P Evon

L Labonne

V Vandenbossche

P Y Pontalier

L Rigal

The twin-screw extruder, a continuous liquid/solid extractor and separator during sunflower

Keywords: sunflower whole plant, biorefinery, twin-screw extruder, aqueous extraction process, oil and extraction, proteins and extraction

The compressing action by the reverse screws (CF2C) is essential for L/S separation.

Positioned in module 9, CF2C screws push part of the mixture upstream against the general movement in TSE, and this counter pressure ensures the L/S separation efficiency above the metal filter, located in eighth position.

Oil is extracted in the form of two emulsions, stabilized by phospholipids and proteins, and usable as co-emulsifiers in cosmetic industry. An aqueous extract containing watersoluble components from whole plant is also generated; it could be recycled. As a mixture of fibers and proteins, the cake can be moulded by thermo-pressing into boards, usable in the furniture and building industries.

In this study, fractionation was conducted from next inlet flow rates: 54 kg/h solid and 183 kg/h water (3.4 L/S ratio). The screw speed varied from 249 to 124 rpm, corresponding to a filling coefficient (ratio of the solid inlet flow rate to the screw speed) from 217 to 436 g/h rpm.

The filling coefficient directly affects the L/S separation efficiency. The latter can be estimated from next experimental data: the outlet flow rates of both cake and filtrate, the cake moisture content, the residual contents of oil and water-soluble components in the cake, and the extraction yields in dry matter, lipids and water-soluble components.

For low filling coefficients (i.e. high screw speed), the L/S mixture compression in CF2C screws is insufficient, not allowing a satisfactory L/S separation. Conversely, for high filling coefficients (i.e. low screw speed), solid particles accumulate more upstream from the pressing zone, obstructing part of the filtering screens and thus reducing the filtration surface.

A less efficient L/S separation is then observed.

From the experimental data evolution, optimal screw speed was estimated at 182 rpm using a second order polynomial regression, corresponding to a filling coefficient of 297 g/h rpm. Extraction yields in dry matter, lipids and water-soluble components were 22%, 49% and 40%, respectively. Such filling would lead to a specific mechanical energy of 103 W/h kg whole plant processed.

Introduction

Biorefinery of sunflower whole plant can be conducted with water using a nine modules Clextral (France) Evolum HT 53 twin-screw extruder (TSE) [START_REF] Evon | The twin-screw extrusion technology, an original and powerful solution for the biorefinery of sunflower whole plant[END_REF]. Oil is extracted in the form of two emulsions, stabilized by phospholipids and proteins, and usable as co-emulsifiers in cosmetic industry [START_REF] Evon | The twin-screw extrusion technology, an original and powerful solution for the biorefinery of sunflower whole plant[END_REF][START_REF] Evon | Procédé de fabrication d'un matériau solide à partir d'une plante oléagineuse et matériau solide obtenu[END_REF]. An aqueous extract containing water-soluble components from whole plant is also generated; it could be recycled [START_REF] Evon | The twin-screw extrusion technology, an original and powerful solution for the biorefinery of sunflower whole plant[END_REF][START_REF] Evon | Procédé de fabrication d'un matériau solide à partir d'une plante oléagineuse et matériau solide obtenu[END_REF]. As a mixture of fibers and proteins, the cake can be moulded by thermo-pressing into boards, usable in the furniture and building industries [START_REF] Evon | The twin-screw extrusion technology, an original and powerful solution for the biorefinery of sunflower whole plant[END_REF][START_REF] Evon | Procédé de fabrication d'un matériau solide à partir d'une plante oléagineuse et matériau solide obtenu[END_REF][START_REF] Evon | Influence of thermo-pressing conditions on the mechanical properties of biodegradable fiberboards made from a deoiled sunflower cake[END_REF].

Because the filling coefficient of TSE directly affects the L/S separation efficiency, this study aimed to evaluate its optimal value.

Keywords: Sunflower whole plant, biorefinery, twin-screw extruder, aqueous extraction process, oil and extraction, proteins and extraction.

Results and discussion

In this study, fractionation was conducted from next inlet flow rates: 54 kg/h solid and 183 kg/h water (i.e. 3.4 L/S ratio). The screw speed (S S ) varied from 249 to 124 rpm, corresponding to a filling coefficient (ratio of the solid inlet flow rate to the screw speed) (C F ) from 217 to 436 g/h rpm.

The filling coefficient directly affects the L/S separation efficiency. The latter can be estimated from next experimental data: the outlet flow rates of both cake (Q C ) and filtrate (Q F ) (Fig. 1), the cake moisture content (H C ) (Fig. 2a), the residual contents of lipids (L C ) and water-soluble components (WS C ) in the cake (Fig. 2b), and the extraction yields in dry matter (R DM ), lipids (R L ) and water-soluble components (R WS ) (Fig. 2c).

Conclusion

From the experimental data evolution, optimal filling coefficient was estimated at 297 g/h rpm using a second order polynomial regression, corresponding to a screw speed of 182 rpm (Table 1). Table 1. Optimal device's filling coefficient and optimal screw speed estimated using a second order polynomial regression from each experimental data, and corresponding mean value and standard deviation.

For low filling coefficients (i.e. high screw speed), the L/S mixture compression in CF2C screws is insufficient, not allowing a satisfactory L/S separation. Conversely, for high filling coefficients (i.e. low screw speed), solid particles accumulate more upstream from the pressing zone, obstructing part of the filtering screens and thus reducing the filtration surface. A less efficient L/S separation is then observed. Extraction yields in dry matter, lipids and water-soluble components were then estimated at 22%, 49% and 40%, respectively (Fig. 2c). Such filling would lead to a specific mechanical energy of 103 W/h kg whole plant processed (Fig. 3).

! "# $ % & ! " # $%& ' ! # " $'()& Experimental data Q C (kg/h) Q C (kg of DM/h) Q F (kg/h) H C (%) R DM (%) L C (% of DM) R L (%) WS C (% of DM) R WS (%)

  The twin-screw extruder, a continuous liquid/solid extractor and separator during sunflower (Helianthus annuus L.) biorefinery P. Evon a,b,* , L. Labonne a,b , V. Vandenbossche a,b , P.Y. Pontalier a,b , L. Rigal a,b a Université de Toulouse, INP, Laboratoire de Chimie Agro-industrielle, ENSIACET, 31030 Toulouse Cedex 4, France b INRA, Laboratoire de Chimie Agro-industrielle, 31030 Toulouse Cedex 4, France * E-mail address (presenting author): Philippe.Evon@ensiacet.fr (P. Evon) Biorefinery of sunflower whole plant can be conducted with water using a nine modules Clextral Evolum HT 53 twin-screw extruder (TSE). Aqueous extraction of oil is an environmentally cleaner alternative technology to solvent extraction. TSE carries out three unit operations: conditioning and grinding, liquid/solid (L/S) extraction and L/S separation.

  Aqueous extraction of oil is an environmentally cleaner alternative technology to solvent extraction. TSE carries out three unit operations: (i) conditioning and grinding, (ii) liquid/solid (L/S) extraction and (iii) L/S separation. The compressing action by the reverse screws (CF2C) is essential for L/S separation. Positioned in module 9, CF2C screws push part of the mixture upstream against the general movement in TSE, and this counter pressure ensures the L/S separation efficiency above the metal filter, located in eighth position.

Fig. 1 .

 1 Fig. 1. Outlet flow rates of the cake (a and b) and the filtrate (c) as a function of the device's filling coefficient.

Fig. 2 .

 2 Fig. 2. Moisture content (a) and residual contents in lipids (b) and water-soluble components (b) of the cake, and extraction yields in dry matter (c), lipids (c) and water-soluble components (c) as a function of the device's filling coefficient.

Fig. 3 .

 3 Fig. 3. Current feeding the motor and specific mechanical energy as a function of the device's filling coefficient.


Charline Sire

Hélène Cattey

Anthonia Tsivery

Jean-Cyrille Hierso
email: jean-cyrille.hierso@u-bourgogne.fr

Julien Roger
email: julien.roger@u-bourgogne.fr

Phosphorus-directed Rhodium-Catalyzed C-H Arylation of 1-Pyrenylphosphines Selective at the K-Region

Keywords: PAH, Phosphorus, Rhodium, C-H Activation, Arylation

Lorsqu'un écrit scientifique issu d'une activité de recherche financée au moins pour moitié par des dotations de l'État, des collectivités territoriales ou des établissements publics, par des subventions d'agences de financement nationales ou par des fonds de l'Union européenne est publié dans un périodique paraissant au moins une fois par an, son auteur dispose, même après avoir accordé des droits exclusifs à un éditeur, du droit de mettre à disposition gratuitement dans un format ouvert, par voie numérique, sous réserve de l'accord des éventuels coauteurs, la version finale de son manuscrit acceptée pour publication, dès lors que l'éditeur met lui-même celle-ci gratuitement à disposition par voie numérique ou, à défaut, à l'expiration d'un délai courant à compter de la date de la première publication. Ce délai est au maximum de six mois pour une publication dans le domaine des sciences, de la technique et de la médecine et de douze mois dans celui des sciences humaines et sociales.

Introduction

Polycyclic aromatic hydrocarbons (PAH) are building blocks useful in organic electronic and medicine, with applications within semiconductor devices, luminescence probes, and as cytotoxic agents. [1] The incorporation of main group elements (like B, N, Si, P, etc.) into these π-conjugated frameworks is a valuable strategy to extend their electronic and photophysical properties. [2] Especially, PAH which contain phosphorus atoms are valuable scaffold with regards to their wide applications as pharmaceuticals, [3] in ligands design for catalysis [4] and in material sciences. [5] In the synthesis of pyrene derivatives, generally 1-, 3-, 6-and 8-positions are substituted by using electrophilic reagents, such as in most common halogenation reactions (Scheme 1). Alternatively, alkylation by aluminum reagents, [6] reactions with triflic acid, [7] and iridium-catalyzed borylation [8] occurs at 2-or 7-positions (Scheme 1). Conversely, the synthesis of pyrene derivatives substituted at the K-region (4-, 5-, 9-and 10-positions) usually requires tedious multistep metalation and halogenation procedures, which results in general in low overall yields. [9] For example, the preparation of 4,9-borylated pyrene from pyrene, is achieved in four steps by sodium reduction, electrophilic bromination at the remaining sp 2 -C K-sites, re-oxidation in the presence of DDQ, and electrophilic borylation via bromide/lithium exchange (Scheme 1). The bromination step also suffers from selectivity troubles.

