Ireneusz Glowacki
email: ireneusz.glowacki@p.lodz.pl

Zbigniew Szamel

The nature of trapping sites and recombination centres in PVK and PVK-PBD electroluminescent matrices seen by spectrally resolved thermoluminescence

Two electroluminescent polymer matrices: poly(N-vinylcarbazole) (PVK) and PVK with 40 wt % of 2-tert-butylphenyl-5-biphenyl-1,3,4-oxadiazole (PBD) were studied using spectrally resolved thermoluminescence (SRTL) in temperature range 15-325 K. The comparison of the SRTL results with the electroluminescence (EL) spectra has allowed identifying the localized (trapping) sites and the radiative recombination centres present in the investigated matrices. In the neat PVK films deep traps with a depth about 200 meV, related to triplet excimers dominate, while in the PVK-PBD (40 wt %) blend films the traps that are related to triplet exciplexes formed by the carbazole groups and the PBD molecules dominate. Depth of the traps in the PVK-PBD blend is somewhat lower than that in the neat PVK. An analysis of the EL spectra shows that in the PVK and in the PVK-PBD blend the dominant radiative centres are singlet excimers and singlet exciplexes, respectively. However in the neat PVK some contributions of the triplet monomer and the triplet excimer states in the electroluminescence were also detected.

Introduction

Polymer light-emitting diodes (PLEDs) are of great current interest due to their potential applications in large-area and flexible displays, which can be fabricated at room temperature, by inexpensive solution-processing methods like spin-casting, screen-printing or inkjet-printing [1,[START_REF] Kalinowski | Organic Light-Emitting Diodes; Principles, Characteristics and Processes[END_REF]. To get optimal efficiency and device lifetime, the injection and transport of holes and electrons must be balanced, so that similar concentrations of these two kinds of charge carriers are achieved. In case of polymers which contain the radiative recombination centres, the single-layer devices can be prepared in simple way but the active layer should assure both hole and electron transport besides light emission [START_REF] Perepichka | Phosphorescent polymer light-emitting diodes Organic light-emitting materials and devices[END_REF].

Poly(N-vinylcarbazole) (PVK), a non-conjugated polymer with a luminescent carbazole side groups, is a well-known and is often used as the optically active material in different optoelectronic devices, due to its excellent film-forming, relatively good hole-transporting properties, and large separation between highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) [START_REF] Yang | Physical processes in polymer-based electrophosphorescent devices Highly efficient OLEDs with phosphorescent materials[END_REF]. PVK is widely utilized especially in the fabrication of blue light emitting diodes in place of conjugated polymers, which have weak emission in blue region due to their long -conjugation and relatively low fluorescence quantum yields [START_REF] Perepichka | Phosphorescent polymer light-emitting diodes Organic light-emitting materials and devices[END_REF][START_REF] Yang | Physical processes in polymer-based electrophosphorescent devices Highly efficient OLEDs with phosphorescent materials[END_REF]. Since the pure PVK has poor electron-transporting properties, oxadiazole derivatives such as 2-tert-butylphenyl-5-biphenyl-1,3,4-oxadiazole (PBD) (figure 1) is often added to PVK [START_REF] Yang | Physical processes in polymer-based electrophosphorescent devices Highly efficient OLEDs with phosphorescent materials[END_REF][START_REF] Luszczynska | Poly(N-vinylcarbazole) doped with a pyrazoloquinoline dye: a deep blue light-emitting composite for light-emitting diode applications[END_REF]. The PVK-PBD blend is particularly used as host for the phosphorescence guest materials at low concentration because PVK has high triplet exciton energy that prevents crossing of the triplet exciton back from the phosphor to the host triplet state [START_REF] Yang | Physical processes in polymer-based electrophosphorescent devices Highly efficient OLEDs with phosphorescent materials[END_REF].

Several groups have reported electroluminescence spectra of pure PVK [START_REF] Kido | Bright blue electroluminescence from poly(Nvinylcarbazole)[END_REF][START_REF] Hu | Electroluminescence of pure poly(N-vinylcarbazole) and its blends with a multiblock copolymer[END_REF][START_REF] Angelo | Electrical transport properties characterization of PVK (poly N-vinylcarbazole) for electroluminescent devices applications[END_REF][START_REF] Qian | Electrophosphorescence from triplet excimers in poly(Nvinylcarbazole)[END_REF][START_REF] Jiang | Effect of carbazole-oxadiazole excited-state complexes on the efficiency of dye-doped light-emitting diodes[END_REF]. In all the cases, a broad and unstructured emission band extending from 350 nm to over 650 nm, with a dominant broad maximum at 420-445 nm, was observed [START_REF] Kido | Bright blue electroluminescence from poly(Nvinylcarbazole)[END_REF][START_REF] Hu | Electroluminescence of pure poly(N-vinylcarbazole) and its blends with a multiblock copolymer[END_REF][START_REF] Angelo | Electrical transport properties characterization of PVK (poly N-vinylcarbazole) for electroluminescent devices applications[END_REF][START_REF] Qian | Electrophosphorescence from triplet excimers in poly(Nvinylcarbazole)[END_REF]. The emission at ca 420-430 nm comes from the low energy singlet excimer (full overlap carbazole units). The shorter wavelength shoulder at 370-380 nm and some contribution of the band at 350-360 nm can be related to the higher energy singlet excimer and to isolated carbazole groups, respectively [START_REF] Hu | Electroluminescence of pure poly(N-vinylcarbazole) and its blends with a multiblock copolymer[END_REF][START_REF] Angelo | Electrical transport properties characterization of PVK (poly N-vinylcarbazole) for electroluminescent devices applications[END_REF][START_REF] Qian | Electrophosphorescence from triplet excimers in poly(Nvinylcarbazole)[END_REF]. All the EL maxima detected for PVK are redshifted by ca 10 nm in comparison to the photoluminescence (PL) spectra. Recently Angelo et al. [START_REF] Angelo | Electrical transport properties characterization of PVK (poly N-vinylcarbazole) for electroluminescent devices applications[END_REF] published broad EL spectra of the neat PVK, where apart from the dominant band at ca 410 nm also the bands at 450-460 nm, 480 nm, 500-550 and over 600 nm can be distinguished. However the authors have not discussed the origin of these additional bands in EL spectra. Also Qian et al. [START_REF] Qian | Electrophosphorescence from triplet excimers in poly(Nvinylcarbazole)[END_REF] reported a broad EL spectrum for single layer PVK devices in the range 380-650 nm with a dominant peak at 420-430 nm and a minor one at 590 nm with additional very weak shoulder at ~630 nm. The long-wavelength emission with weak intensity was also observed in the PL measurements either at 80 K or at room temperature and the authors related these bands to the triplet excimers in the PVK films [START_REF] Qian | Electrophosphorescence from triplet excimers in poly(Nvinylcarbazole)[END_REF]. They found that probability of the singlet and triplet exciton state forming can be changed by using of different solvents for PVK solution preparation or PVK with different molecular weight.

Although PVK has non-conjugated backbone but stacking of side carbazole groups can create conjugated system with the two types of excimers as it is discussed above. The authors argued that the probability of triplet formation in conjugated polymers increases with decreasing effective conjugation length. When the effective conjugation length decreases the intersystem crossing rate increases and the population of triplet excitons those come from singlet excitons increases due to the lower exciton dissociation probability. This conclusion was confirmed by a quantum chemical calculation made by Belionne et al. [START_REF] Beljonne | Chain-length dependence of singlet and triplet exciton formation rate in organic light-emitting diodes[END_REF]. It is known that position of the HOMO/LUMO levels is not only determined by the chemical structure of the molecule itself but also the electronic polarisation of its surrounding. For polymers, the effective conjugation length also affects the position of the HOMO/LUMO levels.

Change of the molecular conformation will lead to a fluctuating surrounding and to fluctuating conjugation length. Qian et al. [START_REF] Qian | Electrophosphorescence from triplet excimers in poly(Nvinylcarbazole)[END_REF] found that the partial overlap conformation has lower triplet/singlet ratio as compared to the full overlap conformation. The influence of molecular conformation of polymer chains on its triplet formation probability has attracted attention of several researcher groups.

Interesting conclusion can be drawn from the recently published EL spectra for PVK spin cast layer obtained after previous irradiation of the solution with UV light [START_REF] Qian | White light emission from single layer poly-(Nvinylcarbazole) polymeric light-emitting devices by mixing singlet and triplet excimer emissions[END_REF]. With increasing UV light irradiation time, the intensity of the emission about 600 nm increased, while the emission band at 420 nm decreased and red-shifted. The authors explained these effects by increasing population of the full overlap carbazole excimers. However they also indicated that several different photophysical and photochemical processes can occur in PVK solution as a result of UV light irradiation, like conversion from partially to full overlap carbazole units, cross-linking of PVK through the carbazole groups with contribution of oxygen, photoscission of PVK, or debonding of carbazole group from a PVK chain [START_REF] Qian | White light emission from single layer poly-(Nvinylcarbazole) polymeric light-emitting devices by mixing singlet and triplet excimer emissions[END_REF].

It is worth to note that up to now the excimeric phosphorescence in the PVK films was related to the emission in the range 480-530 nm; however lower energetic tail down above 650 nm was observed in both phosphorescence and EL spectra [START_REF] Kido | Bright blue electroluminescence from poly(Nvinylcarbazole)[END_REF][START_REF] Angelo | Electrical transport properties characterization of PVK (poly N-vinylcarbazole) for electroluminescent devices applications[END_REF]. This emission bands about 590 nm and above 600 nm were attributed to several different mechanisms, such as aggregation, [START_REF] Hu | Electroluminescence of pure poly(N-vinylcarbazole) and its blends with a multiblock copolymer[END_REF][START_REF] Qian | Electrophosphorescence from triplet excimers in poly(Nvinylcarbazole)[END_REF] electroplex [START_REF] Perepichka | Phosphorescent polymer light-emitting diodes Organic light-emitting materials and devices[END_REF][START_REF] Qian | Electrophosphorescence from triplet excimers in poly(Nvinylcarbazole)[END_REF] or phosphorescence [START_REF] Burkhart | Binding energies of triplet excimers in poly(Nvinylcarbazole) solid films from laser-based kinetic spectroscopy between 15 and 55[END_REF][START_REF] Glowacki | Charge carrier detrapping in PVK films as seen by thermoluminescence after excitation at 15 K Space charge in solid dielectrics[END_REF]. In contrast to PVK, for which photophysical properties were extensively studied since many years, the PVK-PBD system was investigated much less intensively. The EL spectra for the PVK-PBD blends have dominant peak at 430 nm, which is red-shifted by ca 5 nm in comparison to the PL spectrum; this effect is explained by formation of the exciplex states. It was also shown that the EL spectra have some long-wavelength contribution dependent on composition of the blends and on applied electric field [START_REF] Yang | Physical processes in polymer-based electrophosphorescent devices Highly efficient OLEDs with phosphorescent materials[END_REF][START_REF] Jiang | Effect of carbazole-oxadiazole excited-state complexes on the efficiency of dye-doped light-emitting diodes[END_REF].

