Jawhar Chebbi
email: jawhar.chebbi@isae-supaero.fr

François Defaÿ
email: francois.defay@iut-tarbes.fr

Yves Brière
email: yves.briere@isae-supaero.fr

Alban Deruaz-Pepin
email: alban.deruaz-pepin@donecle.com

Novel Model-Based Control Mixing Strategy for a Coaxial Push-Pull Multirotor

Keywords: Aerial systems, mechanics and control, calibration and identification, force control

A Coaxial push-pull multirotor is a Vertical Take-Off and Landing (VTOL) Unmanned Aerial Vehicle (UAV) having 2n (n ∈ IN * ) rotors arranged in n blocks of two coaxial contrarotating rotors. A model-based control allocation algorithm (mixer) for this architecture is proposed. The novelty of the approach lies in the fact that the coaxial aerodynamic interference occurring between the pairs of superimposed rotors is not neglected but rather nonlinear empiric models of the coaxial aerodynamic thrust and torque are used to build the mixer. Real flight experiments were conducted and the new approach showed promising results.

I. INTRODUCTION

U NDERACTUATED multirotors are the most widely used Vertical Take-Off and Landing (VTOL) Unmanned Aerial Vehicles (UAV) both for research and industrial applications due to their easy integration and high versatility. The quadcopter is the precursor of these UAVs and remains the most popular one. However, in order to meet increasing safety and payload requirements, new multirotor configurations with more than four motors have been tested and used over the recent years (like hexarotors [START_REF] Pathak | Design and development of hexa-copter for environmental research[END_REF], [START_REF] Suprapto | Design and development of heavy-lift hexacopter for heavy payload[END_REF] and octorotors [START_REF] Saied | Model identification and validation for translational movements of an octorotor UAV[END_REF]- [START_REF] Adîr | Modelling and control of a star-shaped octorotor[END_REF]). One interesting property of underactuated multirotors is that regardless of the number and disposition of the motors, they can be controlled in the same way, using four control inputs corresponding to the total thrust force and to three torques around the three body axes, as long as these control efforts are dispatched to the motors according to the rotors configuration. The algorithm in charge of this allocation is commonly called mixer.

The present paper introduces a model-based mixing strategy applied to a push-pull octorotor, also called X8. The number of rotors is not important for this study, the same approach could be used for any push-pull multirotor. Designing an adapted mixer for this kind of configuration is more challenging than for a normal plane one, if the aerodynamic interaction between each pair of coaxial rotors is taken into account. The relevance of the proposed mixer is discussed by comparing the flight performances to the case of a conventional model-based mixer assuming isolated rotors.

The main contributions of the present paper are first the incorporation of a knowledge about the interference between the rotors' airflows into the control allocation problem, and secondly the use of a nonlinear coaxial rotor torque model to solve the mixing problem instead of a simplified torque to thrust model. In the sequel, the key steps taken to implement the algorithm are presented, from the acquisition of experimental data to simulation and real flight tests. The approach is tested on a coaxial octorotor.

II. OVERVIEW OF THE MIXING STRATEGY

The idea behind mixing is to make the resultant torques and force applied by the rotors on the UAV body as close as possible to the requested control signals. To do so, it is essential to know the motors input/output behaviour, hence the name given to this approach: model-based.

The following symbols and notations are used: r u ∈ IR 4 is the vector of the actual (unknown) resultant torques and thrust force applied on the UAV body by the motors.

r u * ∈ IR
r P is a virtual function describing the transformation, by the motors, of the throttle commands to thrust forces, P is a model of this function (see IV-A1) and

P † is its pseudo- inverse.
r M is a virtual function describing the transformation of the thrust forces to resultant torques and force on the UAV Using this notation, the mixing algorithm goal is to achieve u = u * . Having u = M (P ( P † ( M † (u * )))), the previous equality constraint means that the composition of the inverse mappings with the real system behaviour functions must be equal to identity.

The model P is identified experimentally and inverted numerically. As for the model M , it is deduced from the motors disposition and symmetries and inverted analytically as explained in the next section.

III. RELATED WORK

Most of the literature on control allocation techniques for multirotor UAVs is focused on motor failure recovery and saturation handling and not on the main model inversion problem (see for instance [START_REF] Liu | Composite robust Hinfty control for uncertain stochastic nonlinear systems with state delay via disturbance observer[END_REF]- [START_REF] Nguyen | Fault-tolerant control of a hexacopter UAV based on self-scheduled control allocation[END_REF]). This is due to the fact that isolated rotors are assumed in most of the cases, making the model inversion straightforward. However this assumption becomes limiting for some configurations where aerodynamic interference between rotors is quite strong like the coaxial case, as in the case of [START_REF] Amin | Finite time position and heading tracking control of coaxial octorotor based on extended inverse multiquadratic radial basis function network and external disturbance observer[END_REF] where the control allocation for the octorotor is performed without taking into account the coaxial interaction which is considered as part of unmodelled dynamics. These are estimated using an extended inverse multi-quadratic radial basis function neural network that needs to be trained offline. There are similarly different control techniques to compensate for unmodelled aerodynamic disturbances like extended state observers or external wrench estimators (see for instance [START_REF] Ruggiero | Passivity-based control of VToL UAVs with a momentum-based estimator of external wrench and unmodeled dynamics[END_REF]). However, unlike adapting the mixer, these methods will account for a lumped disturbance term containing external efforts and modelling uncertainties along with aerodynamic effects. So they should be more efficient when used with a mixer similar to the one proposed in the present work because by doing so, the effects due to rotors' interference are removed (or at least reduced) in feedforward, making the disturbance estimation and rejection easier.

The coaxial propulsion configuration has several advantages such as: the maximisation of available rotor disk surface while keeping a compact UAV body size, the ability to recover motor failures due to hardware redundancy, the enhanced yaw stability given by the disposition of the coaxial contra-rotating rotors which reduces gyroscopic torques on the UAV body and the minimisation of rotor swirl losses for the same reason. With these assets come some complications, mainly the aerodynamic interaction occurring at each pair of coaxial rotors.

This overlapping effect has been identified and studied by aerodynamicists. Leishman [START_REF] Leishman | Principles of Helicopter Aerodynamics[END_REF] for instance models this effect using the simple momentum theory in a particular case where the separation distance equals to the diameter of the rotor, and concludes that this configuration consumes 28% more power than the isolated case. This power efficiency loss is greater when the separation distance is smaller (which is the case for most multirotor UAVs). More recent experimental studies were also performed as in [START_REF] Prothin | A vectoring thrust coaxial rotor for micro air vehicle: Modeling, design and analysis[END_REF] where the thrust (f u and f l ) and torque (Q u and Q l ) produced by each rotor were modelled as secondorder polynomials of both rotor speeds which extends the usual 1D quadratic model used for a single isolated rotor. A similar approach was also used in [START_REF] Koehl | Aerodynamic modelling and experimental identification of a coaxial-rotor UAV[END_REF] where a static coaxial thrust map was built. However the coaxial effect was only modelled by adding a multiplicative loss coefficient to the sum of the thrusts of both isolated rotors. The same approach was followed for the modelling of a coaxial octorotor in [START_REF] Saied | Model identification and validation for translational movements of an octorotor UAV[END_REF]. A different model for a coaxial propulsion unit was used in [START_REF] Gasior | Thrust estimation by fuzzy modeling of coaxial propulsion unit for multirotor UAVs[END_REF] based on Takagi-Sugeno fuzzy interface and surface fitting. However in all of these studies there is no explicit mention of the control allocation problem and it is not clear whether the coaxial models were used for the mixer or not.

The same issue has also been recently raised by new studies on novel omni-directional UAVs where the disposition of rotors makes their aerodynamics mutually influenceable. In [START_REF] Brescianini | An omni-directional multirotor vehicle[END_REF] the aerodynamic interference between the propellers of the eight rotor omnicopter was not taken into account for the mixing problem. Rather, thrust and torque decrease coefficients were identified experimentally and applied to the motor speeds to compensate for all of the aerodynamic effects. More recently, the same problem was addressed in a more direct way in [START_REF] Dyer | Energy optimal control allocation in a redundantly actuated omnidirectional UAV[END_REF] where a static actuator inverse model that accounts for the interactions between rotors is used for the mixer. It is built by varying the constant parameters of a physical thrust-to-PWM model initially built for one isolated rotor. In the present work, the same thing is done for a coaxial propulsion unit but using a different approach based on numerical inversion of 2D static maps. The obtained mixer is then compared to a non-coaxial one in order to assess the relevance of considering the overlapping effect.

IV. APPLICATION TO THE X8 CONFIGURATION

The used X8 UAV is depicted in Fig. 7(b).

