Amer Hamidi-Sakr

Laure Biniek

Jean-Louis Bantignies

David Maurin

Laurent Herrmann

Nicolas Leclerc

Patrick Lévêque

Vishnu Vijayakumar

Nicolas Zimmermann

Martin Brinkmann

A Versatile

come

Figure for title of content

Short Summary

A versatile method is proposed to produce oriented and crystalline conducting polymer films. It combines alignment of semiconducting polymers by high-temperature rubbing with a soft-doping method. The oriented films show important anisotropy of UV-vis-NIR absorption, charge conductivity and thermoelectric properties. The polymer side chain packing plays a key role on the intercallation of dopant molecules in the host polymer.

Conducting polymers were among the pioneering materials in the field of plastic electronics and have been the focus of intensive research efforts and studies in the early eighties. 1,2 Generally, conducting polymers are obtained by redox or acid-type doping of highly conjugated polymers such as poly(diacetylene) or poly(aniline). 2 At present, doped semi-conducting polymers are present in the elaboration of numerous devices in the form of charge transporting or injecting layers.

Poly (3,4ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS) for instance is widely used in the fabrication of photovoltaic devices and more recently in thermoelectric devices. [START_REF] Perepichka | Perepichka in Handbook of Thiophene-Based Materials: Applications in organic electronics and photonics[END_REF][START_REF] Bubnova | [END_REF] However, most conducting polymers are of poor structural quality as compared to semiconducting polymers such as poly(3-hexylthiophene). 2,5 At the same time, structural and electronic disorder are known to be two major hindrances for efficient charge transport properties in polymeric materials. 6,7 High disorder in conducting polymers is mainly due to the random distribution of dopants in the polymer matrix during the fabrication process. Charge transport in conducting and semiconducting polymers is intrinsically highly anisotropic. It is most effective along the chain and the -stacking directions. [8][9][10] This implies that orientation can be an efficient mean to improve charge transport in both conducting and semi-conducting polymer thin films. Importantly, oriented conducting polymer layers could be of interest as alignment layers for other semiconducting films to fabricate polarized light emitting diodes. [START_REF] Scheler | Liquid Crystalline Semiconductors: Materials, properties and applications[END_REF] At present, methods to prepare highly crystalline and oriented conducting polymer layers are scarce. Orientation of polyacetylene was achieved by various methods, including polymerization under shear flow or in an oriented nematic liquid crystal. 12, 13 However, such films present very rough morphologies consisting of large micrometer-scale fibers. 13 Rubbing thin films of PEDOT:PSS leads to surface scratching rather than true chain alignment that is hampered by the strong electrostatic interactions between charged PSS and PEDOT. 14 Controlled doping of crystalline polymer semiconductors appears as a viable alternative approach towards conducting polymers with well-defined structure and electronic

properties. Several recent studies on soft doping from solution or from the vapor phase of polymer semiconductors have demonstrated that both elevated charge conductivities and structural control can be obtained. 7,[15][16][17] For instance, Sirringhaus and coworkers have shown that high vacuum sublimation of F4TCNQ dopant molecules on PBTTT films results in conductivities of the order of 250 S/cm. 7 Podzorov et al. showed that doping of P3HT and PBTTT with hydrolyzed fluoroalkyl silane (FTS) leads to conductivities of 50±20 S/cm and 1000 S/cm, respectively. 18 Several groups investigated the doping of P3HT with 2,3,5,6-tetrafluoro-7,7,8,8-tetracyanoquinodimethane (F4TCNQ) that results in the formation of delocalized charge carriers in the form of polarons or bipolarons. 15- 20 UV-Vis spectroscopy helped to follow the doping process and to characterize the electronic species resulting from doping. Moreover, such conducting polymers were shown to be interesting materials to fabricate thermoelectric devices as these doped polymer semiconductors show high charge conductivities, high Seebeck constants and low thermal conductivities. 22,23 On the other side, means exist to control precisely the crystallization and orientation of conjugated polymers such as P3HT or PBTTT. High orientation of polymer semiconductors in thin films was achieved by using various methods including shear coating, 24 stretch-alignment, 25 epitaxy 26 and mechanical rubbing. 27 Rubbing P3HT at temperatures in the 150°C-240°C range results in remarkable alignment with crystallinity exceeding 60%. 9 Moreover, the lamellar periodicity of the polymer can be precisely controlled by the temperature at which the films are rubbed. 9 Such oriented and crystalline P3HT or PBTTT films are of particular relevance to probe the mechanism of F4TCNQ doping on the resulting electrical conductivities and optical properties of the conducting polymer films.

In this contribution, we propose a general method to produce oriented and highly Polarized UV-Vis-NIR spectroscopy confirmes the orientation and the doping of the rubbed P3HT films. Figure 1.d shows the UV-Vis-NIR spectra for a P3HT film rubbed at 220°C and subsequently doped with a 1mg/ml solution of F4TCNQ in ACN. As seen in Figure 1.d, the absorption is strongly polarized. The spectra recorded for parallel (POL//) and perpendicular (POL) orientations have different and characteristic features of doped P3HT and F4TCNQ -anions, respectively.

For POL//R, the characteristic polaronic bands P1 and P2 located at 2500 nm (0.5 eV) and 795 nm (1.56 eV), respectively, result from the doping of P3HT with F4TCNQ. The angular dependence of the intensity of the P1 band was measured and compared to that of the absorption at 600 nm of the pristine rubbed P3HT films (see Figure S1). Both curves are perfectly matching and show almost identical full widths at half maximum. Thus polarized UV-Vis-NIR shows that the in-plane orientation of P3HT chains is fully maintained upon doping with F4TCNQ from a solution in ACN.

For POL//R, the absorption at 570 nm is close in position to the undoped P3HT but it does not show any vibronic structure. Noteworthy, this band's position is also close to the expected polaronic P3 band (2.1 eV). 17 Most interestingly, the P1 and P2 bands are polarized along the rubbing direction with almost no contribution in the direction perpendicular to the rubbing, leading to a dichroic ratio >50. This indicates the formation of a metallic-like state in doped P3HT with highly mobile polarons moving essentially along the in-plane direction of P3HT chains (rubbing direction R).

The spectrum recorded for POLR is very different. It shows the characteristic bands of the F4TCNQ -anions at 413 nm, 770 nm and 873 nm (note that the 413 nm band is not due to neutral F4TCNQ, 7 that is characterized by a distinct absorption peak at 383 nm. See supporting information, Figure S2). The F4TCNQ -bands are quasi absent in the spectrum obtained for POL//R. Since the transition dipole of the F4TCNQ -anion is oriented along the long axis of the molecule 29 , this result implies that F4TCNQ -anions are oriented with their long axis strictly perpendicular to the chain direction of P3HT. This original result is at variance with some postulated structures of F4TCNQ-doped polymers. In P3HT and PBTTT, the F4TCNQ were thought to be intercalated between and oriented parallel to the conjugated polymer backbones with a strong -overlap between dopant and polymer. 7 As demonstrated below, the perpendicular orientation of F4TCNQ dopants with respect to the polymer chains holds also for other semiconducting polymers such as poly(3-octylthiophene) and C12-PBTTT.

For POLR, the UV-Vis-NIR spectra in Figure 1.d show a broad contribution at 489 nm, i.e. close to the absorption of amorphous P3HT in coiled chain conformation. 27 The absence of significant polaronic absorption and the presence of the absorption band of the amorphous P3HT in the spectra for POLR implies that amorphous interlamellar zones of P3HT are either marginally doped with F4TCNQ or that the doped states are strongly localized. Accordingly, it seems that the chain conformation of P3HT is of utmost importance for the doping by F4TCNQ: planarized rather than coiled chain segments seem necessary for efficient doping.

