Martin Gendrin
email: martin.gendrin@insa-lyon.fr

Jean-Yves Gauthier
email: jean-yves.gauthier@insa-lyon.fr

Member, IEEE Xuefang Lin-Shi
email: xuefang.shi@insa-lyon.fr

A Predictive Hybrid Pulse-Width-Modulation Technique for Active Front-End Rectifiers

Keywords: Bus-clamping PWM, Space Vector PWM, hybrid PWM techniques, Model Predictive Control, Active-Front-End rectifier

Nowadays Active-Front-End (AFE) rectifiers are increasingly used as grid connected devices. Their efficiency and performances have become relevant for reducing the overall grid losses. This paper thus introduces a Predictive Hybrid Pulse-Width-Modulation (PH-PWM) technique, adaptable to any Space Vector PWM (SVPWM) controller. As opposed to hybrid PWM techniques based on sector partitioning, the PH-PWM technique selects the appropriate PWM sequence on-line with the help of a predictive algorithm. This selection is based on a cost-function where users can define a trade-off between various criteria, such as the reduction of current distortion and of switching losses, as presented in this paper. The use of the PH-PWM technique increases performances in comparison with the conventional PWM techniques. The simulation and experimental results are presented to confirm the effectiveness of the proposed PH-PWM technique. Aside from the trade-off capacity of the proposed PH-PWM technique, the simulation results validate a reduction of the switching losses for the converter up to 23% as compared with the conventional SVPWM technique.

I. INTRODUCTION

A CTIVE front-end (AFE) rectifiers are more and more being considered for use as grid-connected devices. When compared to the diode rectifiers, they enable a bi-directional power flow. They also offer a naturally low current distortion and cancel the requirement for heavy inductive filters between the grid and the rectifiers. Therefore, these topologies are increasingly used as active filters, to correct the power factor of loads or to compensate the lack of reactive power in the source grid. Due to good features, AFE rectifiers are the focus of many scientific papers. They aim to produce fast and reliable grid controllers that keep the current distortion low without increasing the size of inductive filters, which at the same time improves the efficiency of the rectifiers.

One possible control structure of an AFE rectifier is the direct controller. At each sample time, it enables the selection of the switching configuration to be applied on the converter. The Direct Power Control (DPC) [START_REF] Zhang | Performance improvement of direct power control of pwm rectifier with simple calculation[END_REF] and the Finite Control Set Predictive-DPC (FCS P-DPC) [START_REF] Quevedo | Finite control set mpc of an afe rectifier with dynamic references[END_REF][3][4] [START_REF] Kwak | Predictive-control-based direct power control with an adaptive parameter identification technique for improved afe performance[END_REF] are both based on this working principle. More recently, a Modified Model Predictive Control (MMPC) was proposed in [START_REF] Akter | Modified model predictive control of a bidirectional ac-dc converter based on lyapunov function for energy storage systems[END_REF]. However despite its good dynamic performances, the direct controller approach suffers from a variable frequency spectrum and requires a high sampling frequency. Therefore in this study, a controller with a space vector Pulse Width Modulation (SVPWM) generator has been preferred, such as the Voltage-Oriented Control (VOC) [START_REF] Zhang | Comparative study of model predictive current control and voltage oriented control for pwm rectifiers[END_REF] or the Predictive -DPC (P-DPC) [START_REF] Aguilera | Generalized predictive direct power control for ac/dc converters[END_REF] [START_REF] Vazquez | Predictive optimal switching sequence direct power control for grid-connected power converters[END_REF]. Those controllers deliver the required dwell-times of the switching configurations to be used and the corresponding sector to the SVPWM generator that produces the switching sequence. For all controllers with a SVPWM generator, the switching frequency is fixed, and the constraint on the sampling time is reduced.

The modulation schemes have in the recent years become the center of a growing number of studies, due to their key role in the development of modern power electronics [START_REF] Leon | The essential role and the continuous evolution of modulation techniques for voltage-source inverters in the past, present, and future power electronics[END_REF]. In particular, the SVPWM generator enables a precise application of the voltage reference to the AC-side of the converter. Furthermore, in SVPWM, a given voltage reference can be applied by different PWM sequences that lead to the same voltage in an average perspective over the PWM period, but have a specific current distortion and specific switching losses. Therefore, several Hybrid PWM techniques have been detailed in the literature as well as coupled PWM sequences. The by far most popular PWM technique is the conventional spacevector PWM (CSVPWM) because it implies a high line-side voltage and a low current distortion over a large range of modulation indexes [START_REF] Hari | Space-vector-based hybrid pulse width modulation technique to reduce line current distortion in induction motor drives[END_REF]. However at high modulation indexes, the bus-clamping PWM (BCPWM) techniques represent good candidates [START_REF] Hari | Space-vector-based hybrid pulse width modulation technique to reduce line current distortion in induction motor drives[END_REF] [START_REF] Vazquez | Predictive optimal switching sequence direct power control for grid-connected power converters[END_REF]. In one study [START_REF] Basu | Minimization of torque ripple in pwm ac drives[END_REF], a hybrid PWM technique using a CSVPWM sequence and BCPWM sequences was developed to reduce the torque ripple linked to the q-axis current component in a permanent magnet synchronous motor. Novel specific BCPWM-type sequences were introduced in [START_REF] Narayanan | Advanced bus-clamping pwm techniquesbased on space vector approach[END_REF] and [START_REF] Narayanan | Space vector based hybrid pwm techniques for reduced current ripple[END_REF], enabling the production of new hybrid PWM techniques. In other investigations [START_REF] Narayanan | Space vector based hybrid pwm techniques for reduced current ripple[END_REF] [START_REF] Hari | Space-vector-based hybrid pulse width modulation technique to reduce line current distortion in induction motor drives[END_REF], the aforementioned sequences were used in hybrid PWM techniques so as to reduce the resultant current distortion. Such hybrid PWM techniques were also used to reduce both current distortion and switching losses in [START_REF] Zhao | Space-vector-based hybrid pulsewidth modulation techniques for reduced harmonic distortion and switching loss[END_REF], to diminish the acoustic noise of an induction motor in [START_REF] Binojkumar | Experimental investigation on the effect of advanced bus-clamping pulsewidth modulation on motor acoustic noise[END_REF] or to lower the torque ripple of an induction motor in [START_REF] Hari | Space-vector-based hybrid pwm technique to reduce peak-to-peak torque ripple in induction motor drives[END_REF] [START_REF] Hari | Space-vector-based hybrid pwm technique to reduce peak-to-peak torque ripple in induction motor drives[END_REF]. Recently [START_REF] Das | Novel switching sequences for a space-vectormodulated three-level inverter[END_REF] [START_REF] Das | Space-vector-based hybrid pulsewidth modulation techniques for a three-level inverter[END_REF], new sequences were drawn for three-level converters and novel hybrid PWM techniques were introduced.

Although the aforementioned Hybrid PWM techniques achieve an improvement in comparison with CSVPWM, they are all based on a sector partitioning to select the appropriate sequence and are therefore fixed designs. For this reason, the latter hybrid PWM techniques cannot be optimized for all the existing operating conditions. The contribution of this paper is to propose a Predictive Hybrid PWM (PH-PWM) technique for an AFE rectifier, that can be coupled to any kind of SVPWM controller. The originality is that the PWM sequences are selected on-line by a predictive algorithm. The choice of the PWM sequence is based on a user-defined tradeoff between various criteria, such as the current distortion and the switching losses. The trade-off can be adjusted on-line, which offers more flexibility than the existing hybrid PWM techniques and enables a better fitting to the working point under consideration. Independent of the used SVPWM-based controller, the proposed PH-PWM technique achieves both a better current Total Harmonic Distortion (THD) and lower switching losses through modulation without change of the AFE converter. Here, a conventional VOC is used since it is more reputed and since the contribution of this paper focuses on the modulation level.

The rest of the paper is organized as follows. Section II describes the AFE rectifier and its control scheme to indicate where the proposed PH-PWM is located. Section III introduces the principle of the PH-PWM technique, including the specification of the considered PWM sequences, the current distortion and switching loss predictions mandatory for the cost function calculation, and the predictive algorithm. Section IV analyzes the simulation results and Section V presents the experimental results and shows the effectiveness of the proposed solution.

II. THE AFE RECTIFIER AND ITS CONTROL SCHEME

The considered AFE rectifier is composed of a basic three-leg two-level converter, a set of three inductances on the AC side and a storage capacitor connected in parallel to the load on the DC side, as depicted in Fig. 1. In order to control this structure, one can use a VOC controller, which is a vector control based on a rotating dq reference frame with the d-axis aligned with the grid-voltage. In this frame, the current behavior is described by the following model:

V d = -R • i d -L • i d + L • ω • i q + V gridd V q = -R • i q -L • i q -L • ω • i d + V gridq (1)
where V d and V q are the dand qaxis voltages on the rectifier side, i d and i q are the dand q-axis currents, L and R are the line inductance and resistance, ω is the grid pulsation, and V gridd and V gridq are the projection of the grid voltage on the dand q-axis, respectively. The functional scheme of the AFE controller is given in Fig. 2. To separately control the dand q-axis currents, the decoupling terms e d = Lωi q + V gridd and e q = -Lωi d + V gridq are added to the outputs, u d and u q , of the current regulators, thus enabling the control of i d and i q by conventional proportional-integral (PI) controllers. To simultaneously achieve the control of the DC bus voltage and a unity power factor, a voltage PI controller delivers a current reference to the d-axis current controller. The q-axis current reference is set to 0. The resultant control voltages, V d and V q , are then translated into a voltage reference V ref delivered to the proposed PH-PWM technique which is the focus of this paper and which is developed in the next section. The PH-PWM technique applies this voltage reference to the AC side of the converter taking into account its discrete characteristics. The resulting PWM sequence can be implemented with a deadtime compensation method as in [START_REF] Lee | A simple and direct dead-time effect compensation scheme in pwm-vsi[END_REF].

III. THE PRINCIPLE OF THE PREDICTIVE HYBRID PWM TECHNIQUE

The principle of the PH-PWM technique is drawn as a functional scheme in Fig. 3. At each sample time k.T s , where T s is the sampling period of the VOC controller, it will select the appropriate PWM sequence, among a finite set Σ of N PWM sequences, and use it to apply V ref (k). This selection is based on a predictive algorithm, whose principle can be summarized in the following steps:

• At each sample time, k, the voltage reference, V ref (k), the three-phase currents, i abc (k), and the DC bus voltage, V DC (k), are acquired;

• For each considered PWM sequences, the prediction of the current distortion and the switching losses for the next sampling period, noted respectively ∆I p SEQ (k + 1) and P p SEQ (k + 1), will be evaluated; • These predictions are integrated in a cost function, given in (2) , expressing the trade-off between the reduction of the current distortion and the lowering of the switching losses. In (2), β is a weighting factor enabling the user to adapt the cost function to its specifications;

g = ∆I p SEQ (k + 1) + β • P p SEQ (k + 1) (2)
• The PWM sequence, Υ(k), whose predictions minimize the cost function, is selected, and applied to the drivers of the converter during the next sampling period. As such, the predictive algorithm has some similarities to the FCS-MPC which has been extensively covered in the literature [START_REF] Rodriguez | State of the art of finite control set model predictive control in power electronics[END_REF]. However, contrary to the FCS-MPC which acts on the current or power level, the predictive algorithm is used in a PWM generator. Thus, it has no impact on either the closed loop dynamic, or the system stability.

