Y Corre

G Laffont

C Pocheau

R Cotillard

J Gaspar

N Roussel

M Firdaouss

J.-L Gardarein

D Guilhem

M Missirlian

Integration of fiber Bragg grating temperature sensors in plasma facing components of the WEST tokamak

Plasma Facing Components (PFC) temperature measurement is mandatory to ensure safe high power and long pulse tokamak operation. IR thermography systems which are widely used in magnetic fusions devices become challenged with the choice of tungsten as a PFC material in the ITER tokamak, mainly due to emissivity uncertainties and reflection issues in a hot environment. Embedded temperature measurements are foreseen to cross-check the IR thermography measurements. Fiber Bragg grating sensors are potentially of great interest for this application because they are immune to electromagnetic interference and allow the measurement of a large number of temperature spots on a single fiber. Four optical fiber temperature sensing probes, each of them including 11 regenerated fiber Bragg gratings equally spaced by 12.5 mm (equivalent to one ITER-like tungsten monoblock), have been specifically designed and manufactured for the WEST project (W-tungsten Environment and Steady State Tokamak). The four probes are embedded in W-coated graphite components at two different distances from the surface, 3.5 mm and 7 mm, to cover a wide range of temperatures up to 900 • C. This paper addresses the design and integration issues and the qualification and performance assessment performed in the laboratory. It also shows the first measurements of this new diagnostic achieved in a tokamak environment during baking of the machine and during early diverted plasma exposure.

I. INTRODUCTION

Fiber Bragg Gratings (FBGs) are well-established strain and temperature transducers finding numerous applications in both scientific and industrial fields. 1 They present great interest in the field of nuclear fusion research because they are immune to electromagnetic interference (EMI). FBG strain or temperature sensors are foreseen in the ITER tokamak in the magnet structure (temperature between 4.5 K and 300 K), 2 in the helium cooled lithium lead Test Blanket Module 3 and also in the vacuum vessel. 4 Such applications rely on specifically developed optical fiber-based sensors that should be tested in a real tokamak environment before integration in the ITER environment. FBG strain gauges and temperature sensors have successfully been developed and installed in the Joint European Torus (JET) [START_REF] Lescure | 23rd IEEE/NPSS Symposium on Fusion Engineering[END_REF] and ASDEX Upgrade (AUG) [START_REF] Vorpahl | ASDEX Upgrade Team[END_REF] tokamaks to measure forces induced on the vacuum vessel during disruption and deformation of the passive stabilizing loop induced during plasma experiment, respectively. In both cases, FBG sensors were fixed to components located in remote areas, not directly exposed to the plasma heat load: on the top and bottom vessel restraints support (legs) in JET and on the copper surface of the stabilizing loops in AUG. The Q2 sensors used in JET and AUG are therefore working mainly in the low temperature or medium range, typically below 400 • C; thereafter, the Bragg grating may vanish. 7 FBG temperature measurement beyond 400 • C is a challenging task a) Author to whom correspondence should be addressed: yann.corre@cea.fr and currently a major research topic. Among the various solutions considered to develop temperature-resistant FBGs, the regeneration process 1 shows that the FBG can survive above 900 • C with long-term use (>9000 h). This is potentially of great interest to monitor the bulk temperature of the Plasma Facing Components (PFCs) and what we propose to test in the WEST (W-tungsten Environment and Steady State Tokamak) project. 8 The WEST project consists in transforming the Tore Supra tokamak in an X-point divertor configuration while keeping its long pulse capability, in order to test the ITER divertor technology. 8 The main goal is to test the actively cooled tungsten (W) Plasma Facing Units (PFUs) representative of the ITER divertor target 9,10 under high heat load (in the 10-20 MW m -2 range). In WEST, each PFU is composed of 35 W monoblocks of individual size 28 mm × 12 mm × 26 mm (width × depth × height) assembled with a gap of 0.5 mm on a CuCrZr heat sink tube. 11 As the completion of the ITER-like target in WEST is expected to require more time than the tokamak platform, it is planned to start the operation in 2017 with a mix of actively cooled ITER-like PFUs made of tungsten and non-actively cooled PFUs made of graphite with a thin coating of tungsten (∼15 µm) in the lower divertor. 12 Under high heat load, the W-coated graphite component will rapidly heat, which affords an opportunity to test the regenerated FBG technology in a real tokamak environment with high temperature excursion (up to or beyond 1000 • C). Graphite is easy to machine, it is a low cost component, and it has no risk of crack formation such as tungsten after machining the space to house the diagnostic (hole or groove). In order to test the feasibility to monitor the PFU bulk temperature, we have designed and manufactured 4 temperature sensors including 11 gratings. Probes are embedded in a side groove of the graphite component at two different distances from the surface. One groove is machined at 7 mm from the surface to test the FBG below 800 • C (lower FBG) and ensure the proper functioning of the FBG diagnostic and one groove at 3.5 mm to test the FBG beyond 800 • C (upper FBG) in order to find the maximum temperature threshold with the FBG system developed for WEST. This paper is organized as follows. The diagnostic specification, WEST environment, and thermal behavior of the W-coated graphite PFU are summarized in Sec. II. The FBG design and setup optimized according to the thermal behavior of the components, as well as the signal processing, are presented in Sec. III. The integration of the fiber in the W-coated graphite PFU and the cabling through the tokamak environment are presented in Sec. IV. The FBG system, standalone or mounted in the PFU, is tested and characterized in laboratory experiments with the thermostatically controlled water bath, tubular furnace, and halogen lamps (Sec. V). First experimental results obtained during baking and early diverted plasma exposure with the FBG diagnostic installed in the WEST tokamak are presented in Sec. VI.

II. SPECIFICATION AND ENVIRONMENT OF THE WEST FBG DIAGNOSTIC

A. Diagnostic specification and requirements

The goal of the FBG diagnostic (called DTFIB#1) in WEST is to monitor the bulk temperature in order to (1) protect the component and its coating to avoid any excessive thermal dilatation and cracks formation, 12 (2) cross-calibrate the IR thermography system which is disturbed by the emissivity uncertainties and potential reflection in the hot environment, 13 (3) compute the plasma heat load as depicted in Ref. 14, and finally (4) test the feasibility to use an FBG system directly into the PFCs. In this context, the diagnostic specifications and requirements are defined as follows:

• The number of fibers to be installed in the tokamak is 4 in order to focus on the feasibility first and investigate the stability of the measurement at different toroidal locations, assuming that the heat load is the same (toroidal symmetry) before any further deployment in the machine which is foreseen after the completion of the full actively cooled divertor (DTFIB#2 project currently under progress). • Temperature measurement is in the range of 70 • C without any plasma (minimum temperature of the machine foreseen in ITER) and 1200 • C during plasma discharge.

The accuracy of the system should be about 20 • C at high temperature.

• The size of the grating and positioning of the Bragg peaks in the spectral bandwidth have to be defined in order to measure the temperature gradient at the FBG sensor up to 45 • C/mm (because the plasma heat load is peaked on the surface 14 ).

• The number of FBGs is 11 by fiber to cover the spatial extent of the plasma heat load along the W-coated graphite PFU. Each of them is equally spaced by 12.5 mm which is the typical width of W monoblocks in ITER. 11 • The optical fiber should be free (to avoid any mechanical strain) and is inserted in a metallic capillary for protection during manipulation and also for the setting in the component (using graphite adhesive). The diameter of the capillary should be of the order of the mm to minimize the intrusive effect of the FBG on the thermal behavior of the component. The total fiber length from the sensors up to the sealing flange should be ∼3 m to reach the port flange (which is then connected to another optical fiber to join the electronic gallery where the FBG interrogator and acquisition system are based). • The time duration of acquisition is expected to be couple of minutes with the non-actively cooled components (plasma experiment will be limited in time to avoid excessive temperature of the component 12 ). Data acquisition should be 10 Hz at minimum (set by the thermal time response of the graphite component and a relatively short time duration of the experiment expected before the completion of the fully actively cooled divertor). • The expected number of cycles during WEST phase I (with inertial W-coated graphite PFUs) is 2000. The diagnostic must survive for about 2 years in the tokamak. • Acceptable degradation of the measurement (long-term drift) along the expected operation period is about 10 • .

