domain: chim phys

text:
Michel Frigoli
email: michel.frigoli@uvsq.fr

Tanguy Jousselin-Oba

Masashi Mamada

Jérôme Marrot

Agnese Zangarelli

Danilo Pannacci

Chihaya Adachi

Fausto Ortica
email: fausto.ortica@unipg.it

Synthesis and photochromic behaviour of a series of benzopyrans bearing an N -phenyl-carbazole moiety: photochromism control by the steric effect

Introduction

Benzo-and naphthopyrans are well known classes of photochromic compounds [START_REF] Van Gemert | Organic Photochromic and Thermochromic Compounds[END_REF][START_REF] Hepworth | Heron in Functional Dyes[END_REF] that, in consequence of their usual fatigue resistance, have received great attention over the latest years in light of their possible practical and industrial applications, [START_REF] Corns | Industrial organic photochromic dyes[END_REF] especially in the field of ophthalmic lens production. The mechanism of photochromic reaction of benzo-and naphthopyrans was first investigated by Becker and coworkers [START_REF] Kolc | Proof of structure of the colored photoproducts of chromenes and spiropyrans[END_REF][START_REF] Lenoble | Photophysics, photochemistry and kinetics of photochromic 2H-pyrans and chromenes[END_REF] and, unlike other photochromic materials which usually display either P-Type or T-Type behaviour, [START_REF] Bouas-Laurent | Organic photochromism[END_REF] they exhibit a more complicate reaction mechanism. Indeed, upon steady UV irradiation, the phenomenology of these compounds can be conveniently described in terms of photoproduction of transoid-cis (TC) and transoid-trans (TT) structures [START_REF] Ottavi | Spectrokinetic study of 2,2-diphenyl-5,6-benzo(2H)chromene: a thermoreversible and photoreversible photochromic system[END_REF][START_REF] Delbaere | Quantitative analysis of the dynamic behaviour of photochromic systems[END_REF] and their complete bleaching to the starting material can only be achieved by both thermal and photochemical pathways. The TC forms are more thermally labile than the TT ones, whilst their thermodynamic stability is generally higher than that of TT. 9,10 This behaviour has also been observed for the reference molecule having this skeleton, 3,3diphenyl-3H-naphtho[2,1-b]pyran (herein named RN, Scheme 1), that was extensively reported in the literature, especially over the last three decades. [START_REF] Lenoble | Photophysics, photochemistry and kinetics of photochromic 2H-pyrans and chromenes[END_REF][START_REF] Ottavi | Spectrokinetic study of 2,2-diphenyl-5,6-benzo(2H)chromene: a thermoreversible and photoreversible photochromic system[END_REF][START_REF] Becker | Photochromism of Synthetic and Naturally Occurring 2H-Chromenes and 2H-Pyrans[END_REF][START_REF] Luccioni-Houze | Kinetic Analysis of Fluoro-[2h]-Chromenes at the Photostationary States[END_REF][START_REF] Luthem | The Effect of Substituents on the Ring Closure Reaction of Photo Activated Diarylnaphthopyrans[END_REF][START_REF] Kumar | The Relationship Between the Structure and the Absorption Spectra of Naphtho[2,1-B]pyran[END_REF][START_REF] Hobley | Photochromism of chromene crystals; a new property of old chromenes[END_REF][START_REF] Aubard | Femto/Picosecond Transient Absorption Spectroscopy of Photochromic 3,3-Diphenylnaphtho[2,1-b]pyran[END_REF][START_REF] Delbaere | NMR characterization of allenyl-naphthol in the photochromic process of 3,3-diphenyl-[3H]-naphtho[2-1,b]pyran[END_REF][START_REF] Gentili | Dynamics of the excited states of chromenes studied by fast and ultrafast spectroscopies[END_REF][START_REF] Brown | The ultrafast dynamics of some photochromic naphthopyrans[END_REF][START_REF] Maurel | SERS Study of 3,3-Diphenyl-naphtho[2,1-b]pyran: Another Evidence for Allenyl-Naphthol Involvement in the Photochromic Mechanism[END_REF][START_REF] Moine | Transient absorption investigation of the photophysical properties of new photochromic 3Hnaphtho[2,1-b]pyran[END_REF][START_REF] Moine | Transient Absorption Studies of the Photochromic Behavior of 3H-Naphtho[2,1-b]pyrans Linked to Thiophene Oligomers via an Acetylenic Junction[END_REF][START_REF] Harada | Solidstate Photochromism of Chromenes: Enhanced Photocoloration and Observation of Unstable Colored Species at Low Temperatures[END_REF][START_REF] Herzog | The photochemical ring opening reaction of chromene as seen by transient absorption and fluorescence spectroscopy[END_REF][START_REF] Inagaki | A Simple and Versatile Strategy for Rapid Color Fading and Intense Coloration of Photochromic Naphthopyran Families[END_REF][START_REF] Brazevic | Photochromic reaction in 3H-naphthopyrans studied by vibrational spectroscopy and quantum chemical calculations[END_REF][START_REF] Brazevic | Ultrafast dynamics of the transoid-cis isomer formed in photochromic reaction from 3H-naphthopyran[END_REF] The transformation of a benzo-or a naphthopyran into a photochromic system possessing only a T-Type or a P-Type behaviour might undoubtedly be of interest from both points of view of basic research and practical applications. This could be achieved by choosing a suitable solvent, the temperature range or introducing modifications of the molecular structure. Scheme 1 Mechanism of the photochromic reaction of 3,3-diphenyl-3H-naphtho [2,1-b]pyran.

On the one hand, a fully thermoreversible photochromic naphthopyran might be interesting in the realization of fast responsive optical switches while, on the other hand, a completely photoreversible molecule could be useful to produce bistable devices and systems for optical storage. Some examples have been recently reported in the literature, especially on the possibility to transform naphtopyrans into thermally reversible compounds, either by substituting the pyran ring with a furan one [START_REF] Sousa | Synthesis of 1-Vinylidene-naphthofurans: A Thermally Reversible Photochromic System That Colors Only When Adsorbed on Silica Gel[END_REF][START_REF] Sousa | Grey colouring thermally reversible photochromic 1-vinylidenenaphthofurans[END_REF] or the synthesis of fused-naphthopyrans [START_REF] Sousa | Control of the Switching Speed of Photochromic Naphthopyrans through Restriction of Double Bond Isomerization[END_REF][START_REF] Sousa | Joining High Coloration and Fast Color Fading with Photochromic Fused-Naphthopyrans[END_REF] or through an on-demand control of the photochromic properties, achieved by increasing the ring-size of the alkylenedioxy moiety on the naphthopyrans. [START_REF] Kuroiwa | On-Demand Control of the Photochromic Properties of Naphthopyrans[END_REF] One alternative approach, based on the attempt to synthesize a prevalently photoreversible naphthopyran, has been reported by one of us, carried out through the control of the photochromism of naphthopyran derivatives by means of intramolecular CH-π bonds. [START_REF] Frigoli | The Control of Photochromism of [3H]-Naphthopyran Derivatives with Intramolecular CH-π Bonds[END_REF] Indeed, the photochromism of naphthopyran was shown to be under thermodynamic control. In the framework of this project, we have also reported afterwards some studies on helicenenaphtopyrans, [START_REF] Frigoli | P-type Photochromism of new Helical Naphthopyrans: Synthesis, and Photochemical, Photophysical and Theoretical Study[END_REF]35 confirming that the improvement of the thermodynamic stability of the TT isomers, compared to the TC ones, played an important role to increase the spectrokinetic contribution of the TT to the overall mechanism of photochromic reaction, along with a reduced importance of the TC role at the photostationary state. In both cases mentioned above, even though TT was more thermodynamically stable than TC, we could argue that the return from TT to TC then to CF through isomerization of one double bond was made more difficult due to the steric hindrance of the helical part of the photochrome on the dienic moiety. One question is raised: is it possible to favour the formation of TT compared to TC at the photostationary state while TT is less thermodynamically stable than TC just by crowding the diene part of the molecule?

Herein, we have specifically designed a photochromic system, namely 3,3,13-triphenyl-3,13-dihydrochromeno[5,6-a]carbazole (CN-Ph-H), to respond to the above question and prepare some derivatives for which one phenyl group located at the 3-position was systematically functionalised with different donor groups, such as di(pyridin-2-yl)amine (CN-Ph-N(Py)2), diphenylamine (CN-Ph-N(Ph)2), methoxy (CN-Ph-OMe) and dimethylamine (CN-Ph-N(Me)2), as shown in Figure 1, in order to study their impacts on the spectrokinetic properties and more specifically to see whether is there any relationship between the rate constants of bleaching of TC and TT.

Experimental General Methods for Synthesis

All reactions were carried out under argon. Dichloromethane was distilled from P2O5, THF and toluene were distilled over Na/benzophenone. Dichloromethane and toluene were kept over activated 3Å molecular sieves. 1,2-Dichloroethane was dried over activated 3Å molecular sieves. All commercial reagents were used without further purification. [START_REF] Van Gemert | Organic Photochromic and Thermochromic Compounds[END_REF] H and [START_REF] Luthem | The Effect of Substituents on the Ring Closure Reaction of Photo Activated Diarylnaphthopyrans[END_REF] C NMR spectra were recorded at room temperature on Bruker Avance-300 MHz NMR spectrometer. [START_REF] Van Gemert | Organic Photochromic and Thermochromic Compounds[END_REF] H NMR spectra were recorded at 300 MHz and [START_REF] Luthem | The Effect of Substituents on the Ring Closure Reaction of Photo Activated Diarylnaphthopyrans[END_REF] C NMR spectra were recorded at 75 MHz. Chloroform residual peak was taken as internal reference at 7.26 ppm for 1 H NMR and 77 ppm for [START_REF] Luthem | The Effect of Substituents on the Ring Closure Reaction of Photo Activated Diarylnaphthopyrans[END_REF] C NMR. Acetone residual peak was taken as internal reference at 2.09 ppm for 1 H NMR and 205.87 ppm for [START_REF] Luthem | The Effect of Substituents on the Ring Closure Reaction of Photo Activated Diarylnaphthopyrans[END_REF] C NMR. DMSO residual peak was taken as internal reference at 2.54 ppm for 1 H NMR and 40.45 ppm for [START_REF] Luthem | The Effect of Substituents on the Ring Closure Reaction of Photo Activated Diarylnaphthopyrans[END_REF] C NMR. High-resolution mass spectra were obtained by using Waters Xevo Q-Tof using positive mode. Infrared spectra were recorded from Nicolet 6700 FT-IR spectrometer.