The energy transfer and the charge carrier trapping play an important role in the optoelectronic materials taking into account their further application. Traps in disordered media are commonly considered as localized states. Trapped charge carriers may be released after a retention time and will become free or may recombine with carriers of the opposite sign. When the release rate is higher than the recombination rate, the localized state is a trap, while for dominant recombination rate the localized state forms a recombination centre. It means that the same state may act as the recombination centre or as the trap, depending on certain parameters, like temperature or a ratio of minority to majority carrier concentrations. It is well known that the traps can reduce the carrier drift mobility and disturb the internal field distribution. Trapped charge carriers can quench emissive optical excitations and thus restrict the EL efficiency of organic materials.

One of the most direct methods of investigation of the trapping phenomena is thermoluminescence (TL). Thermoluminescence is observed when a sample of i.e. a polymeric material is heated after excitation at low temperature. The excitation generates charge carries, most of them recombine in very short time, but some of them gain enough energy to escape the geminate recombination. These charge carriers, after thermalization, can stay in the localized sites-traps. The subsequent heating causes their detrapping, and if they recombine radiatively, a thermoluminescence is detected [START_REF] Glowacki | Charge carrier detrapping in PVK films as seen by thermoluminescence after excitation at 15 K Space charge in solid dielectrics[END_REF][START_REF] Sainova | Thermoluminescence and electroluminescence of annealed polyfluorene layers[END_REF][START_REF] Schmechel | Electronic traps in organic transport layers phys[END_REF]. The TL investigations for PVK [START_REF] Glowacki | Charge carrier detrapping in PVK films as seen by thermoluminescence after excitation at 15 K Space charge in solid dielectrics[END_REF] and for PVK with 30 wt % PBD blend [START_REF] Luszczynska | Thermoluminescence of the blue light-emitting system based on poly(9-vinylcarbazole) doped with a pyrazoloquinoline dye[END_REF] were reported previously but the spectra were obtained in the narrower spectral range (350-580 nm) because the used photomultiplier had the sensitivity maximum in blue range. The indicated above literature review showed that many reports devoted the EL and PL investigation for PVK in the spectral range above 500 nm are not able to provide clear explanation of this emission origin. This reason motivated us to taking trial of the thermoluminescence technique use in extended spectral range for obtaining more information about the emission mechanism in the polymer system.

In the present study, we report investigations of spectrally resolved thermoluminescence (SRTL) in a broad spectral range (350-950 nm) for the neat PVK and for the PVK with 40 wt % PBD blend films. An analysis of the TL, PL and EL spectra has allowed to characterize the excited states, the trapping/transport sites and the recombination centres.

Experimental

The PVK and PBD were obtained from Sigma-Aldrich and were used as received. Chemical structure of the materials are shown in figure 1. For the TL measurements films of PVK and PVK-PBD (40 wt %) were cast from chlorobenzene solutions onto stainless steel substrates at room temperature. Thicknesses of the films were between 5-8 µm range. To remove the residual solvent, the films were dried at 423 K for several hours in the nitrogen atmosphere. For TL experiment the sample was placed in a vacuum chamber (closed-cycle cryogenic system APD Cryogenics, type Displex) and squeezed between a thermostated stage and a sapphire plate, with the aid of a brass frame anchored thermally to the stage. The TL measurements were performed in the temperature range from 15-325 K. The sample was photo excited for 10 minutes using a mercury lamp HBO-200 at 15 K. We used band pass filter in front of the mercury lamp with λ max. = 365 nm yielding light output power of about 2.5 mW/cm 2 . Then the sample was heated gradually with the rate of 7 K/min. Light emitted during the SRTL experiment was detected using specially designed optical system consisting of custom made optical collector, optical fiber, Micro HR Imaging Spectrograph and a CCD camera (Horriba Jobin-Yvon). The system has flat sensitivity response in the whole wavelength range 350-950 nm. The analysis program of the TL measurement system creates TL spectra in the form of 3-D plots (luminescence intensity versus temperature and wavelength) or in a form of TL map. From such map one can extract the monochromatic TL curve for any chosen wavelength or the luminescence spectrum at any chosen temperature.

The activation energies (E a ) of the detrapping processes were determined from the so-called "partial heating" experiments. It consisted of recording the emitted light during subsequent heating/cooling cycles with progressively increasing maximal temperature in each cycle. To monitor the luminescence intensity during the partial heating experiment, we used the photomultiplier tube (Thorn EMI type 9789 QB) in the optical system.

The same detection system as for the SRTL experiment was also used for spectral analysis of the electroluminescence of the single-layer PLEDs. The PLED devices were produced in the following way. We spin coated 30 nm thick layer of poly(3,4-ethylenedioxythiophene) poly(styrenesulfonate) (PEDOT-PSS) onto a clean indium tin oxide (ITO) coated glass substrate (ITO resistivity 15Ω/sq.), purchased from Präzisions Glass and Optik GmbH and then annealed at 423 K for 1 h in nitrogen atmosphere. Then the emitting layers, either PVK or PVK-PBD (40 wt %) layer of thickness about 120 nm were spin coated and the samples were again annealed at 443 K for 2 h. Finally we evaporated 5 nm thick LiF and 100 nm thick Al as contacts on top of polymeric layer using Edwards system (model Auto 306).

Steady-state photoluminescence (PL) experiments were performed using Jobin-Yvon Spectrofluorimeter (model Fluorolog FL3-11). For the PL measurements, we spin coated PVK or PVK-PBD thin films of ca. 150 nm onto quartz substrates. Thickness and roughness of the sample surface were determined by AFM (NT-MDT AFM model SOLVER PRO).

Results and discussion

Photoluminescence and electroluminescence

The PL spectra of the films of PVK and PVK-PBD (40 wt %) obtained after excitations at = 337 nm are shown in figure 2. It should be noted that absorption bands of PVK and PVK-PBD blend in the wavelength range 300-360 nm are similar (see an inset in figure 2). The PL maximum for PVK at ca 410-415 nm with short-wavelength shoulder, is due to the emission from two different types of the carbazole singlet excimers and also from isolated carbazole groups (at 350-360 nm). Similar spectra for PVK were reported by Klöpffer and Fischer [START_REF] Klöpffer | Transfer of Electronic Excitation Energy in Polyvinyl Carbazole[END_REF] and by Bässler [START_REF] Bässler | Charge transport in molecularly doped polymers[END_REF], who have argued that in PVK the traps are neutral and probably connected with carbazole dimers yielding excimer states.

Johnson and Good [START_REF] Johnson | Molecular weight dependent emission properties of poly(Nvinycarbazole) in polymer blends[END_REF], Itaya et al. [START_REF] Itaya | Emission spectra of the vinyl polymers with pedant carbazolyl groups[END_REF] and quite recently Qian et al. [START_REF] Qian | Electrophosphorescence from triplet excimers in poly(Nvinylcarbazole)[END_REF] suggest an existence of two types of excimer species in PVK: the lower energy (corresponding to the emission peak at ca 410-420 nm due to so-called "sandwich"-like full-overlap excimers) characterized by a coplanar arrangement of two neighbouring carbazole units, and the higher energy (corresponding to the emission peak at ca 380 nm) "second excimers" (partially-overlap excimers) created by the overlapping of only one benzene ring from two contacting carbazole groups in the tt conformation of the syndiotactic sequence in PVK.

The PL maximum for the PVK-PBD blend is red-shifted by about 15 nm in comparison to the PL maximum of neat PVK and also of pure PBD, for which the PL maximum appears at 390 nm [START_REF] Gong | Phosphorescence from iridium complexes doped into polymer blends[END_REF]. It is well-known that the oxadiazole and the carbazole groups have a tendency to form the excited state complexes. Therefore the PL maximum at ca 425-430 nm has been assigned to the exciplexes, which are created rapidly after the excitation of the PVK-PBD matrix [START_REF] Jiang | Effect of carbazole-oxadiazole excited-state complexes on the efficiency of dye-doped light-emitting diodes[END_REF][START_REF] Gong | Phosphorescence from iridium complexes doped into polymer blends[END_REF]. Such interpretation was supported by an observation that the PL intensities of the PVK-PBD blends increase with an increase in PBD content. This indicates that PBD is not an electron acceptor which would quench the PL emission of PVK. Formation of exciplexes in PVK-PBD (40 wt %) films was observed by several groups using steady state and time-resolved photoluminescence spectroscopy [START_REF] Jiang | Effect of carbazole-oxadiazole excited-state complexes on the efficiency of dye-doped light-emitting diodes[END_REF][START_REF] Gong | Phosphorescence from iridium complexes doped into polymer blends[END_REF][START_REF] Negres | Origin of efficient light emission from a phosphorescence polymer/organometallic guest-host system[END_REF]. Negres et al.

[23] used time-resolved photoinduced absorption measurements at 77 K and room temperature to show that in PVK-PBD host blend, an additional excited-state (exciplex) is formed and charge trapping plays an important role in excited-state dynamics. It was observed by probing at longer wavelengths (480, 532 and 580 nm) that 35 % of primary photoexcitation evolve into charge trapping states. The trapping states in a film of PVK-PBD blend have an emissive character at 480 nm but become absorptive at longer wavelengths [START_REF] Negres | Origin of efficient light emission from a phosphorescence polymer/organometallic guest-host system[END_REF].

