Dr Petra Dunkel

Dr Anna Barosi

Dr Hamid Dhimane

François Maurel
email: maurel@univ-paris-diderot.fr

Dr Peter I Dalko
email: peter.dalko@parisdescartes.fr

Francois Maurel

François Maurel

Dr F Pr

Maurel

Photoinduced Electron-Transfer (PET) Mediated Fragmentation of Picolinium-Derived Redox Probes

Keywords: Caged compounds, Electron transfer, Redox chemistry, Ab initio calculations, Probes, Nonlinear photonics

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Introduction

Light-sensitive probes ("caged compounds") became popular tools in cellular biology, physiology and neurosciences and are used for the controlled release of a variety of biologically relevant substrates. 1 Although sensitized probes, in which the light-harvesting and working elements are functionally disconnected, allow considerably larger flexibility in the optimization process, somewhat surprisingly only modest interest has been paid for the development of such probes. 2 Redox-gated systems are among those, developed essentially around the 4-picolyl family. 3 The reduction potentials of the parent phenacyl (Ered = -2.20 V vs SCE) and 4-picolyl esters (Ered = -2.62 V vs SCE) were improved by N-alkylation of the heterocycle (N-methyl-4-picolinium: Ered = -1.10 V vs SCE), and also by adding electron-withdrawing groups to the pyridinium ring (2-cyano-picolinium esters Ered ≈ -0.50 V vs SCE). 4 In parallel, N-alkylpicolinium (NAP) + mediator systems with ketocoumarin dyes, 5 gold nanoparticles 6 and tris(bipyridyl)ruthenium(II) (Ru(bpy)) dyes 4 were developed for the liberation of carboxylic acids, amino acids, phosphates, primary aliphatic and aromatic amines, under redox conditions. 7 Liu et al. described a release system composed by an electron donor, typically L-cysteine or DTT, a semiconductor quantum dot electron shuttle and NAP ester prodrug as acceptor. 8 Most of the biological applications require water-soluble probes with controlled, covalently linked donor-acceptor structure, however. Surprisingly the use of the tethered N-alkyl picolinium phenylacetate -carbazole dyad turned inefficient. 9,10,11 Although the unlinked analogues released the carboxylate ligands, in the presence of an appropriate sensitizer with high efficiency, the tethered probe was inert even under prolonged irradiation. 9,12 As no charge-transfer intermediates were detected in laser flash photolysis experiments, neither significant fluorescence was observed, authors suggested that the competing back electron transfer was the main deactivation path that occurred faster than the bond cleavage. 9 Also, a fluorene-sensitized picolinium derivative sensitive to two-photon activation has been prepared by the Anderson group. 13,14 The construct suffered, however, hydrolytic instability and low uncaging efficiency, presumably due to the fast back electron transfer, as was hypothesized in the earlier experiment.

In the wake of our program on the development of lightsensitive probes, 15 we were interested in examining the perspectives and pertinence of picolinium derivatives as redoxsensitive elements in covalently linked electron donor-acceptor dyads under PET conditions. Here we wish to disclose a first systematic study on the NAP platform.

Results and Discussion

N-Methyl picolinium phenylacetates 7, 9 and 11 (Scheme 1, path A) were prepared by reduction of the corresponding pyridine carboxaldehydes followed by acylation using phenylacetyl chloride, and N-methylation of the resulting picolines (compounds 1, 3 and 5) in the presence of methyl triflate (for further details see the Experimental section). In turn, compounds 8, 10 and 12 were prepared by addition of methylmagnesium bromide to the corresponding aldehydes followed by acylation, using phenylacetyl chloride and quaternarization in the presence of methyl triflate (Scheme 1, path B). Redox potentials of the prepared phenylacetates were measured by cyclic voltammetry (Figure 1). Electrochemical experiments were performed at c = 1.0 mM concentration of the picoliniums, in dry ACN with [Bu4N][PF6] as the supporting electrolyte (scan rate: 100 mV/s). Glassy carbon working and platinum auxiliary electrodes were used and the potential was The ET ability of compounds 7-12 was analysed by DFT calculations as well. 16,17 Redox potentials were calculated at the most stable conformations according to the thermodynamic cycle depicted in Scheme 2. Scheme 2. The thermodynamic cycle of the one-electron reduction of picolinium probes in acetonitrile (ACN) solution.

The standard Gibbs free energy of the overall reaction in solution can be expressed as follows:

Δ𝐺 !"#$% !"# = Δ𝐺 !"#$% !"# -Δ𝐺 !"# 𝑀 ! + Δ𝐺 !"# 𝑀 Δ𝐺 !"#$% !"# = Δ𝐺 !"#$% !"# + ΔΔ𝐺 !"#
where

Δ𝐺 !"#$% !"# = 𝐺 !"# 𝑀 -𝐺 !"# (𝑀 ! ) and ΔΔ𝐺 !"# = Δ𝐺 !"# 𝑀 -Δ𝐺 !"# 𝑀 !
and the redox potential is related to Δ𝐺 !"#$% !"# as

Δ𝐺 !"#$% !"# = -𝐹𝐸 !"#$% °
where F is the Faraday constant, 23.06 kcal•mol -1 •V -1 . The standard hydrogen electrode potential, VSHE was taken as 4.43 eV. 18 Experimental values were compared in Figure 1.

Noteworthy, calculated values correlate well with the experimental data (Figure 1). The UV-Vis spectra of 7 (c = 0.1 mM) did not show appreciable solvatochromism as was deduced by comparing spectra in dichloromethane, acetonitrile, methanol and in a mixture of acetonitrile / TRIS buffer (1 / 1) solution at 293 K (see SI-Figure 1). Absorption spectra of compounds 7-12 in acetonitrile / TRIS buffer (1 / 1) showed maxima around 257-264 nm with a shoulder corresponding to a π-π* transition and a very weak absorbance above 300 nm. Upon irradiation at 255 nm, the solution of compounds 7-12 exhibited a blue photoluminescence (PL) with a single peak at the 259 -266 nm region, respectively (Table 1). [a] Stokes shift = 1/λabs -1/λem. [b] See SI for details.

Among various sensitizers, 9-methylcarbazole (9-MC) was selected for the PET study. 9-MC is a well characterized chromophore, with a relatively high wavelength absorption maximum (λabs max = 345 nm) and it is a strong reducing agent at the excited state with an Eox* = -2.51 V vs SCE. 19 Tethered dyads 14-19 were prepared from picolyl phenylacetic esters 1-6, by using carbazoles 13a-c, having propyl-, hexyl-, or, dodecyl triflate side chains, respectively (Scheme 3). Similar to the nontethered analogues, no appreciable solvatochromic effect was found for 14a in dichloromethane, acetonitrile, methanol and in a mixture of ACN / TRIS buffer (1 / 1) solution, at a concentration of c = 0.1 mM at 293 K between 250 -500 nm (SI-Figure 3). UV spectra of 14-19 were recorded in ACN / TRIS buffer 1 / 1 (SI-Figures 456789). All spectra appeared qualitatively similar, showing essentially the strong absorption of the tethered carbazole due to the larger molar extinction coefficient in the 300 -450 nm region compared to picoliniums. First absorption maxima located around λabs max = 341 -346 nm with molar extinction at the absorption maxima between ε max = 2250 and 3600 M -1 cm -1 (SI-Figures 456789). Differences were observed, however, in the UV absorption spectra between regioisomers and compounds having different spacer lengths. Longer spacers resulted invariably in bathochromic shifts: 14a-19a having propyl spacer (n = 3) were slightly blue-shifted (λabs max = 341 and 342 nm) compared to the free 9-MC, while for 14c-19c (n=12) maxima were slightly red-shifted (λabs max = 346 nm) respectively (Table 2).

N N N Me Me Me R R R R=H -1.11 V (-1.14 V) R=CH 3 -1.14 V (-1.14 V) R=H -1.35 V (-1.18 V) R=CH 3 -1.37 V (-1.24 V) R=H -1.09 V (-1.03 V) R=CH 3 -1.15 V (-1.12 V)

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Noteworthy, propyl tethered analogs 14a-17a showed a broad weak absorption shoulder between 350 and 410 nm (C(3) and C(4) isomers).

Scheme 3. Synthesis of tethered picoline phenylacetate-carbazole dyads 14-19. The low-lying LUMOs of 7-12 suggest that photoactivated N-methyl carbazole may easily reduce these substrates. 20 Noteworthy, the energy of the charge-transfer (CT) states of Nmethyl picoliniums, and also dyads, were estimated beneath of the lowest optically strongest allowed excited states.

The fragmentation of compounds 7-12 was studied in the absence and in the presence of 9-MC sensitizer, as well as for the tethered analogs 14-19 in TRIS / ACN (1 / 1) mixture under modified Falvey's conditions at 366 nm, using a 8 W Carl Roth lamp (Scheme 4; for details see Experimental part). Esters 7-12 having only very weak transitions at 366 nm showed no fragmentation upon photolysis under prolonged irradiation (2 h), thus compounds 7-12 can be considered as photochemically inert under the examined conditions. The sensitized PET study of 7-12 was performed in the presence of a stoichiometric amount of 9-MC in TRIS / ACN (1 / 1) mixture at c = 0.1 mM, and the kinetic course of the photolysis is depicted in Figure 2. Noteworthy, efficient fragmentation was observed for all C(2) and C(4) isomers respectively (7, 8, 11 and 12), C(3) derivatives were inert in the presence, or, absence of 9-MC.

The time course of the PET reaction was followed by HPLC and the consumption of the starting materials against the time is plotted in SI-Figures 18 and19

N N OTf n N N n 1 C(4) R = H 2 C(4) R = Me 3 C(3) R = H 4 C(3) R = Me 5 C(2) R = H 6 C(2) R = Me 13a n = 3 b n = 6 c n = 12 O R O Ph OTf O R O Ph

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Monitoring the photolysis of esters 7 and 8 by 1 H NMR confirmed the release of phenylacetic acid and the formation of the corresponding picolyl alcohols as major products (Table 3; for details see Experimental part). The photolysis was run in a mixture of CD3CN / D2O (4 / 1), and the conversion of the reaction was analysed after 2 h irradiation at 254 nm. Although the formation of the phenylacetic acid was observed in 89% (± 5%) and 86% (± 5%) yields (not isolated) at 75% and 59% conversions, respectively, important photobleaching of the picolinium was showed also as merely 36% and 46% (± 5%) of the expected hydroxymethylene derivatives were found at the same conversions. Noteworthy, no trace of decarboxylated product was observed within the detection limit. This observation is in agreement with the mechanistic rational proposed by Falvey et al. (Scheme 5) that suggests heterolytic rather than homolytic bond cleavage as the major photolysis path. 9,11 Table 3. Photolysis of picolinium esters 7 and 8.

Conditions

Ester consumed (%)

[a]

Acid formed (%)

[a]

Alcohol formed (%)

[a] a] Calculated by 1 H NMR using hexamethyldisiloxane as internal standard.

Scheme 5. The mechanism of the photofragmentation according to Falvey.

9,11

Noteworthy, the photolysis of the tethered dyads showed important concentration dependency in acetonitrile / TRIS mixture (1 / 1) (See SI-Figure 11). This dependency was attributed to the intermolecular π-π stacking interaction, and to the formation of aggregates between the carbazole units, rather than to inner filtering. In order to avoid aggregate formations a c = 0.1 mM solution was used in a TRIS (20 mM) / acetonitrile (1 / 1) (pH = 7.4) mixture, where no more dependency of the photolysis on the concentration was observed.

When tethered dyads 14a and 18a having a propyl linker were irradiated (366 nm), modest conversions were observed after 2 h, whereas α-methyl substituted analogs, 15a and 19a, offered clean and fast conversions (Figures 3 and4). No appreciable fragmentation was observed for C(3) derivatives 16a and 17a. Dyads having hexyl or dodecyl linkers (14-19b and c) showed more efficient fragmentations, and α-methyl substituted derivatives offered systematically cleaner and faster conversions.

Accepted Manuscript

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possesses several advantages over more conventional singlephoton activation conditions, such as higher spatial resolution, and also the fact, that scattered IR photons do not produce out of focus activation. 1,21 The uncaging cross section (δu) of phenylacetate 15c was determined directly from the consumption of the starting material. A 45 µL sample of a 0.1 mM ACN/TRIS 1/1 solution was irradiated using mode-locked Ti-Sapphire laser source at 730 nm wavelength (50 fs pulses at 80 MHz). The expanded beam was focused with a 32 mm lens so that the whole of the excitation volume was contained in the cuvette. Sample was irradiated for 4.5 h at 156 mW average power. The loss of the cage was quantified by HPLC, and the photolysis cross section calculated from the rate of reduction of the fractional cage concentration, giving a high, experimentally measured uncaging cross-section of δu = 0.16 GM, a remarkably high value for a non-optimized structure.