According to the aforementioned structure of the PH-PWM, we require definitions of the considered PWM sequences Σ and of the discrete-time model enabling the current distortion and the switching loss predictions. They will thus be the focus of the three following subsections.

A. The considered PWM sequences

As a conventional SVPWM generator, the PH-PWM tends, at each sample time, to apply the voltage reference delivered by the controller, V ref (k), in an average approach over a PWM period. It therefore considers this reference as a vector of a magnitude, v ref (k), and a phase lag, α(k), in the stationary reference frame (Fig. 4). It then applies the two nearest among the six existing active configurations for specific dwell times. The zero vector is set for the rest of the PWM period, T pwm . The magnitude of vectors representing the active configurations in the stationary reference frame and v ref (k) are normalized with respect to 2 3 of the measured V DC (k), and v ref (k) can then be defined as the modulation index. The sum of the resultant vectors equals V ref (k) in an average approach over the PWM period, as can be seen for sector I in Fig. 4. For this sector, between the active vectors 1 and 2, the dwell times T 1 (k) and T 2 (k) are calculated as in (3). The zero voltage vector will be applied during T z (k).

T 1 (k) = v ref (k) • sin π 3 -α(k) sin π 3 • T pwm T 2 (k) = v ref (k) • sin (α(k)) sin π 3 • T pwm T z (k) = T pwm -T 1 (k) -T 2 (k) (3)
The zero voltage vector can be applied by the two switching configurations 0 and 7, leading to the connection of the three phases of the load either on the negative or on the positive DC bus potential. Moreover, the active configurations can be applied more than once in the PWM period as long as the total application time equals the corresponding dwell time. A multiplicity of sequences leading to the application of the same value of V ref (k) arises from these facts. According to the criterium given in [START_REF] Narayanan | Space vector based hybrid pwm techniques for reduced current ripple[END_REF] and considering a maximum of three switchings per half PWM period, seven sequences emerge:

• the CSVPWM sequence (0127;7210), denoted 0127. In the example of Fig. 4, this corresponds to the application of vectors V 0 , V 1 ,V 2 ,V 7 in the half PWM period. In the other half PWM period, a symmetrical sequence is applied as

V 7 , V 2 ,V 1 ,V 0 .
This leads to an equal partitioning of the zero vector between 0 and 7;

• the BCPWM sequences (012;210) and (721;127), denoted 012 and 721 respectively, that use either 0 or 7;

• the special BCPWM sequences (0121;1210), (1012;2101), (2721;1272) and (7212;2127), denoted respectively 0121, 1012, 2721 and 7212, which are derived from the BCPWM sequences by applying one of the active configurations twice.

In order to keep the switching frequency over the fundamental independent of the sequences, the PWM period of the BCPWM sequences is set to 2 3 of the PWM period of the CSVPWM sequence [START_REF] Narayanan | Space vector based hybrid pwm techniques for reduced current ripple[END_REF]. The special BCPWM sequences possess the same PWM period as the CSVPWM sequence. These seven sequences form the finite set Σ of PWM sequences of the PH-PWM technique for the rest of the paper, even if more PWM sequences exist and improve other characteristics such as the common mode voltage. It has to be noted that the more PWM sequences that are included in Σ, the more the computational load increases. Therefore, in order to limit it, it is interesting to adapt the composition of Σ according to the user specifications.

Aside from the finite set of PWM sequences, the discretetime model used in the predictive algorithm to predict the behavior of the converter and load association over the next sample time has to be developed.

B. The current distortion factor

The factor ∆I p SEQ (k + 1), quantifying the current distortion over the next sample time for every PWM sequences, has to be defined.

Two approaches make it possible to define the current distortion due to the PWM sequences. This can be studied directly in the stationary reference frame and the phase currents kept as a three-phase system [START_REF] Grandi | Evaluation of current ripple amplitude in three-phase pwm voltage source inverters[END_REF] [START_REF] Grandi | Analysis and comparison of peak-to-peak current ripple in two-level and multilevel pwm inverters[END_REF]. Another approach cancels the influence of the current fundamental on the current distortions [START_REF] Narayanan | Advanced bus-clamping pwm techniquesbased on space vector approach[END_REF][14] [START_REF] Zhao | Space-vector-based hybrid pulsewidth modulation techniques for reduced harmonic distortion and switching loss[END_REF][11] [START_REF] Hari | Space-vector-based hybrid pwm technique to reduce peak-to-peak torque ripple in induction motor drives[END_REF]. It is based on a dq-frame that rotates synchronously with the voltage reference vector, V ref , and whose q-axis is aligned with V ref . As has been underlined earlier, the instantaneous three-phase voltages resulting from each PWM sequence achieve the value of V ref (k) in a average approach between the sample time k and the next sample time k + 1. However each sequence leads to a specific instantaneous voltage error ∆v over the PWM period, expressed in the dqframe. The time integral of this voltage error is termed the stator flux ripple [START_REF] Zhao | Space-vector-based hybrid pulsewidth modulation techniques for reduced harmonic distortion and switching loss[END_REF] and is denoted Ψ. When the phaseresistance of the load can be neglected, which is most often the case for the AFE rectifier, this stator flux ripple is directly proportional to the current ripple. Fig. 5 gives as an example the evolution of ∆v and Ψ in the dq-frame between the sample time k and the future sample time k + 1 for a specific working point (v ref (k) = 0.75 and α(k) = 20 o ) and for the sequence 0127, with two PWM periods per sampling cycle. The shapes of these curves depend on the actual working point, i.e., v ref (k) and α(k). As the PWM sequences differ in the succession of configurations they induce, the evolution of ∆v over the PWM period, and thus of Ψ, is also specific to the used PWM sequence. In Fig. 5, the use of a PWM sequence other than 0127 for this working point results in different values of ∆v and Ψ. The RMS value of the current distortion over the PWM period between the sample time k and the next sample time k + 1 enables a comparison of the current distortion induced by each PWM sequence, for the actual working point. It is derived from the RMS value of the stator flux ripple, developed for each sequence in [START_REF] Zhao | Space-vector-based hybrid pulsewidth modulation techniques for reduced harmonic distortion and switching loss[END_REF], and leads to:

∆I p SEQ (k + 1) = V DC (k) • T pwm 3 • L • C 0(SEQ,α(k)) • v 2 ref (k) + C 1(SEQ,α(k)) • v 3 ref (k) + C 2(SEQ,α(k)) • v 4 ref (k) 1 /2 (4)
Here, v ref (k) is the modulation index, V DC (k) the measured DC bus voltage, and the coefficients C 0 , C 1 and C 2 depend on the chosen PWM sequence and on the phase lag α(k). They are taken from [START_REF] Zhao | Space-vector-based hybrid pulsewidth modulation techniques for reduced harmonic distortion and switching loss[END_REF].

For the studied AFE rectifier with a phase inductance of 2.3mH and a DC bus voltage of 670V, Fig. 6 shows the evolution of the predicted value ∆I p SEQ (k + 1) for an α(k) varying on the first sector for different PWM sequences with three different values of v ref (k). Due to the axis symmetry between the sectors, a study on the first sector is sufficient to determine the behavior over the entire stationary reference frame. ∆I p SEQ (k+1) induced by the BCPWM sequences using the 0-configuration and the one using the 7-configuration are symmetric around the center of each sector [START_REF] Narayanan | Space vector based hybrid pwm techniques for reduced current ripple[END_REF]. Only the values of the sequences using the 0-configuration are shown in Fig. 6 for the BCPWM and special BCPWM sequences.

C. The switching loss factor

The second part of the discrete-time model included in the predictive algorithm of the PH-PWM is the factor P p SEQ (k+1), which predicts the switching losses of the converter and load association between the sample time k and the following one, k + 1, for each sequences.

If the PWM sequence implies a change of state in one inverter leg, then the energy lost in the switching process during the PWM period, T pwm , is the sum of the turn-on and turnoff switching losses, E on and E of f , of each IGBT and of the turn-off switching losses, E of f D , of each diode. These values are normally given in the datasheets of the IGBT/diode module for specific test conditions, V test and I test . By assuming that E on , E of f and E of f D of one module are proportional to the DC bus voltage, V DC , and to the phase current, i, their values are ruled by [START_REF] Kwak | Predictive-control-based direct power control with an adaptive parameter identification technique for improved afe performance[END_REF] [START_REF] Das | Variation of igbt switching energy loss with device current: An experimental investigation[END_REF].

E of f = 1 2 • 2 • E of f test V test • I test • i • V DC = t of f 2 • i • V DC E on = 1 2 • 2 • E on test V test • I test • i • V DC = t on 2 • i • V DC (5)
E of f D = 1 2 • 2 • E of f D test V test • I test • i • V DC = t of f D 2 • i • V DC
where t on , t of f and t of f D are the resultant equivalent turnon and turn-off times respectively, and E on test , E of f test and E of f D test the energy losses in the test conditions.

A second-order behavioral model between the switching losses and the phase current is actually more accurate [START_REF] Das | Variation of igbt switching energy loss with device current: An experimental investigation[END_REF][26], but as P p SEQ (k + 1) has to be kept simple, the linear model is going to be considered. According to [START_REF] Kwak | Predictive-control-based direct power control with an adaptive parameter identification technique for improved afe performance[END_REF], this factor can be evaluated for the different PWM sequences as the sum of the energies lost in each leg in the switching process over a PWM period. It results in [START_REF] Akter | Modified model predictive control of a bidirectional ac-dc converter based on lyapunov function for energy storage systems[END_REF] for the sequence 0127:

P p 0127 (k + 1)= 1 T pwm • V DC (k) • (t on + t of f + t of f D ) • (|i a (k)| + |i b (k)| + |i c (k)|) (6)
For the BCPWM sequences, it results in (7):

P p SEQ (k)= 3 2T pwm • V DC (k) • (t on + t of f + t of f D ) • (|i i (k)| + |i j (k)|) (7)
where SEQ denotes 012 or 721, i and j denote the two nonclamped phases a, b, or c on the PWM period.

For the special BCPWM sequences, ( 8) is obtained:

P p SEQ (k)= 1 T pwm • V DC (k) • (t on + t of f + t of f D ) • (2 • |i i (k)| + |i j (k)|) (8)
where SEQ denotes 0121, 7212, 1012 or 2721, i denotes the double-switching phase a, b, or c and j denotes the singleswitching phase a, b, or c on the PWM period.