The EL spectra of neat PVK and PVK-PBD (40 wt %) devices are shown in figure 2. It should be noted that the EL spectra are obtained for the same current density 22 mA/cm 2 by adjusting the bias voltage. It is important to compare the contributions of different kinds of excited states in the EL spectra for the two matrices; especially when it is known that without dopants the EL intensity is low. For PVK, we observed a broad and unstructured emission from 350-750 nm along with a dominant broad maximum at 420-445 nm. As mentioned in the introduction, the peak at 420-430 nm results from a low energy singlet excimer (full overlap carbazole units). The shorter wavelength shoulders at 370-380 nm and at 350-360 nm can be related with the higher energy singlet excimer and with isolated carbazole groups, respectively [START_REF] Hu | Electroluminescence of pure poly(N-vinylcarbazole) and its blends with a multiblock copolymer[END_REF][START_REF] Qian | Electrophosphorescence from triplet excimers in poly(Nvinylcarbazole)[END_REF]. The EL maximum is red-shifted by ca 10 nm in comparison with the PL spectra. However, apart from the dominant peak in the EL spectra one can observe a weak, longer wavelength bands with gradually decreasing intensity. These bands are strongly overlapping each other but they are located in the regions: 470-500 nm, 530-550 nm and over 600 nm. Similar EL bands were observed in PVK by several research groups [START_REF] Kido | Bright blue electroluminescence from poly(Nvinylcarbazole)[END_REF][START_REF] Hu | Electroluminescence of pure poly(N-vinylcarbazole) and its blends with a multiblock copolymer[END_REF][START_REF] Angelo | Electrical transport properties characterization of PVK (poly N-vinylcarbazole) for electroluminescent devices applications[END_REF][START_REF] Qian | Electrophosphorescence from triplet excimers in poly(Nvinylcarbazole)[END_REF] but only Qian et al. [START_REF] Qian | Electrophosphorescence from triplet excimers in poly(Nvinylcarbazole)[END_REF] discussed these long-wavelength bands. It was suggested that these bands around 600 nm may arise from the excimer triplet states. It seems that these emissions can be related to different extended staking of carbazole groups (entanglements of chains and some aggregates of carbazole groups) or other unknown species present in the PVK films.

The EL spectrum of the device with PVK-PBD (40 wt %) blend has dominant peak at 430 nm, which is red-shifted by ca 5 nm in comparison with the PL spectrum. It also shows some contributions of both short-and long-wavelength emissions. The rising edge of EL maximum is very similar both in PVK and PVK-PBD systems but considerable difference for longer wavelength can be observed.

Addition of PBD to PVK causes a significant enhancement of the dominant EL band with maximum at 430 nm. This effect is caused mainly because of improved balance of holes and electrons in the PVK-PBD layer. The PBD molecules create transport channels for electrons. Moreover they can also form exciplexes with carbazole groups, which in turn can work as radiative centres rising the EL emission band at 430 nm. One can also see that introduction of PBD to PVK causes some increase of EL emission in the range 600-750 nm and simultaneously a significant reduction of the EL intensity in the range 470-600 nm. To explain the influence of PBD on emission spectra of PVK, extended thermoluminescence (TL) studies were performed.

Thermoluminescence

The 3D plot of the SRTL spectrum for neat PVK film photoexcited at 15 K is shown in figure 3, and the monochromatic TL curves and spectrally resolved spectra at temperatures corresponding to TL maxima are shown in figure 4. As one can see from the TL map, the chosen wavelengths (500 nm and 530 nm), at which the monochromatic TL curves were extracted, correspond to the wavelengths at which the two maxima on TL map appear. One can also see that both monochromatic TL curves have two broad maxima. One maximum is below 50 K and the second one is around 125-135 K. Both maxima have similar intensities but their relative intensities are different. In the spectrum for = 530 nm, high-temperature maximum is slightly higher than the low temperature one. On the other hand, in the spectrum for = 500 nm this relationship is reversed. This indicates that upon heating, the trapped charge carriers are subsequently liberated from two different trapping sites of similar densities.

Simultaneous spectral analysis of the light emitted during the TL experiment allows us to identify the origin of radiative recombination processes giving rise to the TL signal. The spectrally resolved luminescence (SRL) recorded at different temperatures during the TL experiment (see the TL map in figure 4a) reveals that the luminescence extends over entire visible range. The two SRL spectra detected close to the TL maxima, i.e. at 50 K and at 130 K, are shown in figure 4c. In both cases one can distinguish two broad maxima: one weaker at the short wavelength range around 400 nm and the second dominating band at longer wavelength, which shifts its position from ca 500 nm at low temperature to ca 530 nm at high temperatures. Additionally, before the TL run, the isothermal luminescence spectra were recorded at 15 K in the time interval from 10 seconds to several minutes after turning off the excitation. The spectra for PVK shown in the inset in figure 4a have broad band in the range 400-600 nm with a maximum at ca 490 nm and their shapes do not change in time. It was found [START_REF] Glowacki | Charge carrier detrapping in PVK films as seen by thermoluminescence after excitation at 15 K Space charge in solid dielectrics[END_REF] that the isothermal phosphorescence spectra for PVK films registered in range 5-140 K show bands at 425-430 nm and 450-460 nm, which are well observed only at temperatures 5 K and 20 K and they disappear at higher temperatures. At the same time the broad band at lower wavelengths shifts from 490-500 nm to 520-530 nm with increasing temperature. Similar evolution of the phosphorescence spectra for PVK upon the temperature increase was observed earlier by Burkhart and Chakraborty [START_REF] Burkhart | Binding energies of triplet excimers in poly(Nvinylcarbazole) solid films from laser-based kinetic spectroscopy between 15 and 55[END_REF]. It has been explained as a change of photoexcited states in PVK from monomeric triplet states at low temperatures to excimeric ones at higher temperatures. They observed a temperature dependent discontinuity (the Arrhenius graph) of the rate constant for phosphorescence decay in the range 40-55 K. The authors have concluded that the increased rate of decay of nonexcimeric triplets is due to the trapping at excimer-forming sites.

From above analysis it can be concluded that both the monomeric and the excimeric states of carbazole groups are involved in the radiative recombination during the TL processes. At temperatures below 50 K the monomeric triplet states dominate (480-500 nm) and at higher temperatures the excimeric triplet states (520-530 nm) prevail. The weak emission in the range 370-420 nm (see figure 4c) can be due to the contribution from both monomeric and excimeric singlet states of carbazole groups [START_REF] Qian | Electrophosphorescence from triplet excimers in poly(Nvinylcarbazole)[END_REF][START_REF] Burkhart | Binding energies of triplet excimers in poly(Nvinylcarbazole) solid films from laser-based kinetic spectroscopy between 15 and 55[END_REF][START_REF] Glowacki | Charge carrier detrapping in PVK films as seen by thermoluminescence after excitation at 15 K Space charge in solid dielectrics[END_REF]. We observed a shift of the band maximum from 480-500 nm to 520-530 nm (see figure 4c). This evolution of the emission spectra with increasing temperature can be explained by the change of relative conformation of carbazole groups due to molecular relaxation activated at higher temperatures.

In order to determine activation energies of the detrapping processes, which is a measure of trap depth, the partial heating experiments were performed. The results obtained for PVK (not shown here)

indicate the presence of two main trapping levels: around 50 meV and 200 meV corresponding to the low and high-temperature TL maxima, respectively. Similar value of E a in the high temperature range (200 meV) was obtained in a TL experiment performed on PVK film in the temperature range between the liquid nitrogen and room temperature [START_REF] Glowacki | Charge carrier detrapping in PVK films as seen by thermoluminescence after excitation at 15 K Space charge in solid dielectrics[END_REF][START_REF] Glowacki | Simultaneous thermoluminescence and thermally stimulated currents measurements in poly(N-vinylcarbazole)/polycarbonate blends[END_REF]. The activation energy of phosphorescence obtained from temperature dependent isothermal measurements of lifetime of triplet states in the temperature range 10-40 K is 19 meV [START_REF] Glowacki | Charge carrier detrapping in PVK films as seen by thermoluminescence after excitation at 15 K Space charge in solid dielectrics[END_REF]. This agrees well with a value of 21 meV obtained by Burkhart and Chakraborty [START_REF] Burkhart | Binding energies of triplet excimers in poly(Nvinylcarbazole) solid films from laser-based kinetic spectroscopy between 15 and 55[END_REF] from an analogous measurements. These values are at least twice lower than the value ca 50 meV obtained from the TL partial heating experiments which correspond to the lowtemperature TL maximum and are related to shallow traps in PVK film. It should be noted that the shallow traps with the depth much lower than 50 meV can not be detected in TL experiment, which starts at 15 K. Because the charge carriers are already released from such shallow traps soon after the photoexcitation before the start of the heating run.

The TL maxima are directly related to the charge carrier detrapping; however it does not mean that the activation energy values estimated from the partial heating of TL always correspond to the depth of the traps. In polymers, some low polarized energy of the trapping sites can be formed by "physical defects" such as cavities resulting from the specific arrangement of polymer chains, socalled "conformational traps". Thus, the TL maxima often correspond well to the onset of molecular motions, what affords evidence for a significant contribution of the molecular motions to the charge carrier detrapping process. Such mechanism is called as the "wet dog" effect [START_REF] Dobruchowska | The 'wet dog' effect in polymers as seen by thermoluminescence[END_REF]. Akuetey and Hirsh [START_REF] Akuetey | Thermal depolarization measurements on PVK films[END_REF] based on an analysis of dielectric measurements for PVK made by Pochan et al. [START_REF] Pochan | Dielectric relaxation studies of poly(Nvinylcarbazole) and poly(3-chloro-N-vinylcarbazole) including the effects of sorbed oxygen[END_REF], have found that the -relaxation in this polymer extrapolated to the mHz frequency range should appear at around 130 K. This frequency range corresponds to an equivalent frequency of thermally stimulated processes, if the heating rate is a few K/min [START_REF] Akuetey | Thermal depolarization measurements on PVK films[END_REF]. It means that the detrapping which gives rise to the TL maximum at around 130 K could be induced by the -relaxation in PVK. Also the low-temperature TL maximum might be correlated with the -relaxation in PVK, which is attributed to a wagging motion of the carbazole groups [START_REF] Pochan | Dielectric relaxation studies of poly(Nvinylcarbazole) and poly(3-chloro-N-vinylcarbazole) including the effects of sorbed oxygen[END_REF]. On the other hand, the activation energies of molecular relaxations determined from the dielectric measurements are higher in comparison to those estimated from the TL partial heating experiments, e.g. values of 390 meV in the relation to 200 meV and nearly 100 meV to 50 meV for -relaxation and -relaxation respectively [START_REF] Pochan | Dielectric relaxation studies of poly(Nvinylcarbazole) and poly(3-chloro-N-vinylcarbazole) including the effects of sorbed oxygen[END_REF]. This is because only an onset of molecular motions may be sufficient to facilitate detrapping of the localized charge carriers e.g. by lowering the potential barriers of such trapping sites or by decreasing the distance between the neighbouring transport sites, and therefore entire molecular relaxation process does not need to be involved. Similar effect was reported also for other polymers [START_REF] Dobruchowska | The 'wet dog' effect in polymers as seen by thermoluminescence[END_REF].

