Alex Fontana

Richard Pedurand

Vincent Dolique

Ghaouti Hansali

Ludovic Bellon

Thermal noise of a cryo-cooled silicon cantilever locally heated up to its melting point

come

Thermal noise of a cryo-cooled silicon cantilever locally heated up to its melting point

I. INTRODUCTION

Thermal noise is a phenomenon shared by all systems with a non-zero temperature. It is generated by the energy exchanges between the system and the surrounding environment. In equilibrium, it results in fluctuations of the observables of the system, with an amplitude proportional to the equilibrium temperature. While these fluctuations usually go unnoticed due to their intrinsically small amplitude, they become salient in an increasing number of applications: in biology they are paramount for bioelectro-magnetism [START_REF] Vincze | On the thermal noise limit of cellular membranes[END_REF] and survival of cells in vitro [START_REF] Johnson | Thermal noise in cells. a cause of spontaneous loss of cell function[END_REF], in microelectromechanical systems (MEMS) they often limit the sensitivity [START_REF] Mohd-Yasin | Noise in MEMS[END_REF], and in ground-based Gravitational Waves Detectors (GWD) they prescribe the ultimate resolution [START_REF] Harry | Thermal noise from optical coatings in gravitational wave detectors[END_REF]. Their understanding is thus fundamental.

The Fluctuation-Dissipation Theorem (FDT) stands as the fundamental tool for thermal noise estimations in equilibrium. This hypothesis cannot be assumed in many cases: examples range from living systems [START_REF] Gupta | Equilibrium and out-ofequilibrium mechanics of living mammalian cytoplasm[END_REF], aging materials [START_REF] Buisson | Electrical noise properties in aging materials[END_REF] and systems subject to a heat flux [START_REF] Monnet | Extended nyquist formula for a resistance subject to a heat flow[END_REF][START_REF] Conti | Effects of breaking vibrational energy equipartition on measurements of temperature in macroscopic oscillators subject to heat flux[END_REF]. The research of possible non-equilibrium effects on the thermal noise of the test masses employed in GWD recently became a prolific subject [START_REF] Conti | Effects of breaking vibrational energy equipartition on measurements of temperature in macroscopic oscillators subject to heat flux[END_REF][START_REF] Komori | Direct approach for the fluctuation-dissipation theorem under nonequilibrium steady-state conditions[END_REF]. Often higher fluctuations with respect to equilibrium are expected [START_REF] Conti | Effects of breaking vibrational energy equipartition on measurements of temperature in macroscopic oscillators subject to heat flux[END_REF][START_REF] Li | Concentration fluctuations in a polymer solution under a temperature gradient[END_REF], in concordance with theoretical predictions such as the Harada-Sasa relation [START_REF] Harada | Energy dissipation and violation of the fluctuation-response relation in nonequilibrium langevin systems[END_REF]. On the other side, we have shown in previous studies that a lack of fluctuations is also possible. A silicon microcantilever is brought in a Non-Equilibrium Steady State (NESS) by heating its tip at hundreds of degrees higher than its base thermalised at * Corresponding author: ludovic.bellon@ens-lyon.fr room temperature. The system, subject to a strong heat flux along its length, is unaffected by this phenomenon, fluctuating as if it was in thermal equilibrium at room temperature [START_REF] Geitner | Low thermal fluctuations in a system heated out of equilibrium[END_REF][START_REF] Fontana | Extended equipartition in a mechanical system subject to a heat flow: the case of localised dissipation[END_REF]. These results are then interpreted thanks to a minimal extension of the FDT for a system with a non-uniform temperature, demonstrating how the fluctuations are linked to the spatial distribution of the dissipation.

In this work we push the aforementioned experiments to the physical limits, imposing almost the highest temperature difference the cantilever can sustain, and thus bringing it as far from stationary equilibrium as possible. To do so, we place the sample in a cryostat at 10 K and heat its tip close to the melting point with a focused laser, thus prompting a temperature difference of around 1700 K. The interest of this experiment is twofold: from a theoretical point of view, the simple extension of the FDT [START_REF] Komori | Direct approach for the fluctuation-dissipation theorem under nonequilibrium steady-state conditions[END_REF] is put to a test at its limits. From an experimental point of view, this system can be considered an important test bench for cryogenic high-precision measurements, metrology [START_REF] Bon | Cryogenic optomechanic cavity in low mechanical loss material[END_REF] and the GWs community. Indeed, a part of the experimental efforts are heading towards cryogenics (e.g. KAGRA [START_REF] Akutsu | First cryogenic test operation of underground km-scale gravitational-wave observatory KA-GRA[END_REF]) in order to reduce the thermal noise of the test masses and suspensions [START_REF] Khalaidovski | Evaluation of heat extraction through sapphire fibers for the GW observatory KAGRA[END_REF]. The deposited heat may generate a NESS which is then paramount to characterise. Furthermore, future detectors might use silicon for the test masses (e.g. Einstein Telescope [START_REF] Punturo | The third generation of gravitational wave observatories and their science reach[END_REF]), thus the same material as the sample of our experiment.

In the first part, we show how to estimate the temperature of the system in such conditions, through a calibration and a numerical simulation. We then demonstrate how, for a cantilever similar to the one in [START_REF] Geitner | Low thermal fluctuations in a system heated out of equilibrium[END_REF][START_REF] Fontana | Extended equipartition in a mechanical system subject to a heat flow: the case of localised dissipation[END_REF], we retrieve a strong dearth of fluctuations, and we interpret it through an estimation of the dissipation in the system. A discussion concludes this work.

II. METHODS

The experimental setup is depicted in Fig. 1. The physical systems consists in a silicon cantilever (OC-TOSENSIS micro-cantilevers arrays [18]), L = 1000 µm long, B = 90 µm wide and H = 1.1 µm thick. It is monolithically clamped to a macroscopic chip which is kept at T min ≤ 20 K by a cryostat. The cantilever is placed in a vacuum chamber at 10 -7 mbar. The measuring instrument is the CryoQPDI [START_REF] Pedurand | Instrumentation for Thermal Noise Spectroscopy[END_REF], a Quadrature-Phase Differential Interferometer (QPDI) [START_REF] Bellon | Differential interferometry with a complex contrast[END_REF][START_REF] Paolino | Quadrature phase interferometer for high resolution force spectroscopy[END_REF] combined with a cryostat. A laser beam at 532 nm is used to measure the thermal fluctuations of the cantilever. At the same time it acts as a heater when its power P is increased, due to its optical absorption. It is split into two parallel beams by an aberration corrected beam displacer inside the cryostat. The beams are both focused on the cantilever surface with a spot radius R 0 = 3 µm. By design, the distance between the two spots is fixed at x 1 -x 2 = 417 µm. Since we focus one spot close to the cantilever's free end, the second one is roughly in the center along its length. Across its width, both beams are placed off axis at y 1 = y 2 = 37 µm.

The QPDI senses the optical phase difference between these two beams, which can be swiftly expressed as a vertical difference d = d 1 -d 2 . Up to a geometrical factor dependent of the resonant modes shape, d is sensitive to the flexural deformations (denoted from now on by their amplitude δ n , with n the mode number) and the torsional ones (denoted by θ m , with m the mode number). The Power Spectrum Density (PSD) of d, plotted in Fig. 2, shows the lowest frequency resonances of the cantilever. Up to 9 flexural and 7 torsional modes are measurable in the experiment. Due to experimental constraints, some are excluded from the analysis: mode n = 1 is affected by low-frequency external noise (see Fig. 2) and the amplitudes of modes n, m = 5 are too low due to their vicinity to a node in sensitivity (d 1 and d 2 are affected likewise by these modes).

During the measurement, the pulse tube of the cryostat must be turned off: the vibrations it creates during operation are too high for the sensitive thermal noise measurement we perform. We rely on the thermal inertia of the sample holder (lead loaded) to maintain a quasi steady state: the temperature drift is only 0.18 K/min. Each time T min reaches 20 K, we turn off the thermal noise measurement and cool down to below 10 K before starting a new acquisition. Equilibrium (EQ, with P < 1 mW) and non-equilibrium (NESS, with P = 10-40 mW) measurements are alternated to get rid of any drift issue. In addition, we randomise the order of the laser powers and often change the probing point thus shielding the results from particular modifications of the material. Several measurements performed on the same sample also ensure reproducibility [START_REF] Fontana | Thermal fluctuations in an out-ofequilibrium system[END_REF]. [START_REF] Pedurand | Instrumentation for Thermal Noise Spectroscopy[END_REF][START_REF] Bellon | Differential interferometry with a complex contrast[END_REF][START_REF] Paolino | Quadrature phase interferometer for high resolution force spectroscopy[END_REF]. A green laser beam (λ = 532 nm) is divided in two by a beam displacer BD and focused on the cantilever. The interferometer senses the vertical distance d1 -d2 between the beam B1 close the cantilever tip and B2 close to the center. The probing points are separated of ∆x = x1 -x2 = 417 µm, ∆y = 0. The cantilever, in vacuum at 10 -7 mbar, is monolithically clamped to its macroscopic chip which is thermalised at temperature T min . When the laser power is low (P < 1 mW), we consider the system in thermal equilibrium. When the power is raised (10 to 40 mW), a temperature gradient T (x) along the cantilever arises.

A. Temperature

When heating the cantilever with the laser beams, we create a temperature profile T (x) along the cantilever length, which is non-linear: not only there are two heating points, but the thermal conductivity of silicon span 3 orders of magnitude between 10 K and the melting point T melt = 1687 K. It is thus not simple to describe the temperature with a single observable. However, for each power P of the laser, T (x) spans from T (0) = T min to T (L) = T max , and its average value T avg = L 0 T (x)dx/L is used to grasp the out-of-equilibrium character of the system. In this section we describe how to evaluate T avg from the measurement.

The resonance frequencies f n are sensitive to the temperature T , mainly through the variation of the Young's modulus Y of silicon. In refs. 23 and 24, we show that in a first approximation, (c) We measure at equilibrium (P < 1 mW) the frequency shift with respect to the lowest temperature, when the temperature of the cryostat slowly increases up to room temperature. This calibrates the Young's modulus dependency of temperature δY (T ) through Eq. 1 with T uniform.