The quantity of dopants in the films was quantified from the intensity of F4TCNQ -bands the extinction coefficient of which is known (873 nm)= 50 000 mol . l -1 cm -1 ). 30 Typically,

P3HT films rubbed at 220°C and doped with a 1mg/ml F4TCNQ/ACN solution, are characterized by a doping ratio of 17-19% F4TCNQ molecules per 3-hexylthiophene monomer. 31 This value is fully consistent with the reported values for solution cast doped P3HT films. 15 Further essential information on the doped P3HT films is obtained by using polarized FTIR spectroscopy (see Figure 1.e). In the range 1500-4000 cm -1 , the spectrum shows the characteristic P1 polaronic band polarized parallel to the rubbing direction. For the polarization perpendicular to the chains, a broad band of weak intensity and centered around 2800 cm -1 is recorded. In the range 1500-800 cm -1 , the spectrum shows a set of very intense infrared active vibrational (IRAV) modes for POL//R that are absent for POLR. These peaks are absent in the pristine rubbed P3HT films and do not coincide with peaks from the F4TCNQ -anion. 32 Recent studies on PCPDTBT/F4TCNQ, P3HT/FTS or poly(3-decylthiophene) (P3DT)/NOPF6 have evidenced similar FTIR signatures. 33,34 The IR spectrum of poly(3-decylthiophene) + cations in CDCl3 in the range 1000-1500 cm -1 is quite similar to that of P3HT films doped with F4TCNQ. The observed intensity enhancement of absorption is assigned to the presence of dopant-induced hole polarons on the polymer chain. 32,33 Transmission electron microscopy (TEM) was used to evaluate the impact of doping on the thin film structure (see Figure 2). From a morphological point of view, the pristine films rubbed at 220°C show the periodic lamellar structure with alternation of crystalline and amorphous domains. TEM bright field (BF) shows that the doping does not alter this lamellar semi-crystalline structure. The total lamellar period is unchanged after doping (23 nm, see Figure S3, supporting information). In addition, the semicrystalline structure of the doped films is also observed in HRTEM. As seen in Electron diffraction (ED) was used to probe the impact of doping on the crystal structure. Figure 2.a and 2.b compare the ED patterns of doped (1mg/ml F4TCNQ/ACN) and undoped rubbed P3HT films. Most interestingly, the doped samples display a well defined ED pattern revealing high order after doping with F4TCNQ. The pattern is in essence quite similar to that of the undoped film. The presence of both h 0 0 (h=1-3) and 0 2 0 equatorial reflections indicates that the films consist of face-on and edge-on oriented crystals. Careful analysis shows that the 0 0 2 reflection along the rubbing direction is unaltered in position and intensity after doping, showing that doping did preserve both the aligned character of the films (consistent with POM and spectroscopic observations) and the crystalline order along the chain direction. A slight loss in intensity of the 1 0 2 and 2 0 2 reflections suggests some disorder introduced in the arrangement of side chains. In the direction perpendicular to the polymer chains, the equatorial 0 2 0 and the h 0 0 reflections (h=1-3) reveal a change in unit cell parameters after doping. Typically, the layer period d100, i.e. the distance between polymer chains separated by alkyl side chains, increases from 16.5 Å in pristine films to 17.6-18.0 Å after doping (consistent with HRTEM). The -stacking distance shows an opposite trend and decreases from 3.8 Å to 3.55 Å after doping. The analysis of the ED pattern shows that there is no coexistence of the doped and undoped phases of P3HT since the 16.5 Å reflection is absent from the ED patterns of samples doped with F4TCNQ at a concentration above 0.5 mg/ml. Accordingly, doped P3HT films consist of only one type of crystalline domains with expanded a unit cell parameter and reduced -stacking distance (reduced b axis parameter), the c axis remaining unaltered. This implies further that the presence of absorption features around 570 nm corresponding to "undoped" P3HT is not associated with the pristine undoped form I of P3HT but should be attributed to undoped P3HT chain segments within the crystals of the doped phase. the pristine form I of undoped P3HT 35 and the structure after doping with a 3 mg/ml solution.

2) Influence of doping level.

a) UV-Vis-NIR spectroscopy.

Further insight in the doping mechanism is obtained by following the spectroscopic and structural variations of rubbed P3HT films with increasing dopant level. The doping level is readily controlled by adjusting the concentration of the F4TCNQ/ACN solution from 0.01 to 3 mg/ml. 16 Figure 2.e shows the evolution of reticular distances d100 and d020 extracted from the ED patterns as a function of increasing dopant concentration whereas figure 3 shows the evolution of the UV-Vis spectrum as a function of increasing dopant concentration for the incident light polarized parallel and perpendicular to the chain direction for the rubbed P3HT films.

As expected, the intensities of the characteristic absorption peaks of both the polaron and the F4TCNQ -anions increase with the concentration of F4TCNQ in ACN. Even for dopant concentrations as low as 0.01 mg/ml, typical signatures of P3HT polarons and F4TCNQ -anions are observed, indicating charge transfer between P3HT and F4TCNQ. In addition the polaron bands are already strongly polarized parallel to the chain direction.

However, in the range of dopant concentration 0.01-0.1 mg/ml, the crystal structure of the films changes only marginally. The interlayer spacing d100 and the -stacking periods Most importantly, the fact that the P3HT polaron and the F4TCNQ -bands have orthogonal polarizations eases the quantification of these species and helps establish correlations between them. In Figure 3.d, the intensity of each of the P1 and P2 polaron bands is proportional to the absorbance of the F4TCNQ -anion i.e. to the quantity of anions in the films. This result supports an integer charge transfer between P3HT and F4TCNQ for all doping levels investigated herein. 15,19 More importantly, it underlines the possibility to control quite reproducibly the levels of doping in such oriented polymer films. Moreover, the absorbance of F4TCNQ -anions tends to level for solutions with a concentration beyond 1 wt%, suggesting that a maximum doping concentration is indeed reached for this film processing. This is further supported by the presence of small pristine F4TCNQ crystals on the surface of the doped films for 3wt % (similar to those observed previously in vapor-phase doped PBTTT films 7 ). (1 0 0) period. In the present case, the -stacking is also affected. 7 Our results suggest that a threshold concentration of dopants is necessary to induce the structural change to the doped phase with incorporation of F4TCNQ -anions in the layers of alkyl side chains. As seen in Figure 2.d, the h 0 0 spacings remain virtually unchanged up to a doping concentration of 0.1 mg/ml. However, even for such a low doping concentration, the intensities are reduced and the h 0 0 peaks are substantially broadened. As opposed to this, even for a concentration as low as 0.5 mg/ml, the h 0 0 The same alignment and doping protocol was applied to other semi-conducting polymers to validate its generality. First, we have considered the family of poly(3alkylthiophene)s in order to see if the length of the side chains influences on the doping mechanism/efficiency. Therefore, oriented films of poly(3-butylthiophene) (P3BT) and poly(3-octylthiophene) (P3OT) were subjected to the same doping method with F4TCNQ in ACN (1 mg/ml). Figure 4 depicts the change in ED pattern for P3BT and P3OT as a function of doping with F4TCNQ and indicates the same trend as observed for P3HT. The orientation of the films is maintained after doping and the structure of crystals is modified with an expansion of the lattice along the alkyl side chains and a contraction along the -stacking direction. In P3OT, the unit cell expands along the side chains from 20.1 Å to 22.6 Å as compared to 12.6 Å to 14.0 Å for P3BT. In both cases, the -stacking reduces to a similar value of 3.55 Å. For P3OT, polarized UV-Vis-NIR spectroscopy (see To validate the fabrication method of highly oriented conducting polymer films, we also prepared doped films of a different polythiophene, namely C12-PBTTT.

4) Anisotropy of charge transport and Seebeck coefficient.

