Pauline Grondin

Sébastien Manneville

Jean-Luc Pozzo

Annie Colin

Shear-induced fractures and three-dimensional motions in an organogel

Keywords: numbers: 83.60.-a, 83.80.Kn, 47.50.-d, 43.58.+z

The flow behavior of a viscoelastic organogel is investigated using ultrasonic velocimetry combined with rheometry. Our gel presents a decreasing flow curve, i.e., the measured stress decreases as a function of the applied shear rate. Strikingly, we note that the local flow curve calculated from the velocity profiles also exhibits a decreasing part. We attribute this regime to the presence of a fracturing process and three-dimensional motions in the bulk of the sample.

I. INTRODUCTION

Soft glassy materials are disordered materials with very long relaxation times. They encompass many different systems such as foams, emulsions, granular systems, pastes, and gels. The response of such systems to an external shear stress is characterized by two regimes: for stresses below the yield stress σ 0 they lose their ability to flow, remain jammed, and respond elastically, whereas for stresses above σ 0 they flow as liquids [1]. Despite this macroscopic shared behavior, local velocimetry experiments have revealed that the flow of jammed materials is not universal [2]. Nonadhesive emulsions [3], microgels, and pastes were shown to flow homogeneously in the vicinity of the yielding transition [4]. In contrast, Laponite gels [5] or adhesive emulsions [2] display shear localization as they go through the yielding transition [6].

In some particular cases, the applied shear stress decreases as a function of the applied shear rate and the flow curve presents a minimum [7,8]. In a pioneering work, Pignon et al. [5] have studied thixotropic colloidal suspensions displaying such a behavior. They have measured the local strain by introducing a fine filament of colored suspension in the sample and following its deformation. Four flow regimes corresponding to four different states of the strain field were defined by combining visualization techniques and rheometric measurements in cone-and-plate geometry. At small deformations, the gels have an elastic behavior corresponding to a homogeneous strain field. Above a critical strain, the gel is deformed as a function of the applied shear rate. At very low shear rates, the thickness of the sheared layer is of the order of the size of the clay particles and the shear stress decreases as a function of the apparent shear rate. In the intermediate shear rate range, the size of the fluid layer increases and the shear stress remains constant as the apparent shear rate increases. At high shear rates, the flow becomes homogeneous. This points out that the global flow curve does not reflect the local rheological behavior and raises the question of the origin of decreasing flow curves.

In this work, we revisit this problem using an organogel and ultrasonic velocimetry in Couette geometry [9] combined with standard rheometry. We show that threedimensional motions and fractures occur in the decreasing part of the flow curve. This limits the possibility to etablish a valid flow curve even by using local tools such as local velocimetry. Indeed, it is not possible to induce pure shear flow (even locally) in this system. This paper is organized as follows. Section II introduces the organogel under study, a mixture of an organic solvent and a low molecular weight gelator. We describe the synthesis of this system and study its structure as well as its basic linear rheological properties. In Section III, the flow properties of this thixotropic gel are addressed. We first use nonlinear rheology alone to access the flow curve of our system. Then the ultrasonic setup for measuring velocity profiles under shear is briefly recalled. Finally, evidences for fractures, three-dimensional motions, and a multivalued, decreasing local flow curve are provided and discussed.

II. THE ORGANOGEL UNDER STUDY: SYNTHESIS, STRUCTURE, AND LINEAR RHEOLOGY

The present work is devoted to the study of an "organogel." Organogels are thermoreversible, viscoeleastic materials consisting of low molecular weight gelators (LMWG) self-assembled in an organic solvent into complex three-dimensional structures. At high temperature, LMWG are quite soluble in organic solvents and their solutions are liquid [10,11]. At low temperature, multiple nonconvalent interactions such as hydrogen bonding, donor-acceptor, and hydrophobic interactions between the organogel building blocks give birth to a three-dimensional network of entangled and connected fibers. This process is reversible, i.e the gel can be melt again at high temperature and reformed under cooling.

In recent years, these organogels have been the subject of increasing interest mainly due to the fundamental questions raised by the gel structures and assembly mechanisms [12][13][14][15][16]. In this paper, we focus on their rheological properties. A mixture of N-5-hydroxypentylundecanamide (N5HU) in toluene has been studied. We first describe briefly the synthesis of N5HU and the gel formulation. Then the gel structure is characterized together with its linear rheological properties.

A. Synthesis of N-5-hydroxypentyl-undecanamide

The gelator molecule used in this work, namely N-5-hydroxypentyl-undecanamide (N5HU) is shown in figure 1. The synthesis of N5HU was previously described in Ref. [START_REF] Kato | Patent written in japanese CO-DEN:JKXXAF JP 63215789 A2[END_REF]. Lauryl chloride (1 mol equiv) is added dropwise at 0 • C to a solution of 5-aminopentanol (Sigma) (1 mol equiv) in 40 mL of 0.2 N NaOH (Aldrich). The reaction is stirred for one night at room temperature. The precipitate is filtered and dissolved in dichloromethane (Aldrich). The organic layer is washed several times with water and dried over Na 2 SO 4 (Sigma). After evaporation, the white solid is triturated with pentane, filtered, and dried under a vacuum. Toluene (Aldrich) is used as received. Purity of the sample was checked by 1H NMR and IR spectroscopy.

This molecule is derived from previous studies on Nacyl-1, ω-amino acid based gelators [START_REF] Terech | [END_REF] and on N-3hydroxypentyl-undecanamide [19]. It forms a gel in various fluids such as toluene and some mixtures of silicone oil in toluene and of pentanol in dodecane. In the follow- ing, we present a study of gels of N5HU in toluene.

B. Gel formulation and phase diagram

To obtain a gel, heterogenous mixtures of various concentrations of gelator N5HU (from 1 to 4.7 wt %) in toluene were heated (at about 70 • C) until clear liquids were obtained. The homogenous warmed solutions were then cooled rapidly at a given temperature thanks to a temperature-controlled bath.

Figure 2 shows the phase diagram obtained by studying the transition temperature between the liquid and gel phase for the different samples. The procedure used to determine the transition temperature is rather crude. The solution is prepared in a tube which is held upside down once the final temperature is reached. If the sample flows, it is called a liquid, whereas if it sustains its own weight, it is called a gel. For concentrations above 1.2 wt %, gels are obtained at low temperature and become liquid at high temperature. The gel can be melt again at high temperature and reformed under cooling, so that the gelification process is reversible. The melting temperature and the gelification temperature differ by less than 1 • C. For concentrations lower than 1.2 wt % of N5HU, a suspension is observed at low temperature.

In order to characterize the structure of the gel and to understand why a gel is observed at low temperature, microscopic observations and linear rheology experiments have been performed and are presented in the next sections.

C. Microscopic observations

A solution of N5HU at 1.2 wt % in toluene is heated at 65 • C and cooled down to 5 • C at a cooling rate of 20 • C/min. Microscopic pictures of the resulting gel taken immediately after the quench and one week later are displayed on Figs. 3 and4 respectively. This qualitative study leads to the following conclusions. The gel is formed of large aggregates composed of interconnected branches or fibers that have grown from the same center. The size of the fibers ranges from 20 to 200 µm. These aggregates form a network that is responsible for the elastic behavior of the gel. Figure 4 shows that the initial gel state is metastable and that the final state (after 1 week) is a suspension of independent and unconnected rods which has lost its elastic properties. With time some parts of the primary gel fibers melt and reform at other places with a different morphology. The mean diameter of the fibers increases, the new stucture is much less branched, and Oswald rippening seems to occur and to smooth out the stucture. This ageing behavior is similar to the one observed by Lescanne and coworkers on N-3-hydroxypentyl-undecanamide-toluene gels [19].

Such an evolution is very slow, which allows us to consider that the structure does not vary significantly in the first five hours. All our experiments will deal with fresh samples and will be started a few minutes after the quench. Note that in the following, the rheological experiments will be performed on gels with higher N5HU concentrations. We shall assume that the structure involved in these systems is similar to the one presented above for lower concentrations. Indeed, due to the turbidity of the sample, we have been unable to obtain optical pictures for more concentrated systems.