∆f n f 0 n = 1 2 L 0 dx ∆Y (T (x))φ n (x) 2 Y 0 L 0 dx φ n (x) 2 , (1)
where superscript 0 stands for the reference value of the quantity at T 0 = 10 K, ∆ stands for the variation of the quantity with respect to the reference one, and φ n (x) is the curvature of the normal mode. When temperature is uniform, the relative frequency shift is independent of the mode number and can be used to calibrate δ Y (T ) ≡ ∆Y (T )/Y 0 . We perform this calibration of δ Y (T ) experimentally: the resonance frequencies of the cantilever are tracked with a very low injected laser power so that the system can be considered in equilibrium, while we let the temperature of the cryostat increase slowly from 10 K to room temperature [25]. Following ref. [START_REF] Wachtman | Exponential temperature dependence of young's modulus for several oxides[END_REF], we perform a fit of the calibration data with δ Y (T ) = c 1 T e c2T , leading to c 1 = (3.68 ± 0.04) × 10 -5 K -1 and c 2 = 196.7 ± 2.7 K.

δ -1 Y can then be used as a thermometer: from a measured frequency shift, one can then deduce the apparent temperature of the cantilever with

T app n ≡ δ -1 Y (2∆f n /f 0 n ).
In thermal equilibrium, T app n corresponds to the actual temperature of the cantilever for all n. If there is a temperature profile T (x), T app n represents the apparent temperature one would read from such a thermometer. Interestingly, when the mode number is large (n > 5), curvature is mostly distributed all cantilever long and T app n approximates the average temperature of the system T avg [START_REF] Pottier | Resonance frequency shift of silicon cantilevers heated from 300 k up to the melting point[END_REF]. Therefore, we can experimentally estimate T avg in an out-of-equilibrium situation by

T app = δ -1 Y (2 ∆f n /f 0 n n=6-9
), the average of the apparent temperatures of modes 6 to 9.

To further secure our measurement of T avg and have an estimation of the full temperature profile, in appendix A we numerically compute T (x) solving the stationary heat equation, taking into account the temperature dependency of the thermal conductivity, thermal radiation, and the two heat sources corresponding to laser absorption. For a given absorbed power, we therefore get T (x), from which we infer T avg , T max , and the relative frequency shift (from Eq. 1 using the calibrated δ Y (T )). We end up again with a calibration function, giving T avg sim ( ∆f n /f 0 n n=6-9 ). Both calibrations are very consistent, T app overestimating T avg sim by 40 K at most. The temperature profile is however very non-linear with a steep rise close to the end, so that T max on the other hand presents large uncertainties due to the unknown parameters of the problem (mainly the precise knowledge of light absorption).

B. Thermal fluctuations

All the resonances have a high quality factor (Q n,m ≥ 10 3 , see Fig. 4) and are sufficiently apart from each other to be considered as independent oscillators. Up to a geometrical multiplicative factor, the PSD S d around each peak can be seen as the one of the specific mode S δn or S θm only. The mean square amplitude of the thermal noise δ 2 n or θ 2 n can be evaluated by integrating the PSD in a tiny frequency range around the corresponding peak, subtracting the flat background noise contribution. In equilibrium at temperature T , the equipartition principles states that:

k n δ 2 n = κ m θ 2 m = k B T, (2)
with k n , κ m the stiffnesses in flexion and torsion, and k B the Boltzmann constant. When the cantilever is out of equilibrium (under a steady heat flux), we define a fluctuation temperature T fluc as:

T fluc n ≡ k n δ 2 n k B = f n f 0 n 2 δ 2 n NESS δ 2 n EQ T min , T fluc m ≡ κ m θ 2 m k B = f m f 0 m 2 θ 2 m NESS θ 2 m EQ T min . (3)
T fluc represents the temperature we would associate to the system through the measurement of its fluctuations, be it in equilibrium or not. Indeed, in this latter regime no thermodynamic temperature of the cantilever can be defined, and T fluc n,m embody the meaningful value of the fluctuation amplitudes. It is noteworthy that this quantity is in principle mode-dependent, contrarily to the equilibrium case (Eq. 2): indeed, every mode, and thus oscillator, can in principle fluctuate at a different temperature. From an experimental point of view, T fluc is calculated as the ratio of the amplitude of the fluctuations in a NESS and in an equilibrium state (EQ, low laser power P < 1 mW), times the temperature of the thermal bath, corrected by the frequency shift (since

k n = m eff (2πf n ) 2 ,
with m eff the effective mass of the oscillator being independent of temperature, k n ∝ f 2 n ). As mentioned earlier, each NESS measurement is preceded and followed by an EQ measurement, thus canceling most drift issues when computing T fluc . Moreover, using the ratio of amplitudes avoids any tricky calibration step to measure δ n or θ m .

Using an extended equipartition approach for a NESS [START_REF] Komori | Direct approach for the fluctuation-dissipation theorem under nonequilibrium steady-state conditions[END_REF][START_REF] Geitner | Low thermal fluctuations in a system heated out of equilibrium[END_REF][START_REF] Fontana | Extended equipartition in a mechanical system subject to a heat flow: the case of localised dissipation[END_REF], T fluc is expected to be the average of the temperature profile T (x) weighed by the normalised energy dissipation profile w diss (x):

T fluc n,m = L 0 dx T (x)w diss n,m (x) (4)
In this framework, the fluctuations of the cantilever depend on where the dissipation is preponderant, allowing a wide variety of possible results depending on the shape of w diss n,m (x) [START_REF] Geitner | Low thermal fluctuations in a system heated out of equilibrium[END_REF][START_REF] Fontana | Extended equipartition in a mechanical system subject to a heat flow: the case of localised dissipation[END_REF]. We discuss this quantity in the next section.

C. Dissipation

While it oscillates, the cantilever dissipates energy in the surrounding environment. In high vacuum, hydrodynamical damping is efficiently suppressed and dissipation may arise only from the clamping losses and the internal damping, sometimes referred to as viscoelasticity [START_REF] Nowick | Anelastic Relaxation in Crystalline Solids[END_REF], arising from local defects or thermoelastic damping for example. Dissipation will thus be a function of the position x, frequency f , and temperature T which may itself depend on x. A generic way to describe it is to introduce the loss angle ϕ Y (x, f, T ) (respectively ϕ S (x, f, T )), which corresponds to the phase of the Young's modulus Y (respectively S, the shear modulus implied for torsion). Since we are dealing with low dissipation (ϕ Y,S 1), the real part of the elastic moduli can be considered independent of x and f , and for a given mode n only the value of dissipation at the resonance frequency matters:

Y (x, f, T ) ≈ Y 0 (1 + δ Y (T ) + iϕ Y (x, f n , T )) S(x, f, T ) ≈ S 0 (1 + δ S (T ) + iϕ S (x, f n , T )) (5)
Experimentally, we can only probe the global dissipation by measuring the quality factor

Q n,m = 1/ϕ n,m
of the resonances through a Lorenzian fit of the thermal noise PSD (see Fig. 4). This global dissipation is a function of the mode number n and temperature field T (x) [START_REF] Geitner | Low thermal fluctuations in a system heated out of equilibrium[END_REF][START_REF] Fontana | Extended equipartition in a mechanical system subject to a heat flow: the case of localised dissipation[END_REF]:

ϕ n {T (x)} = L 0 dx ϕ Y (x, f n , T (x))φ n (x) 2 ϕ m {T (x)} = L 0 dx ϕ S (x, f m , T (x))φ m (x) 2 (6)
Hence, the experimental estimation of ϕ n,m does not allow us to retrieve the spatial dependency of the normalised dissipation w diss n,m (x), which writes [START_REF] Geitner | Low thermal fluctuations in a system heated out of equilibrium[END_REF][START_REF] Fontana | Extended equipartition in a mechanical system subject to a heat flow: the case of localised dissipation[END_REF]:

w diss n (x) = 1 ϕ n {T (x)} ϕ Y (x, f n , T (x))φ n (x) 2 w diss m (x) = 1 ϕ m {T (x)} ϕ S (x, f m , T (x))φ m (x) 2 (7)
Therefore, we cannot directly calculate the right-hand side of Eq. 4 in order to estimate a theoretical value of the fluctuation temperature, dissipation-wise. This is possible just if some hypotheses are satisfied, such as the linearity of the temperature profile, which is not the case of this experiment. We discuss in the next section how ϕ n,m is nevertheless a good indicator for the evolution of the dissipation.

III. RESULTS

In Fig. 3 we show the apparent temperature T app and the fluctuation temperatures T fluc n,m for all modes as a function of the average temperature of the system T avg sim . At the highest laser power the cantilever begins to melt, which is assessed from camera observations and a reflectivity drop. This indicates that we can reach the highest temperature difference the cantilever can sustain, with T max -T min ≈ 1700 K. For all modes, the fluctuation temperatures are much below the average temperature, except for the highest heating power. The effect is even more striking if we compare T fluc n,m with T max . This indicates a strong lack of fluctuations, as in our earlier experiments on similar cantilevers at room temperature [START_REF] Geitner | Low thermal fluctuations in a system heated out of equilibrium[END_REF][START_REF] Fontana | Extended equipartition in a mechanical system subject to a heat flow: the case of localised dissipation[END_REF]. It is noteworthy that the T fluc n,m show a modest mode dispersion, more pronounced for flexion and almost negligible for torsion. The uncertainties on T fluc have two contributions: statistical and systematic. The first is evaluated from the repeated measurement of the thermal noise of the cantilever at the given power. The second takes into account the possibility of the probing point shifting during the measurement, the maximum magnitude of which is estimated to be dx 1 ≡ dx 2 = 3 µm. We discuss this in details in Ref. [START_REF] Fontana | Extended equipartition in a mechanical system subject to a heat flow: the case of localised dissipation[END_REF]. Both contributions are equally important in yielding the error bars of fig. 3.

In ref. [START_REF] Fontana | Extended equipartition in a mechanical system subject to a heat flow: the case of localised dissipation[END_REF], the lack of fluctuations is such that T fluc is unchanged when T avg increases, leading to the conclusion (through Eq. 4) that the cantilever is dominated by clamping losses. Indeed, if the dissipation is localised at T min , it is straightforward to conclude that T fluc ≈ T min . In the present experiment, however, the fluctuations depend on the average temperature. Indeed, we note how they tend to gently increase with T avg (except the odd point around 150 K), reaching up to 10 times the value of T min for the highest heating power. The cantilever cannot therefore be dominated by clamping losses only. The dissipation along the cantilever length should thus have a noticeable contribution.

