Veyis Gunes

Jean-Yves Botquélen

Gwenaël Corbel

Philippe Lacorre

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Keywords: Computerized instrumentation, Eddy currents, Induction heating, Materials characterization, Nondestructive testing, Programmable control, Thermal gradient

Mobility/Diffusion of ions can occur mainly in two situations. The first one when a potential difference is applied to electrodes of an electrochemical device as in batteries for instance (i.e., charge/discharge). In the second one, the diffusion process is driven by the thermal gradient existing within the material. This paper deals with the design of a controlled Thermal Gradient Generator (TGG) which opens the way to thoroughly study the effect of temperature difference on the chemical diffusion and mechanical resistance of shaped samples (e.g., a pellet, a rod). This TGG uses a combination of two susceptors involving the control of their respective temperatures. One is controlled by adjusting the power of a high frequency generator which supplies an induction heating coil. The other is controlled, mainly, by the displacement of the sample/susceptors set through this same coil, with a motorized stage. The operation and control parameters are defined within a dedicated user-friendly software application. During the whole experiment, the two temperatures can be varied while the inner thermal gradient of the sample is kept constant, as long as these temperatures are high enough.

I. INTRODUCTION

THERMAL gradient devices are useful tools to study material properties such as chemical diffusion, thermal conductivity, temperature resistance, ageing, etc. The purpose of the experimental device described in this paper is to apply a controlled thermal gradient to solid samples (a few millimeters thick and about 1 cm 2 as cross-section) at high temperatures (up to 1000°C and beyond). In our laboratory team, the studied samples were typically ceramics that undergo ionic diffusion and exsolution when heated up. After applying a thermal gradient across a sample in a nondestructive way, the final goal was to study the microstructures generated by the gradient on and inside the V. Gunes is with the Institut des Molécules et Matériaux du Mans, Le Mans University, 72085 Le Mans, France (e-mail: veyis.gunes@univlemans.fr).

J.Y. Botquélen, G. Corbel and P. Lacorre are with the Centre National de la Recherche Scientifique, assigned to the Institut des Molécules et Matériaux du Mans, Le Mans University, 72085 Le Mans, France (e-mail: respectively, jean-yves.botquelen@univ-lemans.fr, gwenael.corbel@univ-lemans.fr and philippe.lacorre@univ-lemans.fr). ceramic through characterization techniques such as X-ray diffraction, SEM (Scanning Electron Microscope) or FIB-SIMS (Focused Ion Beam-Secondary Ion Mass Spectrometry).

More generally, the TGG presented here can be used to apply any temperature/time controlled gradient at moderate to high temperature between opposite faces of any type of solid insulators or semiconductors, may them be inorganic or polymers. For instance, this device would be suitable for the study of ionic thermomigration in solids (e.g. in memristors, as in Shin et al. [START_REF] Shin | Oxygen thermomigration in acceptor perovskite[END_REF]) or for the optimization of the thermal treatment of thin films, as in Metting et al. [START_REF] Metting | Note: A simple thermal gradient annealing unit for the treatment of thin films[END_REF] (these are recent studies using more loosely controlled or conventional heating systems). The current TGG is designed to operate in air, but would perform in controlled atmospheres or vacuum too. It allows nondestructive testing.

The main concern of the study is to validate the use of an induction heating system to automatically control and stabilize both the temperature on one side of the sample (e.g., the lower face) and the temperature differential with respect to the other side of the sample, thus allowing a steady-state thermal gradient. This controlled gradient at high temperatures constitutes the novelty of this work. Heating has to be located on small surfaces and temperatures must be measured on both sides. The temperatures of both faces must be as homogeneous as possible in order to have a uniform gradient throughout the section of the sample.

Bober et al. [START_REF] Bober | Schumacher uranium in mixed (U, Pu) oxide fuel materials in a thermal gradient[END_REF] introduced an induction heating system which is built in a high-vacuum, water-cooled recipient. This setup is well suited to higher temperatures, such as 2577°C (2850K), but the gradient is adjusted manually, without an automatic control. Furthermore, the system is more expensive.

A patented system is described by Pontillon et al. [START_REF]Device for generating a high temperature gradient in a optical monitoring means[END_REF]. It consists in a radial (as opposed to axial in our case) gradient at temperatures up to 2000°C, but it allows a single temperature set point (along the axis of the cylindrical sample). External temperature is fixed by choice of the insulator (depending on its nature and geometry), and chosen by simulation at a temperature of 350°C +/-50°C, without any attempt of automatic control.

A paper by Shihab et al. [START_REF] Shihab | Steady-state thermal gradient induced by pulsed laser excitation in a ferromagnetic layer[END_REF] describes a heating system by pulsed laser excitation, which can be used only on thin layers (typically 50 nm thick) of magnetic materials showing a hysteresis cycle, in order to get a thermal differential (ΔT) of a dozen degrees induced by the laser spot.

> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE Another patent application, from Obbard et al. a device which can establish a thermal gradient within li tissue or an ice core. Two heat sinks are used by a control mechanism at a different temperature. Each heat sink is in contact with a thermal conductor being set on two opposite faces of the sample. thermal gradient is maintained within the the use of heat sinks limits applications to room temperature.

The solution adopted in our device induction coil heating up two susceptors, one on each sample face. Susceptors can be the same if the sample is thick enough to induce a large enough thermal gradient or below the coil center, or have different thicknesses in to increase the gradient. A typical chosen upper susceptor with double thickness relative to one, e.g. 300 and 150 µm, respectively.

The temperature of the lower face and the temperature differential ΔT (therefore, the temperature gradient) are regulated by two independent control loops. heating system with two heating resistors, our solution following advantages: 1) it avoids thermal bridges which inevitably degrade homogeneity in temperatures of the two there are no wires connected to effectors and which could sink-out heat at contact points or contact surfaces). 2) it makes it possible to simulate quenchin quenching more efficiently (with resistors, bridges would slow down the cooling of the susceptors 3) it is more suitable for thermal cycl investigations since it allows higher temperature rise times as explained by Liu [START_REF] Liu | Ceramic Specimen Heating by Induction Power[END_REF]. 4) Finally, our solution is much less expensive heating systems, because even with heating resistors, two heating systems would have to be that are indeed the most expensive part This article is organized as follows. We procedure of the proposed TGG and its preliminary calibration (Section II). Then, the automatic control of the TGG is justified and presented in Section III. Section IV introduces the control software and equipment. This is completed by a validation Section V, with some results. Finally, is drawn and some prospects are proposed in

II. MANUAL TGG OPERATION

Lets Th and Tl be the stabilized temperatures of the upper (higher) and lower susceptors, respectively. Let P be the power dissipated by eddy currents in a sheet/ from an induction coil, see Figure 1).

Under some conditions (mainly, uniform material, without skin effect), as explained by Nickelson [START_REF] Nickelson | Electromagnetic Theory and Plasmonics for Engineers[END_REF], P is given by: where, P is the power lost per unit mass (W/kg), B is the magnetic flux density (T), > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < Another patent application, from Obbard et al. [START_REF] Obbard | Temperature gradient system and method[END_REF], describes thermal gradient within living are used, each maintained emperature. Each heat ontact with a thermal conductor, the two conductors on two opposite faces of the sample. Thus, an axial within the sample. However, limits applications to temperatures below consists in a single two susceptors, one on each sample Susceptors can be the same if the sample is thick enough to induce a large enough thermal gradient when shifted above or below the coil center, or have different thicknesses in order typical chosen configuration is an thickness relative to the lower perature of the lower face and the temperature he temperature gradient) are two independent control loops. Compared to a heating system with two heating resistors, our solution has the avoids thermal bridges which inevitably degrade homogeneity in temperatures of the two susceptors (as there are no wires connected to effectors and which could out heat at contact points or contact surfaces). it makes it possible to simulate quenching or quasiwith resistors, the thermal slow down the cooling of the susceptors), thermal cycling and fatigue higher temperature rise times, much less expensive than two heating resistors, the have to be controlled systems part in such a device. ed as follows. We first study a manual and its preliminary calibration automatic control of the TGG is and presented in Section III. Section IV introduces This is completed by a Finally, a conclusion are proposed in Section VI.

OPERATION Th and Tl be the stabilized temperatures of the upper pectively. Let P be the mass sheet/pellet (induced uniform material, without ickelson [START_REF] Nickelson | Electromagnetic Theory and Plasmonics for Engineers[END_REF], P is given by: , (1) P is the power lost per unit mass (W/kg), d is the thickness of the sheet (m), f is the frequency (Hz), ρ is the resistivity of the material ( D is the density of the material (kg/m Fig. 1: The induction heating system: the two susceptors currents, impose a thermal gradient to a sample constitute the mobile set. The coi Usually, Tl and Th cannot be defined as linear functions of Pl and Ph (respectively, the power in the lower and upper susceptors), mainly because the losses of the susceptors temperatures. In this case, w either Tl or Th and thus the thermal gradient would controlled.