Instruments and methods

UV-vis absorption spectra were recorded on a Perkin-Elmer Lambda 800 double-beam spectrophotometer. For monitoring the spectral modifications of the molecules in real time under either UV or visible irradiation, a HP 8453 diode-array spectrophotometer was used. Photoreaction measurements were carried out in toluene (purchased from Merck, spectrophotometric grade, used as received) in a 1 cm cell path in the spectrophotometer holder with the irradiating and the probe beams forming a right angle. A 125 W xenon lamp, coupled with a Jobin-Yvon H10 UV monochromator for the wavelength choice and a fibre-optic system, was employed as the irradiating source for the photoreaction studies. The quantum yields of the photocolouration and photobleaching processes were determined by spectrophotometry, using potassium ferrioxalate actinometry to measure the radiation intensity, typically of the order of 510 -6 moles of photons dm -3 s -1 .

Fluorescence measurements were recorded on a Spex Fluorolog-2 1680/1 instrument, equipped with a system for spectral correction; the quantum yields were determined by using quinine sulphate in 1N H2SO4 (quantum yield F = 0.546 36 ) as the standard. The corrected areas of the sample and the standard emissions were compared by using the following equation (1), which accounts for the differences in absorbance and refraction index of the sample (AF, nF) and standard (ASt, nSt) solutions.

𝜙 𝐹 = 𝜙 𝑆𝑡 (𝐴𝑟𝑒𝑎) 𝐹 (𝐴𝑟𝑒𝑎) 𝑆𝑡 𝐴 𝑆𝑡 𝐴 𝐹 𝑛 𝐹 2 𝑛 𝑆𝑡 2 (1)
Sample concentrations were always adjusted to keep the absorbance below 0.1. The accuracy in the F values is estimated to be within 10%.

X-Ray diffraction (XRD) analysis was conducted on Single-crystal diffractometer Bruker AXS X8 APEX I using Mo radiation.

For the HPLC analysis, either a Gemini C18, 5 μm, 4.6×150 mm column or a Prontosil 200-3-C30, 3 μm, 4.6×150 mm column were alternatively used on a Waters HPLC facility, equipped with a Waters 600 controller and a Waters 996 photodiode array detector. Pure acetonitrile or an acetonitrile/water mixture up to 95/5 volume ratio were used as the eluent.

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Results and discussion

Synthesis

The synthesis of the photochromic materials relies first on the preparation of 11-phenyl-11H-benzo[a]carbazol-2-ol, which was obtained in two steps from the known 2-methoxy-11Hbenzo[a]carbazole, as depicted in Scheme 2. [START_REF] Oliveira | New benzopyranocarbazoles: synthesis and photochromic behavior[END_REF] The first step was a Narylation of the carbazole moiety using catalyst derived from CuI and trans-1,2-cyclohexanediamine as proposed in 2002 by Buchwald and co-workers. Under this condition, N-arylated product, compound 2 was obtained in 80% yield. [START_REF] Antilla | The Copper-Catalyzed N-Arylation of Indoles[END_REF] The second step was a simple demethylation using boron tribromide as demethylation agent and the desired product was prepared in 95 % yield. The introduction of 2,2′-dipyridylamine and diphenylamine in one phenyl of the photochromic materials lead the preparation of the ketones 4 and 5 respectively, which were obtained by using Ullmann condensation between 4-Bromobenzophenone and the corresponding amine (Scheme 3). The reaction worked well with 2,2′dipyridylamine since the corresponding ketone 4 was obtained in 80% yield. The ketone 5 functionalised with diphenylamine was obtained in only 33% yield. 39 Scheme 3 Preparation of 2,2′-dipyridylamine-and 2,2'diphenylamine-benzophenones.

From commercially available 4-methoxybenzophenone and 4dimethylaminobenzophenone and the benzophenone 4 and 5, the corresponding propargylic alcohols were prepared by the addition of the lithium-trimethylsilylacetylene on the benzophenone, followed by the cleavage of the trimethylsilyl group with an excess of potassium carbonate in MeOH / THF, as shown in Scheme 4. Then, the condensation between compound 3 and 1,1-diphenylprop-2-yn-1-ol commercially available or the propargylic alcohols 6-9 provided the desired photochromic materials (Scheme 4).

Scheme 4

Final steps in the synthesis of the photochromic materials.

X-ray analysis

Suitable monocrystal of CN-Ph-H for X-ray analysis was obtained. The crystals have a monoclinic symmetry with C2/c space group. Two enantiomers are present in the crystals. They differ from the position of the phenyl ring C compared to the chromene ring of the molecule. In Figure 2a, the ring C is behind the chromene ring. The molecule is stabilized with three hydrogen bonds. There is a CH- interaction between proton 3'' and the ring C. The geometry of the edge-to-face interaction is as follows: the distance between the proton and the ring centroid of the ring C is of 3.228 Å and the dihedral angle between the interacting ring planes is of 53.44°. A CH-O bond between proton 3' and oxygen 4 is observed with a distance of 2.308 Å and the angle between C-H3' and O4 is of 102.81°. There is also a CH-N bond between proton 1 and the nitrogen 13 with a distance of 2.583 Å and the angle between C-H1 and N14 is of 120.83°. The distance between protons 1 and 2 is of 1.318 Å, which is typical of a localized double bond. The dihedral angle between the two plans formed by the two phenyl rings A and B is of 77.92°. It should be noted that for the TC form, ring A is slightly less twisted with the diene part of the molecule compared to ring B whereas for TT, it is ring B which is less twisted. Actually, the phenyl group facing the proton is more planar.

Thermodynamic stability

So far, P-type photochromism based on [3H]-naphthopyran was observed for systems for which the TT form was more thermodynamically stable than TC form. Therefore, theoretical calculations were performed at CAM-B3LYP/6-31G(d,p) and M06-2X/6-31G(d,p) level of theory since they are optimized to reproduce well weak interactions that are essential in the investigated compound, and compared with the reference [3H]-naphthopyran (RN) (see Table 1) Table 1 Relative Gibbs free energies [kcal mol -1 ] in toluene computed by using DFT for the different systems under investigation. All values were calculated by using the most stable isomer as a reference CF. For RN and CN-Ph-H, the closed form is the most thermodynamically stable, followed by the TC form, then by TT form, whatever the level of theory. As shown in Figure 2 b) and c), TC and TT are stabilized by at least three hydrogen bonds as for the closed form. As for RN, TT is less thermodynamically stable than TC because the diene part of the molecule interacts less with the rest of the molecule. Indeed, the dihedral angle between carbons 2 and 13a is of 41.62° for TT, larger than that TC for which the dihedral angle is of 31.45°. This difference also explains why TT absorbs at lower wavelengths than TC. Since RN is known to display T-type photochromism in solution, would it be the same for CN-Ph-H and the other derivatives?

Photochromic properties

The quantitative absorption spectra of the five CN-Ph benzopyrans in toluene are shown below (Fig. 3). All compounds exhibit similar features showing a structure that is probably due to at least two different electronic transitions. The small differences are related to the changes in the substituent on one of the benzene rings located in the 3-position. The absorption spectra of the photochromes correspond nearly to the sum of the naphthopyran core and the substituted phenyl at the 3 position. CN-Ph-H When a toluene solution containing one of the N-phenyl carbazole benzopyrans is exposed to UV light, a common trend is observed for the five molecules. Upon UV irradiation, an initial steep rise of absorbance in the visible region is followed by a longer-lived further increase, up to the attainment of a photostationary state. The kinetic behaviour of the photocolouration curve, characterized by a clear biexponential trend, is shown in Fig. 4a for CN-Ph-H. Once the UV irradiation is interrupted, a fast thermal decay occurs, along with a rapid decrease of the absorbance in the visible, which stops after a few hundreds of seconds (second part of the kinetics in Fig. 4a). The residual colouration only bleaches if visible irradiation is carried out, up to a complete fading of the colour (third part of the kinetics in Fig. 4a). Otherwise, if the coloured chromene is kept in the dark after the fast thermal decay following the attainment of the photostationary state and it is not subjected to any kind of further irradiation, it undergoes a very slow thermal decolouration, which only becomes barely perceptible after a few months (Fig. S3).

In addition to that, when the solution containing the chromene was only exposed to UV light for a short time, usually about a hundred of seconds, and then its thermal decay was monitored once the irradiation had been discontinued, a complete rapid decolouration of the system was observed (Fig. 4b).

The decay rate constants for both the "fast" and the "slow" processes, obtained through a first order treatment of the kinetics, are reported in Table 3. The foregoing results can be explained in terms of the following reaction scheme (Scheme 5), which is based on the aforementioned experimental data and on results previously reported in the literature on similar naphthopyrans. [START_REF] Frigoli | The Control of Photochromism of [3H]-Naphthopyran Derivatives with Intramolecular CH-π Bonds[END_REF][START_REF] Frigoli | P-type Photochromism of new Helical Naphthopyrans: Synthesis, and Photochemical, Photophysical and Theoretical Study[END_REF][35][START_REF] Oliveira | Remarkable thermally stable open forms of photochromic new N-substituted benzopyranocarbazoles[END_REF] Please do not adjust margins Please do not adjust margins Based on this reaction mechanism, the initial chromene, in its closed colourless form, upon UV irradiation is transformed through a consecutive 2-step reaction in a transoid-cis open coloured isomer (TC) which in turn, upon prolonged irradiation, eventually evolves into the more thermally stable transoid-trans open coloured isomer (TT). The latter is responsible for the residual colouration that persists over months if the system is kept stored in the dark and bleaches completely to the starting material upon visible irradiation. This reaction mechanism is further supported by the short irradiation experiment reported in Figure 4b, where the thermally unstable TC open isomer, immediately formed upon UV photocolouration, does not further evolve into the TT form once the irradiation is interrupted, but undergoes thermal bleaching up to a complete fading. Indeed, after a prolonged UV irradiation, upon injection of the solution containing the photostationary state mixture of CN-Ph-H into the HPLC column, only two peaks were revealed, related to the residual initial chromene and the TT isomer, respectively. Owing to its relatively fast thermal decolouration process, the presence of the TC species could not be detected in the chromatogram.

