Léopold Sepulchre
email: leopold.sepulchre@laplace.univ-tlse.fr

Member, IEEE Maurice Fadel
email: maurice.fadel@laplace.univ-tlse.fr

Member, IEEE Maria Pietrzak-David

Guillaume Porte
email: guil-laume.porte@actia.fr

Sepulchre

MTPV Flux-Weakening Strategy for PMSM High Speed Drive

Keywords: speed permanent magnet synchronous motor (PMSM), maximum torque per volt (MTPV), torque-speed characteristic, vector control

High speed permanent magnet synchronous motors (PMSMs) are used in electric vehicles because of their intense power density. The high speed implies a significant electromotive force and requires flux weakening. The usual control algorithms realize flux weakening by adding a negative I d current component when the voltage required by the current regulation exceeds the maximum voltage depending on the battery.

If the magnet can be totally defluxed, then it is better to use a maximum torque per volt strategy. Furthermore, there is no speed regulation in the control and the driver gives a torque reference. This reference value has to be limited by the attainable operating points; therefore, the battery power limit has to be taken into account in addition to the voltage and current limits. The d-q current references are calculated to minimize the total current magnitude required to reach the reference torque. This paper proposes a strategy to control a PMSM operating continuously since the speed zero up to the maximum speed without the switching algorithm, in order to take into account the different limitations (current, voltage, and power) and to expand the overspeed zone. In order to validate the proposed strategy, experimental results are shown for a low power machine.

Index Terms-Flux weakening, high

MTPV

E LECTRIC vehicles are the present and the future of the au- tomobile industry because they are environment friendly: low noise levels, better performances than thermal engines, and electrical energy is cheaper than oil-based fuel. So, electrical traction requires motors to have a high torque at low speeds and a wide speed range at constant power.

PMSMs are commonly used because this electrical motor has the best power density and efficiency to date [START_REF] Finken | Comparison and design of different electrical machine types regarding their applicability in hybrid electrical vehicles[END_REF] and is therefore well adapted for embedded applications. The volume and mass of a PMSM are proportional to its torque. An engine containing fewer magnets making it smaller, lighter, and cheaper has been chosen, thereby improving volume and mass. It has less torque but the same power because it operates at higher speeds and the gear can be adapted to the desired torque-speed characteristics, thereby retrieving the qualities of electrical traction. The motor is supplied from a battery through, a three-phase voltagesource inverter (VSI). The control is performed in the Park d-q reference frame. The torque reference is imposed from the accelerator, allowing a calculation of the d-q current references. Motor d-q currents are regulated by two discrete polynomial controllers with a decoupling strategy and the consideration of delays [START_REF] Sepulchre | Improvement of the digital control of a high speed PMSM for vehicle application[END_REF]. A PWM strategy generates the duty cycles sent to the VSI power components. When the speed increases, the electromotive force of the machine increases also, and, because of the battery voltage limit, from a certain speed the magnet flux perceived by the stator windings must be reduced. This is done by imposing a negative I d current that will generate an opposing flux to that of the magnet flux. This process is called flux weakening.

The literature presents several flux-weakening control strategies [START_REF] Dongyun | A review of flux weakening control in permanent magnet synchronous machines[END_REF]- [24], where [START_REF] Dongyun | A review of flux weakening control in permanent magnet synchronous machines[END_REF]- [START_REF] Gao | Control design for PMM starter-generator operated in flux weakening mode[END_REF] are the state of the art in fluxweakening techniques. We suggest classifying these strategies in the following way: analytical direct calculation method [START_REF] Fangyang | Study on flux weakening control for PMSM[END_REF], [START_REF] Morimoto | Wide-speed operation of interior permanent magnet synchronous motors with high-performance current regulator[END_REF], direct open loop algorithm with experimental LUT [START_REF] Huber | Voltage controller for flux weakening operation of interior permanent magnet synchronous motor in automotive traction applications[END_REF]- [START_REF] Meyer | Direct torque control for interior permanent magnet synchronous motors with respect to optimal efficiency[END_REF], SCR method [START_REF] Bolognani | Flux weakening in IPM motor drives: Comparison of state-of-art algorithms and a novel proposal for controller design[END_REF] In a voltage saturation operation, the SCR avoids competition between the classic d-axis and q-axis regulators but this method requires switching to another control algorithm at low speeds. The UDFVC is compatible for all ac machines; however, it requires the use of a flux observer. Furthermore, the maximum load torque has to be determined experimentally which renders this method dependent on the motor. VCC is the classic flux-weakening method. Nevertheless in the current control, the LPF impacts its dynamic performances. The voltage and the regulation of the duty cycles also use LPF with the same consequences. There are overmodulation strategies that increase the maximum voltage available at the expense of additional current harmonics. Finally, the voltage norm regulation is the conventional approach that needs a maximum voltage reference depending on the battery and PWM used to overmodulate. The control developed in this paper is based on this approach. The proposed solution relies on the implementation of an MTPV method taking into account a power limit of the energy source, working continuously from a rotation speed of zero to its maximum value.

It can be noted that the reachable operating points are dependent on the maximum current and voltage and on the power of the battery. In Section II, these limits are discussed and plotted in the torque-speed plane. The previously mentioned flux-weakening strategies usually do not take into account the power limit and only consider the current and voltage limits. This paper proposes an algorithm to calculate the optimal components of the current in d-q frame for smooth-pole or salient-pole PMSM. It takes into account the physical limitations of the system (maximum current, maximum voltage, maximum power), in order to operate continuously since the zero speed to the maximum speed without the switching algorithm and to maximize the overspeed zone. The performance of this solution is observed through simulation and validated with experimental bench.

II. ACHIEVABLE OPERATING POINTS

A. PMSM Model and Electric Limits

The PMSM electrical model equations, expressed in the d-q reference frame, are presented for voltage (1) and ( 2) and for

V d = R • I d + L d dI d dt -ω • L q • I q (1) V q = R • I q + L q dI q dt + ω • L d • I d + ω • ϕ f (2) T = 3 2 • p • (ϕ f • I q + (L d -L q )I d I q ) (3)
where V d , V q and I d , I q are, respectively, the voltage and current d-q components, L d and L q are the d and q axes winding inductances, p is the number of pair of poles, ω presents the electrical rotor angular velocity, R is the phase resistance, Φ f is the linkage flux of the permanent magnet, and T corresponds to the PMSM electromagnetic torque. The maximum current I max (4) is the more constraining current limit which is situated between the nominal current of the motor, the nominal current of the inverter, and the maximum current delivered by the battery (brought back to an equivalent motor current)

I 2 d + I 2 q ≤ I max . ( 4
)
The maximum voltage (5) depends on the voltage limit of the battery and the PWM strategy used; for the space vector modulation (SVM) applied here, V max is defined by (6)

V 2 d + V 2 q ≤ V max (5)
V max = V DC √ 3 ( 6
)
where V DC is the voltage of the battery. At high operating speed, the resistance is usually negligible in ( 1) and ( 2). Consequently, the voltage limit can be written in steady state as follows:

(ωL q I q ) 2 + (ωL d I d + ωϕ f ) 2 ≤ V max . ( 7
)

B. Torque-Speed Characteristic in Electrical Traction

A reduced size salient-pole PMSM is used to perform the experiments and the simulations. Its parameters are displayed in Table I.

To operate, the vehicle requires a high torque available at low speeds and with constant power for wide rotation speed ranges. I. similar to those in Table I, but with L d equal to L q . The fluxweakening operation allows the curve of maximum power to be reached, by acting on the axis d by injecting a current according to a law as explained next.

The blue solid line in Fig. 1 shows the maximum torque at low speed that is given by the MTPA strategy with maximum current expressed by ( 8) and ( 9). Note that the voltage limit is not yet reached, so the operating points below the torque limit are imposed by the control which minimizes the current corresponding to the reference torque in order to reduce the PMSM losses. If this strategy is maintained when the speed increases, then when the voltage limit is reached, it gives the blue-dashed line torque limit explicit in (12), and flux weakening will need to be done to reach operating points at higher speeds. It can be noted that, depending on the sizing of the inverter, the current limit and consequently the torque limit can be lower at speeds near zero in steady state but this case is not discussed here. The MTPA expression in the torque-speed plane is (3) with ( 8) and ( 9) with the torque reference represented by its equivalent current norm I norm . With the help of the Lagrange multiplier [33] method, it is easy to formulate the following expressions:

I d = ϕ f -ϕ 2 f + 8(L d -L q ) 2 I 2 norm -4(L d -L q ) ( 8
)
I q = I 2 norm -I 2 d ( 9
)
where I norm is the total current magnitude and depends on the torque reference or speed regulation. Note that for smooth-pole PMSM, the classic MTPA d and q current references are obtained as follows:

I d = 0 ( 10
)
I q = I norm . ( 11
)
The expression of the voltage limit in the torque-speed plane without flux weakening for a smooth-pole PMSM is (3) with ( 10) and ( 12). For a salient-pole PMSM, the MTPA strategy already adds some I d current and so the expression of the torque depending on the speed and on the voltage limit is (3) with I d solution of (22) and I q respects (7)

I q = V max L q ω 2 - ϕ f L q 2 . ( 12
)
The red-dotted line in Fig. 1 plots the maximum torque that can be achieved if the voltage limit and the current limit are reached, expressed in (13)-(15). When the speed increases, the electromotive force becomes more restrictive for the voltage. To respect the voltage limit, the flux perceived by the stator winding has to be reduced. In this way, a negative I d current is applied that creates a flux opposite to the magnet flux: this is the flux weakening. Note that the operating points below this torque limit are imposed by the controller with a classic flux-weakening algorithm, i.e., VCC that will follow the intersection between the current and the voltage limits. It can also be seen that the torque-speed characteristic is not really a constant power limit if only the current and voltage limits defined in ( 4) and ( 7) are considered especially in the "top right corner" where the torque is high and the voltage limit is just reached. The classic power limit is mainly a battery limit or a mechanical requirement rather than an electric motor limit.

For a smooth-pole PMSM, the direct current component is as follows:

I d = V 2 max -ω 2 ϕ 2 f -L 2 q ω 2 I 2 max 2L d ω 2 ϕ f . ( 13
)
For a salient-pole PMSM, this current is expressed by

I d = L d ϕ f L 2 d -L 2 q + L 2 d ϕ 2 f -(L 2 d -L 2 q ) ϕ 2 f + L 2 q I 2 max - V 2 max ω 2 L 2 d -L 2 q ( 14
)
and

I q = I 2 max -I 2 d . ( 15
)
The solid red line in Fig. 1 shows the MTPV, explicit in ( 16) and ( 17). This magnet must be able to be totally defluxed. It is possible when the critical point is within the current limit. In this case, this strategy gives the highest torque at high speed. The control strategy in Section III presents a way to include MTPV in a flux-weakening method. Note that in such a case the speed is theoretically not limited by the electrical limits. The MTPV expression in the torque-speed plane is (3) with ( 16) and (17). By injecting the relation ( 16) and (17) into the expression (3) and using the Lagrange multiplier method again, we can express V d and V q voltages which correspond to the MTPV strategy. So, the d and q current components are as follows:

I d = V q ω -ϕ f L d ( 16
)

I q = - V d L q ω . ( 17
)
Fig. 2. Scheme of the PMSM control (where AW is a structural antiwindup).

It should be noted that this approach gives two solutions. We chose the one that gives negative I d and positive

I q V q = ϕ f -ϕ f 2 + V 2 max 8 L d -L q L q ω 2 -4 L d -L q L q ω
(18)

V d = -V 2 max -V 2 q . ( 19
)
For nonsalient-pole PMSM, the MTPV references become

I d = -ϕ f L d ( 20
)
I q = V max L q ω . ( 21
)
The black-and cyan-dashed lines in Fig. 1 show two examples of power limits for the battery. For the black-dashed line, the power limit implies a less constraining torque limit than the voltage or current limits and so is not useful for the calculation of the reachable operating points. For the cyan line, the power limit is more constraining than the voltage and current limits and so must be taken into account in the control. Observe that many classic control strategies only consider the voltage and current limitations. The control strategy presented in the next section shows a way to take into account all mentioned limitations to calculate the current references.

III. FLUX-WEAKENING STRATEGY

This section presents the control strategy that calculates the current references in the d-q reference frame from the torque reference. These current references are applied to the motor current regulation with a decoupling strategy [START_REF] Sepulchre | Improvement of the digital control of a high speed PMSM for vehicle application[END_REF]. Other control strategies with high bandwidth can be used for the current regulation, for example, predictive control or optimal control. The operating limits of the machine are imposed by the limits of its power supply, i.e., the battery. For this, we define a maximum voltage and we also define a maximum current. To maximize the speed of the machine while respecting these constraints, we must define particular current references that generate the maximum torque knowing that for a machine with salient poles the two axes d and q contribute to the torque production.

Fig. 2 shows the scheme of the control with this strategy. The current regulation gives a voltage vector reference. The flux-weakening control compares the norm of this voltage to the voltage limit [START_REF] Fangyang | Study on flux weakening control for PMSM[END_REF]. If this norm is superior to the imposed limit, then a negative I d current reference is generated to reduce flux seen by the stator windings. Thus, a part of the voltage is liberated and can be used to generate electromagnetic torque. The controller can be synthesized by a cascade method using the closed-loop model of the current regulation (depending on the current regulation used) and positioning the flux-weakening bandwidth accordingly. Nevertheless, it is preferable that the flux-weakening regulation dynamic be negligible according to the mechanical mode and the speed regulation loop if we add one.

The reference torque is limited by a mask (see Fig. 2 Block 1) of the attainable operating points presented in Section II. It enables the control to be reliable to apply a realizable torque respecting all limitations at any rotation speed.

Block 2 of Fig. 2 allows the calculation of the d-current reference and defines the minimal current norm to obtain the limited reference torque, and consequently PMSM losses depending mainly on the current norm. For salient-pole PMSM, I d current can be calculated by solving (22) obtained by searching the MinCPT

I 4 d (L d -L q ) 3 + I 3 d (L d -L q ) 2 3ϕ f + I 2 d (L d -L q )3ϕ 2 f + I d ϕ 3 f - 4(L d -L q )T sat 9p 2 = 0. ( 22
)
Using ( 16), (17), and (5), we can express this equation as a function of V max and rotation speed ω. This quartic polynomial equation can be solved analytically using the Ferrari method [32]. We can also solve it numerically and establish a LUT of I d and I q according to reference torque T sat and speed ω.

For a smooth-pole motor, the solution is trivial (10) but this is not the case of the motor shown in Table I. Classic flux-weakening algorithms use MTPA (8) instead of MinCPT (22). If the power limit of the battery is not constraining (c.f. Section II), then a speed regulation can give a current magnitude divided in current references between the d and q axes by MTPA. Nevertheless, if the power of the battery is constrained, torque information is required in the control to limit this torque or to impose an equivalent current norm limitation induced by the power limitation calculated from (22).

In conclusion, if the motor is with salient poles and the reference torque is imposed or the power battery limit is constraining, then (22) has to be solved; otherwise, an expression ( 8) can be used as in [31].

It is also possible to inject a negative I d current that creates an opposite flux to decrease the magnet flux and consequently to liberate all the voltage [c.f. (1) and ( 2)] for torque generation which follows the MTPV trajectory ( 16) and ( 17). This improvement of the control strategy is usually not taken into account in classic controls because it increases the torque only at very high speed and requires totally flux weakening the magnet. In this control, an MTPV strategy is introduced by the modification of the torque limitation (Block 1, in Fig. 2), and by creating a variable saturation in the I d flux-weakening saturation.

Block 3 in Fig. 2 represents the management of the voltage limit provided by the battery by action on the reference current on the d axis. The limit of the current is defined between the maximum current (4) that is constant and the I d current required by the MTPV strategy [START_REF] Meyer | Direct torque control for interior permanent magnet synchronous motors with respect to optimal efficiency[END_REF] that shortens to the critical point (I d = -Φ f /L d ) when the speed increases [31]. For this, it is necessary to act on the limits of the reference current I d that must take into account the positive effect of the current I d on the torque produced due to the torque contribution of the saliency.

The regulator of the voltage module uses an integrator with the K FW gain. This gain is calculated empirically to impose a bandwidth of the loop, around 10 rad/s, i.e., ten times faster than the mechanical bandwidth.

The I q current reference is calculated in Block 4 (see Fig. 2) using ( 3) with the knowledge of the I d reference after flux weakening and the limited torque reference. Block 4 also ensures that the final d-q current reference is imposed and respects the current limit.

IV. SIMULATION RESULTS

The performance of the proposed method is observed through a simulation. The PMSM parameters used are shown in Table I. The torque reference is 1.90 N•m and is less than the maximum torque of 2.13 N•m at low speed. We want to analyze the consequences of flux weakening while operating under the current limit, and then observe the PMSM operating in both current and Fig. 3. I q -I d scheme of the current references' trajectories.

voltage limitations, when the speed increases and more negative I d current is required.

Fig. 3 shows the current reference trajectory in the I d -I q plane. In blue, the current limit (4) is given. There is a circle centered on the origin of the plane and its radius is the norm of the maximum current. In green, the voltage limit ( 7) is drowning; its form is an ellipse centered on the critical point, and its size decreases when the speed increases. In the blue circles appears desired current reference trajectory in steady-state according to the evolution of the speed computed analytically. These references respect the limitation while generating the required torque with minimal current magnitude at the given speed. The same is true for the blue triangles but with 1-kW battery power that gives a more constraining power limit than the current and voltage limits. In the red stars, the current reference is given with a classic flux-weakening algorithm that only takes into account the current and voltage limits and does not include an MTPV strategy in the control. Note that the current references generated by this algorithm are oversized at high speed and do not respect the battery power limit. The current reference calculated by the flux-weakening control presented in Section III is shown in the red crosses and the same in the red triangles with a 1-kW battery power limit. One can conclude that this algorithm follows the desired current reference trajectory whatever the speed and the constraining limitations. In particular, the cases with operation in MTPV area or power limit are validated.

Figs. 4 and5 show the torque achieved in steady state for different speeds with a reference torque of 1.90 N•m smaller than its max torque at low rotation speed. Fig. 4 corresponds to the salient-pole PMSM of Table I and Fig. 5 shows for an equivalent smooth-pole PMSM (Table I with L d equal to L q ). In the blue circles, the torque reference limitation is drawn; it depends on the speed from Section II and in the light-blue triangles, the same variable is shown but with a 1-kW power limit in Fig. 4 and 800 W for Fig. 5. The electrical torque generated with the control in Section III is presented in the red Fig. 4. Torque obtained in steady state depending on the speed with a reference of 1.9 N•m for the salient-pole PMSM from Table I (with 1-kW battery limit). Fig. 5. Torque obtained in steady state depending on the speed with a reference of 1.9 N•m for the smooth-pole PMSM from Table I (with 800-W battery limit).

squares, and the same variable is given in the green triangles but with a smaller battery with a more constraining power (1 kW for Fig. 4, and 800 W for Fig. 5). It is interesting to note that the power limit is respected even if it is more constraining compared to the other limits. In the magenta stars, the torque generated with classic flux weakening is given with operating for current and voltage limits. One can observe that the MTPV strategy improves performances at high speed because it is not necessary to overly weaken the flux.

It is especially visible in Fig. 5 for the smooth-pole PMSM. For the salient poles motor, the effect of the MTPV strategy is less visible because the I d negative current for flux weakening also contributes to generating torque. Nevertheless, if it operates at higher speeds, the torque difference would be bigger between the flux-weakening strategy with MTPV and the classic fluxweakening strategy. Finally, the torque error observed in the flux weakening operating between the torque limit and the torque Fig. 6. Torque reference of 1.9 N•m with a 1400-W battery-current I d and I q and their references. generated is due to the motor resistance that is neglected for the calculation of the theoretical torque limits at high speed but that it still has an impact with the small-scale motor used in this paper.

The following figures show the time simulation results for a torque reference of 1.9 N•m for the salient-pole PMSM with a 1400-W battery. The evolution from the flux-weakening strategy for d-q current (see Fig. 6), the electrical torque (see Fig. 7), motor rotation speed (see Fig. 8), the voltage norm, and the current norm versus time is displayed. One can recognize the passage of the operating point between the MinCPT area, the flux weakening with only voltage saturation, the flux weakening with both saturation, and the MTPV area when the speed increases.

In Figs. 4 and5, the different evolutions of the torque are shown. These evolutions correspond to specific trajectories of the I d and I q currents in relation to different strategies (MTPA, MinCPT, MTPV, . . . ), which corresponds to the expressions presented in the part II, from (8) to (22). Some of these evolutions are visible in Figs. 3 and11.

V. EXPERIMENTAL RESULTS

To evaluate the system operation, some experimental tests were realized on the test bench in LAPLACE laboratory shown in Fig. 9. This reduced scale propulsion system is designed with two identical coupled PMSM (parameters given in Table I). One PMSM is the drive motor and the second one can be controlled by imposed load torque or rotation speed and is applied as a load torque emulator. In this way, one can impose the desired load torque to the drive PMSM. The reference torque is imposed by rigorously controlling the current of the loading machine. The torque is not measured but it is known. The VSI operates using an 8-kHz SVM PWM strategy.

The results of the experimental tests are compared with those of the simulation. The corresponding results are shown in Figs. 10-12. It can be noted that the conditions of these tests were the same as in the simulation. Consequently, Fig. 10 compares the mean torque obtained experimentally and by simulation for three control algorithms: without flux weakening, with convenflux weakening, and with weakening associated with Thereby, good concordance is observed between the simulations and the experimental tests in each operating Fig. 11 shows the current trajectory with the flux-weakening algorithms. We observe that experimental current trajectory correctly follows current saturation up to 5000 r/min.

From 5000 rpm experimental results and simulation results follow to the same direction. These trajectories go toward the critical point of total magnet flux weakening corresponding to I d current value equal to 6.1 A.

Figs. 12 and 13 show the experimental results obtained with the evolution of the speed, respectively, for flux-weakening algorithms with MTPV and conventional flux weakening. Finally, the best operation is obtained with the flux weakening and MTPV algorithm where the created torque is greater and al- All real-time control was implemented on dSPACE card (DS1104) (with master Power PC and DSP). A special fieldprogrammable gate array card is added to accelerate the calculation of corrected PMSM position data.

VI. CONCLUSION

High speed PMSMs are used in electrical vehicles because they are lighter, smaller, and cheaper than other classic PMSM. The main point of operation of these machines at high speed is the flux-weakening method associated with a general control strategy. In this paper, the authors present a pertinent control strategy defined in the d-q reference frame that enables these machines to be driven whatever their speed. This strategy satisfies all constraints imposed by reference operating points such as: the voltage limit, the current limit, and the battery power limit. The flux weakening is carried out by a regulation of the reference voltage given by the current regulation and ensures that it does not go over the voltage limit.

So, if the critical point is within the current limitation, then the MTPV strategy is required to maximize the torque achievable at high speed with minimal current and respecting the voltage limit. This MPTV is taken into account in the control by modifying the current limit at high speed with the current required for MTPV in continuous mode and without needing to switch between algorithms. Finally, the performances of the proposed control are observed through simulations. They were also validated experimentally, and satisfactory concordances are observed in the different operating points between experimental and simulation results as shown in this paper.

Consequently, this study confirms that the proposed control strategy with flux weakening and MTPV globally improves the PMSM propulsion operation and especially improves the effectiveness of energy conversion. This study confirms that the control strategy has been improved and that the MTPV has increased the effectiveness of the PMSM with an overspeed regime of more than 9 and a speed increased by 10%.

Fig. 1

 1 shows the maximum torque attainable according to speed and under nominal conditions for different control strategies. It corresponds to smooth-pole PMSM whose parameters are Authorized licensed use limited to: INP TOULOUSE. Downloaded on January 20,2022 at 08:53:48 UTC from IEEE Xplore. Restrictions apply.

Fig. 1 .

 1 Fig. 1. Torque-speed characteristics of the smooth-pole PMSM from TableI.

Fig. 7 .

 7 Fig. 7. Torque reference of 1.9 N•m with a 1400-W battery-electromagnetic torque and rotation speed.

Fig. 8 .

 8 Fig. 8. Torque reference of 1.9 N•m with a 1400-W battery-voltage norm and the current norm.

Fig. 9 .

 9 Fig. 9. Bench test of the PMSM propulsion system with load torque emulation.

Fig. 10 .

 10 Fig. 10. Mean torque generated with flux weakening + MTPV, with classic flux weakening and without flux weakening (simulation results and experimental tests).

Fig. 11 .

 11 Fig. 11. Experimental and simulation trajectories of average current in the I d -I q plane; control algorithms without flux weakening (no FW) and with classic weakening (classic FW), with flux weakening with MTPV.

Fig. 12 .

 12 Fig. 12. Experimental evolution of rotation speed with flux weakening and MTPV.

Fig. 13 .

 13 Fig. 13. Experimental evolution of rotation speed with classic weakening.

  Léopold Sepulchre, Maurice Fadel, Maria Pietrzak-David and Guillaume Porte [19]-[25]. This last method is divided into: regulation on the voltage magnitude [15], [19]-[22], regulation on the voltage error [4], [15], [23], regulation on the current error [15], [24], and regulation on the duty cycle [15], [25].If the magnet can be totally defluxed, i.e., the critical point is within the current limit, then an MTPV is required for flux weakening[START_REF] Bolognani | Flux weakening in IPM motor drives: Comparison of state-of-art algorithms and a novel proposal for controller design[END_REF]-[START_REF] Morimoto | Wide-speed operation of interior permanent magnet synchronous motors with high-performance current regulator[END_REF],

	[12]-[14], [17], [26]-[30]. The analytical direct open-loop cal-
	culation method [7], [26], [27], direct open-loop experimental
	LUT [4]-[7], [28], SCR method [12]-[14], and UDFVC [17]
	enable MTPV flux weakening [29], [30] using the VCC strategy
	associated with MTPV but they also require an algorithm
	switch. The open-loop method with direct calculation from
	the motor equations is very sensitive with regard to parameter
	variation. For salient-pole PMSM, this method needs long
	calculations in real-time controls and also to define torque
	references. LUT working in open loop or TFC operating in
	closed loop are adapted for taking into account the inductance
	of magnetic saturation. This depends on the motor and previous
	experimental tests have to be carried out.

, [12]-[14], TFC method with LUT [15], [16], UDFVC in the stator flux frame [17], [18], and VCC [15], 0093-9994 © 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information. Authorized licensed use limited to: INP TOULOUSE. Downloaded on January 20,2022 at 08:53:48 UTC from IEEE Xplore. Restrictions apply.

Authorized licensed use limited to: INP TOULOUSE. Downloaded on January 20,2022 at 08:53:48 UTC from IEEE Xplore. Restrictions apply.


M R Ciumag

T Tzedakis
email: tzedakis@chimie.ups-tlse.fr

C André Barrès

Voltammetric behavior of triethylamine trihydrofluoride and anisole in acetonitrile as a first approach of studies for electro-fluorination of some adducts

This work focuses on kinetic studies of anisole and triethylamine trihydrofluoride (fluorinating agent) on platinum electrode and acetonitrile as solvent, in order to get a better understanding of their anodic behavior. Results show that both compounds can be oxidized and some kinetic parameters are calculated: the diffusion coefficient within the working media, the anodic electronic transfer coefficient and the apparent intrinsic heterogeneous electronic transfer constant. An unusual variation of these parameters occurs within the chosen reaction conditions, particularly by varying the triethylamine trihydrofluoride concentration. Preliminary experiments for anodic fluorination of dimethoxy ethane (DME) and anisole were carried out and even if results show a possible electrofluorination for the DME (classically used as solvent), there is no fluorination of anisole when electrochemical microreactor was used.

Introduction

Fluoride chemistry is important in various fields: one agrobiological molecule of two has at least one fluoride atom; for the pharmaceutical domain the proportion is one to three. It is also important to note the use of 18 F, fluoride artificial isotope, in medical imagistic for positron emission topography, to diagnose neuro-degenerative cerebral disease (epileptic, Parkinson) or tumors.

Fluoride characteristics, e.g. its strong electro-negativity, can significantly modify the physico-chemical properties of a molecule; this makes fluorination to be difficult and shows the need for new synthesis methodologies and new more efficient fluorinating agents. Chemical fluorination of various molecules involves multi-step reaction process, using gaseous fluorine ("Shiemann and Halex" in the industrial scale, toluene fluorination). For reducing the risks, several electrochemical studies [1][2][3][4][5][6][7][8][9][10][11][12] were carried out, on the anodic fluorination. General conclusions of these works, expressed in terms of fluorination yield, selectivity, number and position in the final product of fluoride atoms, shown the difficulty to fluorinate alkylated groups in alpha position of a hetero-atom, and inform on the optimal conditions (electrolyte nature, solvents, electrode material and electric energy to provide), to choose. Nevertheless, in our knowledge, there are not any electrode kinetic studies considering mixtures of compounds to fluorinate in presence of fluorination agent.

Suryanarayanan and Noel [1] have shown that electrolytes such as Et 3 NF•4HF, Et 3 N•3HF in solvents such as dimethoxyethane, dimethylformamide or acetonitrile act like nucleophylic fluorinating agents, conditioning the selectivity of anodic fluorination process. Selective electrochemical fluorination of indanone compounds was also carried out in Et 4 NF•3HF used as Ionic liquid solvent.

Fuchigami is one of the authors who most studied the organic compounds fluorination [2][3][4][5][6][7][8]. Amines like Et 3 N•5HF and Et 4 NF•4HF were used as electrolyte and fluorinating agent by Hou and Fuchigami for ethyl ␣-(2-pyrimidylthio) acetate [2], for diethylene glycol dimethyl ether or dimethoxyethane [3] as well as for flavones compounds fluorination [4]; fluorination yield can reach 98%, nevertheless 8F/mol of substrate are required.

Baba et al. [5] studied thioazolidins fluorination in dimethoxyethane, in presence of fluorinated salts. The yield in mono-fluorinated product depends on the solvent: in the case of acetonitrile, conversion increases with the number (n) of HF in Et 3 N•nHF molecule. Suzuki et al. [6] studied 4-phenylthyomethyl-1,3-dioxolane-2-one fluorination in presence of Et 3 N•3HF as electrolyte and dimethoxyethane, dichloromethane and acetonitrile as solvents; meanwhile with dimethoxyethane only the mono-fluorinated product is obtained, the use of acetonitrile allows high difluorination yields. Let us note that even if frequently Nomenclature c and c 0 concentration and initial concentration (mol L -1 ) CE counter or auxiliary electrode D diffusion coefficient (m 2 s -1 ) E, E 0 , E 0 ′ potential, standard potential and apparent standard potential (V) Et 3 N•3HF triethylamine trihydrofluoride F Faraday constant (96,480 C mol -1 ) I, I peak , I k current, peak current, and current free of masstransfer effects (A) K triethylamine trihydrofluoride adsorption equilibrium constant (concentration in mol L -1 ) k 0 ′ and k 0 apparent intrinsic, and intrinsic heterogeneous electronic transfer constants (m s -1 ) n gl global number of exchanged electrons n ls number of electrons exchanged within the limiting step r potential scan rate (V s -1 ) R ideal gas law constant (8.31 J mol -1 K -1 ) S working electrode geometrical surface (m 2 ) T absolute temperature (K) ˛ anodic electronic transfer coefficient and max interfacial concentration and interfacial concentration at saturation (mol m -2 ) coverage ratio kinematic viscosity (assumed to be the acetonitrile viscosity: 4.25 × 10 -4 m 2 s -1 ) ω angular velocity (RPM or rad s -1 ).

used as fluorinating agents, there is no available information about the fluorinated triethylamines electrochemical behavior, or kinetic parameters.

Ishii [8] shows that acidity difference between hydrogen atoms substituted at the oxygen or at the methyl carbon (e.g. dimethoxyethane), makes the substitution to occur at the hydrogen atom of the carbonyl group, i.e. the alpha position (the most expected) of the C O bound.

Et 3 N•4HF and fluorohydric acid, even if very corrosive, were also used as fluorinating agents by Ilayaraja et al. [9,10]; for dimethyl glutarate fluorination, monofluoro dimethyl-glutarate were obtained with a 71% yield for a 6F/mol charge.

This preliminary work presents electrochemical kinetic studies, first expecting the understanding of anisole electrochemical behavior in presence or absence of the triethylamine trihydrofluoride, used both as fluorinating agent and electrolyte. On the other hand, the works carried out aim to help to approach the final goal of our study, the direct anodic fluorination of valuable adducts (e.g. anisole) using an electrochemical microreactor, appropriated to this kind of reactions [13][14][15][16].

Experimental

Analytical degree products were provided by Sigma-Aldrich (dimethoxyethane and acetonitrile as solvents), and by Acros Organics (tetrabutylammonium perchlorate and tetraethylammonium perchlorate as electrolytes, anisole and trifluorinated amine). An Autolab 30 potentiostat-galvanostat (GPES software) and a classical thermoregulated 'three-electrodes' electrochemical cell were used. The working electrode was a gold or platinum rotating disk (r = 1 mm), cleaned before each experiment. The counter-electrode was a platinum wire and the reference was a SCE.

Results

Electrochemical study of triethylamine trihydrofluoride (Et 3 N•3HF) on gold anode

Transient state current-potential curves were plotted in order to study the influence of the potential scan rate and concentration on the triethylamine trihydrofluoride oxidation.

Fig. 1(a) shows results obtained for a solution containing 0.1 mol L -1 of triethylamine trihydrofluoride Et 3 N•3HF, used both as supporting electrolyte and fluorinating agent, in dimethoxyethane (DME) solvent. A plateau appears (instead of a peak) in the range 0.2-1 V vs SCE, attributed to the triethylamine trihydrofluoride oxidation. For potentials higher than 1.5 V vs SCE, the exponential shape of the curve translates a pure activation limitation, and this signal could be attributed to the solvent or the gold electrode oxidation. The current magnitude increases with the potential scan rate and shifts towards more anodic potentials. For a higher Et 3 N•3HF concentration (1 mol L -1 ), the plateau appears (Fig. 1(b)) in the range of 1-1.5 V vs SCE, and tends to become a peak when the potential scan rate increases.

By examining the electrode surface at the end of the experiments one can observe corrosion of the gold anode. In absence of the fluorinated agent no corrosion takes place. Fluoride anion arising from triethylamine trihydrofluoride dissociation decrease the gold oxidation potential and cause the anodic oxidation of this material (second signal (E > 1.5 V).

Current-potential curves are also plotted using acetonitrile (CH 3 CN) as solvent, tetraethylammonium perchlorate (Et 4 NClO 4 ) as electrolyte and triethylamine trihydrofluoride (Et 3 N•3HF) as fluorinating agent. A similar behavior was observed for both curve shapes and gold surface corrosion, as in the case of dimethoxyethane.

One can conclude that the gold electrode is not appropriate for this study because of its instability; a platinum electrode will be used as working electrode for the further study of fluorination reactions.

Electrochemical study of tri-fluorinated (Et 3 N•3HF) triethylamine on platinum anode

Influence of the triethylamine trihydrofluoride concentration

The electrochemical behavior of Et 3 N•3HF was studied in acetonitrile containing Bu 4 NClO 4 0.2 mol L -1 , in order to have a better understanding of its anodic oxidation process. Potential current curves (Fig. 2) obtained for various Et 3 N•3HF concentrations show two signals at 0.9 V/1.7 V and 2.2 V/3 V vs SCE.

By analyzing the variation of the current magnitude of the first signal (1.5/1.7 V vs SCE), versus the Et 3 N•3HF concentration, for three potential scan rates (Fig. 3(a)), one can observe the appearance of a plateau for Et 3 N•3HF concentrations higher than 2 × 10 -2 mol L -1 . This behavior could be due to the triethylamine trihydrofluoride adsorption on the platinum surface.

Because of the low electrode area, the adsorbed quantity of Et 3 N•3HF could be assumed negligible, consequently its concentration in the bulk can be assumed constant.

A Langmuir isotherm model was expected to govern Et 3 N•3HF adsorption, and following analysis aims to demonstrate this assumption.

Et 3 N • 3HF + adsorption site () k f ⇄ k b (Et 3 N • 3HF) adsorbed (1)
The interfacial concentration of the adsorbed free Et 3 N•3HF can be expressed (using the coverage ratio (2)), according the Langmuir model (3).

= K max c 1 + KC ( 3
)
where K is the adsorption equilibrium constant = k f /k b and c is the free Et 3 N•3HF concentration, i.e. its initial concentration.

The curves in Fig. 2 (as well as curves in Fig. 6, next section) show that Et 3 N•3HF is an irreversible system: the potential of the second signal shifts towards more anodic values with triethylamine trihydrofluoride concentration. Consequently, the peak current magnitude for a monolayer adsorbed species can be expressed [START_REF] Bard | Electrochemical Methods, Fundamentals and applications[END_REF] by relation (4).

I peak = n gl • n ls • ˛ • F 2 • r • • S 2.718 • R • T (4)
where n gl is the global number of exchanged electrons, n ls is the number of electrons exchanged within the limiting step, ˛ is the anodic electron transfer coefficient, F is the Faraday constant (96480 C mol -1 ), r is potential scan rate (V s -1 ), S is the working electrode geometrical area (m 2 ), T is the absolute temperature (K) and R is the gas constant (8.31 J mol -1 K -1 ). Combination of Eqs. ( 3) and (4) led to relation (5), allowing the access to the adsorption equilibrium constant K.

1 I peak = 1 + 1 • K • c ( 5
)
where

= n gl • n ls • ˛ • F 2 • r • S • max 2.718 • R • T
V ) -1 = f({[Et3N•3HF]} -1
) for different potential scan rates.

Table 1

Results obtained from Fig. 3(b), on the first anodic signal of the tri-fluorinated triethylamine, related to its adsorption on the platinum anode.

Potential scan rate, r (V s -1 ) The average estimated equilibrium constant for the Et 3 N•3HF adsorption at 25 • C is: K = (0.8 ± 0.2) × 10 2 , a relatively low value demonstrating a relatively low affinity of this compound for the platinum anode. The interfacial concentration at saturation ( max ) of the Et 3 N•3HF adsorbed on platinum decreases when the potential scan rate increases (Table 1), indicating an unusual behavior of an adsorbed species.

{I signal at 1.5-1.7 V } -1 = + /[Et3N•3HF] R 2 K (concentration was expressed in mol L -1 ) max (×10 -4 mol m -2 ) (A -1 ) ((mol L -1
However, the first signal appears to be a peak for the lower concentrations (Fig. 2, curves 1-4), while increasing the concentration (Fig. 2, curves 5 and causes the shape of the signal to become a plateau with practically constant current, similar to a limiting current. The limiting current is in accordance with a no limitative adsorption step, meaning a rapid establishment of the adsorption equilibrium, because the higher concentration of the Et 3 N•3HF in the bulk. This opposite behavior will be discussed in the next sections, because other phenomena could take place.

Indeed Et 3 N•3HF is a complex resulted from association of hydrofluoric acid and Et 3 N according to an equilibrium. Nevertheless, a study performed by 19 F NMR on the stability of Et 3 N•3HF 1M in acetonitrile (Fig. 4), showed that resulting complex seem to be instable. Obtained spectra show that the signal of Et 3 N•3HF (-87 ppm/CF 3 COOH) completely disappears after 16 h, and four additional signals appears (-74, -73, -66 and -48 ppm). It seems that Et 3 N•3HF decomposes to various products (Et 3 N•2HF, Et 3 N•HF, Et 3 N and hydrofluoric acid). A similar behavior was observed for other solvents.

On the other hand, studies of Fuchigami et al. [2][3][4] shown that when fluorination was carried out using Et 3 N•3HF, at the end of the reaction free Et 3 N was detected, meaning that the complex dissociates during the fluorination.

The second Et 3 N•3HF oxidation signal (Fig. 2) appears to be a peak located in the range of 2.2 V/3 V vs SCE; its current magnitude shows a linear dependence against the triethylamine concentration (Fig. 5), meaning a diffusion limited reaction. The intercept of theses straight lines is not zero, because the residual current was not removed; indeed, blank elimination is difficult because the Et 3 N•3HF act both as electrolyte and electroactive species, influencing the migration current and causing changes in the blank.

In addition, this signal shifts towards more anodic potentials and its peak potential seems to be strongly influenced by Et 3 N•3HF concentration (Fig. 2), probably because of pH variation induced by a partial decomposition of Et 3 N•3HF, leading to fluorohydric acid.

In conclusion, triethylamine trihydrofluoride can be oxidized both as an adsorbed and free forms. Adsorption on platinum electrode obeys to the Langmuir isotherm model, while the second electrochemical signal translates a mass transfer limitation.

Influence of the potential scan rate on the triethylamine trihydrofluoride oxidation

In order to access to the Et 3 N•3HF kinetic parameters, its electrochemical behavior in the acetonitrile-Bu 4 NClO 4 media was studied (Fig. 6), by plotting the current potential curves for various potential scan rates. As previously (Fig. 2), the current-potential curves obtained for different potential scan rates show the adsorption wave (mainly present in the expected form, i.e. a peak) followed by the diffusion peak.

For the first signal, a linear dependence ( 6) of the potential scan rate on the current magnitude, according to relation (4), was obtained and confirms the electrochemical reaction limitation by the Et 3 N•3HF adsorption on the electrode surface.

I peak = 0.121 + 0.0183r, R 2 = 0.989 (6)
The intercept of this relation is not zero, because the residual current was not removed (same reason as in the case of Fig. 5).

The peak potential of the second signal (2.6-2.8 V vs SCE, Fig. 6) shifts towards more anodic values when the potential scan rate increases; its variation versus the natural logarithm of the scan rate, according to the relation (7), allows having some information about the system reversibility/irreversibility:

E peak = E 0 ′ + R × T ˛ × n ls × F 0.78 + ln D 1/2 k 0 + ln ˛ × n ls × F × r R × T 1/2 (7)
where E 0 ′ is the apparent standard potential of the electroactive system (V) and k 0 is the intrinsic heterogeneous electronic transfer constant (m s -1 ). Results for Et 3 N•3HF concentrations in the range 8 × 10 -3 to 7 × 10 -2 mol L -1 (Fig. 7) show a linear correlation, meaning that the electroactive system is irreversible.

The average value of slopes obtained in Table 2 (x = 2.303 (RT/2˛n ls F)) allows estimating ˛nls ∼0.36.

One can observe that an increased Et 3 N•3HF concentration does not affect the slope, while the intercept increases. Changes in the intercept value (Table 2) with the Et 3 N•3HF concentration are an unclassical observation and they will be discussed at the end of this paragraph.

Taking into account the ˛nls value determined previously, the Et 3 N•3HF diffusion coefficient can be determined using the linear dependence of the potential scan rate square root with the current magnitude (8) and results for four Et 3 N•3HF concentrations are indicated in Table 3.

I peak = 2.99 × 10 5 • n gl • ˛ • n ls • D • S • c 0 • √ r ( 8
)
where D is the Et 3 N•3HF diffusion coefficient in CH 3 CN containing Bu 4 NClO 4 0.2 mol L -1 (m 2 s -1 ); c 0 is the triethylamine trihydrofluoride initial concentration in the bulk (mol L -1 ); n gl = 2 (per mole of produced fluorine).

The relative good linearity of the four curves I peak = f ( √ r) confirms the kinetics limitation by the Et 3 N•3HF diffusion. Nevertheless, determined Et 3 N•3HF diffusion coefficient slightly ((2.85 -1.24)/2.85 = 0.56) changes with concentration, a logarithmic increase of this parameter was observed (Fig. 8), relation (9):

D Et 3 N•3HF (m 2 s -1 ) = 4.77 × 10 -10 + 7.29 × 10 -11 • ln[Et 3 N • 3HF] (mol L -1 ), R 2 = 0.995 (9)
This variation, even if not important, seems unusual. A possible reason explaining this change could be the migration current. Indeed,

Table 2

Results obtained from Fig. 7, on the second anodic signal of the tri-fluorinated triethylamine, related to its diffusion-controlled nature. because the chosen TBAP concentration (0.2 mol L -1 ), the ions arising from Et 3 N•3HF dissociation, especially F -, could migrate and consequently increase the migration anodic current, which cannot be neglected in the whole examined range of Et 3 N•3HF concentration: 8

[Et3N•3HF] (mol L -1 ) E peak (V) = + x log(r) (V s -1 )
× 10 -3 -2 × 10 -2 mol L -1 .
The transference number of the electroactive species, t Et 3 N•3HF can be estimated according follow relation:

t Et 3 N•3HF = z 2 anion arises from Et 3 N•3HF dissociation × F 2 × u anion arises from Et 3 N•3HF dissociation × [Et 3 N • 3HF] all ions j z 2 j × F 2 × u j × [j]
Because we do not know mobility of ions arising from these electrolytes in acetonitrile, we will use the following approximations:

-both TBAP and Et 3 N•3HF are assumed to be binary electrolytes, mobilities u j of all j ions arising from these electrolytes have the same order magnitude.

The transference number can be written as follow:

t Et 3 N•3HF = [Et 3 N • 3HF] 2 × [Et 3 N • 3HF] + 2 × [TBAP]
and its values (Table 3), in the range from 0.01 to 0.13, are relatively low.

Note that these values are simple estimations, because the dissociation of Et 3 N•3HF is partial and the concentration of the arising anion is lower than the Et 3 N•3HF concentration used to estimate the transference number. In these conditions, the estimated transference number is higher than the real one.

For a binary electrolyte, the product (1/(1 -t j )) translates the contribution of the ion j migration flux, in the diffusion flux of this ion. Consequently, relation (8) can be rewritten:

I peak = 1 1 -t j • 2.99 × 10 5 • n gl • ˛ • n ls • D • S • c 0 • √ r (8bis)
Using the relation (8bis), an estimation of the Et 3 N•3HF diffusion coefficient taking into account the migration current was proposed and results are indicated in

6% < {(D D -D M/D )/D D } < 22%.
The variation of D vs concentration seems unusual, as passivation problems could not explain it completely. Increased Et 3 N•3HF concentration leads to a more important passivation and consequently, causes current and diffusion coefficient to decrease. As explained above, Et 3 N•3HF can decompose in free fluorohydric acid and triethylamine; either Et 3 N•3HF and HF oxidation could be attributed to the obtained signal. Thus determined D using the slope of relation (8bis) is an apparent diffusion coefficient because the value of the initial concentration was used instead the real concentration of the corresponding electroactive species (which is lower one the initial concentration) Diffusion coefficient variation versus the concentration of Et 3 N•3HF can also (partially) explain the changes on the intercept value (Table 2) previously observed. Consequently, determination of the intrinsic heterogeneous electronic transfer constant k 0 seems to be difficult because both the concentration of the electroactive species and the E 0 ′ value are unavailable. One will try to access to this parameter in the next section.

Influence of the angular velocity of the platinum anode on the triethylamine trihydrofluoride oxidation

In order to better understand this system, (estimation of k 0 , comparison of the results for D), current-potential curves were plotted at the steady state, for various Et 3 N•3HF concentrations and angular velocities of a rotating platinum disk. Results (Fig. 9) show a similar shape curve for all the examined concentrations. The current magnitude for the first oxidation signal (1.2-2 V vs SCE), previously attributed to the Et 3 N•3HF adsorption on the electrode surface, seems to be affected by the stirring, for the low examined concentrations (Fig. 9(a) and (b)); no effect was observed for higher concentrations: (Fig. 9(c) and(d)).

Theoretically, adsorption is not affected by stirring. Nevertheless, a slow adsorption rate can influence the time required to reach the equilibrium. For a Et 3 N•3HF concentration high enough, the adsorption equilibrium is rapidly reached and the stirring does not affect the curves. Conversely, for concentrations up to 2 × 10 -2 mol L -1 , the time necessary to saturating the electrode is higher and the stirring can have an effect. The low value of Et 3 N•3HF adsorption equilibrium constant (K) and the max Table 3 Et3N•3HF diffusion coefficient calculated with relation (8) and ˛nls values from Table 2; n gl = 2. Results obtained from Fig. 6.

[Et3N•3HF] (mol L -1 ) Slope I peak at 2.6/2.8 V = f(r 1/2 ) R 2
DEt 3 N•3HF (×10 10 m 2 s -1 ) (without migration contribution to the current) variation with the potential scan rate (Table 1), are in accordance with these results. Another reason that could explain this behavior is represented by a temperature variation at the electrode surface, arising from Et 3 N•3HF decomposition, a phenomenon damped by the stirring.

Estimated transference number of Et3N•3HF, tEt 3 N•3HF = [Et3N • 3HF]/(2[Et3N • 3HF] + 2[TBAP]) DEt 3 N•3HF (×10
The second oxidation signal appears to be a peak and its potential shifts to more anodic values (∼2.3 to ∼3 V vs SCE) when the Et 3 N•3HF concentration increases, fact that confirms its irreversible behavior. For a classical electroactive system, this 'diffusion limited' signal, at the steady state, has to show a limiting current plateau; the obtained 'peak'-shaped curve translates passivation phenomena caused by a thin layer of gaseous fluorine produced at the electrode surface. Using the 'net/exempted of the blank' maximum current of this signal, as an approximation for the expected limiting current (Fig. 9), linear correlations (Table 4) were obtained for the four Et 3 N•3HF concentrations, following Levich relation:

I lim = 0.62 • n gl • F • S • D (2/3) • c 0 • -(1/6) • √ ω (10)
where n gl is assumed to be 2 (by molecule of produced F 2 ), ω is the electrode angular velocity (rad s -1 ) and is the media kinematic viscosity, assumed to be the acetonitrile viscosity (4.25 × 10 -4 m 2 s -1 ). The linear correlation I lim = f ( √ ω) obtained, could mean that passivation does not strongly affect the electrode surface, because a strong stirring could contribute to remove bubbles from the electrode surface. Slopes of the four curves allow estimation of triethylamine trihydrofluoride diffusion coefficient D, and the results are presented in Table 4. As previously, D was estimated taking into account the migration current contribution and the results are also shown in Table 4.

The obtained values of diffusion coefficient allow several remarks:

they decrease when Et 3 N•3HF concentration increases, comparison of D values determined by the two methods (influence of both the potential scan rate and angular velocity of the rotating disk electrode (Table 4), taking into account only the diffusion current) show ratios decreasing in the range from 14 to 0.5 within the Et 3 N•3HF concentration examined range.

-for low Et 3 N•3HF concentrations (<2 × 10 -2 mol L -1 ), the obtained diffusivities are relatively high, and that is in accordance with a 'low size' electroactive species, i. 4), is very close to its initially introduced concentration.

In addition, low Et 3 N•3HF concentrations lead to low current, consequently to a low fluorine quantity produced at the interface, and so a minimized effect of passivation. for Et 3 N•3HF concentrations higher than 2 × 10 -2 mol L -1 , the influence of stirring on the Et 3 N•3HF decomposition remains low. The concentration of the electroactive species HF (or F -), arising by Et 3 N•3HF decomposition, is lower than the initial concentration of Et 3 N•3HF, used to estimate D, consequently, it is an apparent diffusion coefficient, and its value was assumed to be close to 1.7 × 10 -9 m 2 s -1 .

In order to estimate Et 3 N•3HF intrinsic heterogeneous electronic transfer constant k 0 ′ , analysis of curves from Fig. 9, using the Kouteck ý-Levich equation, was carried out for the second triethylamine oxidation signal, located in the potential range 2/3 V vs SCE:

1 I = 1 I k + 1 0.62n gl FSD 2/3 c 0 -(1/6) ω 1/2 ( 11
)
where I is the current magnitude in the activation/diffusion 'potential range' of the current-potential curves (i.e. ∼2.6 to ∼2.8V) and I k represents the current free of mass-transfer effects:

I k = nFSck 0 exp ˛nls F RT (E -E 0 ′ ) (12)
Results (Fig. 10) show a linear variation of 1/I = f(1/ω 1/2 ) for the examined potentials and for a Et 3 N•3HF concentration of 2 × 10 -2 mol L -1 . The same analysis was performed for all Tri-fluorinated triethylamine diffusion coefficient in acetonitrile (calculated from results of Fig. 9, using I lim = f(ω 1/2 ) slope for four different initial concentrations) and their comparison with the diffusion coefficient values calculated with I peak = f(r 1/2 ) slope (Table 3). examined concentrations; each concentration allows getting a set of parallels lines 1/I = f(1/ω 1/2 ), and the slope is different for each set (similar behavior to the results indicated in Table 4). The I k determination was carried out from the intercept of these straight lines.

[Et3N•3HF] mol L -1 Slope I peak = f(ω 1/2 ) R 2 DEt 3 N•3HF (×10
Analysis of the I k values, obtained from the intercept of curves 1/I = f(1/ω 1/2 ), was performed according to:

ln I k = ln (n gl nFSc 0 k 0 ′ ) + ˛ • n ls • F RT E ( 13
)
where

k 0 ′ = k 0 exp -˛nls F RT E 0 ′ (14)
Eq. ( 14) is the apparent intrinsic heterogeneous electronic transfer constant. Despite a certain dispersion of points, a satisfactory linear correlation of ln(I k ) = f(E) was obtained for Et 3 N•3HF concentrations in the range 8 × 10 -3 to 3.5 × 10 -2 mol L -1 (results presented in Table 5).

The kinetic parameters k 0 ′ and ˛nls were calculated, and the obtained values allow some remarks:

-˛nls changes with Et 3 N•3HF concentration; this dispersion is mainly caused by the fact that results are very sensitive to the current magnitude: indeed, a 5% change in current values can lead to a change in the intercept of the curves 1/I = f(ω 1/2 ) of about 20%. This could explain the obtained ratios ˛nls(Kouteck ý -Levich) ˛nls potential scan rate Table 2 in a range from 0.6 to 1.2. Nevertheless, the average value ˛nls = 0.35 is very close to the one obtained in the previous section. -A similar variation was obtained for the apparent intrinsic heterogeneous electronic transfer constant k 0 ′ : its values change versus Et 3 N•3HF concentration and are very low because including the exponential term: exp [-(˛n ls F/RT )E 0 ′ ] Moreover, in addition to the current sensitivity previously indicated, changes in the k 0 ′ values could be due to the variation of the apparent standard potential of the electroactive system (HF/F 2 ). E 0 ′ closely depends of the solution pH, which decreases because HF arises from Et 3 N•3HF decomposition. Consequently, the real value of the intrinsic heterogeneous electronic transfer constant k 0 is higher than the one of k 0 ′ . Let us note that k 0 ′ value 1.54 × 10 -11 m s -1 obtained for the highest concentration is 'the most correct', or at least 'the closest' to the real value of k 0 , as the apparent standard potential E 0 ′ is the lowest one (the lowest influence of the exponential term). In order to overcome these difficulties, and to access to more precise kinetic parameters, a possibility could be to operate electrolyses in a buffer media, for example a mixture of polar and non-polar solvents (i.e. HF + heptane). This experimental investigation will constitute a future work in order to go further to the knowledge of this system. Nevertheless current estimated value of k 0 ′ includes apparent standard potential E 0 ′ and is very useful to estimate overpotentials and consequently to perform precise energy balance for fluorination in the microreactor.