Most of these requirements were achieved or are expected to be feasible based on initial testing. Although Q3 the accuracy of the measurement at high temperature and long-term drift cannot be evaluated yet, this would require high power and repetitive plasma experiments which are foreseen later on during the WEST experimental program.

B. WEST environment

WEST is based on the "tokamak" concept of plasma magnetic confinement, in which the plasma is contained in a doughnut-shaped vessel (Fig. 1). The plasma is kept away from the walls by strong magnetic fields produced by superconducting coils surrounding the vessel and an electrical current driven in the plasma. WEST is characterized by a strong magnetic field (3.8 T maximum) in the plasma chamber, a vacuum condition (of the order of 10 -5 Pa), an ambient temperature of 70 • C during plasma operation and 200 • C during baking, thermo-mechanical displacement (up to few mm) and vibration due to plasma instabilities, and radiation exposure such as photons, neutral particles, and neutrons. The fuel-a mixture of deuterium and hydrogen, or helium-is heated to temperatures in excess of 50 × 10 6 degrees in the core plasma. Contrary to ITER, WEST is a non-active tokamak device (there is no tritium injection), and therefore, it is not exposed to high nuclear radiation background. In WEST, the heat flux attributed to the plasma is of the order of 10 MW m -2 on targets. In remote areas, between the divertor and baffle where the cabling has to path through, the heat flux attributed to radiation and neutral particles is of the order of 10 kW m -2 . 15 The device should achieve steady-state and high power plasma operation up to 1000 s after the completion of the full actively cooled divertor target. The diagnostic sensor should be installed in the lower divertor, while the acquisition system (FBG interrogator) is located outside the vacuum chamber (after passing through the vacuum-tight access), in the electronic gallery about 50 m away from the machine.

C. WEST lower divertor and thermal behavior of the W-coated graphite PFUs

The Q4 lower divertor is made of 12 sectors of 38 PFUs each (each sector having 30 • toroidal extension). As the completion Q5 of the ITER-like target is expected to require more time than the tokamak platform, it is planned to start the operation in 2017 with 6 actively cooled ITER-like PFUs (in which three are manufactured by Japanese industrial and three by Chinese industrial) and 450 non-actively cooled PFUs made of graphite with a thin coating of tungsten (∼15 µm) in the lower divertor (see Fig. 1). Each individual graphite PFU is divided into two parts, the High Field Side (HFS) and Low Field Side (LFS) PFU. The size of the W-coated graphite PFUs is about 30 mm large, 26 mm thick (height), and 326 mm and 256 mm long for the HFS and LFS PFU, respectively. The FBG diagnostic is installed in the LFS PFU because the heat load is expected to be higher on this part. The material used is graphite R6710 from SGL Q6 (with the thermal conductivity of K ∼ 82 W m -1 K -1 at T = 200 • C), and the W-coating is about 15 µm thick. Surface temperature should be limited to 1200 • C for standard operation and further (up to 1800 • C) for a limited number of experiments to avoid delamination of the W-coating. 12 The thermal behavior of the W-coated graphite PFU is simulated with finite-element calculation performed with the ANSYS code, as depicted in Ref. 14. The plasma heat load distribution, q n (MW m -2 ), in the poloidal direction is computed with the heuristic formulation (Gaussian-like distribution), built with IR thermography measurement during carbon-wall operation, 16 q n (x) ∝ exp

      S 2λ q 2 - x -x 0 λ q f x       erfc S 2λ q - x -x 0 Sf x ,
where x is the position along the target, x 0 is the strike point position (i.e., the connection of the separatrix with the target), λ q is the heat flux decay length parameter in the edge plasma region 19 at the outboard midplane (usually called the scrapeoff layer width of the order of few mm size), S is the power spreading factor in the "private" region (i.e., the magnetically shadowed region), and f x is the magnetic flux expansion from the outboard midplane to the PFU. The temperature distributions reported at three different depths (surface, FBG upper, and FBG lower locations) in the graphite PFU located on the LFS are presented in Fig. 2 for the nominal high heat flux scenario (i.e., with peak heat load q n = 10 MW m -2 ) and standard magnetic field configuration. After 5 s of heating, the surface temperature reaches almost 1400 • C, while the bulk temperature is expected to be about 850 • C and 600 • C at 3.5 mm (FBG upper) and 7 mm (FBG lower) depths,

III. FBG DESIGN AND SETUP FOR WEST

A. Multiplexed FBG design for WEST

A FBG Q7 consists of a spatially periodic modulation of the refractive index created along a desired length of the core of an optical fiber. A narrow spectral band of the incident light within the fiber is reflected by successive coherent scattering from the index variations. 17 The strongest interaction or mode coupling occurs at the Bragg wavelength given by

λ B = 2 n e Λ,
where n e is the effective index of refraction (∼1.46) and Λ is the grating period. This leads to a single peak and valley in reflected and transmitted light through the optical fiber (as shown in Fig. 3). The principle of the strain or temperature measurement is based on the determination of the wavelength shift of the Bragg peak reflected by the grating that is induced by the changes of the grating period and by the thermo-optic and elasto-optic coefficients. This "peak tracking" function is ensured by using the FBG interrogator device using a wavelength tunable laser and logarithmic trans-impedance circuits for the photo-detection. The most commonly used method to write the FBG on the fiber core is based on conventional interferometric setup with ultraviolet light taking advantage of the photosensitivity of the germano-silicate optical fiber. Multiplexed FBG aims to daisy chain multiple sensors with different Bragg wavelengths (chosen in the spectral bandwidth of the tunable laser) in order to get simultaneous measurements at different locations along a single optical fiber. Standard multiplexed FBGs Q8 for temperature measurements are commercially available below 500 • C; thereafter, Bragg grating may vanish due to the erasure of the photowritten refractive index modulation. One way to extend the temperature measurement range is the regeneration process which allows increasing the temperature measurement beyond 900 • C, while keeping good metrological performances. 1 The Q9 thermal condition foreseen in WEST and depicted in Sec. III (Fig. 2) requires the development of specific multiplexed and regenerated FBG temperature sensors. This has been carried out in the CEA List Institute which is committed to technological innovation in digital systems including architecture, hardware, and software applied to embedded systems.

The FBG diagnostic developed in WEST is equipped with an industrial multichannel FBG interrogator, based on a wavelength tunable laser, featuring full spectrum analysis with data rate at 10 Hz. The spectral bandwidth available to encode the FBG array is 120 nm covering the wavelength range from 1500 up to 1620 nm with a spectral resolution of 8 pm. In such a wavelength range, the thermal response of the Bragg shift varies from 10 pm/ • C at 50 • C up to 20 pm/ • C at 800 • C (as derived from the calibration curves), and the average value is of 14 pm/ • C. To cover the 70-1200 • C temperature range expected in the bulk of the W-coated graphite PFU, the maximum shift of the Bragg peak is 15.8 nm. Due to the limited spectral bandwidth available, it was not possible to include 11 FBG arrays with such a gap between each FBG. The maximum temperature gradient expected between two consecutive FBGs is about 500 • C, which corresponds to about 7 nm shift of the Bragg peak. The Bragg wavelengths of two consecutive FBGs are therefore spatially spaced by 7 nm to avoid spectral overlapping. The Bragg wavelengths at room temperature are given in Table I.

The typical size of the gratings is about 3 mm, and the space between two consecutive FBGs is 12.5 mm. The eleven 12.5 mm spaced FBGs are simultaneously regenerated using a high-temperature annealing process, as depicted in Ref. 1. The process is performed with a homemade tubular furnace and uses a thermocouple near the FBG in order to control the temperature during the thermal treatment. During the regeneration protocol, the temperature of the furnace is raised to 920 • C which is the point triggering the regeneration for all the multiplexed FBGs. The full process, FBG photowriting, followed by the regeneration process, has been applied successfully to the four dedicated temperature probes. The FBGs are photowritten onto a 150 µm diameter single-mode polyimide-coated silica-glass optical fiber inserted within a 1 mm diameter metallic capillary hermetically sealed at its extremity. The reflected spectrum measured at 70 (the standard temperature of the machine before plasma operation) is presented in Fig. 4 for one of the two upper FBGs (once regeneration has been realized). Even if the overall reflected signal is low due to the regeneration process, the Bragg peak is about 5 dB higher than the baseline which is enough for peak detection. The baseline reflected light also shows some fluctuation attributed to back (Fresnel) reflection at the extremity of the fiber.

B. Signal processing and temperature calibration

The first step which further defines the accuracy of the temperature measurement is to get the position of the Bragg peaks in the experimental spectrum (see Fig. 3). For each FBG, the peak is detected using a Gaussian-shape function (non-linear regression) combined with data filtering and amplification due to the relatively low reflectivity of the gratings and the Fresnel reflection introduced at the extremity of the fiber. The following step is the temperature calibration of the sensing line. The sensing lines are positioned in a high temperature furnace together with a bundle of thermocouples to get the temperature distribution along the furnace. The Q10 temperature is first raised to 800 • C, and then heating is switch-off in order to get a slow and regular temperature decrease. The logarithm decrease in the furnace temperature is fitted for all the Bragg wavelengths using a fifth-order polynomial function. FBG, for one of the four sensing lines developed for WEST. Above 800 • C, the calibration curve can be extrapolated based on the polynomial function.

IV. INTEGRATION OF THE FBG DIAGNOSTIC IN WEST

A. Integration in the W-coated graphite PFU

The FBG temperature probe is inserted in the LFS graphite PFU through a 4 mm deep 1.2 mm thick lateral groove, as shown in Fig. 6(a). The probe has a diameter of 1 mm (due to the capillary), is 150 mm long, and has curvature of R = 62 mm downward toward the pumping duct [Fig. 6(b)]. The 4 mm deep lateral groove is shown in Fig. 6(c) for the upper FBG (the center located at 3.5 mm from the surface). The temperature probe is fixed to the component with graphite adhesive made for use up to 1300 • C. After assembling of the instrumented PFU, the connector is clamped to the divertor support plate to prevent any excessive vibration and stresses on the graphite adhesive. A stainless steel box is finally used to protect the overall system from accidental impact during the introduction of the fully equipped divertor sector into the machine. The computer aided design (CAD Q11 ) view and picture of the FBG system after assembling are presented in Fig. 7. The deployment of the FBG system in WEST is based on one set of two optical fibers, upper and lower FBG which are installed in two adjacent PFU, duplicated in two different divertor sectors (each sector having 30 • toroidal extension).

The four temperature probes are connected to a 3 m long optical fiber with a protective sheath made of PEEK composite, one of the few plastics compatible with high vacuum and high temperature applications. The overall is Q12 protected by a flexible stainless steel creased hose Ø = 2.3 mm, up to the sealing flange. In the region between the stainless steel box and the entrance of the pumping duct, the flexible stainless steel creased hose might be exposed to plasma radiation and neutral particles up to 10 kW m -2 , as shown in Ref. 15 which is acceptable for the temperature behavior of the cable. Each sensing line is connected to a vacuum feedthrough (10 -8 mbar l/s) located few meters below the machine. At the outside of the vacuum vessel, the system is connected to the FBG interrogator and acquisition system with a 60 m long remote fiber cable (see Fig. 8).

V. TEST AND QUALIFICATION OF THE WEST FBG DIAGNOSTIC

The full multiplexed FBG system has been manufactured by the CEA List Institute and delivered in June 2016. The system has been tested in the laboratory before the implementation in the tokamak. The laboratory tests include three successive experiments to characterize the performance of the system: a thermostatically controlled water bath, high temperature furnace, and fully instrumented PFU with a set of six halogen lamps.

A. Thermostatically controlled water bath

The four sensing lines are fully immersed (without any component), one after the other, in a thermostatically controlled water bath at 80 • C. The results obtained for each of the 44 FBGs are presented in Fig. 9. The standard deviation obtained at 80 • C is ±5 • , and the temporal variation is below 0.4 • which is consistent with the specification of the system.

B. High temperature furnace

The FBGs are tested successively (without any component) in a high temperature tubular furnace at the atmospheric pressure. Type-N TCs are used to get the temperature in the furnace with a temperature stability of ±1 • C. The furnace is open at the extremity on the entrance side; therefore, the temperature is close to the setpoint value at the bottom and lower at the entrance sides, respectively. The experimental setup and results obtained for a set of three FBGs are presented in Fig. 10. In the experiment presented here, the instruments are introduced in the furnace for about 150 s at 250 • C. The overall dynamic of the TC/FBG measurements is coherent during the transitory phase. FBG#11 heats up first, followed by FBG#8 and #6, as we introduce and take away the sensors (slow movement) in the furnace. After their introduction, the FBG fiber and TC are rapidly thermalized with the furnace and the steady state condition is almost reached. The TC measurements are coherent with the positioning; we found 243 • C at the bottom, 240 • C in the middle, and 228 • C close to the entrance. Although the overall dynamic is well reproduced with the FBG measurements, the absolute values given by FBG are slightly different from TC: FBG#11 shows 10 • C discrepancy with the TC, while FBG#8 shows less than 1 • and #6 less than 3 • C along the temperature excursion. Such a discrepancy can be attributed to sensor positioning in the furnace, thermal convection in the furnace which is open at the entrance, or FBG calibration and accuracy of the system itself. Among Q13 the tested FBGs, the maximum discrepancy is found to be 10 • C with a temperature furnace of 250 • C which is, nonetheless, consistent with the specification of the system.

C. Fully instrumented PFUs heated with halogen lamps

After the test and Q14 characterization of the four FBG systems standalone, the FBG probes are then fixed in the lateral grooves of the W-coated graphite PFUs with graphite adhesive. The fully instrumented PFUs are tested in the laboratory using halogen lamps. Besides the four FBG instrumented PFUs, a fifth PFU is used with 4 embedded thermocouples to derive the thermal time constant of the two systems, the TC and FBG fibre, in the material. The halogen lamp system delivers about 4 kW m -2 continuous and quasi-homogeneous power on each target. The five PFUs are pre-heated to about 80 • C (which is slightly above the nominal temperature of the water cooling system in WEST), this is followed by a 10 min switch-off of the power to thermalize the component, and then we apply successive 30 s-on, 150 s-off power steps to compute the time response of the different diagnostics (τ diag ). The experimental setup is presented in Fig. 11(a) and the measurements are presented in Fig. 11(b) for TC and one FBG probe. We report very good dynamic behaviors of the different systems and accurate measurement of the relative heating (∆T = 2 • C during each power step). However, we also report about 8 • C discrepancy between the two extreme FBGs temperature measurements, similar to the previous experiment. TC data (yellow curve) are slightly lower than FBGs data because the fifth PFU including the TC is slightly out of the center of the beam light [at the bottom as shown in Fig. 11(a)]. The time response of the diagnostic is determined with 2D FEM thermal modeling of the component. The heating is assumed to be uniform along the PFU (the x direction) so that the geometry can be simplified in the toroidal-vertical plan (y, z). The numerical temperature reported at the sensor location is convoluted to the temporal step response of the full system (component with the instrument),

u(t) = 1 -e -t τ diag ,
where τ diag is the time response of the system which is estimated with a Particle Swarm Optimization (PSO) algorithm [START_REF] Kennedy | Particle swarm optimization[END_REF] in order to minimize the residuals between the model and the measurement. We found τ diag = 250 ms with ±50 ms standard deviation attributed mainly to the lighting up and electrical stability of the lamps.