D. Linear rheology

To better characterize the nature of the interconnection between the aggregates, rheological experiments have been performed using a stress-controlled rheometer (TA Instruments AR 1000N) equipped with a cone-andplate geometry made of aluminum (40 mm diameter, 4 • cone angle, and 56 µm gap truncation). To avoid sol- vent evaporation, a solvent trap was placed above the cone. A striated cone-and-plate geometry was used to minimize wall slip. A heated solution (at around 65 • C) of 4.7 wt % of N5HU in toluene is loaded in the shearing gap and cooled down to 5 • C using the Peltier plate of the rheometer. A gel is obtained and the rheological experiment is started 10 minutes after loading the sample. In order to define the so-called linear regime, the sample is first submitted to a periodic stress oscillating at a frequency of 1 Hz and with an amplitude σ that increases exponentially with time. During this experiment, the storage modulus G ′ and the loss modulus G ′′ are recorded as a function of the stress amplitude and plotted in Fig. 5. At low stress values, i.e., in the linear regime, both dynamic moduli are independent of the stress amplitude σ and reveal the properties of the unpertubed gel: G ′ is about 10 times larger than G ′′ which reflects the dominant character of the material. Up to large experimental scatter on G ′′ below 1 Pa, both moduli remain roughly constant below a critical shear stress of about 3 Pa, which can be taken as the limit of the linear domain. Between σ = 3 Pa and 60 Pa, G ′ slightly decreases as a function of the applied shear stress. Above σ = 60 Pa, G ′ drops dramatically while G ′′ decreases sharply. This behavior is due to the partial breakup of the gel. Thus our N5HU gel behaves as a weak gel [20].

In a second set of experiments, G ′ and G ′′ are measured as a function of the angular frequency (which is varied from 0.1 to 10 Hz) for a fresh sample of the N5HU toluene gel and a stress amplitude of 2 Pa. This stress falls into the linear regime so that the frequency sweep is nondestructive and the gel structure remains intact. Two different measurements performed on the same sample within 20 minutes are reported in Fig. 6 showing a good reproducibility of the experiment. A slight increase of the elastic modulus G ′ as a function of frequency is noticed (from 1.5 10 4 Pa at 0.1 Hz to 2 10 4 Pa at 10 Hz), which is consistent with a viscoelastic behavior. On the other hand, the loss modulus is observed to increase as the frequency decreases. Since G ′′ should reach zero at zero frequency, a viscoelastic process occurs with a very long characteristic time, corresponding to a very low frequency value (< 0.1 Hz). This long relaxation time may be attributed to local rearrangements of the aggregates.

To conclude this study, it is important to note that reproducibility is excellent on the same sample in the same day (as shown by Fig. 6) but not as perfect when we compare the properties of two different gel samples loaded and formed in the rheometer. The values of G ′ and G ′′ may vary by 40% from one experiment to another. This behavior is common to many organogels. We believe that these discrepancies are related to a dispersion in the aggregate number density from one gel to another. Indeed, this parameter is very sensitive to cooling velocities, impurities, and filling conditions of the geometry which are difficult to control very precisely. After studying the main linear rheological properties of our organogel, we now focus on its nonlinear rheology.

III. NONLINEAR FLOW BEHAVIOR: EVIDENCE FOR FRACTURES IN THE BULK AND THREE-DIMENSIONAL MOTIONS

In this section, we study the nonlinear rheological response of our NH5U-toluene gels. We first address the question of the sensitivity of these gels to shear. Indeed, most organogels are very sensitive to shear stress which tends to expel the solvent from the three-dimensional network and to break the gel. When the mechanical excitation is stopped, the sample behaves as a suspension and has lost its elastic properties. Usually, the only way to recover a gel is to heat it and cool it down once again.

Here we first present data showing that this is not the case for our NH5U-toluene gels and that recovery occurs spontaneously once shear is stopped. After discussing global nonlinear rheological properties, we present local velocity measurements using ultrasonic velocimetry and extract the local rheological flow curve.

A. Sensitivity of the gel to shear stress

To study the flow properties of the gel and its recovery, we go back to the experiment presented in Fig. 5 and performed on a 4.7 wt % NH5U-toluene gel in the striated cone-and-plate geometry. Figure 7 presents the storage modulus G ′ and the loss modulus G ′′ measured as a function of time. During the first 480 s, the stress amplitude σ is increased exponentially in time from 0.1 Pa to 1000 Pa. These data are thus the same as those presented in Fig. 5 where they were shown as a function of the stress amplitude. The gel breaks at t ≃ 300 s for σ ≃ 60 Pa and then behaves like a viscous fluid (G ′ = 0 for 300 t < 480 s).

For t ≥ 480 s, a small periodic stress of amplitude 1 Pa and frequency 1 Hz is applied. Instantaneously, the sample recovers its elastic behavior. This gel clearly exhibits a thixotropic behavior as defined in 1975 by the British Standards Institution [5]: the apparent viscosity decrease under stress is followed by a gradual recovery when stress is removed [21].

B. Global flow curve

We now study the nonlinear behavior of our gel under constant applied shear rate. As previously, a 4.7 wt % solution of NH5U in toluene is prepared and heated at 50 • C in order to totally dissolve the solid powdered sample. The hot solution is introduced between the two coaxial cylinders of a Couette geometry made of PVC (gap e = 0.5 mm, inner radius R 1 = 24.5 mm and height H = 30 mm) and then cooled down to 5 • C with a cooling rate of about 20 • C/min using an icy water circulation around the outer cylinder. The reason for using a Couette geometry in this section is that we wish to further use ultrasonic velocimetry (which is currently available only Using the shear rate imposed mode of the AR1000N rheometer, a constant shear rate γ is applied to the sample for 10 min and the shear stress σ(t) is recorded as a function of time. This procedure is applied for γ ranging from 0.05 to 1400 s -1 . Figure 8 presents the global flow curve σ versus γ (also referred to as the "engineering" flow curve in the literature) where the measured shear stress values are obtained by averaging σ(t) over the last 300 s of each shear rate step. Waiting for 5 min before starting to average the rheological data ensures that steady state is reached. Errors bars correspond to the standard deviation of σ(t) and indicate noisy or oscillatory signals.

The flow curve of Fig. 8 may easily be divided into two different regimes. First, for 0.05 ≤ γ 70 s -1 (regime 1), the measured shear stress decreases as a function of the applied shear rate. In the case of pure shear flow, a negative slope in the flow curve cannot be observed experimentally since it corresponds to material instability. Thus the global flow curve of Fig. 8 strongly suggests the presence of inhomogeneous flows in regime 1. Second, for γ 70 s -1 (regime 2), the measured shear stress increases as a function of the applied shear rate, consis- tently with a low-viscosity liquid behavior. Note that, if we repeat the experiments after shearing the system at a shear rate of 800 s -1 for 2 min and stopping the shear for 5 min, we get the same rheological behaviour. This confirms the thixotropic nature of our gel. To better analyze this striking flow curve, we have performed local velocity experiments simultaneously to nonlinear rheological measurements.

C. Experimental setup for ultrasonic velocimetry

Our rheo-ultrasonic setup allows the recording of velocity profiles across the gap of a Couette cell simultaneously to rheological data with a spatial resolution of about 40 µm. The time needed to record one velocity profile ranges between 0.02 and 20 s, depending upon the value of the applied shear rate. This setup has been described at length in Ref. [9] and only its main characteristics are recalled here. It is built around the stresscontrolled rheometer (TA Instruments AR1000N) used so far and equipped with the Couette cell described above. The whole cell is surrounded by water whose temperature is kept constant to within ±0.1 • C. A piezo-polymer transducer of central frequency 36 MHz generating focused ultrasonic pulses is immersed in water in front of the stator, as sketched in Fig. 9. The transducer is controlled by a pulser-receiver unit (Panametrics 5900PR) which generates 220 V pulses with a rise time of about 1 ns. The pulse repetition frequency f P RF is tunable from 0 to 20 kHz. Backscattered (BS) signals are sampled at 500 MHz, stored on a PCI digitizer with 8 Mb on-board memory (Acqiris DP235), and later transferred to the host computer for post-processing. Under the assumption of single scattering, the signal received at time t us can be interpreted as interferences coming from scatterers located at position y = c 0 t us /2, where c 0 is the sound speed in the fluid and y is the distance from the transducer along the ultrasonic beam (see Fig. 9). When the sample is submitted to a shear flow, BS signals move along with the scatterers. Two successive pulses separated by a time interval τ = 1/f P RF lead to two similar backscattered signals that are shifted in time. Figure 10 shows forty successive BS signals recorded in a sheared Newtonian latex suspension with a pulse frequency repetition f P RF = 150 Hz. The amplitude of the BS signals is coded in gray levels and the vertical axis t corresponds to the time at which each pulse is sent. The ultrasonic pulses leave the stator and enter the gap at t us ≃ 15.1 µs and the rotor position corresponds to t us ≃ 16.0 µs. The slopes of the traces left by the echoes in this two-dimensional (t us , t) diagram are inversely proportional to the local velocities. Thus, the signature of shear is rather clear: velocities increase from the stator, where the scatterers remain almost fixed, to the rotor. Moreover, the presence of moving echoes for t us > 16 µs is not surprising: these echoes simply correspond to scattering of the wave reflected on the rotor. One can see that the whole range t us = 15.1-16.0 µs gets covered by some significant speckle signal in about 20 ms in that case.

