M S Nikul'shina

A V Mozhaev

Christine Lancelot

Pascal Blanchard

Maya Marinova

Carole Lamonier
email: carole.lamonier@univ-lille1.fr

P A Nikul'shin

M Nikulshina

P Nikulshin
email: p.a.nikulshin@gmail.com

Enhancing the hydrodesulfurization of 4,6-dimethyldibenzothiophene through the use of mixed mows2 phase evidenced by haadf

Keywords: Hydrodesulfurization, Hydrogenation, Heteropolyanion, MoW catalysts, DBT, 4,6-DMDBT

come

Introduction

A release of new stringent standards on the sulfur concentration in the transportation fuels led to an intense research activity on HDS. Conventional Co(Ni)-promoted Mo(W) alumina supported HDT catalysts exhibit high activity in removing sulfur from thiophene and dibenzothiophene (DBT) compounds. However, deep desulfurization and production of ultra-low sulfur fuels are compounded by the presence of resistant molecules such as alkyl-substituted DBTs. Alkyl groups in the 4 and 6 positions in DBT molecules make them more resistant to HDS due to the steric hindrance around the sulfur atom [1]. The HDS of 4,6-DMDBT goes through two reaction pathways: direct desulfurization (DDS) via σ-bonding of the molecule to the catalyst surface with breaking of the C-S bonds and hydrogenation (HYD) via π-bonding with preliminary hydrogenation of one aromatic ring, giving preference to the latter [2,3]. Considering this fact the development of a new generation of catalysts with high HYD activity is a topical task.

Subsequent to the development of high-active bulk NiMoW HDS catalyst (NEBULA) [4] many studies were devoted to investigation of this system. Supported MoW catalysts were also investigated and were prepared from a mixture of conventional ammonium heptamolybdate and ammonium metatungstate or of tetrathiomolybdate and tetrathiotungstate leading to better thiophene HDS catalytic performances [5,6]. Despite these trimetallic NiMoW sulfide catalysts have a potential advantage over bimetallic Ni-Mo and Ni-W systems, in respect to deep sulfur [7][8][9][10], precise determination of the reasons of high activity of these catalysts is not simple.

Nowadays the use of heteropolycompounds as starting oxidic precursor of an active phase is an interesting alternative method for preparation of HDS catalysts with improved catalytic properties [11][12][13][14][15][16][17][18][19]. In the field of hydrotreatment catalysis, Keggin and Keggin-derivated heteropolymolybdate and heteropolytungstate structures have been successfully used to replace conventional precursors. Thus, Ni promoted molybdenum and tungsten HPA-based catalysts showed better performance in deep HDS of 4,6-DMDBT [20] and diesel hydrotreating [21] than the counterparts prepared from traditionally used Mo (W) ammonium salts.

We proposed recently a new approach to prepare (Ni)MoW catalysts using mixed MoW HPA, allowing to introduce together Mo and W from a single molecular entity [22]. MonW12n/Al2O3 mixed HPAs based catalysts sulfided with dimethyl disulfide (DMDS) in liquid phase were found more efficient in the HDS of DBT and HYD of naphthalene than their counterparts obtained by a mixture of monometallic HPAs with the same Mo/W ratio. Moreover, these catalysts had improved HYD properties, which was related to the formation of a mixed Mo-W sulfide phase after liquid phase sulfidation. The procedure of activation of oxide precursors to the active sulfide phase plays an important role and influences to the structure and properties of active phase particles [23][24][25][26]. In addition, Hensen and co-workers [27] have recently shown that sulfidation conditions of trimetallic NiMoW/Al2O3 catalysts prepared from separate Mo and W precursors led to different morphology of active phases and to different catalytic properties. The most commonly used procedures consist in gas phase sulfidation (GS) under a flowing H2S/H2 while liquid phase sulfidation (LS) is performed through the use of sulfiding agents (CS2, dimethyl sulfide, DMDS and etc.).

In the present study, mixed HPA based catalysts are activated under gas phase and characterized by XPS, HRTEM and HAADF. Their catalytic performances are evaluated in the HDS of DBT and also in a more refractory molecule, 4,6-DMDBT, as well as in naphthalene HYD.

A particular attention is also paid to the comparison of sulfidation methods (gas versus liquid phase) and its effect on the nature of the active phase and location of Mo and W atoms in sulfide slabs thanks to the use of HAADF.

Experimental

Catalyst preparation

Hydrotreating catalysts with the same surface density of metals d(Mo+W) ≈ 4 at/nm 2 were synthesized by the incipient wetness method via impregnation of Al2O3 extrudates (SBET = 235 m 2 /g, Vp = 0.9 cm 3 /g) with aqueous solutions containing the required amounts of HPAs [22]. Two bimetallic Mo1W11/Al2O3 and Mo3W9/Al2O3 catalysts were prepared by using corresponding mixed SiMo1W11 and SiMo3W9 HPAs. Two (Mon+W12-n)/Al2O3 reference catalysts were also prepared using mixture of monometallic SiMo12 and SiW12 HPAs with a same Mo/W ratio as in mixed ones. Finally, Mo12/Al2O3 and W12/Al2O3 samples based on corresponding monometallic HPAs were synthesized for comparison. The oxidic catalyst precursors after maturation were dried at 100 ºC for 10 h in air atmosphere without further calcination. The chemical compositions of the prepared catalysts are given in Table 1.

Prior the characterization of the active phase of the catalysts and evaluation of their catalytic activities, the solids were activated by gas phase sulfidation, which was carried out in one step under a flow of a mixture of 10 % of H2S into H2 at atmospheric pressure with heating to 400 ºC over a holding period of 2 h.

Catalyst characterization

High-resolution transmission electron microscopy (HRTEM)

HRTEM characterization of sulfided Mo(W)/Al2O3 catalysts was performed using a Tecnai G2 20 electron microscope with a 0.14 nm lattice-fringe resolution and an accelerating voltage of 200 kV. Slab length and layer stacking distributions of Mo(W)S2 crystallites in each catalyst were estimated on the observations of at least 500 crystallites taken from different parts of the same sample. The average length of the slab ( ) was calculated as simple arithmetic mean and approximately corresponds to the diagonal dimension of the observed Mo(W)S2 slab [28]. The number of slabs per stack was determined to obtain the average stacking degree ( N ):

1..

1.

.

i i i t i i t n N N n = = =   , ( 1
)
where ni is the number of stacks in Ni layers.

High resolution high-angle annular dark-field scanning transmission electron microscopy (HR HAADF-STEM)

HAADF-STEM analyses were performed using a FEG TEM/STEM system (Titan Themis FEI) operated at 200 kV, equipped with a monochromator and a probe Cs corrector. For HAADF acquisition, the spot size was 9 with a screen current of ~50 pA and a camera length of 115 mm, corresponding to inner and outer diameters of annular detector of ∼50 and ∼200 mrad, respectively. Freshly sulfided samples were ground under an inert atmosphere and dispersed in ethanol. The suspension was collected on carbon films supported on copper grids.

X-ray photoelectron spectroscopy (XPS)

The sulfided catalyst samples were analysed by XPS. The spectra were obtained on a Kratos Axis Ultra DLD spectrometer using a monochromatic AlK α source (hν = 1486.6 eV, 150 W). The binding energy (BE) scale of the spectrometer was preliminarily calibrated using the position of the peaks for the Au 4f7/2 (83.96 eV) and Cu 2p3/2 (932.62 eV) core levels of pure metallic gold and copper. The samples were mounted on a holder using double-sided adhesive tape. The analysis chamber was operated under ultrahigh vacuum with a pressure close 10 -10 Torr. For the nonconductive samples, the Kratos charge neutraliser system was used, and the spectra were chargecorrected to provide the Al 2p spectral component at 74. XPS decomposition enabled the absolute quantification of each species:

T 1.. / ( ) (at. %) 100 / i i i i i n A S C i A S = = ×  , ( 2
)
where Ai is the measured area of species i, Si is the sensitivity factor of the atom related to species i (based on Wagner cross sections and on transmission factors provided by the manufacturer) and C(i)T is the absolute content of species j.

Fig. 1 shows the examples of spectra of Mo 3d, W 4f and S 2p photoelectron spectra recorded for Mo3W9/Al2O3 catalyst. It is well known that after sulfidation of Mo or W based catalysts three main W and three main Mo contributions can be identified:

-for W particles: a W 4+ species of the WS2 phase characterized by a doublet (W4f7/2 and W4f5/2) with a BE at about 32.1 and 34.3 eV, , a W 5+ species of W V -OS oxysulfide species at about 33 and 35.2 eV and a doublet at 36 and 37.9 eV correlated with W 6+ oxide species (W VI -O).

-for Mo particles: a doublet at about 229 eV and 232 eV (Mo3d5/2 and Mo3d3/2) correspond to the MoS2 species. A doublet at about 230 and 233.5 eV is related to oxysulfide species (Mo V -OS) and a doublet at about 232.5 and 235.7 eV is correlated with Mo 6+ oxide species (Mo VI -O).

S2p spectra are known to evidence two contributions assigned to sulfide (226 eV) and oxysulfide entities (227.5 eV).

Contact with air (oxygen) was clearly avoided after activation during the transfer in the XPS chamber preventing oxygen contamination, sulfate species are in this case formed during the activation procedure. The absence of any signal at 169.0 eV in the S2p XPS spectra (characteristic of sulfates) indicates that sulfided catalysts were not reoxidized during the transfer of the solid from the sulfiding reactor to the XPS instrument.

To obtain more information about the nature of the Mo and W species, all the XPS spectra were carefully decomposed thanks to previous works [29][30][31][32][33] but also using the appropriate oxide and sulfided references as supported monometallic catalysts for examples. Indeed, several steps are necessary to obtain meticulous decompositions.

Decomposition of Mo 3d spectra

In sulfided molybdenum catalysts, Mo and S coexist. The spectral envelope of Mo3d covers the energy range of 227-238 eV as the chemical oxidation states of Mo vary from 0 to +VI, while that of S2s covers the 224-235 eV range, which corresponds to S chemical states varying from -II to +VI leading to the overlapping of both Mo3d and S2s BE regions. The contribution of S2s must be thus initially ruled out to obtain the true one of Mo3d level. The BE, full width at half maximum (FWHM) and a peak area of S2s contributions were directly deduced from those of the corresponding S2p peaks using the constraints reported in Table 2. Each S2p contribution was thus simulated with two interdependent peaks corresponding to S2p1/2 and S2p3/2 core levels taking into account the constraints in the area, FWHM and position as reported in Table 2. For example, all the constraints concerning S2p and S2s levels were refined thanks to the XPS analysis of the sulfided W12/Al2O3 catalyst.

Each Mo contribution was simulated with a doublet corresponding to Mo3d3/2 and Mo3d5/2 core levels. The spectral characteristics of Mo3d3/2 and Mo3d5/2 peaks being interdependent, each doublet was simulated using constraints in the area, FWHM and BE as well reported in Table 2 (these constraints being deduced from theoretical considerations and/or refined from experimental data).