A. A manual generation of a t

The schematic diagram (Figure are placed on each side of a studied controller holds a setpoint with generator from Celes that supplies the induction coil. The eddy currents induced in the susceptors heat them effect. Thus, the two susceptors across the sample. The temperature of the low being regulated with a temperature controller Th and the thermal gradient can be ensured by moving the mobile set along z (see Figure 2) alumina test sample, 5 mm thick After some manual experiments, for a given z, we noticed that Th and ΔT can be described as linear functions of Tl. Also, for a given Tl, the thermal differential described as a linear function of z. will explain why and in which conditions, be used in a manual operation or TGG, how to calibrate the setup is the resistivity of the material (Ω m), and D is the density of the material (kg/m 3 ). induction heating system: the two susceptors, heated up by eddy impose a thermal gradient to a sample. Susceptors together with he coil is represented in dashed lines.

, Tl and Th cannot be defined as linear functions of the power dissipation of eddy currents in the lower and upper susceptors), mainly because the heat are not proportional to their this case, we can only impose and control the thermal gradient would not be generation of a thermal gradient The schematic diagram (Figure 1) shows two susceptors that a studied sample. A temperature point with a High Frequency (HF) that supplies the induction coil. The currents induced in the susceptors heat them up by joule Thus, the two susceptors generate a thermal gradient across the sample. The temperature of the lower element Tl with a temperature controller, a variation of Th and the thermal gradient can be ensured by moving the igure 2). For instance, we used an thick and 10 mm in diameter.

Schematic diagram of the manual procedure. A temperature controller with a high frequency (HF: 147 kHz, the frequency generated by our equipment) generator to reach the temperature of the mobile set makes it possible to vary After some manual experiments, for a given z, we noticed T can be described as linear functions of Tl. r a given Tl, the thermal differential ΔT can be described as a linear function of z. In the next subsections, we will explain why and in which conditions, this modeling can in a manual operation or in a computerized automated the setup and how to operate it

B. Proof of concept

Let us assume that the two susceptors have much higher thermal conductivity than the sample (at least 10 times) and thus there is not a thermal interference between the two susceptors. Let us define two functions Fh and Fl such as: ℎ

Fh and Fl are mainly functions of geometry losses of the susceptors. C1 and C2 are offsets (const originating from the influence of the ambient temperature. Consistently with (1), Ph and Pl are functions of a magnetic field (Bh and Bl, respectively), the other parameters being the same for the two susceptors.

If the thickness of one susceptor is just a few times higher than the other's (but the two circumferences are at least 10 times higher than the two thicknesses), the thermal losses would be similar for the two, since the specific surface doesn't differ much (meaning that Fh≈Fl). In these conditions and C 1 , C 2 , Tl, and Th are considered constant,

→

The constant A will depend mainly on the thicknesses of the two susceptors. Furthermore, if the thickness of the sample is, at least, 10 times smaller than the coil length, meaning that the two susceptors are very close to each other, Bh and Bl would be very similar and thus A would have a value of 1 if the two susceptors have the same thickness and are made with the same material. From equation ( 3) and posing we obtain: ℎ

In the following section, we introduce our measu that are carried out by manual displacements of (the two susceptors and the sample) modeling is possible. Consequently, ΔT can be model ΔT Tl Th 1

Tl being fixed by the temperature controller be modeled as a linear function of Tl, we can also assume that for a fixed position z:

Where Gh and Gl are mainly functions of geometry heat losses of the susceptors. For the same reas previous case, and with the same conditions, we can 1 →

By posing m = m 1 -m 2 .k, we obtain:

It should be noted that a calibration is needed for each type of material used as samples and for any replacement of susceptors.

C. Calibration measurements

A first series of measurements made it possible to demonstrate a good linearity of Th as a function of fixed z position) in stabilized values, as well as good linearity of the differential ΔT as a function of z, at > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < , in order to generate a required thermal gradient. assume that the two susceptors have much higher thermal conductivity than the sample (at least 10 times) and not a thermal interference between the two define two functions Fh and Fl such as:

!ℎ. ℎ # $ % ! . # $ & ' (2)
of geometry and the thermal C1 and C2 are offsets (constants) originating from the influence of the ambient temperature. Consistently with (1), Ph and Pl are functions of a local peak magnetic field (Bh and Bl, respectively), the other parameters is just a few times higher circumferences are at least 10 times higher than the two thicknesses), the thermal losses would be similar for the two, since the specific surface doesn't n these conditions and as , Tl, and Th are considered constant, we can write that:

() * () + + , (3)
will depend mainly on the thicknesses of the . Furthermore, if the thickness of the sample is, than the coil length, meaning that the two susceptors are very close to each other, Bh and Bl would would have a value of 1 if the two and are made with the posing C 1 -A.C 2 = To, ℎ ,. # -(4)

In the following section, we introduce our measurements by manual displacements of the mobile set showing that this can be modeled as:

1 A/. Tl - (5)
by the temperature controller, since ΔT can be modeled as a linear function of Tl, we can also assume that,

0 . # 1 % 0ℎ. ℎ # 1 & ' (6)
Where Gh and Gl are mainly functions of geometry and the For the same reasons as for the and with the same conditions, we can write:

(2 * (2 3 (7) 3. # 1 (8)
It should be noted that a calibration is needed for each type and for any replacement of easurements made it possible to demonstrate a good linearity of Th as a function of Tl (with a as well as good linearity as a function of z, at a fixed temperature Tl. A second series of measur study the repetitiveness of the measurements. first series. a) Variation of the temperature As shown in Figure 3, the measurements allow a linear regression according to (4), with A=0.8275 and To=71. [START_REF] Bober | Schumacher uranium in mixed (U, Pu) oxide fuel materials in a thermal gradient[END_REF] The mobile set is slightly eccentric u the coil. In this case, Th is lower the distance to the coil center field lower). Therefore, we have positive Figure 4. But, ΔT depends also on z and should verify [START_REF] Nickelson | Electromagnetic Theory and Plasmonics for Engineers[END_REF]. T in the next section, we vary z, keeping b) Variation of the position z Th varies linearly as a function of z (see Figure 5) Figure 6 shows that ΔT can be modeled equation 8), as a function of z.

The parameter k is a displacement calibration constant. our case: k= -3.86°C/mm and At 700°C, we can therefore ha 11°C/mm. This thermal gradient may increase massive upper susceptor, and at c) Conditions of the measurements It is necessary to wait thermal stabilization, before taking into account the measure case). To check if the thermocouples can act as heating elements, we performed a h thermocouple (without the mobile set) follows the set point (tested up to 150 +25°C is reached in about 3 s CLICK HERE TO EDIT) < 3

. A second series of measurements has been undertaken to etitiveness of the measurements. It confirmed the emperature Tl (at z=0) As shown in Figure 3, the measurements allow a linear regression according to (4), with A=0.8275 and To=71.31.

slightly eccentric upwards, with respect to ower than or equal to Tl (because center is larger and the local magnetic have positive ΔTs, as it is shown in of Th as a function of Tl, with constant z. The relationship is linear.

as a function of Tl: linear, in first approximation.

z and should verify [START_REF] Nickelson | Electromagnetic Theory and Plasmonics for Engineers[END_REF]. Therefore, vary z, keeping Tl constant at 700°C. Variation of the position z (at Tl=700°C). Th varies linearly as a function of z (see Figure 5) and can be modeled linearly (according to , as a function of z.

k is a displacement calibration constant. In 3.86°C/mm and m = 56.9 (see Figure 6). C, we can therefore have, at most, a gradient of gradient may increase with a more and at higher temperatures. measurements thermal stabilization, a few minutes the measurement (2 minutes, in our To check if the thermocouples can act as heating elements, we performed a heating cycle with only one thermocouple (without the mobile set): the thermocouple ed up to 150°C). A fast heating of in about 3 seconds. Therefore, the thermal inertia of the thermocouple is low, which means that its temperature adapts to that of the susceptor.

The susceptors have a short response time but a low heat dissipation. For this reason we have chosen a set point rate (SPrr for a Eurothem controller) at 30 reached in 30 minutes). The controller does not keep the set point in case of a power failure.

D. Manual control and operation

Let g be the required thermal gradient (°C/mm) and e, the thickness of the studied sample. A manual control is possi as long as the external disturbances are minimized. a) Manual position adjustment for a required gradient To adjust the position, we can calculate determine Tl with equation [START_REF] Shihab | Steady-state thermal gradient induced by pulsed laser excitation in a ferromagnetic layer[END_REF]. Finally position z to be reached in order to get the pair of (Tl, ΔT), with equation ( 8): b) Typical manual procedure According to our tests, in this configuration, we can reach thermal gradient of up to 20 °C/mm and a temperature of up to 1000°C on one of the two faces. The following procedure allows typically the application of a thermal 1-For a given material and thickness, calibrate the system by determining the equations ( 5) and ( 8). 2-The calibration phase being complete, 3-Choose ΔT, i.e. a gradient g given by g= 4-With equation ( 9), determine and set response time of ΔT is longer than the response time of 5-Finally, determine Tl with equation ( 5> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < inertia of the thermocouple is low, which means that its temperature adapts to that of the susceptor.