In short, with the acquired three-phase currents i abc (k), voltage reference V ref (k) and DC bus voltage V DC (k) at the current sample time, the predictions of the current distortion and the switching losses caused be each PWM sequence between k and k + 1 will be quantified by using ( 4)-( 8).

D. The predictive algorithm

According to the descriptions above, the predictive algorithm included in the proposed PH-PWM technique to select the appropriate PWM sequence can be formulated as an algorithm of Fig. 7.

According to the developed discrete time model, the results obtained with the PH-PWM technique are relatively independent of a variation of inductance of the input filter as long as this value is the same for the three lines. Indeed, since the current distortion model is based on the stator flux ripple for the different PWM sequences, the inductance value does not impact their order. The switching loss model will not depend on the input filter parameters. Thus the only effect of the variation of the inductance value is the same as a modification of the weighting factor β of (2), so it leads to a slightly different trade-off as opposed to the one that the user has defined.

IV. SIMULATION RESULTS

In order to show the effectiveness of the proposed PH-PWM technique, the system which corresponds to the VOC controlled AFE-rectifier, presented in Fig. 2, will be simulated. The resulting electrical signals will be compared to the ones issued from the same VOC controlled AFE-rectifier using two other PWM techniques: the CSVPWM technique and the BCPWM technique. This simulation study will be performed for three different cases, corresponding to three user specifications. In the first considered specification, the user just wants to reduce Fig. 7.

Algorithm of the predictive algorithm that defines the PWM sequence to be used in the PH-PWM technique, with Σ = {0127, 012, 721, 0121, 7212, 1012, 2721}.

the current distortion. In the second specification, the user prioritizes the switching losses. In the last specification, the user wants to achieve a trade-off between the current distortion and the switching losses.

The complete system shown in Fig. 2 is modeled in Matlab/Simulink using the SimPowerSystem toolbox for the electrical elements. The grid is modeled as ideal three-phase voltages, whose values are set to represent the European grid. The line inductances are modeled with their parasitic resistances. The parameters are given in Table I. The resistive load is set to consume a nominal power of 4kW at a nominal DC bus voltage of 670V. All the physical parts are modeled with an ode23tb variable step-solver.

From a control point of view, the control loops of the VOC and the predictive algorithm of the PH-PWM technique are implemented with a sampling frequency, F s , fixed at 3kHz. The PWM sequences are created with a frequency of 2.25MHz, offering a decimation of 250 points per PWM period for the BCPWM sequences.

A. Specification 1: reduction of the current distortion

In order to fulfill this specification, the cost function defined in ( 2) is modified as ( 9):

g = ∆I p SEQ (k + 1) (9)
As the input voltage is set to the fixed grid voltage value given in Table I, the impact of the DC bus voltage level and the modulation indexes is analyzed. The reference of V DC is set to different values from 600V to 1000V. In this case, the resistive load is adapted according to the operating conditions in order to consume the nominal power.

For each considered operating point, VOC is simulated using the PH-PWM technique, the CSVPWM technique and the 30 o clamp, which is the BCPWM technique offering the lowest current distortion. In this last technique, the change of zero configurations used is made at the middle of every sector, so that each phase is clamped in the middle 30 o duration in every quarter cycle of the fundamental [START_REF] Narayanan | Advanced bus-clamping pwm techniquesbased on space vector approach[END_REF]. To quantify the results, the RMS value of the current distortion over several periods of the fundamental is calculated according to [START_REF] Leon | The essential role and the continuous evolution of modulation techniques for voltage-source inverters in the past, present, and future power electronics[END_REF]:

∆I RMS = 1 N s Ns i=1 (di a ) 2 (10)
Here N s is the number of samples (1.10 6 samples), di a is the instantaneous current distortion of the first line current i a , and is defined as the difference between the instantaneous current i a and its fundamental.

The simulated results are given in Fig. 8 according to the voltage reference. For a low DC bus voltage, the modulation index is high, and the 30 o clamp therefore gives less current distortion. As the DC bus voltage increases, the modulation index drops, and the CSVPWM technique becomes more interesting with regard to the current distortion. For all the conditions, the PH-PWM technique demonstrates the lowest current distortion.

B. Specification 2: the reduction of the switching losses

In this specification, the user focuses on the switching losses of the converter. This means that the cost function described in (2) becomes:

g = P p SEQ (k + 1) (11)
The performances of the hybrid PWM techniques developed in literature regarding the switching losses are highly dependent on the phase lag between the three-phase currents and the threephase voltages. Therefore, in order to quantify the performances of the PH-PWM technique compared with the other PWM methods, the DC bus voltage is set to its nominal value 670V. The q-axis current reference, and thereby the reactive power, varies in order to change the phase lag between the three-phase voltages and the resultant three-phase currents.

The simulation results obtained with the PH-PWM technique are compared with respectively the ones with the CSVPWM technique and with those of the continual BCPWM techniques. The continual BCPWM techniques lead to the clamping of every phase continually for a 60 o duration in every half cycle of the fundamental. The angle at which the change between the two zero configurations is made in the sectors, noted γ, can vary from 0 o and 60 o , and it shifts the clamping duration on the half cycle of the fundamental, resulting in different continual BCPWM techniques. These achieve the lowest switching losses among the BCPWM techniques [START_REF] Narayanan | Advanced bus-clamping pwm techniquesbased on space vector approach[END_REF]. The common 60 o clamp, for example, has a γ of 30 o , leading to a clamping of each phase in the middle of every half cycle of the fundamental, and thus to the lowest switching losses at unity power factor. Fig. 9 presents the simulated switching losses normalized by the switching losses obtained with the CSVPWM technique. In this plot, the dotted lines represent the raw simulation data and the solid lines correspond to the resulting polynomial curve fitting. As can be seen, the switching losses with the continual BCPWM techniques have a local minimum at a phase lag of -30 o , 0 o or 30 o depending of the value of γ. The proposed PH-PWM technique demonstrates a better reduction of the switching losses independently of the phase lag. It leads to

C. Specification 3: the trade-off between the current distortion and the switching losses

When the user wants to make a trade-off between the current distortion and the switching losses, (2) has to be implemented as the cost function, and the user has to choose the weighting factor β. To show the influence of β, the simulated normalized switching losses and the simulated normalized current distortion obtained with the PH-PWM technique on the nominal operating point are given in Fig. 10. Here, β is varied from 0 to 0.21, and the CSVPWM technique serves as a reference. As can be seen, an increase in β leads to a decrease of the switching losses and an increase of the current distortion. The resultant values of the switching losses and current distortion stabilize for higher values of β and converge in a slower manner to the values obtained for β = ∞. The distortions on the switching losses presented in Fig. 10 are due to the fact that the switching between two PWM sequences is not taken into account, leading to a difference between the estimated switching losses and their real counterparts.

According to the latter curves and for the nominal operating point, an appropriate trade-off can be obtained by fixing the weighting factor β to 0.039. This enables a 12.7% reduction of the switching losses, and still 10% less current distortion than the CSVPWM technique. Once the value of β is set, the AFE-rectifier controlled by VOC using the resulting PH-PWM technique is simulated for a change in the load from its nominal value to half of its nominal value. The simulated i a , the simulated switching losses and the simulated V DC are given in Fig. 11 and are compared to the ones obtained with the CSVPWM technique. As can be clearly seen in Fig. 11, the PH-PWM technique enables a reduction of both the current distortion and the switching losses in comparison with the CSVPWM technique without impacting the DC bus voltage. Both PWM techniques lead to the same DC bus voltage (Fig. 11). It has to be noted that the shape of the curves presented in Fig. 10 depends slightly on the working point, leading to a variation of the gains obtained with PH-PWM. However, this effect can be countered by an on-line variation of the weighting factor β.

According to Figs. 8-11, the simulation results presented in this section make it clear that the use of the PH-PWM technique enables an increase in performances of the controlled AFE rectifier. It shows the ability of the proposed PH-PWM technique to reduce both the current distortion and the switching losses in this grid connected device. It also demonstrates the adaptability of the proposed design.

V. EXPERIMENTAL RESULTS

A set of experiments has been realized on a laboratory test bench. It is supplied by the grid through an autotransformer with a fixed reduction ratio of 1/4 for safety reasons. As both the current distortion and the switching losses are proportional to the DC bus voltage, it is assumed that if the experimental results validate the simulation results, an increase in the DC bus voltage can only benefit the proposed design. The output of the autotransformer is linked to a set of three inductances connected to the AC side of an Arcel 17kW three-phase twolevels converter. Its parameters are given in Table I.

From an implementation point of view, the VOC and the predictive algorithm of the PH-PWM technique are implemented on a dSPACE DS1006 with a sampling frequency F s of 3kHz. The creation of the PWM sequence, the addition of the deadtime (3µs) and the PWM sequence selector are implemented on a dSPACE DS5203 FPGA board. The choice of the PWM sequence is communicated at each T s at the same time as V ref (k) between the two boards. To ensure the acquisition of the many electrical signals at a proper time independently of the used PWM sequence, the PWM period, T pwm , is set to 2.T s , leading to a PWM frequency of 6kHz for the CSVPWM sequence and for the special BCPWM sequences, and of 9kHz for the BCPWM sequences. The clock frequency of the FPGA is fixed on the DS5203 at 10MHz, enabling over a thousand points per PWM period and thus a high resolution.

The tests on a VOC-controlled AFE with the PH-PWM technique are performed for specification 1 and specification 3. The studied working points are adapted in order to keep the same modulation indexes as in the simulation section.

A. Specification 1: the reduction of the current distortion Nevertheless, the obtained experimental results prove that the proposed PH-PWM technique is able to reduce the current distortion when ( 9) is used as the cost function.

The spectral decomposition of the current distortion obtained in experimentation for a DC bus voltage of 150V, 190V and 250V is given in Fig. 13. It can be seen that in the higher frequency range, the PH-PWM technique presents lower harmonic peaks than the two other techniques regardless of the studied operating point. These peaks are spread over the two PWM frequencies, F pwm1 and F pwm2 , defined in Table I, since all the possible PWM sequences are used. In the lower frequency range, the spectral decompositions of the line current present significant harmonic peaks for all the PWM techniques and all the DC bus voltages. They are mostly due to the harmonic distortions of the voltage grid that are not completely canceled by the decoupling in VOC. These current harmonics result in a THD value calculated for the first 30 harmonics, varying between 4.7% and 6.7%. Throughout, there is no correlation between the use of a specific PWM technique and the minimization of the THD for the first 30 harmonics. Thus, the proposed PH-PWM technique enables a reduction of the current distortion in the higher frequency range without significantly impacting the lower frequency range.