On the other hand, selective direct metal-catalyzed C-H bond activation by transition metals opens more sustainable synthetic routes to reach extended πsystems and heteroatom-substituted derivatives. [10] Accordingly, Zhong et al. reported the first example of N-directed arylation of pyrenes by using a ruthenium-catalyzed C-H activation, specifically selective at 2-(or 7)-position (Scheme 2). [11] More recently, Babu et al. described the selective arylation and alkylation in C2 and C10 positions of Ncontaining pyrene derivatives by palladium-catalyzed C-H functionalization using appropriate bidentate directing groups such as picolinamide and 8-quinoline carboxamide, respectively. [12] Yang et al. developed a copper-catalyzed (O)P-directed C-H arylation of PAH using hypervalent aryl iodanes, [13] illustrated in a single example to occur for a pyrene derivative in γposition of the (O)P-directing group (C9-H arylation in K-region).

Interestingly, Yu and Che et al. employed a pendant phosphine as the directing group for arylation at the peri-position of naphthalene substrates, synthesizing thus in a single step reaction a class of bulky phosphine ligands structurally related to useful Buchwald biarylphosphines. They used with success a dimeric [Rh I Cl2(COD)]2 precatalyst (Scheme 2). [14] The phosphine-directed functionalization proceeded in the presence of bromoarenes and chloroarenes as the coupling partner, with KOtBu as the base in toluene at 110 °C and 150 °C, respectively. Scheme 2. C-H functionalization and selectivity in extended π-aromatics by N-or P-ligand-directed C-H activation in transition metal catalysis (Ru, Rh, Cu, Pd).

The approach by Yu and Che was applied to anthracenyl moieties for yielding the corresponding PAH diphenylphosphine, but was not applied to more challenging extended π-aromatic scaffolds like pyrene derivatives. [1] This extension was potentially very attractive since pyrenes are used in many instance as ligands and linkers for heterogenisation of catalytic systems because of their stacking affinity with current important materials like CNTs and graphene derivatives. [15] We disclose herein practical conditions for the selective rhodium-catalyzed direct C-H functionalization of pyrenes in C10-position using a preserved Ph2P-directing group (Scheme 2, bottom). In addition, we investigated the formation and isolation of pertinent Rh species in this C-H arylation reaction by 31 P NMR, and X-ray diffraction analysis. The data we collected overall support a cationic rhodium catalytic process for this C-H arylation of extended π-aromatic scaffold.

Results and Discussion

Peri-functionalization of small size naphthalene aromatics, [14,16] and other P-directed functionalization studies, [17-18] oriented the present rhodium-catalyzed conditions that we optimized to selectively perform the functionalization on the K-region on pyrene scaffold. We first explored in details the Rh-catalyzed direct C-H 10 arylation of 1-diphenylphosphinopyrene 1 using 4methoxybenzene bromide as coupling partner and various rhodium precatalysts, bases and solvent conditions (Table 1, see full optimization details in SI). The C-H bond activation at peri-position efficiently occurred in the presence of the precursors [Rh I Cl(COD)]2 dimer, the cationic monomer [Rh I (COD)2]BF4, and even starting from the highoxidation state [Rh III Cl2Cp*]2 (all in 5 mol% regarding the pyrene substrate). KOtBu was used as the base in refluxing toluene to produce in excellent yield the arylated pyrenylphosphine 2 (up to 86%, Table 1, entries 1-3).

2

(%) 1 [14] [Rh We observed that the addition of AgSbF6 and KPF6 salts as chloride abstractors dramatically affects the reaction, with only about 40% yield of 2 obtained under these conditions (Table 1, entries [4][5]. Both KOtBu and K3PO4 were found suitable as base, while conversely the use of NaOtBu and KOAc slightly lowered the conversion in 2 (Table 1, entries [6][7][8]. The solvents tested, toluene, 1,4-dioxane, trifluoromethylbenzene and methoxycyclopentane (CPME), showed little influence under the optimized conditions (Table 1, entries [8][9][10][11]. Thus, in the presence of the monomeric cationic [Rh I (COD)2]BF4 at 5 mol%, using K3PO4 as the base, in refluxing PhCF3 (102 °C), arylpyrenylphosphine 2 was isolated in 80% yield (Table 1, entry 10). Under these conditions, the nature of the aryl halide reagent deeply influences the conversion. Indeed, using 4methoxybenzene chloride or the iodide analogue as coupling partners provided significantly lower yield of 2, i.e. 37% and 79% yield respectively (Scheme 3). We further investigated the scope of functionalized (hetero)aryl bromides as coupling partners in the C-H arylation of 1-diphenylphosphine pyrene under the optimized conditions (Scheme 3). The formation of the aryl pyrenylphosphines 3 and 4 bearing in paraposition of the aryl electron-donating methyl and diphenylamino groups, respectively, was achieved in 90 and 60% isolated yields, respectively. 4-Acetyl, 4trifluoromethyl and 4-chloro groups were also tolerated functionalization in the bromoarene coupling partners, giving, respectively, the polyaromatic phosphines 5 (89%), 6 (70%) and 7 (89%) in isolated yields.

The presence of formyl and nitro groups in paraposition of the bromide partner limited the coupling reaction, and 8 and 9 were isolated in somehow lower 45% and 25% yield, respectively. These polyaromatic phosphines were found to be more sensitive to oxidation under air, even in the solid state.

Using as coupling partners meta-substituted aryl bromides bearing a methoxy or a naphthyl group yielded 10 (87%) and 11 (70%) in isolated yields, respectively.

Bulky ortho-functionalized bromoarenes were equally tolerated, and 2-methoxyphenyl bromide coupling furnished 12 in a high 85% isolated yield. The steric congestion from polyaromatic bromides fortunately did not affected much the reaction, and in the presence of 2-naphthyl, 9-phenanthrenyl, 1pyrenyl, 3-fluoranthenyl and 9-anthracenyl groups the corresponding coupling products 13 (79%), 14 (58%), 15 (80%), 16 (80%) and 17 (63%), respectively, were obtained in fairly good to excellent isolated yields.

Concerning more electron-poor heteroaryl coupling partners, 2-pyridinyl bromide led to a moderate yield of 41% in 18 and 2-thienyl bromide gave a modest 7% yield in 19. We tentatively attributed this limitation to a concurrent coordination of heteroaryl groups at the rhodium center. The X-ray diffraction structure of the polyaromatic phosphines 2 and 15 (Scheme 3) confirmed the selectivity of the C-H bond arylation at the 10-position of the pyrene core. In 1 H NMR a singlet is observed at 7.96 ppm for the -H 9 in 2. Consistently, a similar 1 H NMR pattern was observed for all the 10-arylated pyrenylphosphines (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)[START_REF] Fukuda | For selective and recent Ru or Rh-catalyzed P-direct activation/functionalization of aryl phosphines, see also: a)[END_REF](19).

Other polyaromatic hydrocarbon diphosphines were tested under our optimized conditions (Scheme 4). Phenanthryl, fluoranthenyl and naphthyl phosphines gave isolated yield of 73%, 58% and 51% for 23, 24 and 25 respectively in the presence of electron-rich 4bromoanisole, and 57% for 26 using 1-bromopyrene as coupling partner. Because of the low metal:substrate ratio (1:20) which exists under the genuine catalytic conditions, we also tried to synthesize Rh complexes incorporating a second phosphine ligand, as a pertinent potential catalytic intermediate. From the precursor B, the Rh(III) cationic species C is easily formed and stabilized by a second P-coordinated pyrenylphosphine (Scheme 6). The reaction takes place in a mixture of CH2Cl2/MeOH (1/1) using KPF6 as chloride abstractor. The complex C quantitatively formed and could be isolated pure in 60% yield by crystallization in CH2Cl2/heptane. We did not get single crystals suitable for XRD, but the 31 The complexes A-C were tested as catalyst (5 mol%) in the arylation reaction by using 1-diphenyl pyrene and 4-bromoanisole under the general conditions for coupling (Scheme 7). The Rh(III) nonmetallacycle complex A and the cationic metallacycle C achieved similar good yield (88% and 77%, respectively), while the metallacycle B provided a lower 29% yield. This suggests that B, and possibly neutral highly stable Rh(III) complexes in general, might be pitfall out-ofcycle resting states in the catalytic process. Conversely, complexes of type A still conserves the opportunity to form reactive Rh(III) cationic species like C. From B in the absence of KPF6 salt and base, no reaction occurred, while the dibrominated complex A2 (analogous to A) was formed in 58% in the presence of K3PO4 only. The lack of reactivity of complex B (and the formation of D) strongly suggests that the combination of both preformed A and the early presence of the base (K3PO4) is an efficient way to form reactive cationic Rh(III) species, and avoid pitfall resting-states as neutral very stable Rh(III) metallacyle.