The susceptors have a short response time but a low heat dissipation. For this reason we have chosen a set point rate °C/min (i.e., 900°C ). The controller does not keep the set is kept constant in order to study Th as a function of the position z. can be modeled as a function of the Let g be the required thermal gradient (°C/mm) and e, the A manual control is possible are minimized. for a required gradient g calculate ΔT = g.e, then Finally, we calculate the the pair of set points

∆ (2/ 5 (9)
his configuration, we can reach a mm and a temperature of up to The following procedure thermal gradient: or a given material and thickness, calibrate the system by place a new sample. g=ΔT/e. and set the position z. The the response time of Tl. with equation ( 5) and set it as setpoint to the temperature controller

III. A COMPUTER CONTROLLED TGG

The manual procedure has difficult to regulate both simultaneously to set a gradient experimentation can enable the addition, it has the following advantages: a) Do measurements more precisely and b) Make the experiments repeatable and reproducible. c) Allow an automatic calibration (by temperature, then of z). This is very useful if the dimensions of the susceptors different sizes, shapes or compositions are used. d) Allow a sudden stop of the heating and follow the temperatures Tl and Th (equivalent to a quenching).

A. Configuration in piloted mode with two instructions (Tl,

We use a Eurotherm 2404 thermocouple) with a serial communication mo and a Modbus protocol. The be controlled by a PC and a Figure 7 gives a general scheme The real temperature Tl continuously by the PC. The are: J, K, L, R, B, N, T, S, and Th, an external data acquisition (National Instruments: NI cDAQ 9172). thermocouple is used as a sensor. thermocouples are: J,K,N,R,S,T,B, For the control of the motorized stage makes it possible to move the thus to move along z to reach the desired stage, controlled through a USB port, includes a s and its controller: Model L490MZ/ are two ways to control this other is relative. After some test control is more robust. Therefore, we chose this mode

UTER CONTROLLED TGG

The manual procedure has many limitations and makes it difficult to regulate both set points (Th and ΔT)

to set a gradient. Computer-controlled the automation of the process. In the following advantages: urements more precisely and save them in a file. Make the experiments repeatable and reproducible. Allow an automatic calibration (by a leap of the temperature, then of z). This is very useful if the susceptors are changed or if samples of or compositions are used. llow a sudden stop of the heating and follow the (equivalent to a quenching).

mode with two instructions (Tl, ΔT) a Eurotherm 2404 temperature controller (K type a serial communication module EIA 232 he temperature controller can thus be controlled by a PC and a LabView custom application. Figure 7 gives a general scheme of the experimental setup.

(Process Value) is also read . The types of thermocouples allowed and PL2. For the measurement of cquisition module (USB) is used ional Instruments: NI cDAQ 9172). A type K thermocouple is used as a sensor. The possible types of : J,K,N,R,S,T,B, and E. temperature differential ΔT, a makes it possible to move the mobile set and z to reach the desired ΔT. The motorized stage, controlled through a USB port, includes a stepper motor Model L490MZ/M from ThorLabs. There is stage, one is absolute, and the ive. After some tests, it seems that its absolute . Therefore, we chose this mode.

B. Optimization of susceptors

We first tried platinum (Pt) thin layers (by spreading platinum ink on ceramic substrates, then drying). After many tests, we noticed that the platinum layers eventually crack and no longer allow an efficient heating by eddy currents. For this reason, we opted for thin platinum plates that we had at our disposal (currently: 150 µm and about 300 µm thick for the lower and higher susceptors, respectively) of diameter widely greater than that of the sample (our samples are cylindrical pellets). Both Pt plates and PVD (Physical Vapor Deposition) deposited layers could be used to increase thermal contact.

C. Mounting diagram

In Figure 8, the mechanical setup is presented, showing the mobile set under the coil and the possibility of fixing z o (initial z) with a preset wheel in z. In our device, Hs is between 330 mm and 400 mm and can be set with the preset wheel. We fix it once and for all at Hs=350 mm. Let Ht be the height at which the axis of the induction coil must be placed, we need a withdrawal margin such as: Ht = Hp + Hs + Withdrawal margin = 58.5 + 350 + 40 = 448.5 mm (we fix Ht=448 mm). To have a good mechanical stability, the length of the zdisplacement support must be larger than the height of the sample holder and therefore, it is fixed at 325 mm.

D. Control

Since the lower thermocouple is more likely to be in close contact (supporting the weight of the mobile set) than the top one, it is more secure to regulate Tl with the HF generator. If Th thermocouple is not in contact we risk having an unlimited rise of z. For this reason the maximum movement in the control application is limited to 50 mm, which also corresponds to the maximum stroke of the motorized stage. In order to simplify the control, the rise and the decrease in temperature will be done with the same rate/slope. Since the heat goes up, if the elements are introduced from the bottom of the coil to the top, we should reach higher temperature differentials. So we change the configuration, introducing the elements from the bottom of the coil. Thus, in the new configuration, we have : ℎ = 6. + 7 (10) = 3 8 . + 1 (11) We want to regulate Tl and ΔT, at the same time. Note that To and m would not have the same values as before. They depend on the initial positions and temperatures.

Th will be higher than Tl and the roles of Th and Tl will be reversed. Only the slopes are to be kept (a second series of measurements would determine the new To and m values). If we express Tl as a function of Th (from equation 4), the slope will be a = 1/A = 1/0.8275≈1.2. For the value of k', approaching from the bottom (z directed upwards), k would keep its value, so finally k'=k=-3.8611. Thus, we have a new system of equations:

= ℎ -= 6 -1/. + -9:;ℎ 6 > 0/, (12) = 3. + 1 3 < 0 @-A B:ACD;CB EF96ABG/, (13) where a and k are known, but To and m are to be determined as explained in the next section.

E. Automatic calibration of the TGG

We note that the more massive the higher susceptor is, the faster Th rises and ΔT is reached. This allows larger ΔT values. The thermal inertia being higher, the increased mass should also yield less fluctuation. To calibrate the TGG completely (example: for a new type of sample), around an operating point, we can determine k, a, m and To by imposing a known leap in z and then a known leap of Tl: -Calculation of k by a small variation of z: at z 1 : ΔT 1 =Th 1 -Tl= k. We checked that for different Tl leaps, k is constant and for different z leaps, a is also constant. However, m and To depend on the initial temperature (ambient) and position. We choose a set point (e.g., z=0, Tl=200°C). With the equation ( 10), we calculate To=Th -a.Tl. Then, with the equations ( 12) and (13), we calculate:

1 = ΔT -k. z = a -1/. Tl + To -k. z (14)
These four parameters can be determined manually, but we also integrated these automatic procedures in our dedicated Labview application. It should be noticed that an optimal velocity of the stage should be chosen (a low value yields fluctuations on ΔT and a high value leads to a permanently turning motor).

We want a small variation δΔT, due to perturbations, to be compensated by a small displacement in δz, hence, after derivation, we obtain from the equation (13), the relation: (15) This relation is equivalent to a PI (Proportional, Integral) controller which is enough stable in our setup, where the proportional part is null (this is due to the fact that we have a progressively rising or decreasing setpoint).

F. Optimization of the temperature controller parameters

After various tests with our temperature controller, the following PID parameters gave the best results:

Pd=6, ti=13, td=2, where, Pd, ti, and td are respectively the proportional, integral and derivative coefficients. For the regulation of ΔT, an acceleration of 0.25 mm/s 2 and a velocity of 0.5 mm/s are the best motorized stage parameters. A new calibration was done at 300°C and gave the following parameters for the TGG:

a=1.58 k=-1.06°C/mm To=-95.3°C and m=78.4°C. Note: it is logical that the achievable (maximal) ΔT depends on the chosen Tl.

IV. CONTROL SOFTWARE

We designed and built up a dedicated user-friendly LabView application to control the experimental setup. The software environment is as follows: a PC for a development carried out on Windows XP and a LabView license (version 8.6, Full development). The developed application (see Figure 9) saves some values each second (or with a selected period) during an automatic thermal gradient generation with a chosen temperature profile. These values are: Time, Th, Tl, ΔT, z and the phase (increase, decrease, dwell) represented by respectively by ("M", "D" and "-"). The different tabs of the "Gradient" application are: "Parameters", "Experimentation", "Manual Mode", "Reserved" and "Help"). This control software is developed in LabView 8.6 graphical language. In the "Reserved" tab, there is, in particular, the possibility of recalibrating the system (determining a, k, To and m).

One can see the different tabs during the experimentation. Some parameters, such as dwell time, Th and therefore ΔT can be changed throughout the ongoing experiment, if necessary. A certain number of commands and measured values are available in all the tabs (e.g., Th, Tl, action on z) to be able to follow the experiment at any time and react as quickly as possible, if necessary.

Figure 10 shows a general view of the equipment, while Figure 11 shows the top views of the coil and the mobile set during experiments at two different temperatures. Fig. 11: Photographs during experimentations. Left and right pictures: the higher susceptor and thermocouple can be seen at around 750°C and 800°C, respectively. The susceptor appears white in the right picture. This is due to a wider emission spectrum.