Arkhipov et al. [START_REF] Arkhipov | Polaron effects on thermally stimulated photoluminescence in disordered organic systems[END_REF] and Fishchuk et. al. [START_REF] Fishchuk | Transition from trap-controlled to trap-to-trap hoping transport in disordered organic semiconductors[END_REF] proposed that TL in polymers is controlled by thermally assisted hopping relaxation of charge carriers. In this approach the TL spectrum provides information on charge carriers from tail states of intrinsic density-of-states (DOS) distribution and from deeper traps. In disordered media deep traps are extrinsic localized states that differ from the majority of hopping (transport) states where they require substantially higher energy input to release the charge carriers back to the intrinsic DOS. Therefore it is not clear, which sites play a role of traps and which are regular transport states. For instance, hole or electron transport proceeding via one kind of charge transporting material would be affected by trapping on a molecule of another kind, provided that the latter has a lower ionisation potential or a higher electron affinity, respectively. It has been mentioned that traps can be also of structural origin like dimers or aggregates, what can be observed in many polymer systems and also in case of PVK and PVK-PBD blend. Therefore the interpretation of TL phenomena in disordered organic materials with hopping charge transport is not as straightforward as in inorganic crystalline materials. According to Fishchuk et al. [START_REF] Fishchuk | Transition from trap-controlled to trap-to-trap hoping transport in disordered organic semiconductors[END_REF] the activation energy of the dominant TL maximum is proportional to the effective energetic disorder parameter eff . Two models, the effective medium approach proposed by Movaghar [START_REF] Movaghar | Diffusion and relaxation of energy in disordered systems: Departure from mean-field theories[END_REF] and the variable range hoping described by Arkhipov et al. [START_REF] Arkhipov | Hopping model of thermally stimulated photoluminescence in disordered organic materials[END_REF] for energetic relaxation of carriers, could be applied for description of the population of localized sites taking part in the process of low-temperature energetic relaxation of the photogenerated carriers. According to these theories, the energetic relaxation of generated particles in the zero-temperature limit occurs through a non-activated downward hopping with the decay of mean energy according to the expression [START_REF] Bässler | Exciton and charge carrier transport in random organic solids Disordered effect on relaxation processes[END_REF]:

2 1 0 ln ln 3 = t t E R σ ,
where: E R is the mean energy of the charge-carrier packet relative to the centre of the DOS distribution, is the width of the DOS distribution, t is the time, and t 0 is the dwell time of carrier at a lattice site without disorder. In this case (according to ref. 32) t 0 is accepted as 10 -13 s.

The low-temperature relaxation process described by the above expression practically saturates in experimental time scale of minutes, thus the parameter can, at least roughly, be estimated from the activation energy at the TL peak maximum, assuming that the latter corresponds to the mean energy of the relaxed charge carrier packet, E R . It should be noted that in such reasoning one should also take account the fact that the thermal release of carriers occurs to the effective transport energy level that normally is located below the centre of the DOS. Nevertheless, the parameter is roughly proportional to the activation energy measured in the TL maximum and corresponding to the temperature of the TL maximum as the mean activation energy measured by partial heating TL experiment [START_REF] Fishchuk | Transition from trap-controlled to trap-to-trap hoping transport in disordered organic semiconductors[END_REF]. It means that from our partial heating TL results, in case of neat PVK film the parameter reaches the value of 0.2 eV. Taking the value of equal to 0.2 eV and t in the range from 100-1000 s after terminating the excitation inserting the data to the above expression we can obtain information that the charge carrier would be localized by approximately 3 = 0.6 eV below the DOS centre. It agrees well with a value of 0.6 eV obtained by Bässler [START_REF] Bässler | Lokalized states and electronic transport in single component organic solids with diagonal disorder phys[END_REF] and with 0.5 eV reported by Ulanski et al. [START_REF] Ulanski | Transition from Dispersive to Nondispersive Hole Transport in Poly-N-vinylocarbazole/ Polycarbonate Mixtures[END_REF] from the time of flight measurements for PVK films. It should be noted that the comparison of TL and transport data assumes that the energetic disorder, which governs the temperature dependence of charge mobility, does not change notably at low temperatures. Therefore TL method can give practically the same distribution of localized states and its analysis can yield an effective density of states width in quite good agreement with the values estimated from the charge carrier transport investigations [START_REF] Fishchuk | Transition from trap-controlled to trap-to-trap hoping transport in disordered organic semiconductors[END_REF].

Addition of 40 wt % PBD to PVK results in a considerable change in the TL spectrum. The TL map, the extracted monochromatic and isothermal spectra for the PVK-PBD blend are presented in those found in PVK. This is confirmed by the partial heating experiment for the blend which provides activation energy of about 150 meV for charge carriers detrapping process close to the TL maximum at 105 K. Similar value of trap depth was reported for PVK with 30 wt % PBD blend [START_REF] Luszczynska | Thermoluminescence of the blue light-emitting system based on poly(9-vinylcarbazole) doped with a pyrazoloquinoline dye[END_REF].

Figure 5c presents isothermal SRL spectra recorded at temperature close to the TL maximum (105 K). One can see two separated emission bands: a dominant one with a maximum at 550 nm and the second one with a maximum at 430-440 nm. Very similar isothermal spectra were recorded at 15 K before starting the TL heating run (see an inset in figure 5a).

The main maximum is shifted by ca 20 nm towards longer wavelengths in comparison to that for PVK. Both emission bands in PVK-PBD blend can be attributed to the exciplexes formed between the carbazole group and PBD molecule. The dominant band with a maximum at 550 nm originates from the triplet exciplexes. The second one with maximum at 430-440 nm comes from the singlet exciplexes and/or monomeric triplet states of carbazole groups as discussed before.

The TL results evidentially indicate that introduction of PBD to PVK results in a reduction of deep trap contribution due to creation of shallow traps in a form of exciplexes on an expense of the excimers. This improves transport properties in comparison with neat PVK matrix.

3.3.TL versus EL

The comparison of the EL and SRTL spectra for the PVK and PVK-PBD systems (see figures 2, 4c and 5c) shows a variety of recombination states, which take part in radiative recombination processes in these phenomena. Therefore for next analysis and discussion of the results the spectra are presented together in figure 6.

In the EL spectrum for PVK the band connected with the singlet excimer states is dominating while the long-wavelength emission in 470-600 nm range is mainly attributed to the triplet excimer states and has lower intensity. Whereas the interrelationship between these bands in the SRTL spectrum is reversed; the long-wavelength band predominates definitely. For PVK-PBD system, a similar relation of the EL and the SRTL spectra is observed as described above but in this case both main bands are related to the exciplex states. Generally one can state that in PVK-PBD system the singlet exciplexes dominate in the EL emission (band at 420-430 nm), while the radiative deactivation of triplet For the mechanisms of radiative recombination observed in two phenomena (EL and SRTL) the temperature is determining factor. At low temperature (TL experiment conditions) the charge carriers, which are localized mainly on the exciplex site, have a long enough time to recombine radiatively by intersystem crossing. In the EL phenomenon carried out at room temperature the exciplex triplet sites do not act as radiative recombination centres any more but rather work as transport and/or the trapping sites with short residence time for charge carriers.

As it was mentioned in the introduction, the long-wavelength (above ca 600 nm) EL emission in PVK was related to different extended staking of carbazole groups [START_REF] Qian | Electrophosphorescence from triplet excimers in poly(Nvinylcarbazole)[END_REF] or to other species of recombination states present in PVK film [START_REF] Qian | White light emission from single layer poly-(Nvinylcarbazole) polymeric light-emitting devices by mixing singlet and triplet excimer emissions[END_REF]. However the triplet eximer of carbazole groups producing the broad emission band with maximum at 530 nm is known [START_REF] Burkhart | Binding energies of triplet excimers in poly(Nvinylcarbazole) solid films from laser-based kinetic spectroscopy between 15 and 55[END_REF][START_REF] Glowacki | Charge carrier detrapping in PVK films as seen by thermoluminescence after excitation at 15 K Space charge in solid dielectrics[END_REF] and has been demonstrated above. It is worth to underline that some authors undertake the trials to clear the origin of the emission at 600-750 nm range [START_REF] Qian | Electrophosphorescence from triplet excimers in poly(Nvinylcarbazole)[END_REF]. In majority cases the long-wavelength emission with small band about 600 nm has been observed in EL [START_REF] Qian | White light emission from single layer poly-(Nvinylcarbazole) polymeric light-emitting devices by mixing singlet and triplet excimer emissions[END_REF] and also in low temperature PL [START_REF] Qian | Electrophosphorescence from triplet excimers in poly(Nvinylcarbazole)[END_REF] for PVK film without previous, additional UV irradiation. It seems to be probable that the emission in range 600-750 nm can be related to a photochemical species. The photochemical species can be formed in small amount already during synthesis of PVK and/or preparation of the PVK films and they can influence on the observed photophysical processes. This hypothesis can be justified by the appearance of increased emission in range 600-750 nm in both EL and SRTL spectra (see figure 6) after introduction of PBD to PVK. This increase related to the new species can also be caused by improvement of balance between holes and electrons but with much lower contribution in comparison with the enhancement of the dominant band with maximum at 430 nm. The contribution of this emission increases with increasing of driving voltage [START_REF] Qian | Electrophosphorescence from triplet excimers in poly(Nvinylcarbazole)[END_REF][START_REF] Yap | The effect of driving voltage on the electroluminescence property of a blend of poly(9-vinylcarbazole) and 2-(4-biphenylyl)-5-phenyl-1,3,4-oxadiazole[END_REF] and it can be related to enhancement of oxidation processes by high electric field. Such phenomenon is observed especially for PLEDs prepared under ambient conditions.