From these BS signals, one can relate the time shift δt(t us ) between two echoes corresponding to two successive pulses and received at time t us to the displacement of the scatterers δy(y) = c 0 δt(t us )/2 at position y. The velocity profile v y (y) (i.e., the y component of the velocity vector v) is then simply given by v y (y) = δy(y)/τ . A cross-correlation algorithm is used to estimate the time shift δt as a function of t us and the sound speed c 0 is measured independently (see Ref. [9] for more details). In order to get a non-zero projection of the velocity along the acoustic axis, ultrasonic pulses enter the gap with an angle θ ≃ 15 • as shown in Fig. 9.

Using the notations of Fig. 9, the projection v y of the velocity vector v along the y-axis in Couette geometry is the sum of the projections of the radial component v r and of the tangential component v θ of v:

v y = v θ sin θ + v r cos θ . (1)
Assuming the flow field to be purely tangential, one gets:

v θ (x) = v y (y) sin θ ≡ v(x) , (2)
where x is the radial position given by x = e-y cos θ. The determination of v(x) thus requires a precise determination of the angle θ, which is achieved through a careful calibration procedure using a Newtonian fluid [9]. If the radial component v r is non-zero, the term v r cos θ comes into play in Eq. ( 1), so that the definition of v(x) given in Eq. ( 2) leads to

v(x) = v θ (x) + v r (x) tan θ . (3)
Therefore, the interpretation of the experimental velocity profiles v(x) may become problematic whenever the flow is not purely tangential. It should also be mentioned that our setup is insensitive to any contribution of the vertical component v z to the velocity vector (i.e., in the vorticity direction z), since its projection along the acoustic axis is always zero. In principle, a velocity profile could be obtained by cross-correlating only two succesive BS signals. However, in practice the speckle amplitude is never uniform. Locally, destructive interferences or the absence of scatterers may lead to signal levels too small to be well analyzed. To recover a full velocity profile, some averaging is then performed over several successive cross-correlations.

Typically, on a stationary flow, 100 cross correlations are required to get a standard deviation of the velocity measurements of less than 6% [9]. In the following, we will present both time-averaged data and "instantaneous" measurements i.e. data obtained using only two successive cross-correlation.

Finally, thanks to their specific microstructure made of rigid aggregates whose size is comparable to the acoustic wavelength used for velocimetry, our NH5U gels naturally scatter ultrasonic waves in the single scattering regime. Thus it was not necessary to seed the gel with scatterers to perform velocity measurements. The next section displays and analyzes the time-averaged data recorded in the NH5U organogel.

D. Time-averaged velocity profiles

In this section, we focus on the time-averaged velocity profiles recorded using ultrasonic velocimetry once rheological variables have reached steady state for each shear rate step along the flow curve of Fig. 8. To this aim the local velocity measurements v(x) were averaged over 6 to 10 series of 1000 pulses (except for shear rates smaller than 0.3 s -1 where 2 to 5 series of 500 pulses were used in order to fit within the last 300 s of each shear rate step). 15 measurement points are obtained over the gap width e = 0.5 mm correponding to a spatial resolution of 33 µm. The standard deviation of these measurements then reflects the occurence of temporal velocity fluctuations.

Figures 11 and12 show the resulting time-averaged velocity profiles for shear rates ranging within the decreasing part of the flow curve (regime 1). By definition of x, x = 0 (x = e resp.) corresponds to the rotor (stator resp.). Three main features show up. We first note that for all applied shear rates, the velocity of the sample vanishes near the stator and reaches the velocity of the moving wall near the rotor. We conclude that no wall slip occurs for this gel.

Second, the standard deviations of the velocity measurements are huge: they may reach 100% of the measured value at low applied shear rate (see errors bars on Figs. 11 and12). In some cases "instantaneous" negative values of the velocity are even recorded (see Fig. 11). The standard deviation decreases as a function of the applied shear rate. Such large error bars clearly reflect the occurence of strong temporal velocity fluctuations (since error bars of less than 3% would be expected for a stationary flow with the same averaging [9]). We will come back to this point in details in Sect. III F below.

Third, in the bulk, three different zones (or "shear bands") can be clearly distinguished. (i) Close to the stator, the gel does not flow and behaves like a solid (see x/e ∈ [0.55, 1] in Fig. 11 and x/e ∈ [0.75, 1] in Fig. 12). (ii) In the middle of the gap (see x/e ∈ [0.4, 0.55] in Fig. 11, x/e ∈ [0.3, 0.75] in Fig. 12(a), x/e ∈ [0.2, 0.75] in Fig. 12(b), x/e ∈ [0.1, 0.75] in Fig. 12(c), and x/e ∈ [0.05, 0.75] in Fig. 12(d)), the gel is flowing and bears a non-zero local shear rate. The value of this local shear rate increases as a function of the engineering applied shear rate. In the following, this zone will be called the "viscous zone." (iii) Finally, close to the rotor (see x/e ∈ [0, 0.4] in Fig. 11, x/e ∈ [0, 0.3] in Fig. 12(a), x/e ∈ [0, 0.2] in Fig. 12(b), x/e ∈ [0, 0.1] in Fig. 12(c), and x/e ∈ [0, 0.05] in Fig. 12(d)), the gel remains unsheared. The size of this solid-like region located near the rotor decreases as the engineering applied shear rate is increased. At the end of regime 1 (see γ = 70 s -1 in Fig. 12(d)), the solid-like state near the rotor disappears and a flowing liquid coexists with a solid-like region near the stator. velocity profiles using:

γ(x) = -r d dr v(x) r , (4)
where r = R 1 + x. These data clearly reveal that the growth of the viscous zone occurs in the decreasing part of the engineering flow curve (i.e., for γ ≤ 70 s -1 ). This is not the case in clay gels where the growth of this region was shown to take place at a given shear stress [5]. We also note that the flow behavior of this viscous zone is rather complex. Indeed for a given engineering applied shear rate, the local shear rate may vary by a factor of ten within the viscous zone. More precisely the local shear rate increases as a function of the reduced coordinate x/e: highest shear rates are evidenced near the solid-like state close to the stator. This result will be discussed in more details in the next section.

High shear regime (regime 2)

Time-averaged velocity profiles measured in regime 2 are shown in Fig. 14. In this regime, a flowing zone always coexists with a solid-like region near the stator. Increasing the applied shear rate increases the shear rate borne by the flowing zone, but almost does not change the size of the solid-like region near the stator. Error bars are still noticeable in regime 2 but their magnitudes are much less than those recorded at low shear rate.

E. Local flow curve

To go deeper into the analysis of the flow behavior, one may extract a local flow curve from the combined velocity and rheological measurements [2,3,22]. Indeed, the torque Γ imposed on the moving cylinder by the rheometer yields the stress distribution σ(x) across the Couette cell,

σ(x) = Γ 2πHr 2 , (5)
and the velocity profile leads to the local shear rate γ(x) according to eq. ( 4). The resulting σ(x) versus γ(x) data are plotted in Fig. 15. The first striking observation is that the local flow curve is multivalued: for shear stresses ranging between 0.7 and 4 Pa, three different shear rates correspond to the same shear stress. The gel may thus adopt three different states for a given shear stress: (i) a solid-like state ( ), (ii) a viscous state (⋄), and (iii) a low viscosity shear thinning state (+). State (ii) is observed in regime 1 and corresponds to the viscous zone in the velocity profiles of Fig. 12. The shear thinning local behavior (iii) is observed in regime 2 (see solid line in Fig. 15) and corresponds to the flowing region in Fig. 14.

Second, we note that flowing samples are observed for shear stresses below the upper limit of the linear regime σ ≃ 3 Pa. This simply means that during the experiments under oscillating shear stress, only the solid-like state was probed. Moreover, states (ii) and (iii) are obtained after a fracturing process which probably requires a certain amount of strain and thus may not have enough time to develop under stress oscillations.

Finally the most important result is the presence of a decreasing branch in the local flow curve (⋄ and • in Fig. 15). In regime 1, the shear stress decreases from 7 to 0.7 Pa while the applied shear rate is increased from 0.05 to 70 s -1 . Usually the apparent shear viscosity is defined as the ratio between σ(x) and γ(x). Decreasing branches in the flow curve are mechanicaly unstable. It is thus striking to get sound measurements in this zone of the flow curve. Let us recall that the velocity profiles display very large errors bars in this range of applied shear rates, reflecting important temporal fluctuations. In order to get further insight on this decreasing branch, it is thus necessary to focus on the "instantaneous" velocity profiles and to study in details the temporal behaviour of the local velocities. The next section is devoted to this point.

F. Analysis of backscattered ultrasonic signals and "instantaneous" velocity signals

In order to better understand the decreasing part of the local flow curve, we go back to the backscattered ultrasonic signals recorded in regime 1. Figure 16(top) displays backscattered ultrasonic signals recorded in the 4.7 wt % NH5U-toluene gel during the experiment of Fig. 8 at the very beginning of the shear rate step at γ = 0.05 s -1 . More precisely, shear is applied at t ≃ 140 s and 100 successive signals with f P RF = 2 Hz are shown. Once shear is started, a flowing zone is nucleated in the middle of the gap after a few seconds and grows in time until steady state is achieved. The flow is thus clearly inhomogeneous.