VI. BAKING AND EARLY DIVERTED PLASMA EXPOSURE

The Q15 full FBG system has been installed in the WEST tokamak beginning of 2017, before the first plasma breakdown attempts. The system is working properly for more than one year, and we have been able to investigate the variation of temperature during the baking of the machine and during early diverted plasma exposure. During baking, the water cooling system is raised up to 185 • C in order to remove the remaining gas from the wall. As a consequence, the temperature is similar in all the PFUs of the divertor. This provides the opportunity to check the FBG temperature measurement in a real tokamak environment by comparing the results with the set of 20 embedded TCs also available in the W-coated graphite PFUs. The reflected power Q16 passing through one of the FBG probes and measured by using the spectrometer is presented in Fig. 12 with a specific focus on the two first FBG #1 and #2. The resulting signal is about 4 dB above the baseline signal of the spectrum and therefore adequate to detect the position of the Bragg peak. The shift of the Bragg peak measured during baking is also illustrated.

The temperature measurements of the four FBG probes during baking (performed in April 2017) are presented in Fig. 13 to the Fresnel reflection introduced at the extremity of the fiber).

Figure 14 shows the temporal evolution of the temperature as measured with the FBG upper (a) and lower (b) probes as well as the temperature of the water in the cooling loop of the divertor coils (the signal called here as TTBB Q17 ) at the end of another baking phase (performed in March 2017) when the temperature of the machine decreases down to 70 • C for plasma operation. The typical duration to heat or cool the machine for baking is 24 h. As for the laboratory experiment with the halogen lamps, the absolute value shows a 10 • C offset with the expected temperature, but it is important to stress that the overall heating or cooling is well reproduced (we found ∆T = 110 • C between the normal condition and baking).

Plasma breakdown, plasma current ramp-up, and diverted plasma have been developed after the machine commissioning. First diverted plasmas with additional heating power have been achieved in WEST in early 2018. Figures 15(a show the temporal evolution of the temperature rise as measured with the FBG (DTFIB#1) and thermocouple diagnostics, respectively, during a 700 kA plasma current diverted plasma experiment (#52693). The thermocouples are embedded at 7.5 mm distance from the surface of the PFU, close to the lower FBG probes that are embedded at 7 mm. The space between two thermocouples is 37.5 mm, while it is 12.5 mm between two FBG spot measurements (we have therefore one thermocouple every three FBG spot measurements). The two different systems show similar heating distribution along the PFU and similar intensities. Looking at the signal variation as a function of time first, we clearly see the benefit of the optical solution (with noise measurement ≤1 • ) compared to electrical measurement such as TC data which are more sensitive to electromagnetic disturbance (up to few degrees, variation is observed during the plasma current ramp up and ramp down phases). Second, looking at the signal intensity, about 11 • heating is reported on FBG#10 and thermocouple TCI Q19 at the end of the pulse (blue curves), both sensors being located at the same position along the PFU. Such a temperature rise Q20 , regarding the duration of the pulse, corresponds to plasma heat flux of about 100 kW m -2 , a value which is small but also coherent, on top of the TC measurements, with Langmuir probe measurements. The FBG and TC data presented here were obtained in the very first WEST plasmas having an important level of radiated power losses. Further experiments will aim at decreasing radiated power fraction while increasing injected power.

VII. CONCLUSION

This paper shows the design and integration of the new embedded FBG diagnostic called DTFIB#1 to monitor the PFU temperature during tokamak plasma operation. Four Q21 high temperature probes including each having eleven FBGs have been specifically designed and manufactured by the CEA List Institute according to the WEST plasma and material conditions. Each sensing part of probe is inserted in the PFU through a tiny lateral groove (at two different depths 3.5 mm and 7 mm) and attached with graphite adhesive. The multiplexed and regenerated FBG probes have been tested and characterized in three laboratory experiments before installation in the machine. The accuracy of the measurement is found to be about 10 • C at low temperatures (up to about 250 • C in the tubular furnace), which meets the specification even if there is still some margin for improvement (the calibration and peak detection algorithm are currently under review). However, the relative heating of the component which will be further used to compute the absorbed heat load is well reproduced. The time response of the FBG diagnostic in the component is found to be 250 ms with ±50 ms standard deviation, which is relatively small compared to the standard duration of the plasma experiment in WEST (from several seconds up to couple of minutes). The diagnostic DTFIB#1 has been installed in the real tokamak environment and successfully tested during baking (up to 185 • C in WEST) and early diverted plasma exposure (with high radiated power losses and a small amount of power reaching the divertor). It is now foreseen to use the 44 available spot measurements of the new FBG diagnostic to cross-check the IR thermography measurement and characterize the heat load absorbed by the components over the coming plasma experiments. The next step will be to ensure that the diagnostic is working properly during plasma operation with high heat flux and high temperature in the lower divertor.

FIG. 1 .

 1 FIG. 1. Interior picture of the WEST tokamak showing the upper and lower divertor, the baffle, and port plug numbers (Q4A, Q5A, and Q6A).

FIG. 2 .

 2 FIG. 2. (a) Temperature profile at three different locations from the surface (z = 0, z = 3.5 mm, and z = 7 mm) on the W-coated graphite PFU located on the Low Field Side (LFS). After 5 s heating, the surface temperature goes up to almost 1400 • C, while temperatures reported at few mms away from the surface are lower (below 1000 • C). (b) The poloidal section of WEST showing the magnetic flux surfaces, the inner wall, and the graphite PFU housing the FBG sensor.

Corre

  FIG. 3. Schematic picture of FBG showing the transmitted and reflected spectrum. respectively. The predicted plasma heat flux distribution leads to a very steep temperature gradient in the component, about 45 • C/mm and 25 • C/mm in the private flux region for the upper and lower FBGs, respectively (at 3.5 mm and 7 mm below the surface). Such temperature gradients represent a challenge for the design of the multiplexed FBG; the main issues are the choice of the Bragg wavelengths in one side and the position and length of the FBG in the other side.

CorreFIG. 4 .

 4 FIG. 4. Reflected spectrum as measured by the upper FBG installed in the WEST tokamak with a coolant loop at 70 • C.

Figure 5

 5 FIG.5. Calibration curve for one of the 4 sensing lines developed and manufactured for WEST.

CorreFIG. 6 .FIG. 8 . 7 CorreFIG. 9 .

 6879 FIG. 6. Fabrication plan for the FBG upper diagnostic embedded in a 1.2 mm diameter lateral groove at 3.5 mm below the surface. (a) Drawing showing the sensing line integrated in the W-coated graphite component (side view). (b) Full fiber including the 150 mm long sensing line and the connection part, followed by a 3 m flexible capillary to reach the sealing flange. (c) Drawing of the W-coated graphite component showing the lateral groove (back view).

FIG. 10

 10 FIG. 10. (a) Picture of the experimental setup before the introduction of the TC and FBG sensors into the tubular furnace. (b) TC and FBG temperature measurements at three different locations (FBG #6, #8, and #11) with a set point temperature of 250 • C.

Corre

  FIG. 11. (a) Picture of the experimental setup with FBG and TC embedded in the W-coated graphite PFUs and halogen heating system. (b) Temperature excursion during 30 s heating steps of the PFUs as measured with TC (yellow signal) and one FBG probe (11 spots measurements).

FIG. 12 .

 12 FIG. 12. Reflected power as a function of the wavelength at 70 • C (red) and during baking at 185 • C (green), focus on the first and second FBG.

  FIG. 13. Temperature measurement with FBG located in two different divertor sectors (named Q3A and Q4A, plotted with cross and plus signs, respectively) and TC systems during baking. FBG upper (3.5 mm below the surface) and lower (7 mm below the surface) are plotted in red and blue, respectively.