The values of areas, FWHM and positions of BE of the main S2p3/2, S2s and Mo3d5/2 XPS peaks (A, B, C, D, E, F, G) were calculated by the CASA software to obtain good correlation between the experimental XPS spectra and the corresponding simulated ones while respecting all the constraints which were imposed between these peaks and all other peaks.

Decomposition of W 4f spectra

The decomposition of W4f spectra must be undertaken cautiously, especially when the analyzed solids contain molybdenum. Indeed the W5p3/2 and Mo4p (non splitted level) BE ranges overlap that of W4f level. Therefore, the contributions of these peaks must be also ruled out to obtain the true one of W4f level. The BE, FWHM and areas of Mo4p contributions were directly deduced from those of the corresponding Mo3d3/2 peaks using the constraints reported in Table 3 since their spectral characteristics can be considered as being interdependent. All the constraints linking BE, FWHM and areas of Mo4p and Mo3d3/2 peaks were experimentally deduced thanks to the XPS analysis of the oxidic Mo12/Al2O3 catalyst.

The spectral characteristics of W5p3/2, W4f5/2 and W4f7/2 are also interdependent. So the W4f contributions were simulated with doublets corresponding to W4f5/2 and W4f7/2 core levels. Each doublet was simulated using constraints in the area, FWHM and BE as well reported in Table 3.

W5p3/2 was simulated with one peak with BE, FWHM and area linked to the W4f7/2 corresponding one (Table 3). All the constraints linking W5p3/2, W4f5/2 and W4f7/2 were deduced from experimental data obtained after analysis of oxidic W12/Al2O3 catalyst.

The values of areas, FWHM and BE of the main W4f7/2 XPS peaks (H, I, J) were calculated by the CASA software to obtain good correlation between the experimental XPS spectra and the corresponding simulated ones while respecting all the constraints which were imposed between these peaks and all other peaks.

The relative concentrations of each species Mo VI -O, Mo V -OS, MoS2, W VI -O, W V -OS and WS2 were determined for every sulfided catalyst and were reported in Table 4. For example, the relative amount of WS2 was determined using the following equation:

2 V VI 2 WS 2 WS W -OS W -O [WS ] (%) 100 A A A A = × + + , ( 3
)
where AX represents the peak area of species x.

Examination of the catalytic activities

Catalytic properties of synthesized catalysts were investigated in co-hydrotreating of model feed containing DBT (Aldrich, 1500 ppm of S), 4,6-DMDBT (Aldrich, 300 ppm of S) and naphthalene (Aldrich, 3 wt.%) in toluene as a solvent (separate experiments showed that toluene did not undergo hydrogenation under chosen reaction conditions). Prior to testing, the catalysts were activated by the method described above in Section 2.1. The HDT activity tests were performed in a fixed-bed microreactor at 320 ºC, 3.0 MPa of hydrogen, with a LHSV (liquid hourly space velocity) of 10 h -1 and a 500 NL/L volume ratio of hydrogen to feed. In a typical HDT reaction, 0.6 g sample of the catalyst (0.25 -0.50 mm) was diluted with 0.6 cm 3 of low-surfacearea carborundum (0.2 -0.4 mm) and placed in the center of the reactor (the reactor had an internal diameter of 0.8 cm). The liquid product compositions of the samples collected every 1.0 h were determined using a Crystall-5000 Gas Chromatograph equipped with a 30 m OV-101 column. The reaction products were identified by matching retention times with those of commercially available standards and by GC/MS analysis using a Finnigan Trace DSQ. All catalysts exhibited stable performance, achieving a steady state after 7 -10 h on stream.

The rate constants of the pseudo-first-order reactions of the DBT (4,6-DMDBT) HDS and naphthalene HYD were determined using the following equations: The HDS products from DBT included biphenyl (BP) via the direct desulfurization (DDS) pathway, as well as cyclohexylbenzene (CHB) and dicyclohexyl (DCH) from the HYD pathway.

), 1 ln( DBT DBT x W F k DBT HDS - - = ) 1 ln( 6 , 4 6 , 4 6 , 4 DMDBT DMDBT DMDBT HDS x W F k - - - - - = and ), 1 ln( Naph Naph HYD x W F k - - = (4
Only traces of hydrogenated tetrahydro-and perhydrodibenzothiophenes were observed. The HYD/DDS selectivity was calculated according to the reaction network for DBT HDS (Scheme where CMCHT, C3,3′-DMBCH and C3,3′-DMBP are the concentrations (mol. %) of MCHT, 3,3′-DMBCH and 3,3′-DMBP in the reaction products, respectively.

Results and discussion

Characterization of Mo(W)/Al2O3 catalysts after activation under H2/H2S and their performance in co-HDT of DBT and naphthalene

Sulfidation degree of Mo and W after activation under H2/H2S.

The sulfidation degree of Mo and W in all samples was evaluated by XPS after gas phase activation (Table 4). The sulfidation degree of molybdenum was higher than 80 rel. % in all Mo containing samples and varied less than 10 %. Both catalysts prepared from a mixture of two HPAs had slightly higher sulfidation degree of Mo compared to mixed HPAs based ones. The W sulfidation degree was lower than those obtained for Mo, between 51 and 77%, in agreement with data reported in [22,27,30]. Incorporation of one molybdenum atoms into the structure of HPA had no significant effect on W sulfidation while replacing of three W atoms to Mo ones led to an increase of W content in WS2 phase compared to W/Al2O3 catalyst from 51 to 64 rel. %. Raise of tungsten sulfidation degree with increasing of molybdenum content was also observed for both MoW reference catalysts.

Morphology of the active Mo(W)S2 phase after activation under H2/H2S

Typical HRTEM micrographs of gas sulfided Mo(W)/Al2O3 are presented in Fig. 2. The black, thread-like fringes are the Mo(W)S2 crystallites with 0.65 nm interplanar distances. The average dimension of the Mo(W)S2 active phase are presented in Table 1. W12/Al2O3 catalyst consisted predominantly the slabs with length ~ 3.4 nm while Mo12/Al2O3 had shorter slabs ~ 3.1 nm, in agreement with results reported in [22,34,35] showing that WS2 particles are usually larger than MoS2 ones. Adding one Mo atom to the catalysts with Mo/W=1/11 allowed to slightly decrease the average slab length compared to W12/Al2O3 (from 3.4 to 3.2 nm), further increase of molybdenum content to Mo/W=3/9 resulted to decrease in the average length, from 3.4 to 2.9 nm.

The average stacking number for all bimetallic catalysts was higher than that observed for monometallic references. Moreover, the stacking of catalysts prepared from a mixture of HPAs seems to be higher compared to their mixed HPAs based counterparts. These changes can be explained by altering sulfidation rates of Mo and W leading to incorporation of Mo atoms into WS2 slabs.

However, HRTEM characterization gives general morphological information of the sulfided phase but does not allow to distinguish between MoS2 or WS2 slabs. Complementary analysis was thus performed by HAADF, where the Z contrast between Mo and W atoms is favorable to discriminate them. Typical HAADF images of gas sulfided Mo(W)/Al2O3 catalysts are presented in Fig. 3 and reveal the 2D morphology of the sulfided slabs. All images of W12/Al2O3 sample present a very homogeneous intensity of tungsten atoms in the slabs, as illustrated in Fig. 3 (a).

On sulfided mixed Mo3W9/Al2O3 catalysts, differences in contrast between atoms in the slabs are observed, which can be attributed to the difference in Z between Mo and W (Fig. 3 (c)). Differences in thickness of the support cannot explain these differences as they are never observed on the pure WS2 supported catalyst. This is confirmed by the intensity profiles in a row of atoms, where the ratio of intensity is equal to the ratio of the Z 1.7 as expected for this technique (Fig. 3 (d)). It is clearly seen that using mixed MoW HPA contributed to the formation of mixed MonW12-nS2 particles with core-shell structure, where Mo atoms are located predominantly together in the core of the WS2 slab. On the contrary, HAADF images of Mo3+W9/Al2O3 catalyst prepared from two separate HPAs show a large majority of monometallic MoS2 and WS2 slabs with only few bimetallic particles (Fig. 3 (b)).

Catalytic activities in co-HDT of DBT and naphthalene after activation under H2/H2S

The catalytic activities of the MonW12-n/Al2O3 catalysts sulfided under H2/H2S in HDS of DBT and HYD of naphthalene are presented in

Comparison of characterization and performance of Mo(W)/Al2O3 catalysts after activation under gas and liquid phase

The activation of the Mo(W)/Al2O3 catalysts was performed by two procedures: GS in present work and LS as it was previously reported [22]. The sulfidation behavior and catalytic properties of the (Mo)W catalysts were different depending on the sulfiding agent. It should be noted that the sulfidation procedures using the different sulfidation agents were not performed under the same conditions. LS was performed by heating in hydrogen flow at 3.5 MPa with a mixture of DMDS in decane in two steps (first at 240 ºC for 10 h and second at 340 ºC for 6 h).

GS activation was carried out in one step under a flow of H2S/H2 at atmospheric pressure and heating to 400 ºC over a holding period of 2 h. However, the HDT activity tests were performed using the same model feed (DBT and naphthalene) in identical conditions in both cases. Therefore, correct comparison of sulfidation methods (gas versus liquid phase) and its effect on the state of active phase particles determined by XPS and HRTEM as well as the morphology of mixed Mo(W)S2 species evidenced by HAADF and the catalytic properties is possible.

Comparison of the morphology of the active Mo(W)S2 phase

If we compare with the results obtained by LS [22] (Fig. 4), it can be seen that GS resulted in the formation of shorter and mainly slightly higher stacked slabs, thus after GS the average length of particles in all samples in average was 3.1 nm against 4.8 nm for LS. The most significant changes were detected for the catalysts based on a mixture of two HPAs.

The results of HAADF characterization of the liquid phase sulfided Mo(W)/Al2O3 catalysts were shown in [22]. One can observe that the use of mixed SiMo3W9 HPA as an initial precursor led to the formation of mixed MonW12-nS2 particles with Mo atoms inside WS2 slabs in both cases.

However, GS was more preferable to the formation of the particles with core-shell structure, while LS one led to more randomly distribution of molybdenum inside the WS2.

Comparison of the sulfidation rate of Mo(W)S2 phase

The effect of sulfidation method on metal sulfidation degree as determined by XPS was also evaluated. The activation procedure has little effect on the sulfidation rate of monometallic and bimetallic references catalysts with variation below 5 %. A larger difference in metal sulfidation degree (15 % for Mo and 18% for W in favor of liquid phase method) was observed for SiMonW12n HPAs based catalysts. This can be attributed to the formation of the mixed MoWS2 particles with different structure, more strongly affected by the sulfidation agent resulting in different temperatures of H2S availability. In the case of gas sulfidation, the sulfiding agent H2S is present from room temperature and may lead to the formation of partly sulfided intermediate at lower temperature than in the case of DMDS, which decomposition occurs at ~150 °C. We can imagine that these intermediates growth is favored under H2S and leads to larger Mo entities than in the case of LS. In the case of GS the Mo atoms could start sulfiding at room temperature with formation of MoS2 slabs, when tungsten disulfide appears at higher temperature and could then cover the edges of MoS2 particle resulting in core-shell structure, in agreement with HAADF results. LS led to randomly distribution of molybdenum inside the WS2 particle. In this case, Mo starts sulfiding at temperature of DMDS decomposition that is close to the startup sulfidation temperature of W that allows to form mixed MoWS2 sulfide particles, where molybdenum atoms are more randomly distributed inside the slabs [22].