V. RESULTS AND VALIDATION

Since platinum plates are used, cracks can be avoided and higher slopes (temperatures rates) scheduled. Three platinum disks (diameter: 14 mm, thickness: 0.15 mm) were cut in a platinum plate. Two contiguous discs, one on the other, were used as upper (higher) susceptor and one disc on the ceramic support as lower susceptor.

A. Gradient with simulation of a "quench" (alumina sample)

This experiment was done at an early stage of development, where the parameters (To, k, and m) where not well calibrated. Therefore, Th is not rigorously stabilized during the 580°C dwell.

An automatic adjustment of the Tl regulator was done and gave the following parameters: Pd=194, ti=16, td=2. Then, > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE an automatic calibration of the system was done at 250 it gave the following parameters: a=1.21, 0.519°C/mm, m=13.7°C. The regulation in z was with the following motorized acceleration=0.25 mm/s 2 , velocity=0.5 mm/s An experiment at (Th=580°C, Tl=550°C, slope=20 was carried out on a 5 mm thick alumina sample. It is presented in Figure 12 (started at about 500°C). Fig. 12: An experiment with a "quenching". Note that, immediately after a quench, Th becomes lower than Tl because of its higher surface of contact with the air and its low thickness.

Before "quenching", the chosen rate is high (20 the variations around the instructions (setpoints) are important. At t=4.2 min., the heating was stopped abruptly. Th ends with a value lower than Tl. This is due to the fact that the lower element has a higher thermal inertia (this was done in early development, when the lower susceptor was thicker

B. Gradient with an imposed duration (semiconducting ceramic sample)

After adjusting the PID of the Tl regulator and a calibration of the system, an experiment at (Th=850°C 10°C/min) was conducted on a semiconducting sample, 2 mm thick and 9 mm in diameter Figure 13 (experiment started at room temperature).

For information, at around Tl=80°C (an frequency of the HF generator is stabilized at 145.9 Fig. 13: An example of experiment, where it can temperatures higher than 500°C, the temperatures and well maintained. Th, Tl, ΔT, and z are saved during the whole experiment.

> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < n of the system was done at 250°C and he following parameters: a=1.21, To=-40.4°C, k=-

The regulation in z was carried out stage parameters: 0.5 mm/s. °C, slope=20°C/min) was carried out on a 5 mm thick alumina sample. It is (started at about 500°C).

Note that, immediately after a quench, Th becomes lower than Tl because of its higher surface of contact is high (20°C/min), then points) are important. , the heating was stopped abruptly. Th ends with . This is due to the fact that the lower (this was done in early susceptor was thicker).

semiconducting oxide regulator and a calibration °C, Tl=700°C, slope: semiconducting oxide ceramic in diameter. It is presented in (experiment started at room temperature).

(and even before) the stabilized at 145.9 kHz. can be seen that for Th °C, the temperatures and thus the ΔT are very during the whole experiment.

VI. CONCLUSIONS

With the current setup, we generated under the following conditions: with ΔT temperature differentials raised up to 150 mm thick sample (which results in 75°C/mm). The samples had thermal conductivity (alumina: 6.2 W • m oxide ceramic: considered lower than that of alumina).

We are currently using this nondestructive testing equipment to study the ionic migration, previously oxide-ion conductors (see Lacorre et al. [START_REF] Lacorre | Designing fast oxide-ion conductors based on La2Mo2O9[END_REF] The capabilities quoted above For other applications, the conditions of use could be modified. These conditions will depend on the material studied (thermal conductivity, sample shape, etc.) and simple adaptations that can be done between the two platinum plates).

Most of the possible applications development laboratories where, chemical species could be studied characterizations could involve the under fire, the behavior of composite materials materials submitted to thermal gradients submit protection tiles and thermal insulators to known and controlled gradients for aging studies A modified version of this TGG necessary to create a steady directions, e.g., for conductivity measurements in a vacuum chamber. According to Zhang et al. directions, easily carried out with our setup, thermal conductivity measurements. that for small samples (e.g., in thick sensors on the sample, thus a global thermal conductance measurement, consistent with our setup, is better suited. CONCLUSIONS setup, we generated thermal gradients under the following conditions: Th was raised up to 1000°C ature differentials raised up to 150°C for a 2 results in a thermal gradient of a thickness of 2 to 5 mm and low mina: 6.2 W • m -1 • K -1 at 1000°C, considered lower than that of alumina).

using this nondestructive testing equipment , previously in LAMOX Lacorre et al. [START_REF] Lacorre | Designing fast oxide-ion conductors based on La2Mo2O9[END_REF], Selmi et al. [START_REF] Selmi | Thermal stability of alkali and alkaline-earth substituted LAMOX oxide-ion conductors[END_REF]). quoted above are sufficient for our purpose. or other applications, the conditions of use could be . These conditions will depend on the materials to be studied (thermal conductivity, sample shape, etc.) and simple done (e.g., differences in thickness between the two platinum plates).

of the possible applications are in research and development laboratories where, for instance, the diffusion of could be studied. Other studies and characterizations could involve the behavior of materials havior of composite materials and building thermal gradients. The TGG could also submit protection tiles and thermal insulators to known and for aging studies. of this TGG could be used whenever it is necessary to create a steady-state heat flux in one or two conductivity measurements in a vacuum ing to Zhang et al. [START_REF] Zhang | A high-precision method to measure thermal conductivity of solids using reversible heat flux[END_REF], the alternating directions, easily carried out with our setup, allows better thermal conductivity measurements. Zawilski et al. [START_REF] Zawilski | Description of the parallel thermal conductance technique for the measurement of the thermal conductivity of small diameter samples[END_REF] stress that for small samples (e.g., in thickness), it is difficult to fix sensors on the sample, thus a global thermal conductance with our setup, is better suited.

CKNOWLEDGMENT

The authors would like to thank Pierre Rabadeux who some preliminary tests on susceptor materials, and the organization SATT Ouest-Valorisation (Rennes, France), a patent application and further and valorization prospects.

Fig. 2 :

 2 Fig. 2: Schematic diagram of the manual procedure. sets the 4-20 mA current loop with frequency generated by our equipment setpoint Tl. A manual displacement of the Th and thus ΔT.

  thickness of the sheet (m),

Fig. 3 :Fig. 4 :

 34 Fig. 3: Variation of Th as a function of T linear.

Fig. 5 :Fig. 6 :

 56 Fig. 5: Tl is kept constant in order to study Th as a function of the

Fig. 7 :

 7 Fig. 7: Overall scheme of the experimental sets Tl through the power of the HF generator the control of ΔT (and Th).

:

  Overall scheme of the experimental setup. The temperature controller ough the power of the HF generator while a motorized stage allows

Fig. 8 :

 8 Fig. 8: Assembling diagram of the automatic TGG equipment.

z 1 + m at z 2 :

 2 ΔT 2 =Th 2 -Tl= k.z 2 + m ΔT 2 -ΔT 1 =Th 2 -Tl-Th 1 +Tl=Th 2 -Th 1 =k.(z 2 -z 1 ) from where: k=(Th 2 -Th 1 )/(z 2 -z 1 ) -Calculation of a by a small variation of Tl: at Tl 1 =T: Th 1 =a.T + To at Tl 2 =T+T v : Th 2 =a.(T+T v ) + To Th 2 -Th 1 =a.T v , from where: a= (Th 2 -Th 1 )/(Tl 2 -Tl 1 ) -Calculation of m and To to regulate ΔT:

  This is the author's version of an article that has been published in this journal. Changes were made to this version by the publisher prior to publication.The final version of record is available at http://dx.doi.org/10.1109/TIM.2020.3039626 (c) 2020 European Union Copyright. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.

Fig. 9 :

 9 Fig. 9: Global view of the control software (with "Experimentation" tab selected).

Fig. 10 :

 10 Fig. 10: a general view of the experimental setup, with the coil and the mullite support seen in the upper-right corner (in red and white, respectively).

  EFERENCES H.I. Yoo, "Oxygen thermomigration in acceptor-doped Phys. Chem. Chem Phys., vol. 19, no. 18, pp. 11120-11130, Note: A simple thermal gradient annealing unit for the Scientific Instruments, vol. 84, no. 3, pp. 1770-10.1063/1.4795831. Bober, C. Sari, G. Schumacher, "Redistribution of plutonium and uranium in mixed (U, Pu) oxide fuel materials in a thermal gradient," J.

  3, pp. 265-284, June 1971, 10.1016/0022-Device for generating a high temperature gradient in a sample comprising optical monitoring means, by Y. Pontillon, E. Hanus, H. Capdeliva. (2015, US 2015/0098485 A1. [Online]. Lemaître, J.Y. Duquesne, C. Gourdon, state thermal gradient induced by pulsed laser excitation in a Applied Physics, vol. 119, no. 15, pp. 153904, Apr.

This is the author's version of an article that has been published in this journal. Changes were made to this version by the publisher prior to publication.The final version of record is available at http://dx.doi.org/10.1109/TIM.2020.3039626 (c) 2020 European Union Copyright. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.

(c) 2020 European Union Copyright. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.

ACKNOWLEDGMENT

The authors would like to thank P performed some preliminary tests on suscepto the organization SATT Ouest for their help with a patent application and development and valorization


Pierre-Alexandre Deyris

Pauline Adler

Eddy Petit

Yves-Marie Legrand

Claude Grison

Woody species: a new bio-based material for dual Ca/Mg catalysis with remarkable Lewis acidity properties

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Whereas the spread of metal pollutants in the environment continues, a series of novel approaches for the remediation and full-fledged ecological rehabilitation of contaminated soils and aquatic systems is developing [START_REF] Baker | Ecology of Industrial Pollution[END_REF][2][START_REF] Grison | [END_REF] . In order to give viable economic outlets for such ecological programs, metal-rich biomass can be turned into useful tools for sustainable chemistry [START_REF] Grison | [END_REF]4 . Taking advantage of the remarkable adaptive capacity of certain plants to bioconcentrate transition metals in their shoots or roots, our group has explored the direct use of metals derived from contaminated plant waste as green catalysts, also known as ecocatalysts [START_REF] Grison | [END_REF]4 . They were the first bio-sourced metallic catalysts. We have demonstrated that they can serve as efficient tools for valuable supported "Lewis acid" transformations 4,5 . They are excellent promoters of cross-coupling transformations, such as Suzuki and Heck reactions 6,7 , which are ligand-free and work with homeopathic amounts of Pd. Ecocatalysts also represent practical and elegant substitutes of conventional catalysts, enabling green processes for difficult oxidation 8,9 and reduction 10,11 reactions with interesting regio-and chemoselectivities. Ecocatalysts have attracted broad interest among researchers as they combine the merits of both sustainable catalysts and an ecological approach. They constitute the first practical chemical application of new phytoextraction and rhizofiltration technologies. Recently, we reported extensive structural studies of a series of ecocatalysts in order to establish correlations between their structure and their catalytic properties 12 . Fine studies revealed novel mixed salts such as CaMg2Cl6 5 , and KMgCl3 13 . These unusual species were generated from physiological metallic elements of all plants. In this article, we postulate that these mixed salts play an important role in the catalytic process. For instance, KMgCl3 has recently been demonstrated to show unique catalytic activity in Knoevenagel reactions, even better than that achieved with MgCl2 13 . This suggests the interest of evaluating the synthetic potential of bio-based mixed salts of physiological origin.

In this article, we wish to demonstrate that the ecocatalysis concept can be extended to common and abundant plant species that are not metallophytes but that are nevertheless surprisingly appropriate for chemical catalysis (Figure 1). We will show that willow (Salix x, Salicaceae), birch (Betula x, Betulaceae), beech (Fagus x, Fagaceae), plane (Platanus x, Platanaceae), maple (Acer x, Aceraceae), black locust (Robinia pseudoacacia, Fabaceae), oak (Quercus x, Fagaceae), horsechestnut (Aesculus hippocastanum, Sapindaceae) and linden (Tilia x, Malvaceae) trees can be used to produce bio-based and novel Lewis acid catalysts. We will thoroughly characterise newly identified ecocatalysts via MP-AES, XRD, HR-STEM/EDX, IR, ESI-SM and DFT in order to elucidate their chemical compositions, structures and properties. We will illustrate the catalytic potential of these ecomaterials through two representative transformations, oxidative esterification and acetalisation reactions.

Results and discussion

2.1.

Characterisation of ecocatalysts

In a first step, a thermal treatment was applied to the harvested biomass at 550 °C in order to destroy organic matter. In a second step, the resulting residues were treated with hydrochloric acid to convert metallic cations into metal chlorides. The reaction mixture was stirred for 3 h at 60 °C. The resulting aqueous solution, composed of different metal chlorides, was then concentrated under vacuum and dry residues were stored in a desiccator. Microwave Plasma Atomic Emission Spectroscopy (MP-AES) was used to determine the composition of the various ecocatalysts. Results are summarised in Table 1. In all cases, the ecocatalysts obtained from different leaves of common trees appeared as a slightly yellow powder, probably because of the presence of trace amounts of Fe(III). MP-AES analyses showed the presence of varying concentrations of physiological metallic species coming directly from these plants. Each ecocatalyst contained high proportions of calcium and potassium, the most abundant cations in plant constituents. Interestingly, the concentration of magnesium ranged from 0.75 wt% for Eco10 to 2.75 wt% for Eco3. It should be noted that Eco1a&b possessed low but significant proportions of Zn. These data are in agreement with the ability of some willow species to accumulate high Zn concentration in aerial parts 14 . Complementary to XRPD analyses, direct mass injection analysis was performed (Supporting Information 3). Eco1a was dissolved in a highly concentrated solution of HCl in water (9 M) and filtered over Amberlist IRA 400 in order to separate alkali or alkaline earth metals from iron salts 15 . Then a sample was injected by diffusion in the mass detector in negative ESI. The presence of CaCl3 -was confirmed and a new species composed of calcium and chlorine (Ca2Cl5 -) was observed.

Moreover, the presence of MgCl3 -probably showed the presence of KMgCl3, which was not detected in XRPD analysis. Eco1a was then studied by High Resolution Scanning Transmission Electron Microscopy (HR-STEM) coupled with Energy-Dispersive X-ray spectroscopy (EDX) in order to characterise the microstructural features of the ecocatalyst (Figure 2). In the original picture, three crystalline species of about 200 nm length were clearly identified, namely A, B and C, which were surrounded by a very light halo (Figure 2, top left panel).

The mapping process coupled with the crystal form indicated that B probably was NaCl. A and C seemed to correspond to KCl or KCaCl3, consistent with XRPD and mass analyses. What really caught the eye in this picture was the composition of the halo. Indeed, it included neither potassium nor sodium but rather magnesium, calcium and chlorine. This composition strongly suggests the presence of CaMg2Cl6, which confirm the results of XRPD.

Ammonia-temperature programmed desorption (NH3-TPD) analysis was performed on Eco1a in order to evaluate the acidity on the surface of the catalyst (See Supporting Information 7). There was two parts on the curve. The first signal appeared at low temperature as a classical gaussian curve. It was attributed to weak acid sites. The second part was a flat signal between 220 and 280 °C. Eco1a is a polymetallic catalyst, which results from a combination of various pure metallic salts. This means that each pure metallic species, which presents an acid site, can interact with gaseous ammonia in various intensities. Thus, the flat non-gaussian signal could be rationalised with the successive desorptions of each acid sites occurring during the increase in temperature. In order to distinguish Lewis and Bronsted acid sites, the method using sorption/desorption of the pyridine coupled with infrared analyses was performed 16 . FT-IR measurements of the absorbed pyridine on the surface of acidic solids were used to compare Lewis acidity and Brønsted acidity of ecocatalysts and of several pure salts contained by them. As shown in Supplementary Information 4, each species exhibited the presence of Lewis acid sites. After evaporation at 150 °C of Eco1a, we could observe that the Brønsted acid character was stronger than the Lewis acid one. After the ecocatalyst was heated at 450 °C, the IR pattern of Eco1a totally changed. The Lewis acid sites emerged while a large decrease of Brønsted acid sites was observed. This could be explained by the thermal decomposition of metal chlorides into oxides or hydroxides, which possess Lewis acid properties. Interestingly, the bromide form of Eco1a (Eco1b) possessed both Brønsted and Lewis acidities. However, Lewis acid bands of Eco1a had higher values than Eco1b, leading us to think that Eco1a could be a stronger Lewis acid than Eco1b. The XRPD studies of Eco1a highlighted the presence of simple metal chlorides such as CaCl2, but above all, the presence of mixed metal chlorides such as KCaCl3. These salts had a Lewis acid character without Brønsted acidity. The cases of MgCl2 and KMgCl3 are different. The first one possessed the same Brønsted acid band as Eco1a while the second did not show any acidic character. In view of the bands at 1616 and 1464 cm -1 (Supplementary Information 4), KMgCl3 is a far better Lewis acid than other species. For comparison, FT-IR measurements of CaCl2, MgCl2 and CaMg2Cl6 at 150 °C are presented in Figure 3. In view of the bands between 1599 and 1613 cm -1 , it was clear that CaMg2Cl6 was a better Lewis acid than CaCl2 and MgCl2, confirming the interest of studying mixed salts. The catalytic potential of ecocatalysts, and their specific Lewis acidity, suggested interesting opportunities for catalysis in organic synthesis. This view is supported by the study of molecular interactions with the C=O bond of benzaldehyde, the substrate of targeted reactions (For more details, see Supporting Information 4). Spectra involving CaCl2 and KCaCl3 presented approximately the same vibration bands (Supplementary Information 4). Two bands corresponding to a C=O vibration were observed for MgCl2, which were more shifted than those with calcium salts. This meant that C=O-Mg interaction was stronger than C=O-Ca interaction. This trend was confirmed with the spectrum involving the stronger Lewis acid KMgCl3, which showed very shifted C=O stretching vibrations. CaMg2Cl6 presented a single signal, meaning that only one benzaldehyde-CaMg2Cl6 complex was formed. By comparison with KMgCl3, CaMg2Cl6 was more strongly associated with the benzaldehyde. Finally, Eco1a showed a broad signal between 1700 and 1600 cm -1 , which resulted from a succession of many interactions due to the polymetallic composition of the ecocatalyst. Regarding the position of the C=O stretching vibration band, the conclusion was unambiguous: Eco1a possess a very strong Lewis acid character (Supplementary Information 4). As a result, Lewis acidity of CaMg2Cl6 was shown to be stronger than for KMgCl3, which in turn seemed to be stronger than MgCl2. These outcomes were consistent with the pyridine FT-IR analyses. In conclusion, the presence of these mixed salts in the ecocatalysts promotes an unusual Lewis acidity in organic synthesis with interesting potential for application. Regarding these qualitative trends, we decided to perform Corma's experiment on the ecocatalyst Eco1a, in order to quantify Brønsted and hard and soft Lewis acid sites 17 . Corma's acetal was treated with Eco1a in 1,2-dichlorobenzene at 180 °C during 16 h (Scheme 1). The product A, resulting from Brønsted acid catalyst, was formed in 87% yield. The ester B, resulting from a hard Lewis acid activation, was obtained in 13% yield. No product C was observed, leading to the conclusion that the ecocatalysts do not present soft Lewis acid sites. Furthermore, both catalysts MgCl2 and CaCl2 were not efficient enough to convert Corma's acetal. In conclusion these ecocatalyst present lots of Brønsted acid sites and small hard Lewis acidity. Given the experimental differences of reactivity between CaCl2, MgCl2, and CaMg2Cl6 we decided to evaluate theoretically criteria indicating the reactivity of the metal hydrates. As previously mentionned 13 , Denmark 18 , Massa 19 and other groups Scheme 1 Analysis of the acidic properties of the ecocatalyst by Corma's method.

Conditions: Eco1a (4.2 mol%), 1,2-dichlorobenzene (1 M), 180 °C, 16 h supplemented the concepts introduced by Gutmann and a series of rules [START_REF] Gutmann | Donor-acceptor approach to molecular interactions[END_REF] . These studies demonstrated that an acid-base adduct induced an increase in electron density in the acceptor fragment of the adduct. Accordingly, CaMg2Cl6 should be a better Lewis acid than CaCl2 and MgCl2, which was supported by IR data. We performed DFT calculations to evaluate the electronic distribution when comparing those three chloridebased salt hydrates (Supporting Information 5). CaMg2Cl6 is a mixed salt where the calcium cation has a central position and is coordinated by chloride anions and surrounded by hydrated Mg cations, as depicted in Figure 4.

In the catalytic intermediary, the magnesium is very likely partially desolvated, while the central cation does not interact directly in the catalytic cycle but act as an electron sink (donor/acceptor). As shown in Table 2, the Mg centre is more electropositive (1.566 for MK charge) in the case of CaMg2Cl6 than in MgCl2 (1.332 for MK charge), thus has an increased acceptor effect towards the electron rich adduct. Meanwhile the calcium centre is accepting electrons from each side of the complex and this can be confirmed by the less electropositive character of Ca in the case of CaMg2Cl6 compared to CaCl2. This analysis is consistent of the nature of the charge (Mulliken, natural, MK). Using the Pearson acid-base concept [START_REF] Pearson | [END_REF] , the chemical hardness  and softness S were also estimated from the lowest unoccupied and highest occupied molecular orbital energies using the following formalisms 22 :  ~ ELUMO -EHOMO and S = 1/. CaMg2Cl6 presents the softest character (S=2.634) and therefore the smallest HOMO-LUMO gap among the three species, which implies it can have its electron density exchanged more easily than the harder metal hydrates CaCl2 (S=2.559) and MgCl2 (S=2.176). The evaluation of charges and softness has also been performed using a water implicit solvation as reported in Supporting Information 5; no significant variations were observed. These theoretical calculations fit very well with all the experimental data collected for this study and are very useful for the interpretation of the reactivity of these novel ecocatalysts.

Like their transition metal-containing analogues, ecocatalysts obtained from common trees also possessed unique properties owing to their polymetallic compositions and differing ratios between all metal elements. The catalytic activity of the ecocatalysts was investigated with two model reactions, namely oxidative esterification and acetalisation reactions.

Oxidative esterification

Carboxylic esters constitute fundamental intermediates for the production of fragrances, flavours 23 , biomedicines [START_REF] Fukushima | Polymers for Biomedicine[END_REF] , biodegradable polymers [START_REF] Thakur | Handbook of sustainable polymers: processing and applications[END_REF] or biofuel [START_REF] Osatiashtiani | Nanotechnology in Catalysis[END_REF] . Over more than a century, Fischer and Speier synthesis [START_REF] Fischer | [END_REF] have seen many improvements and alternatives 28 . Among these numerous methods, oxidative esterification is a one-pot preparation of ester starting from an aldehyde 29 . The assumed mechanism is based on two steps: the hemicetalisation of aldehyde followed by the oxidation of the hemiacetal intermediate. This direct transformation is a significant reaction in green chemistry. Various metal-based catalysts have been used to perform this reaction, including rhenium 30 , titanium 31 , cerium 32 , copper 33,34 , zinc 35,36 , calcium or magnesium 37 or iron 38 as a non-exhaustive list. Ionic liquids 39 can also be used, as well as supported Brønsted acids 40 . Direct oxidative esterification of alcohols into esters is also possible but requires harsh conditions and/or expensive catalysts [41][42][43][44] . Since then, the reaction has been extensively studied 28,29 and appears to be a very interesting model to prove the efficiency of ecocatalysts. Regarding the presence of both Lewis and Brønsted acidities of nonaccumulating plant-based ecocatalysts, they could act as efficient promoters of oxidative esterification reaction. Benzaldehyde was put into a suspension of Eco1a in MeOH, to which was added a green oxidative reagent, aqueous H2O2. The reaction led to three different products, namely methyl benzoate 1, dimethoxymethylbenzene 2 and benzoic acid 3 (Table 3). Pleasingly, all conversions were excellent (95-99%).

We first investigated the influence of the quantity of hydrogen peroxide on the selectivity (Table 3, Entries 1-4). It should be noted that decreasing the amount of this oxidant led to incomplete conversion of the benzaldehyde, promoting the formation of acetal at the same time (Table 3, Entries 1-3). The use of 4 equivalents of hydrogen peroxide led to the best results by yielding ester 1 at 81% with quantitative conversion (Table 3, Entry 4). The effect of varying the amount of the catalyst was then studied (Table 3, entries 5-8). The best yield (82%) was obtained with a catalyst amount at 19 wt% (Table 3, entry 8). Decreasing catalyst amount to 13, 9 and 6 wt% led to slightly lower conversion and an almost 10% decline in yield of the ester 1 in favour of benzoic acid 3. This result is surprising, because aqueous H2O2 has been considered to have a poor ability to oxidise aldehydes to carboxylic acids. During this investigation, we observed that benzoic acid 3 resulted from the oxidation of benzaldehyde, and not from the hydrolysis of benzoate 1. This observation was in agreement with the results previously reported by Noyori et al. 45 . Therefore, we tried to promote the transformation of benzaldehyde into hemiacetal by increasing the amount of methanol (Table 3, entries 9-12). However, the conversion of benzaldehyde was still incomplete, with concomitant increase of the acetal 2 and a huge decrease in ester yield between 79 and 60%. The entry 8 were found as the best reaction conditions. In order to improve the performance of Eco1a, comparative studies were conducted with various ecocatalysts and pure salts. The results are summarised in Table 4. The systematic search for the most efficient plants revealed that all the studied tree species were excellent for this reaction. The systematic search for the most efficient plants revealed that all the studied tree species were excellent for this reaction. Ecocatalysts yielded the best results (Table 4, entries 1-11). These outcomes compare favourably with those of other systems described in literature (Table 4, entries 12, 14, 19-21). Two ecocatalysts obtained from willow and beech stood out from the crowd and provided total conversion of both benzaldehyde and acetal to only give methyl benzoate and benzoic acid. The selectivity ranged from 76% for Eco6&7 to 80% for Eco1a, making willow the best catalyst for this reaction. As indicated in MP AES analyses, 0.27 wt% of Zn was observed in Eco1a. In order to explain the high activity of Eco1a in oxidative esterification, we studied the activity of an ecocatalyst generated from Zn-accumulating species (Table 4, entry 22). We observed moderate yield (64%), thus showing that the catalytic activity did not depend significantly on Zn concentration. In order to learn more about the active species, reactions were performed with pure salts that are contained in ecocatalysts (Table 4, entries 12-16). Magnesium species converted benzaldehyde up to 62% while calcium chloride and KCaCl3 gave respectively 77% and 71% of conversion. These observations showed that calcium catalysts are more active but less selective than the magnesium ones. Assay with HCl (pH = 5) propelled the conversion to 95% but the selectivity declined to only 55% owing to the competitive oxidation of benzaldehyde into benzoic acid (40%). A Lewis acid catalysis is required to limit this side reaction and to promote the sequence hemiacetalisation/oxidation. CaMg2Cl6 was the most efficient pure salt. It provided a better conversion (up to 80%) and greater selectivity toward production of the ester. The combination of CaMg2Cl6 with HCl at pH = 5 gave a satisfactory conversion but lower selectivity than other pure salts. Despite the better conversion, the selectivity toward the ester remained practically the same compared to CaMg2Cl6 alone.

To our knowledge, this is the first example that describes the Lewis acidity of CaMg2Cl6. This mixed salt revealed an unexpected efficiency, exceeding that of simple calcium and magnesium salts. We can assume that the presence of CaMg2Cl6 in the ecocatalysts explains their high efficiency.

Upon optimising reaction conditions, we extended the scope of substrates to explore the versatility of ecocatalyts as illustrated in Table 5. The results clearly show the interest of ecocatalysis. Trials with activated aromatic aldehydes possessing electron-withdrawing groups such as -CN or -NO2 provided total conversions but yields in ester were satisfactory (up to 60%). The only side product was the carboxylic acid, the formation of which a simple work-up allowed the separation of the diacid from the conditions with 65% (Table 5, entry 3). Optimised reaction conditions gave excellent conversion and good yields for deactivated aldehydes and are compatible with aryl halides or phenols (Table 5, entries 4-8). As expected, electron-rich aldehydes such as 4-methoxy-and 3,4dimethoxybenzaldehyde did not reach total conversion Reaction conditions: 6 mmol of aldehyde, 99 mg of Eco1a, 12 mL of alcohol, 2.5 mL of H2O2 (30 wt%). The mixture was heated at reflux for 16 h. and gave esters in moderate yields up to 55% (Table 5, entries 9 and 10).

In selecting suitable reaction conditions, several alcohols were investigated (Table 5, entries 11-15). Straight-chain alcohols were good nucleophiles (Table 5, entries 11-13). Selectivity decreased with bulky alcohols such as isopropanol (Table 5, entry 14). Interestingly, the use of ethylene glycol gave the monoester with 73% yield (Table 5, entry 15). The direct, clean and green monoesterification of diol is interesting because it could avoid a delicate separation of monoesters from diesters and diols. The differences between conversions and isolated yields are explained by the formations of the corresponding carboxylic acids, which are eliminated by the basic work-up. Several applications could be found, especially for a rapid synthesis of insect sex attractants or the preparation of polyesters and fungicides [START_REF] Thakur | Handbook of sustainable polymers: processing and applications[END_REF] . Distinct advantages of this method are its simplicity, its efficiency and its use of renewable resources.

In addition to their simple and eco-friendly preparation, the performance of ecocatalysts allows performing oxidative esterification reaction up to large-scale synthesis. Moreover, these results show the advantages of polymetallic catalysts compared to monometallic ones, advantages first recognized by Corma and Garcia and substantiated by our previous work. 6,46

Acetalisation

Acetalisation and ketalisation are common and useful reactions, mostly used for protection strategy in carbohydrate chemistry or during synthetic processes of multifunctional molecules [START_REF] Wuts | Greene's protective groups in organic synthesis[END_REF] . Several solutions exist to switch this equilibrium, such as trapping the water formed during the reaction by using Dean-Stark apparatus, orthoformates or a catalytic membrane on a flow reactor 51 . Other methods involving metallic Lewis acids, [52][53][54][55][56][57][58][59][60][61] cationic species such as aromatic tropylium cation 62 or pyridinium salt derivatives 63 and supported materials, 56,64 have been reported. It is also possible to conduct acetalisation reaction by using Eosin Y as a photocatalyst under green light. 65 Recently, Grabowski et al. reported the synthesis of acetals under basic conditions in order to preserve acidsensitive groups. 66 Encouraged by the previous results with oxidative esterification reaction, we studied the acetalisation of benzaldehyde under optimised conditions (Table 6). First reactions were performed using benzaldehyde and 16 wt% of ecocatalysts in MeOH at 25 °C. Conversions were excellent with ecocatalysts and reached up to 93% in the case of Eco9 (Table 6, entries 1-10). As expected, pH seemed to play a key role in the reaction. HCl and FeCl3 (pH = 5) gave good results with respectively 78% and 85% yield (Table 6, entries 18-19). In the case of ecocatalysts, the pH value was measured at 5 (except for Eco1b, which was controlled at 6) and yields were between 78 and 93%. Interestingly, experiments with thermally activated Eco1a and Eco1b (Table 6, entries 11 and 12) exhibited a neutral pH. The resulting Eco1a and Eco1b completely lost their catalytic activity. However, the Brønsted acidity of a catalyst is not the only parameter of the reaction. At pH = 6, MgCl2 gave only 15% yield (Table 6, entry 13). Moreover, the use of KMgCl3, which is a better Lewis acid than MgCl2, provided 23% yield at pH=7. CaCl2 and KCaCl3 were poor promoters of acetalisation, whereas CaMg2Cl6 yield 69% of acetal at pH=7 (Table 6, entry 17). These results lead us to think that synergetic dual Lewis-Brønsted catalysis (Lewis or Brønsted) could explain the very good conversions obtained with ecocatalysts. The excellent result using CaMg2Cl6 at pH = 5 (89%) confirmed this explanation. This conclusion was consistent with results reported by Shi and Houk 67,68 . We can consider that specific interactions and cooperative effects can modulate the overall chemical behaviour of the catalysts. Finally, the ecocatalysts were the best promoters of acetalisation. They exhibited the best combination of metal halides and led to more active systems than the sum of individual components. In other terms, extracts of common tree species allowed the preparation of tailor-made polymetallic catalysts, improving their catalytic performances compared to monometallic ones. In a context of growing environmental consciousness, it is gratifying to be able to propose novel catalysts that combine efficiency, use of renewable resources and eco-friendly processes. These considerations all suggest a promising life-cycle analysis.

Conclusions

The aim of this work was to produce and study novel Lewis acid catalysts originated from common tree species. The synthetic potential of these new systems was illustrated with two important processes in organic chemistry, oxidative esterification and acetalisation reactions. Reaction conditions were devised that gave economic, technical and environmental advantages. From these studies, it might be concluded that the new biosourced catalytic systems showed very interesting activity. We described the unusual structure and composition of these novel ecocatalysts. CaMg2Cl6, a mixed salt whose production in this system was unexpected, was identified by XRPD analyses first and then confirmed by HR-STEM-EDX studies. Its catalytic potential and its specific Lewis acidity are promising. These results suggest new opportunities for sustainable catalysis in organic synthesis. The approach illustrated in this study is a green solution with chemical and environmental benefits: high yields, good selectivity, requirement for only small amounts of catalyst, mild conditions and concrete perspectives for facing the exhaustion of mineral resources. Further experimentation would be required in order to fully determine the potential of these new plant-based catalysts, but there is no doubt that they display very interesting properties for cutting-edge green chemistry.

Experimental section 4.1. Preparation of ecocatalysts

All the leaves were first oven-dried at 40 °C for two days and then coarsely crushed and homogenised. A sample of approximately 50 g of leaves of each species underwent a controlled thermal treatment at 550 °C for 4 hours (6 h for leaves of plane tree) to form residues. These residues (≈ 5 g) were then suspended in a solution of acid (hydrochloric at 37% or hydrobromic at 48%) in water (50 mL). The mixture was heated at 60 °C for 3 h and then cooled and filtered on a previously washed celite pad in order to remove the insoluble material. The filtrate was evaporated under vacuum until it yielded a slightly yellow powder (≈ 5.7 g). The catalyst was crushed using a mortar in order to homogenise the powder, which was then stored at 90 °C for two days. The catalysts were stored in an anhydrous environment.

Preparation of mixed salts

The procedure described by Poddar et al. 69 was applied to synthesise KMgCl3 and extended to the synthesis of KCaCl3. KCl (7.46 g; 100 mmol) was dissolved in pure water (30 mL). A solution of MgCl2 (9.52 g; 100 mmol) or a solution of CaCl2•4H2O (18.3 g; 100 mmol) in pure water (respectively 80 mL and 25 mL) was added. The mixture was stirred and then heated under vacuum to give a white crystalline hygroscopic powder. The salt was quickly crushed with a mortar and stored in an anhydrous environment. The procedure described by Erd et al. 70 led us to obtain CaMg2Cl6 salt. Dry CaCl2 (200 mg, 1.8 mmol) and dry MgCl2 (240 mg, 2.52 mmol) were dissolved in 560 µL of pure water. The mixture was stirred at 80 °C until complete dissolution of the solids. The solution was cooled and kept 2 days at 5 °C. The crystals formed were dried on filter-paper and stored in an anhydrous environment.

General procedure for acetalisation reactions

In a 25 mL round-bottom flask equipped with a magnetic stirrer and a cooler, were added the catalyst (99 mg), the benzaldehyde (636 mg, 6 mmol) and the biphenyl (208 mg, 1.35 mmol, 1.35 eq.), followed by the alcohol (12 mL). The mixture was stirred at room temperature for 1 h. Then a sample was collected to perform GC-MS analyses.