A reasonable assumption is that the local dissipation is dependent on the temperature, and will thus introduce a dependence on space in the weighting of T (x) in Eq. ( 4). We then expect to measure also a dependence on temperature of the global dissipation of each mode. The measured loss angles ϕ n,m are plotted vs T avg sim in Fig. 4, confirming this picture. As mentioned, they cannot in general lead to w diss (x); nevertheless, they give the qualitative evolution of the dissipation with respect to the average temperature of the cantilever. For all modes, ϕ n,m depend on T avg , and increase up to 10 times at the highest heating point. It is important to note here that the estimation of ϕ is not trivial in the experiment: due to the slow change of the temperature of the cryostat T min and the fluctuating laser power P , the resonance peaks shift during the measurement and artificially enlarge the PSD. Furthermore, the cantilever can sometimes enter in a self-oscillation state, which can inject energy into the resonances altering the results. For these reasons, a careful analysis based on the statistical properties of the PSD is performed [START_REF] Fontana | Thermal fluctuations in an out-ofequilibrium system[END_REF], and a large number of spectra are discarded. We choose to show in Fig. 4 the results of the fits with a goodness-to-fit χ 2 < 3 (with 1 being a perfect fit), discarding the others. At each heating power P , we fit with a Lorentzian each spectra passing the selection. Each fit provides a measurement of the loss angle ϕ and its uncertainty. Those measurements are then averaged together to compute the final estimation of ϕ, and the total uncertainty is calculated as the quadratic sum of the dispersion of the ϕ and of the single uncertainties. In the present experiment, due to the small number of spectra satisfying the applied criteria, the dispersion of the data represents the most important source of error.

The non-trivial profile of T (x) and the unknown w diss (x) hinder an estimation of T fluc through the extended FDT (Eq. 4). Nevertheless, it is possible to explain the experimental results through some hypothesis on ϕ(x, f, T ). We believe this system to be dominated by two main sources of dissipation: clamping and distributed losses. The former is the main source of damping for similar cantilevers at room temperature [START_REF] Fontana | Extended equipartition in a mechanical system subject to a heat flow: the case of localised dissipation[END_REF], and it causes the strong lack of fluctuations we observe. The latter is the responsible of the increase of fluctuations. The loss angle could thus be written as:

ϕ Y,S (x, f, T ) ≈ ϕ 0 Y,S (f, T min )δ D (x) + ϕ 1 Y,S (x, f, T ) (8)
with δ D Dirac's delta function, ϕ 0 Y,S ≈ 10 -5 the loss angle at T min and ϕ 1 Y,S an unknown function embedding the evolution of the damping with the temperature and position. With this simple description, we can see that T fluc is brought close to T min by the first term, while the second one acts as a correction, becoming important as T avg increases.

IV. DISCUSSION

A mechanical system in thermal equilibrium shows no surprises from the fluctuation point of view: all the measurable resonances have an energy content proportional to the temperature of the surrounding thermal bath. and ϕm of torsional modes (b) with respect to the average temperature of the cantilever. Due to experimental contraints and low sample size, the fit of the experimental spectra are often hard to compute, thus we show only the results of fits with a χ 2 < 3. For most modes, the general trend is an increase of dissipation with increasing temperatures. In order to visually assess this, in the insets we show the peak of the PSD of the second modes in flexion and torsion, widening from low to high temperature, depicted respectively in cyan (light grey) at T avg sim = 14 K and red (dark grey) at T avg sim = 474 K for flexion and T avg sim = 145 K for torsion. The uncertainties on the loss angles are discussed in the text.

When the system is brought to a NESS through a heat flux along its length, on the other side, the thermal noise of the system is not trivial anymore : it depends both of the temperature profile and of where the dissipation is localised (Eq. 4). Furthermore, it is in principle possible that different resonances show different results, meaning that the frequency is also a relevant actor. Our system, a silicon micro-cantilever, is thus a suitable test bench in order to characterise the dependency of fluctuations from these parameters, as it is possible to alter their dissipation adding a coating [START_REF] Geitner | Low thermal fluctuations in a system heated out of equilibrium[END_REF], study a large range of frequencies due to the high number of measurable modes, and greatly vary the temperature. In this experiment, we focus on this last point, exploring thermal of the cantilever between cryogenic temperatures and the melting point of the material. We show how all the measurable resonances show an important dearth of fluctua-tions, in line with previous experiments on similar samples [START_REF] Fontana | Extended equipartition in a mechanical system subject to a heat flow: the case of localised dissipation[END_REF]. Nevertheless, the fluctuations increase with the temperature difference imposed on the system, as does the measured dissipation. Interpreting this thanks to the extended FDT, we conclude that the dissipation profile is non-trivial with clamping losses and distributed damping.

From a theoretical point of view, this work represents an interesting test bench for the minimal extension of the FDT for systems in a NESS [START_REF] Komori | Direct approach for the fluctuation-dissipation theorem under nonequilibrium steady-state conditions[END_REF]. Indeed, the cantilever is brought as far from equilibrium as possible, with a ratio larger than 100 between the lowest and highest temperatures, where higher-order corrections of the FDT might in principle be more salient. Not only our results can be perfectly embedded in this framework, but the simultaneous measurement of the damping add support to its validity. Moreover, we see how this is true for the whole frequency range explored (10 -500 kHz), in which all the modes show a similar behavior. This suggests that the lack of fluctuations is a global property of this cantilever. Experiments such as the one presented in this work represent then a suitable testing bench for out-of-equilibrium thermodynamics: fluctuation theorems and the relative corrections [START_REF] Harada | Energy dissipation and violation of the fluctuation-response relation in nonequilibrium langevin systems[END_REF] and inequalities [START_REF] Horowitz | Thermodynamic uncertainty relations constrain non-equilibrium fluctuations[END_REF] can be swiftly put to a test in a simple framework.

From an experimental point of view, this experiment can be relevant in other fields. For example, the characterisation of the effects of a temperature inhomogeneity can become salient in the noise estimation of micro and nanoresonators [START_REF] Cleland | Noise processes in nanomechanical resonators[END_REF]. Indeed, the readout laser power needs to be very small in order not to modify the temperature field of the system and thus the amplitude of the fluctuations. Our results show that this condition may be relaxed if the dissipation is localised at the lowest temperature point. Furthermore, as Eq. 4 entangles the temperature field with the dissipation field to give the amplitude of the noise, a measurement of two of these quantities yields important information on the third, in cases where its measurement is not possible (e.g. frequency resolution comparable with the width of the resonance). It is similarly possible to perform measurements where we change the probing point along a system and thus test the presence of defects looking at the amplitude of fluctuations: this paves the way to the localisation of single dissipative points. The interest of exploring cryogenic regimes lies in showing how this can be considered possible no matter the temperature.

As previously mentioned, these results can be useful to the GWs community in characterising the behavior of silicon under a heat flux at low temperatures. The experimental setup of the present work is conceived explicitly to study the temperature dependency of the dissipation of the coatings for the test masses in VIRGO [START_REF] Pedurand | Instrumentation for Thermal Noise Spectroscopy[END_REF]. We show here how we can at the same time study possible non-equilibrium effects on the noise, the reduction of which is paramount to increase sensitivity. Doing so with a pure silicon cantilever, we verify how the thermal fluctuations of our sample are weakly dependent on the deposited heat, as they sensibly increase only when the temperature is hundreds of times the one of the cryostat. For this reason, we might expect the deposited heat on the test masses to be less harmful than the equilibrium prediction [START_REF] Khalaidovski | Evaluation of heat extraction through sapphire fibers for the GW observatory KAGRA[END_REF], fluctuation-wise. It is also important to note that our conclusion for a microscopic system might not hold when we increase in size [START_REF] Conti | Effects of breaking vibrational energy equipartition on measurements of temperature in macroscopic oscillators subject to heat flux[END_REF], or when secondorder effects in the temperature arise [START_REF] Lumbroso | Electronic noise due to temperature differences in atomic-scale junctions[END_REF].

To conclude, this work shows how the thermal fluctuations of a micro-cantilever, which base is thermalised at around 10 K, show a weak dependency on the strong heat flux imposed on the system. This behavior is interpreted thanks to a minimal extension of the FDT, which allows us to link the thermal fluctuations of the cantilever with its dissipation profile. We finally show how the measurement of the global damping is coherent with our theoretical framework. While extended FDT is a valid description for various samples studied in our group [START_REF] Geitner | Low thermal fluctuations in a system heated out of equilibrium[END_REF][START_REF] Fontana | Extended equipartition in a mechanical system subject to a heat flow: the case of localised dissipation[END_REF], further studies may comprehend a thorough investigation of exotic dissipation profiles through different geometries, coatings and materials.

∂ ∂x κ s T ) ∂T ∂x + 2 s σ SB H T 4 -T min 4 + A 1 P 1 √ πHBR 0 e -2 (x-x 1 ) 2 R 2 0 + A 2 P 2 √ πHBR 0 e -2 (x-x 2 ) 2 R 2 0 = 0 (A1)
where κ s is the thermal conductivity of silicon, s its emissivity and σ SB the Stefan-Boltzmann constant, and A i P i the absorbed light power at position x i (i = 1, 2). The boundary conditions are:

T (0) = T min ∂T ∂x (L) = 0 (A2)
The first term of Eq. A1 represents the conduction, the second the radiation and the last ones the two heat sources due to the partial absorption of the laser light. While κ s (T ) is tabulated [START_REF] Warlimont | Springer Handbook of Materials Data[END_REF], the other parameters have large uncertainties the experiment:

• The nominal thickness H of the cantilever is given by the manufacter with an important uncertainty (H = 1 ± 0.3 µm). Nevertheless, we can deduce its value looking at the flexural resonance frequencies and confronting these values with the Euler-Bernoulli prediction. This gives H = 1.1 ± 0.1 µm, which is confirmed by scanning electron microscopy images.

• The emissivity is unknown and it varies greatly at high temperatures [START_REF] Jain | Total emissivity of silicon at high temperatures[END_REF], where the radiation term is more relevant. A first approximation is to consider s as free parameter (between 0 and 1), independent of the coordinates, to be adjusted.

• T min slowly drifts between 10 K and 20 K during our protocol.

• Finally, the absorbed power is also unknown, since during the experiment we measure the total injected power P = P 1 + P 2 , with no control over the absorption A 1 and A 2 (which can be different for each heat source and temperature dependent [START_REF] Pottier | Thermo-optical bistability in silicon micro-cantilevers[END_REF]). It is similarly not possible to know the repartition of the laser power into the two sensing beams, as it could be not equal for B 1 and B 2 . We refer to this balance with a = A 1 P 1 /AP , with AP = A 1 P 1 + A 2 P 2 the total absorbed power. We estimate that a can vary for 0.3 to 0.7 in our experiment.

Since those parameters are unknown, we then perform a parametric sweep of the aforementioned meaningful quantities, in order to retrieve the family of temperature gradients {T (x)} by numerically solving Eq. A1. We report the explored range of the parameters in Table I. For any given set of parameters, we solve the boundary value problem (eqs. A1 and A2) to extract a numerical solution T (x). One example is shown in the inset of Fig. 5, demonstrating the high non-linearity of the profile. As it turns out, a is the most important parameter in prescribing the shape of T (x), and thus T avg . On the other side, a smaller H or s or a higher total power AP yields a higher T max . For each numerical solution T (x), we then compute the average temperature T avg = L 0 T (x)dx/L, the maximum temperature T max = max(T (x)), and the relative frequency shift ∆f n /f 0 n n=6-9 through Eq. 1 (using the experimental calibration for ∆Y (T )/Y 0 ). All results are finally shown in Fig. 5. The solid curve represents the calculated temperature for the central value of the parameters in Table I and the shaded area all its simulated values.

In order to estimate T avg and T max in the experiment, we first average the measured ∆f n /f 0 n for n = 6 -9. Then, to each of these values we associate a range of simulated temperatures {T avg , T max }. As we can see, the maximum temperature varies greatly in the simulation. We set an upper bound to its values at the melting temperature T melt , since we aim to retrieve T max for the measurements where we did not melt the cantilever. In fact, from camera observations and reflectivity estimations we can discern when we damaged the cantilever, hence for the measurements where this is not the case it is reasonable to assume T max < T melt . The central value of the constrained interval is then the retained value of T max , which is depicted as a purple (light grey) dashed curve. The uncertainty associated to T max is then calculated as the standard deviation of the parametric range, taken as if represented by a uniform distribution. Indeed, each value of the parametric range is in principle equiprobable. We perform the same procedure in order to calculate T avg sim and the respective (small) uncertainty, considering the interval of parameters limited by the upper bound for T max . These uncertainties are shown in fig. 5 for the experimental data as cyan (light grey) squares and blue (dark grey) diamonds. We can see that the numerical simulation gives us a reliable way to estimate the aver- I, we estimate the possible values of the average and maximum temperature of the cantilever and at the same time the frequency shift for the mode numbers 6 to 9. The relations between these quantities are shown as yellow (light gray) and red (dark grey) curves. The dispersion of T avg , depicted as a yellow (light grey) shaded area, is small. As a result, the error associated to the experimental value of T avg at a given frequency shift, shown as cyan squares is also small. Conversely, the estimation of T max yields a wide parameter range displayed as a red (dark grey) shaded area. No bijective relation is possible, thus we estimate T max as the average of a uniformly distributed variable between the possible values at a given frequency shift. The purple (dark grey) dashed curve represents the retained value of T max for each frequency shift and the blue (dark grey) diamonds are the experimental values. In the inset we show a typical temperature profile T (x), with each of the two laser beams (at x1 and x2) injecting an absorbed power of 15 mW. We can see how T (x) is highly non-linear and peaked at the heating points.

age temperature of the cantilever, and as we see in Fig. 3 this is very close to T app . Conversely, the uncertainty on the unknown parameters hinders the knowledge of T max , and the results of the simulation must be taken as an order of magnitude guess.

Finally, the simulations allow us to test the hypothesis that when we shine the cantilever with a low power (P < 1 mW), the system can be considered close to thermal equilibrium. Since P is measured before the beam is directed towards the vacuum chamber, losses on the optical elements and windows diminish the total intensity that reaches the cantilever. Furthermore, the cantilever absorbs just a part of the shined beam. A conservative guess is to suppose that AP = 0.5 mW. In this case the simulations give T avg = 15.5 ± 0.2 K and T max = 16.8 ± 0.5 K for T min = 14 K. Therefore, we see how the temperature increase at P < 1 mW are very low with respect to the non-equilibrium measurements and the system can safely be considered in thermal equilibrium.

  FIG.1. (Color online) Experiment setup: the flexion and torsion of a cantilever inside a cryostat are captured thanks to a differential interferometer[START_REF] Pedurand | Instrumentation for Thermal Noise Spectroscopy[END_REF][START_REF] Bellon | Differential interferometry with a complex contrast[END_REF][START_REF] Paolino | Quadrature phase interferometer for high resolution force spectroscopy[END_REF]. A green laser beam (λ = 532 nm) is divided in two by a beam displacer BD and focused on the cantilever. The interferometer senses the vertical distance d1 -d2 between the beam B1 close the cantilever tip and B2 close to the center. The probing points are separated of ∆x = x1 -x2 = 417 µm, ∆y = 0. The cantilever, in vacuum at 10 -7 mbar, is monolithically clamped to its macroscopic chip which is thermalised at temperature T min . When the laser power is low (P < 1 mW), we consider the system in thermal equilibrium. When the power is raised (10 to 40 mW), a temperature gradient T (x) along the cantilever arises.

FIG. 2 .

 2 FIG. 2. (Color online) Experimental thermal noise spectra. (a) The Power Spectrum Density (PSD) of d displays various resonance peaks, which we can distinguish between the flexural ones and torsional ones, respectively indicated by black solid arrows and red dashed arrows. The first resonance n = 1 is plagued by low-frequency noise and is thus discarded in the analysis. (b) Increasing the laser power causes a redshift in the resonance frequencies of the modes (in this case n = 3) as the Young's modulus of silicon decreases with temperature.(c) We measure at equilibrium (P < 1 mW) the frequency shift with respect to the lowest temperature, when the temperature of the cryostat slowly increases up to room temperature. This calibrates the Young's modulus dependency of temperature δY (T ) through Eq. 1 with T uniform.

FIG. 3 .

 3 FIG. 3. (Color online) Fluctuation temperature vs. average temperature, for flexion in (a) and torsion in (b). T avg sim (black solid line) and T max (black dashed line) are evaluated form the measured frequency shift and the calibration function coming from the numerical simulation. The apparent temperature T app (black dotted line) is evaluated from the measured frequency shift and the experimental calibration of the Young's modulus temperature dependency. Albeit dependent of T avg , the amplitude of fluctuations is well below those characteristics temperatures of the cantilever, showing a dearth of thermal noise. The red shaded area on the right covers measurements where at least a partial melting of the cantilever occurred. It is remarkable that in this area T fluc n,m greatly increases for most modes of both families. The uncertainties on T avg sim are discussed in Appendix A, and the ones on T fluc are discussed in the text and in more details in Ref. 13.

FIG. 4 .

 4 FIG. 4. (Color online) Loss angles ϕn of flexural modes (a)and ϕm of torsional modes (b) with respect to the average temperature of the cantilever. Due to experimental contraints and low sample size, the fit of the experimental spectra are often hard to compute, thus we show only the results of fits with a χ 2 < 3. For most modes, the general trend is an increase of dissipation with increasing temperatures. In order to visually assess this, in the insets we show the peak of the PSD of the second modes in flexion and torsion, widening from low to high temperature, depicted respectively in cyan (light grey) at T avg sim = 14 K and red (dark grey) at T avg sim = 474 K for flexion and T avg sim = 145 K for torsion. The uncertainties on the loss angles are discussed in the text.

FIG. 5 .

 5 FIG. 5. (Color online) Estimation of T avg and T max : from the parametric sweep reported in TableI, we estimate the possible values of the average and maximum temperature of the cantilever and at the same time the frequency shift for the mode numbers 6 to 9. The relations between these quantities are shown as yellow (light gray) and red (dark grey) curves. The dispersion of T avg , depicted as a yellow (light grey) shaded area, is small. As a result, the error associated to the experimental value of T avg at a given frequency shift, shown as cyan squares is also small. Conversely, the estimation of T max yields a wide parameter range displayed as a red (dark grey) shaded area. No bijective relation is possible, thus we estimate T max as the average of a uniformly distributed variable between the possible values at a given frequency shift. The purple (dark grey) dashed curve represents the retained value of T max for each frequency shift and the blue (dark grey) diamonds are the experimental values. In the inset we show a typical temperature profile T (x), with each of the two laser beams (at x1 and x2) injecting an absorbed power of 15 mW. We can see how T (x) is highly non-linear and peaked at the heating points.

TABLE I .

 I Parameter range for the temperature profile simulations.

		s	H [µm] T min [K]	a	AP [mW] n
	Parameter 0 -1 1-1.2 range	10-20 0.3 -0.7	1-35	6-9
	Central value	0.5	1.1	15	0.5	1-35	7

ACKNOWLEDGMENTS

The authors would like to thank L. Mereni and all the members of the Laboratoire des Matériaux Avnacés for the access to their clean room and to the Cryo-QPDI, and also for their technical support. Financial support from the LABEX Lyon Institute of Origins (Grant No. ANR-10-LABX-0066) of the Université de Lyon within the program "Investissements d'Avenir" (Grant No. ANR-11-IDEX-0007) of the French government operated by the National Research Agency (ANR) is acknowledged. This work has been also supported by the Fédération de Physique Ampère in Lyon, and the Mission pour l'Interdisciplinarité of the CNRS.

DATA AVAILABILITY

The data that support the findings of this study are openly available in Zenodo at https://doi.org/10. 5281/zenodo.4696490 [START_REF] Fontana | Dataset -Thermal noise of a cryo-cooled silicon cantilever locally heated up to its melting point[END_REF].

Appendix A: Temperature simulation

In this appendix, we describe the numerical resolution of the heat equation governing the cantilever temperature field and how to use the experimental frequency shifts to evaluate the average and maximum temperature with the help of these simulations.

The heat equation relating the temperature field to the heat fluxes in the problem is strictly speaking a 3D equation. However, since we are interested in length scales larger than ∼ L/10 = 100 µm (9 modes in flexion, 6 in torsion), no relevant phenomenon is expected along the thickness H = 1.1 µm. Along the width B = 90 µm, some 2D effects could start being noticeable. In ref. [START_REF] Fontana | Thermal fluctuations in an out-ofequilibrium system[END_REF], we show however that if the goal is to estimate T avg , reducing the problem to 1D yields a difference from the 2D of 5% at most, which we consider small with respect to other sources of uncertainty.