B. Specification 3: the trade-off between the reduction of the current distortion and the switching losses

To validate the trade-off ability of the PH-PWM technique as well as its capacity to reduce the switching losses, the DC bus voltage is set to 160V and the resistive load is adapted in order to consume 1kW. Here, (2) is used as the cost function. To quantify the resulting reductions of switching losses, the temperature variation on the converter using the PH-PWM technique is measured with a FLUKE TI9 thermal camera and normalized with the one obtained with the CSVPWM. The use of a thermal camera makes it possible to avoid the installation of a temperature sensor directly on the converter used in the laboratory, and still offers the required precision. Furthermore, it delivers a global overview of the temperature of the converter. Fig. 14 presents the normalized temperature variation and the current distortion versus the weighting factor β. The results obtained with the CSVPWM technique are given as a reference. The figure proves the predicted behavior: an increase in β induces a decrease of the temperature variation for the converter and an increase of the current distortion. The maximal gain obtained with regard to the temperature variation is about 8.21% and involves both the conduction and the switching losses for the converter. Fig. 15 shows the temperature increase measured for a test of two hours for the PH-PWM technique when β is very large and for the CSVPWM technique. The figure displays a reduced overall temperature increase for the PH-PWM technique in comparison with its CSVPWM counterpart. According to Fig. 14 and to the operating point, fixing β in the cost function (2) at 0.075 enables a reduction of 5% of the temperature variation for the converter for a small increase of the current distortion of 0.02A in comparison with CSVPWM. The measured i a resulting from this operating point is given in Fig. 16 for a β of 0.075, and shows the closed-loop behavior of the complete VOC controlled AFE rectifier. One can also decide to keep the same current distortion as with the CSVPWM by setting β at 0.0083, leading to a temperature increase that is reduced by 2.55%.

Therefore, both the reductions with regard to the current distortion and the switching losses as well as the trade-off ability of the PH-PWM technique are validated by experimental results. Furthermore, in the proposed technique, the weighting factor β can be tuned on-line by a supervisor, in order to more accurately fit the working conditions.

VI. CONCLUSION

This paper describes the integration of a PH-PWM technique in a VOC to control an AFE-rectifier. The method selects the appropriate PWM sequence on-line according to the operating point with the help of a predictive algorithm applied at the level of PWM generation. The effectiveness of the proposed PH-PWM technique has been validated both in simulation and in experimentation, and was found to enable larger reductions of both the switching losses and the current distortions in comparison with the conventional PWM techniques. Furthermore, the trade-off between the current distortion and the switching losses can be adapted by fixing a weighting factor. This weighting factor can also be varied on-line, enabling us to increase the range of performance improvements that are attainable with the proposed PH-PWM. Consequently the resulting PH-PWM technique offers increased performances in comparison with existing PWM generators. The proposed PH-PWM technique can be associated with other PWM based controllers, such as a Predictive Direct Power Controller, to improve the performance of an AFE rectifier both with regard to power control and modulation. This association enables a fixed switching frequency as well as a lower computational load in comparison with the direct control methods. The PH-PWM technique can be extended to enable a reduction of other parasitic phenomena, such as the common-mode-voltage, by taking into account their models in the cost function.

Fig. 1 .

 1 Fig. 1. Functional scheme of an AFE based on a three-leg two-level converter.

Fig. 2 .

 2 Fig. 2. Functional scheme of the complete VOC of the AFE rectifier with the proposed Predictive Hybrid PWM technique.

Fig. 3 .

 3 Fig. 3. Functional scheme of the proposed Predictive-PWM Technique.

Fig. 4 .

 4 Fig. 4. Example of the application of a voltage reference on the load in the normalized stationary reference frame.

Fig. 5 .

 5 Fig. 5. Evolution of ∆v and Ψ between k and k + 1 for the PWM sequence 0127.

Fig. 6 .

 6 Fig. 6. RMS values of the current distortion for different PWM sequences with on the left side v ref =0.2, on the middle v ref =0.6 and on the right side v ref =0.9.

Fig. 8 .

 8 Fig. 8. Simulated RMS values of the current distortion for the three considered PWM techniques.

Fig. 9 .

 9 Fig. 9. Normalized switching losses obtained in simulation for the considered PWM techniques vs the phase lag between the current and the voltage systems.

Fig. 10 .

 10 Fig. 10. Normalized switching losses and normalized current distortion for the PH-PWM technique for different values of β.

Fig. 11 .

 11 Fig. 11. Simulated waveforms of line current, ia, switching losses, P , and DC bus voltage, V DC , for a β = 0.039.

Fig. 12

 12 Fig. 12 presents the experimental RMS values of the current distortion calculated with (10) when (9) is used as a cost function for the PH-PWM technique. The DC bus voltage is set between 150V to 250V, and the resistive load consumes 1kW. Due to the low DC-bus voltage values, the current distortions as well as the resulting gains obtained with the proposed PH-PWM technique in comparison to the two other PWM techniques presented in Fig. 12 are lower than the ones obtained in simulation. However, if the DC bus voltages are normalized with respectively 1000V for the simulation and 250V for the experimentation, the normalized ranges where the CSVPWM technique and the 30 o clamp demonstrate better results are mostly respected when compared with the simulation results. Furthermore, when the gains obtained with the proposed PH-PWM technique are expressed in percent of the RMS values of the current distortion of the other techniques, comparable values in simulation and in experimentation are achieved.Nevertheless, the obtained experimental results prove that the proposed PH-PWM technique is able to reduce the current distortion when (9) is used as the cost function.The spectral decomposition of the current distortion obtained in experimentation for a DC bus voltage of 150V, 190V and 250V is given in Fig.13. It can be seen that in the higher frequency range, the PH-PWM technique presents lower harmonic peaks than the two other techniques regardless of the studied operating point. These peaks are spread over the two PWM frequencies, F pwm1 and F pwm2 , defined in TableI, since all the possible PWM sequences are used. In the lower frequency range, the spectral decompositions of the line current present significant harmonic peaks for all the PWM

Fig. 12 .

 12 Fig. 12. Experimental RMS values of the current distortion for the three considered PWM techniques.

Fig. 13 .

 13 Fig. 13. Experimental spectral decomposition of the line current for the three PWM techniques for a DC bus voltage of 150V, 190V and 250V, respectively.

Fig. 14 .

 14 Fig. 14. Evolution of the temperature variation on the converter and of the current distortion vs β for the PH-PWM technique (experimental results).

Fig. 15 .

 15 Fig. 15. Temperature increase in degrees Celsius measured for the converter for the CSVPWM technique and for the PH-PWM technique.

Fig. 16 .

 16 Fig. 16. Measured ia for the considered working point and for the PH-PWM technique with β = 0.075.

ACKNOWLEDGMENT

As a part of the ELEXC FUI project, the authors have to be thankful for the financial support of the French government. The authors also would like to thank the industrial partners as Volvo CE and Bonfiglioli for the sharing of knowledge and data.


B Lihoreau

B Gauvreau

T Penelon

I Calmet

M Bérengier

Ph Blanc-Benon
email: philippe.blanc-benon@ec-lyon.fr

Outdoor sound propagation modelling in complex environments : A new PE code coupled with a micrometeorological code

HAL is

Introduction

In complex environments the modelling of outdoor sound propagation implies to take into account the mixed influence of ground characteristics (topography, obstacles, impedance, etc.) and atmospheric conditions (refraction and turbulence). We have developed a new PE code coupled with a micrometeorological code in order to calculate the sound propagation above a non flat ground for realistic outdoor situations. Numerical resolution have been developed using the paraxial approximation of the wave equation in bidimensionnal configurations with a split-step Padé marching scheme. Our code can deal with different boundary conditions like the introduction of impedance jumps, thin screens or complex topography. Therefore, predicting long-range sound propagation over a non-urban site with complex propagation media requires the knowledge of micrometeorological fields in the lower part of the atmospheric boundary layer. Thus our modelling is coupled with a dedicated micrometeorological code (SUBMESO) which simulates wind and temperature fields over moderately complex terrain with high resolution. Its output data are used as input data for our PE code through a suited routine.

The SUBMESO atmospheric Code

The SUBMESO atmospheric model is derived from the ARPS model [START_REF] Xue | Advanced Regional Prediction System ARPS User's guide. Version 3.0 " Center for Analysis and Prediction of Storms[END_REF]. SUBMESO is a 3D non-hydrostatic compressible model suited to the study of atmospheric flows at sub-mesoscales. The equations are written in the 'terrain-following' coordinate system. An option for stretching the mesh vertically is available. Second-order accurate finite difference schemes are used to evaluate the derivatives. The solution is advanced in time using a time-splitting method [START_REF] Klemp | The simulation of three-dimensional convective storm dynamics[END_REF] according to an explicit scheme. The simulations are performed using Large-Eddy Simulation, which gives access to turbulence statistics. The sub-grid fluxes are evaluated with the model of Smagorinsky [START_REF] Smagorinsky | General circulation experiments with the primitive equations: I. The basic experiment[END_REF] modified by Lilly [START_REF] Lilly | The representation of small-scale turbulence in numerical simulation experiments[END_REF]. A simplified version of the grid-nesting module AGRIF [START_REF] Blayo | Adaptive mesh refinement for finite-difference ocean models : first experiments[END_REF] was recently coupled with SUBMESO in order to locally increase horizontal resolution at lower cost and introduce the large scale features in the flow prediction at high resolution in a limited-area domain. Submeso code provides wind velocity in the 3 directions as well as the temperature at each point of the mesh (50*50*50 m).

The Padé (1,1) Acoustic Code

We consider the two-dimensional propagation of a point source located at x = 0 and z = h s where x is the direction of propagation and z is the vertical axis. The acoustic code is based on a parabolic equation (PE) solved through a Padé (1,1) method. The PE used is derived from the exact wave equation in a uniform moving media when in the conventional approach the real moving atmosphere is replaced by a hypothetical motionless medium with a effective sound speed [START_REF] Dallois | A wide angle parabolic equation for sound waves in moving media[END_REF]. Introducing the complex amplitude of the sound field φ(r), so that p(r) = φ(r)e ikx , the PE takes the general following form:

F[1, ∂ ∂z , ∂ 2 ∂z 2 ] ∂φ(r) ∂x = G[1, ∂ ∂z , ∂ 2 ∂z 2 , ∂ 3 ∂z 3 ]φ(r), (1)
where F and G represent operators including first, second and third order z-partial derivatives. This equation is discretized on a uniform mesh (i∆x, j∆z) using a standard finite difference method. z-derivatives are evaluated with centered difference approximations, and Crank-Nicholson scheme is implemented as a marching algorithm. In our computations, the ground is modelled with finite complex impedances calculated using the one parameter formula of Delany-Bazley [START_REF] Delany | Acoustical properties of fibrous absorbent materials[END_REF]. Reflexions at the top of the numerical grid are controlled by introducing a thin artificial absorption layer in the upper part of the computation domain. The non flat ground is treated as a succession of flat domains [START_REF] Blairon | Outdoor sound propagation in complex environment: experimental validation of a pe approach[END_REF]. After each flat domain the coordinate system (x, z) is rotated so that the x axis stays parallel to the ground. The calculation above each

Validation

The numerical predictions are quantitatively compared to numerical, analytical and experimental results already published for gradually more complex situations: homogeneous, heterogeneous and/or screened ground [START_REF] Craddock | Sound propagation over a surface with varying impedance: A parabolic equation approach[END_REF][START_REF] Rasmussen | The insertion loss of screens under the influence of wind[END_REF], for a homogeneous, stratified and/or turbulent atmosphere [START_REF] Galindo | Approximations in the PE method. Phase and level errors in a downward refracting atmosphere[END_REF][START_REF] Gauvreau | Traffic noise prediction with the parabolic method: Validation of a split-step Padé approach in complex environments[END_REF]. Concerning non flat ground, the model has been validated through a comparison with results obtained from a method using conformal mapping [START_REF] Blairon | Outdoor sound propagation in complex environment: experimental validation of a pe approach[END_REF].