A second very striking feature of the BS signals at γ = 0.05 s -1 is that the traces in Fig. 16(top) present sudden discontinuities from one pulse to another, i.e., as a function of the pulse time t (see arrows in Fig. 16). For the sake of clarity, we have also plotted the temporal evolution of the "instantaneous" velocity at a given point in the gap (x = 0.29 mm, which corresponds to t us = 15.7 µs) in Fig. 16(bottom). Such "instantaneous" measurements were obtained by cross-correlating two successive signals without further averaging crosscorrelations. Although this procedure leads to rather noisy velocity signals, very fast variations of the "instantaneous" velocity (which in this case becomes negative) are revealed, corresponding to the sudden discontinuties pointed out by arrows in Fig. 16(top). Moreover the fact that these discontinuities do not span over the full range of ultrasonic times t us is an indication that "fast" events occur that are localized in both space and time. The time scale for such events is smaller than the time interval τ between two pulses. Even if more quantitative experiments would be needed (in particular on much shorter time scales) in order to draw definite conclusions, we interpret these events as fractures in the bulk of the fluid. Such a behavior persists when steady state is achieved. Figure 17 shows that discontinuities in BS signals are also found for γ = 0.1 s -1 .

The third important point to notice is that the local slopes of the BS signals present temporal variations on "slow" time scales (typically a few time intervals τ between two pulses). In some cases, the slopes do not only vary but also change sign even when steady state is reached. Such events are highlighted for γ = 0.1 s -1 by white frames in Fig. 17. They are also found at other shear rates in regime 1 (see t ≃ 150-160 s in Fig. 16(top) and Fig. 19). This apparent "reverse" motion of the ultrasonic echoes can be attributed either to some rotational motion of the N5HU aggregates or to some significant radial component of the velocity field. Although we cannot discriminate between these two mechanisms through the present experiments alone, our observations constitute a clear evidence for three-dimensional features of the displacement field with characteristic times of a few seconds. As explained above in Sect. III C, the consequence of the three-dimensional nature of the flow is the possibility to measure apparent negative velocities on rather long time scales. This is illustrated in with τ = 0.25 ms. Arrows highlight discontinuities in the BS signals versus the pulse time t, which we interpret as the signature of fracture-like events. A typical zone of threedimensional motion is surrounded by a white frame. Arrows indicate fracture-like events. Bottom: 'instantaneous" velocity extracted from the above data as a function of time at x = 0.2 mm (corresponding to tus = 15.46 µs). Arrows indicate the fracture events and the dotted frame points to negative velocity data on "slow" time scales, which are indicative of three-dimensional motion.

Fig. 17(bottom) where the velocity remains negative for t ≃ 92-94 s.

Three-dimensional motions and fractures persist throughout regime 1 but these events become more rare and weaker as the shear rate is increased. Figure 18 shows more examples of three-dimensional flow features recorded in regime 1 at γ = 1 and 70 s -1 . However no fracture-like events can be detected on these BS signals.

As illustrated by Fig. 19, three-dimensional behaviors as well as fractures completely disappear in regime 2.

This qualitative analysis allows us to better understand the huge errors bars reported in the time-averaged velocity profiles. As suspected, these error bars originate from very large temporal fluctuations in the flow field. We have shown that these fluctuations arise either from "fast" fracture-like events (on time scales smaller than τ ) or from "slow" three-dimensional motions (on time scales of a few τ ). Such features are not found at higher shear rates. We believe that such fluctuations cancel out when time-averaged data are considered so that the velocity profiles of Figs. terms of tangential velocity. From these observations we may propose an explanation for the negative slope of the local flow curve reported in Sect. III E. Indeed, fractures and three-dimensional flow features lead to enhanced friction losses in the sample. Since their number and amplitude were shown to decrease as the shear rate is increased in regime 1, the loss of energy becomes smaller, which could lead to a decrease of the shear stress. Note, however that as we are unable to submit the gel to pure shear flow, it is thus not possible to identify σ(x)/ γ(x) with the shear viscosity for γ < 70 s -1 . We stress again the fact that the flow behavior along the decreasing branch of the flow curve is very complex since widely different local shear rates are evidenced in the viscous zone for the same value of the shear stress.

Finally note that the exact location of the fractures or of the shear bands may depend upon the interactions of the gel with the walls. Experiments dealing with another organogel have shown that the fracture may locate at the wall [27]. In this case, the gel was not cooled directly in the Couette cell but before being loaded into the cell which clearly limits the links between the gel and the cell.

IV. SUMMARY, DISCUSSION AND CONCLUSION

In this work, we have studied the nonlinear rheological properties of an organogel. Under small applied shear rates (regime 1), a flowing region is nucleated in the middle of the gap of a Couette cell. Increasing the applied shear rate increases the size of the flowing region. Moreover backscattered ultrasonic signals clearly evidence three-dimensional displacements and fracturelike events in this "viscous zone." Time-averaged velocity measurements show that the local flow behavior in the viscous zone is characterized by a decreasing local flow curve and a very large range of accessible shear rates for a given shear stress. At higher applied shear rates (regime 2), an increasing flow curve is recovered but a solid-like region persists close to the stator. When the mechanical stress is released, the fractures heal rapidly and the sample recovers its initial elastic properties.

We believe that the present work sheds new light on the jamming concept and wish to further discuss our results in this context. Indeed the jamming phase diagram suggested by Liu and Nagel [23] provides a unified picture of the ergodic-to-nonergodic transition in systems as diverse as clay suspensions [24], emulsions [25], or microgel solutions [26]. This diagram considers the possibility of unjamming the system by increasing its temperature, releasing its density, or increasing the amplitude of some applied shear stress. Although the jamming transition presents some universal features (universal slow dynamics and ageing behavior have been observed in a wide variety of jammed systems such as colloidal suspensions, concentrated emulsions, and lamellar gels), we argue that the unjamming mechanisms are not universal. In a previous work, we have pointed out that the flow of concentrated emulsions in the vicinity of the yield stress may be homogeneous or heteregeneous depending on the interactions between the droplets: shear banded flow occurs only for adhesive emulsions whereas the flow of nonadhe-sive emulsions remains homogeneous through the yielding transition [2].

With the present work, we bring new elements that corroborate this point of view. First we have found that the viscous (or "unjammed") zone in regime 1 is nucleated in the middle of the gap of a Couette cell. Such a location for the flowing material had not been reported before: previous works have shown that, in the vicinity of the yield stress, flow is usually initiated in the region of higher shear stress i.e., close to the inner cylinder of a Couette cell [6]. Moreover for shear rates in regime 1, the flow in the viscous zone is quite unusual with threedimensional features and fracture-like events. Rotational motions of the aggregates and fractures induce a loss of energy. These events decrease in number and in amplitude as the applied shear rate is increased. Thus a lower shear stress is required to maintain the flow at higher shear rates. This scenario could provide an explanation for the decreasing branch observed in regime 1 on the local flow curve. We also point out that the jammed phase and the unjammed one may coexist over a very large range of shear stresses. In this case, defining and measuring a "yield stress" becomes very difficult. For shear rates in regime 2, fractures and three-dimensional motions disappear. Although the global flow curve points to a low viscosity liquid behavior, local measurements show that the system remains jammed close to the stator over a significant thickness and for the highest investigated shear rates. In the framework of the jamming phase diagram, this last feature remains rather puzzling.

This study clearly shows that local measurements are required to understand the flow of complex fluids such as organogels. It also demonstrates that complex threedimensional flows may occur in viscous systems, even at very low shear rates. In particular, although restricted to a specific organogel with large-scale heterogeneities, the present work reveals the existence of both "fast" and "slow" spatially localized events involved in the unjamming transition. Instead of claiming for any generality, we rather wish to emphasize that yielding mechanisms may well be widely different from one material to another. In our opinion, investigating more deeply the nature of the interplay between the complex local flow behavior observed along the decreasing branch of the flow curve and the three-dimensional motions and fracturelike events revealed by the ultrasonic BS signals constitutes the most promising research direction on such thixotropic systems driven far from equilibrium.

FIG. 1 :

 1 FIG. 1: The N-5-hydroxypentyl-undecanamide molecule.

FIG. 2 :

 2 FIG. 2: Temperature-composition phase diagram for the N5HU-toluene system.

FIG. 3 :FIG. 4 :

 34 FIG.3: Optical microscopy picture of a 1.2 wt % N5HUtoluene gel formed at a quench temperature of 5 • C. The picture was taken just after the quench. The scale bar represents 100 µm.

FIG. 5 :

 5 FIG.5: Viscoelastic moduli G ′ (•) and G ′′ (•) as a function of the amplitude σ of the applied shear stress for a 4.7 wt % N5HU-toluene gel. The frequency of the stress oscillations is 1 Hz.