In the light of all these findings, HPLC separation of the photostationary state mixture allowed the pure TT isomer to be collected. The complete quantitative absorption spectrum of the TT isomer could then be obtained upon selecting a wavelength where only very slight absorbance changes under irradiation are observed and setting the TT molar extinction coefficient equal to that of the initial closed form at that wavelength. A more precise approach would be that based on the use of a real isosbestic point, that however, in the present case, owing to the mechanism of reaction involving three different species could not be detected. The quantitative absorption spectrum of the TT isomer of CN-Ph-H is displayed in Fig. 5.

An algorithm was then used to determine also the quantitative absorption spectrum of the TC isomer. After UV irradiation, followed by HPLC separation, the TT concentration could be obtained by means of the TT, evaluated according to the aforementioned procedure, and the absorbance value of the kinetic profile at 500 nm, measured after the thermal decay following the photostationary state had occurred. This would also allow the conversion % of the starting molecule into the TT isomer to be evaluated. Then, considering the ratio between the peak areas of the closed form and the TT open isomer observed at the HPLC once the TC decay is complete, at a wavelength that best approximates an isosbestic point, the following relation holds:

𝐴𝑟𝑒𝑎 𝑇𝑇 𝐴𝑟𝑒𝑎 𝑐𝑜𝑙𝑜𝑢𝑟𝑙𝑒𝑠𝑠 = [𝑇𝑇] [𝑐𝑜𝑙𝑜𝑢𝑟𝑙𝑒𝑠𝑠′] (2)
Therefore, the concentration of the closed form after the complete TC thermal decay, [colourless'], could be determined. The absorbance decrease at 500 nm on going from the photostationary state to the complete decay of the TC species is correlated to the corresponding increase in the colourless form concentration originated from the TC thermal bleaching, therefore: where the prime symbol refers to the situation after the TC thermal decay has occurred, while the second one is related to the photostationary state. Once the concentration of the closed form at the photostationary state, [colourless"], has been determined from (3), the concentration of the TC isomer can be evaluated, and the molar extinction coefficient of the TC isomer at a particular wavelength can be derived: (5)

[𝑻𝑪] = [𝒄𝒐𝒍𝒐𝒖𝒓𝒍𝒆𝒔𝒔′] -[𝒄𝒐𝒍𝒐𝒖𝒓𝒍𝒆𝒔𝒔′′] ( 4
)
However, once the TC concentration has been obtained (eq.4), one can subtract the contributions of the CF and the TT species from the total absorption spectrum at the photostationary state, using their quantitative spectra and their concentrations at the photostationary state itself ([colourless"] and [TT]). The complete quantitative spectra of the TC isomer can then be derived and it is shown in Fig. 5.

The contribution of the TC isomer is clearly higher at longer wavelengths, as expected from the literature. As clearly visible from the first part of the kinetic profile in Fig. 4a, the UV photocolouration kinetics of the CN-Ph molecules exhibit a biexponential behaviour, as expected in such systems characterized by a consecutive three-step reaction mechanism. A complete quantitative treatment to provide the quantum yields of all the reaction steps involved, by solving the kinetic equations in a rigorous way, is practically impossible in this situation. [START_REF] Delbaere | Quantitative analysis of the dynamic behaviour of photochromic systems[END_REF] However, if one takes into account only the early instants of the UV irradiation, when only the TC isomer is substantially formed, as also pointed out by the short irradiation tests, the initial rate method is helpful to obtain the quantum yield  for the conversion of CF into TC:

Δ𝐴 𝑇𝐶 Δ𝑡 = 𝜀 𝑇𝐶 𝜙 𝐶𝐹⟶𝑇𝐶 𝐼 0 (1 -10 -𝐴 𝑇𝐶 ′ ) (6)
In eq.6, the first term refers to the finite variation of absorbance in the early time interval of the UV irradiation kinetics, therefore corresponds to the formation of the TC coloured isomer. TC is the molar extinction coefficient of the TC, CF→TC is the quantum yield of TC formation, A'TC is the total absorbance at the irradiation wavelength and I° is the intensity of the irradiation light, determined by chemical actinometry. Once the TC at the wavelength where the kinetic has been recorded is known, the quantum yield value of TC formation from the initial closed form, CF→TC = 0.43, could be obtained (Fig. S4).

Even though the TT isomer exhibits a notable thermal stability in the dark at room temperature in toluene solution, its transformation to the CF via TC can be accelerated by means of visible light irradiation. In our case, the CN-Ph-H was irradiated at 435 nm, and the corresponding photobleaching kinetics at 500 nm was recorded (Fig. 6). The TT absorption signal follows a first order decay and a procedure similar to that already employed to determine the quantum yield of UV photocolouration can also be used for visible photodecolouration data treatment, by taking into account the first experimental points of the bleaching kinetics, where only the TT isomer significantly contributes to total absorbance: Δ𝐴 𝑇𝑇 Δ𝑡 = 𝜀 𝑇𝑇 𝜙 𝑇𝑇⟶𝐶𝐹 𝐼 0 (1 -10 -𝐴 𝑇𝑇 ′ ) (7) In eq.7, TT is the molar extinction coefficient of the TT, TT→CF is the quantum yield of visible photobleaching, A'TT is the total absorbance at the irradiation wavelength and I° is the intensity of the irradiation light, determined by chemical actinometry. The value of the quantum yield of visible irradiation, TT→CF, is reported in Table 3. Finally, as previously mentioned, from the concentration value of the TT isomer, determined after the complete thermal decay of the TC following the photostationary state attainment, the percentage of transformation of the initial chromene into the stable coloured form could be calculated (Table 3).

CN-Ph-R

The photobehaviour of the four substituted molecules (CN-Ph-R; with R = -OMe, -N(methyl)2, -N(phenyl)2 and -N(pyridyl)2) is substantially similar to that of the unsubstituted compound (CN-Ph-H). The UV photocolouration was characterized by a biexponential trend and, once the photostationary state had been attained, interruption of the irradiation only caused a partial bleaching of the system, and the residual colouration persisted throughout several weeks. Full decolouration was only achieved upon visible irradiation of the solution with complete restoration of the initial chromene.

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Please do not adjust margins However, unlike CN-Ph-H, when the solution at the photostationary state was injected into the HPLC column, three peaks were observed instead of two, corresponding to three different thermally stable molecules, as shown in Fig. 7 for CN-Ph-OMe. One signal corresponds to the residual initial chromene present at the photostationary state, while the other peaks refer to two different thermally stable TT isomers produced upon UV irradiation, as clearly indicated by the spectral features observed for the two peaks at the diode array detector of the HPLC. Indeed, in the case of the CN-Ph-R compounds, the presence of a substituent on one of the phenyl rings on the sp 3 carbon, gives rise to two different transoid isomers upon UV photocolouration, namely the cis-transoid-trans (CTT) and the trans-transoid-trans (TTT); the latter formed through the corresponding transoid-cis isomers (CTC and TTC) (Scheme 6). HPLC analysis allowed the two TT coloured isomers to be separated and then selectively irradiated by visible light to study their photobleaching behaviour. The photodecolouration from TT to CF occurred through a clear pathway and the presence of an isosbestic point allowed the quantitative spectra of the stable TT coloured isomers to be measured, using the same procedure already described for CN-Ph-H. The quantitative absorption spectra of the TT isomers are displayed in Fig. 8, while their absorption maxima are collected in Table 2, along with the normalized absorption and TCs/TTs absorption ratio at the photostationary state. The ratios between CTT and TTT are different between OMe and the couple N-(Py)2 and N-(Ph)2 derivatives. This can be explained by the geometry of anisole and triphenylamine. The oxygen has a sp [START_REF] Corns | Industrial organic photochromic dyes[END_REF] hybridization and therefore the lone pair of oxygen with the phenyl makes an angle of 120° whereas in triphenylamine, the nitrogen is more planar, with nitrogen-torsion angles varying between ca. 160 and 180° indicating the lone pair of nitrogen is more involved in the -conjugated system. [START_REF] Andrews | The hybridization state of nitrogen as a conformational variable in biologically active molecules[END_REF] Since ring B in TTT is slightly less twisted than ring A (see Fig. 2), the lone pair of the groups is slightly more involved in the whole -conjugated system when the group is attached to ring B favouring the formation of the TTT form. The effect is more pronounced when the nitrogen group is involved since the lone pair of the nitrogen is more implicated in the -conjugation.

Table 2 Absorption maxima (max (nm)) of the TT isomers obtained upon UV irradiation of the CN-Ph molecules at 340 nm; absorption at the photostationary state measured at the longest wavelength in the visible region (A max PSS/A'340nm) and at 500 nm (A 500 PSS/A'340nm) normalized to the initial absorbance of the CF at the irradiation wavelength (340 nm); TCs/TTs absorption ratio at the photostationary state measured at the longest wavelength in the visible region (A% max TC/TT) and at 500 nm (A% 500 TC/TT). CN-Ph-H has an absorption maximum (max) at 471 nm which is bathochromic shifted by 15 nm and 19 nm for CN-Ph-OMe (486 nm) and CN-Ph-N(pyridyl)2 (490 nm), respectively. Larger bathochromic shifts of 47 nm and 62 nm are observed for CN-Ph-N(phenyl)2 (518 nm) and CN-Ph-N(methyl)2 (533 nm) respectively. Indeed, the max is related to the HOMO-LUMO level, which in turn is mainly due to the oxidation potential of the substituent (HOMO) as the acceptor part of the molecule is the same. This journal is © The Royal Society of Chemistry 20xx

Please do not adjust margins Please do not adjust margins The colourability defined as the absorbance reached at PS state is the same for all compounds (around 1) except for CN-Ph-N(methyl)2 which is slightly less important (0.84). At PS state, the absorption contribution of TC form (15.8%) for CN-Ph-H is less important than that obtained for CN-Ph-OMe (23.1%). For CN-Ph-N(pyridyl)2 and CN-Ph-N(phenyl)2, the absorption contribution of TC form increases to around 30% and increases even further for CN-Ph-N(methyl)2 to 38%.

As can be inferred by Fig. 8, the molar extinction coefficients of each pair of TT isomers for a given molecule exhibit values of the same order of magnitude, even though the amounts formed upon irradiation, is different (see Fig. 7 for of CN-Ph-OMe). These is clearly visible for CN-Ph-N(pyridyl)2 and the aforementioned CN-Ph-OMe. In the case of CN-Ph-N(phenyl)2 the unbalancing between the two TT coloured forms was so large that the area of one of the two peaks was only barely perceptible (less than 1% of the total signal of the coloured isomers). Therefore, it was possible isolating only one of the two TT isomers to perform its selective photobleaching experiment and recording its quantitative absorption spectrum. Irradiation of CN-Ph-N(methyl)2 did not allow any of the two TT species to be isolated at the HPLC, due to their relatively fast thermal decay. The different behaviour of this compound originates only from the stronger electronic effect of the substituent, since the steric hindrance is substantially the same for all the molecules investigated. In consequence, it was not possible to measure the quantitative absorption spectra of the TT isomers and only a spectrum at the photostationary state, including of course the residual closed form and the TT coloured species, could be reported (Fig. 8 d). For all compounds, the major TT photoproduct eluates first using silica-C18 as non-polar stationary phase, indicating that the same photoisomer is produced in larger quantity and corresponds to the more polar product. Theoretical calculations indicate that TTT has a dipolar moment higher than CTT (see table S3 in the Supporting Information). Therefore, TTT is likely to be the most abundant species produced at PS state. According to theoretical calculations, TTT should also have a slightly higher molar extinction coefficient than the one of CTT, confirming that peak 1 corresponds to TTT isomer.

The visible photobleaching reaction was also performed at 435 nm for each separated TT isomer, using potassium ferrioxalate as a chemical actinometer. The same procedure based on the initial rate method, already employed for the TT form of CN-Ph-H (eq.7), was then used to measure the visible photobleaching quantum yield, TT→CF, of the various TT isomers isolated at the HPLC for the CN-Ph-R molecules. The values are collected in Table 3.

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The percentage of transformation of the initial colourless chromene into the stable TT isomers was also measured through the analysis of the chromatographic traces at a suitable wavelength where the absorbance values of all the species involved (CF and the two TTs) were easily measurable. By taking into account the molar extinction coefficients of the CF and the TT coloured species and the peak areas, the % values of the stable TT isomers formed could be calculated (Table 3).

When the thermally stable TT isomers were not subjected to visible irradiation, their residual colour faded in the dark, at room temperature, over relatively long times. However, the rate constants for this thermal bleaching process exhibited a certain dependence on the kind of substituent present on one of the phenyl rings on the sp3 carbon of the chromene structure (Table 3). Decay rate constants ranged from the order of 10 -8 s -1 , as in the case of CN-Ph-H (Fig. S5a) and CN-Ph-N(pyridyl)2 to 10 -4 s -1 for CN-Ph-N(methyl)2 (Fig. S5b).

Table 3 Percentage of TT formation from CF, quantum yields of TT visible photobleaching and decay rate constants for the thermal bleaching processes of TC (k1) and TT (k2) isomers. From the data in Table 3, it can be seen that the rate constant of the back reaction from TC to CF (k1) is similar for CN-Ph-H and CN-Ph-N(pyridyl)2 even though the latter absorbs at longer wavelengths (see Fig. 8 and Table 2). k1 increases twice when N-dipyridyl group (0.018 s -1 ) is changed to N-diphenyl (0.035 s -1 ) and increases four times when dimethylamine (0.068 s -1 ) is used. Clearly, increasing the donor strength reduces the stability of the TC form. Surprisingly, k1 of CN-Ph-OMe (0.042 s -1 ) is similar to the one of CN-Ph-N(phenyl)2 (0.035 s -1 ) indicating that a methoxy and diphenylamine groups have similar electronic effect. This result is very interesting since diphenylamine group allows to shift the absorption behaviour by 32 nm in comparison with a methoxy functionalisation, while the rate constants are similar for both groups. The same trend is observed for the rate constant of the back reaction from TT to CF (k2) as that obtained for k1. It is worthwhile to notice that upon increasing k1 by a factor 2 between CN-Ph-N(pyridyl)2 and CN-Ph-N(phenyl)2, k2 increases by two orders of magnitude. In the similar manner, upon increasing k1 by 4 between CN-Ph-N(pyridyl)2 and CN-Ph-N(methyl)2, k2 increases by four orders of magnitude. These results indicate that the electronic effect is much more pronounced on the stability of TT form than that of TC form. The photochemical quantum yield from TTT to CF follows the same trend than that obtained for k1. For the percentage conversion from CF to TT derivatives obtained at PSS state, CN-Ph-H presents the highest conversion of 64%. Even though the stability of the photoproducts of CN-Ph-N(pyridyl)2 is similar to CN-Ph-H, the conversion ratio is only 44%. The reduced conversion ratio is due to the presence of TC forms in larger quantity at PSS state (see Table 2). Decreasing the thermal stability of the photoisomers in CN-Ph-N(phenyl)2, decreases even further the conversion ratio to 29%. Even if the stability of photoisomers of CN-Ph-N(phenyl)2 and CN-Ph-OMe is similar, the latter shows a higher conversion ratio of 43%. Once again, this result is due to the fact that the contribution of TC form for CN-Ph-OMe is less important (see Table 2).

Owing to the presence of two TC forms in the reaction mechanism, in the cases of the CN-Ph-R substituted molecules it was impossible to use the algorithm previously illustrated for CN-Ph-H to obtain the molar extinction coefficients and the quantitative absorption spectra of the TC isomers. In consequence, quantum yields CF→TC for the conversion of CF into TC could not be measured. Nevertheless, upon short-term UV irradiation followed by complete thermal decay we could follow the bleaching kinetics of the signal corresponding to the sum of the two TC isomers converting back to the starting material. The rate constant values of this thermal bleaching are influenced by the presence of the various substituents on one of the phenyl rings linked to the sp3 carbon atom (Fig. 9 and Table 3) and exhibit a trend that is similar to that observed for the thermal decay of the TT species. Fluorescence studies Given that the N-phenyl carbazole is a chromophore that exhibit fluorescence emission [START_REF] Berlman | Handbook of fluorescence spectra of aromatic molecules[END_REF] and that photochromism usually takes place from the lowest excited singlet state, we explored the possible fluorescence emission upon UV excitation of the five molecules investigated. This analysis was carried out to ascertain a possible competition between these two pathways in the deactivation of the lowest singlet excited state. The molecules were excited at 340 nm, the same wavelength employed for the photochromic studies, and the integrated emission spectra were compared to that obtained with quinine sulphate, used as a standard, under the same experimental conditions. However, for all five molecules very weak and noisy emission spectra were recorded, with very low fluorescence quantum yields of the order of F  710 - 4 . Therefore, the possible detrimental contribution of fluorescence to This journal is © The Royal Society of Chemistry 20xx

Please do not adjust margins Please do not adjust margins the photochromic reaction can be neglected under our experimental conditions.

Conclusions

In this paper, the photochromism of a series of newly synthesized N-phenyl carbazole benzopyrans has been investigated in toluene solution. The unsubstituted compound, CN-Ph-H, show P-type photochromism, even though the TC form is more thermodynamically stable than TT form, indicating that the photochromism is not always under thermodynamic control. In the present case, the P-type photochromism is obtained thanks to the steric hindrance provided by the phenyl group connected to the nitrogen on the diene part of TT forms, making the photo-and thermal-isomerisation more difficult.

The mechanism of the photochromic reaction, consisting of two consecutive steps where the TC(s) and the TT(s) coloured isomers are consecutively formed upon UV irradiation, has been elucidated. The spectrokinetic study allowed most of the molar extinction coefficients, the quantum yields of visible photobleaching, and the rate constants of the fast and slow thermal bleaching processes to be estimated.

In the case of the unsubstituted compound, CN-Ph-H, the quantum yield of UV photocolouration was also determined and an algorithm was used to obtain the complete quantitative absorption spectrum of the fast decaying TC isomer. For CN-Ph-H, the highest percentage of conversion (64%) of the initial chromene into the stable TT coloured isomer was measured, under our experimental conditions.

We investigated the effect of substituents with different donor strengths on one phenyl ring located at the 3-position on the spectrokinetic properties. While increasing the donor strengths shifts the absorption maximum of the photoproducts, the stability of TC and TT forms is decreasing. Reducing the stability of TC forms by two or four times, the stability of the corresponding TT forms is reduced by two-or four orders of magnitude, respectively. Interestingly, the electronic effects of N-diphenyl and methoxy groups on the stability of photoproducts are similar, while N-diphenyl group leads to a significant shift of the absorption maximum. This N-diphenyl functionalisation at the 3-position can be interesting for future design of naphthopyrans.

If on the one hand the unsubstituted compound CN-Ph-H, and to a lesser extent also CN-Ph-N(pyridyl)2, CN-Ph-N(phenyl)2 and CN-Ph-OMe point towards a P-type photochromism, on the other hand CN-Ph-N(methyl)2, functionalised with the strongest electron donating group, rather goes in direction of a T-type photochromic compound. These results indicate the possibility to tune the type of photochromism from P-type to T-type by functionalisation. In this perspective, the effect of the substituent is of notable importance in providing some useful hints for the synthesis of new benzopyrans possessing a long term stability of the TT(s) coloured isomer(s) in the dark.

Fig. 1

 1 Fig. 1 Molecular structure of the N-phenyl carbazole benzopyrans (CN-Ph-R).

Scheme 2

 2 Scheme 2 Preparation of 11-phenyl-11H-benzo[a]carbazol-2-ol.

Fig. 2 a

 2 Fig. 2 a) X-ray structure of CN-Ph-H; Optimized structures at CAM-B3LYP of b) TC form and c) TT form.

Fig. 3

 3 Fig. 3 Quantitative absorption spectra of the five N-phenyl carbazole benzopyrans in toluene.

Fig. 4

 4 Fig.4 Kinetic profile monitored at 500 nm for CN-Ph-H obtained upon: a) consecutive UV irradiation at  = 340 nm, thermal decay and final visible decolouration at  = 500 nm; b) short UV irradiation at  = 340 nm, followed by complete thermal bleaching.

  This journal is © The Royal Society of Chemistry 20xx Please do not adjust margins Please do not adjust margins

Fig. 5

 5 Fig. 5 Quantitative absorption spectra of the TC and TT coloured isomers obtained upon UV irradiation of CN-Ph-H in toluene.

Fig. 6

 6 Fig. 6 Kinetics of visible photobleaching (irr. = 435 nm) of CN-Ph-H in toluene, monitored at 500 nm. Inset: linear interpolation of the first points of the decay (see below).

Fig. 7

 7 Fig. 7 Chromatogram obtained at the HPLC upon injection of a solution of CN-Ph-OCH3 in toluene, after UV irradiation until attainment of the photostationary state.

Scheme 6

 6 Scheme 6 Mechanism proposed for the photochromic reaction of the CN-Ph-R chromenes, showing the initial closed form (CF), and the main coloured transoid-cis (CTC and TTC) and transoid-trans (CTT and TTT) isomers.

Fig. 8 .

 8 Fig. 8. a) Quantitative absorption spectra of the TTT (peak 1, see text below) forms produced upon irradiation of the CN-Ph-R molecules, along with that of the TT obtained for the unsubstituted CN-Ph-H; the two TTT (peak 1) and CTT (peak 2, see text) coloured isomers produced upon irradiation of CN-Ph-N(pyridyl)2 (b) and CN-Ph-OMe (c); d) absorption spectrum of the photostationary state mixture obtained upon irradiation of CN-Ph-N(methyl)2.

Fig. 9

 9 Fig. 9 Normalized decay kinetics of the TC isomers obtained after short-time UV irradiation of the five CN-Ph-R molecules.

This journal is © The Royal Society of Chemistry 20xx J. Name., 2013, 00, 1-3 | 5

This journal is © The Royal Society of Chemistry 20xx J. Name., 2013, 00, 1-3 | 9

Acknowledgements F.O., A.Z. and D.P. gratefully acknowledge the financial support of the Ministero per l'Università e la Ricerca Scientifica e Tecnologica (Rome, Italy), the University of Perugia [PRIN 2010-2011, 2010FM738P], the Istituto Nazionale di Fisica Nucleare (I.N.F.N.); M.M. and C.A. acknowledge financial support from JST ERATO Grant Number JPMJER1305, and JSPS KAKENHI Grant Number 19H02790; M.F. and J.M. acknowledge financial support from the Agence Nationale de la Recherche ANR-16-CE07-0024 (GATE). T. J-O. acknowledges CNRS for PhD grant.

Conflicts of interest

There are no conflicts to declare.


H Steiner

S Jakirlic

G Kadavelil

R Manceau

S Saric

G Brenn

on Direct and

Introduction

The role of the ERCOFTAC SIG15 (Special Interest Group for Turbulence Modelling) series of workshops on refined turbulence modelling is closely connected to intensive verification and systematic validation of CFD (Computational Fluid Dynamics) technology for solving problems of both fundamental importance and industrial relevance. Focus is on the credibility and reliability of both the numerical methods and mathematical models simulating turbulence. In such a way a large database of simulation results, along with detailed comparison with the reliable reference data (experimental, DNS and highly-resolved LES databases), has been assembled. The SIG15 workshops promote the discussion and conclusions about predictive performance of a variety of statistical turbulence models, SGS models in the LES-framework, as well as hybrid LES/RANS models in a broad range of well documented flow configurations among the scientists, researchers, users and developers from industry and from the academic field.

The 13th ERCOFTAC Workshop, hosted by the Institute of Fluid Mechanics and Heat Transfer at Graz University of Technology, Austria, was held on 25th and 26th September, 2008. The previous twelve workshops were organized in Lyon (1991), Manchester (1993), Lisbon (1994), Karlsruhe (1995), Chatou (1996), Delft (1997), Manchester (1998), Helsinki (1999), Darmstadt (2001), Poitiers (2002), Gothenburg (2005) and Berlin (2006). Unlike some previous workshops, where up to four complex 3-dimensional, unsteady flow geometries were treated (see for instance Thiele and Jakirlic, 2007), whose computation required several months or even years of intensive work (which could be provided only in the framework of a funded project), only two geometrically simpler benchmarks, but featured by complex flow and turbulence phenomena (3-D unsteady separation and reattachment, swirling effects, etc.) being of great scientific and engineering relevance were chosen as test cases for this workshop: [START_REF] Minagawa | Development of turbulent impinging jet on a rotating disk[END_REF]. Schematic of the flow configuration considered showing the coordinate system used (adopted from [START_REF] Lallave | Numerical analysis of heat transfer on a rotating disk surface under confined liquid jet impingement[END_REF]. In addition to the test case sessions, an oral session was organized accommodating up to ten lectures all dealing with hybrid RANS/LES computational methods with emphasis on their theoretical foundation and predicitive capabilities in different applications. The oral session was divided into a session accommodating the five survey lectures: The presentation files of all lectures and workshop proceedings can be downloaded from the workshop web site (http://130.83.243.201/ercoftac-sig15/workshop2008.html or www.ercoftac.org).

Participation

The 13 th Workshop was attended by 50 participants from Europe, U.S.A. and Japan (13 from Germany, 15 from Austria, 6 from France, 2 from the United Kingdom, 1 from Denmark, 2 from Sweden, 1 from the USA, 1 from Japan, 1 from Italy, 3 from Hungary, 2 from Croatia, 2 from Slovenia, 1 from Bosnia & Herzegovina),: of which 10 from industry, 4 from research institutes and 36 from universities.

SIG 15 Case 13.1: Round jet impinging perpendicularly onto a rotating, heated disc A turbulent jet at Reynolds number Re j = 14500 impinging perpendicularly onto a rotating disc (Fig. 1) represents the workshop's first test case. Detailed velocity measurements in the turbulent boundary layer developing on a rotating disk were conducted by [START_REF] Minagawa | Development of turbulent impinging jet on a rotating disk[END_REF]. The rotation of the disk onto which the jet is impinging is at the origin of a skewing of the wall jet created around the impingement point. Therefore, this case provides an excellent example of a two-dimensional (axisymmetric) flow subject to a complex, six-component strain, pertinent to the investigation of the effects present in complex 3D-flows.

The effect of rotation is primarily manifested through the centrifugal acceleration and the mean flow skewing. The intensification and thinning of the radial wall jet due to centrifugal acceleration strongly promotes turbulent fluctuations in the radial direction. The shear strain ∂V θ /∂z leads to the appearance of shear stresses (compared to the case without rotation) and the intensification of the normal stress in the circumferential direction. Other stress components are indirectly affected, mainly by the redistribution process.

The shape of the solution domain and applied boundary types are indicated in Fig. 3. The flow configuration can be considered as axi-symmetric and steady. Accordingly, 2D computations can be performed when applying the RANS method. The necessary variable profiles at the inflow boundary into the solution domain (within the pipe) are to be obtained by precursor computations of the fully-developed pipe flow with corresponding turbulence models. As shown in Fig. 3, the upper boundary (inflow and pressure/Neuman boundary conditions) are located well above (5D) the pipe outlet, such that a significant portion of the pipe is included in the computational domain. At the disk wall, the rotational velocity (and the temperature) is prescribed, as given in the experiments. Four different cases with respect to four rotational intensities from ωD/U j = 0 (non-rotating case) to ωD/U j = 0.45 were computed. Additionally to the above described computations of the mean flow and turbulence quantities, the heat transfer from the heated disc in accordance to the experiment of Popiel and Boguslawski was considered. The jet Reynolds number being closest to the Minagawa/Obi experiment is Re j = 46000.

The computational groups contributing to this case and the turbulence models used are listed in Table 2. Accordingly, several versions of eddy viscosity models employing different scale-supplying variables (total viscous dissipation rate ε and a specific dissipation rate ω ∼ ε/k) and wall boundary treatment (wall functions and exact boundary conditions) were used. In addition, both Eddy-Viscosity models ( A consequence of the modification of the velocity field is manifested through the intensification of the shear rate ∂V r /∂z, and in turn, of the corresponding turbulence production terms. The strong increase of the radial fluctuation v ′ r due to intensification of its leading production term can be seen in Fig. 5. Such an effect is captured by all the models, even eddy-viscosity models, which include the direct influence of the shear stress. However, eddy-viscosity models give a much too early (r/D = 2 rather than r/D = 4) increase of v ′ r , which can be traced to the fact that the production is assumed quadratic in the shear stress rather than linear.

The effect of the modification of the production in the Reynolds stress transport equations due to involvement of the secondary shearing ∂V θ /∂z (compared to the non-rotating case), which also modifies the turbulence anisotropy and the redistribution among the components, is documented in Fig 6 . Expectedly, such an effect can only be captured by a Reynolds stress model.

SIG 15 Case 13.2: Separated flow in a 3-D diffuser

An incompressible fully-developed duct flow expanding into a diffuser whose upper and one side walls are appropriately deflected, for which the experimentally obtained reference database was provided by [START_REF] Cherry | Geometric sensitivity of three-dimensional separated flows[END_REF][START_REF] Cherry | Pressure measurements in a three-dimensional separated diffuser[END_REF], represented the workshop's second test case, Fig. 2. This flow configuration is characterized by a complex three-dimensional flow separation being the consequence of an adverse pressure gradient evoked by the duct expansion. It should be noted that two three-dimensional diffusers with the same fully-developed channel inlet, but slightly different expansion geometries, were experimentally investigated. Both diffuser flows exhibited threedimensional boundary layer separation, but the size and shape of the separation bubble exhibited a high degree of geometric sensitivity to the dimensions of the diffuser. In the framework of the 13 th workshop, only the first case (with the deflection angles of the upper and one side wall being α = 11.3 o and α = 2.56 o respectively, Fig. 6) was computed. The second diffuser will be a test case of the forthcoming 14 th workshop (which is to be held on September 18, 2009 at the Università di Roma 'La Sapienza', Italy: www.ercoftac.org).

