Olga V Sedelnikova
email: o.sedelnikova@gmail.com

Christopher P Ewe

Dmitry V Pinak

Galina N Chekhova

Emmanuel Flahaut

Alexander V Okotrub

Lyubov G Bulusheva

Nikolaev

Bromine polycondensation in pristine and fluorinated graphitic carbons †

Despite decades of study the precise behavior of bromine in graphitic carbons remains unclear. In this report, using Raman spectroscopy, we reveal two types of bromine structure in graphitic carbon materials. Between fluorinated graphene layers with a composition close to C 2 F, Br 2 molecules are intercalated in a form similar to liquid bromine. Bromination of pristine and low-fluorinated graphitic carbons behaves very differently with distinct Br-related Raman spectra. With the guidance of density functional theory (DFT) calculations, all Raman features are assigned to normal vibration modes of specific bromine species over graphene and fluorinated graphene. When intercalated between extended non-fluorinated sp 2 -hybridized carbon regions, physisorbed Br 2 molecules move freely across the non-functionalized region toward the CF border. Multiple Br 2 molecules then combine spontaneously into Br 3 -based chains, whose coupling activates otherwise Raman inactive modes. Significant charge transfer to bromine species occurs in this case. DFT calculated frequencies match precisely the experimental Br-related Raman bands observed in the intercalation carbon compounds. The fluorine-catalyzed bromine chain-formation process shown here is general and should also operate with edges and other defect species.

Introduction

Among different methods of chemical modification of carbon, halogenation is one of the most promising. Fluorination and bromination can be used to obtain graphene precursor materials and for the individualization of carbon nanotubes (CNTs). This is due to the halogen intercalant layers reducing the π-π interactions between the layers in graphite and the CNTs in bundles. [1][2][3][4] Previously we have shown that the fluorine pattern on the surface of double-walled CNTs (DWCNTs) depends on the fluorination method. 5,6 In particular, roomtemperature fluorination with BrF 3 mostly produces short fluorinated chains with CF bonds. Partially fluorinated graphite with a stoichiometry close to C 2 F has a patchwork fluorine pattern on the basal planes composed of non-fluorinated gra-phene nanoregions, which are separated by sp 3 -hybridized carbon atoms bonded to zigzag fluorine chains. [6][7][8][9][10] Covalent functionalization of the carbon surface can drastically change the electronic structure of the material. Fluorination of graphite layers and metallic CNTs opens a band gap, which can be tuned by tailoring the content and distribution of fluorine. [11][12][START_REF] Bulusheva | Electronic structure of fluorinated graphene, New Fluorinated Carbons: Fundamentals and Applications[END_REF] Bromine has a lower electronegativity than fluorine and bromination of graphite and CNTs usually results in an adsorption of bromine species, 4,[START_REF] Aguiar | [END_REF] although covalent bonding between bromine and carbon atoms is also possible. 4,15,16 Ionic bromine doping enhances the conductivity of graphite, graphene, and CNTs 4,[17][18][19][20] improving their electrochemical properties in Li-ion batteries 21 and gas sensor efficiency. 22 Bromine forms layers between the graphite sheets that promotes isolation of monolayers. [1][2][3] Similarly bromine can intercalate between CNTs in bundles, helping to separate them. 4 Moreover, bromination of CNTs can assist in the separation of metallic and semiconducting nanotubes. 23 Graphite-bromine compounds have been studied over many decades. 17,[24][25][26][27][28][29][30] The structure of the bromine layers is still widely debated. The pioneering works of Eeles and Turnbull, 24 Sasa et al. 25 and Eklund et al. 26 reported formation of Br 2 chains with an interatomic distance close to that in solid bromine. Ghosh and Chung however suggested organization of long-chain polymeric bromine anions. 27 Formation of poly-To obtain fluorinated graphite intercalation compounds lysis. 43 A portion of a sample (3-5 mg) was combusted in an oxygen flow at 900-950 °C. The pyrolysis products were then oxidized and halogens (F, Br) were adsorbed on the ZrO 2 -MgO-AgWO 4 composite system at 750 °C. The resulting CO 2 content was determined by thermogravimetric analysis. The total contents of fluorine and bromine was determined using the Shöniger method. 44 A portion of a sample (1-3 mg) was decomposed at 1300-1400 °C in a flask filled with oxygen. Pt catalyst and special additives were used in order to improve the combustion. The resultant product contains bromine and fluorine ions. The concentration of bromine was determined by the mercurimetric titration of as-obtained solution in acid medium in the presence of diphenylcarbazone indicator. The concentration of fluorine was determined spectrophotometrically via formation of a lanthanum/alizarin complex. Together these methods allow quantification of carbon, fluorine, and bromine concentration with an accuracy of 0.5, 1.5, and 2.0%, respectively.

Raman scattering spectra were recorded on a LabRAM HR Evolution (Horiba) spectrometer using a 514 nm excitation. The spectra recorded at room temperature were normalized with respect to the peak with maximal intensity and are displayed with a slight offset for clarity.

Experimental results

A study of four C 2 F x -Br samples obtained under different conditions using elemental analysis revealed the compositions C 2 F 0.94 •Br 0.22 , C 2 F 0.47 •Br 0.14 , C 2 F 0.24 •Br 0.08 , and C 2 F 0.07 •Br 0.06 . The sample G-Br can be written as C 2 •Br 0.08 .

Raman spectra of G-Br and C 2 F x -Br samples show two regions related to vibrations of the host matrix (1250-2000 cm -1 ) and intercalated species (100-590 cm -1 , Fig. 1), respectively. In the first region, the spectra of C 2 F x -Br samples contains D and G bands located at 1361 and 1597 cm -1 characteristic of sp 2 -hybridized carbon with disorder produced by covalent fluorine attachment. 45 The D band intensity increases with degree of fluorination. Due to the high quality of the starting natural graphite, the D band is absent in the spectrum of G-Br sample and the G band has a double structure with peaks at 1584 and 1602 cm -1 . These peaks correspond to the lattice vibrations of the graphite layers without bromine species between them and those adjacent to an intercalated bromine layer, respectively.