A. Modelling

Step 1) Model P : The actuators of most modern common multirotors consist of fixed-pitch propellers attached to brushless electrical motors driven by Electronic Speed Controllers (ESC). The ESCs monitor the motors' angular rates based on the percentage of throttle δ requested by the pilot (human or automatic).

In this study, the considered propulsion unit is a pair of coaxial contra-rotating rotors. This leads to models with two inputs. To identify the models, the coaxial test bench shown in Fig. 2 was used. This test bench allows to control the two motors independently in hovering-like conditions. It consists of two RCBenchmark thrust-stands equipped with optical speed sensors, load cells and electronic boards to connect the ESCs and the USB data acquisition ports. The available measurements include the electrical currents, the propellers angular rates and the generated thrusts and torques. The distance between both stands is adjustable and was set to 6.14 cm as the UAV used for the experiments. The software used to acquire data and to control simultaneously both motors was developed in MATLAB.

The recorded angular rates, thrusts and torques are used to build maps relating any individual output to both PWM inputs. Individual measurements are added up to obtain total coaxial thrust and torque values. It is worth mentioning that the rotor aerodynamics suggest that the thrust and torque models depend directly on the rotor angular rates. But in our case the ESCs are not equipped with speed measurements, so this information is not accessible on-board. Besides, it is established that the conversion of PWM to angular rate by the ESC is close to a linear mapping [START_REF] Cunningham | System identification of a multi-rotor UAV actuator[END_REF], for a fixed battery voltage. So it makes sense to relate the thrust and torque directly to the PWM values (or equivalently to the throttle inputs). The chosen model structure is inspired from [START_REF] Prothin | A vectoring thrust coaxial rotor for micro air vehicle: Modeling, design and analysis[END_REF] where second-order two-dimensional polynomials are used. The difference is, that in this work, all of the polynomial coefficients were kept as degrees of freedom and not only the homogeneous part, allowing richer models and better data fit. Therefore, the considered total thrust and torque empirical models are as follows

f = δ 2 u δ 2 l δ 2 u δ l δ 2 u δ u δ 2 l δ u δ l δ u δ 2 l δ l ⎡ ⎢ ⎢ ⎣ a 1 . . . a 8 ⎤ ⎥ ⎥ ⎦ (1a) Q = δ 2 u δ 2 l δ 2 u δ l δ 2 u δ u δ 2 l δ u δ l δ u δ 2 l δ l ⎡ ⎢ ⎢ ⎣ b 1 . . . b 8 ⎤ ⎥ ⎥ ⎦ (1b)
where the index u refers to the upper motor and the index l to the lower one.

Polynomial equations 1 could be written in the following compact form

y = A.θ (2)
where θ ∈ IR 8 is the vector of parameters to estimate, y ∈ IR N (N ∈ IN * ) is the vector of all measured torque or thrust data and A ∈ IR N × IR 8 is the regressors matrix. The least-squares solution is chosen, which corresponds to

θ = A T A -1 A T .y. ( 3
)
The result of this second order polynomial fit (Table I) is good as seen in Fig. 3.

2) Model M : Let the actuation vector u be written as u = [τ p τ q τ r T ] T . The thrust and aerodynamic torque produced by the i th coaxial unit of rotors (i ∈ {1, .., 4}) are noted f i and Q i respectively. The lever arm l is also introduced. One can then write the following equations.

⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ τ p = l (-f 1 + f 2 + f 3 -f 4 ) τ q = l (f 1 + f 2 -f 3 -f 4 ) τ r = Q 1 -Q 2 + Q 3 -Q 4 T = f 1 + f 2 + f 3 + f 4 . ( 4
)
Note that those are the same equations for a quadrotor UAV, which is expected because the four pairs of coaxial rotors are considered as a single unit each.

The difference however, is that in the case of a quadrotor mixer, the torques need to be linked to the thrust in order to be able to invert the problem. But in the octorotor case, there are more degrees of freedom allowing to achieve independently torque and force commands as will be shown in Section IV-B2. This is one of the highlights of the proposed strategy which brings in theory more torque and hence yaw stability and efficiency.

Equation 4 can be written in the following compact linear form

u = M f Q . ( 5
)

B. Inverting

Step 1) Inversion of M : This step could be interpreted as a constrained quadratic programming optimisation problem

η * = arg min η T η u * = M η * ( 6
)
where η = [ f Q ] is the effort (force and thrust) vector produced by all four pairs of coaxial rotors.

Note: In reality there are additional inequality constraints related to the motors' saturation limits. But the problem is solved by considering the nominal case and when saturation occurs a "desaturation" routine inspired by the algorithm used in PX4 Pixhawk * Software leads to a reduction in the requested total thrust or torque by the needed amount to prevent saturation. This algorithm was adapted for the presented model-based mixer.

The solution to equation 6 could then be given by the Moore pseudo-inverse, which is commonly used for multirotor mixers *DOI https://zenodo.org/record/3228694

TABLE I COAXIAL THRUST AND TORQUE MODELS PARAMETERS

where n > 4 (see for instance [START_REF] Marks | Control allocation for fault tolerant control of a VTOL octorotor[END_REF], [START_REF] Bouzid | Guidance and control systems for autonomous aerial vehicles navigation[END_REF]- [START_REF] Kotarski | Mathematical modelling and dynamics analysis of flat multirotor configurations 2 multirotor UAV dynamic model[END_REF] and [START_REF] Wang | An adaptive fault-tolerant sliding mode control allocation scheme for multirotor helicopter subject to simultaneous actuator faults[END_REF]).

η * = M T M M T -1 u * (7) = M † u * . ( 8
)
2) Inversion of P : The final step is to find the throttle input commands corresponding to any desired effort vector η * (corresponding to any desired control vector u * ). To do so, the two-dimensional quadratic maps built previously need to be inverted. Note that if the rotors are assumed to be isolated, this inversion taking requested force and torque commands as inputs, is not possible, because for one throttle level, one isolated rotor produces only one possible pair of torque and thrust. That is why in this case, a different torque model is used assuming that for an isolated rotor the steady aerodynamic torque is roughly proportional to the thrust with a constant ratio that depends on blade geometry [START_REF] Leishman | Principles of Helicopter Aerodynamics[END_REF]. With this assumption, the only remaining variable is the thrust and the inversion is then straightforward. In fact, the thrust would be proportional to the squared angular rate [START_REF] Whitehead | Model reference adaptive Control of a quadrotor UAV[END_REF], so the square root is simply taken and finally the mapping from the angular rate to throttle input is linear.

In the considered coaxial two-dimensional case, no torqueto-thrust proportionality is assumed but the additional degree of freedom is used to find the pair of throttle values that give the requested coaxial thrust and torque. This is the main novelty of the present approach. It is not easy to obtain an analytic solution to this coupled problem, so a numerical one was built using MATLAB.

The idea of the algorithm is to first represent the thrust and torque polynomial models in Fig. 3 as planar colour maps an in Fig. 4. Using this data representation, a desired thrust (torque) value corresponds to an iso-curve on the colour map Fig. 4(a) (Fig. 4(b)). So to any thrust-torque pair correspond two curves of pixels on two images. Two masks are then built by setting the pixels on the iso-curve to 1 and the rest of the image to 0. The intersection point, if it exists, is then the pixel having a value equal to 2 on the mask resulting from the sum of both images. The coordinates of the intersection point is the required PWM pair to achieve the requested thrust and torque. This process is made easier thanks to the matrix computation capabilities of MATLAB.

Inverted thrust and torque to throttle maps of an upper bound precision equal to 0.1 N on the thrust and equal to 9.10 -4 Nm on the torque were built, they are shown in Fig. 5. These maps show, among other things, that there is a zone of achievable thrust-torque pairs by the coaxial propulsion unit, meaning that the available range of torque varies with the thrust level. This brings a better physical insight to the mixing problem. In order to 3. Coaxial thrust and torque model maps (red) vs raw data (green). implement these inverted mappings, they were approximated by high order polynomial interpolation functions of two variables.

Note: The voltage effect was also taken into account by multiplying the thrust and torque maps using an experimentally identified voltage correction coefficient that varies with the measured battery voltage on-board.

V. PERFORMANCE COMPARISON WITH A CONVENTIONAL APPROACH

The presented coaxial mixer is compared to a simple one built assuming isolated rotors. The inverted model in this case P † is a simple 1D quadratic mapping transforming a thrust set-point to its corresponding throttle level. As for M † , it is built after relating each rotor torque to the corresponding thrust:

Q i = κ t f i , ∀i ∈ {1..8}.
It should be noted that this torque model not only does not capture the coaxial effect, but is also oversimplistic even for an isolated rotor. In fact, as noted in [START_REF] Faessler | Thrust mixing, saturation, and body-rate control for accurate aggressive quadrotor flight[END_REF], making κ t dependent on the thrust gives more accurate results but it leads to an iterative mixer. In the present work, it is possible to easily avoid such iterative solutions while using the full torque nonlinear model by taking advantage of the additional degree of freedom provided by the coaxial configuration.