The ability to obtain highly oriented crystalline films of conducting polymers provides a means to investigate the anisotropy of both charge conductivity and thermoelectric properties. Both, charge conductivity  and the Seebeck coefficient S can be measured along the rubbing direction and perpendicular to it. The Seebeck coefficient characterizes the heat transported by thermally excited charge carriers. 36,37 The transported heat depends on the band structure and scattering events of the material. Most interesting for thermoelectric applications is the power factor given by the formula PF=S 2 . As seen in Figure 5.d, PF is enhanced along the rubbing direction and reaches a value of approximately 8.5 V . m -1. K -2 for CF4TCNQ=1 mg/ml which is of the same order of magnitude as that obtained in PEDOT:PSS thin films (24 V . m -1. K -2 ). 38 The simultaneous enhancement of  and S via polymer alignment is interesting from the point of view of thermoelectric properties. Indeed, usually, S and  are linked by the relation S -1/4 . 22 Therefore when the charge conductivity is increased with the dopant concentration, one observes a corresponding drop of the Seebeck constant. Because of this correlation between S and , an optimum doping concentration is necessary to maximize the power factors PF of thermoelectric (TE) devices. 22 In the present case, alignment of the polymer films allows to increase both  and S in the direction of the polymer chains. Therefore, a strategy of aligning conducting polymers could help enhance thermoelectric efficiency of polymer TE devices under the condition that the heat conductivity is not substantially enhanced along the chain direction.

III. Discussion.

The impact of dopant concentration on the film structure uncovered in the present investigation helps clarify the mechanism of doping of P3ATs by F4TCNQ. Two regimes of doping can be distinguished. For cF4TCNQ ≤0.1 mg/ml, the structure of the P3HT films is marginally modified although spectral signatures of doped species are observed. This result suggests that a surface doping mechanism is possibly at play without incorporation of dopants in the layers of side chains of the polymers. This situation is similar to the doping of P3HT with a surface layer of hydrolized fluoroalkyl trichlorosilane. 18 For CF4TCNQ >0.1 mg/ml, a doped phase is formed. For both P3HT and P3OT, the cell parameters a and b change simultaneously and progressively as a function of the concentration of incorporated dopants. TEM observations in bright field and HRTEM indicate that the semicrystalline nanomorphology of doped films is almost unaltered after doping. In addition, ED results demonstrate that the order inside the layers of stacked P3HT backbones is preserved upon doping. Therefore, the fact that the intensity of the 0 0 2 reflection is not altered upon doping rules out a doping mechanism whereby the F4TCNQ molecules would be intercalated between polythiophene backbones. 19,21 The present experimental results help support a doping mechanism as illustrated in Figure 2.f. In pristine P3HT, side chains and polythiophene backbones are tilted with respect to the b axis and alkyl side chains are not interdigitated. Accordingly, an expansion along the side chain direction and a contraction along the -stacking direction supports a structural reorganization whereby the -stacking of the backbones tends towards a more co-facial arrangement with the side chains oriented perpendicular to the polythiophene backbone. The evolution of the d100 period with doping concentration suggests that the tilt of backbones and side chains are controlled by the amount of incorporated F4TCNQ in the layers of side chains. For F4TCNQ-doped P3HT, a saturation of the dopant in the polymer is observed and corresponds to a saturation concentration of approximately one F4TCNQ per four hexylthiophene monomers (i.e. one F4TCNQ molecule per unit cell). 7 Our results on the influence of doping concentration support the idea of a progressive modification of the unit cell parameters with increasing doping concentration since we did not observe coexistence of doped and undoped crystals of P3HT. However, some threshold concentration is apparently required to triger the transition to the doped phase, a situation similar to that observed in iodine-doped pentacene. 39 The impact of doping on the family of P3ATs helps better understand the role of the length of alkyl side chains on the F4TCNQ uptake. The UV-Vis-NIR results demonstrate that F4TCNQ -anions are oriented by the alkyl side chains in P3HT and P3OT but not in P3BT. This is not surprising because the inter-layer spacing along the side chains is only 12.6 Å in pristine P3BT whereas the length of the F4TCNQ long axis is 12 Å.

Accordingly, the layer period of such short side chains is incompatible with i.e. cannot accommodate the long axis dimension of the F4TCNQ dopants. This suggests that the long axis of F4TCNQ molecules must be tilted to the backbone direction of P3BT. In other words, the ordering of the dopant molecules is determined by the length of alkyl side chains in poly(3-alkylthiophene)s.

Finally, the case of F4TCNQ doping of C12-PBTTT is further important to understand the impact of the packing of alkyl side chains on the doping mechanism. The P3ATs investigated herein have layers of non interdigitated side chains as illustrated in Figure 2.d. In sharp contrast, in C12-PBTTT the side chains are strongly interdigitated to form a dense lattice. 40 Incorporation of dopant molecules in such interdigitated layers requires major reorganization of the packing of the interdigitated side chains. As observed in our ED patterns, doping of C12-PBTTT with F4TCNQ results in a significant loss of order in the direction of the polymer chains as witnessed by a substantial intensity loss of the 0 0 3 reflection (see Figure 4.h). These results indicate that it is more difficult to incorporate F4TCNQ molecules into the layers of interdigitated side chains in PBTTT than in the layers of non-interdigitated side chains in P3ATs.

Regarding charge conductivity and its anisotropy, the observed trends with increasing F4TCNQ concentration are also interesting. First, the overall anisotropy factors ///  are in the range 5-15, i.e. are similar to the anisotropy of charge mobilities measured in bottom gate bottom contact OFETs of oriented P3HT films. 9 In all cases, the charge conductivity is enhanced along the rubbing direction. However, on a mesoscale, charges must travel through amorphous interlamellar zones that should be marginally doped. Therefore, in order to observe an enhanced charge conductivity on the mesoscale along the rubbing direction (chain direction), the crystalline doped lamellae of P3HT running perpendicular to the rubbing direction must be somehow interconnected. The Mw of the P3HT sample used in this study is such that the average contour length of the chains exceeds the lamellar period of 23 nm i.e. tie-chains that interconnect successive lamellae are indeed present. However, our previous study on high-T rubbed P3HT has clearly demonstrated that the tie chains crossing the amorphous interlamellar zones have a non planar, coiled-like conformation that disrupts -conjugation. Moreover, the UV-vis results indicate that doped interlamellar zones are poorly doped by F4TCNQ.

Therefore, doped tie-chains may not be sufficient to explain the enhanced charge conductivity parallel to the rubbing direction. Interconnection between crystalline lamellae may also occur via so-called tie-crystallites. A previous HRTEM study on oriented high-Mw P3HT films evidenced tie-crystallites that interconnect crystalline P3HT lamellae. 41 It is most likely that such tie-crystallites play also an important role on the mesoscale charge conductivity in such doped and oriented P3HT films. As for pristine aligned P3HT, the very regular periodic lamellar morphology observed in the oriented P3HT films for TR=220°C may be detrimental for mesoscale charge conductivities in doped thin films. It is likely that the percolation between crystalline domains via doped and highly conducting tie-crystallites is the most efficient way to ensure high charge conductivities along the rubbing direction. 9 Remarkably, the results in Figure 5.c show that the conductivity   is relatively constant and independent on the doping concentration. The conductivity   corresponds to a macroscopic charge transport accross multiple crystalline domains of doped P3HT. The films of P3HT rubbed at 180°C consist of a mixture of crystals with face-on and edge-on orientations on the substrate but these domains have the same in-plane direction of the chains parallel to the rubbing R. Accordingly, in the doped films (where the same proportion of edge-on and face-on crystals are present), charges must cross from face-on to edge-on domains and vice-versa. For the face-on domains,   is along the insulating alkyl side chains that correspond to the lowest conductivity. Accordingly, whatever, the doping level, the conductivity perpendicular to the chains,   , is always limited by the poor transport of the face-on crystals along the side chain direction. This may explain the relative constancy of   versus doping concentration. Possibly, if the proportion of edge-on crystals could be increased, one could observe a corresponding increase in   . This is indeed what was observed for the charge mobility   in OFETs for undoped and oriented P3HT when the rubbing temperature was increased. Indeed, for very high rubbing temperatures close to 230°C, rubbed films consist of a majority of aligned edge-on domains and the corresponding   was getting close to  // . 9

IV. Conclusion.

A simple and efficient method to produce large surfaces of highly oriented, crystalline and conducting polymer films by combination of high-T rubbing and soft doping from solution is demonstrated. It is versatile and can be applied to a large palette of polymer semiconductors that can be aligned by high-T rubbing (including n-type polymers). 28 Interesting new perspectives are now open to fabricate model systems of conducting polymers with high in-plane orientation and structural perfection that will help understand fundamental aspects and anisotropy of charge transport. This study has already provided compelling evidence for a high level of order and orientation of V. Experimental section.