We thus write a stationary 1D heat equation for the cantilever:


OPTMix en bref

OPTMix vise à améliorer les connaissances sur le fonctionnement des forêts mélangées en région tempérée avec des applications directes à la gestion forestière en particulier dans le cadre des changements climatiques.

• Un site unique

• Trois facteurs sont contrôlés : la composition du peuplement, la densité du peuplement et la présence des herbivores ;

• le site est équipé de nombreux capteurs ;

• plusieurs services écosystémiques y sont étudiés (e. g. : production de bois, biodiversité) ;

• plusieurs approches scientifiques sont combinées : descriptive, écophysiologique et fonctionnelle, modèles basés sur les processus et modèles basés sur les observations ;

• Trois répétitions pour une surface totale de 40 ha dans la même forêt (47°46' -47°55' N, 2°17' -2°35' E) ;

• Le site est installé dans une forêt tempérée de plaine, avec du chêne sessile et du pin sylvestre, deux espèces importantes par leur surface couverte et par l'utilisation de leur bois ;

• le mélange chêne sessile -pin sylvestre est un des mélanges les plus répandus en France concernant les mélanges feuillus -résineux, et ces deux espèces ont des traits contrastés ;

• OPTMix est un dispositif de suivi à long-terme ;

• A proximité (20 à 50 km) Irstea dispose d'une pépinière expérimentale, de serres et d'un laboratoire.

  OPTMix: experimental site in mixed forest 5-6th Oct. 2021 / Korboulewsky et al.

  site in mixed forest 5-6th Oct. 2021 / Korboulewsky et al.

  Photo: G. Maisonneuve/irstea

  Preztsch et al. 2019, Eur J For Res Kędra et al. 2019, Ann For Sci Bello et al. 2019, Plant Soil p. 11 OPTMix: experimental site in mixed forest 5-6th Oct. 2021 / Korboulewsky et al. et al. 2019, For Ecol Manag Bello 2019, PhD Thesis p. 14 OPTMix: experimental site in mixed forest 5-6th Oct. 2021 / Korboulewsky et al.


Gerges El Haber

Laurent Noel

Ching-Fu Lin

Simon Gree

Loic Vidal

Hsiao-Wen Zan

Nelly Hobeika

Olivier Lhost

Yves Trolez

Olivier Soppera
email: olivier.soppera@uha.fr

Near-Infrared Laser Direct Writing of conductive patterns at the surface of Carbon nanotubes polymer nanocomposites

Keywords: Nanocomposite, Carbone Nanotubes, Laser treatment, Near-Infrared, Conductive polymer

Near-infrared (NIR) laser annealing is used to write conductive patterns at the surface of Polypropylene/Multi-walled carbon nanotube nanocomposite (PP/MWCNT) plates. Before irradiation, the surface of the nancomposite is not conductive due to the partial alignment of the MWCNT which occurs during injection molding. We observe a significant increase of the surface sheet resistance using NIR laser irradiation, which we explain by a randomization of the orientation of MWCNTs in the PP matrix melt by NIR laser irradiation. After only 5s of irradiation, the sheet resistance of PP/MWCNT, annealed with a laser at a power density of 7 W/cm 2 , decreases by more than 4 decades from ~ 100 MΩ/sq to ~ 1 kΩ/sq. Polarized Raman, TEM, and SEM are used to investigate the changes in the sheet resistance and confirm the physico-chemical processes involved. This allows directwriting of conductive patterns using NIR laser at the surface of nanocomposite polymer substrates, with the advantages of a fast, easy, and low-energy consumption process.

Introduction

The introduction of nanofillers in polymer matrices is a privileged approach to introduce specific functions to host matrices [START_REF] Müller | Review on the Processing and Properties of Polymer Nanocomposites and Nanocoatings and Their Applications in the Packaging, Automotive and Solar Energy Fields[END_REF][START_REF] Wang | Surface-tunable, Electrically Conductive and Inexpensive Graphene Platelets and their Hydrophilic Polymer Nanocomposites[END_REF] . Among the possible nanoobjects, carbon nanotubes (CNTs) are today widely used to improve the mechanical [START_REF] Bansal | Effect of MWCNT Composition on the Hardness of PP/MWCNT Composites[END_REF][START_REF] Kumar | A Review on the Mechanical Properties of Polymer Composites Reinforced by Carbon Nanotubes and Graphene[END_REF][START_REF] Wang | Engineering the Mechanical Properties of CNT/PEEK Nanocomposites[END_REF] , thermal [START_REF] Zhou | Thermal Properties and Thermal Stability of PP/MWCNT Composites[END_REF][START_REF] Bonnet | Thermal Properties and Percolation in Carbon Nanotube-Polymer Composites[END_REF][START_REF] Winey | Improving Electrical Conductivity and Thermal Properties of Polymers by the Addition of Carbon Nanotubes as Fillers[END_REF][START_REF] Jackson | Development and Thermal Properties of Carbon Nanotube-Polymer Composites[END_REF] , or/and electrical properties of polymers [START_REF] Wang | Enhancing the Electrical Conductivity of PP/CNT Nanocomposites through Crystal-Induced Volume Exclusion Effect with a Slow Cooling Rate[END_REF][START_REF] Zeng | Increasing the Electrical Conductivity of Carbon Nanotube/Polymer Composites by Using Weak Nanotube-Polymer i-Interactions[END_REF][START_REF] Zhou | Improvement in Electrical, Thermal and Mechanical Properties of Epoxy by Filling Carbon Nanotube[END_REF][START_REF] Yang | Simultaneously Improving the Mechanical and Electrical Properties of Poly(vinyl alcohol) Composites by High-Quality Graphitic Nanoribbons[END_REF][START_REF] Park | Modeling the Electrical Resistivity of Polymer Composites with Segregated Structures[END_REF][START_REF] Taherian | Investigation of the Electrical Properties of Polymer/Carbon Composites Exposed to Joule Heating and Heat Treatment[END_REF] .

Carbon nanotubes, especially multi-walled carbon nanotubes (MWCNTs), can be obtained in large quantities by well-established processes. MWCNTs can be introduced up to a few weight percent wt%, which is sufficient to significantly modify the properties of host matrices. One of the desired effects is to obtain conductive polymers that may be of interest for applications such as 3D printed electronics [START_REF] Ghoshal | Polymer/Carbon Nanotubes (CNT) Nanocomposites Processing Using Additive Manufacturing (Three-Dimensional Printing) Technique: An Overview[END_REF][START_REF] Liu | Precise 3D printing of micro/nanostructures using highly conductive carbon nanotube-acrylate composites[END_REF] , electrostatic discharge materials, and electromagnetic interference shielding materials. [START_REF] Lee | Carbon Nanotubes-Polypropylene Nanocomposites for Electrostatic Discharge Applications[END_REF][START_REF] Pande | Mechanical and Electrical Properties of Multiwall Carbon Nanotube/Polycarbonate Composites for Electrostatic Discharge and Electromagnetic Interference Shielding Applications[END_REF][START_REF] Yadav | Polymer Composite for Antistatic Application in Aerospace[END_REF][START_REF] Hosseini | Filler-Free Conducting Polymers as a New Class of Transparent Electromagnetic Interference Shields[END_REF][START_REF] Zhang | Injection Molding of Segregated Carbon Nanotube/Polypropylene Composite with Enhanced Electromagnetic Interference Shielding and Mechanical Performance[END_REF] Many methods to produce such nanocomposite materials can be listed. Among them, melt blending 23- 24 offers a simple way of dispersing nanoparticles in a polymer matrix and it is now widely used in industries to manufacture polymer parts [START_REF] Dönmez | Influence of Injection Molding Parameters on Electrical Resistivity of Carbon Nanotube Reinforced Polycarbonate[END_REF][START_REF] Mi | Effects of Three Different Injection-Molding Methods on the Mechanical Properties and Electrical Conductivity of Carbon Nanotube/Polyethylene/Polyamide 6 Nanocomposite[END_REF][START_REF] Torres-Giner | Injection-Molded Parts of Polypropylene/Multiwall Carbon Nanotubes Composites with an Electrically Conductive Tridimensional Network[END_REF][START_REF] Stanciu | Rheological, Mechanical, and Electrical Properties of Polypropylene/Multi-Walled Carbon Nanotube Nanocomposites[END_REF] . A weight percentage higher than the percolation threshold can be used to obtain electrically conductive materials. [START_REF] Zare | Simulation of Percolation Threshold, Tunneling Distance, and Conductivity for Carbon Nanotube (CNT)-Reinforced Nanocomposites Assuming Effective CNT Concentration[END_REF][START_REF] Shi | Ultralow Percolation Threshold in Poly(l-lactide)/Poly(ε-caprolactone)/Multiwall Carbon Nanotubes Composites with a Segregated Electrically Conductive Network[END_REF][START_REF] Penu | Rheological and Electrical Percolation Thresholds of Carbon Nanotube/Polymer Nanocomposites[END_REF] For example, Seo et al. [START_REF] Seo | Crystallization Kinetics and Interfacial Behaviors of Polypropylene Composites Reinforced with Multi-Walled Carbon Nanotubes[END_REF][START_REF] Seo | Electrical Resistivity and Rheological Behaviors of Carbon Nanotubes-Filled Polypropylene Composites[END_REF] stated that once the percolation threshold is exceeded ("between 1 and 2 wt%") the volume resistivity drops from 10 9 Ω.cm to reach a value of 10 3 Ω.cm.

Regarding the surface conductivity of nanocomposites, it was reported that the melt blending processes may induce a forced alignment effect [START_REF] Collet | Electrical Conductivity Under Shear Flow of Molten Polyethylene Filled With Carbon Nanotubes: Experimental and Modeling[END_REF] . This alignment does not result in a wellinterconnected network; therefore, surface electrical conductivity is very low, even when the percolation threshold is exceeded in the bulk (typically in the range of 10 7 -10 8 /Sq). Surface electrical conductivity can be enhanced by thermal annealing. When the treatment temperature surpasses the melting temperature of the polymer, entropic effects break the alignment of CNTs, creating connections between the nanotubes that improve the conductivity of the material.

However, thermal curing suffers from certain limitations. First of all, it requires that the entire part obtained after injection is placed in a furnace. Secondly, the process is long, energy-consuming, and for complex 3D objects, annealing above the melting temperature can damage the shape of the object.

Finally, the whole surface is treated homogeneously, which prevents applications for which a local effect would be sought, for example, to create conductive circuits on an insulating surface.