From 100 to 600 cm -1 the Raman spectrum of C 2 F 0.94 -Br (hereinafter referred to as highly fluorinated graphite) resembles the spectrum of liquid bromine, in agreement with a previous study of similar samples. 46 A single peak at ca. 311 cm -1 (denoted IV′) is located between the peaks of solid bromine (296 cm -1 ) 47 and gaseous bromine (323 cm -1 ). [START_REF] Herzberg | Spectra of Diatomic Molecules[END_REF] In contrast, the spectra of C 2 F x -Br samples with x = 0.47, 0.24, 0.07 (hereinafter referred as low-fluorinated compounds) and G-Br have a rich structure. The peak at ca. 235-239 cm -1 (denoted III) and its overtone at ca. 472-474 cm -1 (denoted VI) are usually assigned to the Br-Br stretching of intercalated Br 2 molecules. 4,[START_REF] Aguiar | [END_REF]26,[28][29][30]35,[START_REF] Souza Filho | [END_REF] There are also peaks at ca. 155-158 cm -1 (denoted I), previously assigned to chain-like bromide compounds has been detected in activated carbon material, possessing a diamond-like structure with embedded graphene regions. 31 Some reports have suggested a possibility of stabilizing Br 3 -and Br 5 -polyanions in bromine intercalated CNTs 4,[START_REF] Aguiar | [END_REF][32][33][34][35][36] similar to observed polyiodide structures. 37,38 The formation of bromine chains has also been observed inside the one-dimensional channels of zeolite crystals. 39 This process originates from the charge transfer between guest species and the crystal. Since bromine acts as an electron acceptor for the sp 2 -hybridized carbon surface, its polymerization over this surface is plausible. Co-functionalization of graphite and CNTs with fluorine and bromine is of interest due to an interplay between the band gap opening and metallization effects in the materials. However, to the best of our knowledge, bromination behaviour in fluorinated carbon materials has never been discussed. In this paper, we investigate the peculiarities of bromination of pristine and partially fluorinated graphite and DWCNTs using Raman spectroscopy and density functional theory (DFT) calculations. By increasing the fluorine content in fluorinated graphite C 2 F x with 0.07 < x < 0.94, we reduce the size of nonfunctionalised graphene nanoregions and study how this affects the bromination process. Based on DFT calculated Br-Br vibrational frequencies, we reveal two distinct intercalated bromine species and propose bromination mechanisms of fluorinated carbons depending on the fluorination level.

Experimental section

Experimental methods

Natural graphite from the Zavalievo deposit (Ukraine) was used as starting material to synthesize graphite intercalation compound and fluorinated graphite intercalation compounds with bromine. Bromination of graphite was performed in a Teflon flask in saturated Br 2 vapour for 2 days at room temperature. The fresh sample is the second-stage intercalation compound C 8 Br. When stored under normal conditions, the compound loses the intercalated bromine to the composition of C 24 Br. 40 Such material is denoted G-Br in this communication.

with bromine, we use a procedure described elsewhere. 9,41,42 Briefly, just obtained C 8 Br sample was placed in another Teflon flask in vapour over a solution of BrF 3 in Br 2 at room temperature. The obtained fluorinated graphite materials are the first-stage intercalation compounds with Br 2 and BrF 3 components. The fluorine content in the product is controlled by changing the BrF 3 concentration from 1 to 12 vol% in Br 2 and the synthesis duration from 1 month to 4 months. At the final stage, the samples were held in saturated Br 2 vapour for 2 days. For complete replacement of BrF 3 by Br 2 , the process was repeated 5 times for all samples. Hereafter the fluorinated graphite intercalated compounds are referred to as C 2 F x -Br.

Elemental analysis of the samples was performed as following. The content of carbon was determined by CHNS ana-regions, which grow with an increase of the fluorination level. [6][7][8][9][10] At low coverage, recent first-principle calculations demonstrated the tendency of stripe-like patterns to form along armchair and zigzag directions. 54 Therefore to simulate substrates of fluorinated graphene and its interface with bromine, we considered zigzag chains of fluorinated carbon atoms alternated with 10 chains of bare sp 2 -hybridized carbon atoms. Following previous literature, [6][7][8]54 fluorine atoms were sequentially attached to alternating sides of the graphene sheet. Although the perpendicular orientation of Br 2 relative to graphene and fluorinated graphene is slightly energetically preferable, 55 hereafter the properties of Br 2 lying parallel to the sheet will be discussed since this configuration is expected for the intercalation compounds. Bromine species were positioned either above the centre of the graphene supercell (see ESI †) or near to the fluorine boundary (Fig. 2).

Accurate prediction of binding energies between substrate and physisorbed molecules is a challenging task, especially in extended low-dimension systems. However, while the local density approximation (LDA) does not include dispersion corrections, the over-binding presented in the method is able to compensate this in a large extent. Thereby weak interactions are reproduced rather correctly within LDA approximation. The one example is graphite, where the LDA reproduces with reasonable accuracy both the interlayer spacing and binding energy. 56 This method gives also correct interaction energies of water and polybromine anions, [START_REF] Aguiar | [END_REF] as well as 200-212 cm -1 (denoted II), 318-328 cm -1 (denoted IV), and 407-413 cm -1 (denoted V). The latter can be assigned as a combination of I and III modes. We note that the Br-related Raman spectra are almost the same for the samples with zero and low-fluorination levels. This can be understood from the heterogeneous distribution of fluorine patterning of graphene planes, 9,10,[50][51][52][53] indicating that the bromine signal is coming from species adsorbed on the non-fluorinated regions.

Simulations

DFT calculations were invoked to study the electronic structure and normal vibration modes of bromine species over graphene and fluorinated graphene layers, in order to understand origin of the bromine-related peaks in the Raman spectra of G-Br and C 2 F x -Br samples.

Calculation details

To investigate interaction between Br 2 ,Br 3 , and Br 6 with graphene, we used a hexagonal 11 × 11 supercell of graphene composed of 242 carbon atoms (Fig. S1 †). The separation between slabs was 15 Å. Experimental investigations of fluorinated graphene showed that fluorine atoms form localized with respect to the positions of atoms i and j, d 2 E/dR i dR j , were then obtained by a finite difference formulation of the derivative using the calculated forces. If all second derivatives d 2 E are evaluated then the dynamical matrix can be found directly as E ij /(M i M j ) 0.5 where M i is the mass of the i th atom. This approach is discussed in ref. 63, where it was successfully used to identify stretching frequencies of bromine-and iodine-containing small molecules. Diffusion barriers were calculated using the climbing nudged elastic band (NEB) method with 10 or 12 images between the initial and final structures.

Interaction between bromine species and graphene (fluorinated graphene)

As shown in Table 1, adsorption of bromine species on graphene and fluorinated graphene is energetically favorable due to significant charge transfer. This is most obvious for Br 3 which accepts about 0.8e from graphene and 0.6e from fluorinated graphene, stabilizing the Br 3 anion. We note that the bromine does not form covalent bonds with the carbon.

The binding energy of Br 2 with partially fluorinated graphene is 0.07 eV higher than with pristine graphene (Table 1). NEB calculations show that migration of Br 2 from the centre of a non-fluorinated region towards the fluorine chain (Fig. 2d) is energetically favorable with an enthalpy change of ca. -0.15 eV and an activation barrier of only ca. 0.04 eV (Fig. 2e). When Br 2 is placed above the fluorine chain, relaxation of this structure results in a shift of the molecule to adjacent non-fluorinated region. Therefore, when Br 2 adsorbs on a graphene nanoregion present in a low-fluorinated layer, it should readily migrate to the CF interface.

Normal vibration modes of adsorbed bromine species

We next discuss the vibrational properties of free bromine species and those adsorbed on graphene and fluorinated graphene (Table 1). For an isolated Br 2 molecule, the calculated hydrogen inside CNTs and on graphene. 57 Moreover, Raman spectra are directly related to near-interatomic forces, which are mainly governed by covalent interactions, which are generally well accounted by LDA. Due to the well-known compensation effect between the overestimated interatomic forces and the underestimated bond lengths, the LDA was chosen for investigation of electronic and phonon properties of graphene and fluorinated graphene with adsorbed bromine species. All calculations were carried out with the AIMPRO code. [58][59][60] This method has been successfully used for the study of intercalated boron in graphite. 55,61 For C/F/Br, basis sets containing 22/28/50 independent Gaussian-based functions were used. Core electrons were eliminated using normconserving relativistic pseudopotentials of Hartwigsen, Goedecker and Hutter. 62 Periodic boundary conditions at the Γ-point were used. A cut-off energy of 150 Hartrees was used with a 0.04 eV Fermi smearing function for the electron temperature to aid self-consistent convergence. Geometries of all structures were fully optimized using a conjugate gradient algorithm with no constraints of symmetry until the maximum atomic position change in a given iteration dropped below 1 × 10 -7 eV Å -1 . All calculations were done using a spin-averaged approach. Since the number of electrons of Br 3 molecule is odd, we checked the effect of spin polarization on the total energy and vibration frequencies of Br 3 over graphene (see ESI †). Our results showed that accounting of spin has negligible effect on the vibration properties.

Atomic charge states were calculated using Mulliken population analysis. Binding energies are defined as follows:

E b = E tot -E h -NE Br 2 /2
, where E tot is the total energy of graphene (fluorinated graphene) with bromine, E h is the energy of free layer, E Br 2 is the energy of isolated Br 2 , and N is the number of bromine atoms. Vibrational frequencies were calculated by determining the energy and forces for 0.2 a.u. displacements of the bromine atoms. The second derivatives of the energy Br 5

-could be formed almost without barrier due to charge transfer from the nanotube to the encapsulated species. On the other hand, exothermic formation of polybromine chains over graphene was suggested to have a significant activation barrier for the reaction 2Br 2 → Br 4 . 33 To try and resolve this contradiction we calculated the path for the reaction 3Br 2 → Br 3 -Br 3 over fluorinated graphene (Fig. 3). The initial NEB configuration is the optimized geometries of three bromine molecules evenly spaced over pristine graphene region located between CF chains. These molecules are denoted i and marked by red dashed ovals in Fig. 3a andb. symmetric Br-Br stretching frequency ν 2 s is 326.2 cm -1 in almost coincidence with the experimental value (323 cm -1 ). [START_REF] Herzberg | Spectra of Diatomic Molecules[END_REF] This frequency is downshifted to 233.9 cm -1 due to interaction of Br 2 with graphene (Fig. 2a) that perfectly matches the position of Raman peak III. Previous theoretical investigations of brominated graphene and graphite showed significant overestimation of this frequency (up to 260-290 cm -1 ), [START_REF] Aguiar | [END_REF]20,30,55 and to match experiment, an additional negative charge (ca. 0.5e) was assigned to Br 2 . [START_REF] Aguiar | [END_REF] This overestimation is due to use of periodic cells that are too small. We found that this mode converges rapidly to the experimental value with increasing cell size (Table S2 andFig agreement with previous experimental and theoretical results. 64 We will not consider further the ν 3 b mode. The general expectation is a downshift of the stretching modes when Br 3 interacts with graphene or partially fluorinated graphene layer. Indeed, for Br 3 over graphene (fluorinated graphene), our calculated modes ν 3 a and ν 3 s have frequencies 220.3 and 164.3 cm -1 (229.6 and 176.0 cm -1 , Table 1 and Fig. 2b). According to the selection rules, the mode ν 3 s is only Raman-active for linear Br 3 . However, the host matrix may distort symmetry of Br 3 65 and in this case the Raman spectrum will have additional, low-intensity peak ν 3 a .

Another possible mechanism to overcome the symmetry restriction in Raman is the formation of polybromide chains. When two coaxial Br 3 molecules are placed in line, they can perform asymmetric stretching simultaneously, as mirror images of each other. The chain-like Br 3 -Br 3 species has two Raman-active stretching modes ν 3 s -ν 3 s and ν 3 a -ν 3 a (Fig. 2c, bending modes with frequencies below 100 cm -1 are missed).

For Br 3 -Br 3 over graphene, the first mode ν 3 s -ν 3 s at 158.7 cm -1 corresponds to the simultaneous symmetric stretching of both Br 3 constituents and coincides with the position of the experimental peak I. The mirror asymmetric stretching of Br 3 molecules yields the mode ν 3 a -ν 3 a at 223.1 cm -1 , which is close to the Raman peak III. Several Br 3 -Br 3 configurations on fluorinated graphene were examined (Fig. S3 and Table S3 in ESI †), and we identified other metastable structures. Their binding energies are less by 0.01-0.02 eV than that of the lowest energy configuration (Fig. 2e). These structures show significant variation in frequency of both vibration modes ν 3 s -ν 3 s = 159.6-181.9 cm -1 and ν 3 a -ν 3 a = 225.2-231.9 cm -1 , and thus could lead to some broadening of the related peaks.

Polycondensation of bromine molecules

Theoretical studies on the formation of polybromine chains inside small-diameter CNTs 32 and above graphene layers 33 have shown contradictory results. In particular, it was found that anions from an odd number of atoms, such as Br 3 -and when the last step is omitted, the Raman spectra of low-fluorinated matrices exhibit the peaks I-VI (see Fig. S4 †). The Raman spectrum of C 2 F 0.94 sample without additional bromination does not have any features related with the intercalated bromine species. This confirms a weak interaction between Br 2 and highly-fluorinated graphite matrix. Bundles of CNTs and fluorinated CNTs (F-CNTs) can also be intercalated with bromine. Commonly bromine gets into inter-tubular spaces in the bundles. 4,[START_REF] Aguiar | [END_REF] The donor-acceptor interaction between CNTs and bromine and spatial confinement of intercalated molecules inside 1D-channels between tubes should drive the bromine polycondensation in CNTs and F-CNTs similarly to that in brominated graphite and lowfluorinated C 2 F x . To confirm this assumption, we synthesized brominated DWCNTs (denoted as DWCNT-Br) and fluorinated DWCNTs (denoted as F-DWCNT-Br) using a similar procedure to that described above for graphite. Details of the synthesis is given in our previous studies. [4][5][6]66,67 Briefly, DWCNT powder was put in a perforated Teflon flask and this flask was placed on a stand in a larger Teflon flask containing liquid bromine at the bottom and held at room temperature for 4 days. The product was dried by a flow of N 2 to remove weakly bonded Br 2 . The sample is referred to as Br-DWCNT. Fluorination of DWCNTs was carried out using solution of BrF 3 (3 wt%) in Br 2 at room temperature for 7 days. Thereafter, the product (F-DWCNT-Br) was purged by a flow of N 2 to remove weakly adsorbed Br 2 . Based on X-ray photoelectron spectroscopy analysis, performed at the Berliner Elektronenspeicher ring für Synchrotronstrahlung (BESSY II) using radiation from the Russian-German beamline at a monochromatic radiation of 830 eV, a surface stoichiometry of DWCNT-Br and We explored two final structures of the Br 3 -Br 3 chain located near to or far from the fluorine chain (denoted f 1 and f 2 respectively and marked by blue dashed ovals in Fig. 3a andb). The potential surfaces of transformation of three Br 2 into Br 3 -Br 3 indicate that these reactions are exothermic with a negligible energetic barrier (about 0.04 and 0.05 eV for the reactions i → f 1 and i → f 2 , respectively). Therefore, the formation of Br 3 -Br 3 chains over nanoscale graphene region will occur spontaneously in agreement with polymerization of bromine molecules encapsulated inside nanotubes. 32

Discussion

G-Br and C 2 F x -Br samples (x = 0.07, 0.24, 0.47) have almost identical Raman spectra. The most intense peak III at ca. 237 cm -1 lies close to three calculated modes, namely the symmetric stretching of intercalated Br 2 and Br 3 -Br 3 species and the asymmetric stretching of Br 3 . In practise it is likely to be a combination of the three, which can explain also why it is relatively broad. The symmetrical stretching of Br 3 in Br 3 -Br 3 species supplies the peak I at 157 cm -1 .

Formation of Br 3 -based chains in partially fluorinated graphite was found to be spontaneous. The key role in this process belongs to interaction of adsorbed bromine molecules with small pristine graphene regions framed with C-F borders. Moving across such areas, bromine molecules can meet each other. As the result, bounded Br 3 -Br 3 chains are formed. Moreover, according to the study of bromine species encapsulated in CNTs, 32 Br 5 anions could be formed from Br 3 and Br 2 , and they are observed as the Raman resonances located around 206 cm -1 (peak II). 33 The weak intensity band at ca. 323 cm -1 (peak IV) could be attributed to intercalated bromine molecules sitting above fluorinated regions.

A comparison of the Raman spectra in Fig. 1 suggests that bromine behaves differently in highly fluorinated graphite, and for C 2 F 0.94 -Br the spectrum resembles that of liquid bromine. This indicates the intercalate contains bromine molecules separated by the van der Waals distance. The high fluorination degree in C 2 F 0.94 -Br means that every second carbon atom binds with fluorine, and the extended pristine graphene regions are absent. In this case the bromine molecules are located between CF chains of fluorinated graphite layers above non-fluorinated carbon chains, and interact only weakly with the host matrix.

Remarks about bromination of carbons

We used a gaseous mixture of BrF 3 and Br 2 as the fluorinating agent because of its ability to fluorinate graphite at room temperature. Simultaneously the synthesis procedure results in intercalation of bromine and bromine fluoride species. In order to remove bromine fluorides and enrich the samples with bromine, we held them in Br 2 vapour. However, even F-DWCNT-Br samples is C 2 •Br 0.13 and C 2 F 0.15 •Br 0.09 , respectively. Low fluorine content in the latter sample supposes presence of extended non-fluorinated segments on the DWCNT surface.

Fig. 4 shows the Raman spectra of DWCNT-Br and F-DWCNT-Br samples in comparison with the spectra of pristine DWCNTs and bromine-intercalated fluorinated graphite C 2 F 0.07 -Br. Despite the Br-Br vibrations overlaying the radial breathing modes (RBMs) of the outer and inner DWCNT shells, the features previously denoted as I-VI are clearly visible. We suppose that they arise from the characteristic vibrations of different bromine species intercalated in the DWCNT ropes, i.e. Br 2 is also condensed into Br 3 -based chains if they are located in close vicinity between the nanotubes. Therefore, one can conclude that interaction of bromine with graphite and CNTs takes place in a similar manner if extended non-functionalized sp 2 -regions are preserved.

Bromination and fluorination increase the intertube distance causing a partial debundling of the nanotubes. As a result, bromine is less influenced by interaction with the nanotube surface, softening the Raman bands in comparison with that in C 2 F 0.07 -Br.

Conclusion

In summary, by closely coupling experimental and DFT calculated Raman frequencies on a quantitative level never previously used in the literature, we have explored bromination of different sp 2 -hybridized carbon materials (graphite, partially fluorinated graphite, DWCNTs, and fluorinated DWCNTs). Our results show that depending on the fluorination level two types of intercalated bromine species occur. The first is liquidlike layers of bromine (Br 2 ), confined between highly fluorinated graphitic layers with approximately C 2 F. In this case, the intercalated species shows a single Br-related Raman peak at ca. 311 cm -1 . In contrast, the Raman spectra of brominated pristine and low-fluorinated graphites and DWCNTs are rich, indicating a more complex organisation of the guest molecules. When the fluorination degree is low enough, C 2 F x layers contain extended bare graphene nanoregions, which attract the intercalated bromine. This interaction is accompanied by significant charge transfer from the substrate to Br 2 and can be detected as the Raman band at ca. 237 cm -1 . In addition, polybromide species constructed from Br 3 can be formed spontaneously over such nanoregions, due to the negligible calculated activation barrier and large enthalpy value (-1.4 eV). Formation of polybromides, such as weakly bound chains of Br 3 , arises from free diffusion of the adsorbed Br 2 anions over non-fluorinated regions of the graphene sheet toward the fluorinated border. This condensed species over sp 2 -hybridized carbons is responsible for the additional Raman peaks at 157 and 206 cm -1 as well as contributing to the feature at 237 cm -1 . We propose that this polycondensation mechanism is common for all sp 2 -hybridized carbon materials containing extended graphene nanoregions. Table S3 Calculated binding energy E b per one bromine atom (eV), charge transfer Q Br6 (e), and symmetrical stretching Br-Br frequencies ω s (cm -1 ) for the Br 6 over partially fluorinated graphene (see Fig. S3).

Fig. 1

 1 Fig. 1 Raman spectra taken at 514 nm for G-Br and C 2 F x -Br compounds in comparison with a reference spectrum of liquid bromine. Dashed lines indicate positions of Raman peaks denoted as I-VI, D, and G. Deconvolution shown on the example of G-Br spectrum, where the peaks (thin lines) were described by Voigt functions.

Fig. 2 3 a -ν 3 a and ν 3 s -ν 3 s).

 23333 Fig. 2 Fragments of fluorinated graphene with adsorbed Br 2 (a), Br 3 (b) and Br 6 (c) species. Arrows indicate the directions of atomic motion for normal stretching modes of Br 2 (ν 2 s ), Br 3 (ν 3 a and ν 3 s ), and Br 6 (ν 3 a -ν 3 a

Fig. 3

 3 Fig. 3 NEB simulation of reaction paths of 3Br 2 → Br 3 -Br 3 , when final Br 3 -Br 3 is located near to (a) or far from (b) the fluorine boundary. The initial positions of three Br 2 marked by red dashed ovals (denoted i), the final positions of Br 3 -Br 3 marked by blue dashed ovals (denoted f 1 and f 2 ). Arrows indicate the reaction paths, i → f 1 in (a) and i → f 2 in (b). The Br-Br distance increases from 2.3 Å in Br 2 to 2.5 Å in Br 3 , the distance between Br 3 in the Br 3 -Br 3 chain is ∼3.0 Å. Diffusion barriers calculated for two reaction paths 1 and 2 (c).

  . S2 in ESI †). The actual charge transfer from graphene to Br 2 is much weaker (Q Br 2 = -0.16e). ABr 2 molecule has only a single stretching motion, while polyatomic bromine species exhibit more complex vibrations. Isolated Br 3 and Br 3 -have a linear centrosymmetric structure with deformation vibration ν 3 b (58.2 and 83.4 cm -1 ), symmetric stretching vibration ν 3 s (189.6 and 164.0 cm -1 ), and asymmetric stretching vibration ν 3 a (243.7 and 215.0 cm -1 )in

Fig. 4

 4 Fig. 4 Raman spectra taken at 514 nm for pristine DWCNTs, brominated DWCNTs (DWCNT-Br), brominated fluorinated DWCNTs (F-DWCNT-Br), and fluorinated graphite intercalation compound C 2 F 0.07 -Br. Positions of peaks I-VI in the spectra of DWCNT-Br and C 2 F 0.07 -Br samples are shown by dashed and dot-dashed lines, respectively.

Fig. S1

 S1 Fig. S1 Optimized geometries of graphene supercell (a), Br 2 oriented perpendicular (b) and parallll (c) to graphene sheet, Br 3 (d), and Br 6 (i,j) over graphene sheet.

Br 2 , s Br 3 ) as Br 3 )Frequency, cm - 1 graphene

 2331 Fig. S2 Variation in calculated charge (a) and stretching frequencies (b) of Br 2 , Br 3 and Br 6 located over graphene sheet with the size of graphene supercell and k-point grid. Dashed lines in (b) correspond to peak I and II of experimental Raman spectra of brominated graphite and bromineintercalated fluorinated graphites (see Fig. 1).

Fig. S3

 S3 Fig. S3 Optimized geometries of metastable structures of Br 6 over partially fluorinated graphene sheet.

  Fig. S4Raman spectra taken at 514 nm for graphite intercalation compounds (C 2 F x -Br) synthesized without additional treatment with Br 2 vapors.

Table 1

 1 Calculated geometry parameters (Br-Br bond length h Br-Br , the shortest Br-C distance h C-Br ), electronic structure (binding energy E b per bromine atom, charge transfer Q Br n ) and stretching frequencies of free bromine species and those adsorbed on graphene (Br 2 /G, Br 3 /G, Br 3 -Br 3 /G) and fluorinated graphene (Br 2 /FG, Br 3 /FG, Br 3 -Br 3 /FG). Frequencies ν 3 a (shown in italics) correspond to Raman-inactive vibrations for linear Br 3 structure. Values for isolated Br 2 , Br 3 , and Br 3 -are listed for reference. The last column shows the Raman bands in the spectra of G-Br and C 2 F x -Br samples from Fig. 1. The experimental frequencies are listed alongside the species we are assigning them to

		h Br-Br (Å)	h Br-C (Å)	E b /Br (eV)	Q Br n (e)	ν (cm -1 )		expt. (cm -1 )
	Br 2 (Q = 0e) Br 2 (Q = -1e) Br 3 (Q = 0e) Br 3 -(Q = -1e) Br 2 /G Br 3 /G Br 3 -Br 3 /G	2.3 2.3 2.5 2.5 2.3 2.5 2.5 (Br 3 ) 3.0 (Br 3 -Br 3 )	3.6 3.5 3.3	-0.15 -0.39 -0.39	-0.16 -0.76 -1.28	326.2 (ν 2 151.9 (ν 2 189.6 (ν 3 243.7 (ν 3 164.4 (ν 3 215.0 (ν 3 233.9 (ν 2 164.3 (ν 3 220.3 (ν 3 158.7 (ν 3 223.1 (ν 3	s ) -peak IV s ) s ) a ) s ) a ) s ) -peak III s ) -peak I a ) -peak III s s ) -peak I -ν 3 a -ν 3 a ) -peak III	Peak I: 157 Peak II: 206 Peak III: 237 Peak IV: 323 Peak V: 410 Peak VI: 473
	Br 2 /FG Br 3 /FG Br 3 -Br 3 /FG	2.3 2.5 2.5 (Br 3 )	3.4 3.2 3.2	-0.22 -0.44 -0.36	-0.12 -0.59 -1.13	308.2 -peak IV s ) -peak I 176.0 (ν 3 a ) -peak III 229.6 (ν 3 163.3 (ν 3 s -ν 3 s ) -peak I
		2.9 (Br 3 -Br 3 )				231.9 (ν 3

a

-ν 3 a )peak III

Table S1

 S1 Comparison of stretching frequencies of Br 3 over graphene obtained using LDA within spin-averaged and spin-polarized approaches. kt S av. /S pol. E tot spin av.-E tot spin pol. ν spin. av. / ν spin pol. 0.04 0/0.002 0 eV =164/164 cm -1 ; =220/220 cm -1 

				𝑠 3		𝑎 3
	0.01 0/1	0.1 eV		𝑠 3	=164.5/166.1 cm-1; =222/220.3 cm -1 𝑎  3

Table S2

 S2 Dependence of calculated parameters for the Br 2 in parallel orientation to graphene sheet on the size of unit cell and k-point grid.

	graphene cell size k-point grid	𝑄 𝐵𝑟 2	(e)		𝑠 2	(cm -1 )
	4×4	1×1×1	-0.09296 309.2126
	4×4	9×9×1	-0.161316		258.1
	5×5	1×1×1	-0.08489 310.97708
	6×6	1×1×1	-0.084	318.84834
	7×7	1×1×1	-0.14167 255.47528
	8×8	1×1×1	-0.13815 256.54681
	9×9	1×1×1	-0.09754 291.92995
	10×10	1×1×1	-0.18717 239.85602
	11×11	1×1×1	-0.18168 233.89082

Acknowledgements

The study of graphites was funded by the Russian Foundation for Basic Research (RFBR, grant no. 18-29-19073) and EU IRSES Project 612577 "NanoCF". The study of DWCNTs was supported by the RFBR (grant no. 16-53-150003) and the PRC CNRS/RFBR (grant no. 1023). We also thanks the Academy of Finland (grant no 318345) for support. We are grateful to Prof. B. A. Kolesov for the Raman data and fruitful discussion. Some of the calculations were performed at the CCIPL (Centre de Calculs Intensif Pays de la Loire).

Conflicts of interest

There are no conflicts to declare.

Supporting Information for

Bromine polycondensation in pristine and fluorinated graphitic carbons

Olga V. Sedelnikova,* a,b Christopher P. Ewels,* c Dmitriy V. Pinakov, a,b Galina N. Chekhova, a Emmanuel Flahaut, d,e Alexander V. Okotrub


Antoine Courtay

Mickaël Le Gentil

Olivier Berder

Pascal Scalart

Sébastien Fontaine

Arnaud Carer

Anchor Selection Algorithm for Mobile Indoor Positioning using WSN with UWB Radio

Positioning a person or an object has become essential in many applications. It already exists solutions for outdoor positioning such as satellite based techniques (i.e. GPS) but indoor positioning still remains a great challenge for applications like sports monitoring, contextual visits of museum, Building Information Modeling (BIM) or automated drone missions. Classical approaches using radio communication such as WiFi, Bluetooth, ZigBee only give an accuracy of approximately 2.5 meters when the mobile is static, of course worse when moving. Recently some new radio communication chipsets have emerged based on Ultra Wide Band (UWB) communications. UWB allows accurate Time Of Flight (TOF) measurements, and thus distances estimations between nodes equipped with. A positioning algorithm named Best Anchor Selection for Trilateration (BAST) based on position prediction and noise estimation is proposed. Then a wearable, light and low power Wireless Sensor Network (WSN) prototype (named Zyggie) including an UWB chipset has been developed for algorithms comparison. Finally, an experimental testbed using real cases experiments shows that BAST can give from 1.26 up to 4.17 times better accuracy than low complexity state of the art algorithms when the mobile/person is in movement (e.g. tennis player).

I. INTRODUCTION

Knowing the position of a device in its environment becomes an important issue for applications providing services based on the position. Many solutions have been proposed going from satellite based techniques (i.e. GPS), video tracking or radio-electrical waves combining. However, these techniques reach their limit when very high accuracy is required, especially in indoor environment. There are several approaches to estimate the location of a mobile in an indoor environment. Some of them use optical signals such as infrared, laser or video tracking approaches (like the Vicon system [START_REF]Vicon system[END_REF]) and many others use radio signal. As applications we target need low cost, portable and low power systems which can be deployed in minutes, radio signal positioning system is the best candidate. Last years many radio standards have been explored such as WiFi [START_REF] Dortz | Wifi fingerprint indoor positioning system using probability distribution comparison[END_REF], [START_REF] Shchekotov | Indoor localization methods based on wi-fi lateration and signal strength data collection[END_REF], Bluetooth [START_REF] Wang | Indoor positioning system using euclidean distance correction algorithm with bluetooth low energy beacon[END_REF], ZigBee [START_REF] Fang | An enhanced zigbee indoor positioning system with an ensemble approach[END_REF], [START_REF] Luoh | Zigbee-based intelligent indoor positioning system soft computing[END_REF] concerning indoor positioning. They are all based on the Received Signal Strength Indicator (RSSI) of a signal between two devices. Performances are often disappointing due to the lack of accuracy (approximately 2.5 m) and gets even worse if the mobile is in Non Line Of Sight (NLOS), in movement or if there is multipath (walls, objects). A new radio approach known as Ultra Wide Band (UWB) has recently emerged which has the ability to do accurate Time Of Flight (TOF) measurements. Since 2014, Microsoft has launched an Indoor Localization Competition co-located with the IPSN Conference. When looking at the results of the competition [START_REF]Microsoft indoor localization competition -ipsn 2018[END_REF] we can notice that more than 50% of the 3D competitors use UWB technology including the two first competitors. The best UWB competitor in 2018 has an average error of 27 cm over many fixed points measurements following a trajectory in a building. However, most of the presented prototypes are not enough miniaturized yet to be wearable or use different platforms for the mobile and anchors. Moreover, some of them use wired together anchors for network synchronization. Unlike academic and industrial solutions mentioned above, our wireless sensor node Zyggie [START_REF] Courtay | Zyggie: a wireless body area network platform for indoor positioning and motion tracking[END_REF] is ultra compact and very light which really makes it a good candidate for all applications where weight and size are critical. Both anchors and mobile have the same architecture and the network synchronization is done wirelessly via a 2.4 GHz radio frontend. Respecting low complexity and low memory footprint constraints imposed by such wireless nodes, the main contribution of this paper is the development of a positioning algorithm named Best Anchor Selection for Trilateration (BAST) that outperforms low complexity state of the art algorithms under low power and real time computation constraints. BAST also allows to display output trajectory on portable devices (smartphone, tablet) in real time. An Android application has been developed for this purpose. A last contribution is that all experimental results were obtained using simulations based on real cases experiments. A serpentine walking trajectory and a real tennis playing game were acquired several times to evaluate algorithms performance. The rest of the paper is organized as follows. Section II summarizes the state of the art algorithms applied to a positioning process knowing distances with reference points. Section III introduces our new algorithm (BAST) for indoor positioning of a mobile. In Section IV, the developed prototype node, the experimental setup with two scenarios (walking in a room and playing tennis) are explained. In Section V, the results of all the positioning algorithms are discussed. Finally, conclusions are drawn and future works are commented in Section VI.

II. RELATED WORK ON POSITIONING ALGORITHMS

A positioning algorithm aims at providing 2D/3D coordinates by combining some distances of a (mobile) node with respect to some fixed nodes (which positions are known in advance) named here anchors. In the rest of the paper, resolution will be presented in 2D. For a 3D resolution, just add in the system (1) the z contribution. It is possible by knowing the respective distances of a mobile node to 3 anchors to solve the following system. The more anchors there are the more equations in the system there will be. Here is the system with 3 anchors

     d 2 A1 = (x M -x A1 ) 2 + (y M -y A1 ) 2 + n A1 d 2 A2 = (x M -x A2 ) 2 + (y M -y A2 ) 2 + n A2 d 2 A3 = (x M -x A3 ) 2 + (y M -y A3 ) 2 + n A3 , (1)
where the d Ai are the distances toward the anchor i, the x Ai and y Ai are the coordinates of the anchor i, the n Ai are the noises on the measured distances and x M , y M the mobile' coordinates. All the following algorithms have the same starting point (i.e. the distances) to compute the mobile coordinates.

A. Weighted Centroid Localization

The Weighted Centroid Localization (WCL) algorithm explained in [START_REF] Blumenthal | Weighted centroid localization in zigbee-based sensor networks[END_REF] consists in finding the solution point m in

m = x M y M = N i=1 w Ai • a Ai = N i=1 1 d Ai • x Ai y Ai N j=1 1 d Aj , ( 2
)
where m is the researched point (mobile's coordinates), a Ai the coordinates vectors of the N anchors and w Ai the weighting coefficients of each anchor. In our case, these coefficients are the inverse of the considered distance d Ai divided by the sum of the inverses of d Ai . Using WCL, it is also possible to affect a different weight to each anchor to make its influence higher in the solution.

B. Gauss-Newton

The Gauss-Newton method [START_REF] Nocedal | Numerical Optimization: 10.3 Algorithms for Nonlinear Least-Squares Problems[END_REF] is an iterative algorithm which aims at minimizing the positioning error. Mobile's coordinates m are computed iteratively by solving

m l = m l-1 -H -1 l-1 • g l-1 = x M y M , (3)
where l is the iteration step, H the Hessian matrix and g the gradient vector. Gauss-Newton algorithm has the advantage to quickly converge. On the other side, the Hessian matrix uses a 3/2 power on the distances which leads to more computation.

C. Trilateration

Trilateration algorithm consists here in finding a solution to the previously defined system [START_REF]Vicon system[END_REF]. By doing some transformations, it is possible to write the system to solve such as

u = V • m + e with u = (d 2 A1 -d 2 A2 ) -(x 2 A1 -x 2 A2 ) -(y 2 A1 -y 2 A2 ) (d 2 A1 -d 2 A3 ) -(x 2 A1 -x 2 A3 ) -(y 2 A1 -y 2 A3 ) , V = 2 • (x A2 -x A1 ) 2 • (y A2 -y A1 ) 2 • (x A3 -x A1 ) 2 • (y A3 -y A1 ) and e = n A1 -n A2 n A1 -n A3 . (4)
For this example Anchor number 1 has been chosen for reference and therefore appears twice in the equations. By posing

v 1 = 2 • (x A2 -x A1 ) 2 • (x A3 -x A1 ) and v 2 = 2 • (y A2 -y A1 ) 2 • (y A3 -y A1 ) , (5)
the Cramer's rules give a solution that minimize the Mean Square Error (MSE) to obtain the mobile coordinates below

x M = det u v 2 det (V) and y M = det v 1 u det (V) . (6)
Anchors must not be aligned to obtain a solution for x M and y M due to a null denominator. There exists some other mathematical ways to solve the system such as Cramer-Rao Bound (CRB) [START_REF] Yang | Cramer-rao bound and optimum sensor array for source localization from time differences of arrival[END_REF] and Least Squares (LS) [START_REF] Caffery | A new approach to the geometry of toa location[END_REF]. As we target low complexity computation, only Cramer method was implemented.