Conclusion

In conclusion, we demonstrated that application of SRTL technique provides valuable information on the release and recombination of trapped charge carriers. The origin of the radiative recombination process producing the TL spectra can be identified by spectral resolved monitoring of the emitted light in 15-325 K temperature range. By detailed analysis of SRTL, PL and EL results it was possible to distinguish the excited states, trapping/transport sites and recombination centres existing in PVK and PVK-PBD electroluminescent matrices.

In neat PVK films, deep traps with depth about 200 meV related to a triplet excimer dominate, while in PVK-PBD (40 wt %) blend films the traps are attributed to a triplet exciplexes formed by the carbazole groups and PBD molecules constituting the main trap population. Depth of the traps in PVK-PBD blend is somewhat smaller than that in PVK. The analysis of the EL spectra shows that in PVK and PVK-PBD blend the dominating radiative centres are singlet excimer and singlet exciplex, respectively. However in neat PVK, some contributions of the triplet monomer and at least two kinds of triplet excimer states were also detected in electroluminescence. The triplet exciplexes which are formed at the cost of triplet excimers of the carbazole groups do not take part in the EL emission of PVK-PBD blend. The triplet exciplexes take part in radiative recombination in TL experiment and can take part in the transport of charge carriers in the PVK-PBD blend.

In spite of the fact that new conjugated polymers with large HOMO-LUMO separation are available, the PVK-PBD blend is still a good host matrix for low molecular weight emitters for single layer PLEDs with blue and white emission.

The SRTL is very useful technique for an identification of localized sites and recombination centres in materials used as active layers in organic LEDs.

Figure 1 .

 1 Figure 1. Chemical structures of investigated materials and diagram of energetic levels. The values of energetic levels according to ref. 4.

Figure 2 .

 2 Figure 2. Normalized photoluminescence spectra of PVK and PVK-PBD (40 wt %) thin films under excitation at 337 nm and electroluminescence spectra of single layer PLEDs prepared based on PVK and PVK-PBD (40 wt %) blend, measured for the same current density, 22 mA/cm 2 . The inset shows the corresponding absorption spectra.

Figure 3 .

 3 Figure 3. Three-dimensional thermoluminescence spectra for neat PVK film registered under the heating rate 7K/min after excitation by HBO-200 lamp with band filter at 15 K.

Figure 4 .

 4 Figure 4. TL spectrum map for neat PVK film (a) with separated monochromatic TL curves (b) and spectral resolved curves (c). Marked lines on TL map indicate: chosen wavelengths (horizontal lines) and chosen temperatures (vertical lines). The inset presents spectra of isothermal luminescence decay at 15 K before TL run.

figure 5 .

 5 figure 5. The monochromatic TL curve for = 550 nm (figure 5b) has main maximum at 105 K and a

Figure 5 .

 5 Figure 5. TL spectrum map for PVK-PBD (40 wt %) blend film (a) with separated monochromatic TL curve (b) and spectral resolved curve (c). Marked lines on TL map indicate: chosen wavelength (horizontal line) and chosen temperature (vertical line). The inset shows spectra of isothermal luminescence decay at 15 K before TL run.

  exciplexes (band at 550 nm) results in TL spectra. Moreover the addition of PBD to PVK causes the reduction of EL emission in the range 470-600 nm, what is related to the monomer and the excimer triplet states of carbazole groups, as discussed earlier. It results from two reasons: lower concentration of the carbazole groups in the blend and fact that the triplet exciplexes formation competes with a creation of the triplet excimers. The PBD molecules can cause capturing of carbazole group triplet excitons and simultaneously, the formed triplet exciplex can improve the transport process of charge carriers in the PVK-PBD blend as stated above.

Figure 6 .

 6 Figure 6. The comparison of electroluminescence spectra of single layer PLEDs (extracted from figure 2) and SRTL spectra registered at the TL maximum temperature for PVK and PVK-PBD (40 wt %) films (extracted from figure 4c and from figure 5c).

Figure captions Figure 1 .

 captions1 Figure captions

Figure 2 .

 2 Figure 2. Normalized photoluminescence spectra of PVK and PVK-PBD (40 wt %) thin films under

Figure 3 .

 3 Figure 3. Three-dimensional thermoluminescence spectra for neat PVK film registered under the

Figure 4 .

 4 Figure 4. TL spectrum map for neat PVK film (a) with separated monochromatic TL curves (b) and

Figure 5 .

 5 Figure 5. TL spectrum map for PVK-PBD (40 wt %) blend film (a) with separated monochromatic TL

Figure 6 .

 6 Figure 6. The comparison of electroluminescence spectra of single layer PLEDs (extracted from

Figure 1 (

 1 Figure 1 (Figure6_Glowacki_2010.TIF)

Acknowledgements

The authors are grateful to Prof. J. Ulanski and Prof. J. K. Jeszka for helpful discussion.


N Jidenko

E Bourgeois

J-P Borra

Temperature profiles in filamentary Dielectric Barrier Discharges at atmospheric pressure

The physico-chemical properties of atmospheric pressure filamentary Dielectric Barrier Discharge (f-DBD) depend on its electrical characteristics and thermal profile. In this paper, a method for separating thermal and electrical effects is developed. Therefore, thermal profiles of f-DBD are studied for well defined electrical characteristics of filaments: all filaments are quasi identical with a controlled spatio-temporal density. The temperatures of gas, dielectric surface and plasma depend on the surface density and the temporal frequency of the filaments and can be altered by modifying the heat transfer. Different methods to control these temperatures are depicted. Moreover, heat transfer through conduction and convection from dielectric surface is shown to be the dominant heating mechanism for the flowing gas in the reactor. Finally, experimental results show that the temperature gradient around filaments can be controlled by the frequency of the applied voltage. Actually, the temperature difference between the filament and surrounding gas is independent of the applied frequency below 10 kHz. However, above 10 kHz, it increases linearly with the frequency. At high frequency, the time between two successive filaments occurring at the same position becomes smaller than the relaxation time constant of the thermal exchanges (~0.1 ms). Thus, this rise in temperature can be attributed to inefficient heat transfer from the filament formation zone.

Introduction

Reactive and ionising properties of non-equilibrium plasmas at atmospheric pressure have been investigated for oxidizing properties, for pollution abatement, surface treatments, as well as for aerosol charging and production [START_REF] Kogelschatz | From ozone generators to flat television screens: history and future potential of dielectric-barrier discharges[END_REF][START_REF] Kogelschatz | Dielectric-barrier discharges: Their history, discharge physics, and industrial applications[END_REF][START_REF] Kozlov | Spatio-temporally resolved spectroscopic diagnostics of the barrier discharge in air at atmospheric pressure[END_REF][START_REF] Hammer | Application of plasma technology in environmental techniques Contrib[END_REF][START_REF] Fridman | Non-thermal atmospheric pressure discharges[END_REF]. The AC polarisation of millimetre plane-toplane Dielectric Barrier Discharges (DBD) in air at atmospheric pressure mostly leads to similar thin and brief discharge filaments [START_REF] Kogelschatz | Dielectric-barrier discharges. Principle and applications[END_REF][START_REF] Massines | Experimental and theoretical study of a glow discharge at atmospheric pressure controlled by dielectric barrier[END_REF][START_REF] Rahel | The transition between different discharge regimes in atmospheric pressure air barrier discharge Contrib[END_REF]. In filamentary Dielectric Barrier Discharge (f-DBD), the temperature profiles of the heated volumes of FD and surfaces are critical for the transport of primary species (diffusion, thermophoresis) and for the kinetics of chemical reactions and of nucleation [START_REF] Eliasson | Ozone synthesis from oxygen in dielectric barrier discharges[END_REF][START_REF] Borra | Nucleation and aerosol processing in atmospheric pressure electrical discharges: powders production, coatings and filtration[END_REF][START_REF] Borra | Atmospheric pressure plasmas for aerosols processes in materials and environment The[END_REF][START_REF] Parissi | Electrical discharges for environmental purposes: fundamentals and applications[END_REF].

Despite moderate gas heating (below 500 K), the composition and the concentration of stable chemical species and aerosol particles produced by f-DBD depend on the thermal profile of the discharge gap. In this article, the term "thermal profile" refers to the reactor temperatures (plasma, gas and surface), thermal gradients and their (temperature and thermal gradients) evolution in time. The periodic evolution of local temperature profiles around filaments controls the thermal diffusion of primary species and the kinetics of local surface and volume reactions. Thus, the temperature profile partly controls the unitary production of chemicals per filament and the related total production of the reactor [START_REF] Borra | Nucleation and aerosol processing in atmospheric pressure electrical discharges: powders production, coatings and filtration[END_REF][START_REF] Eichwald | Chemical kinetics with electrical and gas dynamics modelization for NOx removal in an air corona discharge[END_REF][START_REF] Marode | Time Resolved Temperature Measurements and Computation of Streamer Air Discharge and Diffusion Controled[END_REF].

For instance, ozone production is related to both energy density (ratio of input power and gas flow rate in J.L -1 ) and dielectric surface temperature. Ozone decomposition is favoured at high surface temperatures by two main mechanisms i) surface reactions and ii) reactions with NOx formed at high temperatures (> 350 K) [START_REF] Kogelschatz | From ozone generators to flat television screens: history and future potential of dielectric-barrier discharges[END_REF]. The decomposition by NOx is known as discharge poisoning and was first reported in 1860 [START_REF] Andrews | On the volumetric relations of Ozone and the action of the electrical discharge on oxygen and other gases Q[END_REF].

This study is focused on the control of thermal profile in f-DBD. The two main objectives are :

Confidential: not for distribution. Submitted to IOP Publishing for peer review 2 June 2010 i)

to evaluate the main thermal processes and to identify the main operating parameters controlling the temperature profiles, ii)

to show that the temperature as well as the temperature gradient can be partly decoupled from electrical parameters. This study is part of a broader experimental approach that aims to identify the relative influence of temperature and temperature gradient on the chemical and physical processes (e.g. ozone production/destruction kinetics, nucleation of condensable gaseous species, aerosol charging dynamics, aerosol kinematics…) involved in f-DBD [START_REF] Borra | Charging of aerosol and nucleation in atmospheric pressure electrical discharges Plasma Physics and Controlled Fusion[END_REF][START_REF] Jidenko | Kinematics of charged nanometric particles in silent discharges[END_REF].