Corre

  FIG. 14. Temporal evolution of the temperature during the cooling down, from baking of the machine down to 70 • C, as measured by FBG upper (a) and lower (b).

  ) and 15(b) Q18

Corre

  et al. Rev. Sci. Instrum. 89, 000000 (2018)

TABLE I .

 I Bragg wavelengths of the FBGs at room temperature.

	FBG	#1	#2	#3	#4	#5	#6	#7	#8	#9	#10	#11
	λ Bragg (nm)	1512	1519	1526	1533	1540	1547	1554	1561	1568	1575	1582

• C

ACKNOWLEDGMENTS

We wish to thank our colleagues Jean-Claude Vallet, at the CEA IRFM Institute, to have had the bold idea of using FBG sensors in WEST and Pierre Ferdinand, at the CEA List Institute, for his enthusiasm to commit to working in close cooperation with the two institutes. This work has been Q22 carried out with the support of the A * MIDEX Project (No. ANR-11-IDEX-0001-02) funded by the "Investissements d'Avenir" French Government program, managed by the French National Research Agency (ANR).


P Bacchin

J-P Bonino

F Martin

M Combacau

P Barthes

S Petit

J Ferret

Surface pre-coating of talc particles by carboxyl methyl cellulose adsorption : study of adsorption and consequences on surface properties and settling rate

This paper investigates the adsorption of different sized carboxyl methyl cellulose (CMC) onto talc particles (adsorption isotherm, adsorption reversibility), its consequences on the particles properties (electrophoretic mobility and surface wetting) and its effect on their dispersion (settling coefficient). Throughout the paper, the properties of talc particles dispersed in CMC solution are compared to CMC pre-coated talc particles: talc particles dried in a solution of CMC before their redispersion. The adsorption of CMC onto talc was quantified at around 0.4 mg of CMC per m 2 of talc and was seen to be irreversible on washing the talc particles with distilled water. When characterising talc surface properties, it was found that CMC adsorption leads to an increase of the negative surface charge and to an increase of the wettability. The settling velocity of CMC pre-coated talc particles in water can be around 50 % lower than that of the initial talc particles. The pre-coating of talc particles by CMC is then assumed to increase their stabilization : particle aggregation is hindered by adsorbed CMC layer inducing electrosteric repulsion between the talc particles. The technique of talc pre-coating with CMC makes the talc dispersion easier and could open interesting perspectives in engineering processes using talc dispersions.

Introduction

Talc is widely used in numerous applications in the paper, paint and plastics industries. Furthermore, the morphology of talc in sheets confers it interesting lubricant properties which could also be used to develop new low friction composite materials [START_REF] Bonino | Composite Coatings with Talc Particles[END_REF][START_REF]Matériau composite utilisable comme revêtement lubrifiant[END_REF]. However, in these different processes, it is often necessary to have a good dispersion of small talc particles. Because of its hydrophobic properties (low surface surface energy), it is difficult to disperse talc in water and without formation of foam or aggregate [START_REF] Schrader | Wettability of clay minerals[END_REF].

In mineral science, Carboxyl Methyl Cellulose CMC (long chain polysaccharide) is a well known polymer depressant for talc particles [START_REF] Morris | Polymer depressants at the talc-water interface: adsorption isotherm, microflotation and electrokinetic studies[END_REF][START_REF] Shortridge | The effect of chemical composition and molecular weight of polysaccharide depressants on the notation of talc[END_REF] i.e. it reduces the floatability of talc.

Morris et al. [START_REF] Morris | Polymer depressants at the talc-water interface: adsorption isotherm, microflotation and electrokinetic studies[END_REF] proposes that CMC adsorbs both to the edge and the face of talc particles.

The adsorption could occur in a flat conformation via hydrophobic interactions leading the hydrophilic hydroxyl and carboxyl groups of CMC to extend out from the talc surface. Such a conformation could then substantially improve the hydrophilic character of talc particles leading to a better dispersion in water [START_REF] Morris | Polymer depressants at the talc-water interface: adsorption isotherm, microflotation and electrokinetic studies[END_REF]. Floatability studies show that the molecular weight of CMC does not have a decisive effect on talc floatability [START_REF] Shortridge | The effect of chemical composition and molecular weight of polysaccharide depressants on the notation of talc[END_REF] [START_REF] Shortridge | The effect of chemical composition and molecular weight of polysaccharide depressants on the notation of talc[END_REF]).

However, the use of CMC in solution to help dispersion of talc is not always possible.

For a process requiring the use of a complex solution with talc (as for example electrolytes mixtures for electrochemical codeposition), the adding of significant quantities of CMC can disturb solution equilibrium and then alter process efficiency. Furthermore, the adsorption of CMC to the talc can be reduced because of competitive adsorption of other components of the solution on the talc surface. In order to overcome these limitations, we report in this paper the development of a technique for pre-coating talc with CMC to aid dispersion.

The aim of this study was to quantify CMC adsorption on talc particles and to investigate the effect of adsorption on the surface properties of talc and its settling properties when dispersed. Three CMC with different degree of substitution and molecular weights were tested.

Materials and methods

Materials

Talc mineral

-Mineralogical background information

Talc is a 2:1 layer clay (phyllosilicate family) which links two tetrahedral sheets with one octahedral sheet in their structure (Fig. 1). Talc represents the trioctahedral magnesium end member with the formula: Mg 3 Si 4 O 10 (OH) 2 . Studies with various spectroscopic methods show complex and low amonts of cation substitutions in both tetrahedral and octahedral sites [START_REF] Martin | The structural formula of talc from the Trimouns deposit, Pyrénées, France[END_REF] with conservation of the electro-neutrality of the structure. For exemple, the structural formula obtained with standard Trimouns talc (commercial product of Talc Luzenac Europe), on the basis of 11 oxygen atoms, is :

[Mg In the tetrahedral sheet, a charge deficit appears : 0.011. In the octahedral sheet, there is a charge excess of 0.012. However, it appears clearly that a deficiency in tetrahedral charges, due to substitutions of tetravalent cations Si by trivalent cations Fe and Al, are compensated by an excess of octahedral charges generated by the replacement of the divalent cation Mg by trivalent cations Fe and Al [START_REF] Martin | The structural formula of talc from the Trimouns deposit, Pyrénées, France[END_REF]. All pure talc samples from all over the world show complex structural formulae, but with electro-neutrality of the talc-cell.

Talc samples

Two talcs were used in this study.

(i) talc I (labelled Brazil) (used in section 4.3) comes from a mineralogy collection (Toulouse, France), and is a pure talc [START_REF] Ferrage | Talc as nucleating agent of polypropylene: morphology induced by lamellar particle addition and interface mineral-matrix modelization[END_REF] composed of very well defined centimetric plates (photography by SEM observation in fig. 2). The structural formula, according to chemical analyses and various spectroscopic methods [START_REF] Petit | Crystal-chemistry of talcs: a Near Infrared (NIR) spectroscopy study[END_REF] is:

[Mg

Carboxyl methyl cellulose (CMC)

Three different types of carboxyl methyl celluloses (referenced by Sigma Aldrich as 21901, 21900 and 21903) were added to the talc dispersions. The properties of CMC molecules (schema of chemical structure in figure 3) are summarized in table 1. CMC molecules present a relatively high average number of glucose hydroxyl groups substituted by -CH 2 COO --Na + per glucose monomer (degree of substitution) indicating strong surface charge. Furthermore, these CMC present different molecular sizes leading to important changes in viscosity. The water used to prepare the CMC solution was osmosed water without any buffering then typically displaying pH between 5.5 and 6.5 and conductivity less than 20 micro-siemens/cm.

Methods

Talc dispersion

Talc particles (100 g) were progressively dispersed in 1000 ml of osmosed water (or CMC solution) by small additions of water. The dispersion was then homogenized with an UltraTurrax T50 (IKA, Staufen, Germany) at 5200 rpm for 20 minutes. This apparatus generates important stress yield within the small space between the rotating pestle and the tube breaking any clusters of particles resulting from aggregation.