Comparative results show very good agreement for frequencies from 100 Hz to 5 kHz.

Conclusion

We have developed a new numerical code for sound propagation including all most common complex situations. This acoustic code is coupled with a micrometeorological code in order to have an accurate description of the atmospheric conditions. Our numerical results will be further compared with acoustical and meteorological measurements performed on an outdoor site in a complex environment (mixed ground, non flat terrain, stratified and turbulent atmosphere).

Figure 1 :

 1 Figure 1: Definition of the computational domains.

  The Padé (1,1) PE predictions are also qualitatively validated through 2D mapping. For example, figure (2) represents sound pressure level relative to a reference microphone localized close to the source. The sound source elevation is 0.1 m, the frequency is 1 kHz. The mean vertical sound speed profiles are logarithmically shaped: c(z) = c 0 + aln(z/z 0 ) where z 0 = 0.1m is the roughness parameter and a = 2m/s the refraction parameter. The air flow resistivity of the ground turns rapidly from 3 × 10 5 kN sm -4 (sealed concrete for instance) to 3 × 10 2 kN sm -4 (grass) 10 m from the source position. A 2 m high thin screen is placed at middle distance on the top of the embankment. This figure illustrates three kind of diffraction phenomena: one due to the mixed ground (near the source), another due to the slopes of the ground and the last due to the presence of the screen. One can observe an acoustic shadow zone behind the screen. In reality, the sound pressure level is enhanced by the atmospheric turbulence which scatters acoustic energy in this region.

Figure 2 :

 2 Figure 2: Relative sound pressure above an embankment with a screen in the case of downward refraction condition (parameters values: cf text).

CFA/DAGA'04, Strasbourg, 22-25/03/2004 domain

  needs an initial solution. The values of the initial solution for the domain n + 1 are obtained from the interpolated values of the pressure field of the domain n except for the first domain where the source is initialized by a Gaussian starter.


J Mouzay

N Piétri

I Couturier-Tamburelli

T Chiavassa

UV Irradiation of Benzene in N2 Matrix: A Relevant Study For Titan's Chemistry

Keywords: Titan, Benzene isomers, Fulvene

 Photochemistry at >230 nm of benzene in solid nitrogen were investigated by infrared spectroscopy  Fulvene, Dewar benzene, benzvalene, phenyl and benzyne radicals are observed as the photoproducts of benzene by >230 nm irradiation  Acetylene derivatives and substituted benzene are also observed after N2 matrix

Introduction

Titan, one of Saturn's moons, is the only body in the solar system having a thick atmosphere, mainly composed of molecular nitrogen and a small percentage of methane [START_REF] Waite | The Process of Tholin Formation in Titan's Upper Atmosphere[END_REF][START_REF] Lavvas | Aerosol growth in Titan's ionosphere[END_REF][START_REF] Liang | Photolytically Generated Aerosols in the Mesosphere and Thermosphere of Titan[END_REF]. A variety of organic chemicals (hydrocarbons and nitriles) are formed after photochemical dissociation of these molecules by solar UV photons or high energy particles, and the subsequent recombination of the resulting fragments [START_REF] Vinatier | Analysis of Cassini/CIRS limb spectra of Titan acquired during the nominal mission[END_REF][START_REF] Horst | Titan's atmosphere and climate[END_REF]. Among the different photochemical products, benzene has been discovered in Titan's upper atmosphere. The Ion Neutral Mass Spectrometer (INMS) and Cassini Plasma Spectrometer (CAPS) measured a benzene density profile with mixing ratios ranging from 10 -7 in the thermosphere [START_REF] Coustenis | Titan trace gaseous composition from CIRS at the end of the Cassini-Huygens prime mission[END_REF] to 10 -10 in the stratosphere [START_REF] Cui | Analysis of Titan's neutral upper atmosphere from Cassini Ion Neutral Mass Spectrometer measurements[END_REF] (Cassini Huygens mission). This decrease is consider as an indication of a high altitude source and a low altitude sink of this molecule due to photolysis [START_REF] Vuitton | Formation and distribution of benzene on Titan[END_REF]. Moreover, it is suspected that benzene molecules are at the origin of the organic haze layer [START_REF] Horst | Titan's atmosphere and climate[END_REF] that masks Titan's surface by initiating the formation of larger polycyclic aromatics hydrocarbons (PAHs) or polycyclic aromatic nitrogen heterocycles (PANHs) [START_REF] Waite | The Process of Tholin Formation in Titan's Upper Atmosphere[END_REF][START_REF] Delitsky | The photochemical products of benzene in Titan's upper atmosphere[END_REF]. The detection of large amount of benzene vapors [START_REF] Teanby | Active upper-atmosphere chemistry and dynamics from polar circulation reversal on Titan[END_REF] as well as several icy benzene-containing massive clouds [START_REF] Vinatier | Study of Titan's fall southern stratospheric polar cloud composition with Cassini/CIRS: Detection of benzene ice[END_REF][START_REF] Anderson | Organic Ices in Titan's Stratosphere[END_REF] at altitudes crossed by softer UV solar radiation has been reported. The fate of benzene in Titan's stratosphere before and after its condensation around 85 km is still unknown. To our knowledge, the role of benzene photolysis in the stratospheric production of aerosol particles has not yet been investigated experimentally. However, several experimental studies have identified its role in the composition of highest atmospheric layers. At benzene condensation altitude, only solar photons with >230 nm [START_REF] Gudipati | Photochemical activity of Titan's low-altitude condensed haze[END_REF][START_REF] Lavvas | Coupling photochemistry with haze formation in Titan's atmosphere, Part II: Results and validation with Cassini/Huygens data[END_REF][START_REF] Wilson | Current state of modeling the photochemistry of Titan's mutually dependent atmosphere and ionosphere[END_REF] can participate in the photochemistry, the shorter ones been stopped at higher altitude (with a photon flux ~ 10 7 photons.cm -2 .nm -1 .s -1 over an altitude range corresponding to the benzene condensation [START_REF] Gudipati | Photochemical activity of Titan's low-altitude condensed haze[END_REF]). Based on the UV absorption spectrum of benzene published by Dawes et al. [START_REF] Dawes | Vacuum ultraviolet photoabsorption spectroscopy of crystalline and amorphous benzene[END_REF] (2017), the study of the photochemistry at >230 nm is completely justified. Indeed, benzene possesses a vibronic structure associated with the 1 B2u ← 1 A1g transition around 255 nm, even if its cross section is 15 times less than the one located around 180 nm ( 1 E1u ← 1 A1g) and 6 times less than the corresponding to the 1 B1u ← 1 A1g band.

Benzene photo-reactivity can be experimentally reproduced with the help of matrix isolation studies in which benzene is trapped at low temperature in a rare gas matrix. In this environment, benzene molecules are isolated, which can simplify its photochemistry compared to a solid benzene ice. The benzene photochemical behavior in various matrices [START_REF] Johnstone | Matrix-controlled photochemistry of benzene and pyridine[END_REF][START_REF] Bai | Matrix isolation study of the dissociation and isomerization pathways of benzene following corona discharge excitation[END_REF][START_REF] Laboy | 193 nm excimer laser photochemistry of benzene in argon matrices[END_REF][START_REF] Ruiterkamp | Quantitative study of proton irradiation and UV photolysis of benzene in interstellar environments[END_REF][START_REF] Toh | UV Photochemistry of Benzene and Cyclohexadienyl Radical in Solid Parahydrogen[END_REF][START_REF] Lukianova | Radiation-Induced Transformations of C6 H6 Molecules in Solid Noble-Gas Matrices: Is Benzene Intrinsically Resistant in Condensed Media?[END_REF] (Ar, Xe, parahydrogen, halogens, CO, CO2, H2O, CCl4) and submitted to different sources of energy (UV at 193 nm [START_REF] Laboy | 193 nm excimer laser photochemistry of benzene in argon matrices[END_REF][START_REF] Toh | UV Photochemistry of Benzene and Cyclohexadienyl Radical in Solid Parahydrogen[END_REF] or 253 nm [START_REF] Johnstone | Matrix-controlled photochemistry of benzene and pyridine[END_REF][START_REF] Toh | UV Photochemistry of Benzene and Cyclohexadienyl Radical in Solid Parahydrogen[END_REF], Corona discharge [START_REF] Bai | Matrix isolation study of the dissociation and isomerization pathways of benzene following corona discharge excitation[END_REF] or X-rays [START_REF] Lukianova | Radiation-Induced Transformations of C6 H6 Molecules in Solid Noble-Gas Matrices: Is Benzene Intrinsically Resistant in Condensed Media?[END_REF]) has been largely investigated. These experiments have demonstrated that benzene photochemistry is wavelength and environment dependent [START_REF] Johnstone | Matrix-controlled photochemistry of benzene and pyridine[END_REF], resulting in different isomer production rates. However, argon matrices studies are the most numerous in the literature. Moreover, the photolysis performed at 253.7 nm of benzene trapped in argon matrices [START_REF] Johnstone | Matrix-controlled photochemistry of benzene and pyridine[END_REF] and in parahydrogen [START_REF] Toh | UV Photochemistry of Benzene and Cyclohexadienyl Radical in Solid Parahydrogen[END_REF], leads to the formation of three isomers: fulvene, benzvalene and Dewar benzene. Thus, experiments performed at low energy in N2 matrix have two goals. First, to evaluate the influence of N2 on benzene photolysis. Indeed, benzene absorption extends to the origin of its first singlet excited state S1 at 263 nm [START_REF] Parmenter | Radiative and Nonradiative Processes in Benzene[END_REF]. Deactivation of the excited electronic states leads to a transient highly excited state (C6H6*) which can be quenched by collisions with N2 [START_REF] Nakashima | Laser photolysis of benzene. V. Formation of hot benzene[END_REF]. Second, to provide data concerning the products formed during the matrix irradiation, and especially solid fulvene, to examine if they are stable when produced at low energy photons.