Electrochemical study of anisole on platinum anode

Electrochemical kinetic studies were carried out using a platinum disk anode, in order to understand the anisole anodic behavior, in absence and in presence of triethylamine trihydrofluoride. This study expects to help in approach the final goal of our project, 'the direct anodic fluorination of valuable adducts using an electrochemical microreactor'.

The voltammograms in Fig. 11(a), obtained for various potential scan rates, show that anisole can be oxidized for potentials higher than 1.5V vs SCE; nevertheless the curves shape is unusual. The first peak-shaped signal appears at 1.6 to 1.8V vs SCE, meanwhile for higher potentials (1.9-2.7V vs SCE), the current becomes practically constant and the curve presents a plateau. Additional anisole oxidations might take place, causing increase (instead decrease) of current magnitude.

The peak potential shifts towards more anodic values, according to a linear variation versus the scan rate logarithm (15) and confirms an irreversible anisole oxidation:

E peak = E 0 ′ a + RT ˛an ls F 0.78 + ln D 1/2 a k 0 a + ln ˛an ls F RT 1/2 +1.1515 RT ˛an ls F log (r) = 1.8551 + 0.0822 log (r) R 2 = 0.997 (15)
where k 0 a s the anisole intrinsic heterogeneous electronic transfer constant. The curve slope allows estimation of ˛an ls = 0.36. Relation ( 16) illustrates a linear dependence of the potential scan rate square root on the magnitude of the 'peak'-current (i.e. potentials in the range 1.65-1.85 V vs SCE), and confirms the kinetics limitation by anisole diffusion.

I peak = 2.99 × 10 5 • n gl ˛an ls DaSc 0 √ r = 1.62 × 10 -4 √ r R 2 = 0.991 (16) Diffusion coefficient of anisole D a was estimated at ∼2.0 × 10 -8 m 2 s -1 , assuming the transferred electron number n gl = 2, and using the curve slope as well as the previously calculated value ˛an ls . This value appears to be high for a relatively 'big sized' molecule like anisole; acetonitrile low viscosity, as well as its low ability to solvate anisole, could be one explanation for this high value. In addition, as indicate previously, the current magnitude 'captured at the peak' is higher than the expected one, because the presence of more than one oxidation steps.

In order to confirm this diffusion coefficient value, and to access to the kinetic parameters of the system, another set of experiments was carried out. Fig. 11(b) shows current-potential curves obtained at steady state for various angular velocities (ω) of the rotating platinum disk anode. The oxidation signal begins at ∼1.6 V vs SCE and is followed by a diffusion plateau, presenting a limiting current (mainly for ω < 1000 rpm). For higher angular velocities, the current magnitude reaches a maximum in a potential range from 2 to 2.2 V vs SCE, and decreases for more anodic potentials. A strong stirring leads to a current increase and consequently, more important quantities of anisole are involved into the reaction close to the interface. In these conditions, partial electrode passivation can occur and the current decreases.

Using the maximum current as an approximation for the expected limiting current (Fig. 11(b)), and applying the Levich relation (10), a non-linear correlation of I lim = f(ω 1/2 ) is obtained within the ω examined range (Fig. 12(a)), in accordance with the previous passivation explanations. However, for low angular velocities (ω lower than 1000 rpm), passivation effects are reduced and a linear correlation of I lim = f(ω 1/2 ) is obtained [START_REF] Bard | Electrochemical Methods, Fundamentals and applications[END_REF].

I lim (A) = 8.82 × 10 -6 ω 1/2 (rad s -1 ) 0.5 , R 2 = 0.9999 (100 ≤ ω ≤ 500 rpm) [START_REF] Bard | Electrochemical Methods, Fundamentals and applications[END_REF] Anisole diffusion coefficient deduced from the slope is D a ∼ 1.6 × 10 -8 m 2 s -1 (assuming n gl = 2) a value that seems to be more precise than the previous one, because the low passivation effects at low stirring rates.

Analysis of curves in Fig. 11(b) was carried out using the Kouteck ý-Levich Eq. (11), by plotting the variation of the current reverse against the reverse of the angular velocity square root. The current was captured in the activation/diffusion range of current-potential curves, for potentials from 1.7 to 1.75 V vs SCE, and results (Fig. 12(b)), show a linear variation of 1/I = f(1/ω 1/2 ) for the four examined potentials.

Logarithmic analysis of the obtained I k values (from the intercept of curves Fig. 12(b)) versus the anodic potential, according to relation (13), allows determination of the kinetic parameters k 0 ′ a and ˛a n ls and results show a linear correlation [START_REF] Kane | [END_REF]. ln (I k ) = 15.144E -12.241 R 2 = 0.994 [START_REF] Kane | [END_REF] where ˛an ls = 0.39 and

k 0 ′ a = k 0 exp -(aan ls F) RT E 0 ′ ∼8 × 10 -6 m s -1 .
The apparent intrinsic heterogeneous electronic transfer constant (k 0 ′ a ) value is low, indicating an irreversible behavior for anisole oxidation. However, a rigorous analysis requiring additional investigations to calculate the apparent standard potential E 0 ′ of the system, has to be carried out in order to obtain the intrinsic heterogeneous electronic transfer constant (k 0 ). For the pursuit of the fluorination within a microreactor of adducts like anisole the k 0 ′ a value will be used.

Electrochemical study of anisole/triethylamine trihydrofluoride mixture on platinum anode and preliminary set of fluorination

The main goal of this part of the study is to understand the electrochemical behavior of the system anisole/triethylamine trihydrofluoride before approaching the anisole fluorination within an electrochemical microreactor. Because the triethylamine trihydrofluoride is used as a fluorinating agent as well as an electrolyte, its concentration will be higher (8 × 10 -3 mol L -1 ) than anisole concentration (10 -3 mol L -1 ).

Current-potential curves, obtained by varying both the potential scan rate (Fig. 13(a)) and the angular velocity of the rotating disk electrode (Fig. 13(b)), show the presence of three distinct signals, in the potential ranges 1-1.6 V, 1.7-1.9 V and 2-2.6 V vs SCE respectively. These voltammograms correspond to the addition of triethylamine trihydrofluoride and anisole oxidation curves. The second signal (1.7-1.9 V) was attributed to anisole oxidation, while the first (1-1.6 V) and the third (2-2.6 V) were attributed to the triethylamine trihydrofluoride.

The current magnitude for the triethylamine trihydrofluoride oxidation in presence of anisole seems to be lower than the current magnitude for the triethylamine trihydrofluoride alone. Indeed, a comparison of these currents for curves obtained in the same conditions (no. 3 Fig. 13(b), I ∼ 1.71 × 10 -4 A and no. 3 Fig. 9(a), I ∼ 1.31 × 10 -4 A) shows significant differences. An explanation could be that anisole oxidation leads to cation radicals that are further reacting with triethylamine trihydrofluoride (or fluoride). This could be in accordance with the reaction mechanisms proposed by Hou and Fuchigami [3] for dimethoxyethane (Fig. 14).

When operating with anisole alone, for relatively strong stirring rates, its oxidation to cation radicals seems leading to a partial anode passivation, causing a decrease in the current magnitude (Fig. 11(b)). The passivation seems to disappear when triethylamine trihydrofluoride is present, probably because of the electroregenerated radicals consumption, avoiding their duplication and consequently the electrode passivation. This fact allows us to pursue in the designing of the electrofluorination process without need of a special attention to the passivation problems.

This study shows that for anisole electro-fluorination it is important to maintain the anodic potential at 2.2-2.3 V vs SCE during fluorination, in order to avoid tri-fluorinated triethylamin oxidation to gaseous fluorine. A preliminary set of experiments was performed using a filter-press electrochemical microreactor [START_REF] Kane | [END_REF][START_REF] Tzedakis | Microréacteur'. French patent no. 04.12305[END_REF] in order to fluorinate both anisole and dimethoxyethane in various working conditions (-10 • C < T < 40 • C). The results did not show anisole fluorination (either on the aromatic ring nor the methoxy group). Nevertheless, dimethoxyethane was 'mono-fluorinated' (which seems to be more difficult than anisole fluorination) and two reaction products were obtained (FCH 2 OCH 2 CH 2 OCH 3 chemical yield: 62% and CH 3 OCHFCH 2 OCH 3 chemical yield: 38%), when a charge of 7F/mole was used. A more important investigation of the fluorination of anisole will constitute the goal of future works.

Conclusions

The aim of this preliminary study was to examine the electrochemical behavior of anisole and triethylamine trihydrofluoride (fluorinating agent) in order to help to approach the final goal of our study, the direct anodic fluorination of valuable adducts using an electrochemical microreactor.

Several kinetic studies, performed in various conditions, show that both compounds can be oxidized. Triethylamine trihydrofluoride 'doubly' reacts, under both adsorbed and free forms, at two different potentials. Adsorption is governed by the Langmuir model, with an adsorption equilibrium constant K = (0.8 ± 0.2) × 10 2 estimated at 25 • C and indicating a relatively low affinity of the triethylamine trihydrofluoride for the platinum anode.

One signal was observed for anisole oxidation, even if more than one reaction seems to occur. Electrode passivation, observed during anisole oxidation, disappear in presence of triethylamine trihydrofluoride, phenomena that could be an important advantage for the fluorination process.

Triethylamine trihydrofluoride diffusion coefficient within the working media, determined by two different ways (1.2 × 10 -10 < D (m 2 s -1 ) < 1.7 × 10 -9 ), appears to be 'high' and varies versus the triethylamine trihydrofluoride initial concentration in the examined range (8 × 10 -3 -3.5 × 10 -2 mol L -1 ). One can propose for Et 3 N•3HF, an apparent diffusion coefficient values close to 1.7 × 10 -9 m 2 s -1 , determined for the lowest Triethylamine trihydrofluoride concentrations involved in this study.

Anisole diffusion coefficient was estimated by two methods and similar results were obtained: (1.6 × 10 -8 < D (m 2 s -1 ) < 2.0 × 10 -8 ). As for Et 3 N•3HF, anisole diffusion coefficient is relatively high for a relatively 'big sized' molecule and it could be justified by low acetonitrile viscosity. Some kinetic parameters (˛n ls and k 0 ′ ) of both anisole and triethylamine trihydrofluoride were also proposed. For the anodic electronic transfer coefficient, in the case of both anisole and triethylamine trihydrofluoride, results led to the same and reproducible value: ˛nls ∼0.36 validated by two different study methods.

Though, the value of the intrinsic heterogeneous electronic transfer constant (k 0 ) could not be calculated, because it requires additional investigations (E 0 ′ of these systems). However, results show some values of the apparent intrinsic heterogeneous electronic transfer constant for both anisole (k 0 ′ a ∼8 × 10 -6 m s -1 ) and triethylamine trihydrofluoride (k 0 ′ a in the range 4.86 × 10 -23 to 4.52 × 10 -18 m s -1 ). These values are low (even if they contain an exponential term of the standard potential), indicating irreversible systems; for triethylamine trihydrofluoride, the obtained value is very low and varies with concentration, because the pH modification caused by the triethylamine trihydrofluoride decomposition.

Preliminary results of preparative electrolyses, carried out in conditions defined by the electrochemical kinetic study, are encouraging [START_REF] Kane | [END_REF][START_REF] Tzedakis | Microréacteur'. French patent no. 04.12305[END_REF], especially for fluorination of dimethoxymethane, demonstrating that electro-fluorination can be performed in the alpha position of a heteroatom.

Fig. 1 .

 1 Fig. 1. Potential scan rate dependency on the current-potential curves, obtained on gold rotating disk electrode (r = 1 mm) immersed in dimethoxyethane solvent containing tri-fluorinated triethylamine in two concentrations: (a) Et3N•3HF 0.1 mol L -1 ; (b) Et3N•3HF 1 mol L -1 . CE: Pt; 25 • C; no stirring. Curves 1-6: 0, 0.05, 0.1, 0.2, 0.5 and 1.0 V s -1 respectively.

Fig. 2 .

 2 Fig. 2. Current-potential curves obtained for different tri-fluorinated triethylamine concentrations, on platinum disk electrode (r = 1 mm) immersed in acetonitrile solvent containing Bu4NClO4 0.2 mol L -1 ; CE: Pt; 25 • C; r = 0.1 V s -1 ; no stirring. Curves 1-6: Et3N•3HF 10 -3 , 8 × 10 -3 , 2 × 10 -2 , 3.5 × 10 -2 , 5 × 10 -2 and 7 × 10 -2 mol L -1 respectively.

Fig. 3 (

 3 Fig. 3(b) shows the linear dependence of the current reverse against the reverse of Et 3 N•3HF initial concentration, which is in agreement with the Langmuir model. Assuming: n gl = 2 (per mole of produced fluorine), n ls = 1 and ˛ = 0.5, one can estimate from the previous results the Et 3 N•3HF adsorption equilibrium constant K, as well as the number of sites available to adsorption max .

Fig. 3 .

 3 Fig. 3. Et3N•3HF concentration influence on the current of the signal located in the potential range from 1.5 to 1.7 V vs SCE. Curve (2) was obtained from Fig. 2; curves (1) and (3) were obtained from other I/E curves, represented in the next section or no represented here. (1)-(3): 0.01, 0.10 and 0.20 V s -1 , respectively. (a): I signal at 1.5-1.7 V = f([Et3N•3HF]) for different potential scan rates; (b): (I signal at 1.5-1.7 V ) -1 = f({[Et3N•3HF]} -1 ) for different potential scan rates.

Fig. 5 .

 5 Fig. 5. Current magnitude dependence of Et3N•3HF concentration for the second oxidation signal (curves of Fig. 2), located in the range 2.2-3 V vs SCE. (1)-(3): 0.01, 0.10 and 0.20 V s -1 respectively.

Fig. 4 .

 4 Fig.4. Stability of a Et3N•3HF solution at 1 mol/L in acetonitrile, followed by19 F NMR. Reference CF3COOH at 0 ppm; signal of CF3COOH: -77 ppm vs CFCl3.

Fig. 6 .

 6 Fig. 6. Current-potential curves obtained for various potential scan rates, on platinum disk anode (r = 1 mm) immersed in acetonitrile containing Bu4NClO4 0.2 mol L -1 ; CE: Pt; 25 • C; no stirring. 1-4: 0.017, 0.083, 0.170 and 0.500 V s -1 respectively. (a) Et3N•3HF 8 × 10 -3 mol L -1 ; (b) Et3N•3HF 2 × 10 -2 mol L -1 .

Fig. 7 .

 7 Fig. 7. Second anodic peak potential variation against the logarithm of the potential scan rate for various Et3N•3HF concentrations. Results from Fig. 6 and other curves not presented. Curves 1-4: Et3N•3HF 8 × 10 -3 , 2 × 10 -2 , 3.5 × 10 -2 and 7 × 10 -2 mol L -1 respectively.

Fig. 8 .

 8 Fig. 8. Et3N•3HF diffusion coefficient variation with initial tri-fluorinated triethylamine concentration.

Fig. 9 .

 9 Fig. 9. Angular velocity (ω) dependence of the current-potentials curves obtained on platinum rotating disk (r = 1 mm), immersed in acetonitrile solvent, containing Bu4NClO4 0.2 mol L -1 ; CE: Pt; r = 4 × 10 -3 V s -1 ; 25 • C. Curves 1-5: ω = 100 rpm, 250 rpm, 500 rpm, 1000 rpm and 5000 rpm respectively. (a) Et3N•3HF 8 × 10 -3 mol L -1 ; (b) Et3N•3HF 2 × 10 -2 mol L -1 ; (c) Et3N•3HF 3.5 × 10 -2 mol L -1 ; (d) Et3N•3HF 7 × 10 -2 mol L -1 respectively.

  e. HF (or F -), arising from Et 3 N•3HF decomposition, especially in the diffusion layer area. Assuming that Et 3 N•3HF decomposition is an equilibrium reaction, stirring could contribute to favor this equilibrium by a standardization of both the concentration and temperature especially in the diffusion area close to the electrode. For these 'low Et 3 N•3HF concentrations', the determined D value must be correct because most of the introduced Et 3 N•3HF decomposes, and the concentration, used to determine D (Levich slope, Table

Fig. 10 .

 10 Fig. 10. Variation of the current reverse against the reverse of the angular velocity square root. Et3N•3HF 2 × 10 -2 mol L -1 (Fig. 9(b)). The current values are chosen for potentials in the activation/diffusion part of the I/E curve. 1-3: 2.585, 2.611 and 2.637 V vs SCE respectively. The same investigation was performed for all examined concentrations (8 × 10 -3 to 7 × 10 -2 mol L -1 ).

Fig. 11 .

 11 Fig. 11. Current-potential curves obtained on platinum rotating disk (r = 1 mm), immersed in acetonitrile solvent containing anisole 10 -3 mol L -1 and Bu4NClO4 0.2 mol L -1 ; CE: Pt; 25 • C. (a) Curves plotted at different potential scan rates; no stirring. 1-4: 0.017, 0.083, 0.170 and 0.500 V s -1 respectively, and (b) curves plotted at different angular velocities; r = 4 × 10 -3 V s -1 . 1-5: 100, 250, 500, 1000 and 3500 rpm respectively.

Fig. 12 .

 12 Fig. 12. Angular velocity dependence on the anisole oxidation current; results obtained from Fig. 11(b). (a) Limiting current variation against the square root of the angular velocity for anisole oxidation; and (b) variation of current reverse against the reverse of the angular velocity square root. The current was captured in the activation/diffusion range of the I/E curve. 1-4: 1.702, 1.712, 1.725 and 1.751 V vs SCE, respectively.

Fig. 13 .

 13 Fig. 13. Current-potential curves obtained on platinum rotating disk (r = 1 mm), immersed in acetonitrile solvent containing anisole 10 -3 mol L -1 , Et3N•3HF 8 × 10 -3 mol L -1 and Bu4NClO4 0.2 mol L -1 ; CE: Pt; 25 • C; no stirring. (a) Different potential scan rates, 1-4: 0.017, 0.083, 0.170 and 0.500 V s -1 respectively, and (b) different angular velocities, 1-3: 100, 250 and 500 rpm respectively; r = 4 × 10 -3 V s -1 .

Fig. 14 .

 14 Fig. 14. Reaction mechanism proposed for anisole electro-fluorination.

Table 3 .

 3 As previous, obtained values of D change with Et 3 N•3HF concentration; nevertheless: -differences in the D values, are in a narrow range (1.1 × 10 -10 to 2.2 × 10 -10 ) instead 1.2 × 10 -10 to 2.8 × 10 -10 e.g.

	((2.2 -1.1)/2.2 = 0.5), -effect of the migration	term	is	relatively	low:

Table 4

 4

Table 5

 5 Variation of ln(I k ) with the potential E for three Et3N•3HF concentrations.

	[Et3N•3HF] (mol L -1 )	ln(I k ) = X + Q•E (relation (13))	R 2	k 0 ′ (m s -1 )	˛nls (˛n ls = 0.35)	˛nls(Kouteck ý -Levich) ˛nls potential scan rate Table 2
		X	Q
	8 × 10 -3 2 × 10 -2 3.5 × 10 -2	-49.799 -43.982 -36.883	16.436 13.903 10.793	0.986 0.997 0.996	4.86 × 10 -23 6.54 × 10 -21 4.52 × 10 -18	0.42 0.35 0.28	1.2 1.1 0.6
	Results from Figs. 9 and 10 (and figures similar to 10, no present, for all the examined concentrations).

Acknowledgement

We would like to thank Maria Pilar García León for her contributions and very helpful discussions.


Hicham Iken

Frédéric Guillen

Hélène Chaumat

Marie-Rose Mazières

Jean-Christophe Plaquevent
email: plaquevent@chimie.ups-tlse.fr

Théodore Tzedakis
email: tzedakis@chimie.ups-tlse.fr

Scalable synthesis of ionic liquids: comparison of performances of microstructured and stirred batch reactors

a b s t r a c t

A range of alkylpyridinium bromide ionic liquids have been synthesized in a stirred reactor at multigram scale and characterized by physical methods (viscosity, conductivity, melting point, electrochemical window, and water content). One ionic liquid, octylpyridinium bromide, was chosen to be synthesized in both macro and reduced scale reactors, in order to compare its performance and to afford evidence of the advantages of a cross channel micro reactor (channel width = 1 mm) compared to a stirred reactor.

During the last decade, ionic liquids (ILs) became useful tools in organic, bioorganic, inorganic and analytical chemistry, owing to their several exceptional properties such as negligible vapor pressure, low melting point, high thermal stability and electrical conductivity, wide electrochemical window, and liquid range. [START_REF] Wasserscheid | Ionic Liquids in Synthesis[END_REF] ILs usually consist of large organic cations, such as quaternary ammonium, heterocyclic aromatic or pyrrolidinium, associated with a variety of non-or weakly coordinating anions. [START_REF] Wasserscheid | Ionic Liquids in Synthesis[END_REF] Their physicochemical properties arise from both the anion and the cation: this enables some tuning of the properties of ILs by varying the nature of the anion (respectively cation) for a given cation (respectively anion). ILs are new and promising solvents, particularly for catalysis, 2 chiral syntheses, 3 energy and separation processes, 1a where recycling of the solvent is highly desirable. 4 Usually, the cationic parts are synthesized by alkylation, an exothermic reaction, and ILs are still produced at industrial scale in batch or semi-batch stirred reactors. This method is often strongly limited by the dissipation of the generated heat, because of the small interface between solution (in fact the chemical reaction sites) and the heat exchanger (double jacket, external or internal coil). Increasing this surface or the efficiency of the heat exchange (e.g., by reducing the distance between the heat exchanger and the chemical reaction sites, or/and combining the reaction area and the heater into a single device 5 ) allows to improve the heat transfer, supplying or removing the heat almost as rapidly as it is generated by the reaction. Thus, it is possible to operate with a uniform temperature profile, avoiding any high temperature spot and therefore improving selectivity and conversion.