In this paper, we demonstrate that we can enhance significantly the surface electrical conductivity of polypropylene/Multi-walled carbon nanotube nanocomposite plates by near-infrared (NIR) laser treatment and use it to generate conductive patterns at the surface of the nanocomposite. The interest of such a treatment lies in a short curing time (a few seconds) while keeping the same efficiency as a global heat treatment in terms of surface conduction enhancement [START_REF] Colucci | A Novel Approach to Obtain Conductive Tracks on PP/MWCNT Nanocomposites by Laser Printing[END_REF][START_REF] Xiong | Laser-Directed Assembly of Aligned Carbon Nanotubes in Three Dimensions for Multifunctional Device Fabrication[END_REF][START_REF] Chang | Laser Polymer Tattooing: A Versatile Method for Permanent Marking on Polymer Surfaces[END_REF][START_REF] Caradonna | Laser Treatments for Improving Electrical Conductivity and Piezoresistive Behavior of Polymer-Carbon Nanofiller Composites[END_REF] . Above all, the laser treatment can be localized in space, allowing the direct writing of conductive patterns. A continuous wave infrared laser was used, due to the strong absorption of CNTs for such wavelengths (808 nm), as well as the availability of high-power commercial lasers in this wavelength range.

In this article, we demonstrate the effect of the laser on the surface electrical conductivity, which we compare to classical heat treatments. Then, a study of the physico-chemical phenomenon causing the decrease in sheet resistance at the nanocomposite surface was carried out, mainly by combining polarized Raman and TEM results. These new results confirm results reported by other teams on the possibility to modify the surface properties of PP/MWCNTs nanocomposites by laser irradiation. [START_REF] Gedvilas | Percolation Effect of a Cu Layer on a MWCNT/PP Nanocomposite Substrate after Laser Direct Structuring and Autocatalytic Plating[END_REF][START_REF] Ratautas | Laser-Induced Selective Metallization of Polypropylene Doped with Multiwall Carbon Nanotubes[END_REF] These results were also compared polypropylene (PP), filled with carbon black (CB). Finally, we illustrate the interest of this approach by showing a basic circuit written by the NIR laser at the surface of the PP nanocomposite plate allowing the lightening of a LED without any post-treatment after laser writing.

Experimental section

Materials

A MWCNT-Polypropylene (PP) masterbatch has been produced as described in 41 . Average diameter and average length are, respectively, 9.5 nm and 1.5 µm, as measured by TEM. The surface area is 250-300 m 2 /g, as determined from BET surface area analysis. This masterbatch was then diluted in a TotalEnergies commercial grade (PPC12642, a grade characterized by a melt flow index MFI of 70 g/10 min.).

Plates with a dimension of 60 x 60 x 1 mm 3 (length x width x thickness) were prepared by injection molding in a Dr Boy machine (Imposed temperature profile, from the hopper to the injection die: 200, 220, 230, 250 and 250°C, injection speed = 10 mm/s, injection pressure = 43 bars, injection time = 3.92 s, mold temperature = 70°C). Pure PP plates (PPC12642) and PP doped with 4 wt% of MWCNT were used in this study. Both concentrations are above the percolation threshold, [START_REF] Lecocq | Polypropylene/Carbon Nanotubes Composite Materials with Enhanced Electromagnetic Interference Shielding Performance: Properties and Modeling[END_REF] but the surface electrical conductivity is low due to the injection molding process (100 MΩ/sq).

Polypropylene/carbon black (PP/CB) nanocomposites were prepared by the same process, with CB nanoparticles. The CB content is 4 wt %.

Laser treatment

A Coherent-Compact SE Series continuous Near-infrared NIR laser was used for surface treatment of the nanocomposite plates. The nominal power is 50 W. The wavelength is 808 nm, with a typical circular spot diameter of 0.8 cm, with a homogeneous power density produced by a collimating lens at the end of the fiber.

Characterization

Electrical measurements

The sheet resistance R S was the chosen property to evaluate the electrical conductivity at the surface of the nanocomposite. Electrodes were deposited by sputtering of 10 nm of gold (Cressington Sputter Coater 108auto) with a shadow mask to define square areas. The probe area was a rectangle of 2mmx4mm. A digital multimeter, Keithly's Series 2636B, was used to monitor the I-V curves. The sheet resistance R sheet was calculated using the slope of the I-V curve (R measured ) and the following equation: R sheet =2 x R measured .

Polarized Raman spectroscopy

Polarized Raman spectra of the nanocomposite were recorded using a HORIBA -Model Labram 300 spectrophotometer. The polarized laser (532 nm) was focused at the surface of the nanocomposite with an x100 objective (beam diameter of the laser spot about 2 μm). 10 spectra were acquired for each sample, and an average spectrum, with standard error and baseline subtraction, was calculated. The spectra were then normalized with the peak at 2885 cm -1 of the PP.

Electron microscopy

For transmission electronic microscopy (TEM) thin sections (< 100 nm) were prepared by ultramicrotomy. These sections were made in three directions: parallel to the injection direction 0°, perpendicular to the injection direction 90°, and at an intermediate angle of 45° between these two preferred directions. An ARM200F JEOL High-Resolution transmission electron microscope (TEM) was used.

Scanning electron microscopy (SEM) was used to observe the morphological change occurring before and after laser treatment, especially at the surface of the nanocomposite sample (JEOL JSM-7900F LV).

Results and discussion

This first section is aimed at describing the effect of the laser on the surface conductivity of the material. A parametric study of the irradiation conditions and their impact on the electrical properties of the nanocomposite is proposed. The effect of laser on the surface conductivity is expected to be very strongly dependent on the irradiation conditions. As expected, the sheet resistance decreases significantly with the increase of laser energy dose in both cases. The minimum value (10 3 /Sq) was obtained for 35 J/cm 2 . Then a plateau is observed up to about 55 J/cm 2 . Deformation of the sample surface was observed from this value, which shows that the induced thermal effect is too strong to guarantee the sample's integrity. These conditions were ruled out later on.

There is a significant deviation between experiments conducted at a constant time and a constant power density, for low doses (< 35 J/cm 2 ). This deviation highlights the existence of a threshold power below which the phenomenon is not effectively initiated. This threshold power density can be evaluated at about 4 W/cm 2 (i.e., 20 J/cm 2 for an irradiation duration of 5 s). Below this threshold, the heat losses may be such that the melting temperature cannot be reached.

It is interesting to compare these results with those obtained by thermal annealing. To have a point of comparison, the same samples were placed on a hot plate at different temperatures between 50 and 250°C. An increase in surface conductivity could be qualitatively demonstrated (using an ohmmeter), but no reliable measurement could be made because the samples were deformed entirely under the effect of heat, and it was not possible to rigorously deposit the electrodes by controlling the distance between electrodes (see result at 230°C, third raw in Figure 2.b). This point demonstrates the decisive advantage of laser treatment over heat treatment. This second section aims to describe the physico-chemical phenomena explaining the modification of electrical properties induced by the laser. Transmission electron microscopy (TEM) and polarized Raman analyses were performed to describe the evolution of the material upon laser irradiation.

Polarized Raman analysis is very interesting in this context since it allows the detection of the presence of MWCNTs and gives information about their orientations [START_REF] Liang | Sessile Droplets Containing Carbon Nanotubes: a Study of Evaporation Dynamics and CNT Alignment for Printed Electronics[END_REF][START_REF] Yang | Broadband Laser Polarization Control with Aligned Carbon Nanotubes[END_REF][START_REF] Liu | Strengthening Carbon Nanotube Fibers with Semi-Crystallized Polyvinyl Alcohol and Hot-Stretching[END_REF][START_REF] Qian | Mapping Local Microstructure and Mechanical Performance around Carbon Nanotube Grafted Silica Fibres: Methodologies for Hierarchical Composites[END_REF][START_REF] Lee | Carbon Nanotube Fibers with Enhanced Longitudinal Carrier Mobility for High-Performance All-Carbon Thermoelectric Generators[END_REF][START_REF] Choi | Flexible and Robust Thermoelectric Generators Based on All-Carbon Nanotube Yarn without Metal Electrodes[END_REF][START_REF] Arjmand | Electrical and Electromagnetic Interference Shielding Properties of Flow-Induced Oriented Carbon Nanotubes in Polycarbonate[END_REF][START_REF] Abbasi | Flow Induced Orientation of Multiwalled Carbon Nanotubes in Polycarbonate Nanocomposites: Rheology, Conductivity and Mechanical properties[END_REF][START_REF] Khan | Effects of Carbon Nanotube Alignment on Electrical and Mechanical Properties of Epoxy Nanocomposites[END_REF][START_REF] Nam | Improving Mechanical Properties of High Volume Fraction Aligned Multi-Walled Carbon Nanotube/Epoxy Composites by Stretching and Pressing[END_REF][START_REF] Beigmoradi | Engineering of Oriented Carbon Nanotubes in Composite Materials[END_REF] . Raman spectra of nanocomposites before and after laser treatment. Polarization directions are usually referred to V (following Ox) and H (following Oy). Excitation and analysis lights can be polarized. In our case, we consider VV and HH modes, the collection and analysis being done in the same direction.

The configurations used in this study: VV corresponds to the direction parallel to the injection direction, HH corresponds to the direction perpendicular to the injection direction (Figure 3.c). For PP, we clearly observe the band at 808 cm -1 which is related to the presence of PP in crystallized form. The relative intensity of this band compared to the band at 840 cm -1 decreases during the laser process, which is in agreement with previously published results, [START_REF] Ratautas | Laser-Induced Selective Metallization of Polypropylene Doped with Multiwall Carbon Nanotubes[END_REF] showing an increase in defects in the crystallized PP phase. This effect was confirmed by TEM characterization, presented in Figure 4. Thin sections (< 100 nm) were prepared by ultramicrotomy. These sections were made along with three directions: VV (parallel to the injection direction "0°"), HH (perpendicular to the injection direction "90°"), and at an intermediate angle of 45° between these two preferred directions. Samples before and after laser treatment are compared in this Figure . MWCNTs have stronger absorption of the e-beam than the PP matrix, which makes it possible to directly observe them in TEM and define their relative orientation in the sample versus the direction of the e-beam. These observations by TEM should be considered carefully because one of the difficulties is to ensure the representativeness of the selected sample because it is an observation on a very local scale. On the other hand, coupled with polarized Raman, we can deduce that the initial orientation of MWCNT at the surface of the sample after injection is broken during laser irradiation.