Numerous studies deal with rotational temperature measurements of the gas inside the discharge filaments, heat exchange and energy balance in DBD. Whatever the initial gas temperature is, the temperature rise in the filaments in Ar, H 2 O mixtures (i.e. the temperature difference between the neutral species in the filaments and the surrounding gas) is constant of about 50 K [START_REF] Motret | Rotational temperature measurements in atmospheric pulsed dielectric barrier discharge -gas temperature and molecular fraction effects[END_REF].

Methane fed DBD has recently been investigated with a particular focus on the energy balance and it appears that over 50 % of the input power is ultimately converted into heat through the dielectric barriers [START_REF] Nozaki | Energy distribution and heat transfer mechanisms in atmospheric pressure non-equilibrium plasmas[END_REF][START_REF] Kappesa | Energy balance of a dielectric barrier discharge reactor for hydrocarbon stream reforming[END_REF]; for a 0.5 mm gap length, the temperature rise in the filaments is constant of about 100 K whatever the input power and the gas flow velocity are [START_REF] Nozaki | Energy distribution and heat transfer mechanisms in atmospheric pressure non-equilibrium plasmas[END_REF]. Similar results have been obtained in He and air, with a cylindrical arrangement. The fraction of the input power that is dissipated as heat highly depends on the gas composition and decreases with increasing input power [START_REF] Sadat | Conduction heat transfer in a cylindrical dielectric barrier discharge reactor[END_REF].

Models have highlighted that temperature rise in the filaments depends on the energy injection in the filament and on the dynamic of energy dissipation, including the changes in enthalpy due to chemical reactions and radiative decay of excited states [START_REF] Xu | Ion composition of expanding microdischarges in dielectric barrier discharges[END_REF]. The temperature rise in a filament depends on the energy of filament and is not constant along the filament. It varies from 5-25 K in the middle of filament to a maximum temperature of 200-800 K on the cathode for ε r =5-50 [START_REF] Sadat | Conduction heat transfer in a cylindrical dielectric barrier discharge reactor[END_REF][START_REF] Xu | Ion composition of expanding microdischarges in dielectric barrier discharges[END_REF]. Moreover for a 2 mm gap length with ε r =5, the mean temperature rise due to joule heating is about 27 K, after 0.34 µs there is an additional temperature rise of 23 K, due to excited states of N 2 dissipating their energy into translational modes [START_REF] Xu | Ion composition of expanding microdischarges in dielectric barrier discharges[END_REF].

Using smooth parallel dielectric surfaces in a given DBD arrangement, the electrical characteristics of filamentary discharges are the same within 25 % whatever the voltage and the frequency between 1 and 60 kHz are [START_REF] Jidenko | Electrical characterization of microdischarges produced by dielectric barrier discharge in dry air at atmospheric pressure[END_REF]. Under such defined electrical conditions, the control of heat exchange allows the modification of the temperature at constant electrical parameters. The dielectric surface and outgoing gas temperatures are measured to evaluate the thermal exchanges between filaments, surrounding gas and dielectric surfaces. The temperature and thermal gradient around filaments are evaluated through emission spectroscopy of the second positive system of nitrogen.

Experimental setup

Two similar dielectric barrier discharge arrangements with 0.5 and 1 mm gap widths are compared. The dielectric material is alumina. Brass electrodes 3 cm long and 1 cm wide were placed on opposite sides of the two parallel plates of alumina (roughness<0.08 µm, thickness e=0.55 mm, ε r ~9). The electrodes are designed to minimize edge effects. A silicon paste surrounding the electrodes prevented the formation of arcs and other parasite discharges outside the gap. Moreover, the DBD arrangements are conditioned between two half casings made of stumatite (aluminosilicate mineral) to control heat exchange with the environment.

A high sinusoidal AC voltage supplies the plasma reactors. The frequency was tuneable between 1 and 60 kHz, with a maximum peak-to-peak voltage of 21 kV. Current and voltage waveforms were stored with an oscilloscope for data-processing as described in [START_REF] Jidenko | Electrical characterization of microdischarges produced by dielectric barrier discharge in dry air at atmospheric pressure[END_REF] to define the input power, the number of filaments per surface and time unit and the electrical characteristics of the filaments (charge per pulse, maximum of the pulse current, duration).

The flow rate of dry air (relative humidity < 5%) was controlled with mass flow controllers between 1 and 6 L.min -1 . The maximum mean gas velocity (gap width 1 mm) was 10 m.s -1 and the residence time in the DBD was between 3 and 18 ms. Optical emission spectroscopy of the second positive system of nitrogen (C 3 Π u B 3 Π g ) was performed to evaluate the kinetic temperature of neutral molecules in the filament (hereafter referred as plasma temperature, at +/-30 K in the range 300-3000 K) as described in [START_REF] Chelouah | A new method for temperature evaluation in a nitrogen discharge[END_REF]. The rotational temperature of the excited state C 3 Π u is determined by comparison of experimentally measured spectra with simulated spectra of the second positive system of nitrogen. The theoretical spectra are calculated from the analysis detailed in [START_REF] Hartmann | Measurements of relative transition-probabilties and variation of electronic-transition moment for N2 C PI-3(U)-B PI-3(G) second positive system[END_REF]. Rotational and translation temperatures can differ. Nevertheless, at high pressure, low energy collision transfer is efficient and relaxations are fast enough for the equilibrium to be completely established at the photon emission, molecules in the rotational states and neutral gas molecules are thus in equilibrium. Hence, the rotational temperature of the excited state C 3 Π u , corresponds to the temperature of neutral species in the plasma [START_REF] Chelouah | A new method for temperature evaluation in a nitrogen discharge[END_REF][START_REF] Petit | Electrical characterization of gas discharges using a numerical treatment[END_REF]. The light is collected with an optical fibre in a cone of 12.5 °acceptance angle for 30 seconds. As a result, the collected light is an average in time and space of the emission of several filaments. Moreover, the filament temperature is overestimated due to the collection of the light from the spots situated at the filament bases which are hotter than the filament. Nevertheless, we assume that the evolution of this measured temperature is representative of the evolution of filament temperature.

The average (in time and space) temperature of the dielectric surface (Ts) was evaluated by the measurement of electrode temperature (Tel) with a K-type thermocouple. Simulation results show that the average dielectric surface and the electrode temperature are similar within a few Kelvin at thermal quasi-equilibrium state. Calculation have been conducted assuming stationary and uniform heat transfer to the dielectric surfaces and taking into account heat conduction through dielectric plates, electrodes and casing as well as radiative and convective transfers from casing to ambient air,

The temperature of the outgoing gas (Tg) was measured with a K-type thermocouple downstream a copper tube (3 cm long with 10 mm inner diameter leading to transit time from 140 to 840 ms).

Results and discussion

One route to develop aerosol processes by atmospheric pressure electrical discharges is based on the control of physical and chemical mechanisms by electro-thermal decoupling. As the discharge filaments are quasi identical, macroscopic measurements downstream of the DBD (e.g. ozone concentration, aerosol concentration, aerosol mean charge…) can be used to study local mechanisms occurring around one filament. Macroscopic measurement is related to the cumulative effect of the local contributions of different filaments, this contribution should be weighted by a factor depending on the evolution and the mixing along the reactor. The influence of temperature on each mechanism can thus be investigated by electro-thermal decoupling i.e. with (i) different temperature profiles at constant electrical characteristics of the plasma or (ii) similar temperature profile with different charges per filament or (iii) similar temperature profile and charge per filament with different distributions of filaments in time and space. The electro-thermal decoupling thus implies the independent control of the characteristics of quasi-identical filaments, of their distribution in time and space, and of the temperature profiles through heat exchange at constant electrical parameters.

The electrical characterisation of DBD has already been presented in [START_REF] Jidenko | Electrical characterization of microdischarges produced by dielectric barrier discharge in dry air at atmospheric pressure[END_REF][START_REF] Petit | Electrical characterization of gas discharges using a numerical treatment[END_REF]. The frequency of the applied voltage controls the repetition rate of the filament at the same place whereas the applied voltage controls the spacing between filaments. This paper focuses on thermal control and electro-thermal decoupling of filamentary-DBD at constant electrical characteristics of filaments through temperature measurements. One objective of this paper is to help users to dimension the DBD reactor to reach the temperature ranges required by the application (e.g. catalysis, soot combustion, self cleaned filter…).

The first section aims at defining the operating parameter ranges for which filaments are similar. Then, gas and surface temperature measurements are presented versus the number of quasi identical filamentary discharges. Different methods to decouple dielectric surface temperature from electrical parameters are presented. Finally, the temperature of neutral species in the filament and the local temperature gradient around the filament are estimated though optical emission spectroscopy measurements. The objective is to find a way to control the transport of chemical species and aerosol particles through the thermal profile tuned by frequency.

Similarity of discharge filaments

To define the operating parameter ranges (applied voltage, voltage frequency, gas flow rate and surface temperature) leading to quasi-identical filaments, a statistical analysis of the charge per current pulse related to filamentary discharge has been conducted.

The term filament refers here to a filamentary discharge also called microdischarge which develops by the streamer mechanism. The reader should be careful that another definition can be encountered: successive streamers, macroscopically observed as a bright spatially localized filament [START_REF] Fridman | Plasma Chemistry[END_REF]. For a gap of 1 mm, filament lasts 20 ns with typical current amplitude of 20 mA. Filaments are distributed in space but deposited charges on dielectric surfaces on both sides of the filament leads to the formation of a new filament in the axis of the charge spot, every time the polarity changed. The energy per filament is a critical characteristic to study the dynamic of energy injection in the reactor. The energy per filament can be considered as proportional to the charge per filament [START_REF] Kogelschatz | Ozone synthesis in gas discharge[END_REF]. The factor of proportionality depends on the nature of the gas and the discharge arrangement.

The frequency distributions of charge per current pulse at 1 kHz (input power P=1 W and electrode temperature Tel=25 K) and 60 kHz (P=20 Watt, Tel=150 K) for a peak-to-peak voltage (V pp ) of 17.2 kV are plotted in Figure 2 (a). The evolution of the mean charge per filament with the applied peak-to-peak voltage is depicted for the 1 mm gap DBD, at 60 kHz in Figure 2 For a given operating condition, all the filaments are similar within 25 % which validates the experimental approach used.