Comparison of activity in co-HDT of DBT and naphthalene

The catalytic activity of MoW/Al2O3 catalysts activated by GS and LS was examined in the model reaction of DBT HDS and naphthalene HYD in order to evaluate the influence of sulfidation method on their catalytic properties. The differences in catalytic properties of the MoW/Al2O3 catalysts with respect to the sulfidation procedures are shown in Fig. 5. H2S activation of all studied samples led to higher HDS (Fig. 5 (a)) and HYD (Fig. 5 (b)) activity than the DMDS activation.

Increasing of HDS activity when H2S was used for sulfidation was reported by Gochi et al. for bulk MoWNi [24] for CoMo/Al2O3 catalysts [23,25]. Conflicting results have been reported in the literature [26] regarding unpromoted Mo/Al2O3.

In our case better catalytic activity of GS catalysts can be related to the shorter size of formed Mo(W)S2 species compared to LS ones and, therefore, higher active sites content. However, a single size effect cannot explain all obtained catalytic properties and other factors should be considered. For example, both monometallic catalysts differed in ~ 1.5 nm of Mo(W)S2 slab average length after GS (Table 1) and LS activation [22]. At the same time, its delta in catalytic activity after GS and LS sulfidation differed significantly (Fig. 5 (c)). The greatest effect of the type of sulfidation was observed for monometallic W catalyst, GS activation provides increasing DBT HDS by 9 times and naphthalene HYD by 7 times compared to the samples activated by LS.

On contrary, HDS activity of molybdenum monometallic and bimetallic catalysts was increased more than 2 times after H2S activation compared to DMDS sulfidation, while HYD activity increased ~ 2 times. However, the trend in distribution of the catalytic properties was kept whatever the activation protocol. In both cases, the catalysts prepared from the mixed HPA exhibited significantly higher activity in the two reactions than their counterparts prepared from a mixture of monometallic HPAs (Fig. 5 (c)). Moreover, Mo3W9/Al2O3, with only 3 atoms of Mo for 9 of W, showed as good performance in HDS as Mo12/Al2O3 catalyst with the highest HYD properties of the series. The high efficiency of mixed HPAs based catalysts compared to Mo+W ones can be attributed to the presence of mixed MonW12-nS2 active phase evidenced by HAADF being more favorable for HDS as well as HYD catalytic activity.

The selectivity of prepared catalysts toward the HYD pathway of DBT HDS was also estimated (Fig. 6). It was found that HYD pathway is more preferred for mixed HPAs based catalysts compared to their counterparts regardless of the type of sulfidation. Improved HYD properties of these catalysts can be attributed to the appearance of new mixed MonW12-nS2 active sites after sulfidation of mixed molecular precursors. However, all catalysts activated in flow H2S/H2 exhibit significantly higher SHYD/DDS value, in agreement with the observation that DMDS activation enhances C-S hydrogenolysis [24,36]. It is interesting to note that the increment of the rate constant for the catalysts sulfided by gas mixture H2S/H2 linearly depended on the increase of rate constants in naphthalene HYD (Fig. 7). It means that higher HDS activity is rather related to enhanced hydrogenation properties of the catalysts.

Catalytic activities in co-HDT of DBT, 4,6-DMDBT and naphthalene

Taken into account the beneficial effect of gas phase sulfidation on modifying the efficiency of the active sites this activation procedure was chosen for further investigation. The catalytic behavior of the synthesized (Mo)W/Al2O3 catalysts activated by GS was evaluated in simultaneous HDS of DBT and 4,6-DMDBT and HYD of naphthalene. The conversion of reactants is shown in Table 6. Rate constants values depending on the reaction type increased in the order 4,6-DMDBT HDS < DBT HDS < naphthalene HYD. We have never observed toluene undergoing hydrogenation under chosen reaction conditions.

Conversion of naphthalene varied from 16.2 to 34.6%. Under chosen conditions, naphthalene was transformed only into decaline over all tested catalysts. Addition of Mo to the composition of the catalysts prepared from a mixture of monometallic HPAs had no significant effect on naphthalene HYD, compared to W12/Al2O3. On the contrary, incorporation of one Mo atom in case of Mo1W11/Al2O3 catalyst allowed to increase rate constants kHYD from 66.7×10 5 mol h -1 g -1 to 92.2×10 5 mol h -1 g -1 , when the further increase in molybdenum content for Mo3W9/Al2O3 led to reach kHYD=128.8 ×10 5 mol h -1 g -1 , that almost twice higher than for W12/Al2O3 and 1.4 times more than for Mo12/Al2O3. As consequence, both mixed HPAs based samples demonstrated higher HYD activity than their analogs.

It can be seen that DBT conversion over (Mo)W/Al2O3 catalysts changed from 14.3 to 36.6 %, and for 4,6-DMDBT from 22.7 to 64.2 %. As in the case of naphthalene HYD, the use of a mixture of HPAs for catalysts preparation did not give any beneficial effect in HDS of DBT as well 4,6-DMDBT. While substitution of one tungsten atom to molybdenum into SiW12 HPA led to increase HDS activity at least 1.6 times compared to W12/Al2O3. The use of SiMo3W9 HPA resulted in the increase of kHDS DBT from 2.7×10 5 mol h -1 g -1 to 27.7×10 5 mol h -1 g -1 and kHDS 4,6- DMDBT from 4.0×10 5 mol h -1 g -1 to 12.6×10 5 mol h -1 g -1 . At the same time, Mo3W9/Al2O3 had demonstrated significantly better activity in all evaluated reactions compared to Mo12/Al2O3. As previously, both mixed HPAs based catalysts had higher HDS catalytic activity than their counterparts with the same Mo/W ratio.

The changes in the size and stacking number of active phase particles as well as in sulfidation degree in bimetallic catalysts cannot explain the changes in catalytic properties. It can be concluded that the MoW nanoscale proximity in the structure of mixed HPAs resulting in the formation of mixed MonW12-nS2 active phase particles with core-shell structure, is at the origin of higher catalytic activity of the mixed HPAs based catalysts.

Cyclic sulfur compounds as DBT and 4,6-DMDBT react through two pathways: DDS and HYD during HDS reactions. The selectivity ratios SHYD/DDS in HDS reactions of all catalysts were calculated and shown in Table 6. All prepared catalysts had high selectivity in respect of hydrogenation pathway of HDS. Nevertheless, Mo12/Al2O3 as it was expected, demonstrated the lowest SHYD/DDS in HDS of both DBT and 4,6-DMDBT. Fig. 8 shows a dependence of 4,6-DMDBT conversion and corresponding selectivity ratios on the nature of starting precursor. The mixed HPAs based catalysts presented higher selectivity ratios than those obtained for their bimetallic counterparts. In addition, the Mo3W9/Al2O3 catalyst had the highest 4,6-DMDBT HYD/DDS selectivity ratio. This observation supports the formation of mixed MoWS2 active sites developing strong hydrogenation properties required for the treatment of refractory sulfur compounds.

In addition, for a better understanding of the beneficial role of mixed MoW HPAs the rate constants of HDS and HYD reactions over bimetallic catalysts were calculated by the additive way using the values for monometallic catalysts Mo12/Al2O3 and W12/Al2O3 and necessary Mo/W proportions (Table 6). Thus, bimetallic catalysts prepared by using mixed SiMonW12-n HPAs had higher experimental values of the rate constant in all studied reactions than predicted ones. In contrast, the experimental data for the samples prepared by using a mixture of two monometallic HPAs resulted from the linear combination of the two monometallic references or even lower in case of Mo1+W11/Al2O3.

Relative HDS activity (normalized on HDS rate constants on Mo12/Al2O3) was also calculated for DBT and 4,6-DMDBT HDS (Fig. 9). Relative HDS activity of Mo3W9/Al2O3 catalyst was close to monometallic Mo12/Al2O3 one in DBT HDS. Other Mo-W catalysts had lower activity compared to Mo12/Al2O3 reference. In contrast, in 4,6-DMDBT reaction, all Mo-W catalysts have higher relative HDS activity or similar (Mo1+W11/Al2O3) than monometallic ones (Mo12/Al2O3 or W12/Al2O3). It is clearly seen that Mo-W synergetic effect is much higher in 4,6-DMDBT HDS compared to DBT HDS performance. This effect is related with different mechanisms between HDS of DBT and highly refractory 4,6-DMDBT due to the steric hindrance of the methyl groups at the 4-and 6 positions.

Conclusions

In summary, the main results of the work are as follows:

1. It was found that with the increase of Mo content in all bimetallic MoW/Al2O3 catalysts synthesized by using mixed SiMo1W11 and SiMo3W9 HPAs, the increase of W sulfidation degree occurs compared to the monometallic W12/Al2O3 catalyst. In addition, this Mo incorporation into the bimetallic catalysts resulted in a decrease of the average slab length of (Mo)WS2 species after gas phase sulfidation.

2. Using HAADF it was demonstrated that gas phase sulfidation of mixed molecular precursor led to formation of a core-shell structure, where Mo was mostly located in the core and W in the shell. In contrast, Mo3+W9/Al2O3 catalyst prepared from two SiMo12 and SiW12 HPAs (with Mo/W ratio in the catalyst equal to 3/9) show a large majority of monometallic MoS2 and WS2 slabs with only few bimetallic particles.

3. Mo(W)/Al2O3 catalysts, which were sulfided by GS, demonstrated higher activity in DBT HDS as well as naphthalene HYD compared to the analogs activated by LS. GS led to formation a shorter Mo(W)S2 crystallites with core-shell structure having significant HYD activity as evidenced by higher DBT HDS selectivity ratio SHYD/DDS and naphthalene HYD than the catalysts, which have been undergone LS, having Mo(W)S2 species with randomly distribution of molybdenum inside the WS2. Captions for Tables Table 1. Composition of prepared (Mo)W/Al2O3 catalysts, morphological characteristics of the (Mo)WS2 active phase species obtained via GS and calculated from TEM micrographs.

  photoelectron spectra, narrow spectral regions (Al 2p, S 2p, Mo 3d, W 4f, C 1s and O 1s) were

F

  pseudo-first-order reaction constants for the DBT, 4,6-DMDBT HDS, and naphthalene HYD (mol g -1 h -1 ), respectively, conversions (%) of DBT, 4,6-DMDBT and naphthalene, respectively, are the reactant flow in moles (mol h -1 ) and W is the weight of the catalyst (g).

  CCHB, CBCH and CBP are the concentrations (mol. %) of CHB, DCH and BP in the reaction products, respectively. The products of the HDS of 4,6-DMDBT were 3,3′-dimethylbiphenyl (3,3′-DMBP) from DDS pathway and were 1-methyl-3-(2-methylphenyl) cyclohexane (which we will refer to as methylcyclohexyltoluene (MCHT)) and 3,3′-dimethylbicyclohexyl (3,3′-DMBCH) from a hydrogenation pathway (HYD). Only traces of hydrogenated species 4,6-tetrahydro-and perhydrodibenzothiophenes were observed. The HYD/DDS selectivity was calculated according to the reaction network for DBT HDS (Scheme 2):

4 .Figure 1 .

 41 Figure 1. The examples of decomposition od W 4f (a), Mo 3d (b) and S 2p (c) photoelectron

Figure 2 .

 2 Figure 2. HRTEM micrographs of gas sulfided Mo(W)/Al2O3 catalysts.

Figure 3 .

 3 Figure 3. HAADF images of sulfided W12/Al2O3 (a), Mo3+W9/Al2O3 (b), Mo3W9/Al2O3 (c)

Figure 4 .

 4 Figure 4. Average length (a) and average stacking number (b) of the Mo(W)S2 crystallites in

Figure 5 .

 5 Figure 5. Rate constants of DBT HDS (a) and naphthalene HYD (b) over Mo(W)/Al2O3

Figure 6 .

 6 Figure 6. Changing the selectivity ratio SHYD/DDS in DBT HDS depending on of the sulfidation

Figure 7 .

 7 Figure 7. Dependence of DBT HDS rate constants ratio of the catalysts after gas (GS) and

Figure 8 .

 8 Figure 8. Relationship between conversion of 4,6-DMDBT and the selectivity ratio SHYD/DDS

Figure 9 .

 9 Figure 9. Relative HDS activity of Mo(W)/Al2O3 catalysts in DBT and 4,6-DMDBT HDS

15 a

 15 The FWHM constraints (A, E, F, G) regarding S2p3/2 and Mo3d5/2 are obtained from experimental data using the FWHM of Al2p as reference.b The FWHM constraint (C) regarding S2s is obtained from experimental data using the FWHM of S2p3/2 as reference. c e.g. "A = 162.3 ; 161.3" means that the value of BE can only evolve during the fit between 161.3 and 162.3 eV.

Fig. 1 .

 1 Fig. 1. The examples of decomposition od W 4f (a), Mo 3d (b) and S 2p (c) photoelectron

Fig. 2 .Fig. 3 .

 23 Fig. 2. HRTEM micrographs of gas sulfided Mo(W)/Al2O3 catalysts.

Fig. 4 .

 4 Fig. 4. Average length (a) and average stacking number (b) of the Mo(W)S2 crystallites in gas

Fig. 5 .

 5 Fig. 5. Rate constants of DBT HDS (a) and naphthalene HYD (b) over Mo(W)/Al2O3 catalysts

1 )kFig. 6 .Fig. 7 .Fig. 8 . 3 Fig. 9 .

 167839 Fig. 6. Changing the selectivity ratio SHYD/DDS in DBT HDS depending on of the sulfidation

9 Scheme 1 .Scheme 2 .

 912 Scheme 1.Reaction network of the HDS of DBT.

Table 5 .

 5 The reactants conversions varied in a wide range, from 20.8 to 52.9 % for DBT HDS and from 23.6 to 47.8 % for naphthalene HYD over all prepared catalysts. The W12/Al2O3 sample demonstrated the lowest activities in DBT HDS as well

	as in naphthalene HYD. Monometallic Mo3W9/Al2O3 and Mo12/Al2O3 catalysts achieved the
	highest conversion values in DBT HDS and naphthalene HYD. Both samples Mo1+W11/Al2O3 and
	Mo3+W9/Al2O3 prepared from separate monometallic HPA demonstrated a much lower activity
	than their bimetallic Mo1W11/Al2O3 and Mo3W9/Al2O3 analogs synthesized from mixed HPAs with
	the same metal contents.

Table 2

 2

	.	XPS parameters used for the decomposition of S2p and Mo3d spectra of sulfided
		MoW/Al2O3 catalysts.
	Table 3.	XPS parameters used for the decomposition of W4f spectra of sulfided MoW/Al2O3
		catalysts.
	Table 4.	Relative metal fractions measured by XPS for molybdenum and tungsten species
		present at the surface of Mo(W)/Al2O3 catalysts after gas phase (GS) and liquid phase
		(LS) sulfidation.

Table 5 .

 5 Catalytic properties of prepared (Mo)W/Al2O3 catalysts sulfided in gas phase in HDT of a mixture of DBT and naphthalene.

	Table 6.	Catalytic properties of prepared (Mo)W/Al2O3 catalysts sulfided in gas phase in HDT
		of a mixture of DBT, naphthalene and 4,6-DMDBT.

Table 3

 3 XPS parameters used for the decomposition of W4f spectra of sulfided MoW/Al2O3 catalysts.

			Constraint	Constraint	Constraint
	Species	Peak	Area	FWHM	BE (eV)
	W IV	W 4f7/2 (H)	H	a H= FWHMAl2p × 0.76 (±0.1 eV)	b H = 32.6 ; 32
	(WS2)	W4f5/2	H × 0.79	H × 1.05	H + 2.15
	W V	W 4f7/2 (I)	I	a I= FWHMAl2p × 0.92 (±0.1 eV)	I = 34 ; 33.3
	(W V -OS)	W4f5/2	I × 0.79	I × 1.05	I + 2.15
	W VI	W 4f7/2 (J)	J	a J= FWHMAl2p × 0.97 (±0.1 eV)	J = 36.5 ; 35.5
	(W VI -O)	W4f5/2	J × 0.79	J × 1.05	J + 2.15
	W IV
		W 5p3/2 (K)	H × 0.082	H × 1.37	H + 5.85
	(WS2)

Table 4

 4 Relative metal fractions measured by XPS for molybdenum and tungsten species present at the surface of Mo(W)/Al2O3 catalysts after gas phase (GS) and liquid phase (LS) sulfidation.

			Mo fraction (rel. %)		W fraction (rel. %)
	Catalyst
		MoS2 Mo V -OS	Mo VI -O	WS2	W V -OS	W VI -O
	Mo12/Al2O3 GS	81	13	6	-	-	-
	W12/Al2O3 GS	-	-	-	51	16	33
	Mo1W11/Al2O3 GS	85	13	2	51	7	42
	Mo3W9/Al2O3 GS	81	14	5	64	18	18
	Mo1+W11/Al2O3 GS	89	2	9	57	8	35
	Mo3+W9/Al2O3 GS	90	8	2	77	11	12
	Mo12/Al2O3 LS	80	12	8	-	-	-
	W12/Al2O3 LS	-	-	-	56	12	32
	Mo1W11/Al2O3 LS	100	-	-	70	11	19
	Mo3W9/Al2O3 LS	96	4	-	82	5	13
	Mo1+W11/Al2O3 LS	85	13	2	76	5	19
	Mo3+W9/Al2O3 LS	88	7	5	74	8	18

Table 5

 5 Catalytic properties of prepared (Mo)W/Al2O3 catalysts sulfided in gas phase in HDT of a mixture of DBT and naphthalene.

					Rate constants
		Conversion (%)	Selectivity
					(× 10 5 mol h -1 g -1 )
	Catalyst			ratio
		DBT	Naphthalene
				SHYD/DDS	kHDS	kHYD
		HDS	HYD
	Mo12/Al2O3	52.3	40.5	1.7	45.1	157.3
	W12/Al2O3	22.8	23.6	2.3	15.7	81.8
	Mo1W11/Al2O3	49.7	42.7	2.6	41.8	168.6
	Mo3W9/Al2O3	52.9	47.8	3.2	45.9	196.8
	Mo1+W11/Al2O3	20.8	24.4	2.2	14.2	85.0
	Mo3+W9/Al2O3	32.8	27.3	1.8	24.1	96.6

Acknowledgments

The research was financial supported by the Ministry of Education and Science of the Russian Federation, project No. 14.586.21.0054 (unique identifier of project RFMEFI58617X0054) and The Ministry of Foreign Affairs and International Development (France) and the Ministry of National Education, Higher Education and Research (France) in framework of PHC Kolmogorov Programme 2017-2019. M. Nikulshina thanks French Ambassy in Russia for the Vernadsky fellowship and Haldor Topsøe Company for the grant to perform her PhD thesis. Chevreul Institute (FR 2638), Ministère de l'Enseignement Supérieur et de la Recherche, Région Nord -Pas de Calais and FEDER are acknowledged for supporting and funding partially this work.


C El Mertahi

N Grandmaison

C Dupont

R Jellali

D Brancherie
email: delphine.brancherie@utc.fr

A.-V Salsac
email: a.salsac@utc.fr

Microrheometric study

come

Introduction

Capsules, which are liquid droplets enclosed in a thin elastic membrane, are present in nature (red blood cells, phospholipid vesicles) and in various industrial applications (biotechnology, pharmacology, cosmetics...). They are used to protect and transport active ingredients by isolating them from the external fluid suspension.

When placed in an external flow at high shear rates, capsules undergo deformation and damage. Rupture occurs when the capsule membrane loses its rigidity at some locations, making it incapable to resist any longer. Depending on the applications, capsule damage is to be prevented to preserve the encapsulated substance or on the contrary provoked to initiate the rupture and then the release of the inner fluid. It is thus necessary to understand the mechanisms responsible for damage and the parameters that control rupture initiation.

Numerous numerical studies have been conducted on the deformation of capsules [START_REF] Walter | Coupling of finite element and boundary integral methods for a capsule in a stokes flow[END_REF][START_REF] Luo | Deformation of spherical compound capsules in simple shear flow[END_REF] by implementing a fluid-structure interaction model accounting for the membrane large deformations induced on a capsule subjected to an external flow. Recently, a damage model has been developed by Grandmaison et al [START_REF] Grandmaison | Modelling of damage of a liquid-core microcapsule in simple shear flow until rupture[END_REF] that accounts for the initiation and growth of microdiscontinuities and subsequently the local initiation of rupture. On the experimental side, very few studies have been carried out on the rupture of capsules. Chang & Olbricht [START_REF] Chang | Experimental studies of the deformation and breakup of a synthetic capsule in steady and unsteady simple shear flow[END_REF] showed the capsule burst in a simple shear flow at high shear by membrane fatigue. In their study, the break up was initiated from one of the major axis tips of the deformed capsule and propagated in the shear plane. Rehage & Koleva [START_REF] Koleva | Deformation and orientation dynamics of polysiloxane microcapsules in linear shear flow[END_REF] also observed the rupture of thin polysiloxane microcapsule under simple shear flow. The rupture occured in the central region, close to the tips of the flow vorticity axis (zones of maximum tension) at small deformations. Rupture was also observed in hyperbolic flow by Xie & al [START_REF] Xie | Interfacial rheological properties of self-assembling biopolymer microcapsules[END_REF] using Chitosan/PFacidYN thin membrane. When the hydrodynamic stress exceeds the limit for breakup, the microcapsule stretches up leading to the formation of two lobs connected by a thin filament which is then destabilized in droplets.

None of the experimental studies carried out have investigated capsule damage phenoma. However, this is a crucial point in order to control rupture and build a reference set to validate the numerical damage models. To fill this gap, the objective of the present work is dedicated to a rheometric study of the capsule damage and rupture based on an identification of the membrane mechanical properties. A decrease in the capsule surface shear modulus will inform on its damage and upcoming rupture. After having detailed the experimental setup and methods in Section 2, we present the results of the parametric identification of capsule damage in Section 3 and a statistical study of the rupture is presented in Section 4.

Experimental setup and methods

Capsule fabrication

Microcapsules are prepared by means of interfacial cross-linking of an emulsion of 1 ml of an aqueous solution, consisting of 10 % (w/v) ovalbumin (A5253-250G, Sigma) dissolved in phosphate buffer (P3619-1GA, pH=7.4, Sigma), mixed with 10 ml of vegetable oil (ISIO 4, Lesieur) using a laboratory vortex (Heidolph TopMix 94323). Then, 10 ml of vegetable oil containing 2.5 % (w/v) terephthaloyl chloride (120871-250G, Sigma) is added to the emulsion. The interfacial reticulation time is 15 min. Once prepared, capsules are rinsed before use and suspended in glycerol at a concentration of 2 %. Owing to concentration differences leading to osmotic effects, the capsules are pre-stressed with an inflation ratio α = a a o -1 = 53 %, where a o is the reference capsule radius and a the pre-stressed capsule radius.

Microrheometry

Our study of capsule motion is carried out in a Couette flow using two counter-rotating concentric cylinders as illustrated in figure 1 and between which we introduce a volume of 12 ml of capsules suspended in glycerol. The distance between the two cylinders is about 1 mm. After the capsules are placed in the region between the cylinders and the flow is started for a chosen shear rate, their motion and deformation are recorded by a video camera (model LM165M, Lumenera) mounted below the outer cylinder to provide a bottom view of the capsules. The capsule image is inverted by passing through a 45°mirror (figure 1). To enhance the resolution of the recorded images, a spot light (KL 1600 LED, SCHOTT) is used.

Identification of the membrane elasticity

To identify the surface shear modulus G s of the capsule membrane, an experimentalnumerical strategy is used. From the experience, we know the values of the shear rate γ, the viscosity µ of the capsule-in-glycerol suspension and the contour of a deformed capsule observed during the shear flow which is obtained manually using ImageJ. A least squares fit of the contour with an ellipse provides the values of the semi-axes L 1 and L 2 and then the Taylor parameter D 12 = L 1 ´L2 L 1 +L 2 . From previous numerical simulations of capsule deformation [START_REF] Walter | Coupling of finite element and boundary integral methods for a capsule in a stokes flow[END_REF] we exploit the plot of variation of D 12 with the capillary number (Ca = µγa G s ) D 12 = f (Ca) and the plot L 3 /a = g (D 12 ), where L 3 is the third semi-axis of the deformed capsule [START_REF] Wang | A microfluidic methodology to identify the mechanical properties of capsules : comparison with a microrheometric approach[END_REF]. From D 12 = f (Ca) we obtain Ca. L 3 /a is obtained from L 3 /a = g (D 12 ). The capsule radius a is obtained applying the volume conservation of the capsule : a = 3 ? L 1 L 2 L 3 . Finally the surface shear modulus G s is obtained through the expression G s = µ γa Ca .

Probability of rupture

The capsule distribution in glycerol is considered to be homogeneous in this study.

To identify the number of ruptured capsules, we quantify their number in a volume of 10 µl of the capsule-in-glycerol suspension, we shear the mixture using the microrheometer and we quantify the number of sheared capsules. We assume that the disappeared capsules are ruptured during the flow. The results of this study are presented in section 4.

Capsule damage

This section aims at presenting the results obtained in terms of the evaluation of the surface shear modulus G s . We study its dependence on the size of the capsules and its evolution as a function of the exposure time to shear. To this end, we evaluate G s and the capsule radius following the method presented in 2.3 for different exposure times t E . We present in Figure 2 the evolution of G s as a function of the capsules radius for different exposure times. We show that G s increases with the capsule radius and adjusts to a sigmoïd function. When the exposure time to shear t E exceeds 4 minutes, we observe a progressive decrease of the surface shear modulus for capsules of radius larger than 60 µm. In figure 3, we present specifically the evolution of G s as a function of the exposure time for capsules of specific sizes. We attribute this decrease in surface shear modulus to the degradation of the mechanical properties of the membrane.

Capsule rupture

To obtain the percentage of ruptured capsules, we quantify their number before and after exposure to shear suspending them in simple shear flow for different exposure times t E . In this study, we only present the results obtained for t E =10 min. The capsules no longer present at time t E are considered broken. In figures 4 and 5, we present the results obtained for capsules sheared at a rate of 300 s ´1 for 10 min and a viscosity of 0.95 Pa.s. As shown in figure 5, the percentage of disappeared capsules increases with their radius until their total disappearance for capsules having radius larger than 60 µm. This observation provides information on rupture kinetics. The capillary number of broken capsules (ratio of the viscous to the elastic forces), evaluated using equation ( 2) ranges from 0.12 to 0.2.

Conclusion

The study of damage is crucial to control and prevent capsule rupture. To be predictive, the damage models used in the simulations [START_REF] Grandmaison | Modelling of damage of a liquid-core microcapsule in simple shear flow until rupture[END_REF] must be identified. To this aim, we propose a parametric method based on the membrane mechanical properties evolution. Such an identification is a crucial point for the evaluation of the parameters of the damage models. The second point explored in this work is based on a statistical study of rupture kinetics depending on capsule radius.

FIGURE 1 -

 1 FIGURE 1 -Schematic of the Couette apparatus.

FIGURE 2 -

 2 FIGURE 2 -G s evolution as a function of the capsules radius for different exposure times t E

FIGURE 3 -

 3 FIGURE 3 -G s evolution as a function of the exposure time to shear for three sizes of capsules

FIGURE 4 -

 4 FIGURE 4 -Number of capsules in a volume of 10 µl.

FIGURE 5 -

 5 FIGURE 5 -Pourcentage of ruptured capsules as a function of their radius.


Benoît Feildel

Part 4. Coworker Mobility Chapter 11. Daily mobility patterns of coworkers in non-metropolitan areas, a French case study

Keywords: Mobility, coworking, metropolitan area, peri-urban, rural, GPS

The recent surge in coworking spaces outside urban centres calls us to question the assumed positive externalities of these places and especially their contribution to the transition towards more virtuous mobility practices. Daily mobility in low-density areas, heavily dependent on cars, is in fact a major issue in the ecological and social transition. The interest generated by coworking spaces outside of metropolitan areas, especially for public authorities, therefore entails more thorough documentation concerning their effects on mobility. By using both GPS tracking and indepth interviews, we have been able to develop a typology of the daily mobility patterns of coworkers on the margin of metropolitan areas and therefore demonstrate the importance of rationales that integrate the territorial dimension and the embedding of social relations on the structuring of mobility.

Introduction

Coworking spaces outside metropolitan areas, in France and more broadly on a worldwide scale [START_REF] Akhavan | The Rise of Coworking Spaces in Peripheral and Rural Areas in Italy[END_REF][START_REF] Knapp | Coworking Spaces in Small Cities and Rural Areas: A Qualitative Study from an Operator and User Perspective[END_REF][START_REF] Tomaz | Rural Coworking Spaces in the Covid-19 Era. A Window of Opportunity?[END_REF][START_REF] Capdevila | Spatial Processes of Translation and How Coworking Diffused from Urban to Rural Environments: The Case of Cowocat in Catalonia, Spain[END_REF], have experienced constant growth for the past ten years [START_REF] Lévy-Waitz | Mission Coworking. Faire Ensemble Pour Mieux Vivre Ensemble[END_REF]2021), with a significant acceleration since the COVID-19 pandemic [START_REF] Howell | Coworking Spaces: An Overview and Research Agenda[END_REF]Mariotti, Di Marino, and Bednář, 2023;[START_REF] Mariotti | The Preferred Location of Coworking Spaces in Italy: An Empirical Investigation in Urban and Peripheral Areas[END_REF] and its effects on both the organisation of work [START_REF] Tomaz | Rural Coworking Spaces in the Covid-19 Era. A Window of Opportunity?[END_REF] and the transformation of people's relationship with space [START_REF] Choplin | Saint-Patelin : confinement dans les confins[END_REF][START_REF] Leducq | Les espaces de coworking : des instruments de résilience territoriale pour l'après-Covid ?[END_REF]. This heightened interest in coworking spaces [START_REF] Spreitzer | Why People Thrive in Coworking Spaces[END_REF][START_REF] Krauss | Tiers-lieux. Travailler et entreprendre sur les territoires : espaces de coworking, fablabs, hacklabs[END_REF], especially those located on the periphery of major urban centres, calls us to question the assumed positive externalities of these places in France, which are widely acclaimed by public authorities (Lévy-Waitz 2021) as well as their contribution to social, economic and ecological transitions in a territorial system whose focus has shifted to low-density areas. Daily mobility in the French peripheral areas, lacking cohesion with urban agglomerations [START_REF] Cailly | Périurbain[END_REF], heavily dependent on cars and whose populations therefore suffer rising energy prices more than elsewhere [START_REF] Dodier | Innover dans la mobilité : une nécessité pour rendre les campagnes périurbaines habitables ?[END_REF][START_REF] Jouffe | A "Triple Bind": Local Attitudes to the Energy Crisis. A Theoretical Discussion on the Situation of Low-Income Households in French Periurban Neighbourhoods[END_REF], is a major issue in the ecological and social transition [START_REF] Huyghe | Quelles organisations de la mobilité plus durables et moins dépendantes de la voiture dans les espaces ruraux à faible densité ? L'exemple du Parc naturel régional Loire-Anjou-Touraine[END_REF]. Catering for the new aspirations of a population that wishes to develop on the periphery, both geographically and socially, by moving away from urban centres and seeking a new balance between professional and family life [START_REF] Krauss | Tiers-lieux. Travailler et entreprendre sur les territoires : espaces de coworking, fablabs, hacklabs[END_REF], new collaborative work spaces, also known as coworking spaces or third places [START_REF] Flipo | Les dimensions sociales et spatiales du coworking : un état de l'art[END_REF], have been the focus of attention for several years from public authorities and scholars. The interest in these places, when they are mainly envisaged as new work places, originates from their assumed ability to drive a movement of economic revitalisation [START_REF] Vogl | A Systematic Literature Review of the Effects of Coworking Spaces on the Socio-Cultural and Economic Conditions in Peripheral and Rural Areas[END_REF] in sectors long sought-after by populations seeking a rural ideal but suffering from dependence on urban centres. In this dynamic of relocating economic activities in rural and suburban areas, which still has some untapped potential today, the French public authorities see a possible solution for one of the main difficulties of these low-density areas, namely, the daily mobility of their populations which is based essentially on owning and being dependent on a personal vehicle [START_REF] Huyghe | Quelles organisations de la mobilité plus durables et moins dépendantes de la voiture dans les espaces ruraux à faible densité ? L'exemple du Parc naturel régional Loire-Anjou-Touraine[END_REF]. "The engagement of a community and its local, deep-rooted collective action" (Lévy-Waitz 2021, 3) which are meant to foster these new coworking spaces, are seen by decision makers as a motor for more sustainable mobility especially by reducing commuting to and from urban centres [START_REF] Lejoux | Coworking, a Way to Achieve Sustainable Mobility? Designing an Interdisciplinary Research Project[END_REF]. For scholars however, the effects of coworking spaces on structuring the daily mobility of their users, and their participation in the overall reduction of mobility is not so obvious. These issues require closer examination of the daily mobility of coworkers in non-metropolitan areas. This is what we propose as part of this contribution, with a focus on a French case study.

