Lahcene Maachou

Kun Qi

Eddy Petit

Zhaodan Qin

Yang Zhang

Didier Cot

Valérie Flaud

Corine Reibel

Heba El-Maghrbi

Lei Li

† Eddy Petit

Heba El-Maghrabi

Philippe Miele

Daniel Kaplan

Manish Chhowalla

Nicolas Onofrio

Damien Voiry

Biomimetic electro-oxidation of alkyl sulfides from exfoliated molybdenum disulfide nanosheets

come   L'archive ouverte pluridisciplinaire

Introduction

Enzymes are proteins that catalyze key reactions in living organisms. 1 They possess high selectivity, which makes them attractive for enantioselective synthesis of drug molecules in the pharmaceutical industry. 2,3 The catalytically active sites on enzymes typically consist in coordinated transition metals and recent insights into how they catalyze reactions has enabled progress in the design of novel bio-inspired electrocatalysts. 4 For example, understanding of mechanisms that are responsible for hydrogenase activity has allowed the development of electro-active molecular catalysts with structures that reproduce active sites of the natural enzyme. 5 Nanozymes are nanomaterials with enzyme-like characteristics with superior stability compared to natural proteins -making them attractive as electro-catalysts with tunable activity. 6,7 Since the discovery of unexpected peroxidase-like activity of iron oxide nanoparticles, 8 various nanozymes have been realized using metal oxides, noble metals, graphene and derivatives, and metal-organic frameworks (MOFs). [9][10][11] However, two outstanding challenges remain: first, nanozymes show much lower catalytic activity because of the low densities of active sites; 12 and second, the inhomogeneous composition and crystal facet structure 13 make it difficult to identify the active sites. These bottlenecks are significant hurdles for implementation of nanozymes in applications. Exfoliated two-dimensional (2D) materials are known to be good electrocatalysts. 14 In particular, transition metal dichalcogenides (TMDs) have been widely studied for their catalytic properties in reactions such as the hydrogen evolution reaction, as well as oxygen and CO2 reduction reactions. [15][16][17] Despite the large body of work on catalysis with 2D materials, their application in electrosynthesis of organic molecules has yet to be explored. Oxidation of organic sulfide compounds into sulfoxides for production of drugs such as esomeprazole and armodafinil are important reactions in the pharmaceutical industry. 18,19 With an annual production of approaching 100,000 metric tons, dimethyl sulfoxide (DMSO) is widely used as polar and aprotic organic solvent in pharmaceutical and microelectronic industry as well as an intermediate for the synthesis of sulfur-based derivative molecules. Contrary to thiols, organic sulfide are stable in air and the industrial process for the synthesis of sulfoxide relies on the use of undesirable strong oxidizing agents including NOX or peroxy acids. 20,21 Redox processes can be used to oxidize organic sulfides at room temperature and without the use of harsh chemicals -greatly limiting the safety concerns. However, only handful contributions have been reported on the electro-oxidation of DMS in dimethylsulfoxide and dimethylsulfone using platinum 2 | J. Name., 2012, 00, 1-3 This journal is © The Royal Society of Chemistry 20xx

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Please do not adjust margins as anode. 22,23 The use of expensive and scarce noble metals therefore limits practical applications.

In this work, we report metallic two-dimensional MoS2 as biomimietic catalyst with intrinsic enzyme-like active sites for the electro-oxidation of organic sulfides. The atomic structure of MoS2 resembles that of the DMSO reductase active site -an enzyme responsible for reversible reduction of DMSO in DMS.

When tested in oxygen-saturated, non-aqueous electrolyte solution, DMS is electrochemically converted to DMSO on the MoS2 nanosheets with activity and selectivity superior to those of noble metals. Our results show that the production of DMSO from the electrochemical oxidation of DMS using 1T' MoS2 nanosheet catalysts is significantly higher (680 L h-1 per gram) than for Pt nanoparticle catalysts (210 L h -1 g -1 ). Our numerical predictions suggest that the superior activity is ascribed to the lower binding energy of DMS on the basal plane and the edge sites of the 1T' phase.

Results and discussion

Chemically exfoliated MoS2 nanosheets

MoS2 nanocrystals are known catalysts for the oxidation of sulfur-based molecules. For example, Lauristen et al. have observed thiophene adsorption at the brim sites on sulfide MoS2 crystals, suggesting that such sites can play an active role in catalysis. 24 Catalytic oxidation of thiols into disulfides has also been achieved -hinting at nanozyme-like activity of MoS2 for oxidation of sulfur-based molecules. 25 Recently MoS2 with inclusion of cobalt single-atom have been proposed for the heterogeneous oxidation of organic sulfide using H2O2 as oxidizing agent. 26 Alternatively, DMSO can be prepared from the oxidation of DMS with a standard potential of 574 mV vs. NHE in water but the reaction suffers from large overpotential and possible degradation of the catalyst materials (Figure S1). 27 The similarity between the active sites of hydrogenase and the structure of MoS2 edges led to its use as an HER catalyst. 5 DMSO reductase (DMSOR) -an enzyme produced under anaerobic conditions in some bacteria -is known to reversibly reduce DMSO into DMS. In contrast to hydrogenase that contains Fe and Mo metals, DMSOR active site consists only of molybdenum Mo(VI) coordinated with 4 sulfur atoms from two pyranopterin dithiolene ligands (Figures 1a,b). We synthesized the 1T' and 2H MoS2 nanosheets using our previously reported intercalationassisted exfoliation method (Figure 1c,d) (See Experimental Section). 28,29 The nanosheets were exfoliated in water and first characterized by atomic force microscopy (Figure 1e). The size distributions extracted from the AFM measurements reveal that the nanosheets are  200nm in length while the average thickness is  1 nm, consistent with single layer nanosheets (Figure 1f). It is well known that as-synthesized nanosheets by chemical exfoliation possess the 1T' phase structure. 30 The 2H phase is obtained by mild annealing (at 300°C under 5% H2 in argon, See Experimental Section) of the 1T' phase MoS2 nanosheets) of the as-synthesized nanosheets. 29,30 From the deconvolution of the XPS spectra from the Mo3d and S2p regions, we have estimated the 1T' phase concentration in the as-exfoliated nanosheets to be  75%, while the 2H phase is almost entirely restored after annealing. 29 The presence of the 1T' and 2H phases is also detected in Raman of as-exfoliated and annealed MoS2 nanosheets (Figure S2). The catalysts were prepared by loading a controlled amount of 1T' phase MoS2 nanosheets on the electrode via drop casting and controlled evaporation of the solvent. [29] Scanning electron microscopy (SEM) on the electrode reveals that the nanosheets are densely packed on the surface without significant porosity (Figure 2a). The 2H MoS2 electrode is virtually identical (Inset Figure 2a) -meaning that the phase transition during mild annealing does not affect the orientation or morphology of thenanosheets so that only the phase of MoS2 is modified. Next, we determined the electrochemically active surface area (ECSA) by estimating the double layer capacitance (Cdl) of 1T'-and 2H MoS2 electrodes (See "Estimation of the double layer capacitance for MoS2 nanosheets and Pt nanoparticles" in the Experimental Section). To do this, different electrodes were cycled in 0.1M tetraethylammonium tetrafluoroborate (NEt4BF4) in acetonitrile at increasing scan rates from 5 to 200 mV s -1 (Figure 2b,c). The double layer capacitances from the 1T' and 2H electrodes were found to be 284 and 55 µF cm -2 , respectively (Figure 2d). Assuming a Cdl of  10 µF cm -2 for ideally flat MoS2 in organic electrolytes, 32 the ECSA is estimated to 28.4 cm ECSA -2 and 5.5 cm ECSA -2

for electrodes with 1T' and 2H phases, respectively. The reduction of the ECSA values between 1T' and 2H phases MoS2 is likely due to the decrease in the interlayer spacing of the nanosheets after annealing and therefore limited intercalation of ions in the 2H MoS2 electrodes as reported in Ref . 33 The Cdl is also significantly lower in organic electrolyte than in aqueous electrolytes (Figure S3) due to nature of electrochemically active sites being different for different types of electrolyte solutions.

Electrochemical activity of MoS2 nanosheets towards the oxidation of DMS

The electrochemical responses from 1T' and 2H MoS2 nanozymes were measured in 0.1 M NEt4BF4 in acetonitrile and the applied potentials corrected versus Normal Hydrogen Electrode (NHE) after calibrating the reference electrode using ferrocene: Fc/Fc + (Figure S5). The electrolyte solution was saturated with O2 used as a source of oxygen for the reaction.

When sweeping the potential of the working electrodes, the anodic current density rapidly and continuously increased for both phases of MoS2 nanosheets (Figure 3a). The onset potential (the potential at which the Faradaic current begins to increase) from the 1T' phase was found to be 1190 mV vs. NHE -clearly lower than the onset potential of 2H phase of MoS2 (1280 mV vs. NHE). To confirm that the anodic current is solely due to the oxidation of DMS, we performed the same experiment but in the absence of DMS. Virtually no current wasdetected without -confirming that the anodic current is due to the reaction of DMS and not the oxidation of the catalyst itself (Figure S6). To further quantify the catalytic performance of the MoS2 nanosheets with respect to state-of-the art catalysts, we compare the results with 60 mesh palladium: Pd-NP, Polycrystalline platinum: Pt-PolyC, commercial platinum nanoparticles supported on porous carbon (20% in mass): Pd-NP and a dirhodium(II) carboxylate complex: Rh2(esp)2 (esp=α, α',α', α'-tetramethyl-1,3-benzenedipropionic acid) that is a known catalysts for the oxidation of organic sulfides. 34 The results reveal that the 1T' phase of MoS2 catalysts exhibit geometrical current density of 9.2 mA cm geom -2

at 1400 mV vs. NHE compared to 4.3 mA cm geom -2

for Pt nanoparticle electrodes (Figure 3a). 1T' MoS2 catalysts also outperforms Pt nanoparticles, palladium and dirhodium complex with a lower onset potential of  45 mV, 150 mV and 160 mV respectively (Inset Figure 3a). The substantially better electrocatalytic activity of 1T' phase MoS2 is also supported by Tafel plots shown in Figure 3b. The Tafel slope of 1T' MoS2 reaches 75 mV dec -1 . For comparison Tafel slopes of 99 mV dec -1 , 110 mV dec -1 , 125 and 115 mV dec -1 are obtained for 2H MoS2, Pt nanoparticles, Pd and dirhodium respectively. The reduced Tafel slope is attributed to the improved electrocatalytic reaction kinetics due to higher electrical conductivity of metallic 1T' phase of MoS2. 31,35 To assess the true electrocatalytic activity of MoS2 nanosheets for the reduction of DMS, we normalized the geometrical current to the ECSA values obtained from the Cdl measurements. We determined the surface of platinum exposed to the electrolyte for both polycrystalline Pt and Pt nanoparticles using the copper underpotential deposition (Cu-UPD) method developed by Green and Kucernak. 36 Under UPD conditions at +0.3 V vs. RHE, Cu is solely deposited on the active Pt while no copper is deposited on the carbon support. The density of active sites on Pt was determined from the exchanged charges when stripping Cu monolayers deposited on Pt nanoparticles: QStrip. Assuming 420 µC cm -2 of charges exchanged for the deposition of a monolayer of Cu on Pt, 36 the active surfaces for polycrystalline Pt and Pt nanoparticles were estimated to 4.14 and 14.8 cm 2 /cm Geom 2 ("Cu Underpotential Deposition" section in the Supporting Information and Figure S7). We note that while the Cu UPD method has been developed for unsupported platinum, we found that the surface area of the Pt nanoparticles reaches 10 m 2 g -1 of catalyst, which is close to the values for unsupported Pt nanoparticles. 36 applied potential (Figure 4a). MoS2 also compares favorably with Pt nanoparticles that exhibit a current density of 0.28 mA 𝑐𝑚 𝐸𝐶𝑆𝐴 -2

for the reaction (Inset Figure 4a). We performed electrochemical impedance spectroscopy (EIS) on electrodes of the different phases of MoS2 as well as Pt nanoparticles (Figure 4b). The EIS measurements were performed at onset potentials of 1300 and 1350 mV vs. NHE. The impedance responses consist of 2 semi-circles corresponding to the electrolyte response for the highest frequencies and the reaction responses for the lower frequencies. The high frequency responses in the form of quasi semi-circles are independent of the applied potential at the working electrode and are attributed to the responses from the counter electrode, substrate-catalyst interface and the electrolyte. 37 The second semi-circle originates from the working electrode and originated from the charge transfer resistance (RCT) and the capacitances. The equivalent circuit used for fitting the EIS data is shown in inset of Figure 4b. The values of RCT decrease when the applied potential is increased, reflecting improved reaction kinetics (Figure S8a, b and Table S1). At 1300 mV vs. NHE, the charge transfer resistance is estimated to be  370 Ω for 1T' MoS2, which is lower than the values extracted for 2H MoS2 (1480 Ω) and Pt nanoparticles ( 790 Ω).

Quantification of DMSO production and estimation of Faradic efficiency

Next, we investigated the product of the DMS oxidation reaction by holding the potential of the electrode at 1500 mV vs. NHE. The products of the reaction after 4, 8 and 24 hours were analyzed using nuclear magnetic resonance (See "Detection of the products of the reaction via Nuclear magnetic resonance (NMR)" section in the Supporting Information). According to the literature, the oxidation of DMS can form several products including dimethyl sulfoxide, dimethyl sulfone and methyl sulfonates. 38,39 In our NMR measurements, DMS and DMSO signatures are clearly identified at 2.08 ppm and 2.5 ppm respectively (Figure 5a). The NMR peaks from dimethyl sulfone and methyl sulfonates -expected at 2.91 and ~ 3.1 ppm -are not detected even after 24 hours of reaction (Figure S10). These results demonstrate that the electrochemical oxidation of DMS on the MoS2 nanozymes is highly selective towards the formation of DMSO. We note that as the reaction proceeds, the DMSO signals increase continuously with time while the signatures for DMS decrease. Figure 5b shows the production of DMSO over 24 hours from MoS2 and platinum electrodes. The production of DMSO from the 1T' phase of MoS2 is largely maintained up to 24 hours with a total production of 250 mol g - 1 , equivalent to a production rate of 680 L h -1 per gram of catalyst (Inset Figure 5b). This performance is clearly higher than that of 2H MoS2 and Pt nanoparticles that exhibit a production of 30 and 71 mol g -1 after 24 hours equivalent to  89 L h -1 g -1 and  210 L h -1 g -1 , respectively. More importantly our results also demonstrate that 1T' MoS2 can sustain high production rate of DMSO with a quasi linear increase of the evolved DMSO, while the production rates from Pt and 2H MoS2 tend to stabilize after 4 hours of reaction. This demonstrates that 1T' MoS2 does not suffer from rapid deactivation of its catalytic properties compared to Pt or 2H MoS2. To obtain fundamental insight on the mechanisms of the reaction, we have estimated the quantity of electrons involved per molecule of DMSO formed. We found that the ratio: ne -: nDMSO is the slowest for 1T' MoS2 confirming the high efficiency of the 1T' phase. That is, after 24 hours, both 1T' and 2H phase demonstrate a lower ne -: nDMSO ratio than Pt nanoparticles with 1.07 and 1.25 electrons per DMSO molecule, respectively, compared to 1.34 for Pt nanoparticles. Assuming one electron involved in the reaction, the Faradaic efficiency for the initial 4 hours of reaction is close to 96.2±2.1 % for 1T' phase MoS2 and 86.4±1.8 for the 2H MoS2 compared to 89.1±1.9 % for Pt nanoparticles (Figure 5c). After 24 hours, the Faradaic efficiency (FE) is largely maintained for 1T' MoS2 (97%) and 2H MoS2 (92 %) -in contrast to Pt nanoparticle catalysts where the FE retention drops to 83.8%. To confirm the stability of the MoS2 nanosheets, the electrodes were characterized using Raman and XPS spectroscopy (Figure S11) 40,41 . The signatures from the 1T' phase are clearly visible from the E1g, J1 and J3 peaks as well as from the deconvolution of the Mo3d and S2p XPS spectra. Importantly virtually no signals from the oxidized Mo and S are detected in XPS, while the 1T' phase is estimated to ~50 % after the reaction, suggesting minimal relaxation of the metallic structure.