FIG. 6 :

 6 FIG. 6: Frequency sweep experiments for a 4.7 wt % N5HUtoluene gel: G ′ (• and ) and G ′′ (• and ⋄) as a function of frequency. The amplitude of the applied shear stress is 2 Pa, which falls into the linear regime.

FIG. 7 :

 7 FIG.7: Viscoelastic moduli G ′ (•) and G ′′ (•) as a function of time for a 4.7 wt % N5HU-toluene gel. The frequency of the stress oscillations is 1 Hz. For t < 480 s, the amplitude of the applied shear stress is increased from 0.1 Pa to 1000 Pa. For t ≥ 480 s, a periodic stress of amplitude 1 Pa and frequency 1 Hz is applied. The gel recovers instantaneously its mechanical properties.

2 .FIG. 8 :

 28 FIG. 8: Global flow curve: shear stress σ as a function of the applied shear rate γ for a 4.7 wt % N5HU-toluene gel. Two different regimes are evidenced below and above γ ≃ 70 s -1 .

FIG. 9 :

 9 FIG. 9: Experimental setup for ultrasonic velocimetry under shear in Couette geometry. The notations are defined in the text.

FIG. 10 :

 10 FIG. 10: BS signals corresponding to 40 pulses sent every τ = 6.7 ms in a Newtonian latex suspension sheared at γ = 10 s -1 . The normalized pressure p/p0 is coded in gray levels. The horizontal axis is the (fast) ultrasonic time tus and the vertical axis is the (slow) pulse time t. The gap lies between tus ≃ 15.1 µs and tus ≃ 16.0 µs.

1 )FIG. 11 :FIG. 12 :

 11112 FIG.11: Time-averaged velocity profile v(x) as a function of the reduced coordinate x/e for γ = 0.05 s -1 . The horizontal bar on the left axis indicates the rotor velocity. No wall slip can be clearly evidenced and the measurements are very noisy. The profiles have been averaged on the last 100 s of the shear rate step at γ = 0.05 s -1 once rheological variables have reached steady state.

FIG. 13 :

 13 FIG.13: Analysis of time-averaged velocity profiles in regime 1. Top: thickness of the shear bands divided by the gap width e as a function of the engineering applied shear rate γ. correspond to the solid-like state located near the stator, ⋄ to the middle zone, i.e., to the viscous zone, and to the solid-like state located near the rotor. Bottom: local shear rates borne by the sample in the viscous zone as a function of the engineering applied shear rate γ.

Figure 13 FIG. 14 :

 1314 Figure 13 displays the thickness of the three shear bands and the local shear rates in the viscous zone as a function of the engineering applied shear rate in regime 1. The local shear rate is extracted from the time-averaged

FIG. 15 :

 15 FIG.15:Local flow curve σ(x) versus γ(x) inferred from rheological and local velocity measurements. Three different branches are evidenced: a solid-like state ( ), a viscous state (⋄) in regime 1, and a low viscosity shear thinning fluid (+) in regime 2. The solid line corresponds to the shear thinning behavior σ = A γn with A = 0.04 SI and n = 0.6.

FIG. 16 :

 16 FIG.16: Top: BS pressure signals recorded in a 4.7 wt % NH5U-toluene gel under an applied shear rate γ = 0.05 s -1 with τ = 0.5 s. Arrows highlight discontinuities in the BS signals versus the pulse time t, which we interpret as the signature of fracture-like events. Bottom: "instantaneous" velocity extracted from the above data as a function of time at x = 0.33 mm (corresponding to tus = 15.70 µs). Arrows indicate the fracture events.

FIG. 17 :

 17 FIG. 17: Top: BS pressure signals recorded in a 4.7 wt % NH5U-toluene gel under an applied shear rate γ = 0.1 s -1 with τ = 0.25 ms. Arrows highlight discontinuities in the BS signals versus the pulse time t, which we interpret as the signature of fracture-like events. A typical zone of threedimensional motion is surrounded by a white frame. Arrows indicate fracture-like events. Bottom: 'instantaneous" velocity extracted from the above data as a function of time at x = 0.2 mm (corresponding to tus = 15.46 µs). Arrows indicate the fracture events and the dotted frame points to negative velocity data on "slow" time scales, which are indicative of three-dimensional motion.

FIG. 18 :FIG. 19 :

 1819 FIG. 18: BS pressure signals recorded in a 4.7 wt % NH5Utoluene gel under an applied shear rate γ = 1 s -1 with τ = 50 ms (top) and γ = 70 s -1 with τ = 1.4 ms (bottom). Each subfigure displays a series of 20 successive signals. Some typical zones of three-dimensional motion are surrounded by a white frame.

  11 and zone1t may still be interpreted in

	27
	t (s)
	28	15.2	15.4	t us 15.6	(µs) 15.8	16
	t (ms)	740 760
			15.2 15.4 15.6 15.8	16
					t us	(µs)

Low shear regime (regime 1)

Acknowledgments

The authors thank L. Bocquet, R. Clérac, O. Roubeau, and J.-B. Salmon for fruitful discussions.


Thomas Stenger
email: stenger@iae.univ-poitiers.fr

Alexandre Coutant
email: coutant.alexandre@gmail.com

How Teenagers Deal with their Privacy on Social Network Sites? Results from a National Survey in France

case of privacy concerns and privacy management for teenagers on Social Network Sites, according to a national survey being carried out in France since January 2008 by two University research teams in management sciences, sociology and computing, for the French National Postal Service.

Teenagers and social network sites

It is evident that Social network sites (SNS) have been the big internet phenomenon over the past few years. We define these sites as web-based services that allow individuals to:

(1) construct a public or semi-public profile within a bounded system, (2) identify a list of other users with whom they share a connection, (3) view and traverse their list of connections and those made by others within the system -the nature and nomenclature of these connections may vary from site to site (boyd, Ellison, 2007) -and (4) base their interest mainly on these first three points and not on any particular activity (Stenger, Coutant, 2010, 2009a).

From the early success of Friendster to the rise of Facebook, these sites are particularly popular with teenagers in Europe and in the United States, where they represented about 35 % of users in September 20091 (see also Ofcom 2008, ComScore, 2008, 2009). The media link their popular success with the potential risk regarding privacy (cf. infra). On this subject, users around the world behave in very different ways, from ignorance and lack of concern to strong collective demonstration and activism, as Facebook experienced with the "beacon widget" or the "Newsfeed group". Meanwhile, SNS are vigorously requested by regulators, particularly in Europe (cf. the European Commission2 -EC) to help users protect their privacy, especially in the case of young people. The creation of the "social networking task force" in April 2008 within the EC, new EC directives on online privacy, the recent agreement with 17 social platforms and specific EC funded projects such as "Insafe3 ", dedicated to help parents and teachers guide children in their safe exploration of the World, are focusing in particular on teenagers' privacy and SNS. Most of the existing academic research on SNS has focused on identity management, selfpresentation, online friendships and privacy concerns, especially with regard to teenagers. Some SNS (not all of them) enable users to control the level of privacy for their own profile, but this does not mean that users, especially teenagers, actually do so. First it is necessary to explore whether teenagers feel concerned with their privacy whilst using SNS. Secondly, if they do (and some of them do in certain circumstances as will be explained), it is interesting to analyze how they deal with this issue and manage both their privacy and identity online.

Thus, this paper proposes to examine the case of privacy concerns and privacy management for teenagers on SNS, according to a national survey being carried out in France since January 2008 by two University research teams in management sciences, sociology and computing, for the French National Postal Service.

Teenagers' privacy on SNS in Press literature

It is interesting to note that popular press coverage of SNS has emphasized potential privacy concerns, primarily concerning the safety of younger users (boyd and Ellison, 2007). Over the last two years, this phenomenon has increased all around the world, each country identifying potential threats to private information usage (e.g. the New York times and Le Monde -in France -regularly publish articles on online personal exposure and identity theft ; the BBC's investigation into how to harvest personal data on Facebook4 ; the editing of "Marc's biography" by Le Tigre (a French newspaper) based on personal data gathered online5 ...). The idea that giving up your privacy is a cost of living online has even been debated in various magazines in Europe and in the USA.