To sum up, a scheme representing the MWCNTs embedded in the polymer matrix before and after laser treatment is presented in MWCNTs, are aligned due to the injection molding process. Theoretically, the nanocomposite should be conductive regarding to the content of MWCNTs in the PP matrix (4 wt%) that exceeds the percolation threshold, but this was not the case because of the alignment of the MWCNTs. The alignment caused by the manufacturing method prevents the nanotubes from connecting to each other. Therefore, we cannot detect any electrical conductivity even when the percolation threshold is exceeded. The MWCNTs are highly absorbent at the NIR wavelength. Irradiation by the NIR laser makes it possible to locally exceed the melting temperature of the PP, which leads to a random redistribution of the MWCNTs, thus creating the connections between MWCNTs. This physicochemical phenomenon explains the induced electrical conductivity measured at the nanocomposite surface after being insulated with NIR laser. This hypothesis was confirmed by the last experiment in which we showed that conduction could only be obtained in the presence of MWCNTs, e.g., nanofillers with a very high form factor. We compare hereafter the results obtained with a nanocomposite PP/CB, a PP matrix filled with carbon nanoparticles (carbon black CB). Example of conductive track written with 0.75 W (beam diameter 1.2 mm) with a writing speed of 2 mm/sec. The 2 tracks (2 x 1.5 cm) connect a LED that is switched on with a 4.5 V battery.

The images presented in Figure 5.a show that the interaction between the material and the laser is very effective in the case of CB nanofiller. The nanocomposite PP/CB surface was even more deformed for the same irradiation conditions compared to PP/MWCNT. However, even though this observation proves that the melting point was reached, PP/CB had almost no electrical surface conductivity after laser treatment, as shown in Figure 5.b. This result confirms two points about the proposed mechanism. The first point is that the surface electrical conductivity is only obtained with MWCNTs. MWCNTs can generate conduction channels over large distances, and this ability is obtained when contacts occur between them after laser irradiation. The second point is that the surface electrical conductivity cannot be explained by a graphitization of the surface induced by laser treatment. Indeed, this mechanism could be proposed as a possibility considering the high fluence of the laser but it should then be observed not only for MWCNTs but also CB. Moreover, neither the Raman spectra nor the TEM analyses show such a layer. Therefore, we can exclude this mechanism and conclude that the main physico-chemical mechanism is the reorganization by photothermal effect of the MWCNTs, as explained above.

Finally, we illustrate with an example that the laser treatment can be applied on a moving substrate, in order to generate a conductive track of several cm on the nanocomposite surface (Figure 5.c). In this case, a 1.2 mm diameter beam is used to irradiate the sample. The sample moves at a speed of 2 mm/sec with a translation stage. The power is 0.75 W. With these parameters, each point of the irradiated line receives a power of about 40 J/cm 2 , which is of the same order of magnitude as the conditions used in static previously. The written line is visible in Figure 5.d. The resistance of a 1.5 cm line was measured as 100 k. This value allows, as shown on the photograph, to light an LED powered by a 4.5 V battery. This example is only an illustration of potential applications of this process useful to write conductive patterns on the surface of a non-conductive material. One can imagine applications in the field of connectors, sensors or antennas for example.

Conclusion

We have demonstrated that the surface conductivity of PP/MWCNTs nanocomposites can be locally enhanced by NIR laser irradiation. The impact of the main parameters and the study of the physicochemical phenomena have been carried out. By coupling polarized Raman and TEM studies to surface conductivity measurements, it was possible to show that the absence of conductivity, even for CNT levels above the percolation threshold, can be explained by an alignment of the MWCNTs during the injection process. The strong absorption of MWCNTs in the NIR allows the polymer surface to be heated locally above the melting point. The mobility of the MWCNTs allows a random reorganization of the MWCNTs which creates conduction channels in the material. Thus, a 5 sec. irradiation with a power density of 7 W/cm 2 is sufficient to increase the surface conductivity by more than 4 orders of magnitude. These results open the door to the integration of electronic circuits on the surface of plastics by very simple processes.

Figure 1 .

 1 a displays a photograph of the laser head and sample during irradiation. Figure1.b shows a scheme of the laser procedure and pictures of the samples before and after laser treatment. On both samples, gold electrodes were deposited with an identical pattern throughout the study, which allows us to compare the effect of different parameters.In this first example, an irradiation time of 5 seconds and a power density of 7 W/cm 2 were used. A change in the surface morphology of the sample after laser treatment was observed in the SEM image shown in Figure1.c. The insulated area displayed a smoother surface compared to the non-insulated site, proving a melting effect caused by the laser treatment. On a macroscopic scale, the same irradiation conditions caused no noticeable deformation of the nanocomposite plate. This preservation of the integrity of the material is a crucial point sought in this study.The I-V curves are shown in Figure1.d. It is verified that the conduction is very low on the sample surface before laser treatment, even though the concentration of MWCNT exceeds the threshold concentration. This result is in line with the envisaged MWCNT alignment process. This point will also be confirmed by Raman spectroscopy and microscopy analyses afterward. The effect of the laser treatment is clear. After laser treatment, the I-V curve of the insulated zone presents a linear behavior with a significant curvature slope compared to the slope value measured before the laser treatment.These initial results clearly show the effectiveness of laser treatment in increasing the electrical conductivity of the material. The sheet resistance values given in Figure1.e were calculated using the model shown in the experimental part. The laser treatment drops the surface sheet resistance by more than 4 orders of magnitude from 8.4x10 7 /Sq to 1.8x10 3 /Sq. Besides, we did not notice any difference of conductivity parallel and perpendicular to the direction of injection.

Figure 1 .

 1 Figure 1. a) Photograph of the sample during NIR laser treatment. b) Schematic of the laser process

Figure 2 .

 2 a shows the evolution of the sheet resistance as a function of the laser energy dose used to irradiate the sample. This energy dose was defined as the multiplication of the power density by the irradiation time. Here, we compared the effect of the dose on the sheet resistance for constant irradiation time and constant power density.

Figure 2 .

 2 Figure 2. a) Evolution of the sheet resistance versus the light energy dose for a fixed irradiation time (5 sec) with different irradiation power density (pink curve) and a fixed power density (7 W/cm 2 ) with

Figure 3 .

 3 a & 3.b show the

Figure 3 :

 3 Figure 3: a) Polarized Raman spectra before laser treatment, in two configurations HH & VV. b)

Figure 4 .

 4 Figure 4. a, b, c) TEM images of the nanocomposite with three different angles of perspective (0, 45,

Figure 4 .

 4 Figure 4.a, 4.b & 4.c, as well as zoom in the zone of interest (Figure 4.d, 4.e & 4.f). The

Figure 4 .

 4 m & 4.n respectively made based on Polarized Raman and TEM results, showing the orientation of MWCNTs that changed due to the laser treatment. The

Figure 5 .

 5 Figure 5. a) Images of PP / MWCNT and PP / CB nanocomposites (4 wt % for each) before and after


Karin El Rifaii

Patrick Davidson

Laurent Michot

Cyrille Hamon

A Davidson

Gold-clay nanocomposite colloids with liquid-crystalline and plasmonic properties

Electronic Supplementary Information (ESI) available: Materials and methods and table of sample compositions, additional TEM images, sketch of the phase diagram, influence of beidellite concentration, size distributions of beidellite nanosheets and gold nanoparticles, additional SAXS and WAXS data of beidellite/gold suspensions, and influence of an a.c. electric field on a biphasic beidellite/gold suspension See

Imparting liquid-crystal (LC) materials with the plasmonic of metal nanoparticles is actively pursued for applications. We achieved this goal by synthetizing gold nanoparticles onto clay nanosheets, leading to nematic nanocomposite suspensions. Optical observations and structural analysis show the growth of the gold nanoparticles without altering the LC properties of the nanosheets. These colloids display plasmonic structural colours and they can be aligned by an electric field, which is relevant for fundamental and materials chemistry of colloidal LC.

Anisotropic nanoparticles (NPs) can spontaneously self-assemble in colloidal suspension and display liquid-crystal (LC) organizations. The conditions to obtain colloidal LC in aqueous solvent are met for particles with high aspect ratio (e.g. rods, plates) and long-range electrostatic repulsive particle interactions. 1,2 An emblematic example is the LC nematic phase of natural clay nanosheets. 3,4 Interestingly, such LC organizations can often be observed at low volume fraction (e.g. < 1%), resulting in typical distances between objects of hundreds of nanometers. For instance, aqueous suspensions of phosphatoantimonate, niobate, titanate, and zirconium hydrogenphosphate nanosheets display photonic properties that can be tuned by adjusting their volume fraction and thus their lamellar period from 150 to 600 nm. [5][6][7][8] Similarly, aluminosilicate nanotubes form a hexagonal LC columnar phase at volume fractions as low as 0.2%. 9 Detailed studies of colloidal LC have shown that the pH, ionic strength, and the addition of chemicals could be used to control the interparticle distance. 7,8,10 Moreover, colloidal LC readily respond to external fields, providing ways for dynamic control over the orientation of the particles. 11,12 Gold NPs can very efficiently absorb and scatter light because of their ability to support coherent oscillations of electrons, the so-called surface plasmon resonance that is sensitive to the morphology of the NP and the polarization of the incident light. 13 Combining colloidal LC with plasmonic NPs is promising toward reconfigurable metamaterial designs and dynamic colour displays driven by the facile response of the medium and the NPs to external stimuli. [START_REF] Stamatoiu | Liquid Crystals: Materials Design and Self-Assembly[END_REF][START_REF] Neubrech | [END_REF][16][17][18][19][20] However, so far, advances in this direction have been mainly achieved by dispersing gold NPs in molecular LC hosts. Surprisingly, the successful combination of colloidal LC and gold NPs, in which the suspension would be both mesostructured and coloured, are quite scarce and mostly deal with nanowires rather than nanosheets. [21][22][23][24][25] The strong sensitivity of colloidal LC to ionic strength and molecular additives presumably limits the chemistry that can be employed to obtain a plasmonic colloidal liquid crystal. In this work, we achieved a successful marriage between the colloidal LC host and the gold NP dopant by synthetizing gold NPs at the surface of beidellite clay nanosheets, in-situ, forming a plasmonic clay-based nanocomposite colloid. Although beidellite LC suspensions are mesostructured, they are usually colourless because the typical distance between nanosheets is lower than  150 nm. The gold NPs in the gold/beidellite nanocomposites that we prepared impart them with vivid blue or red plasmonic structural colours. In addition, we explored the influence of the concentrations of gold and beidellite on the stability of the colloidal nematic LC. Finally, we show that the nanocomposite colloids can be efficiently manipulated with electric fields. In a typical synthesis (see ESI for experimental details), the proper amount of HAuCl4 was added to a beidellite aqueous suspension, followed by that of ascorbic acid (reducing agent), under vigorous stirring at room temperature. The reaction is instantaneous, as shown by the rapid colour change of the samples. In order to explore the influence of both the beidellite weight fraction and the gold precursor concentration, respectively labelled Cbeid and Cgold hereafter, we prepared series of samples where only one of the two parameters was varied. Moreover, the concentration ratio of HAuCl4 to ascorbic acid, Caa, was kept constant to Caa/Cgold = 10 for all syntheses. This journal is © The Royal Society of Chemistry 20xx

