Florian Cuminet

Sébastien Lemouzy

Éric Dantras

Éric Leclerc

Vincent Ladmiral

Sylvain Caillol

From vineyards to reshapable materials: α-CF 2 activation in 100 % resveratrol-based catalyst-free vitrimers

a Vitrimers are a class of polymers bridging the gap between resistant crosslinked thermosets and recyclable linear thermoplastics. The first vitrimer ever described was a polyester network requiring relatively high catalyst loadings to be reshaped. This feature raises concerns about catalyst potentially leaching out of the materials and accelerated ageing upon reprocessing cycles. Recently, strategies such as activation of the exchange reaction by inductive effects or neighboring group participation have been implemented in vitrimers allowing to produce reshapable materials which do not require a catalyst. Hence, α,α-difluoro esters proved to be very prone to transesterification owing from the strong electronwithdrawing character of the CF2 group resulting from the very high electronegativity of the fluorine atom. This feature implemented in polyester vitrimers enabled the synthesis of catalyst-free reshapable highly crosslinked networks. Moreover, this principle initially designed on petro-based monomers is here successfully adapted to resveratrol, a biobased polyphenol found in high concentration in grapes and Japanese knotweed (Reynoutria japonica). The material presented contains 86 % bio-based carbon, is catalyst-free, durable and recyclable and features a high Tg.

Introduction

Vitrimers are a class of polymer materials which exhibits excellent mechanical properties and the ability to be recycled mechanically.

1,2

Ideally, they combine the best of thermoplastics, which are often easily recyclable, and thermosets, which are endowed with very good mechanical properties and resistance at high temperature. These exceptional properties come from their structure. While thermoplastics are essentially a network of entangled linear chains which cohesion is due to weak bonds, thermosets are a tridimensional network made of strong covalent bonds. 3 Vitrimers are also 3D networks made of covalent bonds, but some of these bonds feature a singular property they are exchangeable with each other, or with free reactive groups on the polymer segments, by a degenerate chemical equilibrium. [START_REF] Capelot | [END_REF][5][6][7] These exchanges are usually activated by heat and are accountable for the vitrimers flow and recyclability at high temperature. Vitrimers were invented a decade ago, and first illustrated with polyesters able to flow thanks to a transesterification reaction. 8 They are of particular interest in the field of composites, in which the polymer matrix needs high mechanical performances and thermal resistance 9,10 but is very a challenge to recycle. 11,12 Vitrimers which can be reshaped upon heating and be depolymerized by solvolysis, could be a solution to address the issue of composites recycling. [13][14][15] However, for such applications it is desirable to obtain rigid materials with high T g . [16][17][18][19] Fourteen examples of vitrimers with T g above 100 °C were already reported. For instance, epoxy-anhydride vitrimers catalyzed by zinc (II) with T g values up to 140 °C were described, but they required hard reprocessing conditions, at 250 °C under 500 bars. 20 A epoxyacid system catalyzed by Sn(II) with 2 equivalents of epoxy compared to the acid allowed to reach a T g at 231 °C thanks to the homopolymerization of the epoxy. 21 However, the resulting ether bonds cannot be reversibly cleaved in the reshaping conditions, which therefore limits the material reprocessability. Furthermore, in the case of transesterification vitrimers, an external catalyst is usually required to accelerate the transesterification reaction, so that the material may flow at a measurable timescale and be recycled. 22 The use of catalysts such as zinc(II) and triazabicyclodecene (TBD) raises concerns about potential leaching of the catalyst out of the material, and premature ageing of the vitrimer after several recycling/reshaping cycles. [23][24][25] For these reasons, the use of catalyst-free vitrimers is preferable. A first strategy is to use other exchange reactions, for instance vinylogous urethanes, 26 polythiourethanes, 27 disulfides, 28,29 imine bonds, [30][31][32][33] silyl ethers, 34 and Si-O-Ph bonds. 35 Several other strategies were described to make catalyst-free vitrimers, in particular in the case of transesterification vitrimers. Hyperbranched vitrimers featuring a loose network allowed catalyst-free reprocessing, but their mechanical properties were fairly limited. 36 A high concentration of free hydroxyl groups in the network also accelerates the transesterification, but it implies limitations in terms of accessible monomers and network structures and properties, and may increase the water intake of such materials. 37,38 The kinetics of the exchange reaction can also be increased by an activating group, linked to the network, in proximity to the exchangeable bonds. 39,40 In particular, fluorinated esters were recently proven to undergo fast transesterification without the recourse to an external catalyst, both in solution 41 and in vitrimers. 42,43 Furthermore, in a context of increasing tension on crude oil supply and price volatility, the pursuit of biobased materials is of booming interest to increase polymers sustainability. [44][45][START_REF] Caillol | Natural Polymers and Biopolymers II[END_REF] The first vitrimer was partly biobased as the polyfunctional carboxylic acid used was made from dimers and trimers of fatty acids.

8

Many naturally occurring building blocks can be used in the synthesis of vitrimers, such as lignins, phenols, furans, oils, polysaccharides, carboxylic acids or natural rubber. [START_REF] Lucherelli | [END_REF] In particular, several examples of biobased vitrimers based on natural phenols such as vanillin, 48-50 eugenol 51,52 or cardanol 53 for instance have been reported. However, only few of them exhibit a T g over 100 °C and high thermal stability, two precious properties for biobased vitrimers. 54 Some example of catalyzed biobased vitrimers with high T g were described 55,56 but only two examples of high-T g catalyst-free biobased vitrimers were reported. The first example is based on acetal exchange, with a T g up to 121 °C. 57 The other example is based on transesterification activated by tertiary amines in polybenzoxazines, with T g ranging from 143 to 193 °C. 58 Many of the high-T g vitrimers reported so far are based on monomers featuring aromatic structures. Biobased phenols and furans, [START_REF] Lucherelli | [END_REF] thanks to their aromatic cycles and often compact structures, can provide high crosslinking density, rigidity, high T g and thermal resistance to vitrimers.

In the work presented here, a catalyst-free, high T g biobased Scheme 1. 2-step synthesis of RvOH-TAF from resveratrol Scheme 2. Synthesis of epoxydized resveratrol RvOGly transesterification vitrimer was synthesized from resveratrol, a biobased triphenol mainly found in grapes, peanuts and a plant called Japanese knotweed (Reynoutria japonica).

59,60

Resveratol can be obtained from the rhizomes of this invasive plant for its valorization after uprooting. 61,62 The goal was to achieve high mechanical properties and reach high T g thanks to the high aromatic carbon content of this bioresource.

Resveratrol was functionalized to prepare two building blocks: a trifunctional epoxy, and a trifunctional α,α-difluorocarboxylic acid. The rationale was that the ring-opening polyaddition of these building blocks would lead to a dense network, endowed with high T g and transesterification capability via fluorine group activation.

Results and Discussion

α,α-Difluoro Carboxylic Acid Monomer Synthesis α,α-Difluoro carboxylic acids were proven to activate the transesterification reaction in polyester networks, without the need for any catalyst, thus enabling the synthesis of catalystfree transesterification vitrimers. 41,43 A biobased tris α,αdifluoro carboxylic acid was synthesized from resveratrol (a biobased compound extracted from grapes). Starting from the triphenol, a 2-step synthesis led to the desired monomer.