D. Multilateration

Multilateration algorithm [START_REF] He | Range-free localization schemes for large scale sensor networks[END_REF] uses the previously seen developments of trilateration and applies it to all of the combinations of 3 non-aligned anchors. By this way, for a configuration with N anchors, we obtain C N 3 trilateration combinations with aligned combinations subtracted. Finally, we obtain the estimated point by doing the mean (centroid) of these points. The main drawback of this method is the fact that the more anchors your system has, the more calculations need to be done in return of a theoretically better accuracy.

There exist some other trilateration/multilateration variant based algorithms such as [START_REF] Chenji | Toward accurate mobile sensor network localization in noisy environments[END_REF]- [START_REF] Dardari | Indoor tracking: Theory, methods, and technologies[END_REF]. Even if proposed results seem to be of interest, these algorithms are either too complex in hardware or software implementation to match our constraints. Indeed we target low cost and energy efficient real time computation/displaying for mobile indoor positioning applications (in-building or sports). Authors from [START_REF] Chenji | Toward accurate mobile sensor network localization in noisy environments[END_REF] propose to use fuzzy logic to compensate noise before multilateration processing. Their approach needs rather complex processing functions (training phases, recursive filters and coefficient updates). Other techniques are based on range free scheme as DV-Hop. They do not require complex computations but need a huge amount of anchors to achieve a relatively low accuracy. The distance between 2 anchors is the finest achievable precision [START_REF] Jo | Multilateration method based on the variance of estimated distance in range-free localisation[END_REF], [START_REF] Assaf | Accurate nodes localization in anisotropic wireless sensor networks[END_REF]. Authors from [START_REF] Jo | Multilateration method based on the variance of estimated distance in range-free localisation[END_REF] can reach 0.85 m of accuracy using a topology of 200 anchors randomly placed in a square of 100 m 2 . An other algorithm based on Bayesian filtering [START_REF] Dardari | Indoor tracking: Theory, methods, and technologies[END_REF] gives interesting results in Indoor Localization Competition of IPSN. This statistical-based method needs Bayesian and particle filtering coupled with a maximum-likelihood estimation. Such amount of computations does not match our previously mentioned constraints.

III. PROPOSED ALGORITHM: BEST ANCHOR SELECTION

FOR TRILATERATION (BAST) The BAST algorithm aims at selecting a triplet of anchors taking into account predicted coordinates for mobile's position

Algorithm 1 BAST Algorithm Input: d A , a A , m k-1 , m k-2 Output: m k 1: d A ← F ilter(d A ) Filter mistaken distances 2: m ← P redictor(m k-1 , m k-2 )
Estimate mobile's coordinates 3: for i ← 1, N bAnchors do 4:

A 1 ← {d Ai ; a Ai } Create reference anchor object 5:

(A 2 , A 3 ) ← N earestN onAlignedAnchors(d A , a A )
Select the 2 nearest non-aligned anchors 6:

m i ← T rilateration(A 1 , A 2 , A 3 ) Compute trilateration 7: δ M Ai ← EuclidianDistance(m i , m)
Compute ED 8: end for 9: m min ← GetM obile(min(δ M A ))

Get mobile's coordinates from minimum ED vector 10:

(A 1 , A 2 , A 3 ) ← GetT riplet(min(δ M A ))
Get triplet of anchors from minimum ED vector 11: n ← N oise(A 1 , A 2 , A 3 , m min )

Compute noise distances vector from triplet 12:

d A T riplet ← Distances(A 1 , A 2 , A 3 ) -n
Subtract noise to measured distances vector 13:

(A 1 , A 2 , A 3 ) ← U pdateDistances(d A T riplet )
Update triplet of anchors 14:

m k ← T rilateration(A 1 , A 2 , A 3 )
Compute final trilateration computation. This computation takes noise into account to improve measured distances. BAST steps are explained hereafter respectively to Algorithm 1. At first, a filtering process aims at replacing mistaken values in d A vector due to impossible or disturbed TOF measurements made by the UWB frontend. Secondly, mobile's coordinates are estimated using a one step linear forward predictor (assuming a mobile's constant speed) as defined in

m = 2 × m k-1 -m k-2 , (7)
where m are the estimated coordinates and m k-1 and m k-2 the two last computed coordinates from BAST. Then, the aim of the f or loop is to compute the Euclidian Distance (ED) between m i and m for N bAnchors triplets.

Triplets are built by selecting a first anchor and then the 2 nearest non-aligned ones. Trilaterations are done on these triplets to get coordinates vector m i . In next step, the triplet corresponding to the minimal ED of δ M A is selected for noise computation n as defined in

n =   d A1 -(x mmin -x A1 ) 2 + (y mmin -y A1 ) 2 d A2 -(x mmin -x A2 ) 2 + (y mmin -y A2 ) 2 d A3 -(x mmin -x A3 ) 2 + (y mmin -y A3 ) 2   , (8)
where m min corresponds to mobile's coordinates with minimal ED. The noise is finally subtracted to the triplet distances vector and a last trilateration allows to obtain the mobile's coordinates m k .

IV. EXPERIMENTAL SETUP

The experimental setup consists here in validating our algorithm and the state of the art ones by doing some measurements on our developed WSN platform in real environments. In general WSN and specific Wireless Body Area Network (WBAN), the unknown location of a node is determined in two steps. The first one is measurement step where one or more position-related metrics are measured to allow the computation of relative distances between each pair of nodes. The second step called position estimation step (Section II) aggregates these distance measurements as input of a position estimator to produce the target/mobile node's position. The Zyggie node [START_REF] Courtay | Zyggie: a wireless body area network platform for indoor positioning and motion tracking[END_REF] is a Wireless Sensor Node with UWB radio capabilities that was developed in our lab. Its architecture is represented in Fig. 1. Zyggie is composed of:

A. Zyggie node architecture

• An Silicon Labs EFM32 ARM CortexM4 micro-controller which is the master of the node and also controls the UWB radio chip,

• An ATMEGA2564RFR2 micro-controller which drives the 2.4 GHz radio for data exchanges and network synchronization, • A DecaWave DW1000 UWB radio chip [START_REF]Decawave uwb chipset[END_REF] for TOF measurements, • An InvenSense Inertial Measurement Unit (IMU) for acceleration, angular speed and magnetic field captures. Unlike solutions presented in [START_REF]Microsoft indoor localization competition -ipsn 2018[END_REF], our node is ultra compact (37 mm by 63 mm) and only weights 32 g (including battery) which makes it a real good candidate for all applications where weight and size are critical. Some experiments with UWB radio enabled at full speed were done; it leads to a battery life time of around 5 hours which is enough for sportsman or in building applications. For both following contexts anchors are Zyggie nodes and the person to localize was wearing a Zyggie node on his wrist. Another Zyggie node is connected to a computer to synchronize the network (i.e. anchors and mobile nodes) via the 2.4 GHz radio and also to collect distances measurements via the UWB radio of the mobile node respect to the anchors. A custom TDMA MAC protocol allocates time slots to each anchor doing their TOF measurements. Data are then processed and plotted on the computer/tablet using the previous presented algorithms. In order to evaluate algorithms' performance, two contexts were defined: a quiet walking context and a fast moving context (i.e. tennis player).