1) Orientation and doping of thin films.

P3HT was purchased from Merck whereas P3OT and P3BT were purchased from Rieke (the macromolecular parameters are collected in Table S1). The preparation of oriented P3HT films by high temperature rubbing followed the protocol described in previous publications. 8,9,27,28 Thin polymer films were deposited by spin-coating at 1500 rpm for 60 s from an o-DCB solution (20 mg/ml) at room temperature, leading to films of thickness  40 nm. Oriented polymer films were prepared by using a home made set up consisting of a translating hot plate on which the sample are fixed and a rotating cylinder covered with a microfiber cloth. The films were rubbed at different rubbing temperatures depending on the polymer : (100 and 220°C

for P3HT, 140°C for P3OT and 125°C for C12-PBTTT). For a precise determination of the film conductivity, the film thickness was also measured after rubbing as it generates some material loss. Therefore, the rubbed films were melt-annealed to randomize the in-plane chain direction and the thickness was extracted from the UV-vis absorbance.

Concerning P3BT, oriented films were prepared by directional epitaxial crystallization in 1,3,5-trichlorobenzene (TCB) since it was observed to yield a better alignment of the films as compared to high-T rubbing. The method for slow directional epitaxial crystallization has been described on the literature. 27

2) Doping protocol.

The doping was performed following the method proposed by Jacobs et al. 16 Typically, 250 µl of a solution of F4TCNQ in anhydrous acetonitrile of variable concentration CF4TCNQ (0.01 -1 mg/ml) was droped on the oriented polymer films. It has been verified that acetonitrile is not dissolving the P3HT films nor altering the orientation/morphology of the films. The solution was left in contact with the films for 10 s and the remaining solution was removed from the films by spin-coating at 1500

RPM for 1 min.

3) Thin film characterization.

Structural analysis: TEM: Oriented areas were identified for TEM analysis by optical microscopy (Leica DMR-X microscope). The polymer films were coated with a thin amorphous carbon film and removed from the glass substrate by floating on a diluted aqueous HF solution (10 wt%) and subsequent recovery on TEM copper grids. TEM was performed in bright field, high resolution and diffraction modes using a CM12 Philips microscope equipped with a MVIII (Soft Imaging System) Charge Coupled Device camera. Calibration of the reticular distances in the ED patterns was made with an oriented PTFE film. Beam exposure was set to a minimum using the low dose system to avoid de-doping under the electron beam that is observed when the same zone is exposed for a prolonged period of time. De-doping is clearly manifested in the ED pattern by a change in reticular distances to those of the pristine undoped P3HT films.

Polarized UV-Vis-NIR absorption: The orientation of the polymer films was probed by UV-Vis-NIR absorption (350-2500 nm) using a Cary 5000 spectrometer with polarized incident light and spectral resolution of 1 nm.

Polarized FTIR spectroscopy: Polarized micro infrared experiments in the middle infrared range (800-4000 cm -1 ) were carried out in transmittance on a Bruker IFS 66 V spectrometer coupled with a Hyperion 2000 microscope (Bruker Inc.). A mercury cadmium telluride detector, a KBr beam splitter, and a blackbody source were used for our experiments. The spectral resolution was 2 cm -1 , and 256 scans were added for each spectrum. The samples used for polarized FTIR spectroscopy are prepared on Si(100) substrates with their native oxide. perpendicular to it. The measurements were performed by using a home made setup made of one heating and one cooling Peltier cells (3 mm gap) (similar to that described by Glaudell et al. 22 ) providing a controllable temperature difference ∆T. Temperatures of the cold and warm sides was measured in non contact mode using two IR sensors avoiding thus thermal contact issues. The Seebeck tension was measured using a Keithley 2634B sourcemeter and a Semiprobe Lab assistant probe station in ambient conditions. The Seebeck coefficient is calculated from the slope of Vtherm versus temperature difference T for ∆T varying in a range ±10K around T=23±2°C. Typical Vtherm=f(∆T) are shown in the supporting information section (see Figure S5).

II. Results and discussion. 1 )

 1 of polymer films by high-temperature rubbing with the softdoping method by spin-coating a solution of acetonitrile-F4TCNQ on top of the oriented polymer films. A combination of TEM, FTIR and UV-Vis-NIR polarized spectroscopies provides compelling evidence for the peculiar orientation of F4TCNQ dopants in the polymer matrix and gives new insight in the doping mechanism at play. Finally, the resulting anisotropic optical, charge transport and thermoelectric properties are demonstrated. Fabrication of highly in-plane oriented conducting polymer films. Highly oriented and crystalline films of polymer semiconductors e.g. P3HT can be readily prepared by high temperature rubbing. 27,28 When a film of P3HT is rubbed above 150°C, oriented crystallization parallel to the rubbing direction R sets in and leads to a well defined semi-crystalline lamellar morphology with periodic alternation of crystalline lamellae and amorphous interlamellar zones. Highest crystallinities of up to 60% are reached for rubbing temperatures close to 220°C. Therefore, we decided to subject P3HT films rubbed at 220°C to soft doping with a solution of F4TCNQ in acetonitrile (see Figures 1.a and 1.b).

Figure 1 .

 1 Figure 1. a) Chemical structures and schematic energy diagram of F4TCNQ, P3HT and

33 b)

 33 Further DFT calculations by Nuzzo et al. indicate that such IRAV modes are well accounted for by considering the formation of dopant/polymer complexes. Structure of doped P3HT films.

Figure 2

 2 .c, face-on crystals showing a characteristic fringed pattern alternate with amorphous areas. Accordingly, doping does not disrupt the layered structure of P3HT consisting of planes of -stacked backbones that alternate with layers of alkyl side chains. The major effect of doping is on the periodicity along the side chains that increases to 17.4-17.8 Å versus 16.5 Å in the pristine P3HT films. Overall, the TEM observations indicate that the nanomorphology of the oriented and crystalline pristine P3HT films is well preserved upon doping with F4TCNQ.

Figure 2 .

 2 Figure 2. Evolution of the structure of oriented P3HT films upon doping with F4TCNQ. a)

  d020 are almost equal to the values of pristine P3HT. The broadening of the h 0 0 peaks observed for CF4TCNQ=0.1 mg/ml may indicate some possible disorder induced in P3HT crystals upon doping.At high doping concentrations of (≥3 mg/ml), a saturation and even a slow decrease in intensity of the anion absorption and polaron peaks is observed. At the same time, TEM indicates that both the interlayer spacing and the -stacking periods saturate at 18.0 Å and 3.55 Å, respectively. Incidentally, the surface of the films doped at 3 mg/ml shows the presence of excess F4TCNQ crystallites.The evolution of the UV-Vis spectrum for POLR as a function of doping level is also very instructive, especially in the 350-650 nm range where the spectrum results from the overlap of the broad absorption of amorphous P3HT (520 nm) and the absorption bands of F4TCNQ -. The evolution with dopant concentration allows to further assess the attribution of the bands. The 413 nm band of F4TCNQ -clearly increases with doping concentration. By contrast, the absorption of the amorphous interlamellar zones around 525 nm remains almost unaffected by the doping: there is only a small blue-shift to 489 nm and its intensity remains relatively constant (Figure3.b). This supports the previous observation that doping of P3HT with F4TCNQ concerns mainly planarized chain segments in the crystalline domains.