To do this, we will present the results of a research conducted between 2018 and 202 21 . Based on two complementary methodology tools, we were able to document coworker's daily mobility. Firstly, we conducted a quantitative survey using an online questionnaire among users (n=226) of a large number of coworking spaces in France and, secondly, we conducted a mainly qualitative survey using GPS data loggers, which allowed us to record all the movements of a certain number of users (n=15) of two coworking spaces and also do some in-depth interviews. The results of these surveys allowed us to develop a typology of the mobility patterns of coworkers in relation to the integration of the territorial dimension and the embedding of social relations. Beyond the influence of the location of the coworking space on the structure of daily mobility, these results tend to suggest the importance of the biographical trajectories of individuals in changing practices [START_REF] Cailly | Les trajectoires mobilitaires : une notion clef pour penser et accompagner les changements de modes de déplacements ?[END_REF][START_REF] Rau | Life Events and Mobility Milestones: Advances in Mobility Biography Theory and Research[END_REF], as well as the impact of how the coworking space is integrated as part of a professional and personal life plan. While the quantitative survey confirms that reducing commuting is not the key motivation for going to a coworking spaces, which is what other studies have also highlighted [START_REF]Mailler Le Territoire En Tiers Lieux ? Etude Qualitative et Quantitative Des Usages Potentiels En Aquitaine[END_REF][START_REF] Bentayou | Les espaces de coworking : des outils au service de la mobilité durable ?' Cerema[END_REF]Flipo, 2021), the qualitative survey goes further by revealing the diversity of daily mobility practices. This result goes against the simplifying representations of the reduced or conversely the increased daily mobility of coworkers in the margin of metropolitan areas. Although it may seem paradoxical at first sight, the more or less intense daily mobility that we have observed seems to merge with the coworkers' level of acceptance of a territorial development model focusing on the local dimension, which is catalysed by coworking spaces. These results thus confirm the role of daily mobility as a driver of links to the local community and highlights the diversity of daily mobility patterns of coworkers in the margin of metropolitan areas.

Coworking in the margin of metropolitan areas for a mobility transition?

The phenomenon of coworking spaces, which appeared at the heart of global, creative and competitive metropolitan areas [START_REF] Florida | Cities and the Creative Class[END_REF][START_REF] Leducq | Diffusion régionale et intégration urbaine des espaces de coworking. Les spécificités d'une région française faiblement métropolisée[END_REF], has recently favored non-urban areas, particularly in the case of France, which is experiencing increased growth of these places in both rural and suburban low-density areas (Flipo, 2021;[START_REF] Leducq | Diffusion régionale et intégration urbaine des espaces de coworking. Les spécificités d'une région française faiblement métropolisée[END_REF]. With 52% of third places outside the 22 French administrative metropolitan areas listed in the latest France Tiers-Lieux 2021 report (Lévy-Waitz, 2021) versus 42% in 2018[START_REF] Lévy-Waitz | Mission Coworking. Faire Ensemble Pour Mieux Vivre Ensemble[END_REF], the tropism of coworking spaces for low-urbanised areas is undeniable. Supported and accompanied in their creation and development by small towns, municipalities and intermunicipal cooperation, these places appear to local and national public authorities as important tools for a new form of rurality [START_REF] Flipo | Espaces de coworking et tiers-lieux. Les réseaux d'une nouvelle ruralité ?[END_REF]. The national association France Tiers-Lieux sees these rural and suburban spaces as an environment conducive to the expression of these new forms of activity. "It is at the heart of peripheries, priority neighbourhoods, medium-sized towns, small towns and villages that the full potential of third places is expressed" (Lévy-Waitz, 2021: 4). This strong link between new rurality and the development of coworking spaces is also underscored by [START_REF] Flipo | Espaces de coworking et tiers-lieux. Les réseaux d'une nouvelle ruralité ?[END_REF]. These spaces in rural areas meet both the need for proximity on an economic level and at the same time enhance links to the local community that are characteristic of new representations of rurality. While these places develop easily in these areas, they nevertheless reflect a certain type of relationship with the rural space, one that is both elective and flexible, characteristic of a rural middle class, made up of executives and intermediate professions with significant cultural capital [START_REF] Bruneau | Une petite bourgeoisie au pouvoir. Sur le renouvellement des élus en milieu rural[END_REF][START_REF] Paranthoën | Processus de distinction d'une petite-bourgeoisie rurale[END_REF]. While questioning the socio-demographic trends observed for some time in low-density areas in France [START_REF] Bontron | Les espaces ruraux résidentiels, configurations et dynamiques[END_REF][START_REF] Pistre | Migrations résidentielles et renouveaux démographiques des campagnes françaises métropolitaines[END_REF], the close link with metropolitisation supporting this renewed interest in rural areas raises another issue, that of the daily mobility of coworkers located in these areas. Known for being a major reason for urban sprawl, population dissemination on the outskirts of major urban areas is also one of the main reasons for the growing number of miles travelled and the disturbances that this generates [START_REF] Bassand | Métropolisation et Inégalités Sociales[END_REF][START_REF] Bassand | Mobilité spatiale et processus de métropolisation : Quelles interactions ?[END_REF]. In just a few years, the question of daily mobility has thus become one of the key issues in the metropolitisation process. This issue has not escaped the attention of public authorities, who see the emergence of coworking spaces in low-density areas, and their assumed ability to retain workers locally, as a potential lever for the transition towards more sustainable mobility. Support by French public authorities for these new places, at all territorial levels ("new spaces, new links" programme by the French National Agency for the Cohesion of Territories, call for projects "workshops of territories"), owes a great deal to the assumption that these places are likely to contribute to relocating employment in rural and suburban areas, and thus to reduce commuting (ADEME, 2014;CGET, 2015). However, as highlighted by researchers, this assumption has little empirical foundation [START_REF] Bentayou | Les espaces de coworking : des outils au service de la mobilité durable ?' Cerema[END_REF]Flipo, 2021). It is based on the apparently trivial but often unquestioned premise that the attendance of coworking spaces in rural and suburban areas may replace commuting trips between large urban centres and their peripheries with local commutes whose spatial extension would then be substantially inferior. However, this assumption is based on the results of studies focused on teleworking employees, who are not the main users of coworking spaces. The population using coworking spaces in low-density areas appears to be made up only partly of teleworking employees [START_REF] Bentayou | Les espaces de coworking : des outils au service de la mobilité durable ?' Cerema[END_REF]Flipo, 2021) but mainly by individual selfemployed entrepreneurs, as our surveys show (PERI#WORK, 2020). The use of a coworking space by these populations does not necessarily imply the replacement of mobility towards urban centres with more local commuting. On the contrary, joining these places may in some cases even trigger additional trips (A'URBA, 2013). Thus, "ultimately, coworking spaces may only make a modest or even marginal contribution to the issues of mobility" (Bentayou et al., 2019: 25). The results of these initial investigations, which prompt us to temper the enthusiasm of public authorities, raise a certain number of questions. Before assessing the ability of these spaces to accompany coworkers towards a reduction in their travel, and more broadly, towards more sustainable practices [START_REF] Lejoux | Coworking, a Way to Achieve Sustainable Mobility? Designing an Interdisciplinary Research Project[END_REF], it is appropriate to ask: What are the daily mobility patterns of coworkers in low-density areas? What type of relationships with space are coworkers seeking and developing in these areas? And to what extent do these coworking spaces create nodes around which spatial practices can be organised?

Daily mobility from the individuals' point of view

To elucidate these questions on coworking spaces, we have deployed a survey protocol for the finegrained documentation of mobility and social practices of coworkers in non-metropolitan areas. While most research on these questions is based on declarative data, collected within the framework of surveys using questionnaires or interviews, we opted for a real and exhaustive measurement of daily mobility, using GPS as we had done in a previous research on low-density areas [START_REF] Baptiste | Quelles Capacités Des Traceurs GPS à Rendre Compte Des Pratiques de Mobilité Quotidienne ? Une Application Sur Des Territoires de Faible Densité En Indre et Loire (37, France)[END_REF][START_REF] Feildel | La Mobilité Révélée Par GPS : Traces et Récits Pour Éclairer Le Sens Des Mobilités Périurbaines[END_REF][START_REF] Feildel | La Mobilité Comme Modalité de l'ancrage : Enrichir l'évaluation de La Durabilité Des Espaces Périurbains[END_REF]. Global Positioning System is a powerful tool for mobility surveys, making it possible to access a particularly fine-grained description and understanding of the spatial and temporal framework of movements [START_REF] Renso | Mobility Data[END_REF]. In this way, we monitored several groups of coworkers, by equipping them with an individual GPS data logger, allowing us to precisely chart all their movements, through the collection of georeferenced data and their timestamp. This mechanism was implemented in a sample of 15 coworkers, users of coworking spaces located in low-density areas outside metropolitan areas in France. The recordings were taken over a 2-week period for each individual, in an asynchronous manner, between December 2019 and January 2022, excluding the periods of lockdown imposed by the French government as part of the fight against the COVID-19 pandemic. We decided to apply this protocol to users of two coworking spaces, which we chose in relation to the specific characteristics (location, length of existence, professional and sociological profiles of the coworkers, type of economic model) in order to obtain a diversity in the use of these places and the territorial dimension influencing the daily mobility of coworkers. The two coworking spaces chosen for this survey were Le Fauteuil à Ressort, located in Peillac in the Morbihan department, and La Canopée, situated in Janzé in the Ille-et-Vilaine department (Map 1). These two municipalities, in the region of Brittany in France, have contrasting geographic and demographic profiles. Peillac is a small rural town that is losing inhabitants (1,897 inhab., 2019), which, in the typology of French country areas [START_REF] Hilal | Typologie des campagnes françaises et des espaces à enjeux spécifiques (littoral, montagne et DOM)[END_REF] falls under the category of farming and industrial country areas under weaker urban influence. Janzé is a small town of relative importance (8,629 inhab., 2019) with a regularly growing population, and falls under the category of densified rural area on the periphery of towns with very strong residential growth and a dynamic economy. These differences in geographic and demographic profiles are explained mainly by the distance between these two municipalities and the metropolitan areas criss-crossing the western part of France that exercise their influence on these rural and suburban areas. Peillac is situated 8.7 mi from Redon (10,032 inhab., 2019), a small town in the south of the Ille-et-Vilaine department, and almost equidistant (29 mi) from the urban centres of Rennes (451,762 inhab., 2019) and Nantes (656,275 inhab., 2019). As for the town of Janzé, it is very clearly situated within the area of influence of the city of Rennes, barely 16 miles away. The coworking spaces we focused on in these two municipalities are located in the village centre. They nevertheless differ in terms of length of existence, the type of economic model, the number and the professional and sociological profiles of coworkers. Le Fauteuil à Ressort in Peillac was founded in 2016 as an association created by a workers' collective. It stems from a communitybased rationale, on the model of a shared, self-managed office [START_REF] Flipo | Espaces de coworking et tiers-lieux. Les réseaux d'une nouvelle ruralité ?[END_REF]. In 2019-2020 this space had about twenty coworkers, hosted in the premises of a former hotel rented by the group and repurposed into shared offices during works managed by the founding members themselves. This coworking space is characterised by a strong collective will that initiated the creation and coordination of the place, as stated on its website, "[…] was born of the desire to exchange views on each other's professions and to work together". Workers who use this space are mainly selfemployed workers, and they work in the arts, entertainment and recreation, information and communication, specialised, scientific and technical activities, but also craftsmanship and construction. Le Fauteuil à Ressort therefore differs from La Canopée in Janzé, insofar as the latter coworking space stems from a public initiative. Open in 2020, La Canopée is a project promoted by La Roche aux Fées community of municipalities, which received aid from the European Union, the French State, the Regional Council of Brittany and the Ille-et-Vilaine department. In 2020, this coworking space, associated with a fab lab, welcomed about thirty coworkers on the first floor of the post office building, with 850 m² divided into open spaces, individual offices and meeting rooms. The professional and sociological profiles of the coworkers are more varied, with independent workers but also teleworking employees in the information and communication sectors, specialised, scientific and technical activities, business, administrative service activities, the arts and training. From these two coworking spaces, we recruited 15 individuals for our survey, 9 coworkers from Le Fauteuil à Ressort and 6 coworkers from La Canopée, while ensuring the representativeness of the professional and sociological profiles of all the coworkers of each space. These 15 individuals were equipped with a GPS data logger for two weeks, including weekends, over normal periods excluding school holidays and lockdowns. The GPS data loggers allowed us to collect all the positions of the individuals over a daily range of 14 hours, between 8 am and 10 pm, with a time frame of 3 seconds between each position. All the recordings allowed us to analyse over 2,000 hours of recordings, with an average of 10 days of exploitable GPS readings per individual, and more than 4850 miles in total, with an average of 330 miles travelled per individual for an average standard deviation of 150 miles across the 15 individuals (Map 1).