Conversely, the same reaction from the cationic complex C (Scheme 9), involving a direct addition of 1.5 equivalents of 4-bromoanisole, leads to the formation in 10% of the expected coupling product 2 (Table 2, line 1), supporting C as a pertinent catalytic intermediate. The formation of the expected pyrenylphosphine 2 increased to 45% yield with an excess of 10 equiv of the arylated bromide (line 2). The addition of a halide abstractor (2 equiv of KPF6, line 3) further increased this yield, and limited the formation of unidentified products. Scheme 9. Formation of 2 from 4-bromoanisole using the preformed Rh(III) cationic complex C. Based on these results, a tentative mechanism of the rhodium-catalyzed 10-arylation of PAH is proposed in Scheme 10. The ortho-metallation occurs from the complex A to B by a concerted metallationdeprotonation assisted by the base, which further leads to the formation of the active cationic species C stabilized by a second phosphine ligand. The oxidative addition of aryl bromide on C may form E, ACS Catal. 2018, 8, 242-257 which may give F by reductive elimination/C-C bond formation. The desired coupling product is released for a sterically less hindered non-arylated phosphine ligand, forming G that is ready for further cyclometallation.

Scheme 10. Catalytic cycle proposal for rhodium 10arylation of polyaromatic phosphines.

We examined the impact that has the introduction of proximate aryl moieties on the Lewis basicity of the phosphino groups. This is achieved by phosphorus selenation and measurement of the 1 JP=Se spin-spin coupling constant (SSCC). [19,20] Quantitative selenation of the phosphorus is achieved from excess of Se powder in dichloromethane (Scheme 11, Table 2). We selected a complementary set of arylatedpyrenylphosphines which incorporate either electrondonating or electron-withdrawing group at the periaryl moiety: the compounds 2 bearing a OMe group, 5 bearing a COMe group, and 15 bearing another 1pyrenyl moiety. The phenanthryl diphosphines 23 was also examined. The 31 P NMR spectroscopy data for these compounds and their corresponding selenide derivatives are summarized in Table 2. As a benchmark, the SSCC 1 JP,Se value for triphenylphosphine selenide Se=PPh3 in CDCl3 is 730 Hz, which is higher than the SSCC for selenated-1diphenylphosphine-pyrene Se=1 1 JP,Se = 722 Hz, indicating that the phosphino group in 1 is slightly more electron-donating. [21] However, pure donating effects are strongly balanced by the functionalization at the β-position, as suggested by the values of SSCCs 1 JP,Se for 2, 5, 15 and 23 which ranges from 735 to 750 Hz. These clearly indicates less basic phosphines than 1, with thus lower electron-transfer to phosphorus. This would be consistent with a better resistance to oxidation (more stable P-ligands). We achieved the complexation of the bulky polyaromatic phosphines 2, 5 and 15 to gold(I)chloride, illustrating thus the linear ligand property with Au(I) of this class of pyrenyl-based phosphines (Scheme 12, Table 2). [22] Ph3P)AuCl] = 57.1 ppm. [23] The coordination to gold was achieved by reacting the ligand with [AuCl(SMe2)] in dichloromethane (Scheme 12).

Conclusion

Overall, we report practical conditions for the efficient peri-functionalization of topical π-extended 1pyrenylphosphine catalyzed by a cationic Rh(III) C-H arylation strategy. The arylation takes place at the Kregion of pyrenyl fragments, which is hardly accessible by conventional organic synthesis. This atom-economic direct C-H arylation tolerates both electron-donating and electron-withdrawing groups on the (hetero)aryl bromide coupling partner, with the resulting products isolated in 25% to 90%. furnished good to high yields (up to 96%) even when bulky polyaromatic hydrocarbon bromides were used General modification of the 1-pyrenylphosphines and other PAH, like presented herein, offers pertinent alternative to popular biphenylphosphine ligands used for transition metal catalysis, as well as potential perspectives to build luminescence probes, cytotoxic reagents and composite catalytic materials based on strong π-stacking of ligands and complexes incorporating pyrene moieties towards common sp 2 -Cbased supports. General Procedures. All reagents were purchased from commercial suppliers and used without purifications. All reactions were performed under an atmosphere of dry argon in oven-dried glassware using Schlenk and vacuum-line techniques. Flash chromatography was performed on silica gel (40-63 μm). The identity and purity of the products were established at the "Chemical Analysis Platform and Molecular Synthesis University of Burgundy" (PACSMUB Platform -SATT SAYENS) using high-resolution mass spectrometry, elemental analysis and multinuclear NMR. 1 H (500 MHz), 31 P (202 MHz), 18 F (407 MHz), 13 C (125 MHz) spectra were recorded on Bruker AVANCE III instrument in CDCl3 solutions. Chemical shifts are reported in ppm relative to CDCl3 ( 1 H: 7.26 and 13 C: 77.16) and coupling constants J are given in Hz. High resolution mass spectra (HRMS) were obtained on a Thermo LTQ-Orbitrap XL with ESI source.

Experimental Section

Synthesis of 1-(diphenylphosphino) polyaromatic (1, 20-22).

To a solution of 1-bromoaryl (1 equiv, 7.8 mmol) in dry diethyl ether (40 ml) cooled below -78 C, n-BuLi (1.56 M in hexane, 1.2 equiv, 7.8 mmol) was added dropwise by syringe, After 10 min, chlorodiphenylphosphine (1.2 equiv, 7.8 mmol) was added. The reaction mixture was allowed to warm to room temperature after 30 min stirring at -0 C in an iced water bath. The solution was stirred for 12 h at room temperature. The crude compound was purified through a flash chromatography packed with silica gel eluted using a mixture CH2Cl2:hexane (1:2) and afforded the corresponding 1-(diphenylphosphine)aryl.

Synthesis of 1-(diphenylphosphino) pyrene (1).

As a white solid (75%, 2.2 g) 1 H NMR (500 MHz, CDCl3): δ (ppm) = 8.77 (dd, J = 4.8 and 9.2 Hz, 1H), 8.23-8.17 (m, 2H), 8.13-7.98 (m, 5H), 7.55 (dd, J = 4.4 and 7.9Hz, 1H), 7.39-7.30 (m, 10H). 31 P{ 1 H} NMR (202 MHz, CDCl3): δ (ppm) = -13.9 (s).

Synthesis of the arylated 1-polyaromatic phosphines (2-19, 23-26

). An oven-dried Schlenk tube equipped with a magnetic stirring bar was charged with 1-PAH phosphine (pyrene: 0.5 mmol, 1 equiv, 194 mg), aryl bromide (1.5 equiv), K3PO4 (1.5 mmol, 3 equiv, 318 mg), and [Rh(COD)2]BF4 (0.025 mmol, 5 mol%, 10 mg), in trifluoromethylbenzene (0.16 M, 3 ml). The mixture was stirred at reflux under argon during 18 h. After extraction using a CH2Cl2/H2O mixture, the organic layer was concentrated in vacuum. The crude product was purified by column chromatography on silica using as eluent a mixture heptane:dichloromethane (4:1).

1-(diphenylphosphino)-10-(4-methoxyphenyl) pyrene

(2): as a yellow solid (70%, 172 mg) 1 6,133.8,133.6,133.4 (d,JPC = 28.0 Hz),131.9,131.8 (d,JPC = 6.9 Hz),131.6,131.4,130.5,128.2 (d,JPC = 6.4 Hz),128.1,128.1,127.8,126.3,126.2

1-(diphenylphosphino)-10-(4-methylphenyl) pyrene (3):

as a yellow solid (90%, 214 mg) 1 H NMR (500 MHz, CDCl3): δ (ppm) = 8.11 (t, J = 7.9 Hz, 2H), 8.04 (d, J = 8.9 Hz, 1H), 8.00-7.95 (m, 3H), 7.93 (d,J = 7.6 Hz,1H),7.77 (dd,J = 4.0 and 7.9 Hz,1H),8H), 7.05 (t, J = 6.9 Hz, 4H), 6.94 (d,J = 7.7 Hz,2H),2.38 (s,3H). 31 P{ 1 H} NMR (202 MHz, CDCl3): δ (ppm) = -8.6 (s). 13 C NMR (125 MHz, CDCl3): δ (ppm) = 141.2 (d,JPC = 5.4 Hz),140.5 (d,J = 4.8 Hz), 140.0 (d,JPC = 17.2 Hz),136.7,135.7,135.7 (d,JPC = 21.6 Hz),133.7,133.6,133.3 (d,JPC = 30.0 Hz),131.9,131.6,131.3,130.5 (d,JPC = 6.9 Hz),130.4,128.7,128.1 (d,JPC = 6.2 Hz),128.1,128.0,127.7,126.3,126.2 (d,JPC = 5.2 Hz),125.4,125.4 (d,JPC = 29.4 Hz) 4): as a yellow solid (60%, 189 mg) 1 H NMR (500 MHz, CDCl3): δ (ppm) = 8.17 (d,J = 7.4 Hz,1H), 8.15 (d, J = 5.9 Hz, 1H), 8.09 (d,J = 8.8 Hz,1H),4H),7.76 (dd,J = 4.1 and 8.0 Hz,1H),16H), 7.10 (t, J = 6.8 Hz, 4H), 7.02 (t, J = 6.9 Hz, 2H), 6.96 (d,J = 8.4 Hz,2H). 31 P{ 1 H} NMR (202 MHz, CDCl3): δ (ppm) = -7.6 (s). 13 C NMR (125 MHz, CDCl3): δ (ppm) = 148. 0,147.0,140.2 (d,JPC = 4.4 Hz),140.1 (d,JPC = 18.1 Hz),138.6 (d,JPC = 5.5 Hz),135.4 (d,JPC = 4.7 Hz),135.3,133.8,133.7,133.5 (d,JPC = 28.4 Hz),131.9,131.5 (d,JPC = 7.3 Hz),131.5,131.4,130.4,129.3,128.3 (d,JPC = 6.3 Hz),128.1,127.8,126.3,126.2 (d,JPC = 4.7 Hz),125.4 (d,JPC = 22.9 Hz),125.4,124.4,124.2 (d,JPC = 1.7 Hz), 124.0, 122. 198.0,149.2 (d,JPC = 4.9 Hz),139.4 (d,JPC = 5.6 Hz),139.2 (d,JPC = 15.9 Hz),135.9,135.6,135.1 (d,JPC = 23.1 Hz),133.7,133.5,132.8 (d,JPC = 26.7 Hz),132.0,131.7,131.3,130.6 (d,JPC = 7.1 Hz),130.0,128.3 (d,JPC = 6.1 Hz),128.3,128.3,128.2,127.7,126.5,126.2 (d,JPC = 5.7 Hz),125.9,125.7,(d,JPC = 32.8 Hz) 6): as a yellow solid (70%, 186 mg) 1 H NMR (500 MHz, CDCl3): δ (ppm) = 8.21 (d,J = 7.4 Hz,1H),8.13 (d,J = 8.1 Hz,1H),8.12 (d,J = 8.9 Hz,1H),3H),7.94 (s,1H),7.78 (dd,J = 4.0 and 7.9 Hz,1H),4H),7.27 (t,J = 7.3 Hz,2H),7.21 (t,J = 7.4 Hz,4H),7.03 (t,J = 7.7 Hz,4H). 31 P{ 1 H} NMR (202 MHz, CDCl3): δ (ppm) = -9.1 (s). 18 F{ 1 H} NMR (470 MHz, CDCl3): δ (ppm) = -62.2 (s). 13 C NMR (125 MHz, CDCl3): δ (ppm) = 147.8 (d,JPC = 6.2 Hz),139.2 (d,JPC = 15.6 Hz),139.2 (d,JPC = 5.0 Hz),136.1,135.2 (d,JPC = 23.1 Hz),133.7,133.6,132.7 (d,JPC = 27.0 Hz),132.1,132.0,131.4,130.9 (d,JPC = 7.1 Hz),130.1,129.3 (q,JFC = 32.2 Hz),128.4,128.4 (d,JPC = 6.4 Hz),128.3,127.8,126.5,126.2 (d,JPC = 5.6 Hz), 126.0 (d,JPC = 33.5 Hz), 125.7 (q, JFC = 3.7 Hz), 125.6, 124.9 (q, JFC = 272. 0 Hz),124.3 (d,JPC = 1.5 Hz). HRMS + p ESI (m/z) [M+H] + calcd.: 531.14895, found: 531.14836. 159.1, 141.2 (d, JPC = 2.3 Hz), 139.8 (d, JPC = 18.0 Hz), 137.3, 135.9 (d, JPC = 5.4 Hz), 135.6, 135.4, 135.4, 135.0, 135.0, 134.0 (d, JPC = 20.8 Hz), 132.1 (d, JPC = 6.8 Hz), 130.9, 130.4, 128.8, 128.1 (d, JPC = 6.4 Hz), 125.3, 124.9, 113.0, 55.4. HRMS + p ESI (m/z) [M+Na]+ calcd.: 441.13787, found: 441.13769.