Researchers have investigated the potential threats to privacy associated with SNS, beginning with work on user practices since 2005. The results are controversial. The first research results identified the gap between users' opinions about privacy and their behavior [START_REF] Acquisti | Imagined communities: Awareness, information sharing, and privacy on the Facebook[END_REF]Stutzman, 2006 ;[START_REF] Barnes | A privacy paradox: Social networking in the United States[END_REF][START_REF] Gross | Information revelation and privacy in online social networks[END_REF], that they would like to protect their privacy but do not necessarily manage to do so. This "privacy paradox" evoked by many authors is explained in several ways. Teenagers are not always aware of the public and open nature of the platforms, nor do they necessarily know that they could set and control their privacy. [START_REF] Dwyer | Understanding Development and Usage of Social Networking Sites: The Social Software Performance Model[END_REF] explain that teenagers do not realize how much their private life is exposed, nor do they realize who else can access their profile. [START_REF] Ellison | The benefits of Facebook "friends": Exploring the relationship between college students' use of online social networks and social capital[END_REF] report in their research on Facebook users that 70% either did not know they could set the privacy settings and control their account, or that their profile was visible by the entire MSU network. Only 13% limited access only to their friends. But other survey results show a different perspective of the situation. The Pew Survey indicates that teens are aware of potential privacy threats online and as a consequence adopt specific behaviors: 66% of teenagers using a profile report that it is not visible to all Internet users [START_REF] Lenhart | Teens, Privacy, and Online Social Networks: How Teens Manage Their Online Identities and Personal Information in the Age of MySpace[END_REF]. Of the teenagers with completely open profiles, 46% reported that they included at least some false information, protecting themselves by doing so -and because fake information is part of the fun on SNS. However, it must be assumed that online privacy management on SNS involves multiple user competences. Technical skills are required and, as the platform evolves, the ability to learn to use online tools and devices is fundamental. The ability to control the impression given and manage social contexts is also of crucial importance as SNS lead to exposure, invasion or social convergence when online, and disparate social contexts glide into one (boyd, 2008). Online, the disappearance or the lack of clear context drives users to imagine their profile's audience and they are often misguided. Because online practice deals with friendship-driven activities in familiar contexts [START_REF] Mizuko | Living and learning with new media: summary of findings from the digital youth project[END_REF], young people are tempted to believe that their friends represent their audience, whereas the audience can be much broader (boyd, 2007). Researchers in social network analysis have also shown some interest in privacy on SNS. [START_REF] Lewis | The taste for privacy: An analysis of college student privacy settings in an online social network[END_REF] observe a mimetism among students as far as privacy management on Facebook is concerned. Students are more likely to have a private profile if their friends and roommates have one. They also observe statistically that women are more likely to have private profiles than men, and that having a private profile is associated with a higher level of online activity. In conclusion, the "taste for privacy" is considered to be a personal and cultural trait. Privacy also deals with social position, as highlighted by a recent French study trying to link the kind of information being shared with socio-professional status6 . Results clearly show that the lower the social status, the higher the amount and intimacy of information shared. Thus, privacy management in online contexts appears to be becoming socially discriminatory and may be associated with the risk that French politicians are calling "digital divide".

Methodology

This research project started in January 2008 and relies on in-depth interviews of 65 French teenagers and young adults (14-27 years old), 22 months of online participative observation on the most popular SNS in France (Facebook, Skyrock, Myspace, Netlog, Lexode), an analysis of the platform design with computer scientists and a systematic profile analysis. The main issues considered deal with a definition of these sites and a specific methodology, what activities are teenagers actually doing online, what do 'profiles' or 'friends' mean for them, how do they learn to use these sites and incorporate them into their everyday life, and is there a link with consumption in these activities (Stenger, Coutant, 2010, 2009a, b, c).

Is privacy on SNS an issue for French teenagers?

In order to understand how teenagers define the kind of information they are giving out on SNS, we asked the teenagers who were interviewed about subjects such as:

Are you aware of the debate dealing with privacy on SNS and do you care? Have you changed the default privacy on your profiles and why? Do you differentiate between some kinds of personal information you wouldn't like to see on these sites? Have you ever had trouble with maintaining your privacy on SNS? Who would you not want to see the information you are sharing on your profile?

As seen in the literature, the results are quite paradoxical, but in different ways. Firstly, the interviews reveal that almost all teenagers admit knowing that this information is public: "one wouldn't publish it if one didn't want others to know" one of them tells us. Having admitted that, they maintain that they are fully responsible, and that they are already sharing this information through other resources, such as emails or off-line conversations. However on the other hand, they are fairly reluctant with regard to what employers might think about them. On this latter point, the older teenagers interviewed said they are concerned that future employers may judge them because of the information available on their profile. Younger people share a very different point of view: basically, they do not care. This is one of the most interesting issues of this survey: linking these anxieties to the prospect of joining the working population. On the one hand, all of those interviewed share the opinion that what they are doing on these sites isn't important. As far as they are concerned, they say they are just « hanging out » (an expression found in both our verbatims and in boyd and Ito & al.'s surveys), (boyd, 2007[START_REF] Mizuko | Living and learning with new media: summary of findings from the digital youth project[END_REF][START_REF] Mizuko | Living and learning with new media: summary of findings from the digital youth project[END_REF] or chatting about parties. On the other hand, an increase in anxiety is clearly perceptible as they progress through the school stages: schoolchildren and high school students do not feel concerned, university level students begin to feel a little anxious when commencing professional training courses (provoking anxiety in barely 50% of students) and only those closest to an outlet to possible job opportunities admit to being very anxious (several talk about quitting SNS, even if they don't do so).

Let's emphasise here the media attitude, which is illustrative of what researchers are calling "media panics" (Milligen, 2006;Mc Robbie, 1994;Critcher, 2003). The media are playing a large role in the rise of anxiety in some teenagers, as early interviews, from the beginning of 2008 before the media started to report regularly on privacy risks on SNS, did not reveal any particular fears of being observed. In fact only one type of "invisible audience" boyd refers to ( 2008) is posing problems. Indeed, being observed by parents or being hounded by predators does not appear to concern teenagers, as they believe that they are easily able to escape them. They spoke of the same kind of tactics boyd has already highlighted in her studies for escaping parents or educators (boyd, 2007, 2008): by creating fake or "official" profiles, using nicknames or changing several letters in their name, disclosing their profile addresses only in places where guardians can't see them (during school breaks or on instant messengers). As far as predators are concerned, teenagers do not regard the risk that they be contacted as important because they don't see how predators could find them on the Web or offline.

One can see that they are confusing protection against their guardians, for whom pen names and false names make it difficult to find a particular person, with that against predators, who are not looking for a particular person and can land on any profile. In this way, we perceive a relative incompetence in protecting themselves against being identified: they do not all give their real address or their phone number but they often indicate their school, talk about their activities and the clubs they belong to, and share numerous photos of themselves in various identifiable locations. The teenagers were also asked about one last type of "invisible audience". Privacy does not appear to be a concern when it comes to brands, marketing services or to data set by SNS. As far as this particular audience is concerned, young people do not feel at all threatened! Discussing the use of their personal information by companies and marketing services or by SNS in order to increase targeted ads leaves them completely indifferent. Neither do they care about what kind of information may be used by an application they install on their Facebook profile. They argue that their activities are mainly "friendship-driven online activities" [START_REF] Mizuko | Living and learning with new media: summary of findings from the digital youth project[END_REF], and even doubt that this data could be useful in any way. In fact, most of their activities must not being interpreted as face values. The understanding of the switch from face value to private joke thus requires an intimate understanding of the people involved.

The answers given show that if teenagers clearly distinguish between their audiences, SNS pose problems only when they do not allow you easily to keep these audiences separate. Technical options as well as social tactics allow young people to deal with most of their audiences and to keep social contexts separate, with the exception of employers. As far as predators are concerned, educators must handle the fact that teenagers do not understand the risks they are facing on SNS, and must teach them to distinguish between a search for an individual and the seeking of a type/category of person, which is possible through more general geographical information. We will now analyze more deeply how teenagers succeed or not in managing this privacy on SNS.

Teenagers' Identity and Privacy Management on SNS: issues, skills and tactics

Privacy management isn't just about one's own feeling of confidence in these sites. Privacy management must be understood as an individual set of skills that goes deeper than conscious and voluntary behaviours. As far as teenagers are concerned, these skills deal on the one hand with creating an autonomous space for their generation and keeping it safe from others, on the other hand with promoting themselves by constructing a space looking « cool » for their peers. This second set of skills is the more obvious, as teenagers are very preoccupied with interacting with their peers so that they look popular. Several studies have already highlighted how teenagers used these sites to watch and imitate the actions of the most popular people (boyd, 2007;[START_REF] Mizuko | Living and learning with new media: summary of findings from the digital youth project[END_REF]. SNS could even be seen as a second chance for the less popular teenagers in offline contexts (Zywica, Danowski, 2008). French teenagers have quite similar preoccupations. Nevertheless, the kind of skills required in what Goffman calls 'interaction order' [START_REF] Goffman | The Interaction Order[END_REF] are shared by everyone. One can observe an importation of the rules of interaction which are easily adapted to the technical specificities of SNS. It bypasses the auto-censorship of potentially delicate information.