B. Indoor Serpentine Walking Context

For this context, data were acquired in a big room of nearly 243 m 2 (26.4 m length by 9.2 m width). The ideal trajectory was marked on the floor and one step per second (around 3 km/h) was done following this trajectory. To study the impact of the trajectory and the used anchors for the positioning algorithms, vertical and horizontal serpentine trajectories were acquired ten times. In order to test our BAST algorithm a six anchors configuration is used as represented in Fig. 2.

C. Indoor Tennis-man Playing Context

For this context, data were acquired on a tennis court during real tennis playing conditions. All acquisitions were done in parallel with a high precision vision positioning system called Vicon [START_REF]Vicon system[END_REF]. Data issued from the Vicon system were considered as the reference to compute the performance of all algorithms. A four anchors configuration is used and the anchors locations were at the four corners of the court.

V. RESULTS

Tables I and II present the performance results of all previously defined algorithms in terms of average error, error variance, variation of average error and variance and computation time. BAST serpentine trajectory is plotted in Fig. 2.

• The average error ( S ) for the serpentine context is the mean error of all the recorded walking scenarios, • The average error ( T ) for the tennis player context is the mean error of all the recorded playing sequences, • The average standard deviation (σ S and σ T ) is the mean of all standard deviations for both contexts,

• The variation of the average error (∆ S and ∆ T ) and the variation of the standard deviation (∆σ S and ∆σ T ) are the average gains of BAST compared to other algorithms, • The computation time (T compS and T compT ) has been obtained running algorithms on Matlab on a desktop computer equipped with Intel Xeon processor and 8 GB RAM. WCL algorithm is the worst algorithm due to the fact that all anchors try to attract the solution point towards them. Consequently, estimated mobile coordinates are not on the real trajectory. For both contexts, trilateration works quite well. But the error can grow a lot when the mobile is not placed inside the virtual triangle formed by the 3 selected anchors. As multilateration does the mean of all the available trilaterations, the previous mentioned phenomenon appears everywhere on the estimated trajectory which leads to a higher error for our contexts. Gauss-Newton results are quite identical as BAST results for the serpentine context. Gauss-Newton works on the 6 anchors and as previously explained BAST chooses the best 3 anchors for trilateration. When movements are faster as in the real tennis playing game our BAST algorithm outperforms all other algorithms by giving at a minimum 1.26 and at a maximum 4.17 times better accuracy, to the penalty of a nearly doubled computation time which is still acceptable for real time executions and displaying.

By analyzing Zyggie IMU results, we have noticed that the TOF measurements were really drifting when the player hits the ball due to a high acceleration. We can conclude that for tennis player, placing a Zyggie node on the wrist may not be the ideal position. Some new experiments could be done with the node on the torso, on a foot or some other places. We have noticed that for some places in the environment between two consecutive iterations, our BAST algorithm has to switch between anchors. This is due to the fact that they are all approximately at the same distance. An improvement could be to introduce a memory effect of the last 3 selected anchors (a temporal filter will be developed for this purpose) in order to decide to switch or not, as the same manner it is done in phone cellular network when your phone switches from a base station to another depending on your map position. VI. CONCLUSION An enhanced algorithm for mobile indoor positioning was presented in this paper. Indoor positioning algorithms are based on distances measurements from a mobile node to anchor nodes. These distance measurements are issued from UWB radio exchanges which allow to do TOF computations. A WSN demonstrator called Zyggie has been developed for this purpose. Zyggie has the advantage to be wearable (small form factor), light and low power. Some real experiments were done using Zyggie in two contexts; a walking context and a tennis playing game context. Collected data were passed through BAST and low complexity state of the art algorithms for comparisons. In all contexts but especially when the mobile moves fast, the BAST algorithm outperforms all other algorithms by giving at a minimum 1.26 and at a maximum 4.17 times better accuracy. Perspectives can be pointed out from the current work:

• An adaptive selection of the used algorithm could be done in real time depending on how fast the mobile moves and how much energy remains in the battery. For instance, as Gauss-Newton is less complex than BAST and gives nearly the same performance when the mobile moves slowly, computation time and energy consumption could be saved.

• Depending on the application, it can be more than one mobile to localize (team sports, visitors in a museum for instance), a multi-user protocol using anchors needs also to be explored.

Fig. 1 .

 1 Fig. 1. Zyggie WSN Hardware illustration.

Fig. 2 .

 2 Fig. 2. BAST results: blue dots are anchors, red one is the mobile and green curve ideal trajectory. The estimated trajectory is in red.


est destinée au dépôt

Wiktrop participatory portal

The

  WIKTROP collaborative portal : sharing and disseminating knowledge on weeds of tropical pastures for better management of grazing land degradation Thomas Le Bourgeois, Vincent V. Blanfort, Cédric Péret, Vincent Petiot, Jean-Marie Capron To cite this version: Thomas Le Bourgeois, Vincent V. Blanfort, Cédric Péret, Vincent Petiot, Jean-Marie Capron. The WIKTROP collaborative portal : sharing and disseminating knowledge on weeds of tropical pastures for better management of grazing land degradation. 9th Multi-stakeholder Partnership Meeting -Innovation for Sustainable Livestock Systems, Sep 2019, Kansas, United States. hal-02299209 Key messages • Aggregation, capitalization and spread of knowledge on weeds and weed management in tropical grazing lands • Sharing weed knowledge and weed problems of stakeholders • Building a multi-actors network • Building individual and institutional capacities to improve productivity and durability of grazing systems Constraints to manage • Intellectual rights and traditional knowledge (Creative Commons licence, Nagoya protocol) • Sharing knowledge and data (everyone gives little bit and everybody gets a lot) • User contribution (needs regular supporting) • ITC technology to adapt (multilingualism En/Fr, Web portal and mobile apps, etc.) Aknowledgements This portal has benefited from different financing such as the European Union (ACP Secretariat-Science and Technology Programme II, Programme de Développement Rural Régional de la Guyane 2014-2020). The coordinators of WIKTROP would like to thank all the members of the portal who contribute in its efficacy sharing and disseminating knowledge on weeds of tropical pastures for better management of grazing land degradation Results and benefits http://portal.wiktrop.org A 1 , Vincent Blanfort 2 , Cédric Péret 3 , Vincent Petiot 3 , Jean-Marie Capron 3 1 CIRAD UMR AMAP, Montpellier, France 2 CIRAD UMR SELMET, Montpellier France, vincent.blanfort@cirad.fr 3 Chambre d'agriculture de Guyane; Macouria, Guyane The WIKTROP collaborative portal: 9th Multi-Stakeholder Partnership Meeting -Innovation for Sustainable Livestock Systems, Kansas, 9-13 sept 2019 This document is licensed for use under the Creative Commons Attribution 4.0 International Licence. May 2017