Estimation of intrinsic activity of 1T' and 2H MoS2 nanozymes towards the oxidation of DMS

To benchmark activity of 1T' and 2H phases of MoS2 with that of platinum towards oxidation of DMS, we normalized the activity per mass of catalysts loaded on the electrode. Figure 6a shows the FE-normalized mass activity of MoS2 compared to Pt nanoparticles. At 1400 mV vs. NHE, the activity of 1T' MoS2 nanosheets reaches 240 A g -1 -compared to 16.4 A g -1 for 2H MoS2 nanosheets. The DMS oxidation performance of the 1T' polymorph is 5-fold larger than for Pt nanoparticles supported on carbon. The required potential to generate a current of 50 A g -1 (equivalent to 132 L g -1 h -1 ) is 1280 mV vs. NHE -120 mV lower than in the case of Pt nanoparticles. To further evaluate the intrinsic electrocatalytic properties of the MoS2 nanosheets, we estimated the turnover frequency (TOF) based on ECSA measurements and assuming active site density of 1.5 × 10 15 cm -2 for a flat MoS2 surface. We note that for the calculations of the TOF, we assume that the whole surface of the MoS2 nanosheets is active. The TOF values from the 1T' and 2H phases were compared to those from the platinum nanoparticles (Figure 6b). The density of active sites for platinum was estimated from UPD measurements and assuming a site density of 1.1 × 10 15 cm -2 . 42 The higher intrinsic activity from the MoS2 nanosheets compared to Pt is clearly visible from the TOF values. When compared to platinum nanoparticles, MoS2 nanosheets demonstrated excellent performance with notably lower onset potential and similar TOF values at lower applied potentials. A TOF of 0.1 s -1 is achieved for an applied potential of 1258 mV vs. NHE in the case of 1T' MoS2. This potential is 73 mV and 180 mV smaller than the potential for achieving similar activity from 2H MoS2 and Pt nanoparticles, respectively.

To gain further understanding on the origin of the high activity of MoS2 towards DMS oxidation, we computed the binding energy (Eb in eV) of DMS adsorption for different levels of DMS coverage on MoS2 and Pt(111) surfaces using density functional theory (See "Calculation of the binding energy (Eb) of DMS" section in Supporting Information and Figure S12). Figure 6c shows the binding energy of DMS on MoS2 and Pt surfaces as a function of the coverage fraction. In the dilute limit, we found that approximate potentials of 0.46 and 2.56 eV are required to desorb DMS from MoS2 and Pt, respectively. Charge density differences and Bader charge analysis show that DMS is charge donor in both cases and that the charge transfer (from DMS to the surface) is of +0.18e and +0.38e when DMS is adsorbed on MoS2 and Pt, respectively (Figure S13). Moreover, the shortest distance between an atom of the DMS and an atom of the catalyst is 3.0 Å and 2.3 Å for MoS2 and Pt, respectively. These key figures demonstrate the strong interaction between DMS and Pt by contrast to mild physisorption of DMS on MoS2. Interestingly, we found the bonding energy to be -0.55 and -0.90 eV at the edges of the 1T' and 2H phases respectively (Figure 6d and Table S2). Our DFT calculations suggest that DMS preferentially physisorbs at both the edges and the surface sites of the 1T' MoS2 nanosheets, leading to more efficient oxidation to DMSO. We anticipate that the strong DMS adsorption in the case of the 2H phase lowers the performance and stability of the 2H phase. Our DFT calculations combined with the examination of the structure of the DMSOR demonstrate that the superior activity from the MoS2 nanosheets originates from its biomimetic structure and composition. Overall, our results reveal the superior activity of the 1T' phase toward the oxidation of organic sulfide. The activation of the MoS2 nanosheets originates from the lower binding energy of the Please do not adjust margins Please do not adjust margins DMS compared to that of platinum. The 1T' phase of MoS2 is expected to be active from both the edges and the basal planes while the active sites from the 2H phase are localized only on the basal planes due to the larger binding energy on the 2H edge sites. Further calculations of the free energy of the overall DMS oxidation reaction that would provide additional information on the reaction pathways are currently ongoing in our group, but are beyond the scope of this study