At voltage frequency of 1 kHz and 60 kHz, the average charge per pulse is 0.23 and 0.22 nC with standard deviation of 0.06 and 0.003 respectively (cf. Figure 2 a).

Varying the applied voltage, from 11 to 20 kV, leads to a decrease of the mean charge per filament by 25 % (cf. Figure 2 b). The filaments lay charges on both dielectric surfaces which reduces the electric field strength to below the extinction field until the next half period. During the next half period, the charges deposited on both dielectric surfaces increase the field strength until the next filament develops at the same place. Decreasing the inter-filament distance results in a shielding effect from surface charges of adjacent filaments which reduces the quantity of charge per filament [START_REF] Gibalov | The development of dielectric barrier discharges in gas gaps and on surfaces[END_REF]. For a given geometry, the number of microdischarges per half period, distributed in time and space on the total surface of the plane-to-plane DBD, depends almost entirely on the applied voltage; the voltage frequency only plays a minor role [START_REF] Gibalov | The development of dielectric barrier discharges in gas gaps and on surfaces[END_REF]. At first sight, one can consider that filaments occur at the same location. Thus, the evolution of the electric field profile is repeated at the frequency as the applied voltage. Planeto-plane DBD leads to the reproduction of quasi identical filament with a controlled number per time and surface unit with respect to voltage and frequency.

Changing the gas flow rate from 1 to 6 lpm results in a 14 % increase of the mean charge per filament (0.18 nC to 0.21 nC) with a reduction of the dispersion (standard deviation from 14.5 to 5.7 pC). This effect is probably due to the fact that the volume in which the filament occurs is better purged the higher the gas flow rate is. Indeed remaining active species produced by the preceding filament, occurring at the same place, modify the physical processes such as ionisation and attachment for the formation of a new filament.

The variation of average gas temperature, from 300 to 420 K, leads to the decrease of the mean charge per filament within less than 5 %. Thus, the reduction of the average charge per filament with the increase of the applied voltage frequency, observed in Figure 2, can be partly attributed to thermal effects. Many parameters driving plasma electrical properties are affected by gas and surface temperature (gas density, surface conductivity of dielectric material, secondary emission...).

Gas temperature affects the gas density which in turn modifies reduced electric field (ratio between electric field and gas density) and hence the related electron energy distribution. Nevertheless, for different temperatures, electrical pulses are quasi identical. The similarity of current pulses proves that filaments occur for identical reduced electric field. This is confirmed by the linear reduction in the applied onset voltage for filament initiation, with the increase in temperature [START_REF] Bourgeois | DBD as a post-discharge bipolar ions source and selective ion-induced nucleation versus ions polarity[END_REF]. For instance, at 21 kV peak-to-peak voltage, the first filament in positive polarity occurs for mean applied voltages of -2.2 kV and -4.5 kV at 300 K and 540 K respectively.

Moreover, the gas density also modifies the distribution of ion space charge required to fulfil Meek's criterion; the propagation of the filament is thus affected. Surface conductivity can modify the surface charge distribution on dielectric surface and the related electric field profile. Finally, the dielectric surface temperature controls the secondary emission. Nevertheless, the electrical characteristics of the filament (charge per filament, reduced electric field profile and electron energy distribution function) can be considered as similar.

To summarize, due to the retro control of the electric field by dielectric surface polarization, filaments can be considered as similar to within 25% (based on charge per filament), whatever the frequency (from 1 to 60 kHz), the applied voltage (from 11 to 20 kV), the average dielectric surface temperature (from 300 to 470 K) and the gas flow rate (from 1 to 6 lpm) are.

The energy per filament depends on the gap length, the specific capacitance of the dielectric material (ε r /e with ε r the relative permittivity of the dielectric material and e the thickness of the dielectric material), the composition and the temperature of the gas. The number of filaments per period depends on the electrode area, applied voltage, gap length and specific dielectric capacitance. Finally, the input power is the product of the energy per filament, the number of filaments per period and the frequency. Operating parameter ranges leading to similar filaments are now defined and thermal exchanges can be investigated.

Gas and surface temperatures versus the number of similar Filamentary Discharges per time and surface unit

Each filamentary discharge is a source of heat, transferring parts of its energy to dielectric surfaces and flowing gas. The dielectric surface temperature depends on the balance between heat sources (input power, area of the electrodes) and heat sinks (shape and mass of the electrodes and of the casing and gas flow regime as well as ambient temperature).

Heat transfer from the plasma to the surface relies on radiative, conductive and convective transfers of charged and neutral species. Moreover, ion neutralization, metastable energy transfer and exothermic chemical reactions on the surface contribute to surface heating. Finally, the high frequency component of the current induces dielectric losses leading to heating of the dielectric material [START_REF] Kappes | Energy balance of a dielectric barrier discharge reactor for hydrocarbon stream reforming[END_REF]. The gas is heated by electron elastic collisions in the plasma but this mechanism is not important since electrons are lighter than gas molecules. Exothermic chemical reaction and metastable de-excitation (in particular for vibrationally excited species) also contribute to gas heating along the reactor.

Surfaces are cooled down by (i) the incoming gas flow which is heated by conductive, convective and radiative transfers from dielectric surfaces (ii) conduction in the bulk of dielectric material and subsequent heat transfer to DBD casing and ambient atmosphere by convective transfers.

The electrode temperature (which differs from the mean dielectric surface temperature by only a few degrees, cf. section 2) is plotted, at quasi-steady state, versus input power for the 1 mm gap DBD with a gas flow rate of 2 lpm in Figure 3 (a) and for the 0.5 and 1 mm gap DBD at constant flow velocity in Figure 3 For a given gas flow rate, the electrode temperature linearly increases with the input power (cf. Figure 3 a). The relation between electrode temperature and input power does not change with the voltage frequency, i.e. whatever the distribution of identical filaments in time and space is (cf. section 3.1).

In Figure 3 (b), for different gap lengths (1 mm and 0.5 mm, leading to charge per filament of 0.22 and 0.5 nC respectively) the relation between electrode temperature and input power is the same. Hence, similar transit times and flow regime (Reynolds numbers of 40 and 70 for 0.5 and 1 mm gap respectively) in the reactors lead to similar heat exchanges. Convective transfers between the dielectric surface and flowing gas seems thus to be dominant as shown hereafter. As a conclusion, the relation between electrode temperature and input power is independent of the dynamics of energy injection (energy per filament and filament distribution in time and space), for a given gas flow rate.

The influence of the gas flow rate on the electrode and gas temperature is plotted in Figure 4 for the 0.5 mm DBD with an input power of 16 Watts (V pp = 16 kV, F=60 kHz). The reduction of the electrode temperature with the gas flow rate is due to the increase in the heat flux transferred in the flowing gas. Indeed, the enthalpy gained by the feed gas (Q m .C p .∆T) increases with increasing gas velocity. Here, Q m is the air mass flow rate (kg.s -1 ), C p is the specific heat capacity of air (kg.s -1 ) and ∆T is the gas temperature increase within the DBD reactor.

Figure 4 shows that the gas temperature, at 4 cm of the DBD exit, presents a maximum versus the flow rate. This maximum depends on the input power or the position of measurement. The copper tube at the exit of the DBD acts as a heat exchanger. At low gas flow rate (below 2 lpm), the residence time in the copper tube is higher leading to lower gas temperature. At high gas flow rate, the reduction of the gas temperature is due to the reduction of the dielectric surface temperature by the gas flow rate. The measured curve is thus an artefact. On approaching the position of measurement to the discharge, the differences between the curves diminish. In laminar flow regime, the average gas temperature at the exit of the discharge is the same as the dielectric surface temperature. Electrode and gas temperatures follow similar evolution with the gas flow rate (cf extrapolation in Figure 4). Three following arguments support the fact that the convective transfer from hot dielectric surfaces, heated by filament, is the predominant transfer that heats the flowing gas.

The flowing gas is heated by electron-molecule elastic collisions in the filaments, by exothermal volume reactions, by de-excitation of vibrationally excited species. However these processes are less efficient than convective transfer from hot dielectric surfaces. Indeed, the gas temperature downstream the DBD never exceeds the electrode temperature by more than a few Kelvin. This difference can be due either to de-excitation of vibrationally excited species in post discharge or to the fact that the measured temperature is not the temperature of the dielectric surface at the hottest position.

Besides, most of heat transfer in mono DBD with cooled electrodes are directed on the dielectric surface because of plasma propagation on dielectric surfaces [START_REF] Nozaki | Energy distribution and heat transfer mechanisms in atmospheric pressure non-equilibrium plasmas[END_REF].

Finally, assuming a filament diameter of 10-100 µm [START_REF] Gibalov | The development of dielectric barrier discharges in gas gaps and on surfaces[END_REF], calculations from plasma temperature measurement (cf. section 3.4) show that the average enthalpy produced per time unit by the filament channel is lower than the enthalpy gained by the feed gas. These arguments tend to support convective transfers from dielectric surfaces to the gas as the predominant heating mechanism. Convection at least dominates at the entrance of the reactor where the maximum temperature difference between the gas and the dielectric surface is located.

As shown in Figure 4, the gas flow rate allows the modification of heat exchange and related temperatures with constant electrical parameters (filament characteristics and number of filaments per surface and time unit). The electro-thermal decoupling can also be achieved with other parameters described below.

Methods to control surface temperature with constant electrical parameters

The intensity of heat transfer by conduction, convection and radiation defines the final dielectric surface temperature. Indeed, the relative importance of the different mechanisms of heat exchange can be modified with respect to the flow regime, gas velocity and thermal exchanges around the reactor casing to control DBD surface temperature. For a given set of electrical working conditions and DBD arrangement (applied voltage frequency, electrode area, gas flow rate and external heat exchanges) leading to similar filaments within 5 %, table 1 gives examples of electrode temperature variations. As already shown in section 3.2, for a given input power, the electrode temperature is constant for all tested frequencies. Decoupling temperature from electrical parameters in DBD is possible by controlling thermal exchanges through the electrode shape, the gas flow rate, and the thermal conditioning of the DBD reactor by modifying heat exchange around the casings (with either insulation or a fan).

Heat exchange around the electrode depends on its shape and its thermal conductivity. The reduction of electrode area at constant input power leads to an increase of dielectric surface temperature. For instance at 13 watt, electrode temperature increases by 20 K for a factor 3 on the number of filament per surface unit. This effect is due to the increase of the number of filaments per surface unit and per period, as well as the reduction of radial heat exchange on the metal electrode.