Experiments were performed to determine the mean velocity field. The streamwise Reynolds stress components have also been measured in the entire flow domain. In addition, the pressure coefficient distribution along the lower diffuser wall was provided [START_REF] Cherry | Pressure measurements in a three-dimensional separated diffuser[END_REF]. Readers interested in more details about the measurement technique are referred to both experimental references. The dimensions of Diffuser 1 and the coordinate system are shown in Fig. 6. The inlet flow corresponds to fully-developed turbulence, and the bulk inlet velocity is 1 m/sec in the x direction, resulting in the Reynolds number of 10000. The origin of the coordinates coincides with the intersection of the two non-expanding walls at the beginning of the diffuser's expansion. The following computational groups contributed to the comparative, cross-plot analysis:

• International University Sarajevo -IUS (Hadđiabdic)

• University Erlangen-Nuremberg (LSTM) / Professorship for Fluid Mechanics, Helmut Schmidt University, Hamburg (Breuer)

• Karlsruhe University (ITS and IFH Institutes; Schneider, von Terzi, Rodi)

• University of Manchester (Billard, Uribe, Laurence)

• Osaka Prefecture University (Suga)

• ANSYS GmbH Germany (Menter, Garbaruk, Smirnov)

• Università di Roma 'La Sapienza' (Borello, Hanjalic, Rispoli, Dalibra, Alfieri)

• Technische Universität Darmstadt (SLA and FNB Chairs; Kadavelil, Kornhaas, Saric, Sternel, Jakirlic, Schäfer)

• RWTH Aachen, E.ON Energy Research Center & Fa. Porsche (Brännström, Müller)

Unlike the first case, LES and LES-related methods (different seamless and zonal hybrid LES/RANS (HLR) models; DES -Detached Eddy Simulation), in addition to different RANS models, were massively applied here. The diversity of the models/methods applied can be seen from the following table. The analysis of the results obtained has been conducted with respect to the size and shape of the flow separation pattern and associated mean flow and turbulence features. A selection of the computational results along with the experimental data is displayed in Figs. 789. 9 upper; denoted by UKA-LES) applying LES method on the grid with uniformly redistributed cells in conjunction with the wall functions for the near-wall treatment. It led to a finer grid resolution within the flow core compared to TUD-LES and HSU-LES (i.e. LSTM-LES). Both latter methods used fine near-wall resolution and integration up to the wall. Coarser grid resolution in the near-wall region and use of the wall-functions were justified by the fact that in this configuration the flow unsteadiness were introduced into the wall boundary layer from the core flow in accordance to the so-called 'top-to-bottom' process (communication with M. Leschziner).

Conclusions

Short summaries of the test cases description and the most important conclusions arising from the computationally obtained body of data are given in this report. In addition to the test case session, two oral sessions accommodating five survey lectures and five flash presentations were organized. This new format with two geometrically simpler benchmarks, but featured by complex flow and turbulence phenomena, led to a substantially improved attendance with 50 participants and computational results contributed by thirteen groups in total.

Figure 1 :

 1 Figure 1: SIG15 Case 13.1: Round jet impinging perpendicularly onto a rotating, heated disc (Exp.: Popiel and Boguslawski, 1986;[START_REF] Minagawa | Development of turbulent impinging jet on a rotating disk[END_REF]. Schematic of the flow configuration considered showing the coordinate system used (adopted from[START_REF] Lallave | Numerical analysis of heat transfer on a rotating disk surface under confined liquid jet impingement[END_REF].

Figure 2 :

 2 Figure 2: SIG15 Case 13.2: Separated flow in a 3-D diffuser. Experimental flow system schematic (Cherry et al., 2008, 2009). Both cases have been selected for the first time. Relevant computational studies were performed by Benim et al. (2007) and Cherry et al. (2006). The second case represents a very recent experimental work.In addition to the test case sessions, an oral session was organized accommodating up to ten lectures all dealing with hybrid RANS/LES computational methods with emphasis on their theoretical foundation and predicitive capabilities in different applications. The oral

Figure 3 :

 3 Figure 3: Solution domain and boundary conditions for the SIG15 Case 13.1.

  v 2 -f and ζf , with ζ = v 2 /k; the latter model version is due to Hanjalic et al., 2004) and Second-Moment Closure models relying on Durbin's elliptic relaxation theory were applied.

Table 1 :

 1 SIG15 Case 13.1 -Contributors and models.

Figure 4 :

 4 Figure 4: Development of the mean (V r ) radial velocity within the wall jet at Z/D = 0.032.

Figure 5 :

 5 Figure 5: Development of the root-mean-square (v ′ r ) radial velocities within the wall jet at Z/D = 0.032.

Fig. 4

 4 Fig.4illustrates the evolution of the mean radial velocity in terms of the rotational intensity. The influence of the centrifugal acceleration becomes especially visible in the wall jet for larger distances from the axis of rotation (r/D > 2.5). The resulting acceleration of the mean flow in the radial direction (and thinning of the wall jet thickness, which can be seen on profiles along the vertical direction; not shown here) is reproduced independently of the turbulence model applied (the results shown here are obtained by the EB RSM model) because of the direct influence of rotation on the velocity field through the term in the momentum equation representing the centrifugal force.A consequence of the modification of the velocity field is manifested through the intensification of the shear rate ∂V r /∂z, and in turn, of the corresponding turbulence production terms. The strong increase of the radial fluctuation v ′ r due to intensification of its leading production term can be seen in Fig.5. Such an effect is captured by all the models, even eddy-viscosity models, which include the direct influence of the shear stress. However, eddy-viscosity models give a much too early (r/D = 2 rather than r/D = 4) increase of v ′ r , which can be traced to the fact that the production is assumed quadratic in the shear stress rather than linear.The effect of the modification of the production in the Reynolds stress transport equations due to involvement of the secondary shearing ∂V θ /∂z (compared to the non-rotating case), which also modifies the turbulence anisotropy and the redistribution among the components, is documented in Fig 6.Expectedly, such an effect can only be captured by a Reynolds stress model.

Figure 6 :

 6 Figure 6: Profiles of v 2 θ at r/D = 5.8 in terms of increasing rotation rates.

Figure 7 :

 7 Figure 7: Geometry of the diffuser considered and the instantaneous velocity field obtained by LES (TU Darmstadt).

Fig. 7

 7 displaying the instantaneous velocity field obtained by LES provides a first impression of the flow topology. Figs. 8 show the contour plots of the axial velocity component in two selected streamwise crosssectional areas, indicating the evolution of the flow separation pattern. Unlike the kω SST results, the results obtained by the LES and Hybrid LES/RANS methods agree reasonably well with respect to both the size and shape of the three-dimensional recirculation zone. The kω SST model resulted in a flow separating at the deflected side wall contrary to the experimental findings indicating the separation zone along the upper deflected

Figure 8 :

 8 Figure 8: Iso-contours of the axial velocity field in the cross planes y-z at two selected streamwise locations within the diffuser section (the bold line denotes the zero-velocity line; h = 1cm)

Figure 9 :

 9 Figure 9: Evolution of the axial velocity and turbulent streamwise stress component profiles in the vertical plane x-y at the spanwise location z/B = 1/2: comparison between experiments and simulations.

Table 1 :

 1 SIG15 Case 13.2 -Contributors & methods.

Short Summary of Results and DiscussionFlow description, instructions for calculations, detailed specification of the shape and dimensions of solution domains, as well as of the inlet data and boundary conditions for the two test cases considered, are given in the workshop proceedings. Here, only a short description of the test cases and a summary of some specific outcomes and the most important conclusions are given.

Acknowledgements

We would like to thank the large number of people who were involved in the preparation and execution of this workshop. This applies especially to the SIG15 Steering Committee and the staff of the Institute of Fluid Mechanics and Heat Transfer at Graz University of Technology and the Chair of Fluid Mechanics and Aerodynamics in Darmstadt, who in one way or the other were all involved in the organization. We are thankful to the ERCOFTAC Administration/Development Office for the student grants. Our special thanks go to the reference data suppliers Erica Cherry (3D diffuser) and Shinnosuke Obi (impinging jet).


Julien Marlet

Camille Petillon

Emma Ragot

Yazid Abou

El Fattah

Antoine Guillon

Sylvain Marchand

Adrien Lemaignen

Louis Bernard

Guillaume Desoubeaux

Hélène Blasco

Yazid Abou El Fattah

Francis Barin

Karl Stefic

Catherine Gaudy- Graffin

Clinical performance of four immunoassays for antibodies to SARS-CoV-2, including a prospective analysis for the diagnosis of COVID-19 in a real-life routine care setting

Keywords: SARS-CoV-2, COVID-19, serology, immunoassay, antibody, ELISA, CLIA, RT-PCR

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.

INTRODUCTION

The novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) firstly reported in late 2019 in Wuhan [START_REF] Zhu | China Novel Coronavirus Investigating and Research Team, A Novel Coronavirus from Patients with Pneumonia in China[END_REF] and causing coronavirus disease (COVID-19) has spread across the world and lead to a worldwide sanitary crisis. Detection of viral RNA using reverse-transcriptase polymerase chain reaction (RT-PCR) in respiratory samples is the gold standard for early diagnosis of COVID-19. However, sensitivity of this molecular diagnosis starts to decrease at week 3 after onset of symptoms [START_REF] Wölfel | Virological assessment of hospitalized patients with COVID-2019[END_REF].

Complementary to RT-PCR in respiratory samples, SARS-CoV-2 serology allows identification of COVID-19 cases with a higher sensitivity than RT-PCR several days after onset of symptoms [START_REF] Peeling | Serology testing in the COVID-19 pandemic response[END_REF]. In addition, it can be used to determine the fraction of the population that has been exposed to the virus [START_REF] Peeling | Serology testing in the COVID-19 pandemic response[END_REF]. However, results of such serosurveys depend on the performance of immunoassays and on the seroprevalence of SARS-CoV-2 which remains quite low, even in COVID-19 hotspots [START_REF] Eckerle | SARS-CoV-2 seroprevalence in COVID-19 hotspots[END_REF]. Given this low prevalence, it is crucial to have robust data evaluating those assays before clinical or epidemiological use. Four immunoassays were evaluated in our study: Euroimmun

MATERIAL AND METHODS

Patients and samples

Two complementary studies were performed. First, clinical performance of immunoassays were evaluated on 63 COVID-19 patients tested positive for SARS-CoV-2 RNA by RT-PCR at Tours University Hospital (Table 1). SARS-CoV-2 RT-PCR were performed in respiratory samples using Allplex™ 2019-nCOV assay (Seegene, Seoul, Republic of Korea), Abbott RealTime SARS-CoV-2 assay (Abbott Molecular, Illinois, USA) or Bosphore 2019-nCoV detection kit (Anatolia GeneWorks, Istanbul, Turkey) depending on reagents and systems availability. Among the positive RT-PCR results, inconclusive RT-PCR results were defined as results positive only for one gene (E, ORF1ab or N). All 63 patients required an in-patient hospital stay for COVID-19 and had plasma samples collected between April 8 th and May 11 th 2020. Retrospective testing for SARS-CoV-2 Ab was performed on these samples, collected between 2 to 36 days after the onset of symptoms. Mild and critical COVID-19 cases were defined according to WHO [START_REF] Who | Clinical management of patients with COVID-19[END_REF]. Specificity was evaluated on plasma collected before the end of 2019 in 89 patients from occupational medicine (n=30), emergency or pneumology departments (n=26) or from patients tested positive by RT-PCR (Allplex™ RP3, Seegene) for seasonal coronaviruses (n=33, OC43, 229E or NL63) between 3 to 82 weeks before serology sampling. Positive and negative predictive values of immunoassays were estimated in a context of low (2.4%) and high seroprevalence (9.8%) of SARS-CoV-2 Ab. These estimates were based on prevalence of SARS-CoV-2 Ab in healthcare professionals (2.4%, 108/4 444 tested from June to August 2020) or from patients (9.8%, 6/61 tested from May to June 2020).

Second, the contribution of SARS-CoV-2 serology in routine care for the diagnosis of COVID-19 was evaluated on 203 patients tested for SARS-CoV-2 infection by RT-PCR between April 8 th and June 11 th 2020 (Table 1). Most of these patients were healthcare professionals (167/203, 82.3%) who did not require an in-patient hospital stay (125/167, 74.9%). Other patients required an in-patient hospital stay (31/203) or had ambulatory testing (6/203). These patients were tested for SARS-CoV-2 antibodies at least 14 days after RT-PCR testing (unless otherwise specified) between June 1 st and June 25 th 2020. The entire study was performed according to French Reference Methodology MR-004, after patient information and anonymization of data. Samples were obtained from the registered biological collection DC-2020-3961.

Statistical analysis

Statistical analysis was carried out using Graphpad Prism v5. Comparison of sensitivity and specificity were performed using McNemar's test. All tests were two-sided at the 0.05 significance level.

RESULTS

Clinical performance of SARS-CoV-2 immunoassays in the retrospective study.

The sensitivity of Euroimmun IgG, Abbott IgG, Wantai Ab, and DiaPro IgG confirmation SARS-CoV-2 assays seven to thirteen days after the onset of symptoms were 30.8, 46.2, 84.6 and 61.5% (Figure 1). In this timeframe, the DiaPro IgG confirmation demonstrated an excellent sensitivity for anti-N Ab (100%), higher than that for anti-S2 Ab (15.4%, p=0.003) and higher, although not significantly, than that for anti-S1 Ab (53.8%; p=0.13).

The sensitivity of Euroimmun IgG, Abbott IgG, Wantai Ab and DiaPro IgG confirmation SARS-CoV-2 assays 14 days after the onset of symptoms were 95.6%, 95.6%, 97.8% and 95.6%, respectively (Figure 1). The DiaPro IgG confirmation assay demonstrated good and similar sensitivities for anti-S1 and anti-N Ab (93.3% and 97.8%), both higher than that for anti-S2 Ab (62.2%, p≤0.002). The single patient who tested negative with all immunoassays was a 61 years old heart transplant patient who experienced fever and myocarditis and had inconclusive RT-PCR result (positive only for the N gene) 26 days post-onset of symptoms (Figure 1). 95% CI 84.5-96.8 93.9-100.0 95.9-100.0 88.9-98.8 95.9-100.0 75.0-91.1 93.9-100.0 dps: days post-onset of symptoms

Contribution of SARS-CoV-2 serology in routine care to confirm or infirm the diagnosis of COVID-19

Agreement between RT-PCR and Euroimmun IgG was 68% (15/22) and 96%

(173/181) for patients who tested positive and negative by RT-PCR, respectively.

Results of other immunoassays (Figure 2), the delay between RT-PCR and serology as well as Ct and targets of RT-PCR results were analyzed for these patients (Figure 3). Patients were considered as suffering from COVID-19 if they tested positive with RT-PCR (all targets positive with Ct<38) and/or with at least two out of four SARS-COV-2 immunoassays (Figure 2). This allowed an accurate definition of We considered that false positive RT-PCR results occurred in four patients. They were characterized by inconclusive RT-PCR results. Only the N gene was detected, with

Ct>38. These patients tested negative with all immunoassays, suggesting the absence of exposure to SARS-CoV-2. Importantly, such inconclusive RT-PCR results were also observed in two COVID-19 patients confirmed positive with all serological assays (Figure 2), precluding any systematic interpretation of inconclusive RT-PCR results as false positive.

False negative RT-PCR results were observed in two asymptomatic patients, and in three symptomatic patients with late RT-PCR sampling (>1 month after onset of symptoms). These three symptomatic individuals were positive with all immunoassays, confirming the benefit of serology testing for patients with late presentation after onset of symptoms.

False negative serology results were observed in 2/23 COVID-19 patients who were sampled too early for serology testing (<14 days after onset of symptoms, Figure 2 and Figure 3). Among the

DISCUSSION

In the first part of our analysis corresponding to the retrospective evaluation, the specificity was 92.1%, 98.9%, 100%, and 98.9% for Euroimmun IgG, Abbott IgG, Wantai Ab, and DiaPro IgG confirmation SARS-CoV-2 assays, respectively. The sensitivity 14 days after onset of symptoms was 95.6%, 95.6%, 97.8%, and 95.6% for Euroimmun IgG, Abbott IgG, Wantai Ab, and DiaPro IgG confirmation SARS-CoV-2 assays, respectively. The sensitivity between 7 and 13 days was suboptimal for Wantai Ab (84.6%) and inadequate (<75%) for other assays. Our results are in accordance with the available data for which the sensitivity ranges 14 days after onset of symptoms have been described as 61.7-96.0%, 77.8-100.0%, 98-100% and specificity ranges as 86.6-100.0%, 95.1-100.0%, 98.0-99.1% for Euroimmun IgG [START_REF] Lassaunière | Evaluation of nine commercial SARS-CoV-2 immunoassays[END_REF][START_REF] Van Elslande | Diagnostic performance of seven rapid IgG/IgM antibody tests and the Euroimmun IgA/IgG ELISA in COVID-19 patients[END_REF][START_REF] Beavis | Evaluation of the EUROIMMUN Anti-SARS-CoV-2 ELISA Assay for detection of IgA and IgG antibodies[END_REF][START_REF] Jääskeläinen | Performance of six SARS-CoV-2 immunoassays in comparison with microneutralisation[END_REF][START_REF] Nicol | Assessment of SARS-CoV-2 serological tests for the diagnosis of COVID-19 through the evaluation of three immunoassays: Two automated immunoassays (Euroimmun and Abbott) and one rapid lateral flow immunoassay (NG Biotech)[END_REF][START_REF] Kohmer | Clinical performance of different SARS-CoV-2 IgG antibody tests[END_REF][START_REF] Montesinos | Evaluation of two automated and three rapid lateral flow immunoassays for the detection of anti-SARS-CoV-2 antibodies[END_REF][START_REF] Kohmer | Brief clinical evaluation of six high-throughput SARS-CoV-2 IgG antibody assays[END_REF][START_REF] Krüttgen | Comparison of four new commercial serologic assays for determination of SARS-CoV-2 IgG[END_REF][START_REF] Weidner | Quantification of SARS-CoV-2 antibodies with eight commercially available immunoassays[END_REF][START_REF] Meyer | Geneva Center for Emerging Viral Diseases, Validation of a commercially available SARS-CoV-2 serological immunoassay[END_REF][START_REF] Tuaillon | Detection of SARS-CoV-2 antibodies using commercial assays and seroconversion patterns in hospitalized patients[END_REF][START_REF] Geurtsvankessel | An evaluation of COVID-19 serological assays informs future diagnostics and exposure assessment[END_REF][START_REF] Theel | Performance Characteristics of Four High-Throughput Immunoassays for Detection of IgG Antibodies against SARS-CoV-2[END_REF], Abbott IgG [START_REF] Jääskeläinen | Performance of six SARS-CoV-2 immunoassays in comparison with microneutralisation[END_REF][START_REF] Nicol | Assessment of SARS-CoV-2 serological tests for the diagnosis of COVID-19 through the evaluation of three immunoassays: Two automated immunoassays (Euroimmun and Abbott) and one rapid lateral flow immunoassay (NG Biotech)[END_REF][START_REF] Kohmer | Brief clinical evaluation of six high-throughput SARS-CoV-2 IgG antibody assays[END_REF][START_REF] Theel | Performance Characteristics of Four High-Throughput Immunoassays for Detection of IgG Antibodies against SARS-CoV-2[END_REF][START_REF] Chew | Clinical evaluation of serological IgG antibody response on the Abbott Architect for established SARS-CoV-2 infection[END_REF][START_REF] Meschi | INMICovid-19 laboratory team, Performance evaluation of Abbott ARCHITECT SARS-CoV-2 IgG immunoassay in comparison with indirect immunofluorescence and virus microneutralization test[END_REF] and Wantai Ab immunoassays [START_REF] Weidner | Quantification of SARS-CoV-2 antibodies with eight commercially available immunoassays[END_REF][START_REF] Zhao | Antibody responses to SARS-CoV-2 in patients of novel coronavirus disease 2019[END_REF][START_REF] Ong | Comparison of diagnostic accuracies of rapid serological tests and ELISA to molecular diagnostics in patients with suspected coronavirus disease 2019 presenting to the hospital[END_REF], respectively. Although we included a collection of serum samples from patients for whom a recent infection by seasonal coronaviruses was documented, we did not notice any specific clustering of false positive results that could be attributed to a particular cross-reactivity.

Clinical performance of the DiaPro IgG confirmation assay (combining S1, S2 and N Ag) were similar to other immunoassays and to the manufacturer's statement (sensitivity 98%, specificity 90%). Interestingly, a higher sensitivity was observed for anti-N Ab and anti-S1 Ab than for anti-S2 Ab (97.8 and 93.3 vs 62.2%, p≤0.002). This confirmed previous studies based on in-house ELISAs [START_REF] Brochot | Anti-Spike, anti-Nucleocapsid and neutralizing antibodies in SARS-CoV-2 inpatients and asymptomatic carriers[END_REF]. In contrast, a higher specificity was observed for anti-S2 Ab (100%) than for anti-N Ab (84.3%, p=0.0005).

As suggested by previous studies [START_REF] Schnurra | Comparison of the diagnostic sensitivity of SARS-CoV-2 nucleoprotein and glycoprotein-based antibody tests[END_REF][START_REF] Sun | Kinetics of SARS-CoV-2 specific IgM and IgG responses in COVID-19 patients[END_REF], combination of S and N Ag probably contributed to the overall good performances of this assay, which had the highest positive agreement of all immunoassays (20/21) with COVID-19 diagnosis in our sub-study performed in real-life routine conditions. Furthermore, this assay has the advantage to allow comparison of the ratio between anti-N IgG and anti-S IgG, which has been associated with the prognosis [START_REF] Sun | Kinetics of SARS-CoV-2 specific IgM and IgG responses in COVID-19 patients[END_REF].

We observed a lack of specificity for the Euroimmun IgG assay (92.1%, CI 95%: 84. [START_REF] Fafi-Kremer | Serologic responses to SARS-CoV-2 infection among hospital staff with mild disease in eastern France[END_REF] to 20% [START_REF] Rijkers | Differences in antibody kinetics and functionality between severe and mild SARS-CoV-2 infections[END_REF][START_REF] Pallett | Point-of-care serological assays for delayed SARS-CoV-2 case identification among health-care workers in the UK: a prospective multicentre cohort study[END_REF][START_REF] Brandstetter | Symptoms and immunoglobulin development in hospital staff exposed to a SARS-CoV-2 outbreak[END_REF] several weeks after disease. This could be due to the high proportion of patients with mild COVID-19, resulting in low rates of seroconversion [START_REF] Rijkers | Differences in antibody kinetics and functionality between severe and mild SARS-CoV-2 infections[END_REF].

Our study confirms that Abbott IgG, Wantai Ab and DiaPro IgG confirmation assays are suitable assays for the diagnosis of COVID-19 at least 14 days after onset of symptoms. Main advantages of these assays are their automation (Abbott IgG), their optimal clinical performance (Wantai Ab) and their ability to differentiate between anti-N, -S1 and -S2 Ab (DiaPro IgG confirmation). DiaPro IgG confirmation assay has a low throughput (four wells per patient) which is adequate for confirmation testing.

Euroimmun IgG assay can also be used for the diagnosis of COVID-19 if positive results are confirmed with another assay to compensate for its low specificity.

The huge impact of the SARS-CoV-2 emergence in public health justifies extensive seroepidemiological studies to survey its spread in various populations and numerous settings. There is a burst of serologic assays rolling out in different formats, including simple rapid tests. Our study shows that specificity may be highly variable among available immunoassays for antibody to SARS-CoV-2. Poor specificity of an assay in a population where prevalence and incidence of COVID-19 are low will lead to irrelevant data. Our study, as others, stresses on the absolute necessity to use only carefully validated assays to provide epidemiological data useful to public health decision makers.

  ELISA SARS-CoV-2 IgG (Euroimmun, Lübeck, Germany), Abbott SARS-CoV-2 IgG (Abbott Diagnostics, Illinois, USA), Wantai SARS-CoV-2 Ab ELISA (Beijing Wantai Biological Pharmacy Enterprise, Beijing, China), and DiaPro COVID-19 IgG Confirmation (Diagnostic Bioprobes, Milano, Italy). The latter assay was used to determine the specificity of SARS-CoV-2 Ab against S1, S2 and N Ag. The first aim was to evaluate the performance of these SARS-CoV-2 immunoassays on a series of 63 COVID-19 patients and 89 pre-pandemic control patients. The second aim was to evaluate their contribution in routine care to confirm or infirm the diagnosis of COVID-19.

Figure 1 :

 1 Figure 1: Clinical performance of SARS-CoV-2 immunoassays.

  respectively. The DiaPro IgG confirmation assay had the highest positive agreement with COVID-19 diagnosis. It detected anti-S1, -S2 and -N Ab in 20, 12 and 21 of these 21 patients, respectively. In contrast, 5 out of 21 COVID-19 patients were not detected with the Abbott IgG assay. Interestingly, these five COVID-19 patients were also negative for anti-S2 Ab with the DiaPro IgG confirmation assay (Figure2). The low positive agreement of Abbott IgG (16/21) with COVID-19 confirmed cases might suggest a lower sensitivity. However, the data could be due to the small sample size and would deserve to be confirmed in larger studies.

Figure 2 :

 2 Figure 2 : Agreement between RT-PCR and serology for 203 patients.COVID-19 confirmed if positive RT-PCR (>1 gene) and/or Ab detected with two or

Figure 3 :

 3 Figure 3: Delay between serology and first RT-PCR or onset of symptoms.Delay between serology and first RT-PCR (plain dots) or onset of symptoms (empty

Table 1 :

 1 Clinical presentation of patients

		First study (clinical performance)	Second study (routine
					care)
		RT-PCR+	Pre-pandemic control	RT-PCR-RT-PCR+
			group
	Nb	63	89	181	22
	Age	79/67-90	30/11-54	39/30-50	49/31-58
	(median/IQR)
	Sex (F:M)	1.52	1.17	1.51	1.75
	Severe outcome 19/63	N/A	N/A	0
		(30.2%)
	ICU 18/63	NA	N/A	0
		(28.6%)
	Death 3/63 (4.7%) NA	N/A	0

SARS-CoV-2 RT-PCR assays: Allplex™ 2019-nCOV (Seegene), Abbott RealTime SARS-CoV-2 or Bosphore 2019-nCoV (Anatolia GeneWorks); NA: not available; ICU: intensive care unit SARS-CoV-2 immunoassays Euroimmun ELISA SARS-CoV-2 IgG, Abbott SARS-CoV-2 IgG (Alinity-I analyzer), Wantai SARS-CoV-2 Ab ELISA, and DiaPro COVID-19 IgG Confirmation assays were performed according to the manufacturer's recommendations. Euroimmun IgG assay was used as first line immunoassay in routine care setting. Positive or undetermined results and results discordant with RT-PCR were confirmed with other assays. For statistical analysis, Euroimmun IgG and Wantai Ab uninterpretable results were considered negative. DiaPro IgG confirmation assay was considered positive when Ab against at least two targets (S1, S2 or nucleoprotein) were detected.

  This patient could have had a false positive RT-PCR result or, less likely false negative serology results because of its immunosuppressive treatments.

	results in control patients were associated with a lower ratio (median of 3.13; IQR 1.90-
	4.40, maximum 5) than those from the COVID-19 patients (median of 7.60, IQR 3.20-
	11.14, p=0.02) (Figure 1). The two different patients with false positive Abbott IgG
	(1/89) or DiaPro IgG confirmation (1/89) results had a history of infection with
	Coronavirus 229E.

The specificity of Euroimmun IgG, Abbott IgG, Wantai Ab and DiaPro IgG confirmation SARS-CoV-2 immunoassay were 92.1%, 98.9%, 100% and 98.9%, respectively (Figure

1

). Specificity of the DiaPro IgG confirmation assay was lower for anti-N Ab (84.3%) than for anti-S1 Ab (95.5%, p=0.02) and anti-S2 Ab (100.0%, p=0.0005).

Specificity of Euroimmun

IgG assay was lower than other immunoassays, with a significant difference versus Wantai Ab assay (p=0.02) but not versus Abbott IgG (p=0.08). False positive Euroimmun IgG results were observed in in an equivalent manner in the different groups of control patients: those with seasonal coronaviruses infections (2/33, both OC43), those from emergency or pneumology departments (3/26) and those from occupational medicine (2/30). False positive Euroimmun IgG Positive predictive values based on a 2.4% and a 9.8% prevalence rate were 22.9%/56.8%; 68.1%/90.4%; 100%/100%, and 68.1%/90.4% for Euroimmun IgG,

Table 2 :

 2 Clinical performance of SARS-CoV-2 immunoassays relative to delay with onset of symptoms

	171
	Assay		Euroimmun IgG Abbott IgG	Wantai Ab		DiaPro IgG confirmation
	Platform		ELISA	CLIA (Alinity-i) ELISA			ELISA
	Antigen		S1	N	S (RBD)	S1	S2	N	≥2 Ag
	Sensitivity
	≥7-13 dps n/N	4/13	6/13	11/13	7/13	2/13	13/13	8/13
		%	30.8	46.2	84.6	53.8	15.4	100	61.5
		95% CI 9.1-61.4	19.2-74.9	54.6-98.1	25.1-80.8 1.9-4.5	75.3-100.0 31.6-86.1
	≥14 dps	n/N	43/45	43/45	44/45	42/45	28/45	44/45	43/45
		%	95.6	95.6	97.8	93.3	62.2	97.8	95.6
		95% CI 84.9-99.5	84.9-99.5	88.2-99.9	81.7-98.6 46.5-76.2 88.2-99.9 84.9-99.5
	Specificity n/N	82/89	88/89	89/89	85/89	89/89	75/89	88/89
		%	92.1	98.9	100.0	95.5	100.0	84.3	98.9

  21 remaining COVID-19 patients tested for antibody to SARS-

	CoV-2 at least 14 days post onset of symptoms, positive agreement with COVID-19
	diagnosis was 90.5% (19/21), 76.2% (16/21), 90.5% (19/21) and 95.2% (20/21) for

Euroimmun IgG, Abbott IgG, Wantai Ab and DiaPro IgG confirmation assay,

Abbott IgG, Wantai Ab and DiaPro IgG confirmation SARS-CoV-2 immunoassays.

Negative predictive values based on a 2.4% and a 9.8% prevalence rate were 99.9%/99.5% for Euroimmun IgG, Abbott IgG and DiaPro IgG confirmation, and 99.9%/99.8% for Wantai Ab SARS-CoV-2 immunoassays.

ACKNOWLEDGMENTS

The authors thanks Brigitte Berthon, Pascale Mezieres and Amélie Grivot for their contribution to the experiments, and Léo Léger for its contribution to data collection and analysis. Dr. Marchand-Adam reports financial relationships from Boehringer

FUNDING

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.