Drs Nedjwa N Bennai

Nada Ibrahim

Jérôme Marrot

Mohamed Belkadi

Mouad Alami

Emmanuel Magnier

Elsa Anselmi

Samir Messaoudi
email: samir.messaoudi@universite-paris-saclay.fr

Migita Cross-Couling

M Ibrahim

S Alami

Mesaoudi

Drs E Magnier

Synthesis of S-Trifluoromethyl S-Arylsulfoximine Thioglycosides through Pd-Catalyzed Migita Cross-Coupling

Keywords: S-trifluoromethyl, S-arylsulfoximines, thioglycosides, Palladium, Migita Cross-Couling

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Introduction

After a long period of latency, the sulfoximines have recently emerged as active pharmaceutical ingredients (APIs) in life and in crop sciences. This very peculiar group slowly evolved from "neglected opportunity in medicinal drug discovery" to an emergent and promising moiety. [1] Some relevant examples are given as follows. BAY 1000394, a potent pan-CDK inhibitor and AZD 6738, an orally bioavailable inhibitor of the serine/threonine protein kinase ataxia telangiectasia mutated (ATM) are currently in phase II of clinical trials (Figure 1). [2] An insecticide including a sulfoximine in its skeleton, the Sulfoxaflor ® was launched on the market in 2013. [3] In this context, the presence of fluorine atoms in a molecule dramatically changes its properties and in a vast majority of cases improves its efficiency for bioactive compounds purposes. [4] Despite the importance of this halogen, S-perfluoroalkyl sulfoximines are extremely rare in the chemistry of life sciences whereas they are more and more present in the toolbox of the chemists as reagent in organic chemistry. [5] One can hypothesize that fluorinated sulfoximines could bring original properties for relevant biological targets. A recent example highlighted indeed the interest of S-trifluoromethyl sulfoximine for antidiabetic activity (Figure 1). [6] A library of pyrazines has been tested for antidiabetic properties. The presence of the fluorinated sulfoximine group proved efficient to increase cytosolic glucokinase levels through the binding to glucokinase regulatory protein (GRKP). In another hand, 1-thioglycosides have emerged as a privileged class of glycosides with a diverse range of potential applications. [7] These glycomimetics are known to be more F Figure 1. Biologically Active Aryl sulfoximines and Thioglycosides resistant to glycosidase cleavage under biologically media. [7f,8] Selected examples of bioactive thioglycosides are disclosed in Figure 1 such as hSGLT1 inhibitor, ligand of lectin A as well as Galactin-3 inhibitors. Moreover, thioglycosides are very useful intermediates in carbohydrate chemistry as they are largely used in sequential glycosylation tactics for oligosaccharides synthesis.

[9] Despite the potential interest of both sulfoximines and thiosugars in medicinal chemistry there is no report, to the best of our knowledge, devoted to synthesis of S-aryl Strifluoromethylsulfoximine thioglycosides. The combination of both these moieties in a designed single structure may however lead to the creation of unique molecular architectures based glycosides of interest for medicinal chemists. They could furthermore serve as potent drug analogues (Figure 1). This assumption is based on the fact that sulfoximines were proposed as alcohol isosteres. [10] To reach our synthetic goal, we planned an approach merging the knowledge of our both research groups: in the chemistry of S-trifluoromethyl sulfoximine [11] and in the development of strategies devoted to the reactivity of thiosugars under transition metal-catalysis [12] including Pd-catalyzed Migita [13] cross-coupling. The synthesis of o-iodo S-aryl S-trifluoromethylsulfoximine and the subsequent [14] selective functionalization of the ortho position, in the presence of the free NH sulfoximine was recently carried out. [15] Another interest of the present study would rely on the chiral pool offered by the thiosugars derivatives. This natural and cheap source of chirality could generate an easy access to pure diastereoisomers of S-trifluoromethyl sulfoximines thioglycosides. This is of particular interest because methods to prepare S-trifluoromethyl sulfoximine diastereoisomers in a pure fashion are rare. [16]

Results and Discussion

To initiate this study, we conducted the coupling of tetra-Oacetylated 1-thio-β-D-galactopyranose 1a with o-iodo Strifluoromethyl S-phenylsulfoximine 2a as a model study under various reaction conditions. Representative results from this study are summarized in Table 1. The reaction of 1a (1.2 equiv) with 2a (1 equiv) was first investigated under our previously reported conditions using 5 mol% of a PdG3-XantPhos [17] precatalyst in the presence of Et3N (1.5 equiv) as a base at room temperature for 12 hours (Table 1, entry 1). However, under these conditions, the desired sulfoximine thioglycoside 3a has never been observed. Increasing the amount of the catalyst from 5 mol% to 20 mol% did not reveal any significant reactivity. This result may be explained by the hindrance effect of the trifluoromethyl arylsulfoximine group which may hamper the oxidative addition of the Pd(0) to the C-I bond. At this stage, we decided to increase the activation energy of this reaction by performing the cross-coupling at 60 °C instead of room temperature. Under these conditions, the desired thioglycoside 3a was isolated in a good 65% yield as a single β-anomer (J1,2 = 9 Hz) in a 1:1 diastereomeric ratio. Pleasingly, the two diastereoisomers showed distinct properties in solution as the pure 3aa-(R) diastereoisomer could be crystallized in Et2O and easily separated from its 3ab-(S) isomer. Its exact structure was elucidated by X-ray analysis (Scheme 1). Moreover, the 3ab-(S) was obtained as a pure product upon evaporation of the liquid layer. It should be noted that the reaction is completely chemoselective and no by-product which could be arisen from the arylation of the nitrogen of the sulfoximine group was observed. Interesting, scale-up experiment (1.5 mmol of 2a) was also performed with thiosugars 1a, which led to the formation of thioglycoside 3a in an excellent 90% yield. Of note, the palladium catalyst is necessary to achieve this transformation since no reaction occurs when the coupling reaction is conducted in the absence of the catalyst. With these results in hand, we subsequently investigated the substrate scope for this process with diverse mono-, di-, and trithiosugars 1b-j (Scheme 1). Gratifyingly, all the coupling reactions proceeded cleanly and selectively in good yields. This reaction is not limited to only O-acetylated 1-thio-β-D-galactose 1a since different others sugars such as β-D-glucopyranose (1b) and β-D-fucose (1h) were used successfully providing 3b and Scheme 1 Scope of Coupling of various Thiosugars 1a-j with 2a-c a

[a] Reaction conditions: A sealable tube was charged with thiosugar 1a-j (1.2 to 2 equiv), iodo-sulfoximine 2a-c (1 equiv) and XantPhos PdG3 precatalyst (10 mol %), Et3N (1.5 equiv) in dioxane. [b] Yield of isolated product. [c] 2 days reaction time 3c in 70% and 78% yields, respectively. Unprotected thiosugars such as 1c and 1f can also serve as partners under our reaction conditions leading to the desired arylsulfoximine thioglycosides 3d and 3e in moderate yields. In addition, this methodology was not limited to only O-acetyl protected thiosugars but other protecting groups are tolerated such as -OBz (3f), -OMe (3g) and -OTBs (3h).

The structural variation of the aromatic partner was then investigated. The introduction of a methyl group on the aromatic ring was not deleterious to the transformation and the resulting compound 3i was isolated in 50% yield. However, although pure diastereosiomers of 3i were separated easily through HPLC purification and kept without alteration of the chiral information, epimerization of the chiral sulfoximine was observed in this only case indicating that the methyl group may alter the configurational stability of these diastereosiomers.

The same reaction with a non-fluorinated sulfoximine, a Smethyl analogue of 2a was rather successful (3j isolated in 49% yield) but required an important increase of the reaction time, 2 days versus 30 minutes. This result illustrates the key role of the trifluoromethyl group in the general reactivity of the aromatic ring.

Next, we moved on to investigate the reactivity of complex and biologically relevant saccharide derivatives. Thus, we found that this coupling could be applied to thio-β-D-cellobiose 1i and thioβ-D-maltotriose 1j delivering 3k and 3l in 60% and 49% yields, respectively. Finally, we decided to investigate whether the chiral information on enantiopure trifluoromethyl sulfoximines was conserved during the cross-coupling process. In case of success, this may open the door to an efficient way to synthesize highly diastereopure trifluoromethyl sulfoximine thioglycosides. Delightfully, the reaction of enantiopure S-trifluoromethyl Sarylsulfoximines 16 2aa(R) and 2ab(S) under our optimized condition furnished the expected chiral products 3aa'(R) and 3ab'(S) in 84% and 78% yields, respectively and without any detectable racemization by HPLC analysis or NMR (Scheme 2). Reaction conditions: A sealable tube was charged with thiosugar 1a (1.5 equiv, 0.2 mmol), iodo-sulfoximine 2aa or 2ab (1 equiv) and XantPhos PdG3 precatalyst (10 mol %), Et3N (1.5 equiv) in dioxane. b Yield of isolated product.

Conclusion

In summary, we described here general protocol for the synthesis of S-trifluoromethyl S-arylsulfoximine thioglycosides. This protocol is based on a Pd-catalyzed Migita cross-coupling between o-iodo S-trifluoromethyl S-arylsulfoximines and a broad range of 1-thiosugars. Interestingly, the sugar part was used as a natural and cheap source of chirality that could generate an easy access to pure diastereomers of S-trifluoromethyl sulfoximines thioglycosides.

Experimental Section

Experimental Details.

General information

Solvents and reagents are obtained from commercial suppliers and were used without further purification. Analytical TLC was performed using Merck silica gel F254 (230-400 mesh) plates and analyzed by UV light or by staining upon heating with vanilin solution (15 g of vanilin in 250 mL ethanol and 2.5 mL of concentrated sulfuric acid). For silica gel chromatography, the flash chromatography technique was used, with Merck silica gel 60 (230-400 mesh) and p.a. grade solvents unless otherwise noted. The 1 H NMR and 13 C NMR spectra were recorded in either CDCl3 or CD3OD on Bruker Avance 300 spectrometers. NMR spectra for 19F (188 MHz) were recorded in either CDCl3 or CD3OD on Bruker Avance 200 spectrometers. The chemical shifts of 1 H, 13 C and 19 F are reported in ppm relative to the solvent residual peaks. IR spectra were measured on a Bruker Vector 22 spectrophotometer.Merck silica gel 60 (0.015-0.040 mm) was used for column chromatography. Melting points were recorded on a Büchi B-450 apparatus. High resolution mass spectra (HR-MS) were recorded on a MicroMass LCT Premier Spectrometer spectrometer. Optical rotations were obtained with a PolAAr 32 polarimeter. Thiosugars were synthesized according the literature protocols. [17] 2-iodosulfoximines 2a-c were prepared as reported. [14] The Xantphos Palladium precatalyst PdG3 was synthetized according to literature protocol. [18] General procedure for the coupling of Thiosugars 1a-j with 2iodosulfoximine 2 a-c A sealable tube purged with argon equipped with a cap was charged with PdG3-Xantphos (10 mol %), ß-thiosugar (1.2 to 2 equiv), 2-iodosulfoximine (1 equiv). Then, Dioxane (1 mL) was added and to the solution was added Et3N (1.5 equiv) dropwise, and the mixture was stirred at 60°C for 30 min. The reaction mixture was cooled to room temperature and passed through celite and rinsed with EtOAc. Then the filtrate was concentrated and the residue was purified by column chromatography on silica gel. The liquid chromatography separation of the diastereoisomers was achieved using an Agilent infinity 1260 (4.6 x 150 mm) 5 µm column.

Compounds characterization (2R,3S,4S,5R,6S)-2-(acetoxymethyl)-6-((2-S-(trifluoromethyl)sulfonimidoyl) phenyl)thio)tetrahydro-2H-pyran-3,4,5-triyl triacetate 3a

A sealable tube purged with argon equipped with a cap was charged with PdG3-Xantphos (28 mg, 0.03 mmol, 10 mol %), tetraacetylated ßthiogalactose 1a (130 mg, 0.36 mmol, 1.2 equiv), 2-iodo-sulfoximine 2a (100 mg, 0.3 mmol, 1 equiv). Dioxane (1 mL) was added to the mixture and then, Et3N (61 µL, 0.45 mmol, 1.5 equiv) dropwise. The solution was stirred at 60°C for 30 min. The reaction mixture was cooled to room temperature and passed through celite and rinsed with EtOAc. This crude was purified by column chromatography on silica gel (Cyclohexane/ EtOAc: 5/5), and 3a was isolated as a white solid in 65% yield. The ratio of diastereoisomers of compound 3a was 1:1 measured by NMR.

Protocol for crystallization and separation of (R) and (S) diastereoisomers for compound 3a:

To a mixture of (R) and (S) diastereoisomers (100 mg) was added 5 mL of diethyl ether and the solution was stored at 4°C for 24h. A white solid crystal was formed and isolated through simple filtration. The exact structure of the crystal was elucidated by X-ray analysis as the diastereoisomer 3aa-(R). Additionally, the diastereoisomer 3ab-(S) was obtained as a pure product upon evaporation of the liquid layer. This operation was repeated 2 to 3 times until the liquid layer delivered only a pure 3ab-(S).

(2R,3S,4S,5R,6S)-2-(acetoxymethyl)-6-((2-((R)-S-(trifluoromethyl)sulfonimidoyl)phenyl)thio)tetrahydro-2H-pyran-3,4,5-triyl triacetate 3aa

Rf (50% EtOAc/Pentane) = 0.57; [α]D 19 = +8.37 (c, 1.66

(2R,3S,4S,5R,6S)-2-(acetoxymethyl)-6-((2-((S)-S-(trifluoromethyl)sulfonimidoyl)phenyl)thio)tetrahydro-2H-pyran-3,4,5-triyl triacetate 3ab

Rf (50% EtOAc/Pentane) = 0.5; [α]D 19 = + 83.43 (c,1.66 in CHCl3); mp: 48.1 -52.3 °C; IR (neat, cm -1 ) 1760, 1367, 1243, 1085, 1069; 1 H NMR (300 MHz, CDCl3) δ 8.19 (d, J = 8.0 Hz, 1H), 7.87 (d, J = 8.0 Hz, 1H), 7.65 (t, J = 7.7 Hz, 1H), 7.47 (t, J = 7.7 Hz, 1H), 5.48 (d, J = 3.2 Hz, 1H), 5.37 (t, J = 9.9 Hz, 1H), 5.09 (dd, J = 9.9, 3.2 Hz, 1H), 4.81 (d, J =

(2R,3R,4S,5R,6S)-2-(acetoxymethyl)-6-((2-(S-(trifluoromethyl)sulfonimidoyl)phenyl)thio)tetrahydro-2H-pyran-3,4,5-triyl triacetate 3b

A sealable tube purged with argon equipped with a cap was charged with PdG3-Xantphos (28 mg, 0.03 mmol, 10 mol %), tetraacetylated ßthioglucose 1b (130 mg, 0.36 mmol, 1.2 equiv), 2-iodo-sulfoximine 2a (100 mg, 0.3 mmol, 1 equiv). Dioxane (1mL) was added followed by Et3N (61 µL, 0.45 mmol, 1.5 equiv) dropwise. The mixture was stirred at 60°C for 30 min.

The reaction mixture was cooled to room temperature and passed through a plug of celite and rinsed with EtOAc. The crude was purified by column chromatography on silica gel (Cyclohexane/ EtOAc: 5/5), and compound 3b was isolated as a white solid in 70% yield. The ratio of diastereoisomers of compound 3b was about 1:0.91 (by NMR).

The chromatographic separation was achieved using an Agilent infinity 1260 (4.6 x 150 mm) 5µm column. The mobile phase was Acetonitrile and H2O in the ratio of 60:40, v/v in 25min. The column temperature was maintained at 25°C and the eluent was monitored at a wavelength of 280 nm. The injection volume was 10 µL. The typical retention time of diastereoisomers of compound 3b was about 19.1 min and 20.8 min, respectively.

Diastereoisomer 3ba

Rf (50% EtOAc/Cyclohexane) = 0.37; [α]D 19 = -58.43 (c, 1.66

Diastereoisomer 3bb

Rf (50% EtOAc/Cyclohexane) = 0.33;

(2S,3R,4R,5S,6R)-2-methyl-6-((2-(S-(trifluoromethyl)sulfonimidoyl)phenyl)thio)tetrahydro-2H-pyran-3,4,5-triyl triacetate 3c

A sealable tube purged with argon equipped with a cap was charged with PdG3-Xantphos (31 mg, 0.033 mmol, 10 mol %), triacetylated ßthiofucose 1h (200 mg, 0.66 mmol, 2.0 equiv), 2-iodo-sulfoximine 2a (110 mg, 0.33 mmol, 1 equiv). Then, Dioxane (1mL) was added and to the solution was added Et3N (67 µL, 0.5 mmol, 1.5 equiv) dropwise and the mixture was stirred at 60°C for 30 min.

The reaction mixture was cooled to room temperature and passed through a plug of celite and rinsed with EtOAc. This crude was purified by column chromatography on silica gel (Cyclohexane/ EtOAc: 6/4), and compound 3c was isolated as a white solid in 78% yield. The ratio of diastereoisomers of compound 3c was about 0.93:1 (by NMR).

The chromatographic separation was achieved using a Chiralpak AD-H (250 x 10 mm), hexane / ethanol (50/50) as mobile phase, flow-rate = 5 mL/min, UV detection at 254 nm. Injections: 50 times 80 L, every 6.2 minutes.

Diastereoisomer 3ca

Rf (50% EtOAc/Cyclohexane) = 0.47; 1 H NMR (300 MHz, CDCl3) δ 8.25 (d, J = 8.0 Hz, 1H), 7.94 (d, J = 8.0 Hz, 1H), 7.65 (t, J = 7.7 Hz, 1H), 7.47 (t, J = 7.7 Hz, 1H), 5.39 (t, J = 10.0 Hz, 1H), 5.31 (m, 1H), 5.09 (dd, J = 9.9, 3.2 Hz, 1H), 4.85 (d, J = 10.1 Hz, 1H), 3.91 (q, J = 6.3 Hz, 1H), 2.25 (s, 3H), 2.04 (s, 3H), 1.98 (s, 3H), 1.26 (d, J = 6.5

Diastereoisomer 3cb

Rf (50% EtOAc/Cyclohexane) = 0.40; 1 H NMR (300 MHz, CDCl3) δ 8.20 (d, J = 8.0 Hz, 1H), 7.86 (d, J = 8.0 Hz, 1H), 7.67 (t, J = 7.7 Hz, 1H), 7.47 (t, J = 7.7 Hz, 1H), 5.39 -5.32 (m, 2H), 5.09 (dd, J = 9.9, 3.2 Hz, 1H), 4.79 (d, J = 10.1 Hz, 1H), 4.23 (bs, NH), 3.93 (q, J = 6.5 Hz, 1H), 2.20 (s, 3H), 2.03 (s, 3H), 1.99 (s, 3H), 1.28 (d, J = 6.5 Hz, 3H);

imino(trifluoromethyl)(2-(((2S,3R,4S,5S,6R)-3,4,5-trihydroxy-6-(hydroxymethyl)tetrahydro-2H-pyran-2-yl)thio)phenyl)-l6-sulfanone 3d

A sealable tube purged with argon equipped with a cap was charged with PdG3-Xantphos (32 mg, 0.034 mmol, 10 mol %), ß-thioglucose 1c (80 mg, 0.41 mmol, 1.2 equiv), 2-iodo-sulfoximine 2a (114 mg, 0.34 mmol, 1 equiv). Then, a mixture of dioxane/H2O (1mL/0.5mL) was added and to the solution was added Et3N (69 µL, 0.51 mmol, 1.5 equiv) dropwise. The mixture was stirred at 60°C for 30 min.

The reaction mixture was cooled to room temperature and passed through a plug of celite and rinsed with EtOAc. This crude was purified by column chromatography on silica gel (DCM/ MeOH 8/2), and the desired product 3d was isolated as a yellow oil in 47% yield. The ratio of diastereoisomers of compound 3d was about 0.97:1 (by NMR).

The chromatographic separation was achieved using a Agilent infinity 1260 (4.6 x 150 mm) 5µm column. The mobile phase was Methanol and H2O + 0.1DEA (Grad MeOH 30 to 80%) in 15 min. The column temperature was maintained at 25°C and the eluent was monitored at a wavelength of 254 nm. The injection volume was 10 µL. The typical retention time of diastereoisomers of compound 3d was about 9.5 min and 11.5 min, respectively.

Diastereoisomer 3da

Rf (20% MeOH/DCM) = 0.6; [α]D 19 = -37.53 (c, 1.66 in CHCl3); IR (neat, cm -1 ) 1634, 1452, 1279, 1042, 991 ; 1 H NMR (300 MHz, CD3OD) δ 8.18 (d, J = 7.7 Hz, 1H), 8.04 (d, 8.1 Hz, 1H), 7.75 (t, J = 7.5 Hz, 1H), 7.52 (t, J = 7.7 Hz, 1H), 4.76 (d, J = 9.6 Hz, 1H), 3.95 (d, J = 11.9 Hz, 1H), 3.78 -3.59 (m, 1H), 3.53 -3.38 (m, 4H); this sample was contaminated by an amount of diethylamine used during the HPLC purification: pics at 3.36 (q) and 1.31 (t),

Diastereoisomer 3db

Rf (20% MeOH/DCM) = 0.5 ; [α]D 19 = -2.11 (c,1.66 in CHCl3); IR (neat, cm -1 ) 1634,1453,1280,1105,1016 ; 1 H NMR (300 MHz, CD3OD) δ 8.23 (d,J = 7.8 Hz,1H),7.97 (d,8.1 Hz, 1H), 7.77 (t, J = 7.7 Hz, 1H), 7.52 (t, J = 7.5 Hz, 1H), 4.90 (s, 1H), 3.50(d, J = 11.8 Hz, 1H), 3.43 (dd, J = 12.1, 5.8 Hz, 1H), 3.56 -3.37 (m, 4H); this sample was contaminated by a small amount of diethylamine used during the HPLC purification: pics at 2.97 (q) and 1.29 (t),;

(2R,3R,4S,5R,6S)-2-(hydroxymethyl)-6-((2-(-imino(l1oxidanyl)(trifluoromethyl)-l5-sulfanyl)phenyl)thio)tetrahydro-2H-pyran-3,4,5-triol 3e

A sealable tube purged with argon equipped with a cap was charged with PdG3-Xantphos (61 mg, 0.064 mmol, 10 mol %), ß-thiogalactose 1f (150 mg, 0.768 mmol, 1.2 equiv), 2-iodo-sulfoximine 2a (213 mg, 0.64 mmol, 1 equiv). Then, dioxane/H2O (1mL/0.5mL) was added before adding Et3N (130 µL, 0.95 mmol, 1.5 equiv) dropwise. The mixture was stirred at 60°C for 30 min.

The reaction mixture was cooled to room temperature and passed through a plug of celite and rinsed with EtOAc. This crude was purified by column chromatography on silica gel (DCM/ MeOH: 9/1), and the desired product 3e was isolated as a yellow oil in 40% yield. The ratio of diastereoisomers of compound 3e was about 1:0.93 (by NMR).

The chromatographic separation was achieved using a Agilent infinity 1260 (4.6 x 150 mm) 5µm column. The mobile phase was Methanol and H2O + 0.1AcF (Grad MeOH 25 to 40%) in 15min. The column temperature was maintained at 25°C and the eluent was monitored at a wavelength of 254 nm. The injection volume was 10 µL. The typical retention time of diastereoisomers of compound 3e was about 8.9 min and 9.8 min, respectively.

Diastereoisomer 3ea

Rf (10% MeOH/DCM) = 0.03 ; [α]D 19 = + 12.53 (c,1.66 in CHCl3); IR (neat, cm -1 ) 1648,1632,1279,1196,1060 ; 1 H NMR (300 MHz, CD3OD) δ 8.24 (d, J = 8.1 Hz, 1H), 8.03 (d, J = 7.9 Hz, 1H), 7.77 (t, J = 7.1 Hz, 1H), 7.53 (t,J = 7.4 Hz,1H),4.83 (m,1H),3.99 (d,J = 3.0 Hz,1H),4H),3.62 (dd,J = 9.1,3.2

Diastereoisomer 3eb

Rf (10% MeOH/DCM) = 0 ; [α]D 19 = + 47.95 (c,1.66 in CHCl3); IR (neat, cm -1 ) 1634, 1625, 1182, 1052; 1 H NMR (300 MHz, CD3OD) δ 8.22 (d, J = 7.9 Hz, 1H), 8.12 (d, J = 8.1 Hz, 1H), 7.79 (t, J = 7.7 Hz, 1H), 7.55 (t, J = 7.7 Hz, 1H), 4.77 (d,J = 9.6 Hz,1H), 4.00 (d, J = 2.9 Hz, 1H), 3.90 -3.71 (m, 4H)

(2R,3R,4S,5R,6S)-2-((benzoyloxy)methyl)-6-((2-(S-(trifluoromethyl)sulfonimidoyl)phenyl)thio)tetrahydro-2H-pyran-3,4,5-triyl tribenzoate 3f

A sealable tube purged with argon equipped with a cap was charged with PdG3-Xantphos (52 mg, 0.054 mmol, 10 mol %), tetrabenzoylated ßthioglucose 1d (400 mg, 0.653 mmol, 1.2 equiv), 2-iodo-sulfoximine 2a (182 mg, 0.54 mmol, 1 equiv). After, dioxane (1mL) was added before adding Et3N (110 µL, 0.815 mmol, 1.5 equiv) dropwise. Then, the mixture was stirred at 60°C for 30 min.

The reaction mixture was cooled to room temperature and passed through a plug of celite and rinsed with EtOAc. This crude was purified by column chromatography on silica gel (Cyclohexane/ EtOAc: 5/5), and compound 3f was isolated as a yellow oil in 45% yield. The ratio of diastereoisomers of compound 3f was about 0.71:1 (by NMR).

The chromatographic separation was achieved using a Agilent infinity 1260 (4.6 x 150 mm) 5µm column. The mobile phase was Acetonitrile and H2O + 0.1AcF in the ratio of 35:65, v/v in 40min. The column temperature was maintained at 25°C and the eluent was monitored at a wavelength of 254 nm. The injection volume was 10 µL. The typical retention time of diastereoisomers of compound 3f was about 22.0 min and 22.9 min, respectively.

Diastereoisomer 3fa

Rf (50% EtOAc/Cyclohexane) = 0.74; [α]D 19 = + 47.95 (c,1.66 in CHCl3); IR (neat, cm -1 ) 1728,1451,1258,1067,1025,800,706 ; 1 H NMR (300 MHz, CDCl3) δ 8.18 (d, J = 7.9 Hz, 1H), 8.01 (d,J = 7.3 Hz,2H),6H)

Diastereoisomer 3fb

Rf (50% EtOAc/Cyclohexane) = 0.7; [α]D 19 = + 35.48 (c,1.66 in CHCl3); mp: 125.4 -128.3 °C; IR (neat, cm -1 ) 1721,1244,1177,1063,736,705 ; 1 H NMR (300 MHz, CDCl3) δ 8.08 (t, J = 8.5 Hz, 4H), 7.92 (m, 6H), 7.82 (d,J = 7.3 Hz,2H),12H + pic of CHCl3), 6.00 (t, J = 9.4 Hz, 1H), 5.74 -5.62 (m, 2H), 5.15 (d, J = 10.0 Hz, 1H), 4.73 (d,J = 8.3 Hz,1H),1H),1H) (l1-oxidanyl)(trifluoromethyl) (2-(((2S,3R,4S,5R,6R)-3,4,5-trimethoxy-6-(methoxymethyl)

tetrahydro-2H-pyran-2-yl)thio)phenyl)-l5-sulfanimine 3g

A sealable tube purged with argon equipped with a cap was charged with PdG3-Xantphos (31 mg, 0.032 mmol, 10 mol %), tetramethoxylated ßthioglucose 1e (160 mg, 0.634 mmol, 2.0 equiv), 2-iodo-sulfoximine 2a (106 mg, 0.32 mmol, 1 equiv). After, Dioxane (1mL) was added before adding Et3N (64 µL, 0.48 mmol, 1.5 equiv) dropwise. Then, the mixture was stirred at 60°C for 30 min.

The reaction mixture was cooled to room temperature and passed through a plug of celite and rinsed with EtOAc. This crude was purified by column chromatography on silica gel (Cyclohexane/ EtOAc: 5/5), and compound 3g was isolated as a yellow oil in 66% yield. The ratio diastereoisomers of compound 3g was about 1:0.92 (by NMR).

The chromatographic separation was achieved using a Agilent infinity 1260 (4.6 x 150 mm) 5µm column. The mobile phase was Methanol and H2O + 0.1AcF in the ratio of 45:55, v/v in 40min. The column temperature was maintained at 25°C and the eluent was monitored at a wavelength of 254 nm. The injection volume was 10 µL. The typical retention time of diastereoisomers of compound 3g was about 10.8 min and 11.5 min, respectively.

Diastereoisomer 3ga

Rf (50% EtOAc/Cyclohexane) = 0.5; [α]D 19 = + 91.8 (c,1.66 in CHCl3); IR (neat, cm -1 ) 1756,1452,1177,1093,1030,820,736 ; 1 H NMR (300 MHz, CD3OD) δ 8.21 (d, J = 8.0 Hz, 1H), 7.98 (d, J = 8.1 Hz, 1H), 7.79 (t, J = 7.7 Hz, 1H), 7.55 (t, J = 7.7 Hz, 1H), 4.78 (d, J = 9.9 Hz, 1H), 3.73 (s, 4H), 3.67 (s, 3H), 3.61 (s, 3H), 3.6 -3.55 (m, 1H), 3.46 (s, 3H), 3.41-3.38 (m, 1H), 3.38 -3.34 (m, 1H), 3.26 -3.14 (m, 2H)

Diastereoisomer 3gb

Rf (50% EtOAc/Cyclohexane) = 0.48; [α]D 19 = -2.11 (c,1.66 in CHCl3); IR (neat, cm -1 ) 1453, 1289, 1177, 1089, 1014, 797; 2-(((2S,3R,4S,5R,6R)-4-((tert-butyldimethylsilyl)oxy) -6-(((tertbutyldimethylsilyl)oxy)methyl) -3,5-dihydroxytetrahydro-2H-pyran-2yl)

thio)phenyl)(imino)(trifluoromethyl)-l6-sulfanone 3h

A sealable tube purged with argon equipped with a cap was charged with PdG3-Xantphos (7 mg, 0.0075 mmol, 10 mol %), 2,4-tertbutyldimethylsilyl ß-thioglucose 1g (64 mg, 0.1516 mmol, 2.0 equiv), 2iodo-sulfoximine 2a (25 mg, 0.075 mmol, 1 equiv). After, dioxane (1mL) was added before adding Et3N (15 µL, 0.112 mmol, 1.5 equiv) dropwise. Then, the mixture was stirred at 60°C for 30 min.

The reaction mixture was cooled to room temperature and passed through a plug of celite and rinsed with EtOAc. This crude was purified by column chromatography on silica gel (DCM/ MeOH: 2/8), and compound 3h was isolated as a yellow oil in 56% yield. The ratio of diastereoisomers of compound 3h was about 1:0.98 (by NMR).

The diastereoisomers were separated directly by column chromatography on silica gel (DCM/MeOH : 2/8).

Diastereoisomer 3ha

Rf (20% MeOH/DCM) = 0.53 ; [α]D 19 = -41.74 (c,1.66 in CHCl3); IR (neat, cm -1 ) 1250,1076,1005,835,811,737 ; 1 H NMR (300 MHz, CDCl3) δ 8.29 (d,J = 8.2 Hz,1H),7.95 (d,J = 8.0 Hz,1H),7.63 (t,J = 7.6 Hz,1H),7.48 (t,J = 7.7 Hz,1H),4.62 (d,J = 9.6 Hz,1H),2H),3.94 (dd,J = 11.2,2.6 Hz,1H),3.85 (dd,J = 10.7,4.7 Hz,1H),3H),2.92 (d,J = 2.4 Hz,1H),2.51 (s,1H), 0.90 (s, 18H), 0.14 (s, 3H), 0.07 (s, 9H); 13 C NMR (75 MHz, CDCl3) δ135.46 (CH),135.35 (CH),133.25 (CH),127.99 (CH),88.41 (CH),79.83 (CH),79.52 (CH),72.40 (CH),71.59 (CH),63.71 (CH2),29.85 (2xCq),26.13 (3xCH3),26.08 (3xCH3), 1.17 (CH3), -4.00( CH3), -4.61 (CH3), -5.

(2R,3S,4S,5R,6S)-2-(acetoxymethyl)-6-((5-methyl-2-(S-(trifluoromethyl)sulfonimidoyl)phenyl)thio)tetrahydro-2H-pyran-3,4,5-triyl triacetate 3i

A sealable tube purged with argon equipped with a cap was charged with PdG3-Xantphos (23 mg, 0.024 mmol, 10 mol %), tetraacetylated ßthiogalactose 1a (125 mg, 0.343 mmol, 1.5 equiv), 2-iodo,4-methylsulfoximine 2b (80 mg, 0.24 mmol, 1 equiv). After, Et3N (48 µL, 0.36 mmol, 1.5 equiv) was added drop by drop. Then, Dioxane (1mL) was added and the mixture was stirred at 60°C for 30 min.

The reaction mixture was cooled to room temperature and passed through a plug of celite and rinsed with EtOAc. This coupling product was purified by column chromatography on silica gel (Pentane/ EtOAc: 6/4), and was isolated as a white solid in 50% yield. The ratio of diastereoisomers of compound 3i was about 1:1 (by NMR).

The chromatographic separation was achieved using a Chromatographic conditions: Lux-Cellulose-1 (250 x 10 mm), hexane / ethanol (70/30) as mobile phase, flow-rate = 5 mL/min, UV detection at 254 nm. Injections: 60 times 50 L, every 4 minutes.

After the separation of the two diastereoisomers, we observed unfortunately epimerization during the storage. Herein we provided only NMR data of a mixture.

1 H NMR (300 MHz, CDCl3) (mixture of diastereoisomermajor + diastereoisomerminor ) δ 8.13 (d, J = 8.2 Hz, 1Hmajor), 8.06 (d, J = 9.0 Hz, 1Hminor), 7.69 (s,1Hmajor),7.65 (s,1Hminor),7.27 (d,J = 8.2 Hz,1Hmajor+ minor+ pic of CHCl3), 5.47 (d, J = 2.4 Hz, 1Hmajor+ minor), 5.37 (td, J = 10.0, 7.1 Hz, 1Hmajor+ minor), 5.10 (dd, J = 9.9, 3.3 Hz, 1Hmajor+ minor), 4.89 (d,J = 10.1 Hz,1Hmajor),4.83 (d,J = 10.1 Hz,1Hminor),3Hmajor+

(2R,3R,4S,5R,6S)-2-(acetoxymethyl)-6-((2-(Smethylsulfonimidoyl)phenyl)thio)tetrahydro-2H-pyran-3,4,5-triyl triacetate 3j

A sealable tube purged with argon equipped with a cap was charged with PdG3-Xantphos (34 mg, 0.036 mmol, 10 mol %), tetraacetylated ßthioglucose 1b (156 mg, 0.43 mmol, 1.2 equiv), S-Methyl-2-iodosulfoximine 2c (100 mg, 0.36 mmol, 1 equiv). After, Et3N (73 µL, 0.54 mmol, 1.5 equiv) was added drop by drop. Then, Dioxane (1mL) was added and the mixture was stirred at 60°C for 2 days. The reaction mixture was cooled to room temperature and passed through a plug of celite and rinsed with EtOAc. This coupling product was purified by column chromatography on silica gel ((EtOAc: 100%), and was isolated as a white solid in 49% yield as a mixture of two diastereoisomers. Both diastereoisomers 3ja and 3jb were separated through a preparative TLC (Cyclohexane/ EtOAc : 5/5).

Diastereoisomer 3ja (amorphous)

1 H NMR (300 MHz, CDCl3) δ 8.14 (d,J = 7.8 Hz,1H),7.78 (d,J = 7.8 Hz,1H),7.56 (t,J = 7.5 Hz,1H),7.46 (t,J = 7.5 Hz,1H),5.27 (t,J = 8,7 Hz,1H),5,2H),4.96 (d,J = 10.0 Hz,1H),2H),1H),3.34 (s,3H)

Compound 3jb (amorphous)

1 H NMR (300 MHz, CDCl3) δ 8.14 (d,J = 7.8 Hz,1H),7.77 (d,J = 7.8 Hz, 1H), 7.55 (t, J = 7.5 Hz, 1H), 7.45 (t, J = 7.5 Hz, 1H), 5.27 (t, J = 9.4, 1H), 5.19 -5.07 (m, 2H), 4.92 (d, J = 9.9 Hz, 1H), 4.24 -4.08 (m, 2H), 3.79 -3.75 (m, 1H), 3.30 (s, 3H), 2.51(bs, NH), 2.08 -2.00 (m, 12H); 13 C NMR (75 MHz, CDCl3) δ 170.53 (Cq) 170.24 (Cq), 169.49 (Cq),169.20 (Cq),143.29 (Cq),134.84 (Cq),133.57 (CH),132.55 (CH),130.06 (CH),127.87 (CH),86.22 (CH),76.01 (CH),73.92 (CH),70.33 (CH),68.26 (CH),62.27 (CH2),42.93 (CH3),20.83 (CH3),20.78 (CH3),20.71 (2xCH3); HRMS(ESI): m/z calcd for C21H28F3NO10S2 [M+H] +518.1151; found 518.1155.

(2R,3R,4S,5R,6S)-2-(acetoxymethyl) -6-(((2R,3R,4S,5R,6S)-4,5diacetoxy-2-(acetoxymethyl)-6-((2-(S-(trifluoromethyl)

sulfonimidoyl)phenyl)thio)tetrahydro-2H-pyran-3yl)oxy)tetrahydro-2H-pyran-3,4,5-triyl triacetate 3k

A sealable tube purged with argon equipped with a cap was charged with PdG3-Xantphos (29 mg, 0.03 mmol, 10 mol %), peracetylated ßthiocellobiose 1i (233 mg, 0.36 mmol, 1.2 equiv), 2-iodo-sulfoximine 2a (100 mg, 0.3 mmol, 1 equiv). After, dioxane (1mL) was added followed by adding Et3N (61 µL, 0.45 mmol, 1.5 equiv) dropwise. Then, the mixture was stirred at 60°C for 30 min.

The reaction mixture was cooled to room temperature and passed through a plug of celite and rinsed with EtOAc. This crude was purified by column chromatography on silica gel (Cyclohexane/ EtOAc : 6/4), and compound 3k was isolated as a white solid in 60% yield. The ratio of diastereoisomers of compound 3k was about 1:0.93 respectively (by NMR).

The chromatographic separation was achieved using a Agilent infinity 1260 (4.6 x 150 mm) 5µm column. The mobile phase was Methanol and H2O+ 0.1AcF in the ratio of 55:45, v/v in 30min. The column temperature was maintained at 25°C and the eluent was monitored at a wavelength of 254 nm. The injection volume was 10 µL. The typical retention time of diastereoisomers of compound 3k was about 16.9 min and 20.9 min, respectively.

  [α]D 19 = -68.85(c, 1.66 in CHCl3); mp: 179.1 -181.8 °C; IR (neat, cm -1 )1753, 1453, 1215, 1033, 737 ; 1 H NMR (300 MHz, CDCl3) δ 8.19 (d, J = 7.9 Hz, 1H), 7.84 (d, J = 8.0 Hz, 1H), 7.65 (t, J = 7.3 Hz, 1H), 7.48 (t, J = 6.9 Hz, 1H), 5.28 (t, J = 9.2 Hz, 1H), 5.15-5.07 (m, 2H), 4.82 (d, J = 10.1 Hz, 1H), 4.22 (m, 2H), 3.92 -3.83 (m, CH+NH), 2.10 (s, 3H), 2.05 -2.00 (m, 9H) ; 13 C NMR (75 MHz, CDCl3) δ 170.53 (Cq), 170.20 (Cq), 169.47 (Cq), 169.34 (Cq), 140.59 (Cq), 135.56 (CH), 133.41 (CH), 132.71 (Cq), 131.16 (CH), 127.17 (CH), 121.34 (q, JCF = 332 Hz, CF3), 86.15 (CH), 75.89 (CH), 73.88 (CH), 69.76 (CH), 68.39 (CH), 62.51 (CH2), 20.81 (CH3), 20.66 (2xCH3), 20.46 (CH3); 19 F NMR (188 MHz, CDCl3) δ -76.14 (CF3); HRMS(ESI): m/z calcd for C21H26F3NO10S2 [M+2H] +573.0939; found 573.0997. Aspect : White solid.

  13 C NMR (75 MHz, CD3OD) δ 142.53 (Cq), 136.61 (CH), 134.53 (CH), 132.11 (CH), 131.64 (Cq), 127.28 (CH), 88.20 (CH), 80.84 (CH), 76.37 (CH), 70.86 (CH), 70.45 (CH), 62.74 (CH2), (one carbon (-CF3) is missing); 19 F NMR (188 MHz, CD3OD) δ -78.58 (CF3); HRMS(ESI): m/z calcd for C13H17F3NO6S2 [M+H] +404.0444; found 404.0460. Aspect : Colorless oil.

  13 C NMR (75 MHz, CD3OD) δ 142.47 (Cq), 136.62 (CH), 134.12 (CH), 132.83 (CH), 131.98 (Cq), 122.69 (q, JCF = 333 Hz, CF3), 88.88 (CH), 80.78 (CH), 76.25 (CH), 70.66 (CH), 70.42 (CH), 62.79 (CH2) ; 19 F NMR (188 MHz, CD3OD) δ -78.12 (CF3); HRMS(ESI): m/z calcd for C13H17F3NO6S2 [M+H] +404.0444; found 404.0460. Aspect : Colorless oil.

  , 3.62 (dd, J = 9.1, 3.1 Hz, 1H); 13 C NMR (75 MHz, CD3OD) δ 142.47 (Cq), 136.62 (CH), 134.12 (CH), 132.83 (CH), 131.98 (Cq), 127.40 (CH), 122.69 (q, JCF = 333 Hz, CF3), 88.88 (CH), 80.78 (CH), 76.25 (CH), 70.66 (CH), 70.42 (CH), 62.79 (CH2) ; 19 F NMR (188 MHz, CD3OD) δ -78.12 (CF3); HRMS(ESI): m/z calcd for C13H17F3NO6S2 [M+H] +404.0444; found 404.0454. Aspect : Yellow oil.

  , 7.81 (d, J = 7.4 Hz, 2H), 7.62-7.28 (m, 13H + pic of CHCl3), 5.99 (t, J = 9.4 Hz, 1H), 5.69-5.60 (m, 2H), 5.27 (d, J = 10.0 Hz, 1H), 4.66 (dd, J = 12.3, 2.8 Hz, 1H), 4.51 (dd, J = 12.1, 6.6 Hz, 1H), 4.30 -4.22 (m, J = 7.0 Hz, 1H), 3.72 (bs, NH) ; 13 C NMR (75 MHz, CDCl3) δ 165.89 (Cq), 165.52 (Cq), 165.23 (Cq), 139.25 (Cq), 135.28 (CH), 133.76 (CH), 133.47 (3xCH), 130.05 (CH), 129.93 (2xCH), 128.83 (6xCH), 128.63 (3xCq), 128.49 (4xCH), 127.72 (5xCH), 85.74 (CH), 74.11 (CH), 70.48 (CH), 69.63 (CH), 63.48 (CH2), some carbons are missing; 19 F NMR (188 MHz, CDCl3) δ -76.26 (CF3); HRMS(ESI): m/z calcd for C41H33F3NO10S2 [M+H] +820.1492; found 820.1474. Aspect : Yellow oil.

  , 4.02 (bs, NH) ; 13 C NMR (75 MHz, CDCl3) δ 166.09 (Cq), 165.85 (Cq), 165.43 (Cq), 165.24 (Cq), 140.69 (Cq), 135.51 (CH), 133.75 (CH), 133.49 (2xCH), 131.28 (CH), 130.04 (2xCH), 129.90 (6xCH), 128.99 (Cq), 128.79 (Cq), 128.64 (4xCH), 128.47 (3xCH), 128.36 (2xCH), 126.98 (CH), 120.97 (q, JCF = 331 Hz, CF3), 86.64 (CH), 76.59 (CH), 74.04 (CH), 70.42 (CH), 69.66 (CH), 63.67 (CH2); 19 F NMR (188 MHz, CDCl3) δ -76.22 (CF3); HRMS(ESI): m/z calcd for C41H33F3NO10S2 [M+H] +820.1492; found 820.1474. Aspect : Yellow solid.

  8.19 (d, J = 8.1 Hz, 1H), 8.04 (d, J = 8.2 Hz, 1H), 7.62 (t, J = 7.7 Hz, 1H), 7.40 (t, J = 7.7 Hz, 1H), 5.80 (d, J = 5.5 Hz, 1H), 4.10 -4.04 (m, 2H), 3.65 (s, 3H), 3.60 (dd, J = 9.0 Hz, J = 3.6 Hz, 1H), 3.55 (s, 3H), 3.46 -3.39 (m, 8H), 3.33 -3.27 (m, 1H) ; 13 C NMR (75 MHz, CDCl3) δ 142.10 (Cq), 135.48 (CH), 133.59 (CH), 131.15 (CH), 130.51 (Cq), 126.06 (CH), 85.61 (CH), 83.80 (CH), 81.58 (CH), 78.94 (CH), 71.55 (CH), 70.96 (CH2), 61.17 (CH3), 60.60 (CH3), 59.29 (CH3), 57.89 (CH3) (one carbon (-CF3) is missing); 19 F NMR (188 MHz, CDCl3) δ -76.16 (CF3); HRMS(ESI): m/z calcd for C17H25F3NO16S2 [M+H] +460.1069; found 460.1068. Aspect : Colorless oil.

(

  , 2.85 (bs, NH), 2.06 -2.01 (m, 12H); 13 C NMR (75 MHz, CDCl3) δ 170.52 (Cq), 170.28 (Cq), 169.48 (Cq), 169.23 (Cq), 143.42 (Cq), 134.10 (Cq), 133.56 (CH), 133.17 (CH), 130.08 (CH), 128.01 (CH), 85.95 (CH), 76.09 (CH), 73.93 (CH), 70.21 (CH), 68.20 (CH), 62.11 (CH2), 43.20 (CH3), 20.83 (CH3), 20.80 (CH3), 20.70 (2xCH3); HRMS(ESI): m/z calcd for C21H28F3NO10S2 [M+H] +518.1151; found 518.1155.

Table 1 .

 1 Optimization of the Coupling Reaction of Tetraacetylated β-

thiogalactose 1a with ortho-iodo-trifluoromethyl-

arylsulfoximines 2a a

					.
	entry	n mol %	T (°C)	T (h)	4a (%) b
	1	5	rt	12	0
	2	10	rt	12	0
	3	20	rt	12	0
	4	10	60	0.5	65
	5	10	60	1	63
	6	5	60	0.5	64

[a] A sealable tube was charged with thiosugar 1a (1.2 equiv, 0.2 mmol), ortho-iodo-trifluoromethyl-arylsulfoximines 2a (1 equiv), [Pd precatalyst] (n mol%), Et3N, (1.5 equiv) in dioxane (1.0 mL).

[b]

Yield of isolated product.

through this methodology. Scheme 2. Coupling of Chiral Sulfoximines 2aa and 2ab with thiogalactose 1a a a

	To our knowledge, this result represent the first example of
	functionalization	of	enantiopure	S-trifluoromethyl	S-
	arylsulfoximines under Pd-catalysis, and may open a new way of
	diversifying the chemical	space of	S-trifluoromethyl
	S-arylsulfoximines

13 C NMR (75 MHz, CDCl3) δ 170

	10.1
	Hz, 1H), 4.26 -4.03 (m, 4H), 2.18 (s, 3H), 2.07 (s, 3H), 2.04 (s, 3H), 1.99
	(s, 3H),; .33 (Cq), 170.24 (Cq), 170.03
	(Cq), 169.44 (Cq), 140.70 (Cq), 135.51 (CH), 133.42 (CH), 131.14 (CH),
	128.41 (Cq), 127.07 (CH), 121.33 (q, JCF = 334 Hz, CF3), 86.49 (CH),
	74.63 (CH), 71.97 (CH), 67.26 (CH), 66.80 (CH), 61.99 (CH2), 20.73,
	20.62 et 20.53 (4xCH3); 19 F NMR (188 MHz, CDCl3) δ -76.25 (CF3);
	HRMS(ESI): m/z calcd for C21H25F3NO10S2 [M+H] +572.0866; found
	572.0864. Aspect : White solid.

13 C NMR (75 MHz, CD3OD) δ

  Hz, 1H);

	142.53 (Cq), 136.61 (CH), 134.53 (CH), 132.11 (CH), 131.64 (Cq),
	127.28 (CH), 88.20 (CH), 80.84 (CH), 76.37 (CH), 70.86 (CH), 70.45
	(CH), 62.74 (CH2) (one carbon (-CF3) is missing); 19 F NMR (188 MHz,
	CD3OD) δ -78.59 (CF3); HRMS(ESI): m/z calcd for C13H17F3NO6S2 [M+H]
	+404.0444; found 404.0454. Aspect : Yellow oil.

Acknowledgements ((optional))

Paris-Sud, ANR (ANR-15-CE29-0002), and by la Ligue Contre le Cancer through an Equipe Labellisée 2014 grant. We thank N. Vanthuyne (iSm2, Marseille) for some preparative HPLC. We also thank the Algerian Ministry of Education and Research for a fellowship (Profas B+) to Nedjwa Bennai. Our laboratory is a member of the Laboratory of Excellence LERMIT supported by a grant (ANR-10-LABX-33). GIS Fluor (French Fluorine Network) is also acknowledged.

Diastereoisomer 3ka

Rf (40% EtOAc/Cyclohexane) = 0.5; [α]D 19 = -39.64 (c,1.66 in CHCl3); mp: 226.1 -228.5°C; IR (neat, cm -1 ) 1756,1452,1259,1035,767 ; 1 H NMR (300 MHz, CDCl3) δ 8.26 (d, J = 7.8 Hz, 1H), 7.80 (d, J = 7.9 Hz, 1H), 7.64 (t, J = 7.7 Hz, 1H), 7.48 (t, J = 7.7 Hz, 1H), 5.24 (t, J = 8.9 Hz, 1H), 5.17 -5.03 (m, 3H), 4.96 -4.85 (m, 2H), 4.53 (d,J = 8.2 Hz,2H),4.36 (dd,J = 10.4,4.3 Hz,1H),2H), 3.95 (bs, NH), 3.81 (t, J = 9.0 Hz, 1H), 3.75 -3.62 (m, 2H), 2.17-1.98 (m, 21H)

Diastereoisomer 3kb

Rf (40% EtOAc/Cyclohexane) = 0.45; [α]D 19 = -50.06 (c, 1.66 (d,J = 7.8 Hz,1H),7.82 (d,J = 7.9 Hz, 1H), 7.64 (t, J = 7.4 Hz, 1H), 7.47 (t, J = 7.6 Hz, 1H), 5.32 -5.18 (m, 1H), 5.18 -5.01 (m, 3H), 4.93 (t, J = 8.5 Hz, 1H), 4.78 (d, J = 10.1 Hz, 1H), 4.55 (t, J = 8.1 Hz, 2H), 4.36 (dd, J = 12.5, 4.2 Hz, 1H), 4. 18 -3.98 (m, 3H), 3.88 -3.74 (m, 2H), 3.72 -3.62 (m, 1H) (2R,3R,4S,5R,6R)-2-(acetoxymethyl) -6-(((2R,3R,4S,5R,6R)-4,5diacetoxy-2-(acetoxymethyl)-6-(((2R,3R,4S,5R,6S)-4,5-diacetoxy-2-(acetoxymethyl)-6-((2-(S-(trifluoromethyl)

sulfonimidoyl)phenyl)thio)tetrahydro-2H-pyran-3yl)oxy)tetrahydro-2H-pyran-3-yl)oxy)tetrahydro-2H-pyran-3,4,5-triyl triacetate 3l

A sealable tube purged with argon equipped with a cap was charged with PdG3-Xantphos (8 mg, 0.008 mmol, 10 mol %), peracetylated ßthiomaltotriose 1j (150 mg, 0.16 mmol, 2 equiv), 2-iodo-sulfoximine 2a (26 mg, 0.08 mmol, 1 equiv). After, dioxane (1mL) was added followed by adding of Et3N (16 µL, 0.12 mmol, 1.5 equiv) dropwise. Then, the mixture was stirred at 60°C for 30 min.

The reaction mixture was cooled to room temperature and passed through a plug of celite and rinsed with EtOAc. This crude was purified by column chromatography on silica gel (DCM/ MeOH : 95/5), and compound 3l was isolated as a colorless oil in 49% yield. The ratio of diastereoisomers of compound 3l was about 1:0.73 (by NMR).

The chromatographic separation was achieved using an Agilent infinity 1260 (4.6 x 150 mm) 5µm column. The mobile phase was Acetonitrile and H2O+ 0.1AcF in the ratio of 50:50, v/v in 25min. The column temperature was maintained at 25°C and the eluent was monitored at a wavelength of 254 nm. The injection volume was 10 µL. The typical retention time of diastereoisomers of compound 3l was about 19.8 min and 21.2 min, respectively.

Diastereoisomer 3la

Rf (10% MeOH/DCM) = 0.6; [α]D 19 = -6.26 (c,1.66 in CHCl3); IR (neat, cm -1 ) 1756, 1452, 1238, 1025, 767 ; 1 H NMR (300 MHz, CDCl3) δ 8.27 (d, J = 7.3 Hz, 1H), 7.84 (d, J = 8.1 Hz, 1H), 7.68 (t, J = 7.3 Hz, 1H), 7.49 (t, J = 7.8 Hz, 1H), 5.44 -5.29 (m, 4H), 5.27 (d, J = 4.0 Hz, 1H), 5.06 (t, J = 9.0 Hz, 1H), 5.03 -4.95 (m, 2H), 4.86 (dd, J = 10.5, 3.9 Hz, 1H), 4.75 (dd, J = 10.3, 3.9 Hz, 1H), 4.53 -4.42 (m, 2H), 4.32 (dd, J = 12.2, 4.9 Hz, 1H), 4.22 (td, J = 12.8, 3.6 Hz, 2H), 4.10 -3.87 (m, 6H), 3.87 -3.77 (m, 1H)

Diastereoisomer 3lb

Rf (10% MeOH/DCM) = 0.51; [α]D 19 = +56.32 (c, 1.66 in CHCl3); IR (neat, cm -1 ) 1739, 1368, 1212, 1027, 735; 1 H NMR (300 MHz, CDCl3) δ 8.18 (d, J = 8.0 Hz, 1H), 7.86 (d, J = 7.8 Hz, 1H), 7.68 (t, J = 7.2 Hz, 1H), 7.48 (t, J = 7.5 Hz, 1H), 5.43 -5.24 (m, 5H), 5.06 (t, J = 9.9 Hz, 1H), 4.98 (t, J = 9.0 Hz, 1H), 4.90 -4.82 (m, 2H), 4.75 (dd, J = 8.4, 4.0 Hz, 1H), 4.54 -4.42 (m, 2H), 4.35 (dd, J = 9.0, 5.2 Hz, 1H), 4.23 (td, J = 12.0, 3.6 Hz, 2H), 4. 12 -3.83 (m, 7H)

Coupling of enantiopure sulfoximines 2aa, 2ab (2R,3S,4S,5R,6S)-2-(acetoxymethyl)-6-((2-((S)-imino(l1oxidanyl)(trifluoromethyl)-l5-sulfanyl)phenyl)thio)tetrahydro-2H-pyran-3,4,5-triyl triacetate 3aa´

A sealable tube purged with argon equipped with a cap was charged with PdG3-Xantphos (9 mg, 0.009 mmol, 10 mol %), tetraacetylated ßthiogalactose 1a (49 mg, 0.13 mmol, 1.5 equiv), (R)-(+)-2-iodosulfoximine 2aa (30 mg, 0.09 mmol, 1 equiv). Then, Dioxane (1mL) was added and to the solution was added Et3N (19 µL, 0.13 mmol, 1.5 equiv) dropwise and the mixture was stirred at 60°C for 30 min.

The reaction mixture was cooled to room temperature and passed through a plug of celite and rinsed with EtOAc. This coupling product was purified by column chromatography on silica gel (Pentane/ EtOAc: 5/5), and 3aa'was isolated as a white solid in 78% yield.

Rf (50% EtOAc/Pentane) = 0.57; [α]D 19 = +8.37 (c,1.66 in CHCl3); mp: 50.3 -54.0 °C ; IR (neat, cm -1 ) 1749,1368,1213,1174,1083,1058 ; 1 H NMR (300 MHz, CDCl3) δ 8.25 (d, J = 8.0 Hz, 1H), 7.91 (d, J = 8.0 Hz, 1H), 7.64 (t, J = 7.7 Hz, 1H), 7.48 (t, J = 7.7 Hz, 1H), 5.46 (d, J = 3.2 Hz, 1H), 5.39 (t, J = 9.9 Hz, 1H), 5.09 (dd, J = 9.9, 3.2 Hz, 1H), 4.89 (d,J = 10.1 Hz,1H),2H),2H), 2.17 (s, 3H), 2.03 (s, 6H), 1.97 (s, 3H); 13 C NMR (75 MHz, CDCl3) δ 170.36 (Cq),170.16 (Cq),160.06 (Cq),169.39 (Cq),138.99 (Cq),135.22 (CH),133.96 (CH),132.45 (CH),131.83 (Cq),127.52 (CH),121.16 (CF3,q,JCF = 333 Hz),85.60 (CH),74.81 (CH),72.08 (CH),67.34 (CH),66.67 (CH),61.84 (CH2),20.74 (2xCH3),20.63 (2xCH3) A sealable tube purged with argon equipped with a cap was charged with PdG3-Xantphos (9 mg, 0.009 mmol, 10 mol %), tetraacetylated ßthiogalactose 1a (49 mg, 0.13 mmol, 1.5 equiv), (S)-(-)-2-iodosulfoximine 2ab (30 mg, 0.09 mmol, 1 equiv). Then, Dioxane (1mL) was added and to the solution was added Et3N (19 µL, 0.13 mmol, 1.5 equiv) dropwise and the mixture was stirred at 60°C for 30 min.

The reaction mixture was cooled to room temperature and passed through a plug of celite and rinsed with EtOAc. This coupling product was purified by column chromatography on silica gel (Pentane/ EtOAc: 5/5), and 3ab' was isolated as a white solid in 84% yield.

Rf


Jacek Jagiello
email: jacek.jagiello@micromeritics.com

Jeffrey Kenvin

Maria Conchi

Ovin Concepcion

José Ania

Alain Parra

Vanessa Celzard

Fierro

Conchi O Ania

Jose B Parra

Alain Celzard

Vanessa Fierro

Exploiting the adsorption of simple gases O 2 and H 2 with minimal quadrupole moments for the dual gas characterization of nanoporous carbons using 2D-NLDFT models

teaching and research institutions in France or abroad, or from public or private research centers.

Exploiting the adsorption of simple gases O2 and H2 with minimal quadrupole moments for the dual gas characterization of nanoporous carbons using 2D-NLDFT models

Introduction

For years, the characterization of carbon pore size distribution (PSD) has been dominated by the analysis of nitrogen (N 2 ) isotherms measured at its boiling point (77 K). From the scientific viewpoint, however, N 2 may not be the most appropriate molecular probe for the PSD evaluation. Its high quadrupole moment may affect the adsorption of N 2 molecules due to the interactions with polar surface sites.

The molecular models used in this work for the evaluation of carbon pore structure assume nonspecific interactions of gas molecules with carbon surface. Real carbon materials may contain various mineral contaminations and chemical surface sites that may interact with adsorbate molecules via specific interactions. If the experimental adsorption isotherms are distorted by such interactions it may affect the PSDs calculated from these isotherms.

To minimize such effects IUPAC Technical Report 2015 [START_REF] Thommes | Physisorption of gases, with special reference to the evaluation of surface area and pore size distribution (IUPAC Technical Report)[END_REF] recommended argon (Ar) as the most reliable for the PSD evaluation. However, Ar adsorption measurements using liquid Ar as a coolant are more costly than the standard N 2 analysis; therefore, from the practical viewpoint, Ar analysis is not a preferred one in a typical laboratory. As a replacement for argon, it was recently proposed to use oxygen (O 2 ) [START_REF] Jagiello | Consistency of carbon nanopore characteristics derived from adsorption of simple gases and 2D-NLDFT models. Advantages of using adsorption isotherms of oxygen (O2) at 77 K[END_REF]. Oxygen was chosen because its quadrupole moment has about three times lower value than N 2 . Moreover, it was shown for several representative carbon samples that their PSDs derived from adsorption measurements of N 2 and O 2 at 77 K and Ar at 87 K are in quantitative agreement.

On the other hand, the Report [START_REF] Thommes | Physisorption of gases, with special reference to the evaluation of surface area and pore size distribution (IUPAC Technical Report)[END_REF] recommended using CO 2 for the characterization of ultramicroporous carbons because, at the recommended temperature (273 K), CO 2 diffuses faster into micropores than N 2 at the cryogenic temperature. This recommendation, however, is inconsistent with the premise of using molecules with low sensitivity to interactions with polar sites, because the CO 2 quadrupole moment is even larger than that of N 2 , which makes it sensitive to the carbon surface chemistry [START_REF] Seredych | Complexity of CO2 adsorption on nanoporous sulfur-doped carbons -Is surface chemistry an important factor?[END_REF]. In the absence of polar sites, the use of CO 2 may be appropriate, and several authors applied CO 2 adsorption to study the porosity of microporous carbons and carbon molecular sieves [START_REF] Garrido | Use of nitrogen vs. carbon dioxide in the characterization of activated carbons[END_REF][START_REF] Lozano-Castelló | Usefulness of CO2 adsorption at 273 K for the characterization of porous carbons[END_REF][START_REF] Schaefer | Assessment of hydrogen storage in activated carbons produced from hydrothermally treated organic materials[END_REF][START_REF] Schaefer | Physisorption, chemisorption and spill-over contributions to hydrogen storage[END_REF][START_REF] Mclaughlin | Analytical options for biochar adsorption and surface area, North American Biochar Conference[END_REF][START_REF] Caguiat | Uncertainties in characterization of nanoporous carbons using density functional theory-based gas physisorption[END_REF].

Another simple gas that diffuses faster into ultramicropores than N 2 at 77 K is H 2 , which is supercritical at this temperature. Furthermore, the H 2 molecule has a small quadrupole moment and smaller diameter than CO 2 , and it has been that H 2 adsorption data may provide meaningful PSD results in an extended range of pore sizes when analyzed alone [START_REF] Lueking | Tests of Pore-Size Distributions Deduced from Inversion of Simulated and Real Adsorption Data[END_REF] or simultaneously with argon data [START_REF] Jagiello | Characterization of pore structure of carbon molecular sieves using DFT analysis of Ar and H2 adsorption data[END_REF]. The grand canonical Monte Carlo (GCMC) model isotherms of H 2 and CO 2 were also used [START_REF] Konstantakou | GCMC simulations of gas adsorption in carbon pore structures[END_REF] to analyze simultaneously adsorption data of H 2 and CO 2

The values of the absolute quadrupole moments of the considered molecules are in the following order [START_REF] Buckingham | Quadrupole moments of some simple molecules[END_REF]: Ar <O 2 <H 2 <N 2 <CO 2 and their ratios to the value of N 2 are as follows 0.0 <0.28< 0.46 < 1.0 <3.1. Other gases such as CH 4 [START_REF] Nguyen | Adsorption of Supercritical Gases in Porous Media: Determination of Micropore Size Distribution[END_REF], CF 4 and SF 6 [START_REF] Lopez-Ramon | Determination of the pore size distribution and network connectivity in microporous solids by adsorption measurements and Monte Carlo simulation[END_REF] with symmetrical molecules, zero quadruple moments and different molecular diameters have been used for the carbon pore size analysis as well as for the evaluation of pore connectivity and molecular sieving effects.

In present work, we use molecular models based on the nonlocal density functional theory (NLDFT) to analyze O 2 and H 2 adsorption data simultaneously. We show comparisons of PSD results derived from O 2 and H 2 data and with those from N 2 and CO 2 data. The approach introduced in this work is advantageous compared to the earlier presented "dual analysis method" [START_REF] Jagiello | Dual gas analysis of microporous carbons using 2D-NLDFT heterogeneous surface model and combined adsorption data of N2 and CO2[END_REF] based on N 2 and CO 2 data, due to the lower quadrupole moments of O 2 and H 2 . It is also more practically convenient because of the same cryogen, liquid N 2 , used for both analyses. The PSD analysis is executed using adsorption models incorporating surface roughness, and energetic heterogeneity derived based on the NLDFT [START_REF] Tarazona | Free-energy density functional for hard spheres[END_REF][START_REF] Tarazona | Erratum: Free-energy density functional for hard spheres[END_REF][START_REF] Evans | Fluids in narrow pores: Adsorption, capillary condensation, and critical points[END_REF][START_REF] Lastoskie | Pore size distribution analysis of microporous carbons: a density functional theory approach[END_REF] in its twodimensional version 2D-NLDFT-HS [START_REF] Jagiello | 2D-NLDFT adsorption models for carbon slit-shaped pores with surface energetical heterogeneity and geometrical corrugation[END_REF][START_REF] Jagiello | Carbon slit pore model incorporating surface energetical heterogeneity and geometrical corrugation[END_REF] herein referred to as 2D-HS where HS stands for the heterogeneous surface.

Experimental

In this work, we have used two series of carbon samples derived from two precursors: (i) polyethylene terephthalate, (PET), and (ii) corn stigmata (CS). Both precursors were first carbonized to obtain chars, and then the chars were activated with CO 2 . The char derived from PET was labeled PC and the activated carbons derived from this char were labeled PCn, where n is the burn-off percent during the activation process. The char derived from corn stigmata was labeled C-CS, and its two activated carbon derivatives were labeled C-CS-0.5 and C-CS-1.0, where the number in the sample label represents the time of activation in hours. Preparation and properties of the samples used in this work were described earlier for the PET series [START_REF] Jagiello | Dual gas analysis of microporous carbons using 2D-NLDFT heterogeneous surface model and combined adsorption data of N2 and CO2[END_REF][START_REF] Parra | Textural characterisation of activated carbons obtained from poly(ethylene terephthalate) by carbon dioxide activation[END_REF] and the CS series [START_REF] Jagiello | Enhanced resolution of ultra micropore size determination of biochars and activated carbons by dual gas analysis using N2 and CO2 with 2D-NLDFT adsorption models[END_REF]. In addition to the porous carbons, a sample carbon black BP 280 (Cabot) was used to obtain H 2 adsorption reference data. This carbon has been used previously [START_REF] Jagiello | Consistency of carbon nanopore characteristics derived from adsorption of simple gases and 2D-NLDFT models. Advantages of using adsorption isotherms of oxygen (O2) at 77 K[END_REF][START_REF] Jagiello | 2D-NLDFT adsorption models for carbon slit-shaped pores with surface energetical heterogeneity and geometrical corrugation[END_REF][START_REF] Ustinov | Pore size distribution analysis of activated carbons: Application of density functional theory using nongraphitized carbon black as a reference system[END_REF] as reference for carbon material with the heterogeneous surface. The measurements of H 2 and O 2 adsorption isotherms at 77 K were performed using the high-resolution Micromeritics 3Flex instrument. The samples were degassed on sample ports at 620 K overnight before the measurements.

Results and Discussion

3.1

The two-dimensional NLDFT model of H 2 adsorption on heterogeneous carbon surface at 77 K At 77 K, hydrogen is far above its critical point of 33 K and thus its adsorption isotherms on the uniform carbon surface do not show the layering transitions that lead to artifacts [START_REF] Jagiello | 2D-NLDFT adsorption models for carbon slit-shaped pores with surface energetical heterogeneity and geometrical corrugation[END_REF][START_REF] Neimark | Quenched solid density functional theory and pore size analysis of micro-mesoporous carbons[END_REF] in the PSD calculations when the one-dimensional NLDFT model was applied. Nevertheless, for the evaluation of H 2 adsorption model, we use the same surface roughness parameters and type of energetic heterogeneity as in the earlier developed models for the other simple gases [START_REF] Jagiello | Consistency of carbon nanopore characteristics derived from adsorption of simple gases and 2D-NLDFT models. Advantages of using adsorption isotherms of oxygen (O2) at 77 K[END_REF]. We calculate the kernel isotherms in the framework of the 2D-HS model [START_REF] Jagiello | Consistency of carbon nanopore characteristics derived from adsorption of simple gases and 2D-NLDFT models. Advantages of using adsorption isotherms of oxygen (O2) at 77 K[END_REF][START_REF] Jagiello | 2D-NLDFT adsorption models for carbon slit-shaped pores with surface energetical heterogeneity and geometrical corrugation[END_REF][START_REF] Jagiello | Carbon slit pore model incorporating surface energetical heterogeneity and geometrical corrugation[END_REF]] using Tarazona's version [START_REF] Tarazona | Free-energy density functional for hard spheres[END_REF][START_REF] Tarazona | Erratum: Free-energy density functional for hard spheres[END_REF][START_REF] Evans | Fluids in narrow pores: Adsorption, capillary condensation, and critical points[END_REF] of the non-local density functional theory (NLDFT). The theory provides a prescription for the evaluation of the density profile (r) of gas molecules confined in a pore of a given shape and dimensions. The equilibrium density profile is calculated by the iterative procedure which finds the minimum of the grand thermodynamic potential functional given by [START_REF] Lastoskie | Pore size distribution analysis of microporous carbons: a density functional theory approach[END_REF] ,

(1)

Ω[𝜌(𝐫)] = 𝐹[𝜌(𝐫)] -∫𝑑𝐫𝜌(𝐫)[𝜇 -𝑉 𝑒𝑥𝑡 (𝐫)]
where F is the Helmholtz free energy functional,  is the chemical potential, and V ext (r) is the so-called external potential which describes the pore-fluid interactions. The theoretical kernel isotherms are obtained by the integration of (r) over a pore space for a series of pressures and pore dimensions.

Standard slit pore model with quantum corrections

Molecular interactions of light molecules such as H 2 may be influenced by quantum effects at low temperatures. Several authors have accounted for quantum effects in modeling the adsorption of H 2 at cryogenic temperatures by using advanced simulation methods such as path integral Monte Carlo formalism [START_REF] Wang | Path integral grand canonical Monte Carlo[END_REF][START_REF] Wang | Thermodynamic properties and phase equilibrium of fluid hydrogen from path integral simulations[END_REF]. A simpler approach to account for quantum effects is based on the Feynman-Hibbs (FH) effective potential [START_REF] Feynman | Quantum Mechanics and Path Integrals[END_REF][START_REF] Sesé | Study of the Feynman-Hibbs effective potential against the path-integral formalism for Monte Carlo simulations of quantum many-body Lennard-Jones systems[END_REF]. In the present work, we apply the second-order FH effective potential that is expressed as a sum of the classical interaction potential and a quantum correction term, indicated below by the superscript "q": ,

(2)

𝑢 𝐹𝐻 (𝑟) = 𝑢(𝑟) + 𝑢 𝑞 (𝑟) where (3) 𝑢 𝑞 (𝑟) = 𝑄 24 [ 𝑑 2 𝑑𝑟 2 𝑢(𝑟) + 2 𝑟 𝑑 𝑑𝑟 𝑢(𝑟) ]
and the composite parameter Q is given by (4) 𝑄 = (ℎ/2𝜋) 2 /𝜇 𝑚 𝑘 𝐵 𝑇

The classical interaction potential  ff (r) is assumed here in the form of the Lennard Jones (LJ) potential .

(5)

𝜙 𝑓𝑓 (𝑟) = 4𝜀 𝑓𝑓[( 𝜎 𝑓𝑓 𝑟 ) 12 -( 𝜎 𝑓𝑓 𝑟 ) 6 ]
In the above equations, r is the distance between two interacting molecules,  ff and  ff are the LJ energy and size parameters, h and k B are the Planck and Boltzmann constants,  m is the reduced mass of the two interacting particles. For the interaction between the two H 2 molecules ] .

 m =m/2,
Based on the analysis of Sese [START_REF] Sesé | Study of the Feynman-Hibbs effective potential against the path-integral formalism for Monte Carlo simulations of quantum many-body Lennard-Jones systems[END_REF], the effective potential given by Eq. ( 2) is reliable for a particle with the reduced de Broglie thermal wavelength <0.5, where

𝜆 * 𝐵 (7) 𝜆 * 𝐵 = ℎ/(2𝜋𝑚𝑘 𝐵 𝑇𝜎 2 𝑓𝑓 ) 1/2
The value for hydrogen at 77 K is 0.47. 𝜆 *

𝐵

To be able to compare our calculations with published results, we start with the slit pore model that is one-dimensional with respect to the z-axis perpendicular to the ideal uniform surface of a graphitic solid. The potential of interactions  sf (z) of a gas molecule with such a model solid depends only on a distance from the center of the molecule to the centers of carbon atoms in the solid surface and is expressed as a sum of interaction potentials with the single surface layer of graphite  1 and interactions and interactions with the rest of the solid. This potential is usually given by the Steele formula [START_REF] Steele | The physical interaction of gases with crystalline solids: I. Gas-solid energies and properties of isolated adsorbed atoms[END_REF] ,

(8)

𝜙 𝑠𝑓 (𝑧) = 𝜙 1 (𝑧) + 𝜙 ∞ (𝑧)
where  1 is evaluated by the integration of the LJ potential over the surface, ,

𝜙 1 (𝑧) = 𝐴 [ 2 5 ( 𝜎 𝑠𝑓 𝑧 ) 10 -( 𝜎 𝑠𝑓 𝑧 ) 4 ] (9)
and  ∞ is represents the interaction potential with other graphite layers summed up to infinity

(10) 𝜙 ∞ (𝑧) = - 𝐴𝜎 4 𝑠𝑓 3∆(𝑧 + 0.61∆) 3
The aggregate parameter A is given by (11)

A = 2𝜋𝜎 𝑠𝑓 2 𝜀 𝑠𝑓 𝜌 𝑠 ∆ Journal Pre-proof
where  sf and  sf are the solid-fluid energy and size interaction parameters,  s is the density of carbon atoms in graphite, and  is the spacing between graphite layers.

The FH correction for the interaction potential of H 2 molecule with a single graphitic plane is obtained by applying formula (3) to the solid-fluid LJ potential and integrating over the plane surface which gives the following expression: The Steele potential [START_REF] Steele | The physical interaction of gases with crystalline solids: I. Gas-solid energies and properties of isolated adsorbed atoms[END_REF] given by Eq. ( 8) sums interactions with the series of parallel graphitic planes expanded to ∞. The FH correction for the graphitic pore wall is given here by the following finite sum:

(13) 𝜙 𝑞 𝑠𝑓 (𝑧) = ∑ 4 𝑖 = 0
𝜙 𝑞 𝑠ℎ𝑒𝑒𝑡 (𝑧 + 𝑖Δ)

A similar formula was derived earlier [START_REF] Kowalczyk | State of Hydrogen in Idealized Carbon Slitlike Nanopores at 77 K[END_REF], and it is justified by the fact that terms in this sum decrease sharply with the distance from the surface.

The total quantum-corrected external potential of interaction between H 2 molecule and standard slit pore may now be written as

+ , (14)
𝑉 𝐹𝐻 𝑠𝑡. 𝑠𝑙𝑖𝑡 (𝑧) = 𝜙 𝑠𝑓 ( 𝐻 2 + 𝑧 ) 𝜙 𝑠𝑓( 𝐻 2 -𝑧 ) + 𝜙 𝑞 𝑠𝑓( 𝐻 2 + 𝑧 ) + 𝜙 𝑞 𝑠𝑓( 𝐻 2 -𝑧 )
Where pore width H is the distance between the centers of atoms composing the surface planes of the opposite walls.

For the comparison of our quantum corrected NLDFT calculations with published results, we used Eq. ( 14) as the external potential in Eq. ( 1) and we calculated several FH-NLDFT adsorption isotherms of H 2 at 77 K using  ff /k B = 36.7 K and  ff = 2.958 Å as the LJ fluid-fluid interaction parameters [START_REF] Darkrim | Monte Carlo simulations of hydrogen adsorption in single-walled carbon nanotubes[END_REF]. The solid-fluid parameters were obtained from the Lorentz-Berthelot combining rules taking the values  s /k B =28 K and  s = 3.4 Å for the carbon-carbon interaction parameters in graphite [START_REF] Steele | The physical interaction of gases with crystalline solids: I. Gas-solid energies and properties of isolated adsorbed atoms[END_REF]. The same LJ parametrization was applied for the modeling of H 2 isotherms at 77 K in three reference papers: (a) [START_REF] Kowalczyk | State of Hydrogen in Idealized Carbon Slitlike Nanopores at 77 K[END_REF], (b) [START_REF] Konstantakou | GCMC simulations of gas adsorption in carbon pore structures[END_REF] and (c) [START_REF] Kowalczyk | Thermodynamics of hydrogen adsorption in slit-like carbon nanopores at 77 K. Classical versus path-integral Monte Carlo simulations[END_REF]. The method used in (a) and (b) papers was the grand canonical Monte Carlo (GCMC) simulation with FH quantum correction FH-GCMC while the method used in the paper (c) was the pathintegral PI-GCMC method, which is considered the most accurate treatment of the thermodynamics of quantum fluids. We digitized the data of Fig. [START_REF] Konstantakou | GCMC simulations of gas adsorption in carbon pore structures[END_REF] and (c) [START_REF] Kowalczyk | Thermodynamics of hydrogen adsorption in slit-like carbon nanopores at 77 K. Classical versus path-integral Monte Carlo simulations[END_REF].

The theoretical isotherms (Fig. 1) calculated using three different methods are highly similar, but not identical. The sequence of the isotherm values is not the same for different pore sizes. The NLDFT-FH isotherms calculated in the present work show values in between the values of other isotherms or slightly below other values in only one case of pore width w=3.6 Å (Fig. 1a). Taking into account the complexity of the methods used in the calculations of the data presented in Fig. 1 and their certain diversity, we may consider our NLDFT-FH results in an overall agreement with the other referenced data.

Two-dimensional slit pore model with quantum corrections

The two-dimensional model used in the present work assumes the corrugated and energetically heterogeneous surface of carbon pores [START_REF] Jagiello | 2D-NLDFT adsorption models for carbon slit-shaped pores with surface energetical heterogeneity and geometrical corrugation[END_REF][START_REF] Jagiello | Carbon slit pore model incorporating surface energetical heterogeneity and geometrical corrugation[END_REF]. The model was formulated on the bases of the graphene carbon structure that was demonstrated in the recent study [START_REF] Guo | Topological defects: origin of nanopores and enhanced adsorption performance in nanoporous carbon[END_REF] using atomic-resolution images obtained from STEM microscopy. The images presented in that study were taken from various parts of nanoporous carbon samples, and they consistently showed the curved and defective graphene sheets that, according to the authors, constitute the carbon building blocks. To describe the spatial curvature of the surface, it is necessary to extend the description of the solid-fluid interaction potential from one-dimensional  sf (z), used in the standard model, to at least two-dimensional  sf (x, z). In the present model,  sf is constant as a function of y variable, and a simple trigonometric function describes the corrugation of the graphene pore surfaces, ,

𝑡(𝑥) = 𝛼sin (2𝜋𝑥/𝜆) (15)
where  is the amplitude and  is the periodicity of the corrugation.

In addition to the corrugation, the surface is energetically heterogeneous, where a trigonometric series describes this heterogeneity , ( 16)

𝐸(𝑥) = 1 + ∑ 𝑛 𝑘 = 1 𝛽 𝑘 sin (2𝜋𝑘𝑥/𝜆)
where n is the number of  k adjustable parameters.

The corrugation and the energetic heterogeneity are introduced only to the carbon surface layer. The solid-fluid potential  1 (x, z) for this layer and its FH quantum correction are 𝜙 𝑞 1 calculated by the integration of the LJ potential and its quantum correction. First, an analytical integration over the y-direction gives the following integrals of one variable:

(17) 𝜙 1 (𝑥,𝑧) = 𝐴∫ ∞ -∞ 𝐸(𝑥 ' )
𝑔 = [1 + ( 𝑑𝑡 𝑑𝑥') 2 ] 1/2 (20) 𝑞 = [(𝑧 + 𝑡(𝑥 ' )) 2 + (𝑥 -𝑥') 2 ] 1/2
Then, the numerical integration using the ten point Gaussian quadrature is performed to evaluate the integrals in Eqs. ( 17) and [START_REF] Tarazona | Erratum: Free-energy density functional for hard spheres[END_REF]. To calculate these integrals in infinite limits the periodic boundary conditions are assumed for the x coordinate.

Finally, using Eqs. (10) (12) (17) (18) the corrugated wall potential with quantumcorrections may be expressed in the following form:

(21) V 𝐹𝐻 𝑤𝑎𝑙𝑙 (𝑥,𝑧) = 𝜙 1 (𝑥,𝑧) + 𝜙 ∞ (𝑧 + 𝛼) + 𝜙 𝑞 1 (𝑥,𝑧) + ∑
where the amplitude  is added to shift potentials   and from  1 to avoid geometrical 𝜙 𝑞 𝑠ℎ𝑒𝑒𝑡 overlapping with the corrugated surface layer.

The potential defined by Eq. 21 is used in Eq. ( 1) as the external potential to calculate the theoretical adsorption isotherm (2D-HS-FH) on the model carbon surface. This isotherm is fitted to the experimental H 2 isotherm on the reference carbon black BP 280 (Fig. 2) to obtain the energetic heterogeneity parameters and the  sf parameter of our H 2 adsorption model. This reference carbon has been consistently used to develop the 2D-HS models for other gases [START_REF] Jagiello | Consistency of carbon nanopore characteristics derived from adsorption of simple gases and 2D-NLDFT models. Advantages of using adsorption isotherms of oxygen (O2) at 77 K[END_REF][START_REF] Jagiello | Dual gas analysis of microporous carbons using 2D-NLDFT heterogeneous surface model and combined adsorption data of N2 and CO2[END_REF][START_REF] Jagiello | Carbon slit pore model incorporating surface energetical heterogeneity and geometrical corrugation[END_REF]. The other interaction parameters are the same as for standard slit pore model (section 3.1.1). The surface corrugation is assumed here to be the same as established for the original 2D-HS nitrogen model [START_REF] Jagiello | Carbon slit pore model incorporating surface energetical heterogeneity and geometrical corrugation[END_REF], but since the surface geometrical parameters,  and  are expressed in terms of the reduced quantities scaled with respect to the molecular diameter; we adjusted these parameters accordingly for H 2 molecule to preserve the corrugation geometry. All parameters applied in the 2D-HS-FH model calculations are reported in Table 1. For comparison, Table 1 also contains the parameters used in the original 2D-HS model for N 2 [START_REF] Jagiello | Carbon slit pore model incorporating surface energetical heterogeneity and geometrical corrugation[END_REF][START_REF] Jagiello | Using a new finite slit pore model for NLDFT analysis of carbon pore structure[END_REF]. The total quantum corrected external potential of H 2 interaction with the corrugated pore is given as sum of the wall potentials defined by Eq. ( 21),

V 𝐹𝐻 𝑝𝑜𝑟𝑒 (𝑥,𝑧) = V 𝐹𝐻 𝑤𝑎𝑙𝑙( 𝑥, 𝐻 2 + 𝑧 ) + V 𝐹𝐻 𝑤𝑎𝑙𝑙( 𝑥, 𝐻 2 -𝑧 ) (22)
A detailed description of a corrugated pore model and the calculation method of the theoretical isotherms have been given earlier [START_REF] Jagiello | Consistency of carbon nanopore characteristics derived from adsorption of simple gases and 2D-NLDFT models. Advantages of using adsorption isotherms of oxygen (O2) at 77 K[END_REF][START_REF] Jagiello | Carbon slit pore model incorporating surface energetical heterogeneity and geometrical corrugation[END_REF]. Here, we calculated the kernel of 2D-HS-FH theoretical isotherms for H 2 at 77 K using the parameters listed in Table 1. This kernel constitutes our quantum-corrected hydrogen model for carbons with the heterogeneous surface.

Fig. 3a shows the excess isotherms of this model for selected effective pore widths, w. To illustrate the effect of FH quantum corrections, the isotherms calculated without these corrections are also shown in this figure. The fact that the quantum corrected model predicts lower H 2 densities than the classical model is because the quantum effects weaken the fluidfluid and solid-fluid interactions [START_REF] Konstantakou | GCMC simulations of gas adsorption in carbon pore structures[END_REF][START_REF] Kuchta | Numerical estimation of hydrogen storage limits in carbon-based nanospaces[END_REF]. To compare the H 2 kernel with the previously developed CO 2 kernel [START_REF] Jagiello | Dual gas analysis of microporous carbons using 2D-NLDFT heterogeneous surface model and combined adsorption data of N2 and CO2[END_REF], in Fig. 3b, we plot the 2D-HS isotherms of CO 2 at 273 K calculated for the same pore widths as for H 2 . The absolute pressures of 1 and 10 atm correspond to 0.03 and 0.3 p/p 0 for CO 2 . It is interesting to note that both sets of isotherms are similar in shape, but CO 2 isotherms show lower densities and are shifted to higher pressures compared to H 2 isotherms. These differences between the two kernels indicate that the H 2 kernel is to a certain extent more responsive to pore sizes than CO 2 kernel under the temperature and experimental pressure conditions. It is important to realize that both kernels presented in Fig. 3 have limited applicability for the PSD characterization of porous carbons. As discussed earlier [START_REF] Jagiello | Dual gas analysis of microporous carbons using 2D-NLDFT heterogeneous surface model and combined adsorption data of N2 and CO2[END_REF][START_REF] Ravikovitch | Unified Approach to Pore Size Characterization of Microporous Carbonaceous Materials from N2, Ar, and CO2 Adsorption Isotherms †[END_REF], the sensitivity of CO 2 adsorption isotherms to pore sizes is limited to w  10 Å. A similar upper sensitivity limit was considered [START_REF] Jagiello | Using DFT analysis of adsorption data of multiple gases including H2 for the comprehensive characterization of microporous carbons[END_REF] for H 2 at 77 K. At this temperature, H 2 is a supercritical gas which does not condense. Its adsorption isotherms are of type I (Fig. 3a), and their shapes for larger pores become increasingly more similar to one another, which in mathematical terms means that they become linearly dependent, and thus less sensitive to pore sizes. To better explain the physical state of H 2 gas confined in the carbon micropores, we plot in Fig. 4-Cross-sectional contours of the local densities of H 2 at 77 K and 1 atm calculated using present 2D-HS-FH model.

The limited sensitivity to larger pore sizes of CO 2 and H 2 implies that to calculate the carbon PSD in a full range of micro and mesopores, it is necessary to use an additional adsorbate that will condense in the larger pores. The concept of using two adsorbates that are sensitive to different pore sizes was implemented for CO 2 and N 2 in the dual gas analysis method [START_REF] Jagiello | Dual gas analysis of microporous carbons using 2D-NLDFT heterogeneous surface model and combined adsorption data of N2 and CO2[END_REF][START_REF] Jagiello | Enhanced resolution of ultra micropore size determination of biochars and activated carbons by dual gas analysis using N2 and CO2 with 2D-NLDFT adsorption models[END_REF].

A similar methodology has been applied earlier using standard NLDFT [START_REF] Jagiello | Characterization of pore structure of carbon molecular sieves using DFT analysis of Ar and H2 adsorption data[END_REF][START_REF] Jagiello | Using DFT analysis of adsorption data of multiple gases including H2 for the comprehensive characterization of microporous carbons[END_REF] and GCMC [START_REF] Konstantakou | GCMC simulations of gas adsorption in carbon pore structures[END_REF][START_REF] Konstantakou | Characterization of nanoporous carbons by combining CO2 and H2 sorption data with the Monte Carlo simulations[END_REF] models.

Comparison of the PSD characterization methods using multiple simple gases

It was recently demonstrated that the PSD results obtained from the 2D-HS models and adsorption isotherms of N 2 , Ar, and O 2 [START_REF] Jagiello | Consistency of carbon nanopore characteristics derived from adsorption of simple gases and 2D-NLDFT models. Advantages of using adsorption isotherms of oxygen (O2) at 77 K[END_REF] were consistent for several representative porous carbons. Here, we attempt to show that the dual gas analysis methods based on two pairs of simple gases, N 2 and CO 2 , and O 2 and H 2 also give consistent results in terms of carbon PSDs.

We use the adsorption data of N 2 , and CO 2 reported in two papers [START_REF] Jagiello | Dual gas analysis of microporous carbons using 2D-NLDFT heterogeneous surface model and combined adsorption data of N2 and CO2[END_REF][START_REF] Jagiello | Enhanced resolution of ultra micropore size determination of biochars and activated carbons by dual gas analysis using N2 and CO2 with 2D-NLDFT adsorption models[END_REF] for two series of porous carbons and new adsorption data of O 2 and H 2 measured at 77 K on the same carbons.

All PSD were calculated using the SAIEUS [START_REF] Jagiello | Stable numerical solution of the adsorption integral equation using splines[END_REF] software that is available at www.nldft.com.

The results of the PSD analysis of PC series of samples are presented in Figs. 5 and6. The PC samples are the activated carbons with systematically changing pore structures upon the increasing degree of activation. The sample labeled PC is a char derived from PET, and the activated carbons derived from this char by CO 2 activation are labeled PCn, where n is the burnoff percent. The goodness of fit of the 2D-HS models to the isotherms measured on these samples is shown in Fig. 5 where we plot experimental data and fitting lines in a linear and logarithmic pressure scale to show the goodness of fit accurately in the range of low and high pressures. Meanwhile, it is interesting to note that the amounts adsorbed of H 2 measured up to 1 atm reach values similar to those of CO 2 measured up to 10 atm. The CO 2 uptake on these carbons at 1 atm is significantly smaller than H 2 at the same pressure.

The isotherms of carbons with narrow PSDs (PC, PC5, and PC23) were fitted using dual gas analysis method applied to two pairs of isotherms, N 2 & CO 2 , and O 2 & H 2 . The version of the dual gas analysis method introduced in the original reference [START_REF] Jagiello | Dual gas analysis of microporous carbons using 2D-NLDFT heterogeneous surface model and combined adsorption data of N2 and CO2[END_REF] was unable to fit the 2D-HS models simultaneously to N 2 & CO 2 isotherms for samples of char PC (Fig. 5 a1, b1) and mildly activated char PC5 (Fig. 5 a2, b2) . These samples have extremely small ultramicropores which hinder the diffusion of N 2 at low temperature and pressure. The problem was then solved by fitting partial data excluding the N 2 data points at pressures below 0.001 p/p 0 and the CO 2 points above 0.03 p/p 0 .

Here, we apply a refined approach to this problem [START_REF] Jagiello | Enhanced resolution of ultra micropore size determination of biochars and activated carbons by dual gas analysis using N2 and CO2 with 2D-NLDFT adsorption models[END_REF], and we slightly increase the lower pore width limit w min of the N 2 kernel. With this modification, we are able to fit simultaneously both isotherms in the full range of pressures. The physical meaning of w min is an estimate of the minimum pore width accessible to N 2 molecules at the measurement conditions. Increasing the w min parameter from its default value w min = 3.6 Å modifies the N 2 kernel by excluding the theoretical isotherms calculated for small pores that contribute to CO 2 but not to N 2 adsorption at low temperature and pressure. We believe that this approach is more accurate and provides higher resolution than the approach that excludes the experimental points as it was done previously. we extended the range of the PSD analysis using this gas to the lower limit than can be achieved by other gases. As a result, the PSDs of PC, PC5, and PC23 (Fig. 5 a1-a3) calculated using O 2 & H 2 have similar shapes to those derived from N 2 & CO 2 but are shifted to lower pore sizes showing an additional contribution to pore volume by the smallest pores accessible to H 2 but not to other gases. These additional pore volumes are visible in the cumulative pore volume plots (Fig. 5 b1-b3) and are reported in Table 2.

The comparison of

For carbons with wider PSDs (PC39 and PC63), we were able to obtain excellent fit of four 2D-HS models to four isotherms simultaneously which implies that the PSDs calculated for these carbons from the general fit of four isotherms should be very similar to those obtained from two gases N 2 & CO 2 being a subset of the four gases. Indeed, this similarity is confirmed by the calculated PSDs and pore volumes (Fig. 6 and Table 2). Results of simultaneous fitting of the NLDFT kernels to adsorption data of several gases measured on the same sample were reported earlier [START_REF] Jagiello | Dual gas analysis of microporous carbons using 2D-NLDFT heterogeneous surface model and combined adsorption data of N2 and CO2[END_REF][START_REF] Jagiello | Using DFT analysis of adsorption data of multiple gases including H2 for the comprehensive characterization of microporous carbons[END_REF][START_REF] Duda | Complementary study of microporous adsorbents with DFT and LBET[END_REF]. The results derived from such a procedure are statistically more robust than those derived from a single isotherm. Moreover, if the goodness of such fit is satisfactory, it confirms that the obtained PSDs are not adsorbate related. Simultaneous fit to all data Only C-CS sample that is a non-activated char requires separate fitting of the two pairs of isotherms with two dual models N 2 & CO 2 , and O 2 & H 2 . In general, a high similarity is observed between the PSDs derived from the two types of analysis for the C-CS carbon series.

(a5) (b5) Fit to O 2 & H 2 Fit to N 2 & CO 2 Fit to O 2 & H 2 Fit to N 2 & CO 2
10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 Amount adsorbed, cm gases. This consistency is demonstrated by the ability of simultaneous fit of two or four 2D-HS models to the relevant isotherms. The fitted isotherms are, in part, mathematically correlated via applied models and the calculated PSD. This correlation is limited to the range of pore sizes to which both models are sensitive. The original work on the dual gas analysis method [START_REF] Jagiello | Dual gas analysis of microporous carbons using 2D-NLDFT heterogeneous surface model and combined adsorption data of N2 and CO2[END_REF] took advantage of this correlation and showed, using PC23 and PC85 samples as examples, that the analysis of N 2 isotherm at 77 K without low-pressure data in combination with CO 2 isotherm at 273 K might give the PSD equivalent to that derived from the full N 2 isotherm. Here, we follow that approach and apply it to O 2 & H 2 data of two samples, PC23 (Fig. 9) and C-CS (Fig. 10). In both cases, the PSDs derived from full data of both isotherms are in a close agreement with the PSDs derived from full H 2 and partial O 2 isotherms. By partial O 2 isotherm, we mean the isotherm without low-pressure points shown as full symbols in Figs. 9 and 10.

Relative pressure or atm for H 2 10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 - To explain the validity of the presented approach in simple terms, we note that the full O 2 isotherm may provide the information about the full range of micro and mesopores, while the information limited to small pores is provided by H 2 isotherm. It follows that in combination with H 2 isotherm only upper-pressure part of O 2 isotherm is necessary to describe the full range of micro and mesopores. At this point, it is interesting to note that in special cases of ultramicroporous carbons, a single H 2 isotherm may be sufficient for evaluating the carbon PSD.

Such a result is presented as a dotted line in Fig. 10c for ultramicroporous char C-CS. This result could be expected based on the fact that the H 2 uptake for this carbon is higher than O 2 .

Finally, following the suggestion of one of the reviewers, we consider N 2 & H 2 as another combination of gases to be employed in the dual gas method. Some researchers may find it convenient to continue using standard N 2 adsorption for carbon materials that are not expected to have a significant amount of the surface polar sites, combine N 2 & H 2 data measured at 77 K for the analysis with the dual gas method. To show that such an approach may be effective, in Fig. 11, we present the results of the dual gas analysis using N 2 & H 2 for the sample of PC char.

As in the case of O 2 & H 2 analysis shown in Fig. 9 and 10, we observe a high similarity between the PSDs derived using N 2 isotherm data in the full and reduced pressure scale. This example demonstrates the general applicability of the dual gas analysis method that may employ various gases chosen based on their molecular properties, such as the molecular diameter or the intermolecular interaction parameters.

Relative pressure or atm for H 2 10 -7 10 -6 10 -5 10 -4 10 -3 10 -

Conclusions

This study is an extension of previous studies [START_REF] Jagiello | Dual gas analysis of microporous carbons using 2D-NLDFT heterogeneous surface model and combined adsorption data of N2 and CO2[END_REF][START_REF] Jagiello | Enhanced resolution of ultra micropore size determination of biochars and activated carbons by dual gas analysis using N2 and CO2 with 2D-NLDFT adsorption models[END_REF] on the dual gas analysis method using The underlying reason of using the isotherms of fast diffusing gases like CO 2 at 273 K or H 2 at 77 K in combination with the N 2 or O 2 isotherms is to obtain reliable information about carbon micro and ultramicropore sizes. The diffusion of CO 2 into micropores at 273 K is faster than N 2 at 77 K, which makes the measurement of equilibrium adsorption data more reliable and obtained faster. The same refers to H 2 adsorption as H 2 is a supercritical gas at 77 K.

The drawback of using N 2 and CO 2 is their high quadrupole moment that may influence the measured isotherms by interacting with the surface polar sites. A replacement of these gases with O 2 and H 2 that have significantly smaller quadrupole moments than the other pair of gases.

To quantify the effects of such substitution, we compare the PSD analysis results using the pairs of isotherms N 2 & CO 2 , and O 2 & H 2 for several reference carbon samples and the comparisons show consistency between the results derived from both pairs of isotherms. For samples with wider PSDs, we were able to fit the relevant 2D-HS models to adsorption data of all four gases simultaneously and as a result, obtain a common PSD from all data.

Samples with narrow PSDs require separate fitting using two dual models N A fundamental and practical benefit of using the dual gas analysis method is the ability of obtaining the full micro and mesopore PSD by using a partial O 2 isotherm without low-pressure data in combination with full H 2 isotherm both measured at 77 K. We presented examples for our reference samples where the PSDs derived from full data of both isotherms are in a close agreement with the PSDs derived from full H 2 and partial O 2 isotherms. By partial O 2 isotherm, we mean the isotherm without low-pressure points, p/p 0 <10 -3 .

We also showed that in special cases of ultramicroporous carbons where the H 2 uptake is higher than O 2 , a single H 2 isotherm might be sufficient for evaluating the carbon PSD. Using this option may be very useful for screening the properties of such materials as chars, biochars, and carbon molecular sieves.

We believe that the results and methods presented in this study may facilitate obtaining highly detailed characteristics of microporous carbon materials. Such detailed and accurate characteristics are critical for the advanced carbon applications such as electrodes in supercapacitors [START_REF] Kleszyk | Carbons with narrow pore size distribution prepared by simultaneous carbonization and self-activation of tobacco stems and their application to supercapacitors[END_REF], gas storage [START_REF] Schaefer | Assessment of hydrogen storage in activated carbons produced from hydrothermally treated organic materials[END_REF], gas sensors [START_REF] Gregis | Detection of lung cancer bio-markers in human breath using a micro-fabricated air analyzer[END_REF][START_REF] Gregis | Characterization of materials toward toluene traces detection for air quality monitoring and lung cancer diagnosis[END_REF], or gas separation using molecular sieves [START_REF] Grau-Marin | Evaluation of the textural properties of ultramicroporous carbons using experimental and theoretical methods[END_REF].

2 ,Fig. 1 -

 21 Fig.1-Comparison of quantum corrected absolute NLDFT-FH isotherms calculated in the present work with literature data calculated using (quantum corrected) FH-GCMC and (path integral) PI-GCMC. Data taken from three reference papers: (a)[START_REF] Kowalczyk | State of Hydrogen in Idealized Carbon Slitlike Nanopores at 77 K[END_REF], (b)[START_REF] Konstantakou | GCMC simulations of gas adsorption in carbon pore structures[END_REF] and (c)[START_REF] Kowalczyk | Thermodynamics of hydrogen adsorption in slit-like carbon nanopores at 77 K. Classical versus path-integral Monte Carlo simulations[END_REF].

Fig. 2 -

 2 Fig. 2-Fit of the 2D-HS-FH model to the experimental isotherm of H 2 measured at 77 K on the reference carbon black BP 280.

Fig. 3 -

 3 Fig.3-The excess theoretical adsorption isotherms of 2D-HS kernels for H 2 at 77 K (a) and CO 2 at 273 K (b) calculated for selected effective pore widths, w from 3.5 to 25 Å.

Fig 4 ,

 4 the density profiles in the pores of different widths calculated by the present 2D-HS model. This illustration shows that at 77 K and 1 atm H 2 may saturate only the small pores of 4 -7 Å. The average density of H 2 decreases in larger pores where it is adsorbed mostly on the pore walls. It follows that the amount of H 2 adsorbed in the larger pores depends on their surface area and not on their widths.

3 (

 3

Fig. 5 -

 5 Fig.5-Multiple gas analysis of the PC series of samples on the basis of the 2D-HS models. Simultaneous fits of the models to two or four isotherms of O 2 , H 2 , and N 2 at 77 K, and CO 2 at 273 K plotted in linear (a) and logarithmic (b) pressure scale.

Fig. 6 -

 6 Fig. 6 -Results of the multiple gas analysis of the PC series of samples on the basis of the 2D-HS models. Comparison of the differential PSDs (a) and cumulative pore volumes (b) derived from the dual fit of N 2 & CO 2 pair of isotherms versus O 2 & H 2 or all four isotherms.

3 (Fig. 7 -

 37 Fig.7-Multiple gas analysis of the CS series of samples on the basis of the 2D-HS models. Notation is the same as in Fig.5.

Fig. 8 - 3 . 3

 833 Fig.8-Results of the multiple gas analysis of the CS series of samples on the basis of the 2D-HS models. Notation is the same as in Fig.6.

Fig. 9 - 2 10Fig. 10 -

 9210 Fig. 9 -PSD analysis of PC23 sample. Simultaneous fit of 2D-HS models to full H 2 isotherm and partial O 2 isotherm in linear (a) and logarithmic (b) scale. (c) Comparison of the differential PSDs derived from H 2 and partial O 2 isotherms with the PSDs derived from full data of both isotherms.

Fig. 11 -

 11 Fig.11-PSD analysis of PC sample. Notation is the same as in Fig.9, but for N 2 instead O 2 .

N 2 and

 2 CO 2 isotherms, which we propose to replace with the analysis of O 2 & H 2 isotherms. In the first part of this work we develop the quantum corrected 2D-HS-FH model for H 2 adsorption on the heterogeneous carbon surface at 77 K. This model is then used in conjunction with the earlier developed O 2 model for the carbon PSD analysis at 77 K.

  where m is the mass of the H 2 molecule. For the interaction between H 2 molecule and the solid  m =m.

	For the LJ potential Eq. (3) takes the following form
	𝜙 𝑞 𝑓𝑓 (𝑟) = 𝑄𝜀 𝑓𝑓 𝑟 -2 [ 22 ( 𝜎 𝑓𝑓 𝑟 ) 12	-5 (	𝜎 𝑓𝑓 𝑟 ) 6	(6)

Table 1 .

 1 Parameters used to calculate the 2D-HS-FH kernel for H 2 and 2D-HS kernel for N 2 adsorption at 77 K on carbons with heterogeneous surfaces.

	Intermolecular
	interaction parameters	H 2	N 2	Heterogeneity parameters	H 2	N 2
	 ff =d HS (Å)	2.96		 1	0.357	0.065
	 ff /k (K)	36.70		 2	0.640	0.565
	 sf (Å)	3.18				
	 sf /k (K)	32.86				

  PSDs obtained from the two pairs of gases N 2 & CO 2 , and O 2 & H 2 show similarities and differences. As reported in Table 1, the H 2 molecule has a smaller molecular

diameter ( ff  3 Å) than the other gases used in this work which means it may access smaller pores than the other gases. Consequently, we assumed w min = 3.0 Å for the H 2 kernel, and thus

Table 2 .

 2 Cumulative pore volumes calculated from the kernel sets including H 2 model. Comparison with volumes calculated from the dual gas N 2 & CO 2 using 2D-HS models.

		Pore volume from the kernel set including H 2 model [cm 3 g -1 ]
	Sample	Pore volume difference from N 2 & CO 2 model [%]
		w <6 Å	w <10 Å	w <15 Å	w <20 Å	w <50 Å
	PC	0.14	0.24	0.25	0.26	0.26
		43%	24%	23%	24%	24%
	PC5	0.16	0.22	0.26	0.26	0.28
		23%	2%	13%	14%	17%
	PC23	0.18	0.31	0.39	0.43	0.43
		34%	9%	3%	3%	0%
	PC39	0.15	0.38	0.54	0.63	0.65
		7%	6%	5%	4%	3%
	PC63	0.08	0.33	0.57	0.84	1.07
		-2%	1%	2%	2%	-1%
	C-CS	0.09	0.12	0.13	0.14	0.14
		1%	13%	18%	22%	22%
	C-CS-0.5	0.16	0.22	0.25	0.25	0.29
		33%	10%	11%	9%	6%
	C-CS-1.0	0.16	0.25	0.31	0.33	0.37
		21%	1%	4%	4%	2%

  2 & CO 2 , and O 2 & H 2 . Because H 2 molecule has a smaller molecular diameter ( ff= 3 Å) than the other gases it can penetrate smaller pores and the range of PSD analysis using this gas may be extended to a lower limit than the standard for N 2 by about 0.5 Å. As a result, the PSDs calculated using O 2 & H 2 have similar shapes to those derived from N 2 & CO 2 but are shifted to lower pore sizes showing an additional contribution to pore volume by the smallest pores accessible to H 2 but not to other gases. These additional pore volumes are visible in the cumulative pore volume plots.

𝑖 = 1 𝜙 𝑞 𝑠ℎ𝑒𝑒𝑡 (𝑧 + 𝛼 + 𝑖Δ),

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Manuscript title: Exploiting the adsorption of simple gases O2 and H2 with minimal quadrupole moments for the dual gas characterization of nanoporous carbons using 2D-NLDFT models

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:

No financial support was received for this work.