Figure 3 .

 3 Figure 3. Evolution of the UV-Vis-NIR spectrum of highly oriented P3HT films (rubbed at

3 )

 3 reflections are shifted to lower q values and become very sharp and intense. The change in peak position indicates an expansion of the unit cell along the side chains. The relative intensity ratio between the 1 0 0, 2 0 0 and 3 0 0 reflections changes with doping concentration. The intensity of the 3 0 0 reflection is strongest for 3 mg/ml. This change reflects variations in the distribution of electron density in the unit cell as a consequence of the presence of variable amounts of F4TCNQ molecules in the lattice of the doped phase. The change is further evidence for a progressive structural modification upon incorporation of F4TCNQ molecules in the alkyl side chain layers, in agreement with the progressive change in a and b unit cell parameters. Doping of other semiconducting polymers. a) Family of pol(3-alyklthiophene)s.

Figure 4 .

 4 Figure 4.f) evidences a situation similar to that for P3HT. The absorption bands of the

Figure 4 .

 4 Figure 4. Electron diffraction patterns of various oriented semiconducting polymers in

Figure 4

 4 .i shows the polarized UV-Vis-NIR spectrum of C12-PBTTT films rubbed at 150°C and subsequently doped with a solution of F4TCNQ in ACN (1mg/ml). As for P3HT, the polaron bands are seen for POL//R whereas bands of the F4TCNQ -anions are observed for POLR. Both POM and ED show that the C12-PBTTT chain orientation is maintained after doping. However, ED reveals substantial structural changes in the films upon doping. Overall, the ED reflections of the doped films show a strong intensity reduction (compare Figure4.g and 4.h) except the enhanced intensity of the -stacking reflection.These variations indicate that the dominant face-on orientation of C12-PBTTT crystals in rubbed films has changed after doping to a dominant edge-on orientation. A similar domain reorientation was observed upon thermal annealing of rubbed C12-PBTTT films.27 Regarding the unit cell parameters, doping C12-PBTTT with F4TCNQ results in a reduced -stacking periodicity of 3.55 Å (vs 3.65 Å in pristine C12-PBTTT films) and a moderate expansion along the side chains from 19.2 Å to 20.0 Å. Accordingly, much like the P3ATs, F4TCNQ doping of C12-PBTTT also generates oriented thin films with a modified unit cell (expanded a axis, reduced b axis (-stacking) and unaltered c axis parameters).

  Conjugated polymers such as P3HT and C12-PBTTT show a substantial anisotropy of charge mobility that is highest along the chain direction and the -stacking direction (b axis) and negligible along the alkyl side chains (a axis of the crystal).27 The strong polarization of the polaronic absorption of doped P3HT films suggests that polarons move mainly along the rubbing direction, which should translate in a corresponding anisotropy of both charge conductivity and thermoelectric properties. Yet, no measure of the anisotropy of thermoelectric properties in oriented conducting polymers is available. Accordingly, we have measured the values of the charge conductivity  and Seebeck coefficient S for different P3HT samples rubbed at 220°C and subsequently doped with F4TCNQ/ACN solutions of different concentrations. Figure5.a and 5.b show the evolution of the charge conductivity // and   as well as the Seebeck coefficients S// and S  . Both, S and  are measured in the direction parallel and perpendicular to the rubbing direction R as a function of the doping concentration of F4TCNQ. Highest values of  and S are always observed in the rubbing direction (polymer chain direction). The conductivity // increases to a value of 22±5 S/cm for 1 mg/ml and tends to decrease beyond that concentration whereas the Seebeck coefficient S// is much less dependent on the doping concentration and levels at a value in the range (58-62) V/K for cF4TCNQ ≥ 0.25 mg/ml. As compared to a non-oriented P3HT film, the Seebeck coefficient is enhanced along the rubbing direction by a factor of 1.5-2.0 whereas the charge conductivity is also improved by a factor 3.5-4.0 .As seen from Figure5.c, a clear anisotropy of both  and S is observed in the aligned films. At all doping concentrations, the anisotropy of the Seebeck coefficient aS=S///S  is smaller than the anisotropy of the charge conductivity a  =///  , typically aS  3 versus a  = 8-10 (see Figure5.c). For the conductivity, the anisotropy decreases when the doping concentration increases whereas the Seebeck constant is little affected by the doping concentration.

Figure 5 .

 5 Figure 5. Evolution of the anisotropic conductivity and thermoelectric properties for

F4TCNQ -anions in

  the matrix of semiconducting polymers such as P3HT. The level of ordering is clearly dependent on the structure of the layers of alkyl side chains that host the dopant molecules. Parameters such as the length of alkyl side chains and their packing into an interdigitated/non-interdigitated sublattice are equally determining for the buildup of ordered doped architectures. Preliminary results indicate that other dopants can likewise be intercalated in the layers of alkyl side chains. Temperaturedependent conductivity and Seebeck coefficient measurements are underway to uncover the impact of orientation on the charge transport mechanism in such highly crystalline conducting polymer films. It remains to evaluate how and to what extent the lamellar semi-crystalline structure affects the observed anisotropy of conductivity and thermoelectric properties. In particular, by changing the temperature of rubbing we will be able to control the crystallinity of the rubbed P3HT films and hence evaluate how this crystallinity impacts charge transport in doped conducting and oriented polymer layers. Acknowledgments. L. Biniek acknowledges financial support from University of Strasbourg through "Investissement d'avenir" (IdEx 2015 "Attractivité") and from the Fédération de Recherche sur les matériaux et nanostructures d'Alsace (FRMNA) via the Région Alsace through contract FRMNA AAP 2015. M. Brinkmann acknowledges support from PROCOPE project as well as the University of Strasbourg for the "Investissement d'avenir" (IdEx) PhD grant of V. Vijayakumar. SIMS platform (Montpellier) is also thanked for providing access to IR facility. T. Heiser is thanked for providing access to the glove box facility at ICube (Strasbourg). B. Lotz is acknowledged for reading the manuscript and useful comments.

4) Charge transport and Seebeck constant.

All devices were fabricated on glass substrates, cleaned by ultrasonication in acetone, hellmanex, deionized water, and isopropanol. The cleaned substrates were dried under nitrogen prior to use. Gold electrical contacts (25 nm thick) in a four-point probe geometry (1 mm spacing between electrodes, 5 mm length) were deposited via controlled thermal evaporation through a shadow mask, at an average rate of 4-6 Å/s. A first layer of Chromium (2.5 nm thick) was deposited prior the gold to promote a good adhesion on the glass substrates (evaporation rate 0.5-1 Å/s). The contact geometry used for the electrical conductivity and thermopower measurements are presented in Figure S4. On the same substrate, two devices are oriented along the rubbing direction (black) and two others in the perpendicular direction (red) which allows us to determine the charge transport and thermoelectric anisotropy on a same substrate.