A third and more important reason to perform experiments in N2 matrix is that from all the aforementioned cryogenic studies, none of them resembles Titan's atmospheric conditions. Therefore, as N2 is the major component in Titan's atmosphere, nitrogen cryogenic matrices are powerful tools for simulating the photochemical activity of molecules present in Titan's atmosphere that can subsequently condense to form ices at lower altitudes, photo-processed, for which few solid-state experimental data are available. Eventually, matrix sublimation leads to benzene amorphous ice in which photoproducts are trapped and can be characterized in solid-state.

Their solid-state characterization is particularly important since the recent detection of icy benzene in the lower part of Titan's atmosphere. For all these reasons we decided to conduct a laboratory experiment to understand which products coming from the photochemistry of benzene can condense and contribute to the molecular diversity of the organic surface layer after the sedimentation process. Hence, these data are particularly interesting for the future Dragonfly mission.

In this study, we investigate the photolysis of benzene at >230 nm using solid nitrogen matrix to characterize the different photoproducts likely to be formed in Titan's stratosphere before benzene condensation, by comparison with previous experiments. We sublimate the nitrogen matrix in order to characterize the solid infrared spectrum of fulvene trapped in solid benzene, one of the photoproducts of benzene. In general, we would like to know if the photoproducts obtained during the photolysis in matrix could be formed during the direct photochemistry of the benzene ice that we will perform in a future work.

Experimental Details

Benzene (for HPLC, assay  99.9%, from Sigma-Aldrich) is purified by freeze-thaw cycles with the help of nitrogen baths. It is deposited from a glass-line on a copper surface, which temperature was controlled between 14K to 300K with a closed-cycle helium refrigerator and maintained using a model 21 CTI cold head cryostat, a resistive heater and a Lakeshore 331 temperature controller, within a high vacuum chamber (10 -8 mbar). The IR spectra are recorded in reflection-absorption mode in the mid-infrared region between 4000 and 600 cm -1 using a Fourier transform infrared spectrometer with DTGS detector [START_REF] Butscher | Formation mechanism of glycolaldehyde and ethylene glycol in astrophysical ices from HCO • and • CH 2 OH recombination: an experimental study[END_REF]. Each spectrum is averaged over 100 scans during the experiments, with a resolution of 0.5 cm -1 (matrix) or 1 cm -1 (solid), except for the background averaged over 300 scans with the same resolutions.

Photolysis experiments are performed using an Oriel 500W high-pressure mercury lamp (=200-2500 nm) with discrete Hg lines in the UV-Vis region between 200 and 600 nm, and very low irradiance at energies lower than 230 nm.

The gas mixtures (N2/benzene (500/1)) used for the matrix isolation experiments are prepared by standard manometric techniques. These mixtures are sprayed onto a copper plate cooled down to 14 K. The sample is warmed using a heated resistance at a temperature below the N2 desorption temperature (around 40K under our experimental conditions) in order to make the matrix more flexible and then at a higher temperature in order to sublime the nitrogen.

All the experiments described below are done in three steps: (i) photochemical products formation from >230 nm photolysis of benzene; (ii) N2 matrix annealing; (iii) N2 desorption at 40K.

For the solid experiment pure benzene was deposited at 16K and then warmed up to 40K with a heating rate of 0.5 K.min -1 . At this temperature the benzene ice is known to be in an amorphous phase [START_REF] Dawes | Vacuum ultraviolet photoabsorption spectroscopy of crystalline and amorphous benzene[END_REF].

Results

Infrared spectroscopy of benzene in nitrogen matrix at 14K

Figure 1 displays the infrared spectrum of benzene trapped in N2 matrix (1/500). All the values relative to the infrared absorption bands (wavenumbers and intensities) are listed in Table 1 and are compared to the work of Fredin and Nelander [START_REF] Fredin | On the structure of benzene halogen complexes: A matrix isolation study[END_REF] which is the most detailed published analysis. The most intense infrared absorption bands of benzene in a N2 matrix are located at 678.5 cm -1 and 1483.1 cm -1 assigned respectively to CH out-of-plane bending mode (4) and C=C stretching mode (13). The νCH stretching mode (ν12), typical of aromatic molecules, is located at 3044.4 cm - 1 . Less intense than the other fundamental modes, the δCH in-plane bending mode is found at 1038.8 cm -1 . Several intense combination modes are located in two different spectral regions. The first region is located in the CH stretching mode area with two bands at 3098.0 and 3077.3 cm -1 , respectively assigned to ν2 +ν13 + ν18 and ν13 + ν16. The other group includes the ν7 + ν19 mode at 1961.1 cm -1 and the ν11 + ν19 mode at 1816.9 cm -1 . A complete identification of benzene fundamental and combination modes of this work, along their respective wavenumbers and assignments are listed in Table 1 and compared to earlier published values [START_REF] Fredin | On the structure of benzene halogen complexes: A matrix isolation study[END_REF].

Irradiation of benzene in nitrogen matrix at 14 K

When matrix isolated benzene is submitted to radiation at >230 nm, we observe the decrease (30% after 3025 min of irradiation) in its infrared features along with the apparition of new absorption bands in different spectral regions. Figure 2 presents subtraction spectrum between the last irradiation time (3025 min) and the time before photolysis of the deposited matrix. The bands that grow during irradiation appear in positive and those that decrease (benzene ones), in negative. 2 and3. Peak attribution is based on previously published data [START_REF] Laboy | 193 nm excimer laser photochemistry of benzene in argon matrices[END_REF][START_REF] Toh | UV Photochemistry of Benzene and Cyclohexadienyl Radical in Solid Parahydrogen[END_REF][START_REF] Griffith | The vibrational spectra of Dewar benzene and benzvalene[END_REF][START_REF] Friderichsen | The Infrared Spectrum of the Matrix-Isolated Phenyl Radical[END_REF][START_REF] Radziszewski | Infrared Absorption Spectroscopy of the Phenyl Radical 2[END_REF][START_REF] Dunkin | Matrix photolysis of unsaturated cyclic anhydrides and the infrared spectrum of tetradeuteriobenzyne[END_REF] taking into account a reasonable shift due to the nitrogen matrix. Indeed, various rigid host matrix may trap a guest molecule in different local environments where these molecules may undergo slightly different external fields or geometrical constraints. Consequently, the frequencies of certain vibrationnal modes may be shifted, either through the influence of the varying external field on the electronic structure of a host molecule, or through an increase in a force constant when the atoms have to work against the rigid environment along some normal mode. So, depending on the type and size of the host material, or on charge transfer effect, this can lead to small frequency shift. So, Perchard et al. [START_REF] Perchard | Structures of HCI and HBr Polymers in Nitrogen Matrix Derived from Infrared and Raman Data: Comparison with Argon Matrix[END_REF] have shown that the shift could be up to 14 cm -1 between argon and nitrogen matrix.

For those bands with sufficient intensity, it is sometimes possible to correlate their evolution as a function of the irradiation time and to sort them into different groups, according to their behavior. This step allows to potentially confirm assignments. In general, dissociation and isomerization pathways are similar between the different matrices except if N2 quenches the photoreactivity as predicted in gas phase [START_REF] Delitsky | The photochemical products of benzene in Titan's upper atmosphere[END_REF].

Fulvene identification

Fulvene 1 is a well-known product of benzene photolysis and has been characterized previously isolated low temperature matrices [START_REF] Laboy | 193 nm excimer laser photochemistry of benzene in argon matrices[END_REF][START_REF] Toh | UV Photochemistry of Benzene and Cyclohexadienyl Radical in Solid Parahydrogen[END_REF][START_REF] Griffith | The vibrational spectra of Dewar benzene and benzvalene[END_REF]. Using literature values and results of theoretical calculation (B3LYP/6-311+G(d,p) [START_REF] Toh | UV Photochemistry of Benzene and Cyclohexadienyl Radical in Solid Parahydrogen[END_REF], absorption bands at 1486.4, 1343.6, 1080.7, 932.4, 894.0, 773.0 and 617.8 cm -1 are attributed to fulvene. Further confirmation of this assignment comes from the similar evolution of the most intense absorption bands (773 cm -1 as a function of 617,8 and 1343.6 cm -1 , correlation factor 0.99) pictured in figure S1). All these bands are well known and are in good agreement with those previously reported by Toh et al. [START_REF] Toh | UV Photochemistry of Benzene and Cyclohexadienyl Radical in Solid Parahydrogen[END_REF] in para hydrogen matrix and Griffith et al. [START_REF] Griffith | The vibrational spectra of Dewar benzene and benzvalene[END_REF] or Laboy at al. [START_REF] Laboy | 193 nm excimer laser photochemistry of benzene in argon matrices[END_REF] in argon matrix (Table 2). The evolution of the integrated area as a function of the irradiation time of the absorption band at 773 cm -1 assigned to fulvene is reported in Figure 3. It demonstrates that the amount of this isomer continues to increase throughout the duration of the photolysis. Nevertheless, comparison with literature spectra [START_REF] Laboy | 193 nm excimer laser photochemistry of benzene in argon matrices[END_REF][START_REF] Toh | UV Photochemistry of Benzene and Cyclohexadienyl Radical in Solid Parahydrogen[END_REF] for this isomeric species leads to the conclusion that only the most intense bands are observed in our experimental conditions (Table 2). Indeed, no absorption bands obtained by Laboy et al. [START_REF] Laboy | 193 nm excimer laser photochemistry of benzene in argon matrices[END_REF], Griffith et al. [START_REF] Griffith | The vibrational spectra of Dewar benzene and benzvalene[END_REF] or Toh et al. [START_REF] Toh | UV Photochemistry of Benzene and Cyclohexadienyl Radical in Solid Parahydrogen[END_REF] above 3000 cm -1 are observed. This is not surprising since these bands are the smallest in experiments performed both in Argon and parahydrogen matrix.

Identification of other products

Two groups of absorption bands increase then decrease during irradiation (Figure 3). The first one, composed of absorption bands at 3070.7, 1441,3, 1432,7, 1062.0, 1025.3, 975.6, 970.7 709.7 and 628,2 cm -1 , is assigned to the phenyl radical 2 based on previous works [START_REF] Friderichsen | The Infrared Spectrum of the Matrix-Isolated Phenyl Radical[END_REF][START_REF] Radziszewski | Infrared Absorption Spectroscopy of the Phenyl Radical 2[END_REF] (Table 3). The intensity of the 1025,3 cm -1 absorption band plots as a function of the one at 709.7 cm -1 , is presented in figure S2 as well as 3070.7 cm -1 as a function of 1025,3 cm -1 and 970,7 cm -1 as a function of 975,6 cm -1 (Supplementary material). The bands at 3070.7 and 970.7 cm -1 are too weak to be plotted as a function of the two others. All of the bands obtained in our study are the same as the most intense formed in an Ar matrix and reported by Radziszewski et al. [START_REF] Radziszewski | Infrared Absorption Spectroscopy of the Phenyl Radical 2[END_REF]. Only shifts of about 1 cm -1 , coming from the difference between the experimental conditions (N2 versus Ar), are observed. which would be structured because of matrix site. All the other bands obtained in the experiments developed in parahydrogen [START_REF] Toh | UV Photochemistry of Benzene and Cyclohexadienyl Radical in Solid Parahydrogen[END_REF] or argon matrix [START_REF] Griffith | The vibrational spectra of Dewar benzene and benzvalene[END_REF] are lower in intensity than the ones we get (Table 3). Although these five bands are observed in our experiment, their low intensities (preventing their correlation) do not allow us to conclude formally on the formation of this isomer in our experiment.