Teenagers are particularly aware of the necessity of portraying another face (Goffman, 1974) and they prove they can handle the fact that identity is a construction made as much by others as by oneself. The negotiations around each self -production are totally fixed, whether that be technically because of the design of the SNS which encourages positive creations (Facebook only permits us to "like" other people's actions, "anti" groups are forbidden), or socially through collective penalties, and exclusion, of tactless participants. The role distance shown by people interacting protect themselves as each interactant plays his own role in an ironic or distanced way: all the teenagers claim that they know that their activity is just a waste of time. SNS are much appreciated by teenagers to manage their everyday relationships with their peers. It allows them to manage more effectively many difficult activities (flirting, dating, quarrels between friends) by benefitting from the specific aspects of the tool: asynchronous discussions, body-effacement which is a specific teenager issue as the body is so hard to handle with during adolescence (breaking of the voice, blushing, sweating…). Teenagers even poach [START_REF] Certeau (de) | The Practice of Everyday Life[END_REF] these specific aspects to allow themselves to break the rules for just a moment: some of them create fake profiles to spy on others, or to say things that they would not normally say publicly. SNS are not concerned with how teenagers are managing their private life as far as self-management is concerned. They largely control the norms of the interaction. Technology allows the merging of a stronger interaction, where the device allows teenagers to learn more easily how they appear in public and that risk relies more on the invasion of other aspects of their offline life. The teenagers interviewed admitted dedicating a great deal of time hanging out on these sites, even going as far as connecting when in class, whenever they have the opportunity. This confession causes real tension with parents and also with teachers.

The first set of skills appears to be shared by fewer people. We already mentioned above that people were usually unaware of their privacy exposure on the Internet [START_REF] Dwyer | Understanding Development and Usage of Social Networking Sites: The Social Software Performance Model[END_REF]. The "privacy paradox" highlighted in the literature could also be explained by the lack of understanding of two characteristics of the new media: the width of their scalability and their persistence, (boyd, 2008). French teens are facing the same situation. If more and more profiles are henceforth inaccessible on Facebook, this change relies more on the decision of the platform to make them closed by default rather than by the active initiative of those being observed. When asked about privacy settings, the majority of the youths never customized their profile and a large number of them were unaware of these options. They were aware that it was possible to ascertain a lot of information about individuals: friends, pages and groups, status, profile photos, etc. As far as Skyrock is concerned, this lack of competence becomes very worrying, as the fact that the profiles are visited is actually appreciated by teenagers because it promotes an ingenious game of popularity evaluation measured by the number of visits and comments. As most of the site users were the youngest of the teenagers we analysed, they were both less concerned and less skilful. This allows any invisible audience to surf on the different profiles without any restrictions.

In this paradox lays an important part of the understanding of the lack of privacy management by users of SNS. The fear conveyed by media panics has not urged users to improve their skills. At best some evoke some advice received from their more skilful friends in computing7 .Users were contradictory when we asked them if these concerns they evoked strongly, often repeating actual media assertions, had prompted a change of behaviour for them or a greater concern about the privacy settings proposed by SNS, simply indicated their intention to find out more, but without real conviction. This paradox lies in their incapacity to conceive that these common, ordinary interactions which they believe to be pointless, uninteresting, can end in not so pointless consequences, in contexts which they do not yet know well. Here they did not show either technical skills to protect their data, or abstract skills to identify what information might be dangerous or examined. Finally they develop a resigned attitude towards the risk of being observed (an 18 year old girl tells us "if I withdraw from Facebook, they can still publish everything all the same... so..."). These difficulties in developing skills in privacy management can be linked to a much more worrying and wider question now faced by our western societies in which classic media evolution already raises the problem of a necessary re-definition of what is meant by the notions of privacy, intimacy, public and professional life, and also the connection that each maintains with the others. The risks associated with the decompartmentalization of contexts, which is putting in danger our ability to manage our own personal dimensions, appear to be surmounted in numerous cases by teenagers thanks to classic tools as protection of the face, the role distance and the play with the limits of the social and technical norms framing our interactions [START_REF] Certeau (de) | The Practice of Everyday Life[END_REF]. On the other hand, effective management of our private lives in all social spheres is even less possible as these spheres are themselves being redefined. Two of those questioned nevertheless claimed to have strong skills in selecting information to be diffused and preserving the separation between the various social spheres within which they evolved. They had naturally set up these safety options even before the media panic began and discussed these precautions in a relatively assured and very knowing way. This control can be connected to a skill which they already exercised offline. In individual interviews these two people both declared themselves to be homosexual and that they had to hide this aspect of their identity in certain contexts. They at once made the connection between their everyday life offline and their need for careful usage of SNS. A skill in privacy management offline was thus reinvested in an online context and initiated a technical learning skill with regard to the environment.

Conclusion and Perspectives

This study highlights that although privacy management is a problem people have to deal with when they are using SNS, several cases must be highlighted. It all depends on evoked above : students whose friends have private profiles will tend to possess private profiles too.

who is the observer. It is only future employers that are worrying users, as they believe they can handle both educators as well as predators. This allows us to propose three kinds of actions for educators: let teenagers make their own generational norms, accompany them in their construction of a space away from professional life, and teach them the difference between the possible audiences and how to prevent anyone undesirable to link their online and offline life. Another distinction has to be made between the various kinds of information that people are sharing on these sites. Users agree, and even want, to share most of this information. The main trouble appears to come from the lack of awareness of how public these spaces are. People believe they are in a public place that remains still quite intimate, just as when they are spending time with their friends in offline public places, whereas in fact their personal data can be accessed in a far wider space. This awareness increases as teenagers grow older but the durability of the information they have shared during their first years of using these sites makes them visible for a very long time. Having acknowledged this fact, educational programs taught to students in their first years of university would be better initiated in secondary school.

A final distinction must be made between SNS that provide different kinds of privacy settings: Skyrock is available to absolutely anyone and one has to find his own tactics to protect his identity, whereas other sites like Facebook or Myspace offer several levels of visibility for the profiles.

As we have seen, privacy cannot be managed only by technical tools or a 'charter of good behaviour'. We have highlighted how teenagers are good at playing with these constraints to build a generational structure for interaction. This interaction structure-remains quite similar to the one people are dealing with in offline contexts. On the other hand, new media give new characteristics to information that people do not seem to be able to deal with: scalability and persistence. Lawyers and educators will have to focus on these particularities to improve the privacy management skills of teenagers in new media concepts.

For daily statistics, see <http://www.checkfacebook.com/>

<http://ec.europa.eu/information_society/activities/social_ networking/index_en.htm>

http://www.saferinternet.org/

<http://news.bbc.co.uk/2/hi/programmes/click_online/7375 772.stm>

<http://www.le-tigre.net/Marc-L.html>

http://sociogeek.admin-mag.com/resultat/Echantillon.html

This offline learning by friendly mutual help seems to confirmLewis, Kaufman and Christakis's results (2008)


Morten Stilling
email: mortenstilling@mortenstilling.com

Kurt Stokbro

Karsten

K Flensberg

Crystalline Magnetotunnel Junctions: Fe-MgO-Fe, Fe-FeOMgO-Fe and Fe-AuMgOAu-Fe

Keywords: spintronics, magnetotunnel junction, magnetic random access memory, MRAM, electron transport spintronics, magnetotunnel junction, magnetic random access memory, MRAM, electron transport

HAL is

INTRODUCTION

A detailed understanding of magnetotunnel junctions (MTJs) of high magneto resistance (MR) is highly beneficial for the development of magnetic random access memory (MRAM) and other novel devices.

MTJs with amorphous Al 2 O 3 barriers have been studied [1], [2], but these devices show only limited MR, and are virtually impossible to model due to the noncrystalline structure of the oxide. Fully crystalline MTJs with MgO barriers currently appear interesting for research and possible development.

MgO has been successfully grown on Fe(001) using molecular beam epitaxy (MBE) [3], and Fe-MgO-Fe devices of good structural quality have been grown by MBE and pulsed laser deposition (PLD) [4]. The electrical properties of such Fe-MgO-Fe devices have been studied using first-principles-and tight-binding methods [5], [6], and tunneling magnetoresistances (TMRs) in excess of 1000% have been predicted [6].

The top-most atomic layer of the Fe substrate, unfortunately, seems to oxidize during MgO growth, and an atomic layer of FeO probably exists at the Fe-MgO interface in such devices [7], [8], although Fe-MgO-Fe can probably be grown without such a layer [9]. These FeO layers have a very significant effect on the electrical properties of the devices [START_REF] Zhang | Amrit Bandyopadhyay[END_REF], and the TMR is predicted to be much smaller for Fe-FeOMgO-Fe devices than for Fe-MgO-Fe devices [START_REF] Zhang | Amrit Bandyopadhyay[END_REF], [11].

To avoid the oxidation of the top-most Fe layer, one could imagine growing a thin layer of Au on the Fe substrate before growth of MgO. Including a Au layer at the top MgO-Fe interface, to make the structure symmetric, such Fe-AuMgO-Fe devices are predicted to possess TMR in excess of 1000% [12], and are therefore interesting for future MRAM devices.

This article describes a preliminary study of the electrical properties of Fe-MgO-Fe, Fe-FeOMgO-Fe and Fe-AuMgOAu-Fe structures.

