function of air pressure and metallic coating

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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Carbon nanotubes adhesion and nanomechanical behavior from peeling force spectroscopy

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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Exploring nano-mechanics through thermal fluctuations

L. Bellon, Habilitation à Diriger des recherches de L’École Normale Supérieure de Lyon, 2010

oai: tel.archives-ouvertes.fr/tel-00541336

Abstract

This mémoire presents my current research interests in micro and nano-mechanics in a comprehensive manuscript. Our experimental device is first presented: this atomic force microscope, designed and realized in the Laboratoire de Physique de l’ENS Lyon, is based on a quadrature phase differential interferometer. It features a very high resolution (down to 10 fm/rtHz) in the measurement of deflexion, down to low frequencies and on a huge input range. The dual output of the interferometer implies a specific handling to interface common scanning probe microscope controllers. We developed analog circuitries to tackle static (contact mode) and dynamic (tapping mode) operations, and we demonstrate their performance by imaging a simple calibration sample.

As a first application, we used the high sensitivity of our interferometer to study the mechanical behavior of micro-cantilevers from their fluctuations. The keystone of the analysis is the Fluctuation-Dissipation Theorem (FDT), relating the thermal noise spectrum to the dissipative part of the response. We apply this strategy to confront Sader’s model for viscous dissipation with measurements on raw silicon cantilevers in air, demonstrating an excellent agreement. When a gold coating is added, the thermal noise is strongly modified, presenting a 1/f like trend at low frequencies: we show that this behavior is due to a viscoelastic damping, and we provide a quantitative phenomenological model. We also characterize the mechanical properties of cantilevers (stiffness and Elastic Moduli) from a mapping of the thermal noise on their surface. This analysis validates the description of the system in term of its normal modes of oscillations in an Euler-Bernoulli framework for flexion and in Saint-Venant approach for torsion, but points toward a refined model for the dispersion relation of torsional modes.

Finally, we present peeling experiments on a single wall carbon nanotube attached to the cantilever tip. It is pushed against a flat substrate, and we measure the quasi-static force as well as the dynamic stiffness using an analysis of the thermal noise during this process. The most striking feature of these two observables is a plateau curve for a large range of compression, the values of which are substrate dependent. We use the Elastica to describe the shape of the nanotube, and a simple energy of adhesion per unit length Ea to describe the interaction with the substrate. We analytically derive a complete description of the expected behavior in the limit of long nanotubes. The analysis of the experimental data within this simple framework naturally leads to every quantity of interest in the problem: the force plateau is a direct measurement of the energy of adhesion Ea for each substrate, and we easily determine the mechanical properties of the nanotube itself.

Keywords

thermal noise, Atomic Force Microscopy (AFM), cantilever, Sader model, interferometry, dissipation, carbon nanotube, high precision, metrology, FDT, Kramers-Kronig, Elastica, stiffness, viscoleasticity, coating

Jury:

  1. -Arezki Boudaoud – Président du jury 
  2. -Joël Chevrier – Rapporteur
  3. -Matteo Ciccotti – Rapporteur
  4. -Philippe Poncharal – Rapporteur
  5. -Mark Rutland – Examinateur

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Steady state fluctuation relations for systems driven by an external random force

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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Direct measurement of spatial modes of a micro-cantilever from thermal noise

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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Frequency dependence of viscous and viscoelastic dissipation in coated micro-cantilevers from noise measurement

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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