Ludovic Bellon

Violation of the fluctuation-dissipation relation during the formation of a colloidal glass

The relationship between the conductivity and the polarization noise is measured in a colloidal glass as a function of frequency in the range 1 Hz-40 Hz. It is found that at the beginning of the transition from a fluid-like sol to a solid-like colloidal glass the fluctuation-dissipation relation is strongly violated. The amplitude and the persistence time of this violation are decreasing functions of frequency. At the lowest frequencies of the measuring range it persists for times which are about 5% of the time needed to form the colloidal glass. This phenomenology is quite close to the recent theoretical predictions done for the violation of the fluctuation-dissipation relation in glassy systems.

Intermittency in ageing

The fluctuation–dissipation relation is measured on the dielectric properties of a gel (Laponite) and of a polymer glass (polycarbonate). For the gel it is found that during the transition from a fluid-like to a solid-like state the fluctuation–dissipation theorem is strongly violated. The amplitude and the persistence time of this violation are decreasing functions of frequency. Around 1 Hz it may persist for several hours. A very similar behaviour is observed in polycarbonate after a quench below the glass transition temperature. In both cases the origin of this violation is a highly intermittent dynamics characterized by large fluctuations. The relevance of these results for recent models of ageing is discussed.

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

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.

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

We measure the mechanical thermal noise of soft silicon atomic force microscope cantilevers. Using an interferometric setup, we obtain a resolution down to 10(-14) m Hz(-1/2) on a wide spectral range (3-10(5) Hz). The low frequency behavior depends dramatically on the presence of a reflective coating: almost flat spectra for uncoated cantilevers versus a 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.

Differential interferometry with a complex contrast

Abstract We present a new design of the Nomarski interferometer, which can measure displacements of several microns, with a resolution better than 10 −13 m / Hz . In the standard design this sensitivity can be achieved only within a 100 nm displacement range. One main advantage of this new set-up of the interferometer is the total independence of the measure sensitivity on the interferometer thermal drifts.

Advanced memory effects in the aging of a polymer glass

Abstract:A new kind of memory effect on low frequency dielectric measurements on plexiglass (PMMA) is described. These measurements show that cooling and heating the sample at constant rate give an hysteretic dependence on temperature of the dielectric constant ε. A temporary stop of cooling produces a downward relaxation of ε. Two main features are observed (i) when cooling is resumed ε goes back to the values obtained without the cooling stop (i.e. the low temperature state is independent of the cooling history) (ii) upon reheating ε keeps the memory of all the cooling stops (Advanced memory). The dependence of this effect on frequency and on the cooling rate is analyzed. The memory deletion is studied too. Finally the results are compared with those of similar experiments done in spin glasses and with the famous experiments of Kovacs.

Quadrature phase interferometer for high resolution force spectroscopy

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 calibrated 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.

Carbon nanotubes adhesion and nanomechanical behavior from peeling force spectroscopy

AbstractApplications 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/√Hz) 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.

Thermal noise of microcantilevers in viscous fluids

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 the surrounding 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 of fluctuations. 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.

Direct measurement of spatial modes of a microcantilever from thermal noise

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/Hz in the frequency range 1–800 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.