MODEL

We have modeled the zero-bias transmission properties of Fe-MgO-Fe (Structure I), Fe-FeOMgO-Fe (Structure II) and Fe-AuMgOAu-Fe (Structure III) using the commercially available Atomistix ToolKit [13], [14] (version 2.0), which is based on density functional theory (DFT) and non-equilibrium Green's functions (NEGFs). The structures, shown in Figure 1, were based on the coordinates given in [8], and include 5 atomic layers of MgO; the lattice constant of the Fe electrodes was held fixed at a = 2.866 Å. The properties were calculated at the Fermi energy using 40,401 k-points, equally distributed in the Brillouin zone parallel to the interfaces, and at the k-point (k x , k y ) = (0, 0) using 401 equally spaced energy points. The SCF calculations were converged to a tolerance of 10 -6 using the SGGA exchange-correlation potential [15], DZP basis sets for all elements, and a mesh-cutoff of 150 Rydberg. We used an 8 × 8 k-point mesh in the plane parallel to the interfaces and an electron temperature of 0.1 eV. The results of the calculations are discussed briefly below. It is clear that the majority-spin conductance calculation is well converged when using (201 × 201) kpoints, while the minority-spin calculation is not converged. This difference is expected, since the transmission occurs through different mechanisms for the two spin-orientations, as described below. Sampling at (201× 201) k-points is quite time-consuming, and it has therefore not been feasible to sample using more k-points in this study; the quantitative results, presented in Section 3.3, should therefore be regarded with caution. Since the minority-spin transmission is similar in nature for all three structures, it must be assumed that this goes for all three, albeit this convergence analysis has only been performed for Fe-MgO-Fe.

RESULTS

Convergence of K-point Sampling

Qualitative Results of k || -Resolved Transmission Calculations

The k || -resolved transmission spectra for majorityspin electron transport at the Fermi energy, shown in Figure 3, look qualitatively very similar for the three systems: The transmission occurs through Bloch states with wavevectors near (k x , k y ) = (0, 0). The spectra correspond nicely with the spectra found in the literature [5], [6], [11], [12]; majority-spin transport seems to occur through simple barrier tunneling. The k || -resolved transmission spectra for minority-spin transport at the Fermi energy, also shown in Figure 3, also look qualitatively very similar for the three systems: All spectra show almost zero transmission in the 2-dimensional Brillouin zone, except for some very sharp peaks at specific values of the wavevectors (this is the reason the minority-spin calculations are difficult to converge, cf. Section 3.1). The specific values are different for the three systems, but the overall "peaked transmission" is similar. The spectra correspond nicely with the spectra found in the literature [5], [6], [11], [12]; minority-spin transport seems to occur through complex resonance tunneling. The conductances calculated using 201×201 k-points are listed in Table 1, along with the relative differences in the conductances found for the majority-and minorityspin, represented by ∆G ≡ Gmajority-Gminority Gminority

. .

I
The results show that the majority-spin conductance, G majority , is much larger than the minority-spin conductance, G minority , for the Fe-MgO-Fe system, while it is only slightly larger for the Fe-FeOMgO-Fe system. This is in correspondence with the results found in the literature [5], [6], [START_REF] Zhang | Amrit Bandyopadhyay[END_REF]. It has been argued that the reason for the smaller value of ∆G for Fe-FeOMgO-Fe than for Fe-MgO-Fe is that the partial electron density of states for the majority-spin state ∆ 1 , which is the main contributor to the majority-spin conductance [5], is greatly reduced in the Fe/MgO interface by the introduction of the O atoms in the surface Fe layer [START_REF] Zhang | Amrit Bandyopadhyay[END_REF]; the surface Fe atoms simply couple to the O atoms in the FeO layer rather than the O atoms in the MgO layer. This strongly reduces the majority-spin conductance, while the FeO layer only slightly reduces the minority-spin conductance, and thus brings down the value of ∆G.

For Fe-AuMgOAu-Fe, the majority-spin conductance is only slightly larger than the minority-spin conductance. The majority-spin conductance is roughly the same size as for Fe-MgO-Fe and Fe-FeOMgO-Fe, while the minority-spin conductance is large compared to these structures. It has recently been argued that this large minority-spin conductance is mediated by quantum well states in the Au layers [12], and for thicker Au layers the minority-spin conductance is even predicted to become larger than the majority-spin conductance, in contrast to the results for Fe-MgO-Fe and Fe-FeOMgO-Fe discussed above.

Quantitative Results of Energy-Resolved Transmission Calculations

The energy-resolved transmission spectra for majorityspin transport at the two-dimensional Γ-point are shown in Figure 4. The spectra show that Fe-MgO-Fe has finite transmission at the Fermi energy (E = 0), while Fe-FeOMgO-Fe has close to zero transmission at this energy. This cooperates the argument that the ∆ 1 state, which has (k x , k y ) = (0, 0), is "de-coupled" by the FeO layer (cf. Section 3.3). The Fe-AuMgOAu-Fe spectrum shows finite transmission at the Fermi energy, and generally shows transmission somewhat similar to that for Fe-MgO-Fe (as expected).

Analogous transmission spectra have been calculated for the minority-spin, but these do not bring any relevant insight, since much more than a single k-point is needed to correctly model the minority-spin transport (cf. Section 3.1); they are not shown.

CONCLUSIONS AND PERSPECTIVES

We have modeled the electrical properties of three related magnetotunnel junctions, namely Fe-MgO-Fe, Fe-FeOMgO-Fe and Fe-AuMgOAu-Fe.

We find that a fine grid of k-points is necessary to correctly model minority-spin transport for such systems, while only a few k-points are necessary to model majority-spin transport. The minority-spin results in this article are not converged, since using a k-point sampling of more than (201 × 201) has not been computationally feasible, and should therefore be regarded with caution. By utilizing the symmetries of the system for increased performance, which is possible in the next version of the software employed, we expect to be able to increase the number of k-points in future studies, and in We also find, in correspondence with results found in the literature, that two different transport mechanisms are involved in the transport of majority-and minorityspin electrons: Majority-spin transport occurs through simple barrier tunneling, while minority-spin transport occurs through complex resonance tunneling. Further analysis of the transport mechanisms is described in [16].

Finally, we find -also in correspondence with results found in the literature -that the FeO layer in Fe-FeOMgO-Fe strongly reduces the majority-spin conductance, while only slightly reducing the minority-spin conductance. In contrast, the majority-spin conductance appears more or less unaffected by the introduction of a single Au layer in the two interfaces, while the minority-spin conductance is strongly enhanced. Transport through such Fe-AuMgOAu-Fe structures is not fully understood, and further investigations are planned.

In this work, we have modeled the electron transport properties of three related, but different, structures. Such studies can provide insight into the transport mechanisms of these systems, and can prove valuable in the design of novel spintronic devices, such as magnetic random access memory. We propose that further investigations of such structures be undertaken, and have developed plans to do so. Specifically, we plan investigations into the effects of small variations of the positions of the atoms in the structures, as the resonance tunneling of the minority-spin electrons is expected to by highly sensitive to such "perturbations". Even small changes in the atomic positions may have a large influence on the calculated conductances, and the "accuracy" of current numerical results can therefore not be assessed without such studies.

We wish to thank the people at Atomistix for many fruitful discussions.

Figure 1 :

 1 Figure 1: The three structures, (a) Fe-MgO-Fe (Structure I), (b) Fe-FeOMgO-Fe (Structure II) and (c) Fe-AuMgOAu-Fe (Structure III). Note the FeO layer in the Fe/MgO interface of Fe-FeOMgO-Fe and the Au layers in the Fe/MgO and MgO/Fe interfaces of Fe-AuMgOAu-Fe.

  The relative conductances of the Fe-MgO-Fe structure -calculated at the Fermi energy for a number of k-point "resolutions", in the range (21 × 21), (31 × 31), • • • , (201 × 201), and normalized by the result found using (201 × 201) k-points -are shown in Figure 2.

Figure 2 :

 2 Figure 2: Relative conductance, calculated with different k-point "resolutions", for (a) the majority-spin and (b) the minority-spin. The results have been normalized by the value found using (201 × 201) k-points.

Figure 3 :

 3 Figure 3: Majority-and minority-spin transmission at the Fermi energy for Fe-MgO-Fe (a and b), Fe-FeOMgO-Fe (c and d) and Fe-AuMgOAu-Fe (e and f).

Figure 4 :

 4 Figure 4: Majority-spin transmission with (k x , k y ) = (0, 0) for (a) Fe-MgO-Fe, (b) Fe-FeOMgO-Fe and (c) Fe-AuMgOAu-Fe.

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Table 1 :

 1 Calculated conductances for Structures I, II and III in units of nS (10 -9 Siemens), and the relative differences in the conductances for the majority-and minority-spins, ∆G ≡

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	G majority	14.3	0.201 19.7
	G minority 0.104 0.0130 1.46
	∆G	136	14.4	12.5
		Gmajority-Gminority
		Gminority

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