Since the obtaining of Dewar benzene and benzvalene is not certain in our experimental conditions, we will not discuss them in the rest of this paper.

Matrix annealing

The second step of our experiment is an annealing step, in which the matrix is heated to 30 K for 10 min and then cool down the system back to 14 K. Warming of the sample increases the diffusion coefficient of embedded species without desorbing the matrix host, allowing them to reorient or even migrate through the matrix.

In particular, radicals may be able to exit from their matrix cage during annealing and participate radical-radical recombination or radical-neutral addition elimination process [ 34 , 35 ]. These processes result in changes in the bands which facilitate their assignment. Annealing the irradiated sample result in changes in the difference infrared spectrum (Figure 4). The study is focused on the 3500-2800, 1700-1100 and 1200-600 cm -1 regions where most of the new absorption bands are obtained during the photolysis. With the exception of bands attributed to acetylene monomer, negative bands correspond to phenyl or benzyne radicals which are consumed during annealing through recombination or reaction with other species. Only few bands clearly increase during the matrix annealing at 30 K located at 3317, 3306, 3252, 3013, 652, 640 and 625 cm -1 (noted with an asterisk on Figure 4). These bands can come from the formation of dimers, trimers, or multimers of acetylene or acetylene derivatives. Indeed, the absorption bands which grow at 3252 and 625 cm -1 are attributed to an acetylene tetramer based on literature reports of the annealing of acetylene trapped in argon matrix [START_REF] Golovkin | Acetylene associates (C2H2)n (n=2-4). IR spectra in argon matrices and quantum-chemical calculations[END_REF]. Based on the work of Karir and Viswanathan [START_REF] Karir | Phenylacetylene-water complex: Is it n⋯σ or H⋯π in the matrix?[END_REF], the bands at 3317, 3306, 652 and 640 cm -1 could be assigned to phenylacetylene.

Friderichsen et al. [START_REF] Friderichsen | The Infrared Spectrum of the Matrix-Isolated Phenyl Radical[END_REF] have shown that phenyl radicals can recombine in a cryogenic argon matrix during an annealing performed up to 45 K, to form diphenyl. This molecule has two particularly intense absorption bands at 738 and 699 cm -1 , based on spectroscopic data from Martin-Drumel et al. [START_REF] Martin-Drumel | Low-energy vibrational spectra of flexible diphenyl molecules: biphenyl, diphenylmethane, bibenzyl and 2-, 3-and 4-phenyltoluene[END_REF] However, none of these bands are observed on the infrared spectrum obtained after our annealing experiment to 30 K. Sufficient mobility of phenyl radicals is probably not obtained to form biphenyl before our matrix sublimed at 45 K. In order to confirm our assignments and investigate the IR spectra of these products that could be obtained in an amorphous state, the solid gas matrix was evaporated by carefully heating the matrix above 30 K. This step allows in particular the identification of the solid infrared spectrum of fulvene trapped in solid benzene. The spectrum obtained at 40 K just after the N2 sublimation is presented in Figure 5b and compared to the spectrum obtained at 14 K at the end of the irradiation (Figure 5a). Warm-up of the matrix above 40 K induces spectral changes (widening and frequency shift of all the absorption bands as previously observed in matrix-annealed experiments [START_REF] Couturier-Tamburelli | A Stable Ketene-Pyridine Prereactive Intermediate: Experimental and Theoretical Identifications of the C 3 O •••Pyridine Complex[END_REF][START_REF] Guennoun | Reaction Path of UV Photolysis of Matrix Isolated Acetyl Cyanide: Formation and Identification of Ketenes, Zwitterion, and Keteneimine Intermediates[END_REF][START_REF] Sessouma | From Molecular Complexes to Zwitterions and Final Products. Reactions between C 3 O and Amines[END_REF] without appearance of any new bands). The infrared spectrum obtained after sublimation (Figure 5a) is dominated by benzene ice signatures. By comparing a spectrum of benzene ice formed by vapor condensation of pure C6H6 at 40 K (Figure 5c) with this spectrum, photoproducts which remain in the solid phase can be seen more easily (Figure 5b) Despite the disappearance of several bands during the warming-up, numerous other bands, previously assigned to different benzene photoproducts (Table 4), are still present in the amorphous ice at 40 K, which makes their solid-state assignment possible.

After sublimation of the N2 matrix at 40 K, we observe the total loss of bands characteristics of the phenyl and benzyne radicals whereas fulvene bands are only shifted by 2 to 6 cm -1 between the cryogenic matrix and the solid phase. The solid absorption bands remaining at 1339, 1076, 939, 896, 778 and 622 cm -1 are assigned for the first time to this isomer in solid phase surrounded by benzene ice.

From the start of the irradiated matrix heating until after N2 sublimation temperature (40 K), the features of isolated monosubstituted acetylene (3314.2 cm -1 ) or acetylene (3275,4, 3268.0 and 3257.0 cm -1 ) disappear and bands around 3270 cm -1 and 3231 cm -1 increase in intensity because of the sublimation of the matrix. Strazzula and Baratta [START_REF] Strazzula | Laboratory study of the IR spectrum of ion-irradiated frozen benzene[END_REF] assigned the increasing bands to solid monosubtituted acetylene and C2H2 aggregates. The two intense bands at 753 and 854 cm -1 remain at 40 K and correspond to substituted benzene as previously observed by Strazzula and Baratta [START_REF] Strazzula | Laboratory study of the IR spectrum of ion-irradiated frozen benzene[END_REF].

Discussion

We have studied the photolysis of benzene at > 230 nm in N2 cryogenic matrix in order to try to understand (i) what kind of photo-chemical processes take place in in Titan's stratosphere when vapour benzene is submitted to soft energy photons, (ii) if nitrogen plays a role in the photolysis and (iii) if the products formed are stable under these conditions. Our studies show the formation of the benzene isomer fulvene, as well as phenyl and benzyne radicals, monosubstitued acetylene and substituted benzene (Figure 6). Since all the products formed have already been obtained in previous experiments, the nitrogen matrix does not promote formation of new products although it does affect the relative amounts of formed products as already observed in previous experiments [START_REF] Johnstone | Matrix-controlled photochemistry of benzene and pyridine[END_REF][START_REF] Toh | UV Photochemistry of Benzene and Cyclohexadienyl Radical in Solid Parahydrogen[END_REF][START_REF] Griffith | The vibrational spectra of Dewar benzene and benzvalene[END_REF]. As illustrated in Figure 3, acetylene, monosubstitued acetylene and substituted benzene are formed during all the photolysis experiment in a relative great amount. This result indicates that they are stable when produced by low energy photons in the presence of N2 and benzene.

As postulated by Yokoyama et al. when benzene is excited to S1 (which is permit at >230 nm), H2 and CH3 eliminations occur from hot benzene. Some of C6H4, produced absorb another photon and dissociate to C4H2 and C2H2. On another hand some C6H5 produced can absorb another photon and dissociate to C4H3 and C2H2 as illustrated in the reactions below.

C6H6 → C6H6 *(hot benzene) → C6H4 + H2 C6H4 → C4H2 + C2H2

Moreover, some • C6H5 produced can absorb another photon and dissociate to C4H3 and C2H2

• C6H5 (phenyl) → • C6H5 (linear) → C4H3 + C2H2

In the study of Johnstone and Sodeau [START_REF] Johnstone | Matrix-controlled photochemistry of benzene and pyridine[END_REF] performed in argon matrix at = 253.7 nm, benzvalene is the major photo-product. In our case in nitrogen matrix at >230 nm, fulvene is the most abundant isomer. This result is not surprising since in the same study the authors had repeated the experiment in a xenon matrix in order to investigate any "heavy atom effect" on the observed photochemistry, and no photo-products were observed. Moreover, even if benzvalene appeared first from S1 state, it was reported that in presence of N2 it is photolyzed in fulvene and benzene [START_REF] Kaplan | Photolysis of Benzene Vapor. Benzvalene Formation at Wavelength 2537-2370 Å[END_REF][START_REF] Harman | Photochemistry of Benzene Isomers. 2. Benzvalene and Dewar Benzene[END_REF]. While all these matrices (Ar, N2 and Xe) crystallise in face-centered cubic lattice, the cage parameters are different and increase from Argon to Xenon (5.31 Å (Ar), 5,66 Å (N2), 6,13 Å (Xe)) [START_REF] Jodl | Chemistry and Physics of Matrix-Isolated Species[END_REF][START_REF] Meyer | Low Temperature Spectroscopy[END_REF]. Therefore, the nature of the matrix has inevitably a significant impact on the quantity of the formed products. The wider the matrix is, the less it promotes isomer formation. [START_REF] Johnstone | Matrix-controlled photochemistry of benzene and pyridine[END_REF] Figure 6: Main products obtained during the photolysis of benzene at > 230 nm As shown in Figure 3, fulvene absorption bands increase until the end of the photolysis step in our experiment indicating that this isomer is a final product and it is most probably formed from the S1 singlet excites state of benzene according to the reaction below [START_REF] Johnstone | Matrix-controlled photochemistry of benzene and pyridine[END_REF][START_REF] Toh | UV Photochemistry of Benzene and Cyclohexadienyl Radical in Solid Parahydrogen[END_REF][START_REF] Lukianova | Radiation-Induced Transformations of C6 H6 Molecules in Solid Noble-Gas Matrices: Is Benzene Intrinsically Resistant in Condensed Media?[END_REF].

C6H6 * (S1) → Fulvene

On the other hand, phenyl radical could be considered as a reactional intermediate since it starts to slowly decrease after a little more than 500 min of photolysis (Figure 3), reflecting that it is produced as quickly as it is consumed. Thus, the phenyl radical can react with benzene or photolysis products leading to the formation of more complex molecules such as substituted benzene. This reaction has already been observed by Friderichsen et al. [START_REF] Friderichsen | The Infrared Spectrum of the Matrix-Isolated Phenyl Radical[END_REF] when performing soft and short warm-up of the matrix up to 45 K. By significantly increasing the diffusion rate of phenyl radicals, the formation of substituted benzene is promoted. As mentioned in the paper of Friedrichs et al. [START_REF] Friedrichs | The Products of the Reactions of o-Benzyne with Ethene, Propene, and Acetylene: A Combined Mass Spectrometric and Quantum Chemical Study[END_REF] the bimolecular reaction of the phenyl radical with acetylene could yield to the phenylacetylene (C6H5C2H) formation according to the reaction written below.