Conformational analysis

In all calculated structures the electron-transfer impacted significantly the geometry of picolinium acceptor resulting generally in increased bond lengths and in the formation of more quinoidal structures. The TD-DFT optimized geometry of 7 in the S1 state is depicted in Figure 9 (see also SI-Table 2). The most significant changes are the rotation of the phenyl group (of the phenylacetic ester) and the elongation of the O-CH2 bond from 1.419 (S0) to 1.502 Ǻ (S1) with an important diminution of the torsion angle from 171° (S0) to 94.7° (S1). These changes are controlled by the energy of the LUMO (see SI-Figure 14) and result in a π-stacked face-to-face arrangement of the picolinium and the phenyl rings, and also, a weakening of the O-CH2 bond. Similar geometric changes were found between the calculated structures for the S0 to S1 transitions of 14a and 14c, respectively (Figure 9).

Conformational analysis of compounds 7-12 was performed by semi-empirical calculations using AM1 Hamiltonian allowing the generation of the potential energy surfaces (SI-Figures 12 and13). All conformation energy minima were optimized at the highest DFT level. In the following, results obtained for compound 7 are discussed, while qualitatively similar results were obtained for compounds 8-12 as well.

Two conformations with energy minima on the potential energy surfaces have been found for compound 7, hereafter named as extended and folded (SI-Figure 13). In the extended conformation dihedral angles α, β, γ and δ are close to 180°. In the folded conformation β is -89.4°, resulting in a more compact arrangement. Noteworthy, the phenyl group is orthogonal to the plan of the ester in both conformations (ε is close to 90°). Remarkably both conformations have similar stability in acetonitrile suggesting that they coexist in the medium.

The absorption spectra of compounds 7-12 were calculated from the extended and folded conformations, respectively, using TD-DFT method (Figure 5). The calculated spectra show similar characteristics to the experimental ones, and the calculated lowest-energy electronic transitions correlate well with experimental values. The absorption spectrum of 7 in the folded conformation is dominated by several very weak bands around 300 nm that originate from electronic monoexcitations between orbitals localized on both aromatic rings and thus can be characterized as a π-π* charge transfer. Accepted Manuscript

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Therefore all these weak transitions show a charge transfer character between picolinium and phenyl rings. Two transitions are calculated at 225 (S0àS7) and 221 nm (S0àS8) and can be assigned to the observed 255 and 258 nm transitions in the experimental spectrum. The S0àS7 transition involves HOMO-3 and LUMO+1 orbitals and corresponds to a picolinium-localized excitation while the S0àS8 transition (HàL+2) is localized on the phenyl group. The character of the lowest excited states of 7, as charge transfer or localized states, can be determined using the S0-Sn differences density plot as presented in Figure 2. The spatial arrangement of the tethered donor-acceptor dyads were considered next and is illustrated by the analysis of compounds 14a-c. Noteworthy, the aliphatic linker allows high degree of conformational flexibility: a systematic conformational study of such element is beyond of the scope of this study. The conformation of compound 14a was generated by the addition of the N-propyl-carbazole fragment to the optimized folded geometry of 7. As was seen with the untethered picolinium probes, two conformation minima were found, denoted as extended and folded (SI-Figure 14). The propyl chain adopts a trans-trans conformation in the extended and syn-pentane conformation in the folded conformation, respectively. Noteworthy, the carbazole and picolinium rings adopt face-toface orientation in the folded geometry (the N-N distance is estimated 3.09 Å). The energy difference between the extended and folded structures is relatively small (0.4 kJ.mol -1 ) suggesting that the energetic penalty associated to the staggered conformation of the propyl chain in the folded geometry is compensated by a π-π interaction between the carbazole and picolinium units. Several conformational minima of 14c were found on the potential energy surface, and labelled as a-d (SI-Figure 14). In the most stable conformation, 14c-a, the dodecyl chain adopts an all-trans arrangement. Others, such as 14c-b, 14c-c and 14c-d display a more folded structure. Noteworthy, the carbazole is in the close proximity of the phenyl group in the second most stable conformation, 14c-b.

The calculated absorption spectrum of 14a (Figure 7) is in agreement with the experimental data (SI-Figure 4) and presents two regions. In the 200-350 nm window the spectrum shows three bands at 241 nm, 271 nm and around 300 nm. These bands reproduce nicely the spectrum of 9-MC 19 and originate from the localized excitation of the carbazole. The second region shows two weakly allowed charge transfer bands at 385 nm and 436 nm. These transitions are dominated by the HOMOàLUMO and HOMO-1àLUMO contributions. From the localization of these orbitals it is obvious that both transitions involve charge transfers from the carbazole to the picolinium (Figure 5 and SI-Table 4). The absorption spectrum of 14c is similar to that of 14a in the region of 200-350 nm. Unlike the calculated absorption spectrum of 14a, the calculated absorption spectrum of 14c shows no charge transfer bands in the low energy region. This is probably due to the large spatial separation between the carbazole and picolinium units in the optimized geometries.

Conclusion

The single-and two-photon photolysis of 9-MC tethered picolinium probes were examined by experimental and theoretical approaches. These probes were considered photochemically inert earlier under similar conditions. Probes undergo tether length-dependent fragmentation: dyads with n = 12 carbon tether were photolyzed 30-40 times more efficiently at 366 nm than that of n = 3 derivatives. α-Methyl substituted derivatives offered systematically cleaner and faster conversions. Communication between the picolinium and carbazole chromophores was observed experimentally and analyzed by density functional theory (DFT) and time dependent-DFT (TD-DFT) calculations. The most efficient dyad, 15c, was photolyzed under TP irradiation conditions at 730 nm showing promisingly high δu = 0.16 GM uncaging cross-section. 9-MC tethered picolinium probes can be considered as new "caging" group leads in which the absorption and fragmenting elements are spatially separated, allowing much easier optimization than that of more conventional probes in which this two functions are intimately linked in the same heterocycle. Further applications in neurophysiology are underway.

Experimental Section

The UV irradiation experiments were accomplished by irradiation of a solution in roughly 0.1 mM concentration in an acetonitrile/TRIS buffer 1/1 solvent mixture (pH 7.4). The plot of lnA versus irradiation time showed a linear correlation for the disappearance of the starting material, which suggested a first order reaction, obtained by the linear least squares methodology for a straight line. For the UV irradiation, an aliquot (1 mL) of the solution was irradiated at approximately 366 nm by using 8W Carl Roth lamp. Between each irradiation a small aliquot (50 µL) of the solution was removed for analysis by reverse-phase HPLC using dual absorbance detection at 260 and 360 nm. Optical densities at 366 nm

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were kept around 0.1 so that aggregate formation /inner-filtering of the irradiation and spatial gradients of concentrations could be neglected, and the progress curves were simple decaying exponentials. Dark hydrolysis rates were measured similarly except without illumination. One-photon quantum yields were determined by using Eq 1:

Qu = [σ( λexc) I0( λexc) t90%] -1 (Eq 1)
where σ( λexc) is the decadic extinction coefficient of the compound at the excitation wavelength (10 3 times ε), t90% is the time at which 90% of the product was converted, as determined by HPLC, and I0( λexc) is the light intensity at the excitation wavelength and is measured in einstein.cm -2 .s -1 . 22 The light intensityI0 value was determined by potassium ferrioxalate actinometry. 22,23 Briefly, a 6.0 mM potassium ferrioxalate solution (3 mL) was irradiated for 60 s. An aliquot of the irradiated solution (2 mL) was added to NaOAc buffer (3 mL), 0.1% phenanthroline solution (3 mL) and 2 M KF solution (1 mL) and the volume was completed to 25 mL by distilled water. A blank sample was prepared the same way, except irradiation. Samples were kept 1 h in the dark for complexation then the absorbance was measured at 510 nm.

The light intensity was calculated by using Eq 2:

𝐼 = !3 !!510 !"""!510V2ϕFet (Eq 2)
where V3 is the final volume after dilution (25 ml), V2 is the volume of the aliquot taken for analysis (2 ml), ΔD510 is the difference of absorption of the irradiated sample and the blank at 510 nm, ε510 is the extinction coefficient of the (Fe(phen)3 2+ ) complex at 510 nm (11100 M -1 cm -1 ), ϕFe is the quantum yield for ferrous ion formation at the irradiation wavelength and t is the irradiation time (s).

Electrochemical experiments were done on a voltammetry analyzer (Autolab PGSTAT101) with [Bu4N][PF6] as the supporting electrolyte (one chamber three electrode cell). The electrodes used were a glassy-carbon working, a platinum auxiliary, and the potential was measured relative to ferrocene/ferrocenium reference. The solution (1 mM for compound studied) was purged with nitrogen for 10 min prior to recording. Values obtained were converted to SCE by adding 0.40 V to the measured potentials.

HPLC analyses were carried out on Water 515 device with a normal inverse phase column X-Terra® MS C18 (length: 75 mm, diameter: 4.6 mm, stationary phase: 2.5 µm) using a Waters 2487 Dual Absorbance Detector (260-360 nm) and an isocratic system of elution (MeOH-MeCN-H2O 7-2-1 / H2O AcONH4 (10 mM) pH 4.6). The volume of injection was 10 µL.

Thin-layer chromatography was performed on aluminium-backed Merck Kieselgel 60 F254 pre-coatedplates. Proton nuclear magnetic resonance ( 1 H NMR) spectra and carbon nuclear magnetic resonance ( 13 (Hz). All solvents and inorganic reagents were from commercial sources and used without purification unless otherwise noted.

The mass analyser was an Agilent from ThermoFisher. The capillary tension was 3.5 kV. The cone tension was 24 V. The temperature of the source was 130 °C and the temperature of desolvatation was 350 °C. Data were treated on ThermoQuest.

Characterization of the photolysis products by 1 H NMR A solution of 4 µmol of picolinium esters 7 and 8, respectively, with an equal amount of 9-MC sensitizer was dissolved in about 0.5 mL of CD3CN/D2O (4/1) solvent mixture. Hexamethyl-disiloxane was added as internal standard. NMR spectra were recorded before irradiation, then the samples were transferred to a quartz cuvette for the irradiation. The solutions were irradiated at 366 nm for 2 h by using a 8 W Carl Roth lamp, then retransferred to an NMR tube for analysis following the irradiation. Yields were determined by 1 H NMR integration of the compound characteristic peaks relative to the internal standard.

TP photolysis NIR photolysis were performed by irradiation of a sample solution (0.1 mM) in acetonitrile/TRIS buffer 1/1 solvent mixture (pH 7.4) for 1-4 hours. Two photon uncaging cross-sections (δu) were calculated from the fractional conversion of the cage with exposures of approx. 4 hours in a 45 microliters cuvette of 3 mm path length. The expanded output of a MaiTai BB (Spectra-Physics) pulsed laser was focused with a 30 mm focal length lens into the cuvette. The two-photon excitation volume was entirely contained within the cuvette volume to obviate the need to measure the beam waist. Beam parameters were 730 nm with 150 fs pulse width at 80 MHz and 100 mW average power after the cuvette. Samples were centrifuged if necessary to remove particles if apparent in the transmitted beam. For reference the two-photon uncaging cross-section for L-glutamate release from the widely used MNI-caged glutamate determined in this way was 0.05 GM (10 -50 cm 4 s/photon). The conversion of the product was assayed by HPLC by monitoring the remaining caged compound. The two-photon uncaging cross section δ u was calculated as follows (Eq 3):

𝛿 ! = 3.41 x conversion % x !!!! !!!! ( !" ! ) ! (Eq 3)
where δ u = TP uncaging cross-section (cm 4 .s/photon); V = sample volume (45×10 -3 cm 3 ); τP= pulse width; f = 80×10 6 Hz; n = 1.3; λ = wavelength (cm); t = exposure time (s); h = 6.6×10 -34 J.sec; c = 3×10 10 cm.s -1 ; P = average power (W).

Synthesis of esters 1-6

To a solution of the appropriate pyridylcarbinol (3.0 mmol) and triethylamine (1.5 eq, 4.5 mmol, 627 µL) in 10 mL acetonitrile, phenylacetyl chloride (1.5 eq, 4.5 mmol, 595 µL) was added. The reaction mixture was stirred at rt for 16 h. Dichloromethane and water were added, the organic phase was washed with water and brine, dried over Na2SO4, filtered and evaporated to dryness. The crude product was purified by column cromatography on silica gel (cyclohexane/EtOAc 4/1).