Chemical microstructured reactors (MSR) are devices containing open paths for fluids with dimensions in the submillimeter range. Mostly MSR have multiple parallel channels with diameters between 10 and several hundred micrometers, where the chemical transformation occurs; 6 their main feature is the high surface to volume ratio, compared to more traditional chemical reactors. Accordingly, the heat transfer coefficient is inversely proportional to the channel size (W/m 2 K), and for liquids, it is one order of magnitude higher than in the traditional heat exchangers; 7 so microstructures allow fast heating and cooling of reaction mixtures. Moreover, the easy transposition from lab processes to the industrial scale (by multiplying the number of microstructured reactors instead of scaling up a batch reactor), reinforces the reactivity against fluctuating market demand, and improves process safety by avoiding the use, during short durations, of large amounts of dangerous chemical intermediates.

Various studies describe the synthesis of ILs. [START_REF] Wasserscheid | Ionic Liquids in Synthesis[END_REF] While several recent reports proved the beneficial use of MSR for the synthesis of imidazolium-based ILs, [START_REF] Waterkamp | [END_REF] to the best of our knowledge no other IL families have been studied. The first part of the present study de-scribes the multigram preparation and characterization of ILs constituted of alkylpyridinium cations (Fig. 1) substituted by various alkyl radicals, and bromide anion; a brief discussion on the effect of the cation size on the ILs physico-chemical properties is presented. Syntheses of the most representative IL were carried out both in a stirred classical reactor and in a heat exchanger/microstructured reactor (HEx/MSR), 9 designed in our laboratory. Comparison of mass balance results for various conditions was performed in terms of conversion rate and selectivity, in order to evaluate the interest to use HEx/MSR at production scale.

The stainless steel heat exchanger/microstructured reactor (HEx/MSR) is composed of a plate (250 mm  120 mm) with rectangular (1 mm  1 mm) micro-channels (Fig. 2). The total volume of the microstructured plate (including inlet and outlet chambers) is 10.2 cm 3 . The specific area of the MSR is S/V = 251/10.2 = 24.6 cm À1 . The reactants were introduced at rt into the reactor by a two syringe pump, and distributed over the micro-channels by appropriate geometry of the inlet channel. The appropriate shape and geometry of the inlet compartment allows a good mixing of reagents, so the solution was assumed to be homogeneous before reaching the reaction area (microchannels). A similarly designed collecting channel allows removing the reaction mixture.

We first embarked in the synthesis in batch reactor of a series of alkylpyridinium salts (Fig. 1); although most of them were already described in the literature, [START_REF] Zhang | Ionic Liquids: Physicochemical Properties[END_REF] we needed to examine by ourselves a wide range of physico-chemical properties (Table 1) in order to select the best example for comparing synthetic performances of batch vs MSR. Experimental and analytical data are given in Supplementary data. The most significant properties for our studies are melting points and viscosity, which are directly relevant to IL behavior, and are discussed below.

Melting points of synthesized ILs are lower than the boiling point of water (100 °C) except for butylpyridinium bromide (Fig. 3). The phase transition temperature of ILs (from solid to liquid phase) is governed by Van der Waals and electrostatic interaction forces. 11 The melting points fall steadily with increasing alkyl chain length from 4 carbons to reach a minimum value of 18 °C for 8 carbons; when the carbon number exceeds 8 the melting points increase (Fig. 3). At the shortest chain length, the melting point is mainly governed by ionic interactions that decrease with the increase of the size of the cation: the melting point decreases when the alkyl chain length increases. However, at the longest chain length, Van der Waals interactions become prevalent, increasing the melting point. ILs are generally viscous liquids, and viscosity is mainly governed by Van der Waals interactions as well as intra or extra molecular H bonding. Higher length alkyl chain exalts these phenomena, 12 and increases the viscosity due to reduced rotation freedom of the IL. Viscosity measurements were carried out versus shear rate for the synthesized ILs under two different experimental conditions: (1) at 5 °C above melting point for each IL; (2) at 110 °C, a temperature where all ILs are liquid. The viscosity increases with the number of carbon atoms in the alkyl group (Fig. 3). Worthy of note is that the viscosity of ILs containing a low carbon number alkyl group does not vary with increasing shear rate, depicting a Newtonian behavior. On the opposite, for [DoDePy][Br] and [OcDePy][Br], increase of the shear rate causes the viscosity to decrease asymptotically, which indicates a shear thinning behavior. Moreover, except for [OcPy][Br], the increase of temperature to 110 °C leads to a significant decrease in the viscosity.

A strong influence of the temperature was observed in the case of [OcDePy][Br] (assumed to be a non-Newtonian IL), in comparison with the [OcPy][Br] (assumed to be a Newtonian IL). Arrhenius analysis allows to determine the viscosity activation energy: 37.9 kJ/mol for [OcPy][Br] (Newtonian IL) and 17.2 kJ/mol for [Oc-DePy][Br] (non-Newtonian IL) and confirms the influence of the temperature in the case of the Newtonian IL.

In order to compare the performance of stirred reactor and HEx/ MSR, the synthesis of octylpyridinium bromide was chosen as the model reaction, because of the appropriate physical properties of this IL (low viscosity and melting point, non-hygroscopic behavior). Pyridine alkylation with 1-bromooctane was achieved under equimolar conditions and mass balances were performed under various operating conditions of temperature and residence time. The efficiency of both reactors for syntheses at the multigram scale was compared in terms of conversion rate by 1 H NMR.

In the stirred reactor, the operating procedure was as follows: the flask was charged with an equimolar amount of pyridine and 1-bromooctane (0.10 ± 0.01 mol) under N 2 atmosphere, and the stirred solution was heated to a fixed temperature using a preheated oil bath. When the reaction duration was reached, the flask was cooled to room temperature and then the content was diluted in chloroform-d to be analyzed by [START_REF] Wasserscheid | Ionic Liquids in Synthesis[END_REF] H NMR. The first experiment was carried out at 60 °C for reaction durations ranging from 0.8 to 4 h. The results (Fig. 4(left)) show that the residual mole number of pyridine linearly decreases against the reaction duration. This means that the apparent reaction order of pyridine is zero, and the estimated reaction rate is constant and equal to 2.7 Â 10 À5 mol L À1 s À1 . During the reaction, the formation of IL involves the apparition of two distinct liquid phases: the lower phase comprises the IL and the upper one contains the residual reagents, which remain practically in the same concentration throughout the reaction because no mixing with the synthesized IL occurs. In order to validate these results, a second reaction was carried out at 70 °C. As expected, the decrease of residual mole number of pyridine was more important than at 60 °C. Compared to 60 °C, the conversion rate increases at least 2 times with a reaction rate of 7.9 Â 10 À5 mol L À1 s -1 , suggesting that the reaction is temperature limited under these conditions. The increase of the working temperature to 80 °C led to a significant increase in the IL rate production with a reaction rate of 1.5 Â 10 À4 mol L À1 s À1 . For higher temperatures (Fig. 4(left), curve at 100 °C), the evolution of residual mole number of pyridine versus time was not linear, indicating that the apparent reaction order of pyridine is not zero anymore. Higher temperature promotes the solubilization of pyridine within the IL, consequently the concentration of pyridine changes during the increase of the volume of synthesised IL. Conversion of pyridine reaches 90% after 4 h of reaction at this temperature. The estimated values of the apparent rate constant (k app = k[Py] 1 [Alk] 1 , alkylation follows SN2 mechanism) allow access to the real rate constant of the alkylation. Arrhenius analysis of k versus temperature led to the activation energy value of 85 kJ mol À1 , a relatively high value.

As for the reaction in stirred reactor, the conversion rates of IL obtained with HEx/MSR were determined by 1 H NMR, and results are presented versus residence time in Figure 4(right). The increase of temperature from 60 to 100 °C also involves an increase in the relative conversion rate, confirming that the reaction is temperature limited. The obtained curves (n py =f(s)) at various temperatures are not linear indicating an apparent reaction order close to zero (order = 0.1). Nevertheless, in almost all experiments, conversion rate were higher from HEx/MSR: for example at 1.3 h reaction time n p Stirred R /n p MSR = 1.04, 1.08, 1.12 for respectively 60, 70, 80 °C, showing that the HEx/MSR was significantly more efficient than the stirred one. For temperatures higher than 100 °C there are no significant differences between conversions obtained with both reactors.

The matrix of interconnected channels allows reaching a surface/volume ratio (S/V) of 24 cm 2 /cm3 , whereas for stirred reactor this ratio does not exceed 8 cm 2 /cm 3 . The high specific area of the Hex/MSR offers a better heat transfer thus maintaining a constant temperature anywhere in the reactor and consequently slightly improving conversion, as shown by the comparison of conversion rates obtained at temperatures lower than 80 °C. However at higher temperature there is competition between both reactors.

The large surface offered by Hex/MSR allows a better heat transfer that promote reaction rate more than in stirred reactor at temperatures lower than 80 °C. Nevertheless, it is important to maintain important volumetric flows in order to avoid accumulation of ILs' drops within the microchannels, which have a negative effect in heat transfer.

In conclusion, a family of alkylpyridinium bromide ILs having different alkyl chains length have been synthesized in the scale of a few ten grams and characterized by the measurement of various physico-chemical properties. Melting points and viscosities of The reaction performs better in MSR for shorter duration time and lower temperature. Last but not least, because of the better conversion/selectivity of the Hex/MSR in comparison with the batch reactor, the quantity of organic solvents required for purification of IL is strongly minimized and the process of synthesis significantly improved. [START_REF] Lévêque | For an overview of ionic liquids synthesis using non conventional activation[END_REF]

Figure 1 .

 1 Figure 1. Structure of the alkylpyridinium salts.

Figure 2 .

 2 Figure 2. Left: Schematic representation of the heat exchanger/microstructured reactor: V = 10.2 cm 3 , S/V = 24.6 cm À1 . Middle: Schematic shape of microstructured reactor. Right: the plate reactor seen from the side.

  v at mp + 5 °C (mS/cm) 10.0 (110 °C) 0.23 (40 °C) 0.22 (23 °C) 0.18 (60 °C) 0.44 (80 °C) Viscosity l (Pa s) at mp + 5 °C shear rate = 0 (b) 0.1 (110 °C) 0.2 (40 °C) 0.5 (23 °C) ca. 4 (60 °C) >5 (80 °C) Electrochemical window DE anode (VBatch reactor; (b) see Figure 3; (c) n.e.: not examined. are highly dependent on the alkyl chain length. The potential to intensify liquid phase reaction by use of a Hex/MSR has been investigated using the alkylation of the most representative model reaction (pyridine/1-bromooctane).

Table 1

 1 Selected physico-chemical properties of alkylpyridinium bromides

	R	Bu	Hex	Oct	Dodecyl	Octadecyl
	Yield (%) (a)	80	87	79	67	77
	Mp (°C)	105	36	18	56	74
	Water content (%)	1	1.6	1.7	1.3	1.2
	Density (g/cm 3 )	1.26	1.18	1.11	1.06	0.93

Conductivity v at 110 °C (mS/cm) 10.0 n.e.

Left: Melting points of alkylpyridinium ILs against alkyl chain length; experimental uncertainty of ±2 °C. Right: Viscosity (measured at ILs melting point + 5 °C) dependency vs shear rate for various alkylpyridinium IL.

Acknowledgments

The authors thank the Région Midi-Pyrénées for financial support, and the Solvionic Company for its contribution.

Supplementary data

Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.tetlet.2012.04.119.