A. Static Simulation Tests

The main advantage of the new coaxial mixer is the way the yaw control is processed. To visualise it, let us consider the case of a thrust command of 40 N (so 10 N per coaxial unit) and several samples of torque commands varying within the maximal available torque range. The (thrust, torque) points in the admissible operating zone are drawn for each of the four coaxial propulsion units in Fig. 6 considering both mixers. It is clear that the coaxial mixer keeps the thrust constant on each propulsion unit while achieving the requested torque, whereas the simple mixer leads to varying thrust levels on the coaxial mixers because the performance degradation of the lower rotor is not taken into account. Another advantage coming from the additional degree of freedom of torque, is that for zero yaw commands, there are in theory no residual torques on the four propulsion units.

It should be noted that even with the coaxial mixer the single thrust levels on the rotors cannot be kept constant under non zero yaw commands because the speeds of motors need to be changed anyway. However having the four pairs of superimposed rotors produce the same thrust should lead to a smoother yaw behaviour and to less mechanical stress on the multirotor arms. It is like having a quadrotor perform yaw manoeuvres without changing the thrust on the opposed rotors.

B. Real Flight Tests

Real flight tests were performed at the ISAE-SUPAERO robotics room equipped with the motion capture system Optitrack. The UAV is a square-shaped X8 with a diameter equal to 0.9 m, it weighs 3.2 kg and has for principal rotational inertia moments I x = 0.0797 kg.m 2 , I y = 0.0874 kg.m 2 and I z = 0.1604 kg.m 2 (see Fig. 7). The UAV controller and mixer were implemented on a Dropix PX4 board. A NVIDIA TX1 board was additionally used to ensure a stable UDP connection with the motion capture system and the ground station software. It communicates with the PX4 board through a serial link. The controller runs at a sampling time of 5 ms and the Optitrack measurement delay is about 50 ms.

The conducted experiment consisted of two hovering flights (one with the simple mixer and the other with the coaxial one) at constant x and y, disturbed with the same manoeuvres on altitude z and yaw, the trajectories are shown in Fig. 8 and Fig. 9. This flight allows to analyse the decoupling performance of the controller in the horizontal plane (x and y axes) while moving along the other degrees of freedom (z and yaw). Baseline position and attitude PID controllers were tuned to guarantee stability and achieve a reasonable trajectory tracking. The sole difference between the two experiments is the mixer algorithm: exactly the same control structure and parameter values were used in both cases in order to be able to isolate the control allocation effect. The results are discussed below.

The main difference between the two mixers is depicted in Fig. 10. The thrust control signal, i.e. the signal sent to the mixer to generate the PWMs based on the inverted rotors model, obtained when the coaxial mixer is used (Fig. 10(b)) is much closer to the hovering equilibrium thrust (the UAV weight). One can see that in contrast, using the simple mixer results in an over-estimation of the needed total thrust (Fig. 10(a)) because the actual equilibrium throttle, reached thanks to the altitude closed loop control, would lead to higher thrust when no coaxial loss is considered. In fact, if the rotors were isolated, the equilibrium would have been achieved for a much lower throttle level because the rotors would be more efficient.

Although the coaxial case leads to a better estimation of the total thrust than the simple mixer, it is still under-estimated as seen in Fig. 10(b). This slowly varying offset of about 2 N cannot be explained by the voltage drop because a compensation is added to adjust the coaxial models when the battery voltage changes. However, it could be due to modelling inaccuracies since those can reach 1.242 N in the worst case (based on thrust residual value in Table I). Additionally, the presence of aerodynamic effects induced in the rather small flying area can cause a change of the rotors aerodynamic performance, for instance the ground effect. This effect increases the lift of the rotors [START_REF] Leishman | Principles of Helicopter Aerodynamics[END_REF] and as a result decreases the power needed to be produced by the motors. This could be the reason why the coaxial thrust control gets slightly higher and approaches more the weight of the UAV as it flies higher (Fig. 10(b)).

Furthermore, analysing the position tracking performances in both cases (Fig. 8) shows that using the coaxial mixer leads to a better precision (see Table II, where z is considered during the 1.5 m phase). This means that by adapting the mixer architecture to the UAV, and without any modification of the control parameters, it is possible to reduce the coupling effects between yaw and the other degrees of freedom. The same tendency was verified on other flights.

No significant yaw tracking amelioration was noticed in the coaxial case. This could be due to the fact that the yaw rate was limited in the considered experiments. Yaw control performance could be further investigated by applying more aggressive manoeuvres.

VI. CONCLUSION

A new mixer algorithm adapted to any push-pull multirotor aerial vehicle has been presented. The main highlight of the proposed strategy is that it does not neglect the aerodynamic interaction between the coaxial rotors.

The actuators models identification was described and the obtained models were used in the mixing problem which is defined as a two-step two-dimensional inversion problem. The first inversion step is a well known pseudo-inversion of the control allocation matrix, and the second step is done numerically. This new strategy was successfully tested on a real UAV. It resulted in a better on-line estimation of the total thrust and less coupling between the multirotor axes compared to a conventional model-based mixer.

  r f * and Q * ∈ IR n are the vectors of the desired thrust forces and torques on the n coaxial pairs of rotors. r δ ∈ IR 2n is the vector of the throttle signals sent to the motors speed controllers, so ∀i ∈ {1..2n}, 0 δ i 1.r f and Q ∈ IR n are the vectors of the actual (unknown) thrust forces and torques produced by the n coaxial pairs of rotors.

Fig. 1 .

 1 Fig. 1. Block diagram of the data flow from the control outputs u * to the actual efforts applied on the UAV body u.

Fig. 2 .

 2 Fig. 2. Coaxial test bench at DCAS (Department of Aerospace Vehicles Design and Control, ISAE-SUPAERO).

Fig. 4 .

 4 Fig. 4. Coaxial thrust and torque colour maps.

Fig. 5 .

 5 Fig. 5. Coaxial inverted model colour maps.

Fig. 6 .

 6 Fig. 6. Mixers' handling of yaw commands.

Fig. 7 .

 7 Fig. 7. The coaxial octorotor used for the experiments.

Fig. 8 .

 8 Fig. 8. Position Trajectory Tracking: Reference (Red) vs Measured (Blue).

Fig. 9 .

 9 Fig. 9. Yaw Profile Tracking: Reference (red) vs Measured (blue).

Fig. 10 .

 10 Fig. 10. Thrust force command (blue) compared to the UAV weight (black) -Upper figures show the corresponding flight altitude phase.

TABLE II POSITION

 II TRACKING (x,y,z): MEAN SQUARED ERROR (MSE), MEAN ABSOLUTE ERROR (MAE) AND MAXIMUM ABSOLUTE ERROR (MaxAE)

supported by the company Donecle (https://www.donecle.com/) and the lab ISAE-SUPAERO (https://www.isae-supaero.fr/en/research/isaesupaero-research/). This letter was recommended for publication by Associate Editor V. Lippiello and Editor J. Roberts upon evaluation of the reviewers' comments.


Quang Nguyen

Ferenc Martinovic

Monica Ceretti

Serena Esposito

Barbara Bonelli

Werner Paulus

Francesco Di Renzo

Fabio A Deorsola

Samir Bensaid

Raffaele Pirone

Samir Bensaida

Co-doped LaAlO3 perovskite oxide for NOx-assisted soot oxidation

Keywords: Soot, Oxidation, NOx-assistance, Perovskite, NOx storage, Oxygen mobility

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

Introduction

Perovskite oxides have general formula ABO3, where the 12-fold cubo-octahedral A site is usually occupied by alkaline earth/alkaline or larger cations and the octahedral B-site by smaller cations [1]. The ideal structure of perovskite is cubic with tolerance factor t (so-called Goldschmidt factor) of 1 (t = (𝑟𝑟 𝐴𝐴 + 𝑟𝑟 𝑂𝑂 )/�2(r 𝐵𝐵 + r 𝑂𝑂 )), where rA, rB and rO are ionic radii of A, B, and oxygen, respectively) [2]. A t parameter between 0.75 and 1 is necessary to form perovskite structures, with decreasing symmetry for t < 1 [1]. Thanks to the wide range of metals able to adapt in the perovskite structures (about 90 % of metallic elements in the periodic table), the physicochemical properties of perovskite oxides can be finely tuned and they find enormous applications in catalysis for, e. g., steam reforming of toluene [3][4][5], ethanol [6,7], CH4 [8][9][10] and bioglycerol [11]; valorization of bio-oil [12][13][14][15], biomass [16] and HMF [17], lignin partial oxidation [18,19] and environmental treatments [20][21][22][23][24]. Particulate matter (PM), which is normally referred as soot (although the latter strictly refers only to its carbonaceous fraction), is a noxious emission of diesel engines, which find enormous applications thanks to their high energy efficiency in fuel consumption [25]. PMs can cause a number of respiratory diseases [26] and deactivation of post-treatment's catalysts for the NOx (NO and NO2) reduction processes [27]. Thus, the control of PM's emission is necessary for diesel engine future developments. Generally, there are two steps of PM's treatment: filtration and regeneration [28]. Filtration consists of capturing soot in a Diesel Particulate Filter (DPF), followed by the regeneration which refers to the combustion of soot at relatively high temperature (around 600 °C [29]) to avoid backpressure across the filter [25]. Alternatively, the Continuously Regenerating Trap (CRT) is able to continuously oxidize soot at lower temperature by using NO2 as a stronger oxidant instead of O2 [30,31]. On the other hand, NOx gases, which are also included in diesel exhaust in extremely small quantity, are highly toxic pollutants. NOx elimination is a technical problem because of mandatory requirements to add extra elements to aftertreatment systems, leading to an increase in overall cost of vehicles. A conventional diesel aftertreatment system combines both oxidation catalysts to oxidize trace substances (unburnt hydrocarbon, soot, CO, NO) and a consecutive NOx reduction catalyst. Many efforts have been made to reduce NOx in lean-rich exhaust cycles such as using lean NOx trap (LNT) or NOx storage/reduction (NSR) catalysts. An alternative way is to employ Selective Catalytic Reduction (SCR) by using extra reductants such as NH3 from injected urea solution [32]. These treatments are only productive in case of a large proportion of NO2 present in the exhaust gases [25,33,[START_REF] Majewski | Diesel Emiss. Their Control[END_REF]. Therefore, finding catalysts for soot combustion at low temperature while maintaining a high proportion of NO2 for further reduction processes is highly desirable. NOx-assisted soot oxidation is a simultaneous approach which involves NO to NO2 conversion and subsequent soot oxidation by the formed NO2 from the gas phase, at relatively low temperature [28]. Many works have investigated this reaction using noble metal catalysts, which are able to reduce the ignition temperature of soot oxidation (T10% -temperature when 10% of soot is combusted) down to 370 °C, depending on the operating conditions [28,[START_REF] Andana | [END_REF][36][37][38]. However, no high NO2 yields of the soot oxidation reaction have been reported whereas a high proportion of NO2 is beneficial for further NOx elimination processes (for instance, NH3-SCR). Obviously, the applications of noble metals are limited by their prohibitively expensive cost and strategic limitations of availability. Recently, Kim et al. suggested that perovskite La0.9Sr0.1CoO3 can be reasonably priced alternative since it can oxidize about 86% of NO at lower temperature (300 °C) than noble metal rival Pt/Al2O3 [39]. The study has been followed by other works on doped perovskites for low temperature soot oxidation such as LaMn0.9Co0.1O3 [40], BaMn0.7Cu0.3O3 [41], La0.9ACoO3 (A=Na, K and Rb) [23], La1-xBxO3 (B=Ce and Sr) [27] and BaCoO3-λ [42], focusing on the substitution of A-or B-sites to promote redox properties of perovskite oxides by generating either defective structure or multiple oxidation state cations. Furthermore, modified LaCoO3 is generally accepted as a highly active catalyst for NO oxidation [20,43,44], whereas Al2O3 supported oxides are reportedly able to catalyze NOx-assisted soot oxidation at relatively low temperature [45]. The combination of Al and Co in La-based perovskite oxides may be a promising approach for the NOx-assisted soot oxidation at low temperature. The present work investigates Co-doped LaAlO3 perovskite oxides for soot oxidation in the presence of NOx gases to correlate the catalytic activity with crystallinity, redox properties and the role of lattice oxygen.

Experimental section 2.1. Catalyst preparation

LaAl1-xCoxO3 were prepared by the sol-gel method with citric acid. La(NO3)3•6H2O (Sigma-Aldrich,99%), Al(NO3)3•9H2O (Sigma-Aldrich, 99%), Co(NO3)2•6H2O (Sigma-Aldrich,99%) were used as metal precursors and citric acid C6H8O7•H2O as a gel-forming agent. Stoichiometric amounts of nitrate salts were dissolved in deionized water. A suitable amount of citric acid (citric acid:metal =2 mol/mol) was added to the solution where the pH was kept at 7.5 ± 0.5 by dropwise addition of ammonia. The solution was stirred and evaporated at 80 °C until the gel was formed. The gel was then kept at 150 °C for 3 h and at calcination temperature (500, 600 and 700 °C) for 5 h with rampup of 5 °C min -1 .

Catalyst characterization

The BET surface area was determined by N2 adsorption at -196 °C using a Micrometrics Tristar instrument with improved vacuum system. Samples were previously degassed at 250 °C until stable 10 Pa pressure was reached. XRD diffractograms were recorded using Cu Kα (λ=0.15418 nm) radiation in a Bruker D8-Advance device. The reducibility of perovskite oxides was studied by H2-temperature programmed reduction (H2-TPR) using ThermoQuest TPDRO 1100 equipment equipped with TCD detector. The quartz tube reactor was loaded with about 50 mg of sample and pretreated with 10 mL min -1 N2 at 500 °C for 30 min and then cooled down to 50 °C. Samples were then heated from room temperature to 950 °C with 5 °C min -1 heating rate under 20 mL min -1 5% H2/Ar. O2-Temperature Programmed Desorption (O2-TPD) was conducted in the same instrument. The samples were previously treated under pure O2 flow (40 mL min -1 ) at 600 °C for 30 min before cooling down to ambient temperature under O2 flow. The desorption was performed from room temperature to 950 °C under He flow (20 mL min -1 ) with heating rate of 5 °C min -1 . The NOx-TPD experiments were conducted in a flow-gas reactor system equipped with ABB Limas and Uras UV and NDIR analyzers to detect NO, NO2, N2O, CO, and CO2 gases separately. Catalysts were placed at the middle position of a 10mm i.d. tubular reactor with thermocouple inserted into the catalytic bed to measure the reaction temperature. In a typical experiment, 200 mg of sample was used. For the NOx desorption tests, NOx (250 ppm NO; 250 ppm NO2, balance N2; total flow 300 mL min -1 ) was adsorbed at 250 °C until stable concentration of NOx and cooled down to room temperature under N2 flow. The sample was then heated under N2 flow (300 mL min -1 ) from room temperature to about 600 °C at 5 °C min -1 . The XPS experiments were done as reported elsewhere [46]. Briefly, XPS analysis was carried out on an XPS PHI 5000 Versa probe apparatus, using the band-pass energy of 187.85 eV, a 45° take off angle and a 100.0 μm diameter X-ray spot size for survey spectra. High-resolution XP spectra were recorded in the following conditions: pass energy of 23.5 eV, resolution of 0.1 eV, and a step of 0.2 eV. Sample charging effects were eliminated by referring to the spectral line shift of the C 1s binding energy (BE) value at 284.5 eV.

Activity tests

The NO oxidation tests were conducted in isothermal mode in the same system for NOx-TPD experiments mentioned above. The feed gas contained 650 ppm NO and 5% O2 in N2 (total flow 254 mL min -1 ) and 200 mg of catalyst was used. The temperature range for the oxidation was 150-400 °C. At each temperature, the stabilization time was about 20-30 min for reaching the steady state reaction in order to avoid the adsorption/desorption effect of NOx on catalysts. NO oxidation was also performed in the temperature ramping mode, in this case the reaction conditions matched those of the NOx-assisted soot oxidation: the feed gas contained 500 ppm NO and 4% O2 in N2 with total flow 600 mL min -1 and 200 mg of catalyst with ramping rate 5 °C min -1 . Besides the LaAl1-xCoxO3 catalysts Pt/Al2O3 with 5% Pt loading (Sigma-Aldrich 205974) was used as commercial reference. The activity of the catalysts in NOx-assisted soot oxidation tests was determined by Temperature Programmed Reaction (TPR) with heating rate of 5 °C min -1 . The soot oxidation was studied by mixing 20 mg of soot (Printex U, a carbon black used as model soot) with 180 mg of catalyst or SiC for the reference non-catalytic test (catalyst:soot=9:1) in loose contact. Feed gas contained 500 ppm of NO and 4% oxygen in a flow of N2 as balance gas, the total flow being 600 mL min -1 . The tests were conducted between 200 °C and 700 °C with a ramp of 5 °C min-1. The soot conversion and CO2 selectivity were calculated as followed:

Soot conversion (%) = ∑ (𝑐𝑐𝑜𝑜 2 +𝑐𝑐𝑜𝑜 𝑡𝑡 0 ) (𝑐𝑐𝑜𝑜 2 +𝑐𝑐𝑜𝑜) 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 100 CO2 selectivity (%) = ∑ (𝑐𝑐𝑜𝑜 2 𝑡𝑡 0 ) (𝑐𝑐𝑜𝑜 2 +𝑐𝑐𝑜𝑜) 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 100
3. Results and discussion 3.1. Characterization 3.1.1. Structural properties X-ray diffraction patterns of all catalysts LaAl1-xCoxO3 (x=0, 0.25, 0.5, 0.75 and 1) calcined at 700 °C are shown in Fig. 1. All catalysts exhibit a well-crystallized perovskite phase, which is the only phase present from x=0 to 0.5 and is accompanied in LaAl0.25Co0.75O3 and LaCoO3 by two minor peaks at 2θ of about 36.7 and 28.1°, which belong respectively to Co3O4 and La2O3. The perovskite phase presents symmetric diffraction peaks in the case of LaAlO3, whereas peak splitting is observed with increasing cobalt. Rietveld analysis has been conducted on all catalysts calcined at 700 °C to understand the lowering of symmetry with Co-doping. The refinement was done with the Thompson-Cox-Hastings pseudo-Voigt peak profile and two space groups: rhombohedral R-3c and cubic Pm-3 m. The refinement data, reported in Table 1, confirm the change of perovskite symmetry with the composition, LaAlO3 being cubic and all other samples being rhombohedral. Interestingly, all samples would be expected presenting R-3c space group at room temperature [47]. Rhombohedral perovskite normally evolves towards cubic structure when the octahedral tilting is reduced at higher temperature. LaAlO3 is normally rhombohedral at room temperature, reaching space group Pm-3m at nearly 530 °C [47,48]. The presence of cubic phase at room temperature is probably due to a metastability effect. Substituted LaAl perovskites remain rhombohedral also at very high temperature and, in the case of LaCoO3, the rhombohedral structure is also stable above 970 °C [48,49]. In the case of solid solutions intermediate between LaAlO3 and LaCoO3, Aswin et al. observed that the rhombohedral phase was accompanied by a secondary monoclinic perovskite phase [50]. No monoclinic phase was observed in our samples. It is tempting to assume that the presence of such a phase is a secondary result of sintering at 1030 °C in the preparation of Aswin et al.

The volume of the formula units LaAl1-xCoxO3 calculated from the cell parameters, taking into account Z=1 for Pm-3m and Z=6 for R-3c space groups, are reported in Table 1 and highlighted in Fig. 2a. They show a systematic increase of volume from LaAlO3 to LaCoO3 once the R-3c symmetry is established, indicating that Co is well incorporated inside the perovskite framework. In fact, trivalent Co is larger than Al3+ [51], so the substitution of Al by Co tends to expand the unit cell. Table 1.

Refinement parameters of LaAl1-xCoxO3 calcined at 700 °C. The effect of calcination temperature on the formation of the perovskite phase is highlighted in Fig. 2b, in which the diffraction patterns of LaAl0.25Co0.75O3 calcined at 500, 600 and 700 °C are shown. The diffraction pattern at 500 °C present no perovskite peaks but exhibits broad bands of Co3O4 and La2O3 phases. Evaluation of the peaks of these phases by the Scherrer method suggests sizes of 27 nm for Co3O4 and 2.6 nm for La2O3, a signature of nano-crystalline form for this last phase. At 600 °C, the perovskite structure emerges beside traces of La2O3 phase, better crystallized than at 500 °C. La2O3 disappears altogether at a calcination temperature of 700 °C, leaving perovskite as the only crystalline phase.

The textural properties of LaAl1-xCoxO3 calcined at 700 °C are listed in Table 2. The average crystallite size of LaAl1-xCoxO3 is calculated from the Rietveld refinement by the Williamson-Hall method. Crystallite size dc slightly varies around 30 nm for x=0 to 0.75, before jumping up for the total introduction of cobalt. The surface areas of all samples, measured by N2 sorption, are between 10-15 m2 g -1 , as expected for samples annealed at high temperature [52]. It can be observed that the observed variation in crystallite size does not correspond to any equivalent change in surface area. Indeed, taking into account the density of the perovskite, the observed surface areas correspond to grain size between 60 and 80 nm, in good agreement only with the crystallite size of LaCoO3. It is tempting to advance the hypothesis that, in the case of all other samples, the 30 nm crystallites are the result of splitting of larger grains during the thermal treatment.

Table 2. Textural properties of LaAl1-xCoxO3 calcined at 700 °C.

Redox properties

Fig. 3 summarizes the H2-TPR profiles of LaAl1-xCoxO3 (x=0, 0.25, 0.5, 0.75, 1) calcined at 700 °C and LaAl0.25Co0.75O3 calcined at 500, 600 and 700 °C. In the literature, the reduction of Co 3+ in LaCoO3 was generally proposed by two different pathways, implying one or two steps. In the two-steps route, Co3 + is converted to Co0 via Co 2+ in two distinguished temperature regions at around 420 °C for Co 3+ to Co 2+ and 550 °C for Co2 + to Co 0 with the formation of intermediate brownmillerite LaCoO2.5 [16,[53][54][55][56][57]. This two-steps mechanism should be confirmed by the area ratio of the first peak to the second one of 1:2 [58]. However, the H2 consumption in the hightemperature reduction region is usually found lower than expected [44,55,59], suggesting that Co 0 might be partially formed in the first stage at lower temperature [55,60]. Indeed, the Co 3+ reduction was also proposed as one-step mechanism, in which Co0 can be produced directly from Co 3+ with the formation of oxygen-deficient compound LaCoO3-y, bypassing the Co 2+ species [60], and splitting of the reduction peak can be attributed to different structural Co3+ species related to the distortion of perovskite structure and oxygen defects [61].

The TPR profile of the as-prepared LaCoO3 reveals two separate peaks with maxima at ca. 395 and 580 °C (Fig. 3a). The H2-consumption, reported in Table 3, corresponds to a 1.5 H2/Co ratio, indicating that all Co3+ has been reduced to Co0. The H2-consumption ratio between the first and second reduction peaks is 1.04/1, indicating that the first peak does not correspond only to the reduction of Co 3+ to Co 2+ but includes some further reduction of Co 2+ . The mechanism of reduction seems hence to be a mixed one-step and two-steps process. The first reduction peak presents several components: the small shoulder located at 310 °C can be ascribed to microcrystalline part or chemisorbed oxygen in the catalyst surface [20]. The two overlapping components at 391 and 418 °C probably include the formation of Co 0 at relatively low temperature [55,60].

When Al partially replaces Co in LaCoO3, the H2-TPR profiles of LaAl1-xCoxO3 follow the onestep reduction mechanism from around 210 °C to 600 °C. The H2/Co ratio (Table 3) is close to the values of total reduction for LaAl0.25Co0.75O3, indicating that Co 3+ is completely reduced to Co 0 up to around 600 °C. This suggests that, in bimetallic Al-Co perovskites, Co 3+ can be reduced to metallic species at low temperature without any clear intermediate formation of Co 2+ , and the asymmetry of peak shape may be due to variously distinct Co 3+ species in perovskite lattice [61]. LaAl0.5Co0.5O3 and LaAl0.75Co0.25O3, the most Al-rich mixed samples, present a H2consumption lower than the value expected for complete reduction of Co 3+ (Table 3). This effect could be attributed to a lower than expected average oxidation state of cobalt, probably related to cation vacancies. In the case of the Co-free LaAlO3, a small peak observed above 800 °C is not related to reduction phenomena but corresponds to CO2 release from decomposition of carbonate species from the surface of this highly basic solid. Fig. 3b shows H2-TPR profiles of LaAl0.25Co0.75O3 calcined at 500, 600 and 700 °C. The sample annealed at 500 °C exhibits two peaks at 388 and 646 °C. The first peak closely correspond to the expected temperature for reduction of the Co3O4 phase observed in the sample [62]. The second peak does not correspond to a reduction peak but it is at the temperature expected for the decarbonation of the carbonate species at the surface of the extremely dispersed La2O3 evidenced by the XRD pattern [63]. LaAl0.25Co0.75O3 calcined at 600 °C reveals two overlapped peaks at LaAl0.25Co0.75O3 at a temperature nearly 90 °C lower than in the case of the same material calcined at 700 °C. This may be linked with lower surface area, narrower crystal size distribution and higher crystal size with higher calcination temperature, which leads to more diffusional resistance [24].

It is generally accepted that perovskite LaCoO3 exhibits two type of desorbed oxygen. The αoxygen, which is desorbed below 750 °C, is usually ascribed to oxygen weakly bound to perovskite surface. β-oxygen is lattice oxygen which diffuses from bulk and it is considered as an indicator of oxygen mobility in the structure [54,59,64,65]. The latter species can come from inner bulk oxygen vacancies or can be directly associated with the B-site cation reduction in the perovskite oxide framework [56]. LaCoO3 shows two desorption peaks at around 650 °C and 827 °C, probably corresponding to α-and β-oxygen, respectively (Fig. 4). LaCoO3 releases 77.5 μmol g -1 of β-oxygen (nearly 2% of bulk oxygen), as a result of Co 3+ to Co 2+ reduction and anion vacancy generation [20,64]. The amount of β-oxygen release from LaCoO3 and the desorption temperature are comparable with the results of other groups [66,67]. Decreasing the cobalt fraction x from 1 to 0.75 significantly raises the quantity of β-oxygen, LaAl0.25Co0.75O3 releasing 158.1 μmol g -1 at a lower desorption temperature of 849 °C. The oxygen species in LaAl0.25Co0.75O3 occupies almost 3.7% of total oxygen anion in perovskite, revealing the highest oxygen mobility among the studied samples. It should be noticed that Royer et al. suggested that βoxygen is likely to originate from grain boundaries between two neighbor crystal domains due to higher oxygen diffusivity within boundaries than bulk, and the feature was significantly enhanced by substituting 20% of Co by Fe to form LaCo0.8Fe0.2O3 [66]. Therefore, the highest amount of lattice oxygen for LaAl0.25Co0.75O3 may be related to the smallest crystallite size among the studied samples. For further decrease of cobalt content, the oxygen evolution dramatically drops to 9.1 μmol g -1 when 50% of Co is replaced by Al and no β-oxygen is measured when only 25% cobalt is left (Table 4). LaAl0.75Co0.25O3 exhibits no oxygen evolution during the experiment, as it is the case for LaAlO3 due to non-reducibility of aluminum cations. The decrease of β-oxygen with the increase of cobalt content closely matches the decrease of H2-consumption in H2-TPR and confirms that the cobalt-richest samples present abundant cation vacancies and a lower than expected cobalt oxidation state.

Table 4. Calculated quantity of desorbed oxygen of LaAl1-xCoxO3 obtained by integration of O2-TPD profiles.

Surface properties

The Fig. 5a shows XPS profiles of LaAl1-xCoxO3 (x=0, 0.25, 0.5 and 0.75) with Co 2p3/2 and 2p1/2 binding energy at 780-780.4 eV and 795.4 eV respectively, both ascribed to Co3+ species [67,68]. Moreover, distorted 2p3/2 Co pattern is distinctive for Co 3+ species [69], with a similar gap between 2p1/2-2p3/2 of 15.4 eV [70] and no Co 2+ shake up peaks at 785-788 eV [69] [71], suggesting that mainly Co 3+ species can be detected at the surface of the prepared samples. However, the satellite signal at 790.2 eV and broadening region at about 805 eV can be seen in LaAl0.5Co0.5O3, and more pronounced in the sample with more cobalt: LaAl0.25Co0.75O3. This profile is reported for Co3O4 [72], indicating that there may be some cobalt oxides not incorporated in perovskite structure when more than 50% of Al is replaced by Co, which is in agreement with XRD profiles. Table 5 listed the ratios of surface Co/Al which increase from 0.4 for LaAl0.75Co0.25O3 to 3.2 for LaAl0.25Co0.75O3. This ratio for LaAl0.75Co0.25O3 is higher than its bulk composition (0.33) by around 20% and the surface is slightly enriched with Co. By contrast, LaAl0.5Co0.5O3 has surface Co lower than in the bulk composition: 0.6 in comparison with theoretical 1.0.

The O 1s XPS spectra are deconvoluted to two oxygen species: peaks at 529.1-529.3 eV are characteristic of surface lattice oxygen (denoted as Olat) and signals at 531.1-531.3 eV can be ascribed to oxygen adsorbed on perovskite surface (denoted as Oads) [73,74] (Fig. 5b). Concerning the LaCoO3 sample, its O 1s curve was satisfactorily curve-fitted by using 3 peaks. Besides the two components previously described, the signal at higher BE (533 eV) has been assigned to O species in some segregated oxide phases. Such an assignment is in agreement with the XRD pattern of the sample, in which the main peak of the La2O3 and Co3O4 phases was detected (see Fig. 1). The ratios Oads/Olat of LaAl1-xCoxO3 with x=0, 0.25, 0.5 and 0.75 are 0.77, 0.80, 0.65 and 0.75, respectively (Table 5). These four samples, with similar surface area, show Oads/Olat ratios in the same range, whereas the LaCoO3 sample, with much lower surface area, shows a much higher Oads/Olat surface ratio. These data clearly indicate that the oxygen distribution at the surface in non-reactive conditions poorly reflects the bulk mobility of oxygen as revealed by H2-TPR or O2desorption experiments. The quantity of Oads is relatively correlated to surface area values which are similar for LaAlO3.

NOx-temperature programmed desorption

For the NOx-TPD measurement, the samples were adsorbed by equal quantities of NO and NO2 (about 250 ppm of each balanced by N2) at 250 °C until the saturation, cooled down under N2, and followed by heating up under N2 atmosphere with a rate of 5 °C min -1 . Fig. 6a reveals the NOx-TPD profiles of LaAl1-xCoxO3 (x up to 0.75), while a similar figure for LaCoO3 is plotted in Fig. 6c. The first small NOx desorption can be ascribed to physically adsorbed species which peaks at about 150 °C for LaAlO3, and decreases by around 60 °C when Al is substituted by Co.

It is reported that the NOx desorption below 250 °C is mostly related to B-site of perovskite, while at high temperature the basic A-site may take a role [44]. The adsorbed species is reportedly in dependence with adsorption temperature [75]. When NOx is adsorbed below 250 °C, it is mainly stored as nitrite species, which can convert Fig. 4. O2-TPD profiles of LaCo1-xAlxO3 samples calcined at 700 °C. into nitrate at higher adsorption temperature [75]. In contrast, at high temperatures NOx can be released by the nitrate decomposition followed by the oxides formation and the destruction of perovskite structure. [42]. It is also suggested that at low adsorption temperature NOx is stored as chemisorbed NOx and converted to nitrate by interaction with surface hydroxyl groups [76]. This chemisorbed species may be unstable, and it can be released during TPD experiment up to 350 °C. Fig. Generally, NO2 is desorbed at a lower temperature in all studied samples compared to NO [77], and its desorption temperature drops with increased Co doping, from 351 °C for LaAlO3 to 275 °C for LaAl0.25Co0.75O3, and almost disappears in case of LaCoO3 (Table 6). The quantity of desorbed gases is similar in all cases except LaCoO3, varying from around 53 to 75 μmol g -1 . The values partially depend on the surface area which may be not promoted by high calcination temperature of perovskite oxides. Furthermore, deficient perovskites favor NO adsorption on oxygen vacancies before oxidizing to NO2 [43,78] which may not be found in our compounds persevering charge neutrality. Table 6. Desorbed NOx quantity and relative desorption temperature of LaAl1-xCoxO3.

NO desorption temperature has the same trend of NO2 but at a higher temperature. It decreases with Co content from 412 °C for LaAlO3 to a similar range of 347-350 °C for both LaAl0.75Co0.25O3 and LaAl0.5Co0.5O3, and drops to the minimum of 320 °C for LaAl0.25Co0.75O3. Surprisingly, a decrease in Al quantity weakens the bond with acidic NOx, leading to lower desorption temperature. The introduction of Co may induce some modifications of the perovskite surface which leads to variation in desorption temperature of NOx [44]. It is reported that calcination temperature up to 1000 °C induces the formation of oxygen-deficient BaCoO3-λ which promotes the trap of NOx on oxygen vacancies; however, when the synthesis temperature is lower than 700 °C, surface areas may significantly contribute to the quantity of absorbed species [42]. For the sample LaAl0.25Co0.75O3 calcined at different temperatures (Fig. 6b), the one annealed at 500 °C releases the most NOx with a value of 258 μmol g -1 in comparison with 45 and 61 μmol g -1 of LaAl0.25Co0.75O3 calcined at 600 and 700 °C respectively. On the other hand, the specific surface areas of the sample decrease from ~22 to ~16 m2 g -1 with calcination temperature from 500 to 600 °C, and drops to 13.1 m 2 g -1 at 700 °C. Furthermore, it can be seen that calcination temperature from 700 to 600 °C shifts the desorption peak of NOx by around 96 °C, whereas sample calcined at 500 °C possesses the highest desorption temperature at 420 °C. The presence of La2O3 in the samples calcined at low temperatures may be attributed to a stronger bond with NOx and higher adsorbed quantity since La2O3 is supposed as the main NOx storage site [43].