Map 1: GPS tracks from La Canopée and Le Fauteuil à Ressort

These data made it possible to precisely quantify the movements of the individuals. However, in view of the "new mobility paradigm" [START_REF] Sheller | The New Mobilities Paradigm[END_REF][START_REF] Urry | Sociology beyond Societies: Mobilities for the Twenty-First Century[END_REF][START_REF] Hannam | Mobilities, Immobilities and Moorings[END_REF], our approach was not limited to this quantification. After being processed2 and mapped, the individual GPS tracks were used as reactivation material [START_REF] Feildel | La Mobilité Révélée Par GPS : Traces et Récits Pour Éclairer Le Sens Des Mobilités Périurbaines[END_REF] as part of more in-depth interviews, leading to the semantic enrichment of the GPS track [START_REF] Chardonnel | La trace : notion partagée pour une recherche interdisciplinaire sur la mobilité des enfants[END_REF].The survey protocol was designed so as to use the cartographic representation of the GPS track as a conversation starter, bringing the individuals to question themselves on their daily mobility and the meaning they give to it [START_REF] Bailleul | Le Sens Des Mobilités à l'épreuve Des Identités Spatiales : Un Éclairage Par Le Récit de Vie Spatialisé et l'herméneutique Cartographique[END_REF]. The in-depth interview established a discursive outline of the individuals' daily mobility in relation to their life (including the main places of residence, their location, their habits in terms of travel and the activities in the places concerned by mobility). It also highlighted the opportunities and the constraints felt by the individuals as being a burden on their current mobility, from both a spatial and a social aspect [START_REF] Canzler | Tracing Mobilities: Towards a Cosmopolitan Perspective[END_REF][START_REF] Urry | Sociology beyond Societies: Mobilities for the Twenty-First Century[END_REF]. This in-depth reactivation interview, which resembles a "cartographic elicitation" [START_REF] Bailleul | Le Sens Des Mobilités à l'épreuve Des Identités Spatiales : Un Éclairage Par Le Récit de Vie Spatialisé et l'herméneutique Cartographique[END_REF][START_REF] Baibarac | Spatial-Technological Experiments in the Environment: Eliciting and Representing Experiences of Urban Space[END_REF], allowed individuals to independently put into perspective their daily trips in terms of the evolution of systems of constraints and habits, resources, skills, inclinations and values that structure their mobility [START_REF] Cailly | Les trajectoires mobilitaires : une notion clef pour penser et accompagner les changements de modes de déplacements ?[END_REF][START_REF] Müggenburg | Mobility Biographies: A Review of Achievements and Challenges of the Mobility Biographies Approach and a Framework for Further Research[END_REF][START_REF] Rau | Life Events and Mobility Milestones: Advances in Mobility Biography Theory and Research[END_REF]. The material collected from the sample of 15 individuals was examined in the context of an online questionnaire which we had sent to a large panel of users of coworking spaces in France. This other survey (PERI#WORK, 2020) was conducted between April and July 2020. It reached a total of 226 coworkers in France (107 different coworking spaces), 72% of which were urban (154 respondents were users of an urban coworking space) and 28% outside metropolitan areas, with 20% being suburban (46 respondents) and 12% rural (26 respondents). They were mainly questioned on the effects of the COVID-19 pandemic on their professional practices, but also more broadly on their key motivations for attending a coworking space and their daily mobility before the coworking space was established.

Coworkers and daily mobility: working better to commute better

The data from the online questionnaire (PERI#WORK, 2020) confirm what other research has highlighted [START_REF] Bentayou | Les espaces de coworking : des outils au service de la mobilité durable ?' Cerema[END_REF], namely that the key motivations of users of coworking spaces are above all linked to the professional activity (social and professional interactions) and to the working environment (seeking a collective and a collaborative dimension). For coworkers located in urban centres and for those in suburban or rural settings 3 , reducing commuting emerges as a reason of little or even no importance (for 67% of coworkers in urban centres and 71% in lowdensity areas). The key motivation for attending coworking spaces for both of these populations is above all linked to their desire to benefit from a pleasant and convivial work environment (for 85% of coworkers in urban centres and 82% in suburban or rural areas). The second reason is to avoid being isolated (for 71% of coworkers in urban centres and 67% in suburban and rural areas). While the dynamic of coworking spaces today does not seem to be driven by the desire of coworkers to reduce their mobility, it is nevertheless appropriate to try to measure more finely the behavioural changes that these places are likely to foster. In this way, some 22% of coworkers in urban centres declare having changed their main transport modes for commuting to work. When the car represented 53% of the modal share before joining a coworking space, afterwards it represents 46%, to the benefit of public and soft transport. What may seem like a modest result is confirmed and even accentuated for coworking spaces in low-density areas, with an evolution of 14% in the transport modes of their coworkers, and a modal share of the car representing 70% before joining the coworking space to 69% after. While mobility does not seem to be a decisive dimension today in the use of a coworking space, in urban or suburban and rural areas, a definite influence of these places can nevertheless be seen on choices in terms of transport modes, with a difference between urban coworking spaces and those located in the margin of metropolitan areas. The effects of attending a coworking space on the daily mobility of users, and the contrasts that are emerging between urban, suburban and rural areas, leads us to question the expectations of public authorities that underlie and justify their support for the dynamic of these places in low-density areas. From this point of view, the developments observed in terms of daily mobility should be seen in the context of the role of virtual communications, traditionally envisaged as the key driver in reducing mobility according to the telework model. Indeed, while 56% of respondents to our survey intend to change their mobility practices by replacing commuting with remote work more often, this figure once again varies according to the location of the coworking space. For coworkers in urban spaces, this propensity to replace physical commuting with remote work is around 61%, whereas for coworkers in suburban or rural areas it stands at 44%. Broadly speaking, these results (PERI#WORK, 2020) lead us to better understand how the daily mobility patterns of coworkers in the margin of metropolitan areas are structured, and especially to better measure the differentiated impact of these coworking spaces according to location and reasons to join it. The main idea that emerges from these results is that coworkers in low-density areas have less options in organising their daily mobility. This raises new questions: what are the systems of constraints and specific opportunities likely to influence the structuring of the daily mobility of users of these spaces in low-density areas? To what extent is daily mobility around coworking spaces in suburban and rural environments influenced by the professional and personal life plan of the individuals?

Mobility around coworking spaces in the margin of metropolitan areas: the issue of proximity

The data collected through the exhaustive measurement of the movements of a panel of the two coworking users confirm the figures obtained in response to the online questionnaire and more broadly to national surveys. The average distance travelled daily by our sample (all causes and modes combined) is 33 miles and the time spent commuting is 1 hour and 9 minutes. Out of the ten days on average of GPS recordings, the modal share of the car represents 67.1% (equivalent to 93.1% of all distances travelled), while the modal share of public transport is only 1.1% (for 5.5% of distances travelled). Similarly, the daily distances travelled by our sample in the distance bands analysed are roughly equivalent to the available national data (Ministère de la Transition Ecologique and INSEE, 2019). The coworking spaces in the margin of metropolitan areas therefore do not appear as potential drivers in the overall reduction in travel (in number of trips or by travel distance), especially by car. Nevertheless, neither do they seem to generate additional trips. But beyond these overall results, which help to confirm the limited effect of suburban and rural location on reducing the number of trips, some interesting trends have been observed at local level (Table 1). While the data collected from the individuals surveyed by GPS illustrate the dominance of the car as a transport mode in rural and suburban areas, they also highlight, in coworking space located in a low-density area, an over-representation of soft modes for short trips. This difference is particularly salient for trips of less than 1.2 miles (2 km) with a modal share (in number of trips) for walking at 28% (representing 1% of the distances covered) when this is around 18% at national level in rural areas (Ministère de la Transition Ecologique and INSEE, 2019). It was also observed that according to the type of environment concerned, whether rural or suburban, this contrast is even more accentuated (Table 1). In this respect, the coworkers at Le Fauteuil à Ressort use soft modes for almost 40% of their trips (of which 35.5% by foot and 4.5% by bicycle) while coworkers at La Canopée use these for just 13.3% (11% by foot and 2.4% by bicycle). This phenomenon reflects on the modal share of the car between the users of these different types of coworking spaces, with 58.7% of trips made by car for coworkers at Le Fauteuil à Ressort versus 86.3% for coworkers at La Canopée.