Adsorption isotherms

Adsorption isotherms were determined by a classical method based on analysis of equilibrium CMC concentration in solution after a contact with talc particles. Experiments were conducted by dispersing talc at 100 g/l in 1000 ml of CMC solution with an initial concentration of between 0.5 g/l and 3 g/l. After a contact time with a continuous stirring of 24 hours, the dispersion was centrifuged. Initial concentration and residual concentration were determined by COT analysis (TOC 5050A, Shimadzu). The quantity of CMC adsorbed was determined by mass balance.

Zeta potential and size measurements

Zeta potential and particle size were measured with a Zetasizer 4 (Malvern Instruments, Malvern, UK). Samples were diluted (1:1000 in weight) in pure water buffered with 0.001 M in KCl. Mobility measurements were performed at 25°C from pH 3 to pH 12 by adding small quantities of HCl and NaOH with a titrator. Zeta potential was calculated using the Smoluchowski equation. For a given pH, three experiments were conducted in order to check the repetability of the analysis.. Size was determined by dynamic light scattering at 90° with same dilution and same apparatus.

ATR MIR analysis

ATR FT-MIR (Attenuated Total Reflectance on Fourier Transform Middle InfraRed)

analysis was performed on talc particles with a Nicolet 510 FTIR spectrometer (Hydr'Asa Laboratory, Poitiers University). In the ATR technique, the IR beam samples a surface by internal reflection of the light ; the IR light penetrates the molecules placed at the surface via the evanescent field. The MIR approach can enhance the ATR technique by bouncing the light off the surface several times. This method can then be sensitive to the vibrational modes of molecules at the surface.

Settling experiments

Sedimentation was studied with a Turbiscan MA (Formulaction, Toulouse, France). This apparatus determines variations of sample turbidity along the sample height at different times.

The stability and the homogeneity of the dispersion can thus be estimated and the settling velocity is quantified from the movement with time of the sedimentation front. The glass tube containing the sample has an internal diameter of 12 mm and a height of 140 mm. The turbidity is measured by an optical head (infrared light) recording the transmitted and backscattered light intensities and the sample is scanned every 40 μm over its whole height. This allows clear identification of the sedimentation front (between the settling particles and the supernatant). Its position is defined in this study as the position where the back-scattered intensity is 50% of the total front height. The settling velocity, determined as the rate of variation of front position with time, can be defined as a mean settling velocity : 50 % of the particles having a settling velocity below this value and 50 % above.

Talc wetting

Wetting experiments were performed on a large sheet of talc from Brazil (collection of mineralogy, Toulouse, France), in order to determine the effect of CMC on the wettability of talc particles. With the large surface of talc, we were able to deposit a drop of water on the surface or an air bubble under the immerged surface. The latter technique was chosen to avoid drying the talc surface after contact with the CMC solution. The contact angle between the bubble and the surface was measured with a Digidrop Fast (GBX, Romans sur Isère, France).

The contact angle is defined as the angle made by the liquid/solid line and the liquid/air line.

The contact angle obtained with the classical sessile drop technique, θ, is then determined as 180-θ', where θ' is the angle of the bubble as it could be determined for a drop a water on a surface.

Pre-coating of talc with CMC

A procedure was developed in this work to have dry talc particles pre-coated with CMC. A first dispersion of talc was prepared with 3g/l of CMC. The dispersion was then centrifuged

for 1 hour at 4000 rpm. The centrifugation pellet was then dispersed in osmosed water and centrifugated again to wash off the excess CMC. The CMC concentration in the supernatant was analyzed to quantify the reversibility of CMC adsorption. This is discussed later in the paper. This last operation was repeated once. The resulting pellet is then dried and ground manually. These talc particles are referred to as CMC pre-coated talc.

Study of CMC adsorption on talc

CMC adsorption on talc particles

Adsorption isotherms for three different CMC on talc particles are presented in figure 4 where adsorbed CMC amount (in mg) per particle surface area (in m 2 ) is plotted versus CMC concentration at equilibrium. The adsorption isotherm shows classical monolayer adsorption behaviour with a plateau. Plateau coverage was reached for a concentration of free CMC in solution of around 1 g.L -1 and corresponds to around 0.4 mg.m -2 . This value is below that determined by Morris et al. [START_REF] Morris | Polymer depressants at the talc-water interface: adsorption isotherm, microflotation and electrokinetic studies[END_REF] (0.6 mg.m -2 ) but higher than that of Steenberg et al. [START_REF] Steenberg | Adsorption of carboxymethyl cellulose, guar gum, and starch onto talc, sulphides, oxides and salt-type minerals[END_REF] 0.22 mg.m -2 . These differences could be attributed to the physico-chemical properties of talc particles, the CMC molecule used (size and degree of substitution) and characteristics of the solution (pH and ionic strength). The adsorption seems greater when the size of the CMC molecules is low. Steric exclusion between polymer chains may occur leading to slightly greater adsorption with small CMC. On another hand, the high degree of substitution of CMC 21903 does not lead to an increase in adsorption which could mean that adsorption is not controlled by electrostatic effects. This tends to support the adsorption mechanism controlled by hydrophobic interactions as proposed by Morris et al. [START_REF] Morris | Polymer depressants at the talc-water interface: adsorption isotherm, microflotation and electrokinetic studies[END_REF].

The fraction of talc area occupied per adsorbed CMC molecule, σ, can be estimated from the following relationship :

CMC A w a S N M m = σ [1]
Where m a is the amount of CMC adsorbed per surface area of talc (figure 4), N A is Avogrado's number and S cmc is the estimated area occupied by a CMC molecule. The area of a glucose unit of the CMC can be estimated at 0.47 nm 2 [START_REF] Morris | Polymer depressants at the talc-water interface: adsorption isotherm, microflotation and electrokinetic studies[END_REF]. For a molecule of 100 000 g/mol, i.e. 455 monomer units, the area occupied by a CMC molecule is around 212 nm 2 if adsorption is assumed to occur in an extended, linear flat conformation. The area occupied on the talc surface is reported in table 4 from the calculation for different molecular weight of CMC at an equilibrium concentration of 1 g/l. When assuming that adsorption occurs in flat conformation, the adsorbed molecules represent around 60% of the total surface area. SEM FEG micrographes were taken on talc particles without CMC and after a coating withCMC (respectively in fig. 5a and5b). Comparing them reveals a difference in topography of the talc layers. On the untreated talc surface, successions of planes and steps occur, characteristic of piling up of talc layers, whereas on the surface of particles treated by CMC, the pattern is diffuse unlike that caused by the presence of steps. The covering "veil" seems to result from the irreversible adsorption of CMC on the greater part of the talc surface. These observations were confirmed by Attenuated Total Reflectance on the Middle InfraRed region (ATR MIR) of talc particles with and without precoating. The observations were made on the well extended (a, b) plane (Figure 2) and the InfraRed beam was perpendicular to this plane and parallel to the OH-direction (Figure 1), here accounting for the absence of OH stretching vibrations in the 4000 -3600 cm -1 region (not presented in this article). Figure 6 shows that CMC precoating leads to the detection of vibrational bands characteristic of CMC molecules.

These bands mask the Si-O bands which are detected on naked talc particles. Adsorption of CMC to the surface of talc particles is then confirmed by these analysis.

Analysis of adsorption reversibilty

After CMC adsorption, talc particles were washed twice with osmosed water as detailed in the methods section relative to the pre-coating procedure. Table 2 gives the loss in adsorbed CMC after one and two washing. Then, after the two washing steps, the centrifugation pellets were dried and reground to be dispersed again in water. When analysing the water where dispersion of CMC pre-coated talc particles was made it was found by total organic carbon TOC analysis that the concentration of CMC was equivalent to 5-10 % of the total amount adsorbed remaining after two washings (table 3). The reversibility of adsorption is again greater with long-chain CMC.

To conclude, CMC adsorbs irreversibly for a great part to the talc surface. Pre-coating of talc with CMC is possible leading to talc powder with CMC adsorbed on the surface.

Effect of adsorption on properties of talc particles

Zeta potential measurements

Zeta potential measurement of talc particles were performed in the absence or in the presence of the CMC polymer at 1, 2 and 3 g/l within the pH range 3 to 11. Results for the 3 CMC are plotted in figure 7 for the same concentration of 3 g/l and compared to the zeta potential for bare talc particles in water. The evolution of zeta potential with pH is classical with a slightly positive value at low pH and an increasingly negative value as the pH rises. The isoelectric point of talc is around 3. This value is higher than that found by Morris et al. [START_REF] Morris | Polymer depressants at the talc-water interface: adsorption isotherm, microflotation and electrokinetic studies[END_REF] (pH=2). For a neutral pH around 8, the zeta potential of bare particles is around -35 mV whereas with CMC (21900 and 21901) it reaches a value of -42 mV and -49 mV for CMC 21903. It can be noted that the zeta potential is directly correlated to the degree of substitution of the CMC (table 1): the same results being observed for CMC with same substitution degree (078 and 0.79) whereas larger negative values were observed with the CMC with the highest degree of substitution (0.92). Experiments with lower CMC concentrations (1 and 2 g/l) showed exactly same trends. For high pH a cross-over in zeta potential versus pH can be observed for CMC 21900 and 21901. This cross-over has already been observed and explained by Morris et al. [START_REF] Morris | Polymer depressants at the talc-water interface: adsorption isotherm, microflotation and electrokinetic studies[END_REF]. Adsorption leads to a shift of shear rate plane away from the particle surface leading to a smaller apparent zeta potential. Particles coated with negative macromolecules can then exhibit zeta potentials slightly below the ones determined for bare particles. Furthermore, zeta potentials were determined on CMC pre coated talc particles (figure 8). The zeta potential is always more negative when talc is precoated with CMC. The negative charge is greater with CMC 21900 and 21903 (-48 mV at neutral pH). These results confirm that the CMC adsorbed after precoating the talc remains.

CMC adsorption and apparent particle size

Particle size was determined by dynamic light scattering. Figure 9 presents the mean hydrodynamic diameter of talc as a function of CMC solution concentration. These measurements show an increase of particle size when CMC is adsorbed on the particle surface being greater for CMC having a higher molecular weight. For the larger CMC an increase of 1 μm of the initial particle diameter of 1.5 μm is observed on adding CMC. This can not be attributed to the adsorption of extended molecule on the surface (the macromolecular chain can not increase the apparent hydrodynamic size to this extend). As it will be discussed later, the increase of particle size could result of the formation of aggregate between particles because of bridging flocculation.

CMC adsorption and talc wetting phenomena

CMC is a macromolecule with carboxyl groups and hence relatively hydrophilic chain. In contrast, talc is hydrophobic. Wetting experiments were performed to study talc wetting. The experiments were carried out on a large sheet of Brazilian talc by a bubble captured under the immerged talc surface. Figure 10 shows the evolution of the bubble contact angle, θ', for different CMC in solution and for a precoated talc surface. It can be noted that talc is found to be hydrophobic when immerged in water: the bubble contact angle is equivalent to a contact angle with a sessile drop technique of 92°. This value is close to that found by Shrader and Yariv [START_REF] Schrader | Wettability of clay minerals[END_REF] between 81-88 °. In the presence of CMC, the bubble contact angle increased meaning that talc loses its hydrophobicity when immerged in a CMC solution. These variations cannot be explained only by the change in surface tension of the liquid. To prove this, measurement of wettability were performed on a talc surface after CMC contact and washing (pre-coated talc) and talc still exhibited a hydrophilic character. On the another hand, experiments were carried out on capillary elevation in a tube containing talc particles with a Wilhelmy balance method (Balance 3S, GBX, France). These complementary experiments showed same trend; no water rising in the initial talc powder because of its hydrophobicity and a rise of water in precoated talc particles at a significant rate meaning that talc particles are then hydrophilic.

Dispersion and settling of talc particles with CMC

First, CMC facilitates dispersion of talc in aqueous solution. We noted that the use of CMC reduces the formation of foam and leads to equivalent dispersion with less energy. This can be explained by the effect of CMC on the hydrophobicity of the talc surface. Wettability experiments have shown that the talc surface becomes hydrophilic in the presence of CMC because of CMC adsorption on talc particles. With a hydrophobic surface, air can be trapped between talc particles leading to foam whereas in the presence of CMC the dispersion of particle in aqueous solution is improved. Recent experiments confirmed the presence of air nano-bubblues between sheets of talc leading to floatation "air entrapment in the porous structure of talc are possible causes for the poor dispersability of micronised talc" [START_REF] Zbik | Dispersion of kaolinite in aqueous solution: nanomorphology and nano-bubble entrapment[END_REF]. By reducing the hydrophobicity of talc surface with CMC (see section 4.3), air entrapment can be limited then leading to a better dispersability of particles.

Settling properties of talc suspensions were determined for talc particles in the absence and presence of CMC and for CMC pre-coated talc particles. Figure 11 presents the variation of settling velocity with the CMC concentration for various CMC molecules.

Settling of bare talc particles occurs at around 1.5 mm/h. A plateau with lower settling velocity was found for CMC concentrations above 1 g/L. For these conditions, the settling velocity decreased as the molecular weight of CMC increased. Table 5 presents the particle diameter calculated for various CMC concentrations from settling experiments. Calculations were made with the classical settling law by accounting for the change in supernatant viscosity (experimentally determined by a co-axial rheometer) and a talc density of 2.8. For bare particles, the settling corresponds to particles of around 2 μm in diameter. For talc particles in CMC solution with a concentration of over 1 g/L, the settling is fully linked to CMC viscosity : the apparent size calculated from settling law by using the experimental supernantant viscocity is almost constant in presence of CMC (Table 5) . However, these calculated talc particle size is two times less than the one obtained for bare particles.. So, dispersion of talc particles is better in the presence of CMC at concentrations over 1 g/L. This suggests the existence of electrosteric repulsion between particles because of the brush-like talc surface induced by charged CMC adsorption which is fully linked to an increase in negative zeta potential (see above). On the other hand, for concentrations less than 1 g/L CMC 21903 (highest molecular weight) a higher settling rate was measured than with bare particles. This can be attributed to flocculation between particles because of dilution of polymer adsorbed to the talc surface and leading to the formation of bridges between particles (bridging flocculation). For higher polymer concentrations the phenomenon of stabilisation by electrosteric repulsion occurs leading to a decrease of settling velocity.

Settling velocity was determined for CMC pre-coated talc particles dispersed in water.

The results are presented in table 6. It shows that the settling velocity is slightly lower than that obtained with bare particles which can not here be attributed to changes in viscosity but to a stabilization of particles after pre-coating. Furthermore, it was experimentally found that dispersion of pre-coated particles was very easy requiring less energy than with bare particles.

Conclusions

Determination of adsorption isotherms has shown that the three CMC tested adsorb on the talc surface. This adsorption on talc particles was confirmed by Attenuated Total Reflectance on the Middle InfraRed region (ATR MIR) and SEM FEG observations. Washing of talc particles leads to a weak desorption of CMC meaning that CMC adsorption is mainly irreversible (except for the CMC with the highest molecular weight). Furthermore, precoating the talc with CMC is possible leading to talc powder with CMC irreversibly adsorbed on the surface.