Pyridin-4-ylmethyl 2-phenylacetate (1)

Yellow oil (498 mg, 73%). 1 H NMR (CDCl3, 250 MHz): δ 8.60 (d,J=4.7 Hz,1H),7.68 (td,J= 7.5 ,1.5 Hz,1H),5H),2H), 5.28 (s, 2H), 3.77 (s, 2H). 13 C NMR (CDCl3, 125 MHz): δ 171.0, 149. 8, 145.2, 133.6, 129.4, 128.9, 127.5, 122.0, 64.6, 41.4 5.83 (q, J=6.5 Hz, 1H), 3.67 (s, 2H), 1.50 (d, J=7.0 Hz, 3H). 13 C NMR (CDCl3, 125 MHz): δ 170. 6, 150.7, 149.9, 133.7, 129.3, 128.7, 127.4, 120.7, 71.8, 41.6, 22. Yellow oil (586 mg, 86%). 1 H NMR (CDCl3, 500 MHz): δ 8.58-8.56 (m, 2H), 7.61 (dt, J=8.0, 2.0 Hz, 1H), 7.34-7.31 (m, 2H), 7.28-7.25 (m, 4H), 5.14 (s, 2H), 3.67 (s, 2H). 13 C NMR (CDCl3, 125 MHz): δ 171. 3, 149.6, 149.6, 136.1, 133.7, 131.7, 129.4, 128.8, 127.4, 123.6, 64.1, 41.4 7.28 (m, 4H), 7.25-7.23 (m, 2H), 5.91 (q, J=7.0 Hz, 1H), 3.65 (bs, 2H), 1.55 (d,J=6.5 Hz,3H). 13 C NMR (CDCl3, 125 MHz): δ 170. 8, 149.3, 147.9, 137.1, 133.9, 133.8, 129.4, 128.8, 127.3, 123.5, 70.7, 41.7, 22 13 C NMR (CDCl3, 125 MHz): δ 171. 2, 155.7, 149.3, 137.0, 133.8, 129.4, 128.7, 127.2, 122.9, 121.7, 67.0, 41.3 (d,J=6.5 Hz,3H). 13 C NMR (CDCl3, 125 MHz): δ 170. 9, 160.3, 149.2, 137.1, 134.0, 129.4, 128.7, 127.2, 122.8, 120.4, 73.4, 41.6, 20.8

N-Methylation of esters 1-6

To a solution of compounds 1-6 (0.20 mmol, for 1,3,5: 45 mg, for 2,4,6: 48 mg) in dry dichloromethane (1 mL) is added methyl trifluoromethanesulfonate (1.0 eq, 0.20 mmol, 23 µL). The mixture is allowed to stir at rt for 1 h (TLC shows no sign of starting material), under argon and protected from light. The solvent is evaporated and the product obtained is used without further purification. CAUTION: methyl trifluoromethanesulfonate is a powerful methylating agent, handle with extreme care in a well ventilated hood.

1-Methyl-4-((2-phenylacetoxy)methyl)pyridinium trifluoromethanesulfonate (7) Pale yellow oil (quant.). 1 H NMR (CDCl3, 500 MHz): δ 8.70 (d,J=6.5 Hz,2H),7.74 (d,J=6.5 Hz,2H),2H),3H),5.31 (s,2H),4.36 (s,3H),3.77 (s,2H). 13 C NMR (CDCl3, 125 MHz): δ 170. 9, 156.2, 145.4, 133.2, 129.5, 129.0, 127.8, 125.4, 63.3, 48.5, 41.0 (8) Pale yellow oil (quant.). 1 H NMR (CDCl3, 500 MHz): δ 8.69 (d,J=6.5 Hz,2H),7.70 (d,J=6.5 Hz,2H),5H),5.90 (q,J=6.5 Hz,1H),4.40 (s,3H),3.72 (s,2H),1.57 (d,J=6.5 Hz,3H). 13 C NMR (CDCl3, 125 MHz): δ 170. 7, 161.0, 145.9, 133.3, 129.5, 128.9, 127.6, 124.7, 70.5, 48.3, 41.1, 21.4 (9) Pale yellow oil (quant.). 1 H NMR (CDCl3, 500 MHz): δ 8.73 (d,J=6.5 Hz,1H),8.68 (s,1H),8.22 (d,J=8.5 Hz,1H),7.88 (dd,J=8,6 Hz,1H),5H),5.27 (s,2H),4.35 (s,3H),3.72 (s,2H). 13 C NMR (CDCl3, 125 MHz): δ 171. 2, 144.9, 144.5, 143.9, 138.1, 133.4, 129.6, 128.9, 128.1, 127.6, 61.9, 49.0, 40.9 [START_REF] Thum | On PET induced fragmentation of covalently linked anthraquinone-N-alkylpicolinium dyads see[END_REF] Pale yellow oil (quant.). 1 H NMR (CDCl3, 500 MHz): δ 8.72 (d,J=6.0 Hz,1H),8.60 (s,1H),8.17 (d,J=8.5 Hz,1H),7.87 (dd,J=8.0,6.0 Hz,1H),5H),5.94 (q,J=6.5 Hz,1H),4.32 (s,3H),3.69 (s,2H), 1.58 (d,J=6.5 Hz,3H). 13 C NMR (CDCl3, 125 MHz): δ 170. 7, 144.9, 143.3, 143.2, 142.3, 133.5, 129.5, 128.9, 128.3, 127.6, 69.1, 49.0, 41.2, 21.5 (11) Pale yellow oil (quant.). 1 H NMR (CDCl3, 500 MHz): δ 8.77 (d,J=6.0 Hz,1H),8.27 (td,J=8.0,1.5 Hz,1H),7.81 (d,J=8 Hz,2H),5H),5.40 (s,2H),4.22 (s,3H),3.73 (s,2H). 13 C NMR (CDCl3, 125 MHz): 170.8, 151.7, 147.5, 145.7, 133.0, 129.5, 128.9, 128.1, 127.7, 127.5, 61.2, 45.9, 40.7 (12) Pale yellow oil (quant.). 1 H NMR (CDCl3, 500 MHz): δ 8.83 (d,J=5.5 Hz,1H),8.31 (td,J=8.0,1 Hz,1H),1H),7.72 (dd,J=8.0,1.5 Hz,1H),3H),2H),6.00 (q,J=6.5 Hz,1H),4.29 (s,3H),3.67 (s,2H),1.63 (d,J=7.0 Hz,3H). 13 C NMR (CDCl3, 125 MHz): δ 171. 1, 157.3, 147.5, 146.2, 132.7, 129.4, 129.0, 127.8, 127.4, 125.4, 67.3, 46.4, 40.9, 19.

FULL PAPER

N-Alkylation of carbazole

To a solution of carbazole (10.0mmol, 1.67 g) in DMF (25 mL), NaH (60% dispersion in mineral oil, 1.5 eq, 15.0mmol, 600 mg) was added at 0°C. After 30 min stirring, 1.5 eq of alkyl bromide was added (15.00 mmol, 3-bromopropanol:

1.34 mL; 6-bromohexanol: 2.72 g; 12bromododecanol: 3.98 g) and the mixture was stirred at rt for 24 h. The mixture was poured onto water and extracted by DCM. The organic phase was washed with water and brine, dried over Na2SO4, filtered and evaporated to dryness. The crude product was purified by column cromatography on silica gel (cyclohexane/EtOAc 4/1).

3-(9H-Carbazol-9-yl)propanol

White solid (1.36 g, 60%). 1 H NMR (CDCl3, 250 MHz): δ 8.16 (d,J=7.3 Hz,2H),4H),7.30 (ddd,J=7.3,5.3,2.2 Hz,2H),4.46 (t,J=6.6 Hz,2H),3.57 (t,J=6.6 Hz,2H), 2.10 (qn, J=6.6 Hz, 2H), 1.80 (s, 1H). 13 C NMR (CDCl3, 125 MHz): δ 140. 5, 125.8, 122.9, 120.4, 119.0, 108.7, 59.6, 39.2, 31.4.

6-(9H-Carbazol-9-yl)hexanol

White solid (1.70 g, 64%). 1 H NMR (CDCl3, 500 MHz): δ 8.08 (d,J=7.5 Hz,2H),7.44 (td,J=8.0,1.5 Hz,2H),7.37 (d,J=8.0 Hz, 2H), 7.21 (td, J=8.0, 1.0 Hz, 2H), 4.27 (t, J=7.0 Hz, 2H), 3.55 (t, J=6.5 Hz, 2H), 1.86 (qn, J=7.5 Hz, 2H), 1.49 (qn, J=7.0 Hz, 2H), 1.39-1.33 (m, 4H). 13 C NMR (CDCl3, 125 MHz): δ 140. 5, 125.7, 122.9, 120.5, 118.9, 108.7, 62.8, 43.1, 32.7, 29.0, 27.2, 25.6.

12-(9H-Carbazol-9-yl)dodecanol

White solid (2.53 g, 72 %). 1 H NMR (CDCl3, 500 MHz): δ 8.07 (d, J=8.0 Hz, 2H), 7.42 (td, J=8.0, 1.0 Hz, 2H), 7.35 (d, J=8.0 Hz, 2H), 7.19 (td, J=8.0, 1.0 Hz, 2H), 4.22 (t, J=7.5 Hz, 2H), 3.56 (t, J=6.5 Hz, 2H), 1.81 (qn, J=7.0 Hz, 2H), 1.50 (qn, J=7.0 Hz, 2H), 1.36-1.18 (m, 16H). 13 C NMR (CDCl3, 125 MHz): δ 140. 5, 125.6, 122.9, 120.4, 118.7, 108.7, 63.0, 43.1, 32.8, 29.7-29.5 (6C), 29.0, 27.4, 25.8.

Synthesis of compounds 13a-c

To a solution of the appropriate alcohol (1.80 mmol, 3-(9H-carbazol-9yl)propanol: 406 mg, 6-(9H-carbazol-9-yl)hexanol: 481 mg, 12-(9Hcarbazol-9-yl)dodecanol: 633 mg) and pyridine (1.0 eq, 1.80 mmol, 146 µL) in DCM (10 mL), trifluoromethanesulfonic anhydride (1.0 eq, 1.80 mmol, 303 µL) was added at 0°C. The mixture was stirred at rt for 2 h, then was poured onto water. The organic phase was washed with water and brine, dried over Na2SO4, filtered and evaporated to dryness. The crude product obtained was used directly for the next reaction step.

3-(9H-Carbazol-9-yl)propyl trifluoromethanesulfonate (13a)

Colourless oil (643 mg, quant). 1 H NMR (CDCl3, 250 MHz): δ 8.15 (d,J=8.4 Hz,2H),7.53 (ddd,J=8.4,7.5,1.3 Hz,2H),7.39 (d,J=8.4 Hz,2H),7.31 (ddd,J=7.5,7.5,0.8 Hz,2H),4.46 (d,J=6.2 Hz,2H),4.44 (d,J=6.5 Hz,2H),2.36 (qn,J=6.4 Hz,2H).

6-(9H-Carbazol-9-yl)hexyl trifluoromethanesulfonate (13b)

Colourless oil (719 mg, quant). 1 H NMR (CDCl3, 250 MHz): δ 8.13 (d,J=7.9 Hz,2H),7.50 (ddd,J=7.5,7.2,1.0 Hz,2H),7.41 (d,J=7.9 Hz,2H),7.27 (ddd,J=7.9,7.5,1.0 Hz,2H),4.47 (t,J=6.2 Hz,2H),4.32 (t,J=7.0 Hz,2H),2H),2H),4H).

12-(9H-Carbazol-9-yl)dodecyl trifluoromethanesulfonate (13c)

Colourless oil (870 mg, quant). 1 H NMR (CDCl3, 500 MHz): δ 8.11 (d,J=7.5 Hz,2H),7.47 (ddd,J=9.5,7.0,1.5 Hz,2H),7.41 (d,J=8 Hz,2H),7.25 (ddd,7.5,7.0,1.2 Hz,2H),4.53 (t,J=6.5 Hz,2H),4.31 (t,J=7 Hz,2H),4H),16H).