Please do not adjust margins Please do not adjust margins Fig. 1a shows a series of samples, observed in natural light, with constant Cbeid but with Cgold increasing from left to right, in a logarithmic way. The first sample is a control with no HAuCl4 and is completely colourless and homogeneous. By comparison, in the other vials, the growth of gold NPs induces the appearance of blue (Cgold = 0.047 and 0.16 mM) or red colours (Cgold = 0.47 and 1.6 mM). electron microscopy (TEM) observation confirmed the conjugation of gold NPs at the surface of the nanosheets, with a number of NPs per nanosheet varying from one to a few (Fig. S1-3, ESI). The number of gold NPs per nanosheet increased with Cgold but bare nanosheets were still frequently observed at all Cgold. This heterogeneity presumably induces differences in sedimentation, with heavier nanocomposite colloids localized at the bottom of the vials (smaller gravitational length), resulting in the vertical absorption gradient observed in Fig 1b .  Such gradient is hardly visible in sample 6, which could be due to its very strong light absorption and the fact that it is a gel. Overall, the growth of gold NPs in the beidellite suspensions does not compromise their colloidal stability. In contrast, gold NPs prepared without beidellite flocculated within 2h after synthesis, except for the lowest Cgold (Fig. S4). Nanocomposites were dialyzed against MQ water to remove molecular species from the dispersion and reduce the ionic strength. While samples 3-4 were biphasic before dialysis and 5-6 were gels, samples 3-6 turned monophasic (Fig. S6). This experiment shows that the salts used in the synthesis destabilize the LC properties of the host, which can be recovered upon dialysis. It also shows that the nanosheets stabilize the gold NPs since the system is stable without capping ligand (ascorbic acid). The stability of the gold NPs synthetized at the surface of beidellite is presumably due to the long-range electrostatic repulsions between the negatively-charged nanosheets. 25 Close inspection of the nanocomposite in TEM revealed beidellite nanosheets, visible in light-gray and gold NPs as black objects (Fig. 2, Fig. S1-3, ESI). The beidellite size distribution (Fig. S5, ESI) has a mean of  280 nm and a polydispersity of 50%, values which remain very close to those of the initial beidellite batch. The gold NPs usually appear at the rim of the beidellite nanosheets (Fig S3 ,ESI), possibly due to an electrostatic attraction between oppositely-charged objects. The TEM images also revealed the formation of two different kinds of gold NPs. Nanostars were detected at moderate Cgold (samples 3 and 4, Fig. 2c) whereas compact spherical NPs were found at higher Cgold (samples 5 and 6, Fig. 2b). The two different morphologies in samples 3-4 and 5-6 explain why the corresponding colours of the suspension are markedly different. The star-like particles are  21 nm in size whereas the spherical ones are  18 nm in diameter. (Fig. S5, ESI.) The colour variation of the samples was studied more quantitatively by extinction spectroscopy (Fig. 1c). The pure beidellite suspension shows no absorption peak in the visible range, as expected, 26 and sample 2 does not either, probably due to the high dilution of the gold species. In contrast, samples 3 and 4 display broad absorption peaks at  650 nm, consistent with their blue colour, with peak intensity increasing with Cgold. Furthermore, samples 5 and 6 have broad and strong absorption peaks at  530 nm, in line with their red colour, with peak intensity also increasing with Cgold. The dark coloration in sample 6 is due to the high Cgold. The observation of the samples between crossed polarizers (Fig. 1b) shows that they remain birefringent after gold NP synthesis. More precisely, the pure beidellite suspension has a single birefringent phase which is nematic. 4,27 Sample 2, which has the lowest Cgold, behaves in the same way. In contrast, samples 3 and 4 spontaneously demix in two phases: an isotropic phase at the top and the denser birefringent nematic at the bottom. Therefore, these samples belong to the biphasic domain in between the stability regions of the nematic and isotropic liquid in the phase diagram of the beidellite suspensions. In other words, although the nematic phase is not suppressed by the presence of gold NPs, it is destabilized with respect to the isotropic liquid phase (see a sketch of the phase diagram Fig. S7a,ESI). Very similar observations were made when beidellite clay suspensions were doped with either silica spheres or non-ionic flexible polymers. 28,29 Moreover, as expected, the nematic phase Please do not adjust margins Please do not adjust margins vanished when the beidellite nanosheet concentration was decreased from 1.61 wt% to 0.805 wt% (Fig S8). 4,27 This however did not impact the plasmonic properties of the nanocomposite colloid (Fig. S9). Upon further increase of Cgold, the phase separation disappears, which is probably due to the fact that the samples become weak gels.

The small-angle X-ray scattering (SAXS) patterns of the birefringent phases of the samples only show broad scattering peaks typical of a liquid-like organization (Fig. 3a,b). Yet, these patterns are anisotropic. These two features together prove that the birefringent phases are actually nematic LC, as already reported for pure beidellite suspensions. 4,27 The SAXS patterns are mostly dominated by the contribution of the beidellite nanosheets and the gold NPs must then be randomly distributed within the nematic phase. The azimuthallyaveraged scattered intensity I(q) (see Materials and Methods) of samples with and without addition of HAuCl4 are qualitatively very similar (Fig. 3c,d). The peak position shifts towards lower angle in the presence of gold NPs, which points to an increased separation (65 nm instead of 47 nm) between clay nanosheets in the nematic phase. This might be due to the steric hindrance imposed by the gold NPs to the clay nanosheets, which could keep them further apart. The SAXS signal of dilute suspensions has a q -2 dependence typical of 2-dimensional objects (Fig. S10, ESI) while the WAXS signal shows the diffraction peak typical of the internal structure of the beidellite nanosheets (Fig. S11,ESI). Both of these features confirm that the growth of gold NPs does not alter the structure of the beidellite nanosheets. Hereafter, we show that the electric-field alignment property of the colloidal suspensions is preserved in the presence of the gold NPs. Fig. 4 shows the effect of an a.c. electric field on the nematic phase of a beidellite/gold suspension filled into a cylindrical glass capillary. In the absence of field (Fig. 4 a,b), there is no marked light-transmission variation when the capillary axis lies parallel or at 45° from the polarizer direction. However, under field, the sample appears almost completely dark when the capillary is parallel to the polarizer direction (Fig. 4c) but much brighter when it lies at 45° (Fig. 4d). This is proof of the good macroscopic alignment of the nematic phase. The alignment proceeds from the tendency of the clay nanosheets to rotate parallel to the electric field due to the polarization of their counter-ion clouds. 30 This property is kept after the growth of the gold NPs. The isotropic phase of beidellite/gold suspensions, at lower volume fraction than that of the nematic phase, also has similar field-alignment properties. Without field, it appears completely dark between crossed polarizers but it becomes very bright as soon as the field is applied (Fig. S12,ESI). This giant Kerr effect of the isotropic phase, well known for pristine beidellite nanosheets, 30 is also kept when gold NPs are grown onto the nanosheets. In contrast with the nematic phase, it can be used to adjust the degree of nanosheet orientational order, from none to complete alignment, simply by tuning the intensity of the field. In this work, we successfully combined the mesostructuration of a colloidal LC with the vivid colours imparted by gold NPs grown on beidellite nanosheets. Altogether, our optical, UVvis, and X-ray scattering experiments show that gold NPs of two different morphologies (stars and spheres) could be grown on clay nanosheets, preserving the nematic organization of the beidellite nanosheet suspensions. Moreover, both the isotropic liquid and the nematic phases kept their electric-field Fig. 3 SAXS patterns of nematic samples with constant Cbeid = 1.61 wt% a) with no HAuCl4 (sample 1 in Fig. 1); b) with Cgold= 0.16 mM (sample 4 in Fig. 1);(c,d) the corresponding curves of azimuthally-averaged scattered intensity in Kratky representation, q 2 I(q) vs q.

Fig. 1

 1 Fig. 1 Photographs of beidellite/gold samples observed in a) natural and b) polarized light, with Cbeid = 1.61 wt % and Cgold increasing from left to right : Cgold = 0, 0.016 , 0.047, 0.16,0.47, and 1.6 mM; c) their respective UV-Vis absorption spectra.

Fig. 2

 2 Fig. 2 TEM images showing gold NPs grown at the surface of beidellite nanosheets. (a) is a representative image of sample 5, showing gold NPs on beidellite nanosheets as well as bare nanosheets. (b,c) respectively show magnified images of a NP and a nanostar observed in samples 5 and 4 respectively.

Fig. 4

 4 Fig. 4 Polarized-light microscopy images showing the alignment by an electric field of the nematic phase of a beidellite/gold suspension (Cbeid = 1.61 wt%, Cgold = 0.16 mM, sample 4 in Fig 1.) in a cylindrical capillary of 1 mm diameter. (a,b) Without field; (c,d) in an a.c. field (red arrow, 500 kHz, 125 V rms). (Dashed lines show the borders of the electrodes. The white arrows show the polarizer and analyzer directions.)

Acknowledgements

Claire Goldmann and Thomas Bizien are gratefully acknowledged for help with, respectively, the synthesis of the gold/beidellite nanocomposite colloids and the use of the Swing beamline. We acknowledge SOLEIL for provision of synchrotron radiation facilities (under the approved proposal # 20191221). TEM observations were performed at the Imagerie-Gif core facility supported by l'Agence Nationale de la Recherche (ANR-11-EQPX-0029/Morphoscope; ANR-10-INBS-04/FranceBioImaging; ANR-11-IDEX-0003-02/Saclay Plant Sciences).

Notes and references

Conflicts of interest

There are no conflicts to declare.