Dispersion and settling studies of talc have shown that the presence of CMC drastically improves the dispersion of talc particles by avoiding foam and aggregate formation. This effect can be explained by wettability experiments showing that CMC adsorption confers more hydrophilic properties to talc. Furthermore, when dispersed in CMC solution at concentrations over 1 g/l (in 100 g/l talc suspension), the settling velocity is reduced mainly because of the high viscosity of the CMC solution. But results also show that presence of CMC induces a complementary decrease in settling velocity which could be due to the better dispersion of the talc in the solution induced by electrosteric repulsion between talc surfaces where CMC is adsorbed. This is confirmed by measurement of zeta potentials of talc where adsorption leads to a higher negative zeta potential. This positive effect of CMC is also observed when CMC pre-coated talc particles are dispersed in water.

For future applications, it has been shown that it is possible to pre-treat talc particles with CMC to improve their dispersion in aqueous solution. This method [START_REF]Matériau composite utilisable comme revêtement lubrifiant[END_REF] could be very interesting for the dispersion of talc in complex aqueous solutions where the presence of CMC could change the properties of the solution or where competitive adsorption could occur at the talc surface.

  Around 75-80 % of CMC (21900 and 21901) adsorbed on particles was still present after two washings. Only 35-40 % of CMC 21903 remained on the talc after two washing. The larger size of CMC 21903 could lead to greater reversibility of adsorption by washing as the polymer chain can be stressed by the hydrodynamic forces exerted by centrifugation.

Fig. 1 :Fig. 2 :Figure 3 :Figure 4 :Figure 5 :

 12345 Fig. 1: Talc structure along the c*-axis : two Si inverted tetrahedral sheets (with few Fe 3+ and Al substitutions) sandwich one Mg octahedral sheet (with few Fe 2+ , Al, Mn, ... substitutions)

Figure 6 :Figure 7 :Figure 8 :Figure 9 :Figure 10 :

 678910 Figure 6 : ATR MIR analysis of talc particles without added CMC -white squares -of talc particles precoated with CMC -grey triangles -and of a large talc sheet precoated with CMC -black circles -. IR Vibrations bands of CMC are detected on precoated talc. These bands cover the Si-O band of the talc.

  /L CMC eau + 4g/L CMC talc traité (4h) talc traité (4h) talc traité(4h)

Figure 11 :

 11 Figure 11 : Settling velocity of talc particles as a function of CMC concentration.

Table 1 :

 1 Main properties of the CMCs used for dispersion of talc

	CMC type	Degree of Substitution	Molecular weight
	21900	0.79	100-150 000
	21901	0.78	50 000
	21903	0.92	250 000

Table 2 :

 2 Reversibility of CMC adsorption on talc particles after one or two washings

	(centrifugation and dispersion in water) by analysis of CMC in the supernatant. Calculations
	based on initial quantity adsorbed.
	CMC type	Loss in % (of initial adsorbed	Loss in % (of initial adsorbed
		amount) after one washing	amount) after two washings
	21900	16	22
	21901	18	23
	21903	47	63

Table 3 :

 3

	CMC type	Loss in % (of amount adsorbed after 2 washings)
		after drying and regrinding of the talc
	21900	7
	21901	6
	21903	22

Reversibility of CMC adsorption onto talc particles after centrifugation, drying of the pellet and dispersion in water after regrinding. Calculation based on quantity adsorbed

after two washings.

Table 4 :

 4 Calculation of the fraction of talc surface covered by CMC when assuming macromolecular adsorption in a flat conformation.

				Amount of CMC	Fraction of talc
	CMC	Mw (g/mol)	Molecule area (nm 2 )	adsorbed on talc (mg/m 2 )	surface covered by CMC
	21901	50000	107	0.46	0.59
	21900	125000	267	0.42	0.54
	21903	250000	535	0.39	0.50

Table 5 :

 5 Talc particle diameter deduced from settling experiments for talc dispersion in the absence and presence of various CMC.Calculations used a classical settling law corrected with the supernatant viscosity.

		No CMC	CMC 21900	CMC 21901	CMC 21903
		added	2 g/L	3 g/L	2 g/L	3 g/L	2 g/L	3 g/L
	Settling velocity (mm/h)	1.5	0.21	0.16	0.50	0.46	0.10	0.08
	Supernatant viscosity (Pa.s)	0.001	0.0018	0.0021	0.0008	0.0011	0.0038	0.0048
	Particle diameter (μm)	2.04	1.02	0.97	1.05	1.19	1.03	1.03

Table 6 :

 6 Settling velocity of talc particles in the absence of CMC and for CMC pre-coated talc particles.

		No CMC		Pre-coated talc particles with
		added	CMC 21900	CMC 21901	CMC 21903
	Settling velocity (mm/h)	1.5	1.58	1.04	0.69

Acknowledgements

We have benefited over the years from results obtained by Reda El Berrichi and William Vautrin and from very helpful discussions with Stephane Vaillant and Jean-Luc Trompette. We are grateful to the CNRS for supporting this study through the projet "Traitements de surface et dépôts de couches minces" and to Luzenac Europe (Richard Baëza and Sandrine Péjo-Soucaille) for providing the talc material, infrared data and for research discussions.


Michael Heusener

Richard Weidmann

A remark on Whitehead's cut-vertex lemma

We observe that Whitehead's cut-vertex lemma is an immediate consequence of Stallings folds.

Introduction

Whitehead's cut-vertex lemma [5] implies that the Whitehead graph of a primitive element of the free group is either not connected or has a cut vertex. This result was generalized by Stong [4] and Stallings [3] to separable subsets of free groups. In this note we observe that this is an essentially trivial consequence of Stallings folds. To do so we relate the connectivity properties of the Whitehead graph of a set of conjugacy classes of elements to the readability of cyclically reduced representatives of these classes in a class of labeled graphs that we call almost-roses.

Free groups and graphs

In the following we denote the free group in X = {x 1 , . . . , x n } by F n . Throughout this note n ≥ 2 and X are fixed. As usual we represent elements of F n by words in X := X ∪ X -1 . For any g ∈ F n we denote the conjugacy class of g by [g] and for S ⊂ F n we set [S] := {[s] | s ∈ S}. We say that g ∈ F n is primitive if g in contained in a basis of F n . We further call a set S ⊂ F n separable if there exists a non-trivial decomposition

F n = F 1 * F 2 such that any w ∈ S is conjugate into F 1 or F 2 , see [3]. Clearly {g} is separable for any primitive element g ∈ F n .
An X-labeled graph Γ is a directed graph (with inverse edges) with a labeling map ℓ : EΓ → X such that ℓ(e -1 ) = ℓ(e) -1 for any edge e ∈ EΓ. Multiple edges and loops are permitted. The label of a path γ

= e 1 • • • e k in Γ is the word ℓ(γ) = ℓ(e 1 ) • • • ℓ(e k ).
In the following R n is the X-labeled graph whose underlying graph has vertex set V = {v 0 } and edge set {e ±1 1 , . . . , e ±1 n } such that ℓ(e ε i ) = x ε i for all ε ∈ {-1, 1} and 1 ≤ i ≤ n. As usual we identify F n with π 1 (R n , v 0 ) in the obvious way. For any Xlabeled graph Γ there is a unique label preserving morphism f : Γ → R n .

We say that a word w is readable in Γ if there exists a closed path in Γ with label w. We will say that an element g ∈ F n is readable in Γ if the corresponding reduced word is readable in Γ. We will further say that a conjugacy class [g] is readable in Γ if some (and therefore all) cyclically reduced word representating [g] is readable in Γ.

We will be mostly interested in connected X-labeled graphs Γ such that associated map f * : π 1 (Γ) → π 1 (R n ) = F n is surjective. In this case the morphism f can be written as a product of Stallings folds, see [2].

Recall that a graph Γ is called a core graph if it contains no proper subgraph such that the inclusion is a homotopy equivalence; for a finite graph this just means that Γ has no vertex of valence 1. We also call a pair (Γ, v 0 ) a core pair if Γ contains no proper Date: February 26, 2019.