• C6H5 + C2H2 → C6H5C2H + H • Similarly, benzyne reaches a plateau after 800 min of photolysis, suggesting that it also reacts as quickly as it is formed. Moreover, the disappearance of benzyne upon sublimation of N2 could be explained by the recombination of two radicals to form biphenylene. The infrared spectrum calculated by Pauzat and Ellinger [START_REF] Pauzat | The infrared signatures of non-regular PAHs[END_REF] (2002) indicates the most intense absorption band at 741 cm -1 (13.499 nm). Hence, the large and intense band observed at 753 cm -1 may be evidence of formation of a substituted benzene. On the other hand, Friedrishs et al. [START_REF] Friedrichs | The Products of the Reactions of o-Benzyne with Ethene, Propene, and Acetylene: A Combined Mass Spectrometric and Quantum Chemical Study[END_REF] put in evidence that the reaction between the o-benzyne and C2H2 could lead to the benzocyclobutadiene or phenylacetylene, two substituted benzenes.

Accordingly, the dissociation of vapour benzene may be a source of diverse volatile photoproducts in Titan's stratosphere. So far, no benzene isomers have been detected in Titan's atmosphere. As they come from the specific photochemistry of benzene and the amount of photoproducts obtained in our photolysis experiment is low, the fact that they have not yet been detected on Titan makes sense. Condensation of benzene occurs near the tropopause where the temperature diminishes. It contributes to the formation of several kind of icy clouds : one in which benzene is predominantly mixed with hydrogen cyanide [START_REF] Anderson | Organic Ices in Titan's Stratosphere[END_REF] and another one, detected by Vinatier et al [START_REF] Vinatier | Study of Titan's fall southern stratospheric polar cloud composition with Cassini/CIRS: Detection of benzene ice[END_REF], at higher stratospheric altitudes (between 168 and 278 km), composed of benzene among other unassigned molecules. This shows the interest of the detection of new species in solid phase which could include products like monosubstituted acetylene, C2H2 aggregates and substituted benzene.

In order to determine if the photoproducts obtained during the photolysis in matrix could be formed during the direct photochemistry of the benzene ice, that we will perform in a future work, we have performed the nitrogen sublimation. The infrared spectrum obtained after this sublimation shows that fulvene is the only isomer observable in solid benzene under our experimental conditions, while others isomers are not detectable. Small amounts are probably still trapped in the solid benzene undetectable by infrared spectroscopy.

Conclusion

In this study, we have formed fulvene, phenyl and benzyne radicals and monosubtituted acetylene and substituted benzene by UV irradiation in nitrogen matrix at λ>230 nm. After N2 sublimation, we obtained the infrared signature of the fulvene isomer in benzene ice for the first time. Infrared band characterization of fulvene in the solid phase is very important since benzene ice has been detected in the low atmosphere of Titan. Submitted to long UV radiation, photoprocessing of this benzene cloud could result in the formation of benzene isomers in solid phase.

Figure 1 :

 1 Figure 1: Infrared spectrum of benzene trapped in nitrogen matrix at 14 K. The spectrum has been truncated in the middle in order to omit the gaseous CO2

Figure 2 :

 2 Figure 2: Subtraction spectrum between the last irradiation time (3025min) and before irradiation of benzene in N2 matrix performed at λ > 230 nm. Negative bands correspond to the benzene one and positive bands correspond to products formed during the experiment 1: fulvene. 2: phenyl radical. 3: benzyne. 4: substituted acetylene. 5: acetylene. 6: substituted benzene. 7: benzvalene. 8: Dewar benzene. The absorption bands, produced during the experiment, are listed in Table 2 and 3. Peak attribution

Figure 3 :

 3 Figure 3: Evolution of the integrated absorbance of fulvene, phenyl radical (top) and monosubstituted acetylene, substituted benzene and acetylene (bottom) with error bars, during the photolysis (λ>230 nm) of benzene in nitrogen matrix (1:500). The error bars correspond to the discrepancy of the different integration performed.

Figure 4 :

 4 Figure 4: Infrared spectrum of benzene/N2 after irradiation at 14 K (a) at 14 K after 30 K (b) and subtraction spectrum (c). * correspond to the products formed during the annealing. 2: phenyl radical. 3: benzyne radical

1 Figure 5 :

 15 Figure 5: Infrared spectra recorded during the warming-up performed at the end of the photolysis experiment (λ>230 nm) of benzene trapped in N2 matrix: (a) at 14 K after 30K, (b) at 40 K after N2 sublimation (c) benzene ice at 40K 1:fulvene. 4: substituted acetylene. 5: acetylene. 6: substituted benzene.

Table 1 : Experimental vibrational wavenumbers (cm -1 ) of benzene in solid nitrogen at K 145 and in solid phase at 40 K compared with the study of Fredin and Nelander [27] in nitrogen 146 matrix and in gas phase. 147 Int: Relative intensities of band: 148 Assignment Benzene in N2 matrix (this work) Benzene in N2 matrix[27]

 1

	Solid benzene	Benzene in
	40K	Gas
	(this work)	phase[27]

Table 2 : Experimental vibrational wavenumbers of fulvene in solid N2 compared with those in Ar matrix and solid parahydrogen Fulvene 1 Our Work Laboy et al.[19] Griffith et al. [29] Toh et al.[21] N2 Matrix (1/500) Int

 2

				Ar Matrix (1/250)	Int	Ar Matrix	Int	pH2	Int
				3157	0.071			3104.7	0.01
				3116	0.155	3104	w
						3088	m	3088.0	0.05
						3008	s	3007.6	0.03
				1857	0.097
				1853	0.233
		1486.4	0.12	1488 1486	0.422 0.352	1486	s	1486.1 1485.5	0.25 0.12
		1343.6	0.59	1342 1334	0.778 0.169	1342	s	1342.6	0.46
		1080.7	0.07	1080	0.288	1077	m	1078.5	0.09
		932.4	0.45	926	1.198	926	s	927.9	0.74
				908	0.166	907	m	907.5	0.06
		894.0	0.14	894	0.427	894	m	895.3	0.16
		773.0	1	770	1.626	769	s	779.0	1
		617.8	0.98	615	1.293	613	vs	616.4	0.58
	206	.
	207

Table 3 : Experimental vibrational wavenumbers of Benzvalene 7, Dewar benzene 8, Phenyl 2 and Benzyne 3 in solid N2 compared with those in Ar matrix, nitrogen matrix and solid parahydrogen

 3

Table 4 : Experimental wavenumbers (cm -1 ) of main photoproducts of benzene photolysis performed in Nitrogen matrix and in solid phase (after N2 sublimation)

 4

	Band (cm -1 )
	N2	solid Assignment
	matrix

Acknowledgments

This work was supported by the Programme National de Planétologie (PNP).

The second group composed of four other bands (1447.9, 1054.0, 848.0 and 740.6, cm -1 ) present the same behavior during irradiation (two panels in figure S3 with 848.0 cm -1 plotted as a function of the other features (740.6 and 1447.9 cm -1 ) and having correlation factors of 0.985 and 0.982). These new bands are assigned to benzyne 3 (Table 3). Our assignment of these peaks are confirmed by comparison with previous experimental works performed in argon matrix [START_REF] Bai | Matrix isolation study of the dissociation and isomerization pathways of benzene following corona discharge excitation[END_REF][START_REF] Laboy | 193 nm excimer laser photochemistry of benzene in argon matrices[END_REF], nitrogen matrix, [START_REF] Dunkin | Matrix photolysis of unsaturated cyclic anhydrides and the infrared spectrum of tetradeuteriobenzyne[END_REF] and parahydrogen matrix [START_REF] Toh | UV Photochemistry of Benzene and Cyclohexadienyl Radical in Solid Parahydrogen[END_REF]. These bands were assigned to o-benzyne on the basis of the parahydrogen matrix work of Toh et al. [START_REF] Toh | UV Photochemistry of Benzene and Cyclohexadienyl Radical in Solid Parahydrogen[END_REF] in which three bands of o-benzyne were identified at 1057, 844 and 735 cm -1 . The appearance of o-benzyne is not surprising since it is the most stable of the three benzyne isomers.

Based on previous works [18, 19, 21 ,33], the intense band observed at 3314,2 cm -1 and the broad one observed at 652,0 cm -1 can be assigned to a ≡C-H stretching mode and C-H out of plane bending mode of monosubtituted acetylene 4. The presence of two other broad bands observed at 854,0 and 749,1 cm -1 in matrix will be discussed in the next section. Finally, three bands, observed at 1316.0, 807.1 and 744.7cm -1 are attributed to benzvalene 7 based on the work of Griffith et al. [START_REF] Griffith | The vibrational spectra of Dewar benzene and benzvalene[END_REF] performed in N2 matrix (Table 3). As observed by Toh et al. [START_REF] Toh | UV Photochemistry of Benzene and Cyclohexadienyl Radical in Solid Parahydrogen[END_REF], only three bands are strong. They are located at 1313.3 cm -1 , 811, 6 cm -1 and 742,8 cm -1 in their parahydrogen matrix. Other bands observed by Toh et al. [START_REF] Toh | UV Photochemistry of Benzene and Cyclohexadienyl Radical in Solid Parahydrogen[END_REF] have lower intensities and are not observed in our experiments. Based on the work of Griffith et al. [START_REF] Griffith | The vibrational spectra of Dewar benzene and benzvalene[END_REF] the band at 657,9 cm -1 might also be attributed to this isomer. However, due to the fact that the band at 657.9 cm -1 grows on top of a larger feature in our spectrum and is not among the most intense features in other N2 matrix experiments [START_REF] Griffith | The vibrational spectra of Dewar benzene and benzvalene[END_REF], this assignment remains tentative.

Based on the work of Johnstone and Sodeau [START_REF] Johnstone | Matrix-controlled photochemistry of benzene and pyridine[END_REF], Griffith et al. [START_REF] Griffith | The vibrational spectra of Dewar benzene and benzvalene[END_REF], and Toh et al. [START_REF] Toh | UV Photochemistry of Benzene and Cyclohexadienyl Radical in Solid Parahydrogen[END_REF], the formation of Dewar benzene in our experimental conditions can be considered by the growth of new bands at 1536.0, 1271.9, 937.0, 793.0, and 704.1 cm -1 , but these bands are too weak to be correctly integrated in order to plot the evolution of one band in function of the others. Moreover, the band at 937 cm -1 is very close to a fulvene band and could be assigned to this fulvene band,