Synthesis of carbazole-linked esters 14-19

To a solution of the ester (1-6) (0.25 mmol) in 1.0 mL DCM, a solution of the triflate (13a-c) (1.0 eq, 0.25 mmol) in DCM (0.5 mL) was added, and the mixture was stirred at rt for 4 h under argon, while protected from light. After evaporation to dryness, if necessary, the crude product was purified by column cromatography on silica gel (DCM/MeOH 95/5). During work-up, purification and upon storing the products were carefully protected from light. Yellow oil (121 mg, 83%). 1 H NMR (CD3CN, 500 MHz): δ 8.25 (d,J=7.0 Hz,2H),8.01 (d,J=7.5 Hz,2H),7.52 (d,J=8.0 Hz,2H),7.48 (ddd,J=8.0,7.0,1.2 Hz,2H),7.43 (d,J=6.5 Hz,2H),2H),3H),7.21 (ddd,J=8.0,7.0,1.2 Hz,2H),5.18 (s,2H), 4.52 (t, J=7.0 Hz, 2H), 4.51 (t, J=7.0 Hz, 2H), 3.80 (s, 2H), 2.56 (qn, J=7.0 Hz, 2H). 13 C NMR (CD3CN, 125 MHz): δ 171. 7, 157.1, 144.2, 140.8, 134.9, 130.4, 129.5, 128.2, 127.0, 125.4, 123.6, 121.2, 120.3, 110.0, 63.9, 60.1, 41.1, 40.7, 30. Yellow oil (136 mg, 87%). 1 H NMR (CDCl3, 500 MHz): δ 8.50 (d,J=6.5 Hz,2H),7.99 (d,J=8 Hz,2H),7.53 (d,J=7 Hz,2H),7.39 (ddd,J=8.0,7.0,1.0 Hz,2H),7H),7.15 (ddd,J=8.0,7.0,1.0 Hz,2H),5.07 (s,2H),4.27 (t,J=7.5 Hz,2H),4.19 (d,J=7.0 Hz,2H),3.69 (s,2H),4H),2H),2H). 13 C NMR (CDCl3, 125 MHz): δ 170. 7, 156.0, 144.2, 140.3, 133.1, 129.4, 128.9, 127.7, 125.9, 125.3, 122.7, 120.4, 119.0, 108.9, 63.1, 61.5, 42.7, 40.9, 31.2, 28.5, 26.4, 25.4 Yellow oil (142 mg, 80%). 1 H NMR (CDCl3, 500 MHz): δ 8.69 (d,J=6.5 Hz,2H),8.06 (d,J=8.0 Hz,2H),7.72 (d,J=7.0 Hz,2H),7.43 (ddd,J=8.0,7.0,1.5 Hz,2H),7.38 (d,J=8.0 Hz,2H),2H),3H),7.19 (ddd,J=8.0,7.0,1.0 Hz,2H),5.22 (s,2H),4.46 (t,J=7.5 Hz,2H),4.25 (t,J=7.5 Hz,2H),3.74 (s,2H),4H),2H),14H). 13 C NMR (CDCl3, 125 MHz): δ 170.8, 156.3, 144.4, 140.5, 133.1, 129.5, 128.9, 127.7, 125.7, 125.6, 122.8, 120.4, 118.8, 108.8, 63.2, 62.0, 43.1, 40.9, 31.5, 29.4-28.9 (8C), 27.3, 26.

Accepted Manuscript

Theoretical calculations

The calculations have been performed with Gaussian 09 16a using Density Functional Theory (DFT) and the 6-311G (d,p) Pople basis sets and the PBE0 functional. The first low-lying electronic singlet excited states have been calculated using the time-dependent density functional theory (TD-DFT) method 16b to obtain theoretical absorption spectra. The calculations (geometry optimizations, TD-DFT calculations) have been performed in acetonitrile as in the experiment and solvent have been included in the calculations by means of the polarizable continuum model by the integral equation formalism (IEFPCM). 16c All the geometry optimizations were led without symmetry constraints and followed by a vibrational frequency computation to ensure that they correspond to true energetic minima.

Scheme 1 .

 1 Scheme 1. Synthesis of N-methyl picolinium phenylacetates 7-12.

  ferrocene / ferrocenium reference. Cyclic voltammograms (see SI) showed irreversible redox processes for all six substrates, 7-12. The first reduction potential was observed between Ered = -1.09 V and Ered = -1.37 V, with Ered = -1.11 V for 7 which is very close to the reported Ered = -1.08 V value measured for the corresponding perchlorate salt.3 Compounds 7, 8 and 11, 12 (i.e. the C(2) and C(4) regioisomers)showed invariably smaller reduction potential than C(3) derivatives, 9 and 10. The nature of the side-chains i.e. primary vs secondary esters affected only marginally the reduction potentials.

Figure 1 .

 1 Figure 1. Experimental and calculated (in parenthesis) reduction potentials of N-methyl picolinium phenylacetates.

  .

Scheme 4 .

 4 Scheme 4. Photolysis of picoline phenylacetates 7, 8 and 11, 12 in the presence of N-methylcarbazole sensitizer.

Figure 2 :

 2 Figure 2: Relative time course of the photolysis of compounds 7, 8 and 11, 12 in the presence of 1 equivalent of 9-MC sensitizer at 366 nm as determined by HPLC.

  R = H; a n = 3; b n = 6; c n = 12 15 C(4) R = Me; a n = 3; b n = 6; c n = 12 16 C(3) R = H; a n = 3; b n = 6; c n = 12 17 C(3) R = Me; a n = 3; b n = 6; c n = 12 18 C(2) R = H; a n = 3; b n = 6; c n = 12 19 C(2) R = Me; a n = 3; b n = 6; c n

[

Scheme 6 .

 6 Scheme 6. Photolysis of tethered N-carbazole picoline phenylacetates 14a-c, 15a-c, 18a-c and 18a-c.

Figure 3 :

 3 Figure 3: Relative time course of C(2) regioisomers photolysis at 366 nm determined by HPLC.

Figure 4 :

 4 Figure 4: Relative time course of C(4) regioisomers photolysis at 366 nm determined by HPLC.

Figure 5 .

 5 Figure 5. Calculated absorption spectrum of compound 7 representing main orbitals implied in the electronic excitations and Sn-S0 density plots.

Figure 6 .

 6 Figure 6. The S1 optimized geometries of 7, 14a and 14c.

Figure 7 .

 7 Figure 7. Calculated absorption spectra of compound 14a (black) and 14c-b (red), main orbitals involved in the first electronic excitations of 14a.

  0. MS (ESI): m/z = 242.2 [M+H] + . HRMS (ESI): m/z calcd for [C15H15O2N+H] + 242.1176, found 242.1169.Pyridin-3-ylmethyl 2-phenylacetate(3)

  . MS (ESI): m/z = 228.1 [M+H] + . HRMS (ESI): m/z calcd for [C14H13O2N+H] + 228.1019, found 228.1013.

  ): m/z calcd for [C15H16O2N+H] + 242.1176, found 242.1170.HPLC: MeOH-MeCN-H2O 7-2-1 / H2O AcONH4 10 mM 4/6, flow rate: 0.45 mL/min, RT: 5.57 min.

  . MS (ESI): m/z = 256.3 [M+H] + . HRMS (ESI): m/z calcd for [C16H18O2N] + 256.1332, found 256.1331. HPLC: MeOH-MeCN-H2O 7-2-1 / H2O AcONH4 10 mM 4/6, flow rate: 0.45 mL/min, RT: 5.05 min.

  . MS (ESI): m/z = 256.2 [M+H] + . HRMS (ESI): m/z calcd for [C16H18O2N+H] + 256.1332, found 256.1323. HPLC: MeOH-MeCN-H2O 7-2-1 / H2O AcONH4 10 mM 4/6, flow rate: 0.45 mL/min, RT: 4.19 min.

  . MS (ESI): m/z = 242.1 [M+H] + HRMS (ESI): m/z calcd for [C15H16O2N+H] + 242.1176, found 242.1170.HPLC: MeOH-MeCN-H2O 7-2-1 / H2O AcONH4 10 mM 4/6, flow rate: 0.45 mL/min, RT: 4.03 min.

  7. MS (ESI): m/z = 256.3 [M+H] + . HPLC: MeOH-MeCN-H2O 7-2-1 / H2O AcONH4 10 mM 4/6, flow rate: 0.45 mL/min, RT: 4.55 min.

  This article is protected by copyright. All rights reserved.

  0. MS (ESI): m/z = 435.2 [M+H] + . HRMS (ESI): m/z calcd for [C29H27O2N2+H] + 435.2067, found 435.2078. HPLC: MeOH-MeCN-H2O 7-2-1 / H2O AcONH4 10 mM 7/3, flow rate: 0.7 mL/min, RT: 3.34 min.

  . MS (ESI): m/z = 477.3[M+H] + . HRMS (ESI): m/z calcd for [C32H33O2N2+H] + 477.2537, found 477.2529. HPLC: MeOH-MeCN-H2O 7-2-1 / H2O AcONH4 10 mM 7/3, flow rate: 0.7 mL/min, RT: 5.66 min.

  0. MS (ESI): m/z = 561.4 [M+H] + . HRMS (ESI): m/z calcd for [C38H45O2N2+H] + 561.3476, found 561.3466. HPLC: MeOH-MeCN-H2O 7-2-1 / H2O AcONH4 10 mM 9/1, flow rate: 0.7 mL/min, RT: 5.71 min. 10.1002/chem.201801684

Table 1 .

 1 Photophysical properties of compounds 7-12.

		λabs	max		ε	max		λem	max	Stokes shift	Qu
		(nm)	[a]	(M	-1 cm	-1 )	(nm)	(10	3 cm	-1 )	a	(%)	b
	7	257	4250	260	0.45	0.36
	8	257	4200	259	0.30	0.45
	9	263	4300	265	0.30	nd
	10	263	4500	266	0.40	nd
	11	264	6650	266	0.30	0.21
	12	264	5450	266	0.30	0.25

Table 2 . Photophysical properties of compounds 14-19.

 2

		λabs	max		ε	max		λem	max	Stokes shift	Qu
		(nm)	(M	-1 cm	-1 )	(nm)	(cm	-1 )	a	(%)	b
	14a	342					354	1.00	0.02
	14b	345					354	0.75	0.11
	14c	346					350	0.35	0.91
	15a	342					354	1.00	0.06
	15b	345					354	0.75	0.12
	15c	346					350	0.35	2.06
	16a	342					354	1.00	nd
	16b	345					354	0.75	nd
	16c	346					351	0.40	nd
	17a	342					354	1.00	nd
	17b	345					354	0.75	nd
	17c	346					351	0.40	nd
	18a	342					354	1.00	0.01
	18b	345					354	0.75	0.07
	18c	346					352	0.50	0.46
	19a	341					354	1.10	0.12
	19b	345					354	0.75	0.06
	19c	346					352	0.50	0.69

[a] Stokes shift = 1/λabs -1/λem.

[b]

See SI for details.

Methyl-3-(1-(2-phenylacetoxy)ethyl)pyridinium trifluoromethanesulfonate

	. MS (ESI): m/z = 242.2 [M+H] + . HRMS
	(ESI): m/z calcd for [C15H16O2N+H] + 242.1176, found 242.1169.HPLC:
	MeOH-MeCN-H2O 7-2-1 / H2O AcONH4 10 mM 4/6, flow rate: 0.45
	mL/min, RT: 4.80 min.
	1-

Acknowledgements

This research was supported by grants from Région Ile-de-France -DIM Nano-K 2014 (France) Fellowship and a Marie Curie Intra European Fellowship within the 7th European Community Framework Program (FP7-PEOPLE-2013-IEF: 629675). Authors acknowledge also the generous financial support of the ANR-2014-BLAN-1436-01 grant.

FULL PAPER


N Esnouf

Gammella

Solène Legand
email: solene.legand@cea.fr.

Vincent Dauvois

Stéphane Esnouf

Nicolas Gammella

THERMAL DECOMPOSITION OF RADIO-OXIDIZED POLYMERS

Thermal decomposition of radio-oxidized polymers

Introduction

Many polymers are used in nuclear industry and are then stored in nuclear waste packages. In case of accidental conditions of transportation, the temperature of packages may increase and reach 150°C. The accumulation of the gases formed may affect the integrity of the waste container. Therefore, for safety purpose, it is important to predict the gas quantity released by different organic materials and measure the kinetic of thermal decomposition of radio-oxidized polymers [1] [2] [START_REF] Boughattas | 7 th Conference MoDeSt[END_REF]. The purpose of this work is to present the results of a multi-year study performed on four polymers (polyethylene, cellulose, polyurethane, polyvinyl chloride). The effect of dose, atmosphere and degradation temperature on the quantity of gas release was investigated.

Experimental

High density polyethylene (Sigma), cellulose (commercial cotton), polyurethane (Plastunion) and plasticized polyvinyl chloride (Plastunion) were gamma-irradiated under air atmosphere at room temperature at different doses (0, 1, 2 and 4 MGy). After irradiation, the thermal degradation of polymers at different temperatures (60°C, 80°C, 100°C, 120°C and 150°C) for 48 hours in air or inert conditions was analyzed by thermogravimetric analysis (TGA) and infrared spectroscopy. In addition, in order to quantify the volatiles species a known amount of polymer was conditioned in a small vessel (made on stainless steel or glass) equipped with a pressure gauge. The pressure build-up was recorded as a function of the time during the thermal treatment. An example of the pressure measurement is shown in Figure1 for the pre-irradiated polyvinyl chloride, at 4 MGy, heated at different temperatures for 48 hours under air. Identification and quantification of gases were performed by high resolution mass spectrometry and gas chromatography coupled with mass spectrometry (GC-MS). For the experiments under air, oxygen consumption was also measured.

Results and discussion

Even at 150°C, non-irradiated polymers were rather stable. The results are different for radio-oxidized materials. A rapid increase of the pressure is observed during the first hours after heating followed by a stabilization or a slow increase. For all polymers, the production of volatile species is almost proportional to the dose and is thermally activated. The main degradation products are water and carbon dioxide. The production of hydrogen and inflammable gases is rather limited. Under air atmosphere, the pressure increase is partially compensated by oxygen consumption.

Conclusions

A comprehensive study performed on different polymers representative of organic materials present in nuclear waste shows that the thermal decomposition of pre-oxidized polymers is a rapid phenomenon. The majority of the gases is released in the first hours. Water and carbon dioxide are the predominant species. Although irradiation reduces the thermal stability of the polymers, our results show that the risk of inflammation is not exacerbated.

Acknowledgement

The authors are grateful to M. Cornaton, D. Durand and J.L. Roujou for their contribution to ATG, IRFT and MS analysis. Figure 1 -Pressure increase measured for polyvinyl chloride gamma-irradiated at 4 MGy under air heated at different temperatures for 48 hours under air.


Sofiane Dairi

Marie-Annette Carbonneau

Teresa Galeano-Diaz

Hocine Remini

Farid Dahmoune

Omar Aoun

Amine Belbahi

Céline Lauret

Jean-Paul Cristol

Khodir Madani

Antioxidant effects of extra virgin olive oil enriched by myrtle phenolic extracts on iron-mediated lipid peroxidation under intestinal conditions model

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.


Christophe Girold

Sébastien Francois

Laurence Petit

Stéphane Catherin

Thierry Prevost

Etienne Fourcy

Guillaume Lecomte

Alain Viand

French Innovative Processes in the Field of Thermal Treatment For Decommissioning and Legacy Waste -18085

In order to optimize decommissioning waste management and better anticipate related issues, French nuclear waste producers CEA and AREVA, and the French Agency in charge of radioactive waste disposal (ANDRA) have decided to collectively develop technologies mastering costs, schedules and dose uptake as well as optimizing waste volumes and repository safety. In this context, several innovative projects have emerged over the past few years to develop specific thermal treatment processes. This paper focus on four new processes, presenting their goals, technical descriptions and first experimental results.

INTRODUCTION

The decommissioning of nuclear facilities and legacy waste treatment represent a global industrial challenge. In France, decommissioning activities will generate large volumes of radioactive waste, mainly low activities with a fairly homogeneous typology (metallic components, rubble), for which disposal routes already exist. However, some types of waste, due to their radiological and/or physical-chemical characteristics, cannot be easily conditioned and disposed of and, in a few cases, has no disposal route. Such waste may arise from former activities for which requirements for conditioning and disposal have evolved. This is particularly true for legacy waste.

In order to optimize decommissioning waste management and better anticipate related issues, French nuclear waste producers CEA and AREVA, and the French Agency in charge of radioactive waste disposal (ANDRA) have decided to collectively develop technologies mastering costs, schedules and dose uptake as well as optimizing waste volumes and repository safety. In this context, several innovative projects have emerged over the past few years to develop specific thermal treatment processes. The paper focus on four new processes, presenting their goals, technical descriptions and first experimental results:

 The IN CAN MELTER process, developed in the frame of the "DEM & MELT" project, a small and inexpensive in can vitrification tool, specifically designed to be used directly on site for high level inorganic solid or liquid waste such as tank deposits, zeolites, sludge…  The PIVIC Process, a plasma and induction coupled incineration / vitrification process to treat mixed organic and metals stream highly contaminated with plutonium (ILW),  The IDOHL process, a small induction plasma treatment process for organic liquid waste,  The ELIPSE process, a very innovative organic liquid treatment process (solvents, TBP…), implementing a submerged non transferred oxygen arc plasma.

THE "DEM & MELT" PROJECT

Scopes and objectives

Some waste streams from dismantling operations are identified as an issue in terms of handling, transportation, adapted conditioning matrix for disposal within the existing regulations. This is for example the case of high active deposits remaining in the equipments of shut down facilities. The numerous constraints associated with the management of such waste leads to investigate the implementation of an in situ conditioning treatment able to produce a waste package complying with existing disposal routes and/or on-site storage facilities.

As grouting or cement matrixes are prone to hydrogen production or anyway would lead to a huge increase in volume, they seem excluded. In this context, only a glass matrix seems able to bring a satisfying answer as the glass material and the vitrification processes have demonstrated to be adapted to high level waste and can be flexible enough to accommodate a variable waste stream.

In this frame, the "DEM & MELT" (D&M) project is a project of Industrial Research, between CEA, AREVA, ECM Technologies and ANDRA. It has the ambition to bring a new solution by developing a specific vitrification tool to be implemented in situ and specifically designed to match the requirements and constraints of a Decommissioning and Dismantling (D&D) project. The amounts of identified high level waste from dismantling operation to be treated are low, generally around a few hundred kilos for a given spot but scattered in different locations. This is significantly a different case than known industrial vitrification processes and shops which are devoted to treat, in a single place, large stream for a long period of time.

The challenge is then to develop a process and a technology, flexible enough to match various waste streams and making it cost effective to have one tool per spot, designed from the start and to be dismantled after use (disposable vitrification tool). The rate of treatment could therefore be compatible with a small size installation with limited capacity. The challenge is then to develop a compact vitrification technology:

 For high or medium level waste,  Flexible enough to accommodate uncertainties on waste composition and however producing a describable package with source term calculation methodology for long term storage,  Adequately dimensioned and compact to be installed and operate inside a decommissioned cell,  Designed for a short duration of use as a decommissioning tool aimed to be dismantled just after the treatment operation,  Producing a small amount of secondary waste,  At low investment and operation cost.

To achieve the objective of delivering a Technology Readiness Level (TRL) 6 process and provide all the basic data necessary to start an industrial application at the end of the project (2020), the project took as a basis a previous development which is nearly completed, the IN CAN MELTER technology (see next paragraph). The D&M project started in 2016 and is sequenced in 2 periods:

 A first phase to study the feasibility, 2016-2018. During this phase, a reference D&D waste has been chosen and a preliminary assessment of glass matrix is performed as well as the definition of the fundamentals of the process (functional analysis, engineering studies for industrial layout and nuclearization feasibility). First tests using and existing IN CAN MELTER pilot scale equipment are realized and a first approach of process flowsheet is done to provide sizing figures, TRL 5. A pilot scale prototype will also be designed during this period.  A second phase of development and tests, 2018-2020. This phase will be used to design build the pilot scale prototype, refine glass design and define glass sustainability studies with regards to the development of package description methodology in the face of waste variability. This phase will provide a preliminary book of final process and a preliminary package description, TRL 6.

DEM&MELT Process description

The D&M project takes as a basis a previous development made by CEA for its own needs, the IN CAN MELTER technology for defense waste (Figure 1) [START_REF]Qualification of In-Can Melting Process Applied to Vitrification of High Activity Waste Solutions (HAWS) at the CEA's Valduc Center: Description of Process and Equipment, Methodology and Initial Results[END_REF][START_REF] Gruber | Development of In-Can Melting Process Applied to Vitrification of High Activity Waste Solutions (HAWS): Glass characterizations and process tests results[END_REF]. In this process, the container is used as a crucible ("IN CAN") that is renewed with each batch:  As the crucible is renewed for each batch, that greatly simplifies the equipment and makes it very robust,  There is indeed no need to drain the glass,  Corrosion problems are limited by the batch limited time,  The secondary wastes are limited to the heater as there do not remain after use any components that have been in contact with the molten glass,  Thanks to its small size, the crucible can be easily heated by a simple and robust resistance heated furnace, inexpensive, easy to maintain, easy to implement. This heating mean allows to have a metallic fraction in the canister,  The process has shown considerable flexibility as it will for example for the CEA application be exploited only with two shift teams, idling without operators during night shifts,  The compactness and basic technology of the IN CAN MELTER makes it a low investment equipment compare to other technologies.

The gases treatment is composed of a compact liquid gases treatment adapted from the proven High Level Waste vitrification process used in La Hague facility: a dust scrubber whose retention is continuously recycled with the main feed, a condenser and a gas scrubber.

DEM&MELT State of the R&D 2017

Prototype development

A new prototype has been designed and is under construction for a startup at the beginning of 2019. This prototype will use a 110 liters canister (approximatively 300 kg of glass) which can be inserted after the vitrification operation in a standard qualified canister (French "CSD" canister) as over pack (canister already used in nuclear industry in several countries for compacted waste conditioning). The furnace will have three separate heating zones from bottom to top to manage thermal treatment in the canister. The melter can be fed either with liquid waste or with solid waste. As it can be seen on Figure 2, the studies have focused on the optimization of the footprint, all the major equipments of the process being embedded on a single frame (melter, feeders, and first stage of gases treatment). During these detailed studies, all the nuclearization aspects have been taken into account, such as the choice of the materials, the maintenance operations, to provide a process that can be operated in a hot cell if required by the activity of the waste to treat. Surrogates of a mean composition of this waste have been prepared both in liquid and solid form with inactive cesium spiking. The liquid form simulating the waste recovered from the tanks with an aqueous retrieval process and the solid form simulating the same waste after a drying treatment for interim storage. A specific borosilicate glass has been calculated to incorporate 10% of waste loading.

For the liquid feeding test, 110kg of glass at 6kg/h of mean glass production have been produced at 1100°C from simultaneous feeding of the glass frit and the solution at 4 l/h (with an dry extract of 150g/l). For the solid treatment test, the IN CAN MELTER was preloaded with the glass frit and the dry waste. The thermal treatment consisted in rising progressively the temperature at 1100°C while marking temperature levels stops for the decomposition of the waste species and finally complete the canister with additional glass frit to obtain 110 kg of glass with a 10% waste loading. In both cases, the obtained glass was visually homogeneous (Figure 3). The cesium volatility has been measured during these tests. For the liquid feeding test the cesium volatility in the gases treatment is 0.6 % and for the solid test it is 0.2 %.

THE "PIVIC" PROJECT

Scopes and objectives

Transuranic Mixed metallic and organic wastes are produced during the MOX (Mixed Oxides) fuel manufacturing cycle, where MOX powders and pellets are handled in gloveboxes. Their characteristics are to contain a mixture of organic elements, metal and mineral materials contaminated with uranium, plutonium and americium (ILW). Those waste are source-separated and collected in a selective way according to different "families":

 Organic wastes: gloves from glove boxes, wipes, windows of glove boxes, plastics (PVC…),  Metallic wastes and various elements: electric equipment, defective mechanical products, tooling,  Filters: first filtration barrier, second filtration barrier, grinding machine prefilters, labs filters.

A new thermal process is under development to study a treatment scenario where the waste is stabilized by incineration / vitrification [START_REF] Girold | Mixed Metallic and Organic Transuranic Waste Incineration / Vitrification[END_REF]. This new conditioning process has to meet various requirements:

 Full destruction of organic matter,  Confinement of the radionuclides,  No pre-treatment or sorting,  The process will have to reduce the waste volume,  The final waste package must be compliant with the waste acceptance criteria for the French geological disposal facility CIGEO.

The expected benefits from this development is to provide a better safety in final disposal thanks to the organic mineralization, to stabilize the actinides in a solid matrix, to preserve disposal resources thanks to a volume reduction of around 7.

PIVIC Process description

The purpose of the PIVIC process is to perform in a single reactor the incineration of the organic fraction of waste, the fusion of the metallic fraction, and the incorporation of the incineration residues in a glass matrix.

 The waste are directly fed without preprocessing from the top of the introduction chamber. The gradual lowering of the load in the combustion chamber allow the control of the incineration velocity of the waste.

 The water jacket combustion chamber, receives an oxygen non transferred plasma torch to perform the organics incineration.

 The fusion module is using an in can melting technology, heated by direct low frequency induction. The power is deposited in the metallic phase from the waste found in the bottom of the crucible. This crucible is used as part of the process for the duration of its filling, and as primary container, a new container is placed after each filling. The gases exhausting from the heart of the process are treated in an afterburner chamber to complete the combustion if necessary (only for degraded mode since the oxygen plasma is likely sufficient to achieve a full combustion of the gases in the combustion chamber), a filtering step with an electrostatic precipitator and finally a gas scrubber to treat acidic gases (HCl) generated by the incineration.

The process is not designed to perform the oxidation of metals present in waste and this is not a requirement. This leads to the production of a biphasic package with metal at the bottom and glass as a supernatant due to the difference in density (Figure 5).

PIVIC State of the R&D 2017

The R&D started in 2011, for the development and the qualification of the process and the package, a strategy of using inactive full scale prototypes has been chosen, technologically as close as possible to an industrial nuclearized release.

The first mockup was only the fusion module without the combustion chamber in order to study first the direct low frequency induction heating. This module was started in 2014 and has been operated for two years. During 2017, this first module has been upgraded to the full version of the PIVIC process as described in the previous paragraph. This full prototype is now starting.

Below are the significant achievements of the R&D program:

 The low frequency induction melting concept of a biphasic material has been validated with the elaboration of thirty canisters of roughly 200 kg of metallic alloy made of stainless/copper/Aluminum (melting temperature ~ 1450 °C) and 50 kg of glass (melting temperature ~1250 °C). The canister is correctly cooled and the internal ceramic liner has sufficient corrosion resistance with respect to both the glass and metal phases.

 The metallic fraction is strongly agitated by the electromagnetic forces (Figure 5). As an example, the surface velocity is around 0.1 m.s-1. The glass phase is also correctly agitated, being dragged by the molten metal, the surface velocity is around 0.01 m.s-1.  The package has good macroscopic separation of glass and metal phases (figure 5). In the absence of aluminum in the metals, the glass is homogeneous with a low enrichment of oxidized steel elements (Cr, Mn and Fe) which can crystallize at high concentrations. High concentrations of aluminum in the metals lead to a more crystalline oxide phase since the aluminum is fully oxidized by the glass phase (Figure 6)  The simulants of the actinides are exclusively found in oxides form, dissolved in the glass or in the form of silicates in the case of high concentrations of aluminum.

 Thanks to an oxygen plasma mockup, the feasibility to manage the combustion of the organics by the selected feeding mode (gradual lowering of the load to the bottom of the reactor) has been validated.

 Early studies, based on thermal / hydrodynamic modeling and plasma benchscale with surrogates has shown that the plutonium retention rate will be low enough to be compatible with industrial exploitation, in term of criticality management.

THE "MILOR" PROJECT

Scopes and objectives

The MILOR project, started in September 2017 for four years, is a tripartite project of Industrial Research, between CEA, ANDRA and A3i, which aims the development up to pilot scale of a process of mineralization of Radioactive Organic Liquid Waste (ROLW) by plasma. Two variants of complementary plasma technologies are evaluated: aerial plasma with the "IDOHL" process and submerged plasma with the "ELIPSE" process.

IDOHL Process description

The principle of IDOHL is described in Figure 7 left. The plasma is generated by a 5kW generator and a high frequency inductor (> 1MHz) inducing in the plasma gas. The liquid to be treated is injected directly into the heart of the plasma by means of a suitable rod with the aim of the total destruction of the vaporized liquids in the plasma. The gases produced are then directed to a wet gas treatment system. IDOHL has been designed for organic liquids without mineral load and for treatment rates less than 0.5 l/h. Fig. 7. "IDOHL" (left) and "ELIPSE" (right) process descriptions.

IDOHL State of the R&D 2017

The studies started with a reference liquid waste surrogate: chloroform (CHCl3), an organic low level liquid waste with high amount of chloride and contaminated with tritium and carbon 14. The operating conditions are described in table II. The first results obtained through the treatment at 100g/h rate showed a good efficiency of destruction, but they highlight that the use of water as oxidative agent leads to limit the feeding rate because of two main issues: the high energy requirement to vaporize the water and the immiscibility of some organic liquids in water. These results led to propose the substitution of water by oxygen in order to increase sensibly the throughput of liquid supposed to be incinerated in the plasma [START_REF] Kamgang-Youbi | Inductively coupled plasma torch efficiency at atmospheric pressure for organo-chlorine liquid waste removal: Chloroform destruction in oxidative conditions[END_REF]. The experiments performed with this new running mode have been carried out with CHCl3 for feeding rates ranging from 100 to 400g/h. As forecast through a thermodynamic approach, the results display a destruction efficiency upper than 99% (Table III) and assure that the production of phosgene COCl2 remain small even if the hydrogen coming from water previously has been eliminated (Table IV). Indeed, less than 1g/h of phosgene is produced when HCl and Cl2 content remain within the regulation limits in exhaust gas. This shows that the temperatures inside the plasma area are high enough to transform molecules into atoms and also that the oxygen content is sufficient during the cooling step to obtain finally oxidized stable and non-toxic molecules such as H 2 O and CO 2 . Based on these results, the IDOHL process can know be installed in a radioactive environment to validate the destruction of contaminated wastes. Some design modifications are on the way to accept ROLW containing a small amount of mineral (around 1%w). The gas cleaning system is also being modified in order to be able to use wet or dry way depending on the needs (a dry treatment would allow to produce a solid residue directly compatible with grouting).

ELIPSE Process description

A schematic diagram of the ELIPSE process is shown in Figure 7 right. A plasma torch is submerged in an aqueous solution of demineralized water flowing in a semiclosed loop. During the combustion of the organic charge of the waste introduced in the plasma plume, this solution is progressively loaded with the mineral part of the waste and also heat up under the effect of the thermal radiation of the plasma torch and the calorific value provided by the combustion of the waste. The aqueous solution is thus continuously cooled using a heat exchanger and if necessary, neutralized by controlled addition of NaOH for pH stabilization. The mineral fraction of the waste is recovered by continuously filtering the solution.

The organic liquid waste is injected into the heart of the oxygen plasma via a nozzle placed at the end of the plasma torch. This plasma nozzle is the only hot point of the process, all the rest is maintained at the temperature of the aqueous solution which provides a triple role for the combustion gases: quenching, cooling and gas washing. The combustion gases produced, mainly CO2 and CO in a smaller quantity, are discharged into the gas extraction unit comprising a demister/condenser. This original configuration (submerged plasma) allows the process to be compact while locally offering a high density of power. Thus, the process as a whole remains generally cold, which strongly limits the presence of corrosion phenomena in the other circuits of the process. It thus opens the way to the development of a versatile process for the treatment of a varied range of organic effluents chemically different. ELIPSE has been designed to treat several liters per hour of mineral loaded ROLW.

ELIPSE State of the R&D 2017

Treatment tests were carried out for a phosphorus organic liquid, a mixture of TBP / dodecane, at a flow rate of between 1 and 5 L / h [6]. The efficiency of destruction of the organic effluent is established by Total Organic Carbon Content (TOC) measurement. Knowing the molarity and the initial amounts of carbon introduced into the process, it is possible to establish a destruction efficiency defined by the following relation (1):

(t) = (Q Ci (t)-Q Cs (t))/Q Ci (t) (1)
Q Ci (t) is the total introduced carbon at t, Q Cs (t) is the total measured carbon in the solution at t.

Figure 8 shows the evolution of the residual organic carbon in the aqueous solution of the process circuit during a combustion test campaign at different injection rates of a TBP / dodecane mixture. Four different treatment rates were qualified in this example. Figure 8 also shows the evolution over time of the destruction efficiency (t) established according to relation [START_REF]Qualification of In-Can Melting Process Applied to Vitrification of High Activity Waste Solutions (HAWS) at the CEA's Valduc Center: Description of Process and Equipment, Methodology and Initial Results[END_REF]. The results obtained show that the residual organic carbon increases regularly over time with the feed rate, but without, however, degrading the destruction efficiency. The TOC concentration drop down in several minutes after stopping the feeding. This destruction efficiency is excellent since it remains at a value between 99.7 and 99.9% with a minimum value of 99.1% recorded at the very beginning of combustion. The calculation uncertainty associated with this destruction efficiency value was evaluated at 0.3%.

Figure 8: Change in TOC and performance of processing over time for different TBP/dodecan feeding rates

In order to further improve the performance of the ELIPSE process, further work has recently shown that the radiative properties of the plasma can be used to initiate Fenton-type photochemical reactions by means of the hydrogen peroxide produced in the aqueous solution of the process under the effect of plasma radiation [7].

CONCLUSION

The decommissioning of nuclear facilities and legacy waste treatment bring extremely variable waste in form, compositions and activity levels. Thermal treatments can provide interesting benefits such as volume reduction or chemical stabilization, helping waste producer to master costs, schedule, or to optimize final volume and repository safety. Various processes have to be developed to match the waste specificity with the reasonable balance of development. We have presented in this paper four specific chosen examples of processes currently being developed for particular needs: The DEM&MELT process for a small high level vitrification unit usable in a dismantling environment, the PIVIC process to stabilize mixed organics and metallic transuranic waste with high criticality risk management challenge, the IDOHL or ELIPSE processes for the destruction of the organic fraction of liquid waste.

Fig. 1 .

 1 Fig. 1. The IN CAN MELTER: melter and whole process.

Fig. 2 .

 2 Fig. 2. D&M prototype under construction (top), D&M feasibility studies for hot cell operation.

Fig. 3 .

 3 Fig. 3. Canister of the IN CAN MELTER cut in half after vitrification preliminary tests of a dismantling tank deposit high level waste.

Fig. 4 .

 4 Fig. 4. PIVIC process description.

Fig. 5 .

 5 Fig. 5. PIVIC canister cut in 2 (left), thermal and hydrodynamic behavior of the direct induction heating process (right)

Fig. 6 .

 6 Fig. 6. PIVIC glass product, without aluminum on the left And with high concentration of Al in the waste on the right.

  6. ELIPSE: An innovative technology for the treatment of radioactive organic liquids, F. Lemont, M. Marchand, M. Mabrouk, D. Milelli, JM. Baronnet, Nuclear technology, 198 :1, 53-63, DOI : 10.1080/00295450.2017.1289009 7. Thermo-and photo-oxidation reaction scheme in a treatment system using submerged plasma, D. Milelli, F. Lemont, L. Ruffel, T. Barral, M. Marchand, Chemical engineering journal, 1385-8947/ 2017. Elsevier B.V. All rights reserved

  Using the existing IN CAN MELTER prototype, preliminary tests have been performed before starting the building of the new DEM&MELT prototype. The objective was to test the vitrification of an identified waste from dismantling operation in Marcoule (Nuclear Site in Chusclan -France)[START_REF]Management of HL deposits for the D&D of UP1 reprocessing plant. Retrieval and treatment scenarios including onsite simplified vitrification device[END_REF] both in liquid and solid feeding. The waste range composition is given in table I, it represents deposits that are found in old tanks or evaporators from Marcoule shutdown reprocessing facility (named UP1). Cs_137 represent more than 95% of the activity of these deposits. The main elements (about 50% in weight) composing the deposits are Zr, Si, Mo, Fe and P. Phosphorus exists as phosphate, which is the end-product of the solvent degradation. Comprehensive reviews of these results, of the reprocessing literature and of the operating history lead us to conclude that the deposits are mainly composed of 4 types of components:

WM2018 Conference, March 18-22, 2018, Phoenix, Arizona, USA 6 Preliminary tests  Zr complexes : Zr(HPO4)2,nH2O and/or ZrMo2O7(OH)2  Cs complex of the type CsxPMoyOz  Pu complexes : Pu phosphate and/or Pu Molybdate,  Oxides and hydroxides: ZrO2,nH2O, PuO2,nH2O, MoO3,nH20.

Table I .

 I Major constituents of the High Level deposits considered for a vitrification test[START_REF]Management of HL deposits for the D&D of UP1 reprocessing plant. Retrieval and treatment scenarios including onsite simplified vitrification device[END_REF]

	Element	Elementary composition of the deposits (%w of dry sample)
		Tank 71.21A	Tank 71.21B	Tank71.21C
	Zr	14 -17	10 -18	16 -21
	P	7 -11	4 -11	5 -36
	Si	3 -10	4 -23	3 -33
	Mo	3 -7	0.4 -8	3 -30
	Fe	0.5 -3	1 -2	1 -4
	Al	0.5 -1.4	0.5 -1	0.5 -2
	Dose rate in contact with the deposit	245	150	38
	(Gy/h)
	Cs Specific activity of the deposits	2.10 9 _ 1.3 10 10	2.10 9 _ 1.1 10 10	4.410 8 _ 1.1 10 10
	(Bq/g of dry sample)

Table III .

 III Conversion of CHCl 3 in IDOHL

	CHCl 3 feed rate (g•h -1 )	O 2 (NL•min -1 )	CHCl 3 destruction (%)	Conversion to CO 2 (%)	Initial Cl conversion to HCl (%)	Conversion to Cl 2 (%)
	100	7 10	99.95 99.96	99.16 99.34	32.70 31.55	62.98 64.04
		7	99.09	88.59	31.14	ND
	150	10	99.71	99.67	29.44	66.75
		14	99.95	>99.99	28.72	69.14
		14	99.70	98.45	27.40	64.50
	200	17	99.95	>99.99	28.44	70.00
		20	99.98	>99.99	26.38	73.35
	300	20	99.96	97.20	24.88	ND
		20	99.94	>99.99	24.32	ND
	400	24	99.98	96.18	25.74	ND
		28	99.98	94.33	26.30	ND
	ND: Not Determined

Table IVV .

 IVV Maximum phosgene release per chloroform injected in IDOHL

	Initial composition CHCl 3 (g•h -1 ) O 2 (NL•min -1 )	COCl 2 conc. (ppm)	Mass of COCl 2 released (g•h -1 )
	100	7	11	0.30
	150	14	12.5	0.37
	200	20	30	0.93
	300	20	22.5	0.70
	400	20	28	0.93

ACKNOWLEDGEMENTS

The PIVIC, DEM & MELT and MILOR projects are partnership between CEA, industrial partners (AREVA, ECM Technologies, and A3I) and ANDRA. They are supported by the French government program "Programme d'Investissements d'Avenir" whose management has been entrusted to ANDRA.


Minjia Shi

Patrick Solé

Three-weight codes, triple sum sets, and strongly walk regular graphs

Keywords: Strongly walk-regular graphs, Three-weight codes, Triple sum sets Mathematics Subject Classification Primary 05 E 30, Secondary 94 B 05

We construct strongly walk-regular graphs as coset graphs of the duals of three-weight codes over F q . The columns of the check matrix of the code form a triple sum set, a natural generalization of partial difference sets. Many infinite families of such graphs are constructed from cyclic codes, Boolean functions, and trace codes over fields and rings. Classification in short code lengths is made for q = 2, 3, 4.

Introduction

Since the seminal article of Delsarte [START_REF] Delsarte | Weights of linear codes and strongly regular normed spaces[END_REF], there is a well-known interplay between two-weight codes and strongly regular graphs (SRG) via the coset graph of the dual code [START_REF] Brouwer | Distance-Regular Graphs[END_REF][START_REF] Brouwer | Spectra of Graphs[END_REF][START_REF] Shi | On two weight Z k 2 -codes[END_REF]. Strongly walk-regular graphs (SWRG) were introduced in [START_REF] Van Dam | Strongly walk-regular graphs[END_REF] as a generalization of strongly regular graphs. Instead of a regularity condition bearing on paths of length 2, the notion of SWRG demands a regularity on paths of length > 1. Specifically, a graph is -SWRG if there are three integers (λ, μ, ν) such that the number of paths of length between any two vertices x and y is • λ if x and y are connected; • μ if x and y are disconnected;

• ν if x = y.
Thus = 2 is the case of SRGs. Note that, by definition SRGs are -SWRG for all > 1. In [START_REF] Courteau | On triple sum sets and two or three-weight codes[END_REF] was introduced the notion of triple sum set, a natural generalization of partial difference sets, which enter the study of two-weight codes [START_REF] Calderbank | The geometry of two-weight codes[END_REF][START_REF] Ma | A survey of partial differences sets[END_REF]. Let F q denote the finite field of order q. The set ⊆ F k q is a triple sum set (TSS) if it is stable by scalar multiplication and if there are constants σ 0 and σ 1 such that a nonzero h ∈ F k q can be written as h = x + y + z, with x, y, z ∈ ,

• σ 0 times if h ∈ , • σ 1 times if h ∈ F k q \ .
This was generalized in [START_REF] Griera | On s-sum sets and three weight projective codes[END_REF][START_REF] Griera | On s-sum sets and projective codes[END_REF] to the notion of s-sum set by replacing the equation h =

x + y + z by h = s i=1

x i where each x i ∈ .

The aim of this note is to connect these two notions by means of a third one: the coset graph of a projective code [START_REF] Brouwer | Distance-Regular Graphs[END_REF]. The graphical approach of [START_REF] Van Dam | Strongly walk-regular graphs[END_REF] makes several results on multiple sum sets of [START_REF] Courteau | On triple sum sets and two or three-weight codes[END_REF][START_REF] Griera | On s-sum sets and three weight projective codes[END_REF][START_REF] Griera | On s-sum sets and projective codes[END_REF] more transparent. Sometimes, new results are obtained (Theorem 6). In the other direction, three-weight codes with known weight distributions provide many infinite families of SWRGs with integral spectra that would be hard to construct otherwise. Some classical tools of coding theory (Pless power moments, MacWilliams transform) allow us to classify short codes over F q with q = 2, 3, 4, that satisfy the hypotheses of Theorem 6, thus yielding s-sum sets for all odd s > 1.

The material is organized as follows. The next section collects the necessary definitions, notations, and background material. The theoretical results are contained in Sect. 3. Section 4 classifies the three-weight codes of short length with the parameters of Theorem 6 for q = 2, 3, 4. Sect. 5 is devoted to many examples of constructions. Section 6 puts the results into perspective and lists several challenging open problems.

Definitions and notation

Graphs

All graphs in this note are finite, undirected, connected, without multiple edges. Loops, however, will be allowed. The neighborhood (x) is the set of vertices connected to x. The degree of a vertex x is the size of (x). A graph is regular if every vertex has the same degree. The i-neighborhood i (x) is the set of vertices at geodetic distance i to x. A graph is distance regular (DR) if for every pair of vertices u and v at distance i apart the quantities

a i = | i+1 (u) ∩ (v)| c i = | i-1 (u) ∩ (v)|
solely depend on i and not on the special choice of the pair (u, v). In that situation the graphs i are regular of degree v i and we will refer to the v i s as the successive degrees of . A DR graph of diameter 2 is called a Strongly Regular Graph (SRG). Its parameters (ν, κ, λ, μ) denote the number of vertices, the degree, the number of common neighbors of a pair of connected vertices, the number of common neighbors of a pair of disconnected vertices. The spectrum of a graph is the set of distinct eigenvalues of its adjacency matrix. It is denoted by {λ m 1 1 , λ m 2 2 , . . . }, where m i stands for the multiplicity of the eigenvalue λ i .

Linear codes

A linear q-ary code of length n, dimension k, minimum distance d is called an [n, k, d] q , or an [n, k] q code for short. The (Hamming) weight of x ∈ F n q is the number of indices i where x i = 0. A two-weight code is an [n, k] q linear code having two nonzero weights w 1 and w 2 . A three-weight code or 3-weight code is an [n, k] q linear code having three nonzero weights w 1 < w 2 < w 3 . In general, the weight distribution of the code is written in compact form as [ i, A i ] where i runs over the weights in the code, and A i is the number of codewords of weight i. The dual weight distribution is the weight distribution of the dual code. The duality is understood with respect to the standard inner product. The external distance of a linear code is the number of nonzero weights in its dual. A coset of a linear code C is any translate of C by a constant vector. A coset leader is any coset element that minimizes the weight. The weight of a coset is the weight of any of its leaders. The covering radius is the maximum weight of a coset. The coset graph C of a code C is defined on the cosets of C, two cosets being connected if they differ by a coset of weight one. Thus the diameter of this graph equals the covering radius of the code. A code is completely regular if the weight distribution of each of its cosets only depend on the weight of its coset leader. It is known [START_REF] Brouwer | Distance-Regular Graphs[END_REF] that a code is completely regular iff its coset graph is a DR graph. In that case its covering radius equals its dual distance.

From [1, Theorem 1.11.1], we have the following fact.

Theorem 1 If C is a q-ary code, of minimum distance at least three, with dual weight distribution [ i, A i ], then the spectrum of C is {(n(q -1)qi) A i }. Thus A i is the frequency of weight i in C ⊥ and the multiplicity of the eigenvalue n(q -1)qi.

A code is projective if the minimum distance of its dual code is at least three. The coset graph with b loops b C of a code C is obtained from C by adding b loops around every vertex. The following result is immediate from the previous theorem.

Corollary 1 If C is a q-ary code, of minimum distance at least three, with dual weight distribution

[ i, A i ], then the spectrum of b C is {(b + n(q -1) -qi) A i }.
Thus A i is the frequency of weight i in C ⊥ and the multiplicity of the eigenvalue b + n(q -1)qi.

Main results

If ⊆ F k q and 0 / ∈ , we denote by C( ) the projective code of length n = | | q-1 obtained as the kernel of the k × n matrix H with columns the projectively non equivalent non zero elements of . Thus H is the check matrix of C( ). To simplify notation, let C( ) = ( )

and b C( ) = ( ) b .
The following result is immediate from the definitions in the Introduction, and will be used repeatedly and implicitly in the rest of the paper.

Theorem 2

The following are equivalent

• (resp 0) is an s-sum set, • ( ) (resp. ( ) 1 ) is an s-SWRG.
Proof Observe that ( ) is a Cayley graph on the group (F k q , +) with generators the columns of H . Thus the definition of an s-sum set can be regarded as a statement on the number of paths of length s between 0 and h.

123

The following result comes from the well-known connection between SRGs and twoweight codes [START_REF] Brouwer | Distance-Regular Graphs[END_REF][START_REF] Brouwer | Spectra of Graphs[END_REF]. It was observed implicitly in [START_REF] Courteau | On triple sum sets and two or three-weight codes[END_REF].

Theorem 3 If C( ) ⊥ is a two-weight code, then both 0 and are s-sum sets for all s > 1.

Proof If C( ) ⊥ is a two-weight code, it is well-known that ( ) is an SRG [START_REF] Brouwer | Distance-Regular Graphs[END_REF][START_REF] Brouwer | Spectra of Graphs[END_REF]. The result follows by Theorem 2, and the observation, made in the Introduction, that SRGs are s-SWRG for all s > 1.

The following result was observed in [START_REF] Griera | On s-sum sets and projective codes[END_REF]Theorem III.6].

Theorem 4 If or

0 is an s-sum sets, then C( ) ⊥ has at most three non-zero weights. Furthermore, if s is even, then C( ) ⊥ is an s-weight code.

We come to the coding-theoretic characterization of 3-sum sets which is contained in a slightly less detailed form in [4, Theorem 2.1]. The consideration of coset graphs with loops might seem artificial but is justified by the existence of several non trivial examples, as evidenced by Sect. 4.

Theorem 5 Assume that C( ) ⊥ is of length n and has three nonzero weights w 1 < w 2 < w 3 . Let b be any integer.

• is a 3-sum set iff w 1 + w 2 + w 3 = 3n(q-1) q ; • 0 is a TSS iff w 1 + w 2 + w 3 = 3(1+n(q-1)) q ; • b C( ) is a 3-SWRG iff w 1 + w 2 + w 3 = 3(b+n(q-1)) q .
Proof Follows by [START_REF] Van Dam | Strongly walk-regular graphs[END_REF] Proposition 4.1, upon using either Theorem 1 or its corollary.

Remark

In general, the parameters λ, μ, ν of a 3-SWRG graph are related to the three nontrivial eigenvalues of the graph by the system of three equations in three unknowns given by [20, Prop. The following result is new in the context of s-sum sets.

Theorem 6 Assume that C( ) ⊥ is of length n and has three nonzero weights w 1 < w 2 = n(q-1) q < w 3 , with w 1 + w 3 = 2n(q-1)

q

. Then is an s-sum set for all odd s > 1.

Proof Follows by [START_REF] Van Dam | Strongly walk-regular graphs[END_REF] Proposition 4.2, upon using Theorem 1.

The following result improves Prop. 4.3 of [START_REF] Griera | On s-sum sets and three weight projective codes[END_REF] by giving a simpler and more explicit diophantine equation bearing on the weights of C( ) ⊥ .

Theorem 7 Assume that C( ) ⊥ is of length n and has three nonzero weights w 1 < w 2 < w 3 . Let b be any integer.

• is an s-sum set iff (w 3 -w 2 )(n(q -1) -qw 1 ) s + (w 1 -w 3 )(n(q -1) -qw 2 ) s + (w 2 -w 1 )(n(q -1) -qw 3 ) s = 0. • 0 is an s-sum set iff (w 3 -w 2 )(1 + n(q -1) -qw 1 ) s + (w 1 -w 3 )(1 + n(q -1) - qw 2 ) s + (w 2 -w 1 )(1 + n(q -1) -qw 2 ) s = 0. • b C( ) is an s-SWRG iff (w 3 -w 2 )(b + n(q -1) -qw 1 ) s + (w 1 -w 3 )(b + n(q -1) - qw 2 ) s + (w 2 -w 1 )(b + n(q -1) -qw 2 ) s = 0.
Proof Follows by [START_REF] Van Dam | Strongly walk-regular graphs[END_REF] Proposition 4.3, upon using Theorem 1 or its corollary.

Example 4 If n = 24, q = 2 the only triples (w 1 , w 2 , w 3 ) satisfying the first condition of the above theorem for s = 5 are those satisfying the conditions of Theorem 6, namely {11 + i, 12, 13 + i}, for i = 0, 1, . . . , 10.

Motivated by many similar examples, we are led to the following conjecture.

Conjecture

is an s-sum set for some s > 3 iff

(w 1 , w 2 , w 3 ) = (w 1 , n(q -1) q , 2n(q -1) q -w 1 ),
for some 0 < w 1 < n(q-1) q . In other words, the only s-sum sets for s > 3 are those satisfying the hypotheses of Theorem 6. This is consistent with the observation in [20, p. 808]: "It remains open whether there are -SWRG with > 3 that are not m-SWRG for all odd m = ". The next result shows that, when the conditions of Theorem 6 are not satisfied, a given code can yield an s-sum set for at most one value of s. Theorem 8 Assume that C( ) ⊥ is of length n and has three nonzero weights w 1 < w 2 < w 3 . If w 2 = n(q-1) q , or w 1 + w 3 = 2n(q-1) q , then there is at most one s > 1 such that is an s-sum set.

Proof Follows by [20, Theorem 4.4], upon using Theorem 1 or its corollary.

Classification in short lengths

In this section we classify three-weight codes satisfying Theorem 6 for q = 2, 3, 4, and n small. For a 3-weight code C of parameters [n, k] q with weights w 1 < w 2 < w 3 , dual distance ≥ 3, and respective frequencies

A 1 = A w 1 , A 2 = A w 2 , A 3 = A w 3 , denoted here by [A 1 , A 2 , A 3 ],
we recall the Pless power moments (PPM) [START_REF] Huffman | Fundamentals of Error Correcting Codes[END_REF].

A 1 + A 2 + A 3 = q k -1 A 1 w 1 + A 2 w 2 + A 3 w 3 = n(q -1)q k-1 A 1 w 2 1 + A 2 w 2 2 + A 3 w 2 3 = n(q -1)(1 + n(q -1))q k-2 .
123

The dimension of C is constrained by the fact that the distance of C ⊥ is ≥ 3. This gives an upper bound on nk by the tables of [10] , and thus, a lower bound on k. The Delsarte bound [START_REF] Huffman | Fundamentals of Error Correcting Codes[END_REF]Theorem 11.3.3] states that the covering radius of a code is at most its external distance. Since C is a 3-weight code, the covering radius of C ⊥ is ≤ 3. This implies by the sphere-covering bound [5, p. 18] that

q k ≤ 1 + n(q -1) + n 2 (q -1) 2 + n 3 (q -1) 3 .
When q = 2, we can also use the tables on t[N , K ] the smallest covering radius of an [N , K ] 2 code [5, p. 191]. This provides an upper bound on k. We denote by B K LC(G F(q), n, k) the code given by Magma [15], as an [n, k, d] q with the largest d.

Binary codes

Observe first that, from the expression for w 2 , the length n must be even.

• -The Pless power moments return negative frequencies for a 3-weight codes with weights [START_REF] Calderbank | The geometry of two-weight codes[END_REF][START_REF] Courteau | On triple sum sets and two or three-weight codes[END_REF][START_REF] Cohen | Covering Codes[END_REF] and dual distance ≥ 3.

• If n = 10, the PPM eliminate all parameters.

• If n = 12, similar arguments as for n = 8 only allows the weights (5, 6, 7) and [START_REF] Courteau | On triple sum sets and two or three-weight codes[END_REF][START_REF] Delsarte | Weights of linear codes and strongly regular normed spaces[END_REF][START_REF] Ding | Binary linear codes with three weight[END_REF]. The first set admits the unique frequencies [START_REF] Calderbank | The geometry of two-weight codes[END_REF][START_REF] Calderbank | The geometry of two-weight codes[END_REF][START_REF] Ding | Three-weight cyclic codes and their weight distributions[END_REF]. This is impossible since we must have k ≥ 5. The second set admits eight possible triples of frequencies which reduce to 4 after using 5 ≤ k ≤ 8. These triples are [START_REF] Riera | A complete characterization of plateaued Boolean functions in terms of their Cayley graph[END_REF][START_REF] Griera | On s-sum sets and projective codes[END_REF][START_REF] Calderbank | The geometry of two-weight codes[END_REF] 123

These are B K LC(G F(2), 12, 5) and B K LC(G F(2), 12, 6) respectively. We do not know if they are unique with these weight distributions.

Ternary codes

Observe first that, from the expression for w 2 , the length n must be a multiple of 3. Note also that a ternary code can only have even frequencies since the map x → -x is a Hamming isomorphism.

• If n = 3, we obtain the solution (1, 2, 3) for the weights, and [START_REF] Delsarte | Weights of linear codes and strongly regular normed spaces[END_REF][START_REF] Griera | On s-sum sets and projective codes[END_REF][START_REF] Ding | Binary linear codes with three weight[END_REF] for the frequencies, which determines uniquely the universe code

F 3 3 . • If n = 6,

Quaternary codes

Observe first that, from the expression for w 2 , the length n must be a multiple of 4.

• If n = 4, there is no possible triple of weights.

Binary cyclic codes

There are many examples from binary cyclic codes. If we consider the codes of length n = 2 m -1 with either the weights in [9, Tables 1,2], that is either {2 m-1 , 2 m-1 ± 2 m-1-}, or {2 m-1 , 2 m-1 ±2 (m-2)/2 }, we see that the second condition of Theorem 5 is satisfied. These codes are cyclic codes with two zeros, closely related to preferred pairs of m-sequences [START_REF] Sarwate | Crosscorrelation properties of pseudorandom and related sequences[END_REF].

q-ary cyclic codes

If we consider the codes C ⊥ of length n = q m -1 with the weights in [9, Tables 678] they satisfy the relation

w 1 + w 2 + w 3 = 3(1 -1/q)(n + 1).
This shows, upon applying the third condition of Theorem 5 that the coset graph q-1 C with q -1 loops is a 3-SWRG.

Codes from Boolean functions

In [START_REF] Riera | A complete characterization of plateaued Boolean functions in terms of their Cayley graph[END_REF] it is proved that so-called plateaued Boolean functions f on F n 2 have a Cayley graph G f on the group (F n 2 , +) with generating set the support of f that is

f = {x ∈ F n 2 | f (x) = 1},
that is 3-SWRG and -SWRG for all odd [16, Theorem 2]. Actually, this is the situation of Theorem 6. Thus, f is a TSS, and an -sum set for all odd . Moreover, C( f ) is a three weight code of length | f | and codimension n. In that case the weights of

C( f ) are { n 2 , n±2 (n+s-2)/2 2 }
, where s is a parameter depending on f . These codes were introduced first in [START_REF] Ding | Linear codes from some 2-designs[END_REF].

Trace codes over fields

The binary codes C ⊥ of length n = 2 m-1 -1 with the weights in Table 1 of [START_REF] Ding | Binary linear codes with three weight[END_REF], satisfy the relation

w 1 + w 2 + w 3 = 3(1 -1/2)(n + 1).
This shows, by the third condition of Theorem 5, that the coset graph 1 C is a 3-SWRG. It also shows, by the second condition of Theorem 5, that the corresponding with 0 adjoined is TSS. The p-ary codes C ⊥ of length n = p m-1 -1 with the weights in [21, Tables 34] satisfy the relation

w 1 + w 2 + w 3 = 3(1 -1/ p)(n + 1).
This shows, by the third condition of Theorem 5, that the coset graph p-1 C with p -1 loops is a 3-SWRG.

n q Graph References 2 m -1 2 3 1 C [9] q m -1 q 3 q-1 C [9] 2 m 2 O d d C [16]
2 m-1 -1 2 3

Trace codes over rings

Trace codes over rings can give few-weight codes over fields by application of a Gray map.

The three-weight p-ary codes C ⊥ of length n = p 2mp m in [START_REF] Shi | Two and three weight codes over F p + uF p[END_REF] satisfy the relation

w 1 + w 2 + w 3 = 3(1 -1/ p)n.
This shows, by the first condition of Theorem 5, that the coset graph C is a 3-SWRG, or, equivalently, that the such that C( ) = C is a TSS.

Summary

We summarize the previous subsections in the following table.

Conclusion and open problems

In this article, we have developed the dictionary between multiple sum sets and strongly walk-regular graphs via the coset graph of the code attached to such a set. Motivated by concrete examples we have considered coset graphs with loops. In comparison with the classical works on the topic [START_REF] Courteau | On triple sum sets and two or three-weight codes[END_REF][START_REF] Griera | On s-sum sets and three weight projective codes[END_REF][START_REF] Griera | On s-sum sets and projective codes[END_REF] our note contains many infinite families of such sets or graphs. It seems that most known families of three-weight codes were constructed in the last five years. Classification in short length has been made for q = 2, 3, 4. It might be of interest to go for larger fields or longer lengths.

One aim of research would be to find more three-weight codes satisfying the first condition of Theorem 5. Only one infinite family can be found in §4. Another open problem would be to characterize by their parameters three-weight codes the coset graph of the dual code of which is both DR and SWRG. Example 3 shows that this is not always true. Eventually, the main open problem is the Conjecture of Sect. 3, which can be summarized as follows: an s-sum set for some s > 3 is an s-sum set for all odd s > 3.

  If n = 4 or n = 6 the PPM eliminate all sets of parameters, returning non integral or non positive solutions. • If n = 8, q = 2 the only triples (w 1 , w 2 , w 3 ) satisfying the first condition of the above theorem for s = 5 are {(1, 4, 7), (2, 4, 6), (3, 4, 5)}. -It is easy to see that 1, 4, 7 cannot be the three weights of a binary code since 4-1 = 3, and 4 + 1 = 5. -It can be proved, using Pless power moments, and MacWilliams transform, that there are exactly two codes of length 8, distance ≤ 3, and dual weights (2, 4, 6), a [8, 2, 3] and a [8, 3, 3] with respective weight distributions [ 0, 1 , 3, 1 , 5, 1 , 8, 1 ], and [ 0, 1 , 3, 2 , 4, 2 , 5, 2 , 8, 1 ].

  If C( ) is the perfect binary Golay code, its dual weights are 8, 12, 16, and the second condition of the above theorem is satisfied If C( ) is the extended ternary Golay code, its coset graph is distance regular[START_REF] Brouwer | Distance-Regular Graphs[END_REF]. Still, since its dual weights are 8, 12, 16, neither condition is satisfied, even though ( ) is DR. This is a case where DR does not imply SWRG.

	8 + 12 + 16 =	3(23 + 1) 2	.
	Example 3

3.1]. The resulting formulas are too messy to be displayed. Example 1 If q = 2 and n = 8, then the possible triples of weights are {345, 246, 156, 237, 147, 138}. Example 2

  , [26, 24, 13], [42, 40, 45], [90, 72, 93].The last two can be eliminated by MacWilliams transform. There are two codes with

[ 0, 1 , 4, 16 , 6, 12 , 8, 3 ] or [ 0, 1 , 4, 26 , 6, 24 , 8, 13 ].

  the only admissible triple of weights is[START_REF] Brouwer | Spectra of Graphs[END_REF][START_REF] Courteau | On triple sum sets and two or three-weight codes[END_REF][START_REF] Delsarte | Weights of linear codes and strongly regular normed spaces[END_REF] which is impossible by the PPM.• If n = 9, the only admissible triple of weights are[START_REF] Calderbank | The geometry of two-weight codes[END_REF][START_REF] Delsarte | Weights of linear codes and strongly regular normed spaces[END_REF][START_REF] Ding | Three-weight cyclic codes and their weight distributions[END_REF],[START_REF] Courteau | On triple sum sets and two or three-weight codes[END_REF][START_REF] Delsarte | Weights of linear codes and strongly regular normed spaces[END_REF][START_REF] Ding | Binary linear codes with three weight[END_REF],[START_REF] Cohen | Covering Codes[END_REF][START_REF] Delsarte | Weights of linear codes and strongly regular normed spaces[END_REF][START_REF] Ding | Linear codes from some 2-designs[END_REF]. Observing that 3 ≤ k ≤ 6, the possible triple of frequencies given by the PPM are, respectively, -[6, 66, 8], [24, 192, 26] and [78, 570, 80]. The last two can be ruled out by MacWilliams transform. We leave the construction of a ternary 3-weight code with weight distribution [ 0, 1 , 3, 6 , 6, 68 , 9, 8 ] as an open problem. -None that is integral. -[6, 8, 12]. A code with the dual weight distribution is B K LC(G F(3), 9, 6) in Magma notation. This code has covering radius 2, missing the Delsarte bound by one. Hence it is not completely regular. So its coset graph is not DR, hence not a SRG, but it is an s-SWRG for all odd s! • If n = 12, the only triple of weights not eliminated by PPM is (6, 8, 10). We know that 3 ≤ k ≤ 6. The only admissible triple of frequencies compatible with this condition are [17, 42, 21], [71, 96, 75] and [233, 258, 237] which all contain odd components. No code for n = 12.

  • If n = 8, the possible triples of weights are (4, 6, 8) and[START_REF] Cohen | Covering Codes[END_REF][START_REF] Delsarte | Weights of linear codes and strongly regular normed spaces[END_REF][START_REF] Ding | Linear codes from some 2-designs[END_REF]. The respective triple of frequencies are [27,[START_REF] Calderbank | The geometry of two-weight codes[END_REF] 33], in the latter case, and

	5 Infinite families
	[6, 48, 9], [42, 168, 45], [186, 648, 189]
	in the former, using the conditions 3 ≤ k ≤ 5. The triple [27, 3, 33], leads to a
	MacWilliams transform with negative coefficients. A similar phenomenon happens for
	[186, 648, 189]. The triple of frequencies [42, 168, 45] is realized for the binary first
	order Reed-Mueller code R M(1, 3) read over F 4 . The existence of an [8, 3] 4 with weight
	distribution
	[ 0, 1 , 4, 6 , 6, 48 , 8, 9 ],
	is left as an open problem.
	123

Table 1

 1 Constructions from codes

Communicated by J. H. Koolen.

This research is supported by National Natural Science Foundation of China (61672036), Excellent Youth Foundation of Natural Science Foundation of Anhui Province (1808085J20).

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