1-(diphenylphosphino)-10-(1-pyrene) naphthalene (26):

as a yellow solid (57%, 152 mg) 1 H NMR (500 MHz, CDCl3): δ (ppm) = 8.16 (d,J = 8.7 Hz,1H),.00 (m, 5H), 7.96 (t, J = 7.6 Hz, 1H), 7.90 (d,J = 7.8 Hz,1H),3H),7.49 (d,J = 8.5 Hz,1H),2H), 7.20 (t, J = 7.9 Hz, 1H), 7.17-7.09 (m, 3H), 6.83 (t, J = 7.4 Hz, 1H), 6.70 (t, J = 8.3 Hz, 2H), 6.64 (t, J = 6.9 Hz, 2H), 6.35 (t, J = 8.2 Hz, 2H). 31 P{ 1 H} NMR (162 MHz, CDCl3): δ (ppm) = -9.57 (s). 13 130.8,129.6 (d,JPC = 7.5 Hz),129.6 (d,JPC = 1.8 Hz), 128.0 (d,JPC = 6.2 Hz),128.0,127.7,127.7 (d,JPC = 2.6 Hz),127.3,127.0,126.0,125.8,125.6,125.1,124.9 (d,JPC = 1.7 Hz),124.7,124.1. HRMS + p ESI (m/z) [M+Na] + calcd.: 535.15916, found: 535.15814.

Synthesis of the rhodium complex A:

In an oven-dried Schlenk tube equipped with a magnetic stirring bar was charged with 1-pyrene phosphine (0.259 mmol, 1 equiv, 100 mg), the dimeric rhodium [RhCl2Cp*]2 (0.129 mmol, 0.5 equiv, 80 mg), and degassed before addition of CH2Cl2 (0.25 M, 10 ml). The solution was stirred at 60 °C under argon for 4 h. The solvent was removed in vacuum to give the corresponding rhodium complex as a reddish solid (99%, 145 mg). 1 H NMR (500 MHz, CDCl3): δ (ppm) = 8.77 (d, J = 9.5 Hz, 1H), 8.27 (d, J = 7.6 Hz, 1H), 8.21 (t, J = 8.1 Hz, 2H), 8.12 (dd, J = 8.7 and 17.5 Hz, 2H), 8.09-8.04 (m, 1H), 7.98 (d,J = 9.3 Hz,1H),3H),3H),2H), 1.23 (s, 15H). 31 P{ 1 H} NMR (202 MHz, CDCl3): δ (ppm) = 32.2 (d,JPRh = 144.6 Hz). Insolubility troubles precluded proper NMR, especially for 13 C NMR. 13 C NMR (125 MHz, CDCl3): δ (ppm) = 135. 0, 133.6, 133.5, 130.7, 129.7, 129.3, 129.2, 129.1, 128.1, 127.3, 126.7, 126.2, 124.3, 123.7, 9.1, 1.2. HRMS + p ESI (m/z) [M-HCl-Cl] + calcd.: 623.13694, found: 623.13590.

Synthesis of the rhodium metallacycle B:

An oven-dried Schlenk tube equipped with a magnetic stirring bar was charged with 1-pyrene phosphine (0.259 mmol, 1 equiv, 100 mg), the dimeric rhodium [RhCl2Cp*]2 (0.129 mmol, 0.5 equiv, 80 mg), KOAc (0.777 mmol, 4 equiv, 76 mg), and degassed before addition of CH2Cl2 (0.25 M, 10 ml). The solution was stirred at 60 °C under argon for 4 h. The solvent was removed in vacuum to give the corresponding rhodium complex, which was further purified through a flash chromatography packed with silica gel and eluted with a mixture of CH2Cl2:diethyl ether (9:1) and by crystallization operated using CH2Cl2 solution and slow addition of heptane as a reddish solid (80%, 129 mg). 1 H NMR (500 MHz, CDCl3): δ (ppm) = 8.40 (s, 1H), 8.32-8.24 (m, 3H), 8.21 (dt, J = 4.9 and 10. 4 Hz,3H),2H), 8.06 (t, J = 7.6 Hz, 1H), 7.58 (d, J = 5.1 Hz, 3H), 7.38 (t, J = 7.3 Hz, 1H), 7.30 (t, J = 8.4 Hz, 2H), 7.06-7.00 (m, 2H), 1.68 (s, 15H). 31 P{ 1 H} NMR (202 MHz, CDCl3): δ (ppm) = 66.4 (d,JPRh = 161 Hz). 13 C NMR (125 MHz, CDCl3): δ (ppm) = 164.5 (dd, J = 10.2 and 32. 1 Hz),151.0 (dd,J = 1.6 and 37.4 Hz),136.3 (dd,J = 1.0 and 44.6 Hz),135.8 (d,J = 1.4 Hz),135.7 (d,J = 10.8 Hz),133.6 (d,J = 2.1 Hz),133.2,132.5 (d,J = 9.8 Hz),132.1 (dd,J = 2.4 and 33.0 Hz),131.1,131.0 (dd,J = 2.4 and 133.0 Hz),129.6 (d,J = 47.0 Hz),129.3,128.4,128.4 (dd,J = 10.3 and 23.0 Hz),126.3,126.1,124.9 (d,J = 7.6 Hz),123.9,123.7 (d,J = 17.5 Hz),123.1,122.6,100.6 (dd,J = 3.2 and 4.8 Hz),9.3. HRMS + p ESI (m/z) [M-Cl] + calcd.: 623.13749, found: 623.13667.

Synthesis of the rhodium cationic metallacycle C: An oven-dried Schlenk tube equipped with a magnetic stirring bar was charged with metallacycle B (0.076 mmol, 1 equiv, 49.8 mg), 1-(diphenylphosphino) pyrene (1) (0.076 mmol, 1 equiv, 30.5 mg), KPF6 (0.152 mmol, 2 equiv, 28 mg), and degassed before addition of a solution MeOH/CH2Cl2 (1/1, 0.25 M, 3 ml). The solution was stirred at RT under argon overnight. The solvent was removed in vacuum to give the corresponding rhodium complex, which was further purified by crystallization operated using CH2Cl2 solution and slow addition of heptane as a reddish solid (60%, 46 mg). 1 H NMR (500 MHz, CDCl3): δ (ppm) = 8.77 (dd,J = 17.8,7.8 Hz,1H),8.51 (d,J = 7.6 Hz,1H),8.41 (d,J = 7.6 Hz,2H),8.36 (d,J = 8.9 Hz,1H),2H),8.28 (s,1H),2H),8.12 (d,J = 8.9 Hz,1H),3H),2H),7.67 (t,J = 7.9 Hz,1H),7.42 (m,4H),2H),7.23 (m,3H),6.51 (d,J = 9.5 Hz,1H),6.42 (t,J = 7.3 Hz,1H), 1.43 (t, J = 3.0 Hz, 15H). 31 P{ 1 H} NMR (202 MHz, CDCl3): δ (ppm) = 56.1 (dd, JPP = 38. 3 Hz,JPRh = 146.8 Hz), 32.6 (dd, JPP = 38 Hz, JPRh = 140 Hz), -133.5 (PF6, hept, JPF = 712 Hz). 13 C NMR (125 MHz, CDCl3): δ (ppm) = 140. 7,140.4,139.5 (d,JPC = 3.1 Hz),135.4 (d,JPC = 2.4 Hz),133.9,133.3,133.2,132.6 (d,JPC = 8.2 Hz),132.1,131.9,131.5 (d,JPC = 3.8 Hz),131.1,131.0,130.5 (d,JPC = 2.8 Hz),130.3,129.9,129.8,129.7,129.2 (d,JPC = 10.2 Hz), 129.1 (d,JPC = 3.2 Hz), 128.9 (d,JPC = 10.6 Hz),128.3 (d,JPC = 9.4 Hz),127.9,127.6 (d,JPC = 4.1 Hz), 127.5 (d,JPC = 16.1 Hz),126.9,126.8,126.7,125.8 (d,JPC = 8.2 Hz),125.2,124.3 (d,JPC = 16.7 Hz),124.1,123.7,122.8,106.2,31.1,9.7. HRMS + p ESI (m/z) [M-2H-e] + calcd.: 1009.25938, found: 1009.25943.