The modification of heat exchange around the DBD casing either by limiting or forcing the convection allows the control of the dielectric surface temperature at constant input power (e.g. at 12 Watts per 3 cm 2 , the dielectric surface temperature is 300 K and is tuneable from 280 to 330 K). For the same input power and the same distribution of the filaments in time and space, the thermal conditioning of the DBD reactor leads to tuneable temperature within 50 K.

In most industrial processes based on DBD, accurate control of heat and mass transfer and kinetics is required. As the temperature profile depends not only on plasma properties but also on external cooling, the reactor design is thus important. Depending on the application, the discharge gap, the size of the discharge and the reactor as well as the operating conditions can be chosen to define the temperature range of the DBD. The key parameters governing the heat source (filaments) are the input power and the average surface input power. The key parameters governing the heat sink are the external surface of the reactor, the ambient temperature as well as the mass flow rate and the initial temperature of flowing gas in the DBD. The reduction of reactor size, for space requirement, often imposes the use of additional cooling systems to control the optimal temperature range.

However, the control of average gas and surface temperatures is not sufficient to control the transport of chemical species and aerosol particles. The temperature profiles around each filament have to be considered to account for transport phenomena (diffusion, convection and thermophoresis). Thus, the following section is devoted to local temperature gradients around filamentary discharges.

Plasma temperature and local temperature gradient

The aim of this section is to show that the thermal profile can be tuned by varying the applied voltage frequency.

Without any gas flow in the reactor, the evolution of mean gas temperature is evaluated from electrode temperature. Temperature of neutral gas molecules in the plasma channel (here after referred as plasma temperature), is evaluated as described in the experimental setup. This evaluation overestimates the plasma temperature in the filament due to the collection of the light from the spots situated at the filament bases. Figure 5 (a) represents the evolution of mean gas temperature and plasma temperature in the 1 mm gap width DBD reactor, at 60 kHz versus the input power (i.e. versus the number of filaments per half period and per square centimetre).

The average difference of temperature between the plasma and the surrounding gas, referred as the temperature rise in the filament is plotted versus the voltage frequency in Figure 5 (b). At 60 kHz, the plasma temperature is about 230 K higher than the surrounding gas temperature (cf. Figure 5 a), no matter what the number of filaments per surface and time unit is. This result is confirmed during the initial warm-up of the reactor, from ambient temperature to thermal equilibrium, during which the same temperature difference between the filament and the bulk gas is measured. For a given voltage frequency, the difference of temperature between plasma temperature and surrounding gas is constant. Thus, for a given energy per filament and voltage frequency, the local gradients around a filament are constant leading to similar transport phenomena around each filament.

The thermal gradients around a filament can be controlled either by the energy per filament or by the frequency of the applied voltage. The average temperature difference between the filament and surrounding gas increases with increasing energy per filament and frequency. If an adiabatic expansion of the filament channel occurs after the filament propagation [START_REF] Marode | Time Resolved Temperature Measurements and Computation of Streamer Air Discharge and Diffusion Controled[END_REF], then the modification of temperature gradient can be smoothed. With a 0.5 mm gap, the energy per filament is half smaller than with 1 mm gap and the temperature rise in the filament is reduced from 230 K to 100 K, as already observed in [START_REF] Braun | Two-dimensional modelling of the dielectric barrier discharge in air Plasma Sources[END_REF].

In Figure 5 (b), for frequencies the below 10 kHz, the temperature rise is constant at about 80 K (cf. Figure 5 b). For the frequencies above 10 kHz, the temperature rise in the filament increases with the frequency. This effect has already been reported in N 2 /Ar at 100 Torr where filament temperature increased from 380 to 400 K with the frequency from 0.5 kHz to 30 kHz [START_REF] Williamson | Gas temperature determination in a N2/Ar dielectric barrier discharge by diode-laser absorption spectroscopy and resolved plasma emission[END_REF]. The residual heating of the filament channel between two successive filaments occurring at the same location in successive half periods is involved. Hence, the relaxation time constant of temperature can be estimated at about 0.1 ms in dry air at atmospheric pressure, which is consistent with [START_REF] Marode | Time Resolved Temperature Measurements and Computation of Streamer Air Discharge and Diffusion Controled[END_REF][START_REF] Eichwald | Chemical kinetics with electrical and gas dynamics modelization for NOx removal in an air corona discharge[END_REF].

Above 15 kHz, the residual heating of the filament channel leads to a lower onset voltage for filament development. As filaments have similar charge per pulse (cf. section 3.1) the reduction of onset voltage should lead to a reduction of the energy per filament. This is confirmed in Figure 6 which represents the mean surface energy density per period (the input power divided by the frequency and the electrode surface area) versus the peak-to-peak applied voltage for the 0.5 mm gap DBD. For a given frequency, the mean surface energy density injected by period (Ps/F in J.m -2 , with Ps, the ratio of input power and surface electrode, and F the frequency) increases linearly with the applied voltage due to increasing number of similar filaments per surface unit and per period. For a given voltage, the energy per period is constant from 0.8 to 1.5 kHz and is lower for frequencies above 15 kHz. This reduction of energy is due to the increase of the gas temperature in which the filament develops. This is confirmed by the reduction of the measured input power while the gas temperature increases at 60 kHz for a given voltage.

Assuming a constant number of filaments per period, the reduction of energy per period is related to the reduction of the energy per filament. As the charge per filament is constant (cf. section 3.1), the reduction of the energy per filament is due to the reduction of the onset voltage of the filament. At 20 kV, the energy per period is 0.72 mJ at 1 kHz and 0.47 mJ at 60 kHz. Assuming a constant reduced field threshold for the formation of the filament, the ratio of filament energy is the inverse of temperature ratio. As the gas temperature is around 300 K at 1 kHz, the gas temperature at 60 kHz should thus be around 459 K (0.72/0.47*300 K). In fact, the average gas temperature is about 435 K, the difference being due to filament channel residual heating.

To summarize, the reduction of energy per period with increasing frequency is due to the reduction of the energy per filament. The lower energy per filament is due to lower onset voltage at constant charge per filament, related to both increasing average gas temperature and residual heating of the filament channel for frequency higher than 10 kHz.

Conclusions

This paper presents a method to identify the influences of gas and surface temperatures as well as temperature gradient on the relative importance of different physical and chemical mechanisms at constant filamentary discharge electrical characteristics. The main regulating parameters to control temperature and thermal gradient are depicted.

For given operating conditions, the mean dielectric surface temperature linearly increases with the input power density and is independent of the dynamics of energy injection (energy per filament and filament distribution in time and space).

Gas flow rate and thermal conditioning (forced or limited convection around the reactor) allow the modification of the equilibrium temperatures without changing the electrical parameters.

The invariance of the temperature rise in the filament, for a given discharge arrangement at a given frequency, no matter what the surrounding gas temperature is, as well as the increase of the temperature rise in the filament with the energy per filament have been confirmed.

Moreover, it was shown that the temperature rise is constant below 1.5 kHz (80 K with a 1 mm gap DBD) but increases for frequencies higher than 15 kHz (up to 230 K with a 1 mm gap DBD, at 60 kHz) due to residual heat from the preceding one at the same location. The temperature gradient around filaments can thus be controlled by the frequency of the applied voltage above 15 kHz.

Based on these results, the respective influences of transport (diffusion, convection and thermophoresis) and kinetics (chemical, nucleation) involved in the production of chemical species and aerosol may be determined by controlling radial thermal gradients around filamentary discharges as well as gas and surface temperatures with constant filament electrical characteristics (charge per filament, reduced electric field and electron energy distribution function).

These results are of particular interest when DBD is used for specific chemical reaction and especially for thermal conditioning of catalysts or for thin film deposition processes by chemical vapour deposition. Moreover, the kinematics of aerosols injected or produced in DBD depends on the thermal profile of the DBD and has to be controlled to develop aerosol processes based on DBD.

Figure 1 :

 1 Figure 1: Experimental setup for electrical and thermal characterizations.

  (b).

Figure 2 :

 2 Figure 2: (a) Frequency distributions of charge per filament at 1 kHz (P=1 Watt, Tel=25 K) and 60 kHz (P=20 Watts, Tel=150 K) for the 0.5 mm gap length DBD at 4 lpm (b) Mean charge per filament versus applied peak-to-peak voltage, the error bars correspond to standard deviation, 1 mm gap, at 60 kHz and 1 lpm.

  (b).

Figure 3 :

 3 Figure 3: Electrode temperature versus input power (a) at different frequencies of applied voltage 1.5, 30 and 60 kHz (b) for 0.5 and 1 mm gap length at constant gas flow velocity.

Figure 4 :

 4 Figure 4: Electrode and gas temperatures versus gas flow rate at 60 kHz in the 0.5 mm gap DBD.

Figure 5 :

 5 Figure 5: (a) Mean temperatures of gas and plasma versus input power (60 kHz) (b) Temperature rise in the filament versus frequency.

Table 1 :

 1 Evolution of electrode temperature at constant electrical characteristics of filaments

	Parameters	Variation	Input Power (Watt) ∆Tel (K)
	Frequency	from 1 to 60 kHz	For any given	< 10
	Electrode area	from 3 to 1 cm 2	13	+20
	Gas flow rate	from 1 to 6 L.min -1	14	-50
	Heat exchanges	Limited (thermal cover) Forced (fan)	12 12	+30 -20

  Mean surface energy density per period at different frequencies from 0.8 to 60 kHz, 0.5 mm gap.

		0.3
			800 Hz, 2 lpm	15 kHz, 1 lpm	F<1.5 kHz
			1 khz, 0.5 lpm	15 khz, 1 lpm
			1 khz, 1 lpm	30 khz, 1 lpm
			1 khz, 2 lpm	60 khz, 0.5 lpm
	Ps/F (mJ.cm ) -2	0.1 0.2	1 khz, 3 lpm 1.5 kHz, 2 lpm	60 kHz, 1 lpm 60 kHz, 1 lpm	F>15 kHz
		0
		6	10	14	18	22
				Vpp (kV)
	Figure 6:

Acknowledgments

The authors wish to thank Dr. Robert Haug for his contribution in thermal simulations as well as Dr. Michael Kirkpatrick and Dr. Syed Salman Asad for English corrections.