Table 1: Breakdown of the modal share (in number of trips) of coworkers at Le Fauteuil à Ressort (FàR) and La Canopée (LaC)

While the relatively small size of our sample must not be underestimated when interpreting these data, they nonetheless seem to reflect an interesting phenomenon that is worth highlighting. The mobility around these coworking spaces seems to differ according to the type of environment in which they are located. The differences previously mentioned in terms of modal share in number of trips in fact suggest increased investment in spaces in close proximity to the most isolated coworking spaces. Furthermore, the absence of any significant difference in terms of distances travelled by modes between the two sub-samples surveyed confirms this. While this phenomenon is partly due to the structure of each territory, especially its remoteness from the urban centre and access to locally available public transport (by train and bus), it should also be compared with the distance when working from home, and above all the differentiated trajectories of coworkers. Indeed, Le Fauteuil à Ressort and La Canopée do not stem from the same dynamics in the emergence and operational processes, which reflects on the professional and sociological profiles of their users, on the reasons for joining the coworking space and on their mobility patterns.

The key motivation for attending coworking spaces in rural areas

The in-depth interviews with coworkers allowed us to uncover processes of territorial identification linked to the rationales of embedding differentiated social relations. In Peillac, coworkers at Le Fauteuil à Ressort have unique profiles, characteristic of a portion of users of coworking spaces in rural settings, made up of active residents recently arrived from major neighbouring agglomerations [START_REF] Flipo | Espaces de coworking et tiers-lieux. Les réseaux d'une nouvelle ruralité ?[END_REF]. For a certain number of these users, joining the coworking space is part of a process of spatial, social and professional transition, through which they show a desire to take distance in relation to the metropolitan areas and their former professional activities. This transitional rationale, including on a psychological level [START_REF] Liefooghe | Le tiers-lieu, objet transitionnel pour un monde en transformation[END_REF], can be found in the organisation of mobility and the discursive patterns produced by some of these individuals.

For these users, their vocational retraining plan, mirrored by the use of a coworking space, corresponds to a desire to break with the urban centre. For these individuals, the metropolitan area is synonymous with mobility considered as both time-consuming and unsustainable, from a social, economic and ecological perspective. The ecological dimension in a broad sense also including the relationship with nature, food supply, energy consumption in homes, and the rationalisation of travel, is a key motivation for joining a coworking space in a rural environment. From this viewpoint, the different coworking spaces in low-density areas seem to clearly stand out from each other, between those closest to metropolitan areas, situated in suburban areas, and those most remote, situated in rural areas. The motivation of coworkers in rural places also corresponds to another set of values linked to lifestyle, the organisation of family life, and the quest for meaning through a professional activity. The daily trips of the individuals surveyed at Le Fauteuil à Ressort bear witness to this desire for roots in the local community, from a spatial level, with a shift to the local dimension through the coworking space and the place of residence. Local integration relies on the coworking space, through the social relations between the coworkers. They not only find a common professional interest on which they can exchange views and cooperate, but also shared values far exceeding the limited framework of professional activity. In this case, the group of individuals and the social dynamic created by the coworking space, which is comparable to what other researchers call "concrete utopias at local level" [START_REF] Flipo | Espaces de coworking et tiers-lieux. Les réseaux d'une nouvelle ruralité ?[END_REF][START_REF] Rouvière | Migrations utopiques et révolutions silencieuses néorurales depuis les années 1960[END_REF] when speaking of the new generation of rural inhabitants, are important drivers for development of the local territories. These processes do not however exclude greater mobility as illustrated by the GPS recordings (Map 1).

Daily mobility patterns of coworkers: differentiation according to the type of coworking spaces Mobility and especially that geared towards urban areas, remains a key condition of professional activity for a very large majority of coworkers in low-density areas, including the most isolated ones. However, a difference in the variability of the daily mobility patterns of coworkers in rural areas has been observed, in relation to coworking spaces that are closer to metropolitan areas, which show more homogenous mobility patterns that are more systematically geared towards major metropolitan areas. By analysing the GPS tracks of coworkers (Figure 1), it was possible to identify patterns and to build a typology of the forms of territorial cohesion, according to the extent to which coworkers daily mobility was more or less polarised by metropolitan areas. In this respect, we have identified at least five daily mobility patterns of coworkers in low-density areas (Figure 2). The first pattern, which can be called "local recentred", illustrates limited mobility that is refocused on the area close to the coworking space. This diagram is dominant in the rural coworking spaces that are farthest from metropolitan areas (Fauteuil à Ressort), whereas this is absent in users of suburban coworking spaces relatively close to major urban centres (La Canopée). The local dimension, which is characteristic of this first diagram, is spelled out in two other idealtypical configurations, according to the extent to which the daily mobility of the users appears as more or less polarised or even multipolarised. The second pattern, "local multipolarised", sketches a dense network of daily mobility around the coworking space but still contained within a local space, while the third pattern, "local polarised", gears mobility towards a hub, essentially metropolitan. These two patterns are generally common to users of rural and suburban coworking spaces, and are those which we have observed most frequently. Lastly, two final patterns have been identified, which are called "global" as opposed to local, and for which mobility occurs at a spatial level going beyond the local level. The fourth pattern, "global multipolarised", represents intense daily mobility occurring in multiple places beyond the local space, whereas the fifth pattern, "global polarised" or "metropolitan" presents intense daily mobility centred on the metropolitan area. This fifth and last pattern is observed in our sample exclusively among users of the coworking space located in the area closest to metropolitan centres (La Canopée).

Figure 2: Typology of the daily mobility patterns of coworkers in low density areas

Greater variability in the mobility patterns of users of coworking spaces located in the most isolated low-density areas is discernible particularly at inter-individual level, in relation to the professional activity of the users, but also for an individual in relation to the time and periods of activity. The indepth interviews with coworkers helped to clarify the rationales underlying this greater or lesser variability, and more generally, the different types of relationship with daily mobility on which they are based. Above all, what emerges from this analysis is a point that is common to all the coworkers surveyed. Whether users of a rural or suburban coworking space, mobility and especially by car appears for them as a necessity that is characteristic of a lifestyle associated with low-density areas [START_REF] Feildel | La Mobilité Comme Modalité de l'ancrage : Enrichir l'évaluation de La Durabilité Des Espaces Périurbains[END_REF]. Daily mobility by car, which is synonymous with flexibility and openness to the world, is rarely called into question by these users, even when an alternative transport mode is available. This is generally the case on the suburban peripheries that are closest to metropolitan areas, and especially in Janzé with a train connection (regional express train) and seven trains operating every day to the metropolitan centre of Rennes. Here again, nevertheless, there is a difference between the users surveyed in coworking spaces which are the closest to metropolitan areas, and those in the most remote spaces. In this respect, for the former, the use of a private car, especially for trips polarised by the metropolitan area, generally appears to be taken for granted, and any possible reconsideration is only envisaged in light of the criteria of efficacy and rapidity. For coworkers situated in the more isolated areas, daily mobility in general and by car especially, although considered inevitable, is more systematically called into question by putting into context all the dimensions of living (accommodation, food, consumption, leisure, etc.) and more particularly of work. On these two points, rationalisation and compensation can be observed, which bring individuals to envisage and implement new balances between necessary mobility and willful connections with the local community. Rationales of compensation take place in terms of habitat, with the growing of a vegetable garden for example, but also the investment in renovating an old dwelling or using a green and local electricity provider. In this first category, the knowledge acquired by other members of a coworking space appears as a non-negligible resource in order to share opportunities and knowhow. Concerning rationalisation, these may emerge as part of the professional activity, by drawing from the social and professional relations forged within the coworking space, which then facilitates finding and implementing shared mobility solutions, particularly in terms of carpooling. Certain professional projects in which coworkers are led to collaborate, especially due to the proximity of their fields of activity, quite naturally give rise to shared trips. However, other forms of daily mobility not necessarily linked to a professional activity also benefit from the networking of users, thanks to the coworking space, and to their commitment to common values. While this rationalisation remains difficult to quantify, it is visible on the GPS recordings as well as in coworkers' discourse, especially from the most isolated coworking spaces. In these spaces, we can see quite clearly the "strength of weak ties" [START_REF] Granovetter | The Strength of Weak Ties[END_REF], i.e. the effect of the embeddedness of social relations, and the role of coworking spaces in creating a "sense of community" [START_REF] Garrett | Co-Constructing a Sense of Community at Work: The Emergence of Community in Coworking Spaces[END_REF][START_REF] Spinuzzi | Coworking Is About Community": But What Is "Community" in Coworking?[END_REF].

Conclusion

While reducing mobility does not clearly appear to coworkers as a key motivation for joining a coworking space, the fact remains that these spaces have an impact on the structure of their daily mobility. However, this influence seems differentiated according to the type of locality in which they are established or from which they emerge. Furthermore, the conditions for the contribution of these coworking spaces to the daily mobility patterns are not just linked to the level of spatial remoteness from metropolitan areas, facilities or the availability of transport, but more fundamentally on the ability of these places to create real nodes in a non-metropolitan mobility system that is refocused on the local dimension. Unlike other surveys based mainly on declarative data, we were able to objectively measure the movements of users of coworking spaces located in low-density areas. The results obtained from a relatively small sample of coworkers show that these spaces do not lead to an overall reduction in mobility with regard to national surveys, neither do they increase it. These initial results, which need to be confirmed by additional surveys, nevertheless go against simplifying representations and discourse, and encourage scholars and public authorities to take a closer look to better understand the conditions to the daily mobility patterns. In this respect, through the phenomenon of the overrepresentation of soft modes in trips around coworking spaces the farthest from major urban centres, we were able to identify a deeper dynamic. This dynamic, based on professional activity and the embeddedness of social relations, draws from the coworking and enhances the nearby space. This dynamic depends not only on the locality in which the coworking space is established, but seems to be linked more broadly to the sociological and professional profiles of the coworkers, to the reasons for attending the coworking space, and to the intensity of social relations that this space is likely to create. Daily mobility seems to depend on the level of adherence to a territorial development model centred on local links, which is catalysed by the coworking space. According to the type of locality and of coworking space, the implementation of more virtuous mobility practices seems to depend less on infrastructure policies than on identifying, encouraging and supporting local initiatives. What remain only lines of inquiry at this stage, however pleads for the need to extend the understanding how coworking spaces contribute to various transitions, social, professional and ecological, in a systemic perspective. Through the emerging phenomena of rationalisation and compensation, it is more broadly the contribution of coworking spaces to more sustainable ways of living in low-density areas, including all the dimensions of living and not just mobility practices, that should be considered. In addition, the contrasts identified between suburban and rural areas argue for a differentiated approach of public support policies to coworking spaces.

Figure 1 :

 1 Figure 1: GPS tracks of coworkers at Le Fauteuil à Ressort in Peillac (56) and La Canopée in Janzé (35)

This research is part of the PERI#WORK programme: "Working in the margin? Coworking spaces as nodes of a new mobility system outside metropolitan areas", funded by the French National Research Agency (ANR-18-CE22-0010-01).

The processing of GPS tracks mainly consists of the manual or automated selection of relevant data by eliminating outliers, or erratic data points or itineraries.

The categorisation of the types of area where coworking spaces are established (urban, peri-urban and rural environments) was created according to the zoning of urban areas, based on the urban areas 2010 report by INSEE (French National Institute for Statistics and Economic Research) updated on 1 January 2020.