Synthesis of rhodium metallacycle D:

An oven-dried Schlenk tube equipped with a magnetic stirring bar was charged with the metallacycle B (0.026 mmol, 1 equiv, 100 mg), 4-bromoanisole (0.040 mmol, 1.5 equiv, 5 µl), K3PO4 (0.052mmol, 2 equiv, 11.0 mg), KPF6 (0.052 mmol, 2 equiv, 9.6 mg), and degassed before addition of CH2Cl2 (0.25 M, 10 ml). in trifluoromethylbenzene (0.16 M, 3 ml). The mixture was stirred at reflux under argon during 18 h. After extraction using a CH2Cl2/H2O mixture, the organic layer was concentrated in vacuum to give the corresponding rhodium complex, which was further purified by crystallization using a CH2Cl2 solution and heptane as a reddish solid (45%, 7 mg). 1 H NMR (500 MHz, CDCl3): δ (ppm) = 8.27 (s,1H),7H),8.08 (dd,J = 4.0,8.3 Hz,2H),7.98 (t,J = 7.6 Hz,1H),7.51 (m,J = 4.6,3H),1H),7.22 (td,J = 2.2 and 7.8 Hz,2H),6.94 (t, J = 10.9 Hz, 2H), 1.68 (s,15H). 31 P{ 1 H} NMR (202 MHz, CDCl3): δ (ppm) = 65.3 (d,JPRh = 161.7 Hz). 13 C NMR (125 MHz, CDCl3): δ (ppm) = 136.7, 135.9 (d,JPC = 10.6 Hz),133.6,133.1,132.6 (d,JPC = 9.8 Hz),131.1,130.9,129.8,129.3,128.6,128.3 (d,JPC = 7.3 Hz),128.2 (d,JPC = 6.7 Hz),126.4,126.1,124.8,124.8,123.8,123.1,122.6,100.6,31.1,9.6. HRMS + p ESI (m/z) [M-Br]+ calcd.: 623.13694, found: 623.13525.

Synthesis of the pyrenylphosphine selenides. [20] A round flask (50 ml) equipped with a magnetic stirring bar was charged with 50 mg (0.125 mmol) of phosphine and an excess of elemental selenium powder (1.25 mmol, 100 mg) in 20 ml of dichloromethane. The solution was stirred at room temperature overnight, and the mixture was filtrated on Celite and rinsed with dichloromethane. The solvent was removed under vacuum to give the corresponding selenide phosphine. 27): [20] as a yellow solid (99%, 57 mg) 1 131.3,131.1,130.8,130.5 (d,JPC = 2.8 Hz),129.5,128.4 (d,JPC = 15.8 Hz),128.1 (d,JPC = 12.3 Hz),127.2,126.9,126.7 (d,JPC = 10.5 Hz),126.4,126.0,126.0,125.4,124.0 (d,JPC = 14.2 Hz) 198.0,149.2 (d,JPC = 4.9 Hz),139.4 (d,JPC = 5.7 Hz),138.2 (d,JPC = 15.9 Hz),135.9,135.6,135.1 (d,JPC = 23.1 Hz),133.7,133.5,132.8 (d,JPC = 26.7 Hz),132.0,131.8,131.3,130.6 (d,JPC = 7.1 Hz),130.1,128.3,128.3,128.3,128.2,127.7,126.5,126.2 (d,JPC = 5.7 Hz),125.9,125.7 (d,JPC = 32.7 Hz) (d,J = 7.5 Hz,1H),3H),8.19 (d,J = 8.9 Hz,1H),5H),7.96 (t,J = 8.8 Hz,3H),7.70 (dd,J = 8.0 and 15.8 Hz,1H),7.45 (d,J = 9.3 Hz,1H),7.33 (t,J = 7.2 Hz,1H),6H),6.59 (d,J = 8.5 Hz,1H),6.18 (sb,2H),6.05 (sb,1H). 31 P{ 1 H} NMR (202 MHz, CDCl3): δ (ppm) = 38.3 ( 1 JPSe = 735 Hz). 13 C NMR (125 MHz, CDCl3): δ (ppm) = 138.7 (d,JPC = 5.5 Hz),137.6,135.9 (d,JPC = 8.7 Hz),135.0,134.0 (d,JPC = 4.7 Hz), 134.0 (d,JPC = 34.7 Hz), 132.5 (d,JPC = 9.9 Hz),131.3,132 (sb),131.1,131.0,130.7 (d,JPC = 2.8 Hz),130.5,130.4,130.0 (sb),129.8 (sb),129.2 (d,JPC = 3.0 Hz),128.2 (d,JPC = 12.2 Hz),127.5,127.3,127.2,127.0,127.0,126.6 (d,JPC = 10.4 Hz),126.6,126.3 (d,JPC = 13.2 Hz),125.9,125.4,125.3,125.2,124.8,124.7,124.5,123.9,123.4,123.3 (d,JPC = 13.0 Hz). HRMS + p ESI (m/z) [M+H] + calcd.: 667.10938, found: 667.10751. 1-(diphenylphosphino)-10-(4-methoxyphenyl) phenanthrene selenide (31): as a yellow solid (99%, 68 mg) 1 H NMR (500 MHz, CDCl3): δ (ppm) = 8.76 (d,J = 8.2 Hz,1H),8.72 (d,J = 8.4 Hz,1H),8.20 (d,J = 20.6 Hz,1H),7.77 (t,J = 7.7 Hz,1H),2H),7.59 (t,J = 7.4 Hz,1H),5H),2H),7.17 (td,J = 3.1 and 7.8 Hz,4H),6.15 (s,2H),3.89 (s,3H),3.75 (s,6H). 31 P{ 1 H} NMR (202 MHz, CDCl3): δ (ppm) = 40.0 ( 1 JPSe = 753 Hz). 13 C NMR (125 MHz, CDCl3): δ (ppm) = 152. 4,142.3 (d,JPC = 2.7 Hz),141.2 (d,JPC = 11.1 Hz),137.4,137.2,132.2 (d,JPC = 8.0 Hz),131.8,131.7,130.9,130.5 (d,JPC = 2.8 Hz), 130.0 (d,JPC = 15.5 Hz),129.6,129.4,128.8,128.3 (d,JPC = 6.3 Hz),128.2,128.0 (d,JPC = 12.4 Hz),127.6,126.8,123.0,122.1,108.0,60.9,55.8. HRMS + p ESI (m/z) [M+H] + calcd.: 549.08865, found: 549.08871. [22d] A round flask (50 ml) equipped with a magnetic stirring bar was charged with 100 mg of phosphine (0.17 mmol) and 50 mg of gold precursor [AuCl(SMe2)] (0.17 mmol) in 5 ml dichloromethane. The solution was stirred at room temperature overnight, and the mixture was filtrated on Celite and washed with dichloromethane. The solvent was removed under vacuum to give the corresponding complex. Crystallization was operated using CH2Cl2 solution, and slow addition of heptane in the case of complex G. Au(I)Cl complex (E) stabilized by 1-(diphenylphosphino)-10-(4-methoxyphenyl) pyrene (2): as a yellow solid (99%, 116 mg) 1 H NMR (500 MHz, CDCl3): δ (ppm) = 8.31 (d,J = 7.6 Hz,1H),8.26 (d,J = 8.6 Hz,2H),8.11 (t,J = 7.8 Hz,3H),8.01 (s,1H),7.77 (dd,J = 8.1 and 14.8 Hz,1H),7.47 (t,J = 6.4 Hz,2H),8H),7.11 (d,J = 8.0 Hz,2H),6.64 (d,J = 8.5 Hz,2H),3.89 (s,3H). 31 P{ 1 H} NMR (202 MHz, CDCl3): δ (ppm) = 35.2 (s). 13 C NMR (125 MHz, CDCl3): δ (ppm) = 159. 1,138.6 (d,JPC = 5.0 Hz),134.9 (d,JPC = 9.1 Hz),134.8 (d,JPC = 8.6 Hz),134.7 (d,JPC = 1.1 Hz),134.1,134.0,133.6 (d,JPC = 2.6 Hz),133.2,132.8,132.2,131.8 (d,JPC = 1.7 Hz),131.4 (d,JPC = 2.3 Hz),131.1 (d,JPC = 0.7 Hz),130.5,128.9 (d,JPC = 11.9 Hz),127.1 (d,JPC = 8.4 Hz),126.8,126.7 (d,JPC = 9.1 Hz),124.4 (d,JPC = 11.6 Hz),123.3,122.5,122.0,114.6,55.5 5): as a yellow solid (99%, 118 mg) 1 H NMR (500 MHz, CDCl3): δ (ppm) = 8.36 (d,J = 7.6 Hz,1H),2H),3H),8.09 (s,1H),7.81 (dd,J = 8.1 and 14.6 Hz,1H),7.67 (d,J = 8.2 Hz,2H),7.50 (t,J = 7.1 Hz,2H),10H),2.70 (s,3H). 31 P{ 1 H} NMR (202 MHz, CDCl3): δ (ppm) = 34.8 (s). 13 C NMR (125 MHz, CDCl3): δ (ppm) = 197. 9,146.7,137.9 (d,JPC = 5.3 Hz),135.5,135.1 (d,JPC = 8.7 Hz),134.1,134.1 (d,JPC = 3.6 Hz),134.0,133.7 (d,JPC = 2.6 Hz),132.1,131.7 (d,JPC = 2.4 Hz),131.6,131.1 (d,JPC = 0.8 Hz),130.7 (d,JPC = 1.7 Hz),130.2,130.0,129.1,129.1 (d,JPC = 12.1 Hz),127.4 (d,JPC = 10.2 Hz),127.3,124.2,126.7 (d,JPC = 9.2 Hz),124.8 (d,JPC = 11.4

1-(diphenylphosphino)pyrene selenide (

Synthesis of the Au(I)Cl complexes (E-G).

Scheme 3 .

 3 Scheme 3. Selective arylation of P-directing 1diphenylphosphine pyrene from functional aryl bromides.

Scheme 4 .

 4 Scheme 4. Selective arylation of other polyaromatic hydrocarbon diphosphines.

Scheme 6 .

 6 Scheme 6. Synthesis of the Rh(III) cationic metallacycle C and its 31 P NMR spectra (CDCl3, 202 MHz).

Scheme 7 .

 7 Scheme 7. Peri-C-H arylation of 1-diphenylphosphine pyrene with 4-bromoanisole using preformed Rh(III) complexes A-C. To better assess this proposal, the neutral Rh(III) metallacycle B was reacted with 1.5 equiv of 4bromoanisole in both the presence of K3PO4 and KPF6 (Scheme 8, top). After 18 h at reflux of PhCF3, no evolution towards the expected coupling product 2 was observed, nor the formation of cationic rhodium species, but instead the formation of a new brominated Rh(III) neutral metallacycle complex D in 45% yield ( 31 P NMR 65.3 ppm, 1 JPRh = 162 Hz) was achieved. In the solid state, the single crystals XRD analysis of D (Scheme 8, bottom) confirmed the conservation of the metallacycle structure with d C11-Rh = 2.065(2) Å and d P-Rh = 2.2631(6) Å (similar to values for B). In the structure, the chlorine atom has been replaced by a bromine with a d Rh-Br = 2.5222(4) Å (d Rh-Cl = 2.4025(5) Å for B).

Scheme 11 .

 11 Scheme 11. Selenation of 10-arylated pyrene phosphines 1, 2, 5, 15 and 23.

Scheme 12 .

 12 Scheme 12. Au(I)Cl complexes E, F and G stabilized by pyrenylphosphines 2, 5 and 15, respectively. Molecular structure of complex G (thermal ellipsoids at 30% probabilities, H atoms and one CH2Cl2 are omitted for clarity).For pyrenylphosphines 2 and 5, the reaction quantitatively leads to complexes E and F, respectively, and the complex G was obtained in 85% isolated yield by crystallization in a dichloromethane/heptane mixture. The single crystal XRD structure of G, beside a classical linear coordination of gold, revealed the conservation of phenyl/pyrenyl stacking interactions already evidenced from XRD of 15.

  H NMR (500 MHz, CDCl3): δ (ppm) = 8.20(d, J = 7.4 Hz, 1H), 8.15 (d, J = 5.9 Hz, 1H), 8.12 (d, J = 8.8 Hz, 1H), 3H), 7.96 (bs, 1H), 7.73 (dd, J = 4.0 and 7.9, 1H), 6H), 7.16 (d, J = 8.3 Hz, 2H), 7.04 (t, J = 6.5 Hz, 4H), 6.69 (d, J = 10.3 Hz, 2H), 3.82 (s, 3H). 31 P{ 1 H} NMR (202 MHz, CDCl3): δ (ppm) = -8.1 (s).13 C NMR (125 MHz, CDCl3): δ (ppm) = 159.2, 140.2 (d, JPC = 4.6 Hz), 140.1 (d, JPC = 17.4 Hz), 136.5 (d, JPC = 5.5 Hz), 135.7 (d, JPC = 21.0 Hz), 135.

  (d, JPC = 5.0 Hz), 125.3 (d, JPC = 28.2 Hz), 125.3, 124.1 (d, JPC = 1.0 Hz), 113.5, 55.4. HRMS + p ESI (m/z) [M+H] + calcd.: 493.17212, found: 493.17164.

  , 124.1 (d, JPC = 1.5 Hz), 21.5. HRMS + p ESI (m/z) [M-H] + calcd.: 475.16156

  7. HRMS + p ESI (m/z) [M+H] + calcd.: 630.23506, found: 630.23490. 1-(diphenylphosphino)-10-(4-acetylphenyl) pyrene (5): as a yellow solid (89%, 224 mg) 1 H NMR (500 MHz, CDCl3): δ (ppm) = 8.22 (d, J = 7.5 Hz, 1H), 8.16 (d, J = 7.4 Hz, 1H), 8.12 (d, J = 8.9 Hz, 1H), 8.09-8.00 (m, 3H), 7.96 (s, 1H), 7.79 (dd, J = 4.0 and 7.9 Hz, 1H), 7.71 (d, J = 8.2 Hz, 2H), 7.37 (d, J = 8.2 Hz, 2H), 7.27 (t, J = 6.7 Hz, 2H), 7.21 (t, J = 7.4 Hz, 4H), 7.03 (t, J = 7.1 Hz, 4H), 2.60 (s, 3H). 31 P{ 1 H} NMR (202 MHz, CDCl3): δ (ppm) = -9.2 (s). 13 C NMR (125 MHz, CDCl3): δ (ppm) =

  , 124.2 (d, JPC = 1.5 Hz), 26.8. HRMS + p ESI (m/z) [M-H] + calcd.: 503.15647, found: 503.15585.

  C NMR (125 MHz, CDCl3): δ (ppm) = 139.6 (d, JPC = 4.2 Hz), 139.4 (d, JPC = 17.1 Hz), 138.7 (d, JPC = 4.6 Hz), 138.4 (d, JPC = 18.3 Hz), 137.5, 136.4 (d, JPC = 21.2 Hz), 135.7 (d, JPC = 29.9 Hz), 135.0 (d, JPC = 4.7 Hz), 133.5 (d, JPC = 22.7 Hz), 133.4 (d, JPC = 24.0 Hz), 131.9, 131.6, 131.3 (d, JPC = 8.1 Hz), 131.2 (d, JPC = 12.1 Hz),

  P{ 1 H} NMR (202 MHz, CDCl3): δ = 38.8 ( 1 JPSe = 750 Hz). 13 C NMR (125 MHz, CDCl3): δ (ppm) = 139.3 (d, JPC = 4.4 Hz), 135.1, 134.9 (d, JPC = 7.1 Hz), 133.5 (d, JPC = 11.8 Hz), 133.0 (d, JPC = 6.2 Hz), 132.2, 131.9 (d, JPC = 10.1 Hz),

  , 123.5 (d, JPC = 0.7 Hz), 113.7, 55.3. HRMS + p ESI (m/z) [M+H] + Calcd.: 573.08865, Found: 573.08541. as a yellow solid (99%, 75 mg) 1 H NMR (500 MHz, CDCl3): δ (ppm) = 8.33 (d, J = 7.5 Hz, 1H), 8.30-8.09 (m, 6H), 8.03 (s, 1H), 7.55 (sb, 2H), 7.46 (dd, J = 7.8 and 13.2 Hz, 4H), 7.39 (t, J = 7.1 Hz, 2H), 7.31-7.23 (m, 6H), 2.64 (s, 3H). 31 P{ 1 H} NMR (202 MHz, CDCl3): δ = 38.70 ( 1 JPSe = 749 Hz). 13 C NMR (125 MHz, CDCl3): δ (ppm) =

  . HRMS + p ESI (m/z) [M-Cl] + calcd.: 689.130863, found: 689.130851.

Table 1 .

 1 Optimization

			of P-directed Rh-catalyzed arylation
	using 1-diphenylphosphine pyrene (1) and 4-bromoanisole as coupling partners. a)
	Entry	[Rh] (5 mol%)	Base (3 equiv)	Solvent (0.16 M)	Conv. (%)

Table 2

 2

	Species formed from C after
	16 h reaction (Scheme 9)

A2 is [Rh III Br2(Cp*)(

1

)]. a) Added KPF6 (2.0 equiv.); b) Unidentified products.

Table 2

 2 31 P NMR data (CDCl3, 202 MHz) for polyaromatic phosphines 1

, 2, 5, 15, 23 and

  their corresponding selenium products and complexes with Au(I)Cl. a)

	Ligand	31 P (ppm)	31 P=Se (ppm)	SSCC 1 JP,Se (Hz)	Au(I) / 31 P (ppm)
	1	-13.8	27: 31.7	722	-
	2	-8.1	28: 38.8	750	E: 30.2
	5	-9.2	29: 38.7	749	F: 34.8
	15	-9.5	30: 38.4	735	G: 31.0
	23	-6.8	31: 39.5	746	-

a) Benchmark SSCC 1 JP,Se value for (Se)PPh3 = 730 Hz; 31 P NMR (CDCl3, 162 MHz) for [(

  2074196 contain the supplementary crystallographic data for the paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/cif, or by emailing data_request@ccdc.cam.ac.uk, or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44 1223 336033.

	Accession Codes. 2: 2074194; 15: 2074195; CCDC A:
	2109009; CCDC B: 2074193; CCDC D: 2109022; CCDC
	G:

-(diphenylphosphino)-10-(4-methoxyphenyl) pyrene selenide (28): as

  H NMR (500 MHz, CDCl3): δ (ppm) = 8.83(d, J = 9.3 Hz, 1H), 8.23 (dd, J = 7.6 and 14.2 Hz, 2H), 8.16 (d, J = 8.9 Hz, 1H),.00 (m, 4H), 7.91 (dd, J = 7.4 and 13.7 Hz, 4H), 7.61 (dd, J = 8.0 and 14.9 Hz, 1H), 7.54 (t, J = 7.1 Hz, 2H), 7.47 (t, J = 7.5 Hz, 4H).31 P{ 1 H} NMR (202 MHz, CDCl3): δ (ppm) = 31.7 ( 1 JPSe = 722 Hz). 1a yellow solid (99%, 71 mg)1 H NMR (500 MHz, CDCl3): δ (ppm) = 8.24-2.18 (m, 4H), 8.08 (t, J = 8.6 Hz, 2H), 8.02(t, J = 7.6 Hz, 1H), 7.91 (s, 1H), 7.44 (dd, J = 7.7 and 13.1 Hz, 4H), 7.31 (t, J = 7.2 Hz, 2H), 4H), 7.03 (sb, 2H), 6.50 (sb, 2H), 3.80 (s, 3H).31

  , 124.2 (d, JPC = 1.5 Hz), 26.8. HRMS + p ESI (m/z) [M+Na] + calcd.: 607.07059, found: 607.07010.

	1-(diphenylphosphino)-10-(1-pyrenyl) pyrene selenide
	(30): as a yellow solid (99%, 82 mg) 1 H NMR (500 MHz,
	CDCl3): δ (ppm) = 8.98 (s, 1H), 8.35

Acknowledgements

This work was supported by the CNRS, the Universite ́ de Bourgogne, the Conseil Re ́gional Bourgogne-Franche-Comte ́, the ISITE-BFC program (I-SITE UB180013.MUB. IS_SmartTZ, for JR), and the "Fonds Europe ́en de De ́veloppement Re ́gional" (FEDER). This work was also partly funded by the French "Agence Nationale de la Recherche" via the ANR-JCJC program 2018 FIT-FUN (ANR-18-CE07-0015, for JR and grant for CS) and the ANR PRC program 2020 CARAPH (ANR-20-CE07-0001-01, for JCH). Thanks is due to the PACSMUB platform for analyses (SATT SAYENS).


Yi Yu
email: yi.yu@isep.fr

Lina Mroueh
email: lina.mroueh@isep.fr

Shuo Li
email: shuo.li@isep.fr

Michel Terré
email: michel.terre@cnam.fr

Multi-Agent Q-Learning Algorithm for Dynamic Power and Rate Allocation in LoRa Networks

Keywords: LPWAN, LoRa, Internet of Things (IoT), resource allocation, machine learning, Reinforcement Learning, multi-agent Q-learning, energy efficiency

In this paper, we consider a Low Power Wide Area Network (LPWAN) operating in a licensed-exempt band. The LoRa network provides long-range, wide-area communications for a large amount of objects with limited power consumption. In terms of link budget, nodes that are far from the collector suffer collisions caused by nodes that are close to the collector during the data transmissions. Chirp Spread Spectrum (CSS) modulation is adopted by assigning different Spreading Factors (SF) to active sensors to help reduce destructive collisions in LoRa network. In order to improve the energy efficiency and communication reliability, we propose an application of multi-agent Q-learning algorithm in the dynamic allocation of power and SF to the active nodes for uplink communications in LoRa. The main objective of this paper is to reduce power consumption of the uplink transmissions and to improve the network reliability.

I. INTRODUCTION

Reinforcement Learning (RL) is a branch of Machine Learning (ML) techniques which is of great interest because of its large number of practical applications in control engineering, multi agent systems and operation research. It is an efficient and dynamic decision-making tool.

Thanks to the environment-agent interaction scheme in RL, it enables a system to be controlled in such a way as to maximize a numerical measure of performance that expresses a long-term objective [START_REF] Szepesvári | Algorithms for reinforcement learning[END_REF]. It shows great potential for system controls in real engineering cases.

In particular, we are interested in this paper in the Qlearning which is a popular RL algorithm. It adopts off-policy Temporal-Difference (TD) methods for agents to learn how to act optimally to control problems. Considering multi-agent systems in a variety of fields, including robotics, distributed control, and telecommunications, multi agent Q-learning algorithm gives outstanding performance in decision-making problems for these complicated scenarios [START_REF] Bu | A comprehensive survey of multiagent reinforcement learning[END_REF]- [START_REF] Kaisers | Frequency adjusted multi-agent q-learning[END_REF]. Based on it, we propose in this paper to apply it to the SF and power allocation problems in LPWAN.

LPWAN is well suited for massive IoT network deployment as it can provide long-range, wide-area, low-power consumption communications for thousands of connected devices. There are different types of low power wide area communication technologies on the market, i.e unlicensed LoRa [START_REF] Goursaud | Dedicated networks for IoT : PHY / MAC state of the art and challenges[END_REF]- [START_REF] Sornin | Lorawan specification[END_REF] and Sigfox [START_REF]Sigfox official website[END_REF] technologies and licensed NB-IoT technology [START_REF]Cellular system support for ultra low complexity and low throughput internet of things[END_REF], [START_REF] Ratasuk | NB-IoT System for M2M Communication[END_REF], etc. In this paper, we focus on LoRa network.

LoRa technology uses Chirp Spread Spectrum modulation which allocates spreading factors to each active sensor node to mitigate destructive collisions in the overall network. Higher spreading factors can protect the devices from the interference caused by signals transmitted simultaneously from devices closer to the collector. To improve network reliability, we need to assign different spreading factors in an adaptive way to the active sensors.

In LPWAN, energy efficiency always attracts a lot of attention. Normally, a single IoT module is expected to serve for around ten years with very low energy consumption. By reducing power consumption during each message transmission for uplink communications in LPWAN, it can improve the lifetime of IoT devices and offer remarkable financial benefits. In this paper, we fully consider the energy efficiency by select distinct transmit power values for each sensor node for uplink communications to achieve a better power control solution for LoRa network.

Some relative work has been done by using different methods. For example, in [START_REF] Reynders | Power and spreading factor control in low power wide area networks[END_REF], a power, channel and spreading factor selection algorithm is proposed to avoid nearfar problem and decrease the packet error rate in LoRa network. A distributed learning approach is introduced for self-organized LoRa networks in [START_REF] Azari | Self-organized low-power iot networks: A distributed learning approach[END_REF]. Inspired by them, we use multi-agent Q-learning approach to solve the concerned power and SF allocation problems dynamically.

The rest of the paper is organized as following. An unlicensed LoRa network model is defined in section II. Then, we review in Section III the multi-agent Q-learning scheme. Next, in section IV, multi-agent Q-learning algorithm is applied to solve the problems of SF selection and power allocation in LoRa network. In section V, the performance evaluation in resource allocation with respect to network reliability and power efficiency is presented. Finally, section VI concludes the paper.

II. LORA NETWORK MODEL

In this section, we consider a single unlicensed LoRa network cell. The cell coverage radius is R. Assume the collector is located in the cell center which is marked as origin o. Number of N active sensor nodes are randomly distributed in the given cell. Let |x| denotes the distance between the active sensor node x and the collector o. The out-of-cell interference is ignored in our case. Considering the uplink transmission of LoRa network, each active sensor has 5 different choices for the transmission power P t : 2, 5, 8, 11 and 14 dBm [START_REF] Reynders | Power and spreading factor control in low power wide area networks[END_REF]. The sensor nodes and the collector have omnidirectional antennas with 0 dBi of antenna gains. For the sensor node x, the received power P r at the collector is:

P r (x) = P t α|x| -β A f , (1)
where α and β are respectively the attenuation factor and the path-loss exponent that are computed from Okumura-Hata model. A f is the random fading coefficient with Rayleigh distribution.

The LoRa network adopts CSS modulation, which is a spread-spectrum technology [START_REF]Lora official website[END_REF], [START_REF]Semtech official website[END_REF], [START_REF] Vangelista | Frequency shift chirp modulation: The lora modulation[END_REF]. According to [16], CSS modulation has several key properties, it offers high robustness and resists the Doppler effect while having a low latency.

In LoRa network, the active sensors located far away from the collector suffer the collision caused by sensors that are closer to the collector. This CSS spreading technique can protect the cell edge sensor nodes from the nodes in the proximity of the network collector. It features 6 possible spreading factors (SF = 7 to 12) to the active sensors according to the receiver sensitivity and hence by the threshold communication ranges. Table I shows the corresponding SINR threshold ranges according to the values of SF with the sub-bandwidth equal to 125 kHz. With CSS modulation, each symbol transmits SF bits, has a time duration T and occupies a bandwidth B, we have

2 SF = T × B (2)
For the same sub-bandwidth, the high spreading factor transmits longer time on air which means the communication distance increases. Concern the data rate R b (bits/s),

R b = SF × B 2 SF 4 (4 + CR) (3)
with CR being the code rate. A high spreading factor better prevents transmission errors, but at the cost of a reduced data rate. LoRa network uses high spreading factors for the weak signal or the signal suffering high interference. γ SF (dB) -7.5 -10 -12.5 -15 -18 -21

In this paper, our objective is to manage the resource allocation in a dynamic manner. Transmission power and SF are allocated to each active sensor node to ensure the overall network communications. We aim at increasing the communication reliability for each sensor while keeping the energy consumption as low as possible. In LoRa network, the access to the shared medium is managed by Aloha protocol. The transmitted signals on the same sub-medium interfere with each other. The collector receives in addition to its intended attenuated signal.

Assume that Φ i denotes the set of interfering nodes. For an intended signal sent by node x, the interferer y ∈ Φ i . The power of the interference is weighted by a correlation factor denoted by c(x, y). The expression of the interference is then,

I x ≈ y∈Φi c(x, y)α|y| -β A f P t (y), (4)
where P t (y) is the transmit power of interferer y. The inter-correlation factor c(x, y) is calculated in [START_REF] Yi | Adaptive multi sub-bands allocation in lora networks[END_REF]. Table II presents the c(x, y) values according to different spreading factors of the transmitter x and the receiver y with the subbandwidth of 125 kHz. The received SINR for the sensor node x at the given collector o is calculated as follows,

SINR x = P t α |x| -β A f N 0 + I x , (5)
with N 0 = KT B being the additive thermal noise. K is the Boltzmann constant, T is the noise temperature and B is the bandwidth.