General procedure for oxidative esterification reaction

In a 25 mL round-bottom flask equipped with a magnetic stirrer and a cooler, were added the catalyst (99 mg) and the aldehyde (6 mmol), followed by the alcohol (12 mL). The mixture was stirred at room temperature for 1 h. Hydrogen peroxide 30 wt% in water (2.5 mL; 24 mmol; 4.0 eq.) was added and the resulting mixture was heated at reflux for 16 h. The reaction medium was left to cool to room temperature. A sample was collected to perform quantitative GC-MS analyses. Treatment: the solution was diluted in Et2O (50 mL) and washed two times with a saturated aqueous solution of sodium hydrogenocarbonate. The aqueous phases were brought together and extracted with 25 mL of Et2O. The organic phases were combined, dried on MgSO4, filtered and then evaporated to give the product.

Figure 1

 1 Figure 1 From leaves of common trees to chemical reactions

Table 1

 1 Major cationic species determined by MP-AES analyses of catalysts (wt%). The Relative Standard Deviation percentage is written in brackets.

	Ecocatalyst	Plant material	Acid	Ca	Fe	K	Mg	Zn
	Eco1a	Willow	HCl	14.34 (± 0.57%)	0.11 (± 1.47%)	8.27 (± 1.15%)	2.04 (± 1.03%)	0.27 (± 8.04%)
	Eco1b	Willow	HBr	7.51 (± 0.74%)	0.09 (± 1.86%)	6.72 (± 0.89%)	1.09 (± 0.37%)	0.15 (± 38.3%)
	Eco2	Linden	HCl	16.18 (± 2.09%)	0.14 (± 2.02%)	2.73 (± 0.97%)	2.75 (± 1.15%)	0
	Eco3	Horse Chestnut	HCl	14.72 (± 0.85%)	0.14 (± 2.80%)	8.72 (± 0.61%)	2.59 (± 1.27%)	0
	Eco4	Black locust	HCl	19.32 (± 1.41%)	0.08 (± 7.26%)	2.92 (± 1.68%)	0.87 (± 0.84%)	0
	Eco5	Beech	HCl	16.8 (± 0.96%)	0.11 (± 1.41%)	2.98 (± 0.50%)	2.32 (± 0.57%)	0
	Eco6	Birch	HCl	17.31 (± 0.93%)	0.13 (± 3.71%)	4.64 (± 0.20%)	2.13 (± 0.54%)	0
	Eco7	Oak	HCl	14.71 (± 0.44%)	0.22 (± 4.14%)	12.49 (± 0.71%)	1.19 (± 0.25%)	0
	Eco8	Plane	HCl	19.75 (± 0.55%)	0.04 (± 13.63%)	7.04 (± 1.13%)	0.75 (± 1.87%)	0
	Eco9	Maple	HCl	11.39 (± 2.48%)	0.32 (± 9.94%)	8.51 (± 0.39%)	0.97 (± 1.59%)	0

Table 2

 2 Mulliken, natural and Merk-Kollman charges on cationic centres in CaCl2, MgCl2 and CaMg2Cl6, and molecular softness of the three hydrates obtained by DFT calculations.

	Compound		CaCl2•4H2O	MgCl2•6H2O CaMg2Cl6•12H2O
	Mulliken Charge (a)	Ca Mg	0.886 -	-0.764	0.764 0.788
	Natural (NBO)	Ca	1.268	-	0.611
	Charge (a)	Mg	-	1.366	1.375
	MK Charge(a)	Ca Mg	1.331 -	-1.332	1.004 1.566
	ɲ (a,b)		0.3907	0.4595	0.3796
	S (a,b)		2.559	2.176	2.634

a Using MPW1PW91/cc-PVTZ, implicit solvation: methanol, b chemical hardness ɲ and softness S.

Table 3

 3 Screening of conditions for the oxidative esterification reaction.

	Entry	X (wt%)	Y (eq.)	Z (mol.L -1 )	Conv (%)	1 (%)	2 (%)	3 (%)
	1	16	1.1	0.41	95	64	13	18
	2	16	2	0.41	98	79	2	17
	3	16	3	0.41	99	77	1	22
	4	16	4	0.41	>99	81	0	19
	5	6	4	0.41	98	73	1	24
	6	9	4	0.41	99	74	0	24
	7	13	4	0.41	>99	72	0	28
	8	19	4	0.41	>99	82	0	18
	9	16	4	0.23	97	79	5	13
	10	16	4	0.16	97	76	10	11
	11	16	4	0.12	96	63	19	12
	12	16	4	0.1	96	60	17	19

Table 4

 4 Comparing catalytic activities of ecocatalysts and classical salts. Classical salts (entries 12-18) were added to obtain the same amount of metal than in Eco1a.

	Entry	Plant material	Catalysts	Conversion f (%)	1 f (%)	2 f (%)	3 f (%)
	1	Willow	Eco1a a	>99	80 g	0	20
	2	Willow	Eco1b a	>99	74	0	26
	4	Linden	Eco2 a	98	78	1	19
	5	Horse chestnut	Eco3 a	>99	79	0	21
	6	Black locust	Eco4 a	99	76	1	23
	7	Beech	Eco5 a	99	76	1	23
	8	Birch	Eco6 a	99	78	0	21
	9	Oak	Eco7 a	99	77	1	21
	10	Plane tree	Eco8 a	99	79	0	20
	11	Maple	Eco9 a	99	79	0	20
	12	-	MgCl2 b	62	50	4	8
	13	-	KMgCl3 b	62	56	4	2
	14	-	CaCl2 c	77	54	2	21
	15	-	KCaCl3 c	71	50	3	18
	16	-	CaMg2Cl6 b	80	68	3	9
	17	-	HCl at pH = 5	95	55	<1	40
	18	-	CaMg2Cl6 at pH=5 b	93	60	< 1	32
	19	-	MnCl2 e, 35	72	57	< 1	15
	20	-	ZnCl2 e, 35	82	60	< 1	22
	21	-	LiCl e, 35	80	56	< 1	24
	22	Willow	Eco-S.T. a, 13	>99	64	0	36

a 16 wt% of ecocatalyst. b 1.4 mol%. c 5.9 mol%. d 0.03 mol%. e 10 mol%. f Reactions were monitored by GC-MS with biphenyl as internal standard. g isolated yield.

Table 5

 5 Extension of the reaction to other aldehydes and alcohols.

	Entry	Aldehyde	Ester	Conv. (%)	Isolated yield (%)
	1			>99	43
	2			>99	60
	3			>99	65
	4			>99	83
	5			>99	82
	6			>99	82
	7			>99	75
	8			>99	79
	9			88	55
	10			86	52
	11			>99	58
	12			>99	46
	13			>99	62
	14			>99	25
	15			>99	73

Table 6

 6 GC-MS yields and pH measures of acetalisation reactions as a function of the catalysts.Classical catalysts (entries 13-20) were added to obtain the same amount of metal than in Eco1a. Reaction conditions: Benzaldehyde (636 mg, 6 mmol), catalyst, MeOH (12 mL), 1 h at r.t..

	Entry	Plant material	Catalyst	BA f (%)	Acetal (%)	pH
	1	Willow	Eco1a a	8%	92%	5
	2	Willow	Eco1b a	10%	90%	6
	3	Linden	Eco2 a	22%	78%	5
	4	Horse chestnut	Eco3 a	9%	91%	5
	5	Black locust	Eco4 a	15%	85%	5
	6	Beech	Eco5 a	10%	90%	5
	7	Birch	Eco6 a	8%	92%	5
	8	Oak	Eco7 a	12%	88%	5
	9	Plane	Eco8 a	11%	89%	5
	10	Maple	Eco9 a	7%	93%	5
	11	Willow	Eco1a b	100%	0%	7
	12	Willow	Eco1b b	100%	0%	7
	13	-	MgCl2 c	85%	15%	6
	14	-	KMgCl3 c	77%	23%	7
	15	-	CaCl2 d	92%	8%	7
	16	-	KCaCl3 d	95%	5%	7
	17	-	FeCl3 e	15%	85%	5
	18	-	CaMg2Cl6 c	31%	69%	7
	19	-	HCl to pH = 5	22%	78%	5
	20	-	CaMg2Cl6 at pH=5 c	11%	89%	5

a 16 wt% of ecocatalyst. b Catalysts were heated at 450 °C for 5 min. c 1.4 mol%. d 5.9 mol%. e 0.03 mol%. f BA: benzaldehyde Moreover, at the same pH, most of the ecocatalysts work better than Brønsted acid catalysis alone (Table

6

, entry 19).

Acknowledgments

Authors would like to thank Franck Pelissier (ChimEco/CNRS-UM UMR 5021) for the MP-AES analyses, Clotilde Boulanger and Sebastien Diliberto for the XRD analyses and also Nicolas Donzel (CNRS/UM, UMR 5253) for NH3-TPD analyses. Authors thank CNRS for financial support.

Conflicts of interest

Authors assure that there are no conflicts to declare.