In many works for NOx storage and reduction, NO is fed with O2 to be oxidized to NO2 which is more readily trapped by basic catalysts [77]. In the present study, NO and NO2 are supplied in an approximately equal amount at 250 °C without the presence of O2. However, NO2 almost disappears while NO is higher than its original value (250 ppm) during the adsorption process over LaCoO3 (Fig. 6d). This behavior cannot be found in other samples (for example LaAl0.25Co0.75O3 in Fig. 6d) where both NO and NO2 gets saturated after around 10 min. This suggests that during the NOx adsorption at 250 °C, NO2 may be adsorbed and partially reduced to NO. This is confirmed by the presence of more intense peaks of Co3O4 and La2O3 phases in XRD pattern of LaCoO3 after TPD treatment, which may be a result of Co 3+ to Co 4+ oxidation by NO2 reduction. Moreover, the NOx-TPD of LaCoO3 shows no NO2 peaks whereas NO is desorbed at significantly higher than those of other samples (Fig. 6c). The difference between NO adsorption (calculated by integration of NO adsorption curve with time) and desorption is 88.2 μmol g -1 , indicating the additional amount of NO from NO2 reduction. It should be mentioned that NO2 can be adsorbed by basic La2O3 observed in XRD pattern for LaCoO3 to form nitrate salt, which can be decomposed at higher temperature than that in the experiment [79]. It may be suggested that NO2 may be adsorbed on LaCoO3 and completely reduced to other species together with both Co 4+ formation and partially perovskite structure collapse.

Catalytic activities 3.2.1. NO oxidation

The NO oxidation tests aim at investigating the NO2 production at low temperatures, which is beneficial for the NOx storage/reduction process and soot combustion [77]. Fig. 7a shows NO to NO2 conversion profiles obtained from the isothermal mode, whereas the dashed line represents the thermodynamic equilibrium of NO oxidation reaction as a reference. The peaks of the curves indicate the temperatures where maximum NO2 generation is achieved. At temperatures below the peak temperature the NO oxidation is kinetically limited, while at higher temperatures the thermodynamic equilibrium is the limiting factor. Among the as-prepared samples, LaAl0.25Co0.75O3 perovskite presents the best performance (Table 7), with a maximum NO conversion of about 78% at 320 °C. Table 7. NOx performances of LaCo1-xAlxO3 calcined at 700 °C.

In contrast, LaAlO3 exhibits the worst activity with 38% at a remarkably high temperature of about 399 °C and the NO conversion increases with Co, from 38% for LaAlO3 to 56 and 60% for LaAl0.75Co0.25O3 and LaAl0.5Co0.5O3 catalysts, respectively. The conversion reaches the maximum value for LaAl0.25Co0.75O3 before reverting to 68% when Al is totally substituted by Co as reported for LaCoO3 [20]. The same catalysts were also tested in the temperature ramping mode and under lower residence time (Fig. 7c andd) in order to obtain the same test conditions as the soot oxidation tests and to get a closer correlation between the two kind of experiments. As can be appreciated, the order of the catalytic performance (LaAl0.25Co0.75O3 > LaCoO3 > LaAl0.5Co0.5O3 > LaAl0.75Co0.25O3 > LaAlO3) was the same in both steady state and dynamic conditions. Furthermore, by comparing the LaAl0.25Co0.75O3 sample with a Pt/Al2O3 commercial oxidation catalyst, the NO oxidation rate of the perovskite is obviously lower although the equilibrium is reached by both catalysts at almost the same temperature, which is the one of interest for the soot oxidation, offering a viable alternative for the PGM-based catalysts under certain conditions. It should be noticed that NO-to-NO2 oxidation ability is due to the generation of oxygen defects and redox property [80], which can be created by adjusting cation doping at A or B sites in the perovskite compounds. Others suggest that higher oxidation capacity is associated with higher oxygen mobility and exchange between lattice oxygen and gas phase oxygen [20]. This may be related to LaAl0.25Co0.75O3 with the higher amount of β-oxygen desorption (Table 4), implying the pivotal role of lattice oxygen species in the improvement of the oxidation reaction. Furthermore, all samples have negligible α-oxygen quantity released during O2-TPD experiment, but still possess comparable NO oxidation activity. This result indicates that surface oxygen may not play a critical role in NO oxidation but the diffusion of lattice oxygen to the surface is more important [81]. However, LaCoO3 desorbs significantly more oxygen than its rivals (LaAl0.75Co0.25O3 and LaAl0.5Co0.5O3) but its oxidation activity worsens despite more Co content. The higher NOx desorption temperature for LaCoO3 indicates strong interactions between NOx and the catalyst, while partial doping Al slightly weakens the bonds facilitating the NOx release at low temperatures. Thus, oxygen mobility may be not the only factor for NO oxidation but the synergetic interaction between two B-site cations (Al and Co) may enhance oxidation performance of the catalysts, as suggested by Ma et al. with a small substitution of Co by Fe to promote NO conversion [82]. Furthermore, under H2/Ar flow in the H2-TPR experiment, LaAl0.25Co0.75O3 is reduced at a temperature of 437 °C, higher than 394 °C for LaAl0.75Co0.25O3. However, the NO conversions of these samples reveal different trend for the reduction temperature, which may imply the negligible effects of reducibility on NO oxidation. Furthermore, LaCoO3 produces less NO2 at low temperatures but higher above 275 °C than LaAl0.75Co0.25O3 and LaAl0.5Co0.5O3 (Fig. 7a). This may be related to the fact that LaCoO3 can adsorb NO2 at low temperatures and partially reduce to NO, as can be seen in the NOx-TPD experiment. Besides, the temperature of maximum NO2 production is lowest for LaAl0.25Co0.75O3 at 320 °C, and increases by around 30 °C with x=0.25 and 0.5 (Table 7). A similar trend can be found for NO desorption profiles (Table 6), where NO desorbs at 320 °C for LaAl0.25Co0.75O3 and increase to 350 and 347 °C for LaAl0.5Co0.5O3 and LaAl0.75Co0.25O3 respectively. This highlights the suggestion in which the oxidation reaction commences with the chemisorption of reactants NO and O2, followed by the dissociation of O2 and NO2 on the surface [28]. Many works have found that substitutions of A-site generate oxygen vacancies, for example La1-xSrxBO3 [20,43], or of B-site to support the co-existence of multivalent states, e.g. LaCo1-xMgxO3 [67], in order to promote NO oxidation. Furthermore, it was shown that the partial substitution of cations can promote the formation of preferential oxidation active states (e.g. metallic isolated or biactive sites) that can promote the NO oxidation [83,84]. However, there are fewer investigations regarding the effect of the degree of perovskite crystallinity on the NO oxidation. Fig. 7b shows profiles of NO2 molar percentage in the NOx mixture of LaAl0.25Co0.75O3 which is calcined at 500, 600 and 700 °C. It is clear that the sample annealed at 500 °C reveals the lowest oxidation activity, with about 66% at ˜ 350 °C despite the highest surface area (21.9m2 g-1), probably due to the presence of segregated phases such as Co3O4 and La2O3 [20]. The samples calcined at 600 °C show superior oxidation performances at low temperatures, but at above 300 °C the solid calcined at 700 °C slightly outperforms. Despite the reduction in surface area, the calcination temperature up to 700 °C has positive effects on oxidation activity, which may be associated with higher crystallinity and less minor phases as detected in XRD profiles (Fig. 2b). However, further increase calcination temperature beyond 700 °C may lead to deterioration of oxidation activity due to low surface area as studied elsewhere [20].

Soot oxidation

Fig. 8 reveals the results of soot oxidation tests over LaAl0.25Co0.75O3 (calcined at 700 °C) in the presence and absence of NOx gas. Table 8 shows the testing outputs: T10% represents the ignition temperature, when 10% of soot is burnt; T50% and T90% are the temperatures when 50% and 90% of soot is consumed respectively; Tmax is the temperature when maximum CO2 production is achieved, and (NO2/NOx)max/T is the maximum percentage of NO2 over NOx mixture and its temperature. Generally, the NOx-assisted soot oxidation reaction starts with the oxidation of adsorbed NO to produce NO2, which is a stronger oxidant than O2 [38,45,85]. Soot can be also oxidized by O2 but at a relatively higher temperature than with NO2. In the presence of NO2, it interacts with soot surface to form surface oxygen complexes (SOC), which decomposes further to CO, CO2 and NO [28,86]. O2 is first adsorbed at the catalyst's surface and undergoes the dissociation to form active oxygen species. This species is possibly transferred to the surface of soot forming SOC via spill-over mechanism [86]. The results clearly show that soot is oxidized at a significantly lower temperature in the presence of NOx (T10% are 377 and 513 °C for with and without NOx respectively). Moreover, NOx also remarkably supports to reduce the temperature of 50% of soot conversion by around 111 °C although at higher temperatures the role of NOx in soot oxidation becomes less prominent with the decrease of T90% by only 27 °C because of limited NOx availability (Table 8). In terms of CO2 production, NOx promotes the total oxidation with CO2 selectivity of 99.8% compared to 98.5% of that without NOx. Without the presence of NOx, the Tmax increases by around 120 °C and the formation of CO is significant. The results highlight the vital role of NO2 in soot oxidation and its further applications in NOx reduction process by the selective catalytic reduction reaction. The improvement in the oxidation activity is likely to be related to not only the better performance in the NOx oxidation but also the NOx adsorption [START_REF] Andana | [END_REF], as the Co doping reduces the NOx desorption temperature thereby facilitating the oxidation reactions at a lower temperature range (Fig. 6). As expected, both samples LaAl0.75Co0.25O3 and LaAl0.5Co0.5O3 (violet and black curves) exhibit similar soot oxidation activity, which is in line with the NOx-TPD experiments. This suggests that the NOx-assisted soot oxidation is mainly governed by the adsorption of NOx on the catalyst's surface and directed to the soot-catalyst interface before initiation of the oxidation [START_REF] Andana | [END_REF]. LaAl0.25Co0.75O3 is the most active catalyst with T10% of 377 °C, which is 12 °C lower than that of LaCoO3. The complete substitution of Al by Co deteriorates the soot oxidation performance at low temperatures while there is no difference at middle temperature with T50% of 467 °C for both LaAl0.25Co0.75O3 and LaCoO3. The difference between these two catalysts is signified in terms of NO2 production which plays an essential role in abatement reduction. LaAl0.25Co0.75O3 maintains high formation of NO2 with NO2/NOx of 0.71 at 321 °C compared to 0.42 at 352 °C for LaCoO3. The low ignition temperature allows to uninterruptedly oxidize soot while keeping high NO2 production. In comparison with soot-free NO oxidation, NO2 production obtained from NOx-soot oxidation for all catalysts is lower, confirming the participation of NO2 as a strong oxidant in the reaction leading to its consumption. LaAlO3 shows no formation of NO2 at all, explaining that the soot oxidation is practically the same as non-catalytic [86]. The outstanding performance of LaAl0.25Co0.75O3 is likely to be associated with the prominent lattice oxygen mobility which may be facilitated by coincorporation of Co-Al elements in perovskite structure [86,87]. Fig. 9c andd show the evolution of CO2 and CO concentration during the NOx-assisted oxidation tests over the catalysts with various Co content. Obviously, LaAlO3 has the highest Tmax (the temperature at which the maximum CO2 is produced) at 563 °C with low quantity of CO2 formed, evidenced by the CO2 selectivity of 82.3%. The substitution of Co by Al shifts the Tmax to lower range by about 81 °C for x=0.25 and 0.5, and by around 96 °C for LaAl0.25Co0.75O3. However, LaCoO3 shifts the temperature towards 493 °C which is similar to that reported elsewhere [27] and produces relatively a large amount of CO at high temperature. The CO2 evolution profile for LaCoO3 has a relatively similar trend as NO desorption curve with a broader shoulder at a low-temperature range (Fig. 6c), indicating the key role of NO adsorption on soot oxidation. When SiC was used as a reference for the non-catalytic soot oxidation, the promotional effect of NOx was lost as the peak of the soot oxidation rate was shifted to 626 °C coupled with a very high CO production. Fig. 10 summarizes soot conversion and NO2/NOx percentage as functions of temperature over catalyst LaAl0.25Co0.75O3 calcined at different temperatures, and Table 9 sums up the oxidative characteristics of the catalyst. The calcination at lower temperatures enhances the surface areas but deteriorates the oxidation activity. The sample annealed at 500 °C has the highest T10%, T50% and T90% at 399, 492 and 583 °C respectively, compared to 370, 478 and 578 °C for LaAl0.25Co0.75O3 calcined at 600 °C. Moreover, the treatment at 600 and 700 °C shows similar soot oxidation but the NO2 production of the later is ameliorated with 71% compared to 64.9% for the former. It has been already mentioned that LaAl0.25Co0.75O3 calcined at the lowest temperature adsorbs the largest amount of NO due to high surface area but releases this gas at the highest temperature, suggesting that stronger interaction between NOx and substrate surface does not support the oxidation reaction and the products fail to dissociate as it can be described by the Sabatier principle [START_REF] Rothenberg | Catalysis: Concepts and Green Applications[END_REF]. This finding emphasizes the crucial role of crystallinity promoted by high calcination temperature in both NO and NOx-assisted soot oxidation. Table 9. Catalytic performances of LaAl0.25Co0.75O3 at different calcination temperatures.

Conclusions

Among the prepared catalysts, LaAl0.25Co0.75O3 exhibits superior catalytic activity for both NO oxidation and NOx-assisted soot oxidation. For the NO oxidation, NO2 production can reach 78% at relatively low temperature (320 °C) which is considered as a potential alternative for noble metal catalysts. Furthermore, LaAl0.25Co0.75O3 is also the most active catalyst for NOx-assisted soot oxidation with T10% of 377 °C and NO2/NOx of 0.71, and results in almost 100% of CO2 selectivity. The correlation between NOx desorption and oxidation activity is well established suggesting that NOx adsorption on catalyst surface is a key role in soot oxidation with NOx. The effect of NO2 for soot oxidation is obvious, since in its absence the oxidation activity remarkably decreases. The excellent performance of LaAl0.25Co0.75O3 is likely to be linked with high lattice surface oxygen supported by well-crystallized perovskite structure. Full replacement of Al by Co deteriorates the catalytic activity, suggesting that the combination of Al-Co has synergetic effects on the catalysis.

Fig. 1 .

 1 Fig. 1. X-Ray diffractions of LaAl1-xCoxO3 calcined at 700 °C: (a) x=0; (b) x=0.5; (c) x=0.5; (d) x=0.75; (e) x=1.

Fig. 2 .

 2 Fig. 2. (a) Volume of the formula units LaAl1-xCoxO3 as a function of the cobalt fraction; (b) diffraction patterns of LaAl0. 25Co0.75O3 calcined at different temperatures.

Fig. 3 .

 3 Fig. 3. H2-TPR profiles of the samples LaAl1-xCoxO3 calcined at 700 °C (a); LaAl0.25Co0.75O3 calcined at different temperatures (b).

Fig. 4 .

 4 O2-TPD profiles of LaCo1-xAlxO3 samples calcined at 700 °C.

Fig. 5 .

 5 XPS spectra of Co 2p (a) and O 1s (b) of LaAl1-xCoxO3 (x=0, 0.25, 0.5, 0.75, 1).

Fig. 7 .

 7 NO2 percentage of (a) LaAl1-xCoxO3 calcined at 700 °C and (b) LaAl0.25Co0.75O3 calcined at different temperatures in steady state conditions and (c) LaAl1-xCoxO3 calcined at 700 °C and (d) LaAl0.25Co0.75O3 calcined at different temperatures in dynamic conditions.

Fig. 8 .

 8 Fig. 8. (a) Soot conversion and (b) CO2 and CO concentration as function of temperature during soot oxidation catalytic tests with and without NOx supply over LaAl0.25Co0.75O3 catalyst.

Fig. 9

 9 summarizes soot conversion, NO2/NOx percentage, CO and CO2 concentrations as functions of temperature during the experiments with NOx-assisted soot oxidation over LaAl1-xCoxO3 catalysts. Among the prepared solids, LaAlO3 possesses certainly the lowest activity with T10%, T50% and T90% of 470, 562 and 623 °C respectively. Doping Co shifts the reaction temperature to lower ranges, LaAl0.75Co0.25O3 obviously outperforms LaAlO3 by reducing these temperature values by about 60-80 °C.

Fig. 9 .

 9 Fig. 9. (a) Soot conversion, (b) NO2 percentage, (c) CO2 and (d) CO concentrations of LaAl1-xCoxO3 calcined at 700 °C.

Fig. 10 .

 10 Fig. 10. (a) Soot oxidation and (b) NO2 percentage of aAl0.25Co0.75O3 calcined at different temperatures.

Table 3 .

 3

H2-consumption of LaAl1-xCoxO3 with different composition.

Table 5 .

 5 Relative

abundances of oxygen species derived from the deconvolution of O 1s XPS spectra and Co/Al surface ratio.

Table 8 .

 8 Catalytic performances of LaCo1-xAlxO3 calcined at 700 °C.

Acknowledgements

This work was co-funded through a SINCHEM Grant. SINCHEM (Sustainable Industrial Chemistry) is a Joint Doctorate programme selected under the Erasmus Mundus Action 1 Programme (FPA 2013-0037).