Resveratrol could be easily functionalized via Williamson-type etherification in the presence of ethyl bromodifluoroacetate at 70 °C for 40 hours. 63,64 Dimethylformamide (DMF) was used for the feasibility study, but a 1:1 mix of green solvents γvalerolactone and dihydrolevoglucosenone (Cyrene™) could also be used as a greener alternative. After a filtration on silica gel, the expected α,α-difluoro triester (RvOEt) was obtained in 87 % yield. The isolated tris (ethyl ester) product underwent facile saponification in mild conditions to yield, after appropriate workup, the desired α,α-difluoro triacid (RvOH-TAF) as a brown waxy solid with an overall yield of 85 % and a biobased carbon content of 70 % (Scheme 1).

Trifunctional Epoxy Synthesis

In parallel to the modification of resveratrol into an activated trifunctional acid, this triphenol was also functionalized with epichlorohydrin to yield a trifunctional epoxy (Scheme 2). The glycidylation of phenols is very efficient, easily scalable and was extensively described already on biobased phenols including resveratrol. [65][66][67][68] The targeted building block RvOGly was prepared in large quantities (> 40g) by simple reaction of resveratrol with epichlorohydrin and tetrabutylammonium bromide (TEBAB). RvOGly features high functionality (EEW = 185 g/eq) and a 52 % aromatic carbon content (for RvOGly alone), close to the 57 % value of bisphenol A diglycidyl ether (BADGE), two features which are beneficial to obtain materials with high T g.

Polymerization and Curing

RvOGly and RvOH-TAF were mixed at room temperature (ca. 20 °C) in PTFE molds to avoid any transfer step, because of the fast gelation of the mixture even at room temperature (ca. 20 °C). The reaction between both monomers was exothermic and the mixing step needed to be performed on small scale, typically 1-2 g, to better control the heat transfer and to avoid gelation before complete mixing. This fast gelation is caused by the strong activation of the carboxylic acids toward the epoxy opening by the fluorine atoms. A reaction on larger scales may benefit from the addition of a solvent to control the heat release. This pathway was not explored in this study though, to avoid the plasticizing effect of potential residual solvent and its effect on mechanical properties. The mixture formed a material within a few minutes, and was left at room temperature for 3 h.

The curing was checked by DSC (Figure S9). On the first heating ramp, an exothermic enthalpy is visible starting from 150 °C. On the second ramp this phenomenon does not appear and a T g is visible in the 100-130 °C range. The exothermic phenomenon was attributed to a residual polymerization occuring when the material is heated higher than 150 °C. Thus, a 1 h curing step at 150 °C was applied and the DSC analysis was repeated (Figure S10). After this curing step, two consecutive heating ramps overlaid almost perfectly. There was no sign of ongoing polymerization by DSC. The curing was also checked by mechanical analysis. The evolution of the modulus was monitored with time at 150 °C. The stabilization of the value happened after 7 h (Figure S11). Therefore, the materials were left 10 h at 150 °C to ensure complete polymerization, resulting in a hard brittle dark brown material (Vm-RvOH, Figure 1). The resulting material exhibits a 86 % biobased carbon content.

Vitrimer Characterization

After complete polymerization three consecutive DSC ramps were carried out on the resulting material. The first ramp was meant to erase the thermal history of the material, then the thermograms of the second and third ramps overlaid perfectly, and no residual exotherm was observed. The T g is visible in the 92-125 °C range, but the transition is broad and the ΔCp is low (0.241 J.g -1

.K -1 ). Therefore, the T g was determined as the minimum of the heat flow derivative, at 117 °C (Figure S12 and Table 1). The high T g compared to previously reported covalent adaptable networks 42,43 This last case benefits from a 50 % aromatic carbon content, close to the 56 % value reported here, but also a 17 % cycloaliphatic carbon content caused by the isosorbide core of its monomer, which brings additional rigidity. Thus, the performance of Vm-RvOH in term of T g is consistent with its structure.

A DMA analysis was also performed to confirm the results observed by DSC, and to characterize the mechanical properties of the material (Figure S13). T α was determined as the maximum of the loss modulus E" at 94 °C. As observed by DSC, the mechanical relaxation was broad and the temperature of the maximum of tan(δ) was 117 °C, which is consistent with the T g measured by DSC. The moduli on the glassy plateau and on the rubbery plateau were respectively E' G = 2.1 GPa and E' R = 46 MPa. The modulus on the glassy plateau is comparable to values reported for a material made from epoxydized resveratrol and 4,4'diaminodicyclohexylmethane (PACM), 68 and with the value of a lignin-based catalyst-free vitrimer. 57 For the modulus on the rubbery plateau, the value for Vm-RvOH is 14 times lower than the epoxydized resveratrol-PACM thermoset, 68 but still in the 11-73 MPa range reported for other high-T g vitrimers, 18,21 included for aerospace applications. 29 Additionally, this value is 2.5 times higher than the value reported on the similar α,αdifluoro vitrimer previously reported. 43 At temperatures over 200 °C, the modulus decreases from the rubbery plateau. This could be the manifestation of the beginning of the flow.

The thermal stability of Vm-RvOH was assessed by TGA under nitrogen. The 2 % and 5 % degradation temperatures T d2% and T d5% were 237 °C and 275 °C respectively (Figure S14 and Table 1). The residue at 900 °C under nitrogen was 28.9 % of the initial weight. The T d5% value is low compared to the values superior to 300 °C reported for other high-T g vitrimers, 18,32,33,35,56,69 but still higher than the value at 224 °C for a lignin-based catalyst-free vitrimer. 57 The residue (char yield) was comparable with an epoxy vitrimer in the same range of T g . 31 The relatively high char yield depends essentially on the monomers structures, thanks to the high aromatic carbon content (56 %). Solubility tests were performed in THF (which easily solubilizes both resveratrol-based precursors). After stirring for 24 hours, a swelling of 278 % and an insoluble fraction of 73 ± 2 % were measured. This result seemed low for a 3+3 crosslinked material, and might be attributed to hydrolysis due to water in the THF. Therefore, it was repeated in anhydrous THF. A swelling of 68 % and a gel content of 100 ± 1 % was found (Table 1). These results prove the formation of a 3D crosslinked material. Reprocessing trials were performed on Vm-RvOH by compression molding. In a previous study on a similar system, the reprocessing temperature was set at 100 °C, 50 °C above the T g , under 16 bars. 43 At 170 °C, the material could be reprocessed in 2 h under 80 bars (Figure 2). The reprocessing temperature is 50 °C above the T g , like the previous system. The pressure applied is lower than for many high-T g vitrimers, which often require a pressure of at least 100 bars. 28,32,35,56,70 The thermal stability of the material at this reprocessing temperature was assessed. An isothermal experiment at 170 °C was performed in air atmosphere, to simulate the reprocessing conditions (Figure S15). After 2 h, the relative mass loss was 2.48 %. Between 2 h and 4 h the additional mass loss was 0.29 % and between 4 h and 6 h, 0.47 % to attain an overall mass loss after 6 h around 3 %. This value is small, but cannot be ignored. Reprocessing trials were made at 170 °C under 80 bars. Therefore, the DMA analysis of the material needs to be assessed and compared before and after reprocessing at 170 °C, to monitor a possible degradation. Two consecutive reprocessing cycles at 170 °C were made, and the mechanical properties after each cycle were studied by DMA (Figure 3). The value of the modulus on the glassy plateau remains quasiconstant. The value of T α decreased from 94 to 75 °C after the first reprocessing cycle, and remained at 76 °C after the second cycle (Table 2). Similarly, the values of the modulus on the rubbery plateau E' R decreased from 46 to 23 MPa with the first reprocessing, and then remained the same after the second cycle. These results suggest a decrease of the crosslinking density upon the first cycle, which might be due to a slight hydrolysis at the reprocessing temperature. Then the crosslinking density remains constant for the subsequent cycle, thus the hydrolysis remains very limited. This is likely due to the aromatic carbon content (56 % aromatic carbon) which brings a hydrophobic behavior to the material and balances the hydrophilic behavior brought by the esters and hydroxyl groups. Moreover, the high T g probably plays an important role, as the water uptake is very limited when the material is in the glassy state, but much easier in the rubbery state. Indeed, in the rubbery state, the mobility of the polymer makes easier the penetration of water in the network. Finally, the results obtained by DMA were confirmed by DSC, with a T g of 117 °C for the pristine material, 97 °C after the first reprocessing and 91 °C after the second cycle. The flow from the rubbery plateau was studied by isothermal stress-relaxation experiments to evaluate the kinetics of this phenomenon (Figure S16). The modulus of the material was monitored under a 0.3 % strain between 170 and 210 °C. For all temperatures, a plateau around 5 % was reached at the end of the relaxation experiment. This is likely due to a proportion of permanent linkages in the network. The presence of such permanent linkages can be explained by a minor homopolymerization of the epoxy. 21 Indeed, the strong acidity of α,α-difluoro acids may favor this reaction.

21

The stress-relaxation experiments were normalized, and a Kohlrausch-Williams-Watts "stretched exponential" equation with an added constant y 0 was used to fit the experimental data (Figure 4 and Table S1). The constant y 0 translates the final plateau of the relaxation, and the stretch parameter β translates a distribution of behaviors centered on the value of the relaxation time τ KWW . The closer to 1 β is, the narrower the distribution is. This parameter is linked to the heterogeneity in the vicinity of the exchangeable bond. Here, the values of β ranged between 0.486 at 170 °C and 0.797 at 210 °C and increased with the temperature. The broad distribution might be due to the influence of weak bonds hindering the relaxation. The number of weak bonds probably decreases when the temperature increases, which would result in an increasingly homogeneous behavior of the exchangeable bonds, and the increasing value of β. The constant added y 0 allowed a better accuracy on the fitting, with 0.99264≤R²≤0.99639 without constant and R² = 0.99937 to 0.99979 with a constant. The mean value of this constant y 0 (Table S1) is 0.054 (values between 0.043 and 0.064). Thus, a mere 5 % of the applied stress is not relaxed because of the permanent linkages, which does not impede the reprocessing of the material. The relaxation times τ KWW obtained for each temperature were plotted in an Arrhenius diagram (Figure 4 inset). A linear fit was obtained (R² = 0.983) and the flow activation was calculated from the slope E a = 107 kJ mol -1

, in accordance with the 29-163 kJ mol -1 range reported for transesterification vitrimers. 40 This E a is higher than that reported in previous studies of transesterification vitrimers activated by fluorinated groups (67-77 kJ mol -1

). 42,43 It is likely caused by the higher crosslinking density and lower mobility at the local scale of Vm-RvOH.

Conclusions

A catalyst-free polyester vitrimer was synthesized from resveratrol, a biobased triphenol found mainly in grapes. This material exhibits a high biobased carbon content of 86 %. A trifunctional epoxy and a trifunctional α,α-difluoro carboxylic acid were synthesized by functionalization of resveratrol with epichlorohydrin and ethyl bromodifluoroacetate, respectively. When these two resveratrol derivatives were mixed together, the ring opening polymerization of the epoxy by the carboxylic acid occurred at room temperature owing from the increased acidity of the carboxylic acid O-H bond due to the neighboring electronegative fluorine atoms. After a curing step at 150 °C, a rigid slightly brittle material was obtained. This material exhibited a high T g (117 °C), comparable to other high-T g vitrimers, 28,31,71,72 which makes it relevant for structural applications. The synthesis described could be adapted to other biobased compounds with similar structures and higher functionality, such as quercetin, to reach even higher T g values. Moreover, the α,α-difluoro esters can exchange with free hydroxyl groups without any added catalyst. This feature allows the efficient reprocessing of the material at 170 °C for 2 h by compression molding. Two recycling cycles were achieved and the mechanical performance remained worthwhile for structural applications. This material is one of the first high-T g catalyst-free biobased vitrimers. 17,57

Experimental section

Materials

Trans-Resveratrol (Fluorochem, 98 %), 1,8-Diazabicyclo(5.4.0)undec-7-ene (DBU, Fluorochem, 98 %), ethyl bromodifluoroacetate (Fluorochem, 98 %), epichlorohydrin (Sigma-Aldrich, ≥ 99 %), tetrabutylammonium bromide (TCI, > 98 %), benzophenone (Avocado Research Chemicals Ltd, 99 %), were used as received. Dimethylformamide (DMF, ≥ 99.5 %), tetrahydrofuran (THF, ≥ 99 %) and NaHCO 3 were supplied by VWR Chemicals, diethyl ether (≥ 99.5 %) and pentane (≥ 95 %) were supplied by Carlo Erba, ethyl acetate (≥ 99 %) was supplied by Fisher Chemicals, acetonitrile (≥ 99.9 %) was supplied by Acros Organics, sodium hydroxide (≥ 98 %) and chlorohydric acid ≥ 37 % were supplied by Honeywell Fluka, anhydrous THF was supplied by Carlo Erba (anhydrous for analysis stabilized with BHT, on 4A molecular sieve). Deuterated solvents were supplied by Eurisotop (99.8 %). γ-valerolactone (GVL, BioRenewable, ≥ 99 %) and dihydrolevoglucosenone (Cyrene™, BioRenewable, ≥ 98.5 %) were obtained from Sigma-Aldrich.

Synthetic Procedures

"RvOEt" compound:

Determination of the Epoxy Equivalent Weight (EEW):

The EEW of the RvOGly was evaluated by NMR titration using benzophenone as standard in deuterated chloroform (experimental details are given in ESI Section A). "TPE-TAF/BDGE" vitrimer: Typically, 1 g (2.0 mmol, 5.9 meq COOH, HEW = 170 g/eq) of RvOH-TAF was quickly mixed manually directly in a PTFE mold with 1.07 g (5.9 meq epoxy, EEW = 185 g/eq) of RvOGly at room temperature (ca. 20 °C) until a light brown viscous homogeneous mixture was obtained. The mixture was left at least 3 h at room temperature for gelation. The resulting material (TPE-TAF/BDGE) was then removed from the molds and cured 10 h at 150 °C. 3 ) was applied while heating at a rate of 3 °C min -1 from -50 °C to 270 °C, keeping the frequency at 1 Hz. Curing monitoring experiments were performed on a ThermoScientific Haake Mars 60 rheometer equipped with a Peltier heating cell and a 8-mm plane-plane geometry. A 0.1 % deformation was applied to 8 mm diameter and 2 mm thickness circular samples at ω = 1 rad.s -1 under a normal force of 100 grams every 2 minutes, and G' evolution over time was monitored. Stress relaxation experiments were performed with a 0.3 % torsional strain applied on 8 mm diameter and 2 mm thickness circular samples, and the rubbery modulus evolution with time was monitored. TGA: thermogravimetric thermograms were recorded on a TA TGA G50 instrument using a 40 mL min -1 flux of nitrogen or synthetic air as purge gas. Approximately 10 mg of sample were used for each analysis. Ramps were applied at a rate of 20 °C min -1

. DSC: analyses were carried out using a NETZSCH DSC200F3 calorimeter. The calibration was performed using adamantane, biphenyl, indium, tin, bismuth and zinc standards. Nitrogen was used as purge gas. Approximately 10 mg of sample were placed in perforated aluminum pans and the thermal properties were recorded at 20 °C min -1

. The reported values are the values measured during the second heating ramp. Reprocessing: the material was grinded with a manual stainless steel coffee grinder (for DSC and DMA) or cut into 6 to 9 mm 3 pieces (for pictures) and then pressed in stainless steel molds for 2 h at 170 °C under 80 bars of pressure using a manual heating press.

Figure 1 .

 1 Figure 1. Polymerization of RvOGly and RvOH-TAF resulting into the Vm-RvOH material, insert : optical image of Vm-RvOH (1 cm x 4.5 cm x 0.3 cm)

a

  determined as the maximum of E" | b at Tα -50 °C | c at Tα + 50 °C | d in anhydrous THF | e N2 atmosphere | f at 900 °C, N2 atmosphere | g after 6 h at 170 °C, air atmosphere

Figure 3 .

 3 Figure 3. DMA thermograms (a) E', (b) E" and (c) tan (δ) of Vm-RvOH pristine, after one reprocessing cycle and after two reprocessing cycles Figure 2. Vm-RvOH reprocessing for 2 h at 170 °C under 80 bars (scale of pristine material: 1 cm x 4.5 cm x 0.3 cm, diameter of recycled materials: 1 cm)

Figure 4 .

 4 Figure 4. Normalized stress-relaxation curves from 170 to 210 °C with 10 °C steps fitted with the Kohlrausch-Williams-Watts equation (KWW) and τKWW relaxation times reported in the Arrhenius diagram (inset, R² = 0.983)

13 C

 13 NMR 101 MHz, d 6 -acetone: δ 160.9, 159.3, 140.7, 131.0, 129.5, 128.6, 127.1, 115.5, 106.0, 101.3, 70.1, 50.6, 44.4.

19 F

 19 were acquired on a Bruker Avance 400 MHz spectrometer at 23 °C. External reference was tetramethylsilane (TMS) with chemical shifts given in ppm. Samples were diluted in 0.5 mL of CDCl 3 , DMSO-d 6 or acetoned 6 depending on their solubility. Mechanical characterizations: temperature ramps in elongation mode were carried out on Netzsch DMA 242 E Artemis cooled by liquid nitrogen. Uniaxial stretching of samples (1 × 3.5 × 12 mm

  (T g = 121 °C), but lower than the value of the catalyst-free biobased polybenzoxazine vitrimers recently reported by Adjaoud et al. (T g from 143 to 193 °C).

	17

was expected because of the high aromatic carbon content of the polymer (56 % aromatic carbon content for the polymer). This value of T g is comparable to that of the catalyst-free biobased vitrimer synthesized from lignin by Moreno et al.

57

Table 1 .

 1 Physicochemical main properties of Vm-RvOH

Table 2 .

 2 Evolution of the thermomechanical properties of Vm-RvOH with reprocessing cycles.

	Reprocessing Cycle	Tg	Tα	Max tan(δ)	E'G	E'R
		(°C)	(°C) a	(°C)	(GPa) b	(MPa) c
	Pristine	117	94	117	2.1	46
	Reprocessed once	97	75	101	2.4	23
	Reprocessed twice	91	76	104	2.7	23
	a determined as the maximum of E" |	b at Tα -50 °C |	c at Tα + 50 °C

W. Denissen, J. M. Winne and F. E. Du Prez, Chem. Sci.,

2016, 7, 30-38. 2 N. J. Van Zee and R. Nicolaÿ, Prog. Polym. Sci., 2020, 104, 101233.

Acknowledgements

This work was funded by the Institut Carnot Chimie Balard CIRIMAT (16CARN000801).

Notes and references

Author Contributions

Conceptualization: FC, SC, ED, SL, EL, VL. Funding acquisition: SC, ED, EL, VL. Investigation: FC, SL. Methodology: all authors. Project administration: SC, ED, EL, VL. Supervision: FC, SC, ED, EL, VL. Validation: all authors. Visualization: FC. Writingoriginal draft: FC. Writing -review & editing: all authors.

Conflicts of interest

There are no conflicts to declare.


Emmanuel Poizot
email: emmanuel.poizot@lecnam.net

Yann Méar

Sylvain Guillou

Eric Bibeau

High

Keywords: tide currents, fishnets, vorticity, wavelet, aquaculture

INTRODUCTION

Fish farming started in the seventies. Aquaculture is poised to take an increasingly significant part as a food source [START_REF] Duarte | Will the Oceans Help Feed Humanity?[END_REF][START_REF] Holmer | Environmental issues of fish farming in offshore waters: perspectives, concerns and research needs[END_REF][START_REF] Food | The State of World Fisheries and Aquaculture[END_REF]. The growing number of farms has consequences on the marine environment and on the use of natural resources.

Increasing environmental control is required to preserve environmental quality and to enhance product quality.

These controls are necessary due to the ecological disturbance of the breeding site linked, in particular, to metabolic discharges from fishes. Faeces are particularly rich in nitrogen, ammonia, phosphorus, trace metals and organic carbon. These faeces can be released in particulate or dissolved form. The accumulation of theses wastes can lead to anoxic conditions that affect fish welfare and growth [START_REF] Thetmeyer | Growth of European sea bass (Dicentrarchus labrax L.) under hypoxic and oscillating oxygen conditions[END_REF]. Their dispersion can also affect the farm environment both locally and on a more global scale [START_REF] Skogen | Modelling the environmental effects of fish farming in a Norwegian fjord[END_REF].

With the aim of improving the quality of the environment and consequently the health of the farm, many studies have been carried out [START_REF] Klebert | Turbulence and flow field alterations inside a fish sea cage and its wake[END_REF] to reduce the impact of production structures and, if necessary, promote the dilution of waste.

Since the work of [START_REF] Gowen | The use of simple models in assessing two interactions between fish farming and the marine environment[END_REF] who pioneered the application of numerical models to study local cage-environment interactions and the dispersion of effluents in the environment, much work has been carried out. At the local scale, [START_REF] Masaló | Analysis of sedimentation and resuspension processes of aquaculture biosolids using an oscillating grid[END_REF]; [START_REF] Gjøsund | Flow through nets and trawls of low porosity[END_REF]; [START_REF] Gorle | Hydrodynamics of Atlantic salmon culture tank: Effect of inlet nozzle angle on the velocity field[END_REF] studied the hydrodynamic performance of the different cage models and their behavior. The action of the flow current on the cages [START_REF] Lader | Current induced net deformations in full-scale sea-cages for Atlantic salmon (Salmo salar)[END_REF][START_REF] Gansel | Drag forces and deformation of aquaculture cages-Full-scale towing tests in the field[END_REF] has been addressed because of the deformations of these cages limiting the space dedicated to fish and modifying their hydrodynamic behavior. In the same theme, [START_REF] Bi | A numerical analysis on the hydrodynamic characteristics of net cages using coupled fluid-structure interaction model[END_REF] studied the action of waves while considering biofouling of the nets.

Recently, [START_REF] Xu | An industry-scale modeling for the turbulence agglomeration of fine particles[END_REF] showed that vertical mixing plays a key role in the hydrodynamic environments of the sea-cage farms. Eddies can be generated in the wake or in different part of the cages. The turbulence appears to be a key parameter for the understanding of the cages-hydrodynamic interaction [START_REF] Gansel | Drag forces and deformation of aquaculture cages-Full-scale towing tests in the field[END_REF].

Since [START_REF] Panchang | Modelling hydrodynamics and aquaculture waste transport in coastal maine[END_REF], the numerical approach to model the impact of farming at greater distances has also been the subject of several works. [START_REF] Cromey | DEPOMODmodelling the deposition and biological effects of waste solids from marine cage farms[END_REF] proposed one of the first numerical tools concerning the modeling and biological effects of solid waste deposit. Used worldwide, this tool subsequently evolved [START_REF] Chamberlain | Modelling the effects of biodeposition from shellfish farms on the near field benthic environment[END_REF][START_REF] Chamberlain | Simulating the effects of parameter uncertainty on waste model predictions of marine finfish aquaculture[END_REF]. Computational Fluid Dynamic (CFD) to study flow perturbations in and around gravity cages is largely used [START_REF] Patursson | Flow through and around fish farming nets[END_REF][START_REF] Patursson | Development of a porous media model with application to flow through and around a net panel[END_REF][START_REF] Zhao | Numerical simulation of the flow field inside and 29 around gravity cages[END_REF][START_REF] Bi | A numerical analysis on the hydrodynamic characteristics of net cages using coupled fluid-structure interaction model[END_REF][START_REF] Cornejo | Numerical studies on the hydrodynamic effects of a salmon farm in an idealized environment[END_REF]. Performed on scaled cages, most of these CFD simulations results had been verified with experimental measurements in flumes and tow tanks. Recently, [START_REF] Winthereig-Rasmussen | Flow through fish farming sea cages: Comparing computational fluid dynamics simulations with scaled and full-scale experimental data[END_REF] performed a CFD simulation of the flow through a full-scale commercial salmon farm and compared the results with field mea-surements made at the same farm [START_REF] Klebert | Three-dimensional deformation of a large circular flexible sea cage in high currents: Field experiment and modeling[END_REF][START_REF] Johansson | The Interaction between Water Currents and Salmon Swimming Behaviour in Sea Cages[END_REF]. Discrepancies between simulated and measured data were due to an increased net solidity from cages deformed by the flow and a block effect from the fish inside the cage. [START_REF] Poizot | Selfcontamination of aquaculture cages in shallow water[END_REF] showed that in spite of favourable environmental conditions (sea protection and tide currents which regularly refresh the water), periods of non-negligible fish mortalities can be observed to occur without clear evidence of their origin. They showed through turbidity measurements and numerical modelisation, that in some cases the flow acceleration under the cages can be at the origin of sediment re-suspensions and bio-deposits. As a consequence, particles which enter the fishnet can have different origins: external source, sea-bottom, or nets themself. They observed that turbulent dispersion is a key ingredient for such a behaviour, as it can lead particles towards a large recirculation cell behind the net and force particle faeces, unheated food and more generally other wastes, from the bottom to be lifted up and reach the rear of the net. They observed that the numerous vortices downstream from the cages are responsible for complex transfers of re-suspended particles from the sea bottom to the sea surface. Therefore, high turbidities due to a self-contamination process in the vicinity of the cages can exist under the sole effect of the turbulence tied up to high velocities below the fishnets and are likely to happen even in the absence of external sources of pollution in the upstream flow.

One of the main conclusions of the various works aiming to numerically model the transport of effluents linked to aquaculture in the marine environment is that the variability of water flows on the various temporal and spatial scales and their action on flexible cages leads to complex interactions [START_REF] Klebert | Three-dimensional deformation of a large circular flexible sea cage in high currents: Field experiment and modeling[END_REF][START_REF] Gansel | Drag forces and deformation of aquaculture cages-Full-scale towing tests in the field[END_REF][START_REF] Poizot | Selfcontamination of aquaculture cages in shallow water[END_REF]. In order to be able to model more precisely the dynamics of the structure of the water column and the dispersion of effluents from breeding cages, it appeared necessary that the numerical models have an accurate representation of transfers due to turbulent diffusion. To test turbulence closure patterns with field data, measurements of the turbulence parameters can now be made in the field [START_REF] Winthereig-Rasmussen | Flow through fish farming sea cages: Comparing computational fluid dynamics simulations with scaled and full-scale experimental data[END_REF].

Acoustic Doppler current profilers (ADCP) allow to obtain partial information on the turbulence of the water flow [START_REF] Guerra | Turbulence Measurements from Five-Beam Acoustic Doppler Current Profilers[END_REF][START_REF] Lu | Using a Broadband ADCP in a Tidal Channel. Part II: Turbulence[END_REF][START_REF] Stacey | Measurements of Reynolds stress profiles in unstratified tidal flow[END_REF]. Their relatively low sampling frequency, up to 16 Hz, only allows to capture turbulent structures whose size is pluri-decimetric. It was only recently [START_REF] Klebert | Turbulence and flow field alterations inside a fish sea cage and its wake[END_REF]) that a free-fall profiler was implemented to measure the micro-scale turbulence near cages from sea surface to the bottom. Vertical micro-structure profilers (VMPs) are high resolution instruments specifically developed to produce in-situ measurements of turbulence characteristics [START_REF] Lu | Using a Broadband ADCP in a Tidal Channel. Part II: Turbulence[END_REF]. It allows to measure vortices from ∼0.003 m to 1 m, over the water column [START_REF] Mcmillan | An assessment of the dissipation rates at a tidal energy site using a vmp and an adcp[END_REF].

A VMP is used to give precise and accurate measurements of turbulent characteristics around a fish farm production site in this study. It should be used to reproduce the detailed flow inside a fish farm by CFD modelling.

The fish farm is introduced in Section 2. Materials and processing are introduced in Section 3, in particular, this section contains a review of VMP's technology and measurement principles. Results and discussions are presented in Section 4 before the conclusion in Section 5.

FISH FARM

Measurements were conducted in the Cherbourg roadstead, Normandy, France, the European's largest artificial roadstead. It has an area of ∼ 1,500 ha, divided into the "Grande rade" and the "Petite rade", as shown in Fig. 1. The "Grande rade" (1,300 ha) is in contact with the open sea through "West gate", "East gate" and "Collignon gate". The roadstead is under the influence of a semi-diurnal tide, giving an oscillating volume of ∼ 80,000 m 3 during spring tide and a tidal amplitude of ∼ 6 m (Merceron et al., 2002). The maximum depth is 25 m with a mean depth of ∼ 15 m. The mean water temperature is below 8-9 • C in winter and reaches 17-18 • C at the end of the summer. The Cherbourg roadstead is characterized by a particular tidal hydrodynamic. The predominant current is eastward during the flood and westward during the ebb. The flood stream enters through the West gate and stand out mainly through the East gate and to a lesser extent, through the Collignon gate. This is the opposite to ebb. During the flood, depending on the interactions between the bathymetry, the coastline and tidal currents, gyres may form locally with counter-clockwise rotation (Merceron and Gaffet, 1994). This is the case at the south edge of the central dike (Fig. 1). In the fish farm site, tidal currents are asymmetric: the flood currents are oriented eastward 30% of the time and ebb currents are oriented westward 70% of the time (Merceron and Gaffet, 1994). The aquaculture farm has been operational since 1990. It is located 50 m south the central dike (Fig. 1) and covers an area of ∼ 15 ha (1.5 km long and 100 m wide). Nowadays, around 1,000 tons of salmonids (Salmo salar ) are produced per year. The mean water depth below the farm ranges from 11 m to 13 m from the zero tidal level. The production structures are composed of a mix of cylindrical (∅ 40 m) and cubic nets (40 m x 160 m) as shown in Fig. 2 and Fig. 3. The average bottom of the nets lies between 7 to 8 m below the sea surface. ADCP and VMP measurements took place around a structure containing eighteen square nets (2 x 8). The nets were made with synthetic ropes organized in square meshes of size 2 x 2 cm. The mean density of fish in each net was around 12 kg.m -3 . As the nets are regularly cleaned, biofouling is minimum. A few small algae (< 1 cm) form on the net ropes.

MATERIALS AND METHODS

Vertical Microstructure Profiler (VMP)

Figure 4: Shear stress probe located on VMP 250 (Rockland Scientific). W is fall rate of the profiler, u is the horizontal component of the turbulence velocity, U is the total velocity and α is the AOA.

The VMP has two shear probes (Fig. 4) and two thermistors. VMPs are mainly shaped as cylinders with sensors located at one end (Fig. 4). Generally, measurements are taken with the instrument falling freely vertically along the water column, with sensors first. The VMP is shaped so as to fall vertically at a constant velocity. To do so, it is equipped with a drag brush which control the falling velocity of 0.8 m.s -1 . According to the VMP model employed, the drag brush is specific to the instrument so that the drag forces are taken into account. The probe moves axially through the water at a speed W high enough to apply Taylor's frozen turbulence hypothesis [START_REF] Taylor | The spectrum of turbulence[END_REF][START_REF] Moin | Revisiting Taylor's hypothesis[END_REF]. The horizontal component of the turbulent velocity, u, turns the total velocity, U, into the vectorial sum of W and u, i.e.

-→ U = -→ W + -→ u . It induces an angle of attack (AOA), called α (Fig. 4). The AOA induces a lift force over the surface of the probe which bends the piezo-ceramic of the probe. The bending of the probe is converted into an electrical signal (e = SW u, with S as the sensitivity of the probe). This electrical signal is sampled at 1 kHz with a sign function of the direction of the bending. Under the hypothesis of Taylor "frozen field ", the time rate-of-change of u is converted into a spatial gradient, to yield the vertical shear of horizontal velocity, according to:

∂u ∂z = E W 2 S (1)
The shear probe is only sensitive to a single component of velocity-the component oriented at right angles to the probes' axis and oriented normal to the wide surface of the piezo beam. Two shear probes are used, one of which is rotated by 90 • around its axis. This gives two shear components, ∂u/∂z and ∂v/∂z. As sensors are very sensitive, instrumental noise and disturbance of the main body need to be removed from the shear signals [START_REF] Macoun | Modeling the spatial response of the airfoil shear probe using different sized probes[END_REF]).

In the present work, a VMP-250 model from Rockland Scientific [START_REF] Lueck | Measuring tidal channel turbulence with a vertical microstructure profiler (VMP)[END_REF] allowed eddies measurements in the range ∼ 0.003 m to 1 m. The length of the probe acts as a low pass filter, vortex with size greater than the length of the probe cannot be measured. Two temperature sensors (thermistors) are also present on that model. They measure temperature fluctuations along the water column and their signal is sampled at the same frequency as the shear probes.

Several VMP profiles were carried out at each station around the immersed structure. One profile is studied per station according the following criteria:

• the probe velocity, W, should be fairly constant,

• body vibrations must have a low impact on the shear signals,

• the VMP roll angle must be within an acceptable range (less than ± 5 • ).

Acoustic Doppler Current Profiler (ADCP)

In order to quantify the tidal current characteristics, an acoustic Doppler current profiler (ADCP) was moored from the 4th to the 9th of April 2015. It was placed at the eastern part of the fish farm (Fig. 1). The instrument used was a Teledyne RDI Workhorse Sentinel with a frequency of 600 kHz. During the VMP survey, the measurements of the flow characteristics were made at a frequency of 1 Hz and averaged over 5 minutes to obtain the mean flow velocities and directions. The ADCP was set to sample the water column along 13 cells of 1 m height each (Fig. 5). Directly above the device's head, no measurement can be made, due to technical limitations. This area is called the blanking zone. In the present study, this zone is about 1 m and the ADCP's transducers are at 0.7 m above the sea bottom, so that the first cell of measurements starts at 1.7 m above the sea bottom.

Sea bottom

Sea surface

Beams

Data treatments

Classical treatments of the VMP data sets are made through Matlab scripts [START_REF] Lueck | Calculating the rate of dissipation of turbulent kinetic energy[END_REF] provided by Rockland Scientific. These scripts allow in a first time to apply a set of corrections and filtering on the raw data to obtain different graphs to assess data validity. Then, fast Fourier transform (FFT) based analysis are computed to highlight turbulence characteristics. The FFT analysis can be performed under the assumption that the signal is stationary [START_REF] Massel | Wavelet analysis for processing of ocean surface wave records[END_REF]. If that's not the case, the use of FFT is not relevant (del Alamo and Jimenez, 2009).

In order to enhance the study of VMP shear signals, a wavelet analysis was conducted. Wavelet analysis is considered superior to Fourier analysis because it unfolds a time series in both frequency and time domains [START_REF] Torrence | A practical guide to wavelet analysis[END_REF], it requires no assumption of stationary, and can determine not only the dominant modes of variability in frequency but also how those modes vary over time [START_REF] Torrence | A practical guide to wavelet analysis[END_REF][START_REF] Tseng | Validation of the kuroshio current system in the dual-domain pacific ocean model framework[END_REF]. Wavelet analysis of a time series is essentially the systematic application of a set of band-pass filters whose bandwidths are proportional to the central periods [START_REF] Torrence | A practical guide to wavelet analysis[END_REF][START_REF] Mallat | A theory for multiresolution signal decomposition: the wavelet representation[END_REF]. Wavelet analysis is able, at a minimum, to give the same information as FFT, but with less constrains of application. The main interest of wavelets is that they localize frequencies over time. This last information is essential in the case of 3D CFD models which needs not only to simulate the right range of turbulent frequencies, but also the same location in the modelized domain.

Wavelet computation was realized using R Language (R Core Team, 2016), through the use of the "WaveletComp" library [START_REF] Roesch | Wavelet-Comp: Computational Wavelet Analysis[END_REF].

RESULTS AND DISCUSSIONS

As the flow direction was 280 • during VMP surveys (Fig. 6), DAT 026 station is at the inlet of the studied domain and DAT 029 at the outlet, i.e. in the wake of the fishnet. The two other stations, DAT 027 and DAT 028 are located respectively North and South were the water flows on the longest sides of the structures (Fig. 1 and3). VMP measurements were performed the 7 th of April 2015. The measurement period was chosen to correspond to the maximum flow velocity of the tidal cycle (Fig. 6). Under these environmental conditions, the hydrodynamic constraints are at their maximum between currents and fish farm structures, so that the turbulence generation is expecting to be also at its maximum, allowing better highlighting fish farm structure impacts on flow characteristics. The two thin dashed lines on Fig. 6 represent the start and the end time period of the survey, i.e. 90 min.

At the ADCP location, the water flows westward during ebb in the direction 270 • -280 • , 2/3 of the time. It flows eastward during flood in the direction 90 • -100 • , 1/3 of the time. Flow velocities during the ebb are not constant and range from 0.20 to 0.50 m.s -1 . The maximum speed is reached during the first half of the ebb current period, and ongoing fallout until the current changes back to flood. During flood, flow velocities are globally more constant but three or four times lower, ranging from 0.10 to 0.15 m.s -1 . During the VMP measurement time, the mean water velocity was 0.45 m.s -1 and the mean direction was 280 • (Fig. 3).

Figures 7 and8 show intensity variations of VMP shear probes Sh 1 and Sh 2 , and of the temperature gradient measured by the thermistors, i.e. T 1 and T 2 at stations DAT 026-027 and stations DAT 028-029, respectively for the four chosen profiles. Intensity of the signal variations of the shears is a high frequency indication of the level of turbulence on the water column. Temperature gradient variations are low frequency qualitative information of turbulence characteristics modifications. It can be used to suspect presence of vortices with size greater than 1 m. Figures 7 and 8 allow to classify the different profiles in terms of intensity variations of shears. DAT 026 profile is the less energetic one, since few variations are present both on shears and temperatures. The profile DAT 027 has some more variations on its signals. Near the sea surface at 3.5 m strong fluctuations are present. Until 8 m, they decrease slightly. From this depth to the end of the profile, fluctuations are constant but more pronounced. In terms of intensity variations on shears and temperatures, various energetic domains are highlighted for DAT 028 station. A first domain is recognized with high fluctuations until 4 m depth. A succession of highly characterized episodes of high and low energy followed one another until 11 m. Below this latter depth, energetic level is low. At DAT 029 station, after a level of high fluctuations until 3.5 m, the energy falls abruptly. From this depth, both Sh 1 and Sh 2 highlight growing intensity variations to the end of the profile.

Figures 9 and10 show the wave number spectra of the shears at the four stations. These graphics allow to highlight main vortices structures present on the water column. Abscissa corresponds to wave number, k, in count per metre (cpm) and the ordinate is the dissipation rate, Φ (k) (s -2 .cpm -1 ). The thin black lines correspond to the fit of the Nasmyth model [START_REF] Lueck | Calculating the rate of dissipation of turbulent kinetic energy[END_REF][START_REF] Nasmyth | Ocean turbulence[END_REF] for dissipation rates defined on ∂u 1 /∂z clean (i.e., Sh 1 ) clean and ∂u 2 /∂z clean (i.e., Sh 2 ) clean (i.e., filtered) signals [START_REF] Oakey | Determination of the rate of dissipation of turbulent energy from simultaneous temperature and velocity shear microstructure measurements[END_REF] respectively. The value used to compute the Nasmyth model is indicated in the graphic legend. Wave numbers are considering as significant when 1) the signal is higher to its corresponding Nasmyth curve, and 2) the signal is located between the lowest value of wave number and the integration limit, marked by a blue and red triangle for respectively ∂u 1 /∂z clean and ∂u 2 /∂z clean . These graphics are computed through a Fourier transform of the original signal.

DAT 026 inlet station shows the less energetic spectrum ( ≈ 10 -4 W.kg -1 ) which confirms previous observations on Fig. 7. This low energetic level makes detection of particular frequency/size difficult. This is in particular the case for the highest frequencies, i.e. small size vertex (1/k). Sh 1 signal highlights three main peaks (0.035 m, 0.040 m), 0.058 m and 0.18 m, whereas Sh 2 shows two sizes, 0.52 and 0.13 m. These characteristics are in agreement with the two different Nasmyth fitted models which are shifted, indicating an anisotropy of the two signals Sh 1 and Sh 2 .

The three other stations are more energetic in the range ≈ 10 -3 W.kg -1 to ≈ 10 -2 W.kg -1 , that is 10 to 100 times more than DAT 026 station.

DAT 027 is also characterized by an anisotropy of the signals, but more important than at DAT 026 station. Sh 1 shows three main peaks, (0.025, 0.028) m, (0.045, 0.050) m and 0.062 m respectively. The Sh 2 signal have same peaks, except the 0.062 m. Some vortices are also present near the limit of integration of the signals, respectively 114 cpm for Sh 1 and 102 cpm for Sh 2 , but are difficult to detect clearly on the graphic.

DAT 028 station is mainly characterized by a low limit of integration of both shear signals, i.e. 34 cpm for Sh 1 and 31 cpm for Sh 2 . At this station, Sh 1 and Sh 2 signals have different behaviour as indicated by the gap between the two Nasmyth models (the highest of the data set). Sh 1 has some significant vortices at (0.33, 0.05) m, 0.07 m, 0.10 m, 0.125 m and 0.285 m. Sh 2 highlights significant vortices only in the range (0.33, 0.05) m and at 0.285 m.

At DAT 029 station is characterised by both the various vortices recognized and the similarity of the two Nasmyth models on Sh 1 and Sh 2 . Both signals share same size of turbulent structures, except for 8.3 m vortices only presents on Sh 1 . For each station, wavelet analysis of Sh 1 and Sh 2 signals are showed on Fig. 11 and Fig. 12. In order to simplify interpretations, power wavelet coefficients with a p-value > 0.01 are removed from the figures. With such wavelet graphics, both vortex sizes and their location along the water column, can be defined. For each station, the colour scale is adapted as a function of each specific energetic range (from black for highest values to dark blue for the lowest ones), to better highlight wavelet coefficient variations inside each analysed signal. The abscissa represents the depth from -3.5 m to maximum depth reached by the VMP at the corresponding station and the y axis is the size of the vortices. The higher the coefficients, the more significant are the size.

Graphics on Fig. 11 and Fig. 12 were built so as to focus on main characteristics of the analysed signals. As an example of such graphics interpretation, Fig. 11a shows Sh 1 power spectrum at station DAT 26. The first colour stain observed between depth from -3.5 to -5 m and for sizes from about 0.25 to 0.05 m, indicates that in the range depth (-3.5, -5) Both Sh 1 and Sh 2 signals at DAT 026 station show wavelet significant coefficients characteristic of very small vortices, i.e. 0.05 m (Fig. 11a-b). These structures represent the electronic noise of the VMP, thus the global energetic level of the signal at this station is very weak. A comparative study of Sh 1 and Sh 2 dataset highlight significant vortex (0.050, 0.250) m all along the water column.

Most of the turbulent energy at DAT 027 station is located between the surface to 4.5 m (Fig. 11c-d). Below this depth, the wavelet analysis confirms the weak energy of the studied environment on two aspects, at the scale of the turbulent structures and at the scale station itself with a succession of depths without any turbulent structures.

DAT 028 station shows a higher energetic level both near the surface and at the end of the profile (Fig. 12a-b). Between these two areas, the central part of the profile is characterized by both lower energetic and smaller sizes turbulent structures.

DAT 029 station, at the outlet of the studied area, highlights also two turbulent domains (Fig. 12c-d). The first is at the top of the water column, from surface to 4.5 m deep. The second turbulent domain is located between 6 m to the end of the profile. In this station, differences between the two shear signals are significant underlining the anisotropy of turbulent structures. Analysis of VMP measurements allows to define an organization of the turbulence around a set of fish production structures compound composed of floating metallic frames on which nets are fixed.

The inlet current with a velocity of 0.45 m.s -1 flowing at 280 • has a low level of turbulence along the water column (DAT 026 station). Some few isotropic vortices of small sizes (< 0.2 m) are present along the depth which confer a high degree of homogeneity to this station. The outlet flow (DAT 029 station) has cross the set of fishnets along its longer side (180 m). At the rear of the cages, the energetic level is higher (x100) than at the inlet one. This is in particular the case from the sea surface to 4.5 m deep. The energetic vortices located in this area are due to the action of the flow on the floating metallic frame of the nets.

Near the bottom, the growing speed of the current and the wavy morphology of the sea-bed are responsible of highly energetic turbulent structures of bigger sizes (> 0.25 m). Between these two areas, interactions cages-current generate turbulent vortex tied up to the wake effect as showed in [START_REF] Poizot | Selfcontamination of aquaculture cages in shallow water[END_REF]. These two latter interactions, i.e. wake effect and bottom friction, create vortices of sizes ranging from 0.10 m to nearly 1 m. Wake effect vortices being clearly more anisotropic.

At the two stations DAT 027 and DAT 028 located sideways the fishnet structure, a high energetic level of turbulent vortices is present from the sea surface to 4.5 m deep. It corresponds to the same set of vortices highlighted at station DAT 029. Below this top area, the two stations highly differ in both size and intensity of the turbulent structures.

North the cages (DAT 027 station), most of the energetic turbulent structures are located in the upper part of the water column. Below, vortices, when present, are of small sizes and with low energy. Isotropic shape of both Sh 1 and Sh 2 signals can be due to the channelization of the current between the fishnets and central dike of the Cherbourg roadstead (Fig. 1). Effects of the channelization prevailing on disturbances due to fishnets and could be the origin of small size vortices.

South, at DAT 028 station, the water column is more disturbed in relation with chains used to anchor the cages. The water flow action on the anchor chains and the mooring weights generate anisotropic vortices of variable sizes.

It appears that a weakly energetic current of 0.45 m.s -1 crossing a set of production nets of 180 m long, undergoes strong deformations. A first modification noticed on three sides of the net structure, is due to the metallic floating part on which nets are anchored. At the rear of the cages, strong anisotropic eddies of various sizes confirm the presence of a water transport and associated particles (sediment, non-heated food, faeces, etc.) upward. This particular water circulation is reinforced by the flow acceleration under the cages and the associated eddies, produced by the growing bottom critical constraint. Environment of the cages has also to be taken into account.

Here, the presence of a dike channelize the current flow making it more homogeneous, elsewhere, anchor chains disturb more or less locally the flow.

CONCLUSION

Analysis of VMP measurements performed around fishnet structures of on the salmon farm located in the Cherbourg roadstead, allow to give precise information of the turbulent characteristics of the water column in the near vicinity of the nets. This information is important for industrial and environmental interests.

Sizes of vortices, their isotropy/anisotropy, their intensity and also their localization along the water depth, have been quantify in an area under medium to high tide currents (up to 0.5 m.s -1 ). The wavelet analysis conducted after the classical Fourier approach, demonstrated that the turbulence is not evenly distributed along the water column. Such information is for the first time highlighted here around fishnet production structures.

To help fish farmers to a better manage their production, complementary knowledge of turbulence characteristics must be conduct. The constant progress of technologies allows now to consider new monitoring approaches. With the growing measurement rate of ADCPs, turbulent structures up to 3-4 cm can be detected. New shape of VMPs allows simpler and safer deployments. The mix of both instruments family could gain access to more precise time and space understanding of the turbulence behaviour on the field.

Numerical simulations aiming to model currents/fishnet interactions under high Reynolds number conditions will also gain of such works. For example, it could help to set more accurately the turbulent model characteristics.

Figure 1 :

 1 Figure 1: The Cherbourg roadstead (France). Red triangles represent the locations where VMP profiles were realized around fishnet structures of the aquaculture farm. Green triangle is the location where the ADCP was moored.

Figure 2 :

 2 Figure 2: View of the aerial parts of fishnet structures of the salmon fish farm located in the Cherbourg roadstead (from https://www.keldelice.com/producteurs/saumon-de-france).

Figure 3 :

 3 Figure 3: Vertical (up) and horizontal (down) details of the rectangular fishnet structures around which measurements were performed. The direction of the current during the measurement period is indicated on both vertical and horizontal view. The four cardinal directions show general orientation of the nets. Red numbers surrounding with a red circles are respectively locations of DAT 026, DAT 027, DAT 028 and DAT 029 measurements stations.

Figure 5 :

 5 Figure 5: ADCP physical deployment settings during the period of measurements. Only two from the four beams are represented.

Figure 6 :

 6 Figure 6: Mean direction (red) and speed (blue) of current at the fish farm (Fig.1) the 7 th of April 2015. Dashed lines represent the start and end of the time period of the VMP measurements.

Figure 7 :

 7 Figure 7: Raw data for each profile at stations DAT 026 and DAT 027, with δu 1 /δz for Sh 1 and δu 2 /δz for Sh 2 . T1 and T2 correspond to the two thermistors.

Figure 9 :

 9 Figure 9: Wavenumber spectra of shear (blue and red) at DAT 026 and DAT 027 locations. The thin blue and red lines are the spectra without coherent-noise correction and the thick lines are the spectra after correction. The solid black lines are the empirical Nasmyth spectra for the dissipation rates indicated in the legend. Blue and red arrows highlight main k values recognized on respectively Sh 1 and Sh 2 clean signals. Both horizontal and vertical axis are in log scale.

Figure 10 :

 10 Figure 10: Wavenumber spectra of shear (blue and red) at DAT 028 and DAT 029 locations. The thin blue and red lines are the spectra without coherent-noise correction and the thick lines are the spectra after correction. The solid black lines are the empirical Nasmyth spectra for the dissipation rates indicated in the legend. Blue and red arrows highlight main k values recognized on respectively Sh 1 and Sh 2 clean signals. Both horizontal and vertical axis are in log scale.

  m, vortices in the range size (0.25, 0.05) m are present. The most significant sizes are ∼0.15 m at ∼-4 m deep and ∼0.10 m at ∼-5 m deep corresponding to two yellow colour spots. Other colour stains are indicators of existing vortices until the maximum depth.

  Figure 11: Power wavelet spectrum of Sh 1 and Sh 2 at stations DAT 26 and DAT 27. Power wavelet coefficients which are considered as non-significant (p-value > 0.01) are not showed. First column (a and c) contains power spectrum of Sh 1 and second column (b and d), those of Sh 2 , for each stations.

Table 1

 1 summarize the information presented on figures 910 and , for each profile.

	Profile	Energy Sh 1 (cm)	Sh 2 (cm)	Anisotropy
	DAT 026	Low	(3.50, 4.00), 5.80,	5.20, 13.30	Low
			18.00		SH1	SH2
	DAT 027	Medium (2.50, 2.80), (4.50,	(2.50, 2.80), (4.50,	Low
			5.00), 6.25	5.00)	SH1	SH2
	DAT 028	Medium (3.33, 5.00), 7.70,	(3.33, 5.00), 28.50 Medium
	DAT 029	High	10.00, 12.50, 28.50 (1.11, 1.60), 2.00,	(1.50, 1.16), 2.00,	SH1 ≈ SH2 High
			8.33, 13.30	(3.50, 4.00), 13.30	SH1 < SH2

Table 1 :

 1 Characteristics summary of signals Sh 1 and Sh 2 . Numbers indicate the size (cm) of recognized vortices.

(a) Profile DAT 028 (b) Profile DAT 029Figure 8: Raw data for each profile at stations DAT 028 and DAT 029, with δu 1 /δz for Sh 1 and δu 2 /δz for Sh 2 . T1 and T2 correspond to the two thermistors.

ACKNOWLEDGEMENTS

Funding was provided by the Normandy Regional Council, the Syndicat Mixte du Cotentin and the Conseil Départemental de la Manche. We thank AMP/GMG society and Construction Mécanique de Normandie (CMN) for their technical help and nautical support during the surveys. The authors would also like to thank anonymous reviewers for their constructive comments on the original manuscript.

Declaration of interests

⊠ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: