Philippe Tordjeman

Imaging dielectric relaxation in nanostructured polymers by frequency modulation electrostatic force microscopy

We have developed a method for imaging the temperature-frequency dependence of the dynamics of nanostructured polymer films with spatial resolution. This method provides images with dielectric compositional contrast well decoupled from topography. Using frequency-modulation electrostatic-force-microscopy, we probe the local frequency-dependent (0.1–100 Hz) dielectric response through measurement of the amplitude and phase of the force gradient in response to an oscillating applied electric field. When the phase is imaged at fixed frequency, it reveals the spatial variation in dielectric losses, i.e., the spatial variation in molecular/dipolar dynamics, with 40 nm lateral resolution. This is demonstrated by using as a model system; a phase separated polystyrene/polyvinyl-acetate (PVAc) blend. We show that nanoscale dynamic domains of PVAc are clearly identifiable in phase images as those which light-up in a band of temperature, reflecting the variations in the molecular/dipolar dynamics approaching the glass transition temperature of PVAc.

Broadband nanodielectric spectroscopy by means of amplitude modulation electrostatic force microscopy (AM-EFM)

In this work we present a new AFM based approach to measure the local dielectric response of polymer films at the nanoscale by means of Amplitude Modulation Electrostatic Force Microscopy (AM-EFM). The proposed experimental method is based on the measurement of the tip-sample force via the detection of the second harmonic component of the photosensor signal by means of a lock-in amplifier. This approach allows reaching unprecedented broad frequency range (2-3 × 10(4)Hz) without restrictions on the sample environment. The method was tested on different poly(vinyl acetate) (PVAc) films at several temperatures. Simple analytical models for describing the electric tip-sample interaction semi-quantitatively account for the dependence of the measured local dielectric response on samples with different thicknesses and at several tip-sample distances.

Nanoscale dielectric properties of insulating thin films: From single point measurements to quantitative images

Dielectric relaxation (DR) has shown to be a very useful technique to study dielectric materials like polymers and other glass formers, giving valuable information about the molecular dynamics of the system at different length and time scales. However, the standard DR techniques have a fundamental limitation: they have no spatial resolution. This is of course not a problem when homogeneous and non-structured systems are analyzed but it becomes an important limitation for studying the local properties of heterogeneous and/or nano-structured materials. To overcome this constrain we have developed a novel approach that allows quantitatively measuring the local dielectric permittivity of thin films at the nanoscale by means of Electrostatic Force Microscopy. The proposed experimental method is based on the detection of the local electric force gradient at different values of the tip-sample distance. The value of the dielectric permittivity is then calculated by fitting the experimental points using the Equivalent Charge Method. Even more interesting, we show how this approach can be extended in order to obtain quantitative dielectric images of insulating thin films with an excellent lateral resolution.

Modelling the mechanical behaviour of pit membranes in bordered pits with respect to cavitation resistance in angiosperms.

BACKGROUND AND AIMS Various correlations have been identified between anatomical features of bordered pits in angiosperm xylem and vulnerability to cavitation, suggesting that the mechanical behaviour of the pits may play a role. Theoretical modelling of the membrane behaviour has been undertaken, but it requires input of parameters at the nanoscale level. However, to date, no experimental data have indicated clearly that pit membranes experience strain at high levels during cavitation events. METHODS Transmission electron microscopy (TEM) was used in order to quantify the pit micromorphology of four tree species that show contrasting differences in vulnerability to cavitation, namely Sorbus aria, Carpinus betulus, Fagus sylvatica and Populus tremula. This allowed anatomical characters to be included in a mechanical model that was based on the Kirchhoff-Love thin plate theory. A mechanistic model was developed that included the geometric features of the pits that could be measured, with the purpose of evaluating the pit membrane strain that results from a pressure difference being applied across the membrane. This approach allowed an assessment to be made of the impact of the geometry of a pit on its mechanical behaviour, and provided an estimate of the impact on air-seeding resistance. KEY RESULTS The TEM observations showed evidence of residual strains on the pit membranes, thus demonstrating that this membrane may experience a large degree of strain during cavitation. The mechanical modelling revealed the interspecific variability of the strains experienced by the pit membrane, which varied according to the pit geometry and the pressure experienced. The modelling output combined with the TEM observations suggests that cavitation occurs after the pit membrane has been deflected against the pit border. Interspecific variability of the strains experienced was correlated with vulnerability to cavitation. Assuming that air-seeding occurs at a given pit membrane strain, the pressure predicted by the model to achieve this mechanical state corresponds to experimental values of cavitation sensitivity (P50). CONCLUSIONS The results provide a functional understanding of the importance of pit geometry and pit membrane structure in air-seeding, and thus in vulnerability to cavitation.

AFM tip effect on a thin liquid film.

We study the interaction between an AFM probe and a liquid film deposited over a flat substrate. We investigate the effects of the physical and geometrical parameters, with a special focus on the film thickness E, the probe radius R, and the distance D between the probe and the free surface. Deformation profiles have been calculated from the numerical simulations of the Young-Laplace equation by taking into account the probe/liquid and the liquid/substrate interactions, characterized by the Hamaker constants, Hpl and Hls. We demonstrate that the deformation of a shallow film is determined by a particular characteristic length λF = (2πγE(4)/Hls)(1/2), resulting from the balance between the capillary force (γ is the surface tension) and the van der Waals liquid/substrate attraction. For the case of a bulk liquid, the extent of the interface deformation is simply controlled by the capillary length λC = (γ/Δρg)(1/2). These trends point out two asymptotic regimes, which in turn are bounded by two characteristic film thicknesses Eg = (Hls/2πΔρg)(1/4) and Eγ = (R(2)Hls/2πγ)(1/4). For E > Eg, the bulk behavior is recovered, and for E < Eγ, we show the existence of a particular shallow film regime in which a localized tip effect is observed. This tip effect is characterized by the small magnitude of the deformation and an important restriction of its radial extent λF localized below the probe. In addition, we have found that the film thickness has a significant effect on the threshold separation distance Dmin below which the irreversible jump-to-contact process occurs: Dmin is probe radius-dependent for the bulk whereas it is film-thickness-dependent for shallow films. These results have an important impact on the optimal AFM scanning conditions.

Note: Void effects on eddy current distortion in two-phase liquid metal

A model based on the first order perturbation expansion of magnetic flux in a two-phase liquid metal flow has been developed for low magnetic Reynolds number Rem. This model takes into account the distortion of the induced eddy currents due to the presence of void in the conducting medium. Specific experiments with an eddy current flow meter have been realized for two periodic void distributions. The results have shown, in agreement with the model, that the effects of velocity and void on the emf modulation are decoupled. The magnitude of the void fraction and the void spatial frequency can be determined from the spectral density of the demodulated emf.

Towards Quantitative Void Fraction Measurement With an Eddy Current Flowmeter for Fourth Generation Sodium Cooled Fast Reactors: A Simplified Model

We propose an experimental methodology for the purpose of quantitative void fraction measurements in fourth generation Sodium cooled fast reactors with a standard Eddy Current Flow Meter (ECFM) sensor. The methodology consists of using the technique of ellipse fit and correlate the fluctuations in the angle of inclination of this ellipse with the void fraction. This methodology is applied in this paper to an ideal configuration of periodic grooves on solid aluminium cylinder with various volumic fractions. The effects of physical parameters such as coil excitation frequency, coil current and motion have been studied. The first results show that ECFM is sensitive to void fractions between 0.3% and 6.9%. It further demonstrates that the response to void fraction is insensitive to the mean velocity of the two-phase medium.

Magnetoconvection transient dynamics by numerical simulation

Abstract.We investigate the transient and stationary buoyant motion of the Rayleigh-Bénard instability when the fluid layer is subjected to a vertical, steady magnetic field. For Rayleigh number, Ra, in the range 103-106, and Hartmann number, Ha, between 0 and 100, we performed three-dimensional direct numerical simulations. To predict the growth rate and the wavelength of the initial regime observed with the numerical simulations, we developed the linear stability analysis beyond marginal stability for this problem. We analyzed the pattern of the flow from linear to nonlinear regime. We observe the evolution of steady state patterns depending on

Magnetic flux distortion in two-phase liquid metal flow: Model experiment

Ra/Ha^{2}

Thermo-magnetic behaviour of AFM–MFM cantilevers

Ra/Ha2 and Ha. In addition, in the nonlinear regime, the averaged kinetic energy is found to depend on Ra and to be independent of Ha in the studied range.Graphical abstract