Four-point-probe measurements of electrical conductivity were performed using a Keithley 4200 -SCS and a Lab Assistant Semiprobe station in a Jacomex glovebox under N2 atmosphere. To derive the resistivity from the sheet resistance R measured on the device geometry given in Figure S4, we have first determined the geometrical correction factor C such that R=Cρ/t where t is the film thickness. To that aim, we have used a classical four point probe system on a non-oriented doped P3HT film to obtain a reference value of the resistivity ρ given by R=4.53/t. Using this value of the resistivity we determined the geometrical correction factor for our four-line electrode geometry by measuring the sheet resistance on the same sample and obtained C=1.81 i.e. R=1.81ρ/t. Thermopower measurements were conducted in air on the same devices. The thermopower was measured via the differential temperature method: a temperature gradient is established across the sample either along the rubbing direction or


Peter Riviere
email: peter.riviere@toulouse-inp.fr

Yamine Ait-Ameur
email: yamine@toulouse-inp.fr

Neeraj Kumar Singh
email: neeraj.singh@toulouse-inp.fr

Data-types definitions: Use of Theory and Context instantiations Plugins

Introduction

In the context of the French national research agency (ANR) EBRP-EventB-Rodin-Plus [4]1 (Enhancing Event-B and Rodin) project, an extension of the Rodin platform [START_REF] Abrial | Rodin: An open toolset for modelling and reasoning in event-b[END_REF] supporting the design of Event-B [START_REF] Abrial | Modeling in Event-B: system and software engineering[END_REF] models has been designed in the form of a plugin [START_REF] Verdier | Context instantiation plug-in: a new approach to genericity in Rodin[END_REF], namely the context Instantiation plugin. It allows the definition of generic contexts and their instantiation to define generic and reusable theories. Instantiable Sets and Constants with their axioms and theorems are defined in a context has been designed. A mechanism for instantiating such generic contexts by importing useful axioms and theorems in another context. A language for describing such instantiations has been defined. It is parsed in order to generate instantiated contexts.

In the work of [START_REF] Butler | Mathematical extension in Event-B through the rodin theory component[END_REF][START_REF] Hoang | Theory plug-in for rodin 3[END_REF], a mathematical extension of Event-B allowing the definition of theories was proposed and implemented in the so-called Theory Plugin.

In this paper, we investigate the correspondence between theories formalised in the theory plugin and those formalised in the context instantiation plugin. We present transformation rules that allow us to describe theories through contexts and their instantiation. The goal of these transformations is to provide an additional way to model theories in the core Event-B modelling language.

These correspondences for possible data-type definitions are described further below.

Direct definitions of data-types

The correspondence between data-types (non-inductive) and operators defined as direct definitions in the Theory Plugin is presented in this section.

Data-type transformation

Figures 1a and1b show the correspondence between a data-type defined in a theory with type parameters and constructors (parameterised or not) and a context. Only two type parameters and two constructors have been defined for the sake of clarity in the presentation. As shown on Figures 2a and2b, theory based direct definitions of operators correspond to partial functions (defined using a lambda expression) where typing and the Well-definedness conditions are used to define the domain of these functions.

CONTEXT D i r e c t E x p r S c h e m a SET T1 , T2 CONSTANTS op AXIOMS a x m n : op = (λargs1 → args2• args1 ∈ T 1∧ args2 ∈ T 2∧ W D1 ∧ W D2 | Exp(args1, args2) ) (b) A context

for operators definitions: expression

Fig. 2: Direct definitions of operators: expression

Direct definitions of Operators: predicates

The same principle applies to operators defining predicates as it does to operators defining expressions. The correspondence for operators defined as predicates is shown in Figures 3a and3b.

THEORY D i

Inductive data-types definitions

In the Event-B modelling language, inductively defined data-types do not have their direct correspondence. This correspondence requires the introduction of a generic definition for inductive structures.

Generic context for inductive definitions by JR. Abrial and D. Cansell

To define Theory based inductive data-types correspondence, we use the generic definitions introduced by J.R. Abrial and D. Cansell in the EBRP project.

CONTEXT SchemaRecGen SETS S t y p e , B t y p e CONSTANTS w e l l f o u n d e d , f i x , FrSB , S , B AXIOMS a x m 0 : S ⊆ S t ype a x m 6 : B ⊆ B t ype @axm1 :

wellf ounded = {r • r ∈ S ↔ S ∧ (∀p • p ⊆ S ∧ p ⊆ r[p] ⇒ p = ∅} @axm2 : f ix ∈ (P(S × B) → P(S × B)) → P(S × B) @axm3 : ∀h • h ∈ P(S × B → P(S × B) ∧ (, b • a ⊆ b ∧ b ⊆ S × B ⇒ h(a) ⊆ h(b)) ⇒ f ix(h) = h(f ix(h)) a x m 4 : F rSb = {r → g → f r | r ∈ wellf ounded ∧ g ∈ S × (S → B) → B∧ (∀x, f • x ∈ S ∧ f ∈ S → B ∧ r [{x}](f ) ⇒ x → f ∈ dom(g))∧ f r = f ix(λp • p ∈ S ↔ B | {x, h • x ∈ S ∧ r [{x}] h ⊆ p ∧ r [{x}] h ∈ r [{x}] → B | x → g(x → r [{x}] h)})} l e m 1 : F rSb ∈ {r → g | r ∈ wellf ounded ∧ g ∈ S(S → B) → B ∧ (∀x, f • x ∈ S ∧ f ∈ S → B ∧ r [{x}] ⊆ dom(f ) ⇒ x → f ∈ dom(g))} → (S ↔ B) THEOREMS t h m 1 : ∀r, g, f r • r → g → f r ∈ F rSB ⇒ f r ∈ S → B t h m 2 : ∀r, g, f r • r → g → f r ∈ F rSB ⇒ (∀x • x ∈ S ⇒ f r(x) = g(x → r [{x}] f r))
Fig. 5: A generic context with inductive sets definition operator F rSb.

The context SchemaRecGen of Figure 5 uses the definitions of well-founded relations and the fixpoint operator from contexts not shown in this paper. They are brought up for clarity.

The most important feature is the constant F rSB allowing to define the semantics of operators defined on inductive types. It use the type constructors and the fixpoint operator. This function is further applied to formalise the theory based defined inductive types and operators.

Correspondence schema

Inductive definitions are given in two steps: first the data-type definition using inductive sets definitions and second the operators manipulating this data-type.

Inductive data-type definition. A recursive definition is based on an inductive type, which is depicted in Figures 6a and6b as a set comprehension in which the inductive properties are encoded and the constants are elements of this set. The IndT ype theory data-type corresponds to the set IndT ype, which is defined from the carrier set IndT ypeT Y P E. The IndT ypeSET defines the set of n-uplets corresponding to the n constructors of the data-type. In our case, cons1 El → cons2 El → consinduc1 El → consinduc2 El.

IndT ypeSET = {indtype El → cons1 El → cons2 El → consinduc1 El → consinduc2 El | indtype El ⊆ IndT ypeT Y P E∧ cons1 El ∈ indtype El∧ cons2 El ∈ T (indtype El \ (ran(consinduc1 El)∪ ran(consinduc2 El) ∪ {cons1 El}))∧ consinduc1 El ∈ indtype El (indtype El \ (ran(cons2 El) ∪ ran(consinduc2 El)∪ {cons1 El}))∧ consinduc2 El ∈ T (indtype El \ (ran(consinduc1 El) ∪ ran(cons2 El)∪ {cons1 El}))∧ (∀tr • cons1 El ∈ tr ∧ cons2 El[T ] ⊆ tr∧ consinduc1 El[tr] ⊆ tr∧ consinduc2 2[T × tr] ⊆ tr ⇒ indtype El ⊆ tr) } a x m 2 : IndT ype → cons1 → cons2 → consinduc1 → consinduc2 ∈ IndT ypeSET (
(∃el • el ∈ T ∧ ind el = consinduc1(el → e)∨ (∃el • el ∈ T ∧ ind el = consinduc2(el → e)) } → { e → f → res | e ∈ IndT ype∧ f ∈ {ind el | ind el ∈ IndType ∧ WD1 ∧ WD2} → Res Type / / F u n c t i o n d o m a i n d e f i n i t i o n (∀el, ind el • el ∈ T ∧ ind el ∈ IndT ype∧ (e = consinduc1(el → ind el)∨ e = consinduc2(el → ind el)) ⇒ ind el ∈ dom(f ))∧ / / D e f i n i t i o n

Conclusion

We provided a set of correspondences that allow theory-based data types to be translated as contexts. Except for the inductive definitions, which require the use of operators defining inductive sets borrowed from a generic context, this transformation is straightforward. When we translate theories to context, we obtain context definitions expressed in the native Event-B modeling language, but we lose the structuring and semantic information available in the theories.

THEORYFig. 1 :

 1 Fig. 1: Data-type correspondence

THEORY

  D i r e c t E x p r S c h e m a TYPE PARAMETERS T1 , T2 OPERATORS op < e x p r e s s i o n > ( arg1 : T 1, arg2 : T 2 ) w e l ld e f i n e d n e s s WD1,WD2 d i r e c t d e f i n i t i o n Exp ( arg1, arg2... ) (a) Theory based Direct definitions of operators: expression

Fig. 3 :

 3 Fig. 3: Direct definitions of operators: predicates

Fig. 4 :

 4 Fig. 4: Correspondence for axiomatic definitions of operators.

THEORY

  I n d D a t a T y p e S c h e m a TYPE PARAMETERS T DATATYPES IndType : c o n s 1 / / b a s e c a s e 1 c o n s 2 ( e l : T) / / b a s e c a s e 2 c o n s i n d u c 1 ( e l : IndType ) / / i n d u c t i v e c a s e 1 c o n s i n d u c 2 ( e l 1 : T , e l 2 IndType ) / / i n d u c t i v e c a s e 2 (a) Inductive type definition CONTEXT I n d D a t a T y p e S c h e m a SETS IndTypeTYPE , T CONSTANTS IndType , IndTypeSET , c o n s 1 , c o n s 2 , c o n s i n d u c 1 , c o n s i n d u c 2 AXIOMS a x m 1 :

  b) Corresponding context with sets and constants

Fig. 6 :

 6 Fig. 6: Correspondence for inductive type

  THEORY TYPE PARAMETERS T1 , T2 OPERATORS op < e x p r e s s i o n > ( arg1 : T 1, arg2 : T 2 ) w e l ld e f i n e d n e s s WD1,WD2 . . . r e c u r s i v e d e f i n i t i o n c a s e c o n s 1 = Exp1 ( • • • ) / / b a s e c a s e 1 c a s e c o n s 2 = Exp2 ( • • • ) / / b a s e c a s e 2 c a s e c o n s i n d u c 1 = ExpInd1 ( op, • • • ) / / i n d u c t i v e c a s e 1 c a s e c o n s i n d u c 2 = ExpInd2 ( op, • • • ) / / i n d u c t i v e c a s e 2 (a) A theory based on Recursive definition CONTEXT INSTANCIATES SchemaRecGen I n d D a t a T y p e S c h e m a SETS T , T1 , T2 CONSTANTS op AXIOMS a x m n : op = FrSB( { e → ind el | e ∈ IndT ype∧ ind el ∈ IndT ype∧

Fig. 7 :

 7 Fig. 7: Corresponding schema of recursive definition of operators

https://www.irit.fr/EBRP/


C Perrine
email: clency.perrine@sic.sp2mi.univ-poitiers.fr

C Chatelllier

S Wang

C Olivier

A joint source channel coding strategy for video transmission

Keywords: Joint source channel coding, vector quantization, video transmission, GOP

This paper presents a joint source channel coding designed for video transmission application. The aim is to improve the visual quality of the reconstructed video even when transmission errors occur while keeping the processing as simple as possible. The BER excepted is higher than 10 -4 . This coding is based on an association of a wavelet transform (WT) and a vector quantization (VQ) optimally mapped on a QAM-M modulation. The whole of the transmission chain is jointly exploited in order to make it well-adapted to the complex and low data rate channel.

I. INTRODUCTION

Nowadays, most of telecommunication systems allow transmitting video in real time. Furthermore, the quality of the received video is an important parameter for the Quality of Service (QoS) supplied by the providers. This quality depends on the compression algorithm, the channel coding strategy and the transmission conditions in the wireless channel. The latest norms as H.264 or MPEG-4 [START_REF]H264/MPEG-4 Part 10 Tutorials[END_REF] [2] have shown good performances related to the compression rate (optimized motion vector coding) and the scalability aspects. However, when errors occur over the wireless channel, video remains sensitive.

The aim of this paper is to present a joint source channel coding strategy based on a wavelet transform increasing the robustness of the transmission chain by reducing the impact of transmission errors (Bit Error Rate -BER > 10 -4 ) on the quality of restored images while contributing a good rate-distorsion. Wavelet-based coding is promising for efficient and scalable compression of video [START_REF] Agostini | Model-based bit allocation between wavelet subbabds and motion information in MCWT video coders[END_REF]. The real-time application constraint is taken into account insomuch as the complexity is reduced.

The video coding we suggest in this article is based on a vector quantization [START_REF] Aitsab | Turbo codes et codage conjoint source canal : application à la transmission d'images[END_REF] for each sub-band of wavelet coefficients followed by an optimally QAM (16 or 256) mapped strategy. This video coding is named WTSOM (Wavelet Transform Self Organized Map) video. This algorithm based on fixed length coding has the advantage in opposition to the variable length coding (entropy coding) to be more robust regarding the transmission error but obviously with a lower compression rate.

The application expected in this study is videoconference which means limited scene change and low data rate channel.

In section II, the WTSOM video coding method is described, resorting to WTSOM strategy for fixed images [START_REF] Souhard | Codage conjoint source canal : Application à la transmission d'images fixes sur canal ionosphérique[END_REF] [START_REF] Chatellier | A robust joint source channel coding scheme for image transmission over the ionospheric channel[END_REF]. It is shown its adequacy with a digital QAM-256 modulation and the high performances related to the High BER. We propose, as for MPEG-4, to use the Group Of Pictures (GOP) layer containing 12 successive frames but from wavelet transform coefficients.

In section III, several transmission results through AWGN channels are presented involving the WTSOM video coding. The BER expected is higher than 10 -4 . This video coding is more efficient in terms of robustness than in terms of compression aspects.

II. WTSOM VIDEO PRINCIPLE

After showing the difficulties to transmit video sequences when BER is high, the principle of WTSOM for fixed images is described [START_REF] Souhard | Codage conjoint source canal : Application à la transmission d'images fixes sur canal ionosphérique[END_REF] [10] and an extension to the video applications is detailed.

A. Issue

An example of video transmission is given in the figure 1. The standard of compression is MPEG4. It is transmitted through the AWGN channel using à QAM-16 modulation. The BER is closed to 10 -4 . We can notice that MPEG-4 encoding is extremely sensitive to errors due to the Variable Length Codes (VLC). In order to avoid this phenomenon, a source coding based on vector quantization is used which has the particularity to be a fixed length coding and well adapted to loss data compression. Before presenting the WTSOM algorithm for video, we suggest to give a brief description of WTSOM algorithm for fixed images [START_REF] Chatellier | A robust joint source channel coding scheme for image transmission over the ionospheric channel[END_REF].

B. WTSOM algorithm for fixed images

In our application, we use the Daubechies (9/7) biorthogonal wavelet such as in the JPEG 2000 case. The wavelet decomposition is applied at scale three and we preserve the five most significant sub images (LL 3 , HL 3 , LH 3 , HL 2 et LH 2 ) and discard the less important subbands. This choice is a good compromise between compression rate and visual quality of restored images. It is strengthened by an information entropy study for the 10 subbands related to our image sequence training basis. The size of the entire data before and after quantization is given in table 1.

The compression rate for this first step is 5,88 for any n x m image [START_REF] Wang | Stratégie de codage conjoint de séquences video base ondelettes[END_REF] :

88 , 5 2 ) 8 / 8 / ( 3 ) 8 / 8 / ( ≈ × × + × × × = m n m n m n T c (1)
The second stage is to apply a vector quantization on the remaining subbands of the wavelet decomposition. To do this, we use Kohonen's Self-Organizing Map (SOM) algorithm, because of its interesting property of autoorganization: close vectors in terms of Euclidian distance correspond to close indices in terms of location in the self-organized codebook. This method is named WTSOM coding [START_REF] Kohonen | Self Organization and associative memory[END_REF]. It requires 5 codebooks known by the transmitter and the receiver. The number and the vector shape depend on the subbands, the compression rate and the restored image quality expected. For our example in the figure 2, each codebook is composed of 256 vectors V i for which the size is all the more important since the subband is more informative. The compression rate for the quantization step is 4,4 [START_REF] Wang | Stratégie de codage conjoint de séquences video base ondelettes[END_REF] with n =m = 512 (see table 1) : The global compression rate is 25,6 (5,88 x 4,4).

1) Robustness against transmission errors

Only the indexes of the codebook's vectors are transmitted through the channel using the right digital modulation. The size of the codebook is well-justified by the QAM-256 or QAM-16 modulation (figure 3). The codebook is optimally mapped on high spectral efficiency modulation and Kohonen topological maps (figure 3). They are more appropriate to QAM modulation because the layout of the codebook elements on the digital modulation points (in red) minimizes the average distortion during the transmission of codebook elements. The robustness of the scheme suggested in this article is justified by the interdependence between the WTSOM video coding and the QAM modulation.

In the figure 3, a 256-QAM has been used but in order to minimize the BER a 16-QAM modulation can be used. In this case, the optimal mapping of a 256-vector codebook is no longer possible. In order to solve this problem, Pyndiah [START_REF] Kangas | Increasing the error tolerance in transmission of vector quantize image by self organizing map[END_REF] suggests reorganizing the codebook differently, that is to say using a four-dimension codebook (4x4x4x4) suitable for 4 bits (16-QAM). The results are not as good (1,5 dB loss in PSNR) as in the 256-QAM case but the system remains robust.

C. WTSOM video

In this section, WTSOM video (based on WTSOM for fixed images) is presented. This algorithm allows us to code image sequences by introducing GOP technique in order to increase the compression rate while keeping a good visual quality taking inspiration from the latest video standards. These techniques are applied to wavelet subband and a quantization.

1) Principle

We adopt the same strategy as they use in MPEG-4 standard, that is to say based on GOP technique using 12 successive images. Our method requires the construction of 2x5 codebooks obtained with differential video references : Mom-daughter, Claire, Missa, Grand-mom. For the codebooks, each vector has variable size as mentioned in section 2.2. The method we use based on GOP technique is performed from DWT sub-band.

In order to exploit the temporal redundancy GOP scheme is defined as follows:

the I-frame (intra coded picture) reference picture corresponds to a fixed image and is independent of other picture types -the P-frame (predictive coded picture) contains difference information from the preceding I or Pframe the B-frame (bidirectionnally predictive coded picture) contains difference information from preceding and/or I or P-frame

The figure 4 illustrates the GOP structure with 13 frames. The reference pictures (I-frame) are transformed related to the DWT algorithm. These pictures are encoded according to the WTSOM algorithm for fixed images as mentioned before. These pictures will serve as reference to calculate P and B-frame and for decoding. The Pframes are predictively coded. A motion compensation of preceding pictures is done so that this image prediction could be realized. The B-frames are bidirectionally coded. Motion-compensated prediction is obtained with preceding and succeeding pictures.

Differential wavelet transform coefficients are calculated for each subband and between these images. Dif 1 , Dif 2 , Dif 3 , …, will be the reference vectors. Thus, we are able to construct 5 codebooks for reference images and from difference vectors we are able to construct the new difference codebooks.

The difference equations are the following: where WTSOM(I j ) means a wavelet coefficient of I j plan. Dif 4 , Dif 5 , Dif 6 , etc …, are obtained in the same way.

Dif 1 = WTSOM(I 4 ) -WTSOM(I 1 ) Dif 2 = WTSOM(I 2 ) -[WTSOM(I 1 ) + 1/3Dif 1 ] Dif 3 = WTSOM(I 3 ) -[WTSOM(I 4 ) -1/3Dif 1 ] Dif 4 = WTSOM(I 7 ) -WTSOM(I 4 ) Dif 5 = WTSOM(I 5 ) -[WTSOM(I 4 ) + 1/3Dif 1 ] Dif 6 = WTSOM(I 6 ) -[WTSOM(I 7 ) -1/3Dif

In the figure 5 is shown the WTSOM GOP principle.

I. VIDEO TRANSMISSION THROUGH AWGN CHANNEL

In this section, we show the results obtained with WTSOM video coding detailed above compared to MPEG-4 standard. The digital modulation is a QAM-16. Each symbol is coded using 4 bits what is easy to adapt to our method [START_REF] Kangas | Increasing the error tolerance in transmission of vector quantize image by self organizing map[END_REF]. The main advantage, in comparison with QAM-256 modulation, is that it is easy to implement and more robust against the noise without disorganizing the initial scheme designed for 256 vectors (coded using 8 = 2x4 bits). The compression rate is about 44:1. The video "Mom" is transmitted over the AWGN channel (figure 6a The results obtained with WTSOM video are illustrated in the figure 6c and those obtained with MPEG-4 in the figure 6d. In the figure 6c, the PSNR value remains constant compared to the figure 6b. In the figure 6e, we show a result with a high BER (BER = 1,34.10 -2 ) still using WTSOM video coding and with the same compression rate. This underlines the robustness of the method suggested in this article and its interest for video transmission through complex channels compared to MPEG-4 where the result is unacceptable.

IV. CONCLUSION AND OUTLOOKS

This paper presents a joint source channel coding designed for video application, the WTSOM video coding. It is based on an association of a wavelet transform, an appropriate codebook for each image of decomposition and a classical predictive coding involving a sequence of 12 images. We show that this strategy is particularly welladapted to video transmission through complex and low data rate channel while keeping the useful bit rate as optimum. A comparison with MPEG-4 shows clearly the performances of WTSOM video in terms of visual quality and compression rate compromise.

The visual quality can be improved by introducing as for video standard motion vector what will allow a significant reduction in the residual distortion on the restored images [START_REF] Agostini | Model-based bit allocation between wavelet subbabds and motion information in MCWT video coders[END_REF]. Its encoding will be done by using vector quantization adapted to the modulation in order to keep the global strategy related to the robustness and the optimal useful bit rate.

Finally, some errors (figures 6c and 6e) could be attenuated by using video PDE (Partial Differential Equations) -based restoring algorithm as we developed [START_REF] Bourdon | A multi-resolution, geometry-driven error concealment method for corrupted JPEG color images[END_REF] for fixed images.

Figure 1 .

 1 Figure 1. Transmission through ideal channel (without errors) and through AWGN channel: (a) original sequence (b) MPEG-4, BER = 1,9.10 -4

Figure 2 .

 2 Figure 2. WTSOM video method :VQ principle for 1 plan.

Figure 4 .

 4 Figure 4. GOP structure with 13 frames

Figure 3 .

 3 Figure 3. Codebook superimposing to QAM-256 modulation

Figure 5 .

 5 Figure 5. WTSOM GOP

  : video clip from Mom: original : Mom_024, Mom_025, … Mom_035). The codebooks are constructed in the same way as previously relatively to the chosen compression rate and from 4 basis video : Mom-daughter, Claire, Missa, Grand-mom. The result of this sequence obtained with WTSOM video is given in the figure 6b. The restored sequence appears quite good in terms of visual quality. The PSNR equals 27, 28 dB , that is obviously less efficient than MPEG-4 or H264 standards. The original sequence (figure 6a.) is then transmitted through an AWGN channel with the following features: -BER ≈ 2.10 -4 -SNR = 8 dB -T c = 63.5 for WTSOM video -T c = 61 for MPEG-4 standard -Modulation : QAM-16

Figure 6 . 2 I1

 62 Figure 6. Sequence transmitted through ideal and AWGN channel comparable compression rate : (a) original sequence (b) WTSOM video, without errors, (c) WTSOM video, BER = 1,8.10 -4 , (d) MPEG-4, BER =1,9.10 -4 (e) WTSOM video, BER = 1,32.10 -2