III. MULTI-AGENT Q-LEARNING ALGORITHM

Reinforcement Learning has achieved many successes in decision-making systems. Figure 1 demonstrates the general RL framework. The environment and the agent can have interaction and learn from it to make decisions. S is the set of possible environment states. At time t, observing the environment, a state s ∈ S is observed and passed to the agent. Then, according to the policy π, the agent decides to take action a ∈ A, where A is the set of actions available for state s. As a is performed, the agent earns a reward r(s, a) and the environment turns to a new state s . Since the agent determines a policy π, the choose of action a in a given state s can be described as π(s) = a. To evaluate the performance of policy π, the state-action value function Q(s, a) is introduced as follows:

Q(s, a) = E [G t |s t = s, a t = a] , (6)
where G t is the discounted future cumulative reward,

G t = r t + γr t+1 + γ 2 r t+2 + • • • + γ n-t r n , (7)
with γ as the discount factor which is a constant and γ ∈

[0, 1].
The objective of reinforcement learning is to find the best policy π that maximizes the state-action value function which can be described as:

π (s) = arg max a∈A Q(s, a). (8)
A. Q-learning Function Q-learning uses a non-deterministic policy, i.e. a function mapping each state to a set of actions so that the agent can choose one among them, while it is based on a sampling of other policies instead of the current policy alone. The Qlearning process keeps an estimate and an update of the Qfunction, it can be written as follows:

Q(s, a) = Q(s, a) + σ r(s, a) + γ max a∈A Q (s , a ) -Q(s, a) , (9)
where σ ∈ [0, 1] is a learning rate.

B. Multi-Agent Q-Learning Algorithm

Assume that there are n agents in the system. At a given time t, action a = {a 1 , a 2 , ..., a n } is executed by all the agents with a i ∈ A being the action chosen by the i-th agent. Observing the environment, a current state s ∈ S and a total reward r(s, a) are obtained and passed to all the agents. Based on state s and reward r, each agent updates its own Q-learning function and chooses a new action a i for next operation separately. Then, the action a = {a 1 , a 2 , ..., a n } is executed. The workflow of multi-agent Q-learning keeps the same as the single-agent Q-learning algorithm. But the state and reward information are distributed to all the agents and then a decision is made by each agent independently.

IV. SF ALLOCATION AND POWER CONTROL WITH MULTI-AGENT Q-LEARNING ALGORITHM

The framework of multi agent Q-learning is presented in section III. In this section, we try to solve the problems of SF allocation and power control in a licensed-exempted LoRa network with multi-agent Q-learning algorithm. According to the network model mentioned in section II, for each active sensor node connected to the collector o, it must be assigned one SF value among 6 possible spreading factors [START_REF]Lora official website[END_REF][START_REF] Sornin | Lorawan specification[END_REF][START_REF]Sigfox official website[END_REF][START_REF]Cellular system support for ultra low complexity and low throughput internet of things[END_REF][START_REF] Ratasuk | NB-IoT System for M2M Communication[END_REF][START_REF] Reynders | Power and spreading factor control in low power wide area networks[END_REF] and one transmit power value out of 5 achievable transmit power values including [START_REF] Bu | A comprehensive survey of multiagent reinforcement learning[END_REF][START_REF] Kaisers | Frequency adjusted multi-agent q-learning[END_REF][START_REF] Sornin | Lorawan specification[END_REF][START_REF] Ratasuk | NB-IoT System for M2M Communication[END_REF][START_REF]Semtech official website[END_REF] dBm. Set the initial observation state s.

4:

for t = 1 : until s is a terminal state do 5:

For each agent: with the probability select a random action a i = (SF, P t ), otherwise select a i = max a Q i (s, a i );

6:

Execute action a = {a 1 , a 2 , ..., a n } in emulator and observe reward r and state s ; If s is a terminal state, set the value function target y i to r(s, a); Otherwise set it to:

y i = r(s, a) + γ max a Q i (s , a i ); 8:
Compute the critic parameter update

∆Q i = y i - Q i (s, a i ); 9:
Update the critic using the learning rate σ:

Q i (s, a i ) = Q i (s, a i ) + σ * ∆Q i ; 10:
Set the observation state s to s 11: end for 12: end for 13: return Results Following the multi-agent Q-learning algorithm, the LoRa network model is the environment that provides the state s and reward r information for the agents. We set n = N agents for the system. Each agent corresponding to an active sensor node. A single agent here is a Q-learning function which selects an action for an active node. The action is a pair of SF and P t values with probability or selects an action with probability (1 -) by maximizing the Q value,

a i = arg max a Q i (s, a i ) .
After the execution of the action a i , the agents obtain the new state information s → s and a reward r. Considering the network reliability and the power efficiency, the reward r i for the i-th sensor node is calculated as follows:

r i = δ i (t) • ϕ + δ i (t) • (1 -ϕ) • P t max P t . ( 10
)
where ϕ is a design parameter offering a tradeoff between the network reliability and energy efficiency. P t is the transmit power for the i-th sensor node. δ i (t) ∈ {0, 1} which indicates whether the i-th sensor has a stable connection to the collector o or not. With a given SF value SF i and a transmit power P t for the i-th sensor node, we can calculate the SINR i on the collector side for each sensor node. In table I, the SINR threshold γ SF for different SF values is given in detail. Hence, if SINR i γ SFi , the i-th node can successfully send the message to the collector. Otherwise, the transmission fails.

δ i (t) = 1 SINR i γ SFi 0 SINR i < γ SFi ( 11
)
The state of the environment after the execution of the action a is the decimal value corresponding to a binary number consists of all the δ i . For example, if the number of agents n is equal to 5. There are 2 5 = 32 states ranging from 0 to 31. At time t, if {δ 1 δ 2 ...δ 5 } = {10110}, then the state equals 22 which is the decimal value for this binary number. Obviously, the terminal state is when all the δ i = 1. In case n = 5, the terminal state s = 31.

The total reward for the action a is then calculated as follows:

r(s, a) = 1 N N i=1 r i . ( 12
)
Algorithm 1 demonstrates the selection of SF and transmit power for the active sensors in LoRa with multi-agent Qlearning algorithm.

V. NUMERICAL RESULTS

We consider a single LoRa network cell with coverage radius of R = 10 km. Assume that N sensor nodes are activated simultaneously with random positions. The sensor nodes and the collector have omnidirectional antennas. Nodes transmitting in the same frequency band generate additive interference with power. The power of the additive thermal noise is N 0 = KT B with K = 1.379×10 -23 W Hz -1 K -1 , T = 290 K and B = 125 kHz. The system parameters are shown in detail in Table III.

We assume without loss of generality a Q-learning algorithm with 5 agents. Set the learning rate σ = 0.9. Following Algorithm 1, we can obtain the expected SF and transmit power values for all 5 nodes after the training. Figure 2 shows the distribution of active nodes for 500 times of simulation with 5 agents. There are 30 different colors which represent 30 pairs of SF and P t values. We can notice that the joint allocated SF and transmission power is made in a dynamic way depending on the instantaneous network configuration. To make a comparison with our multi-agent Q-learning algorithm, we introduce a static allocation algorithm in which the whole cell is divided into 30 rings. Within each ring, a static SF and P t is attributed to the active nodes depending on its location. Low SF and low power are attributed to the nodes in the proximity of the collector.

Figure 3 illustrates the Cumulative Distribution Function (CDF) of the SINR. Multi-agent Q-learning algorithm outperforms the static one which means the former has higher reliability then the latter. Meanwhile, it also achieves higher data rate during the transmission as shown in Figure 4.

Figure 5 presents the comparison of the CDF of transmit power for all sensor nodes based on two different algorithms. Our multi-agent Q-learning algorithm shows large improvements in the energy efficiency. Using the multi-agent Qlearning algorithm, the average value of the transmit power for all active sensors is equal to 4.81 dBm while for the static algorithm it is 8.66 dBm.

VI. CONCLUSION

In this paper, we have considered the unlicensed LPWAN LoRa network with random Aloha access to the network. We have proposed a multi-agent Q-learning algorithm to jointly allocate a SF and power in the uplink of LoRa network. Each agent has interactions with the environment and based on that, it updates dynamically the policy. We have also evaluated its reliability and energy efficiency performance and compared it with a static allocation algorithm. The simulation results show the advantages of our Q-learning algorithm with respect to SINR, data rate and transmit power.

Algorithm 1

 1 Multi-agent Q-learning algorithm for SF allocation and Power Control in LoRa Network Input: Positions of N active sensor nodes Output: SF and transmit power values for each active sensors 1: Sort N sensor nodes by distance to the collector from near to far; Set n = N agents and generate n Q-learning functionQ i (S, A), i ∈ [1, n]; Initialize each Q-learning function Q i (S, A), i ∈ [1, n]with random values; 2: for episode = 1, M do 3:

Fig. 2 .Fig. 3 .

 23 Fig. 2. The distribution of active sensor nodes in a single cell with different choices of SF and transmit power

Fig. 4 .

 4 Fig. 4. The Cumulative distribution function of the Data Rate

Fig. 5 .

 5 Fig. 5. The Cumulative distribution function of the Transmit Power

TABLE I SINR

 I THRESHOLD γ SF WITH SUB-BANDWIDTH B = 125 KHZ

	SF	7	8	9	10	11	12

  Urban path-loss model α = 10 -10.07 , β = 3.52

	TABLE III
	NETWORK PARAMETERS
	Parameter	Value
	Carrier frequency	868 MHz
	Sub-bandwidth	B = 125 kHz
	Coverage radius	R = 10 km
	Transmit power	[2, 5, 8, 11, 14] dBm
	Spreading factor	[7, 8, 9, 10, 11, 12]
	Collector height	30 m
	Device average height	1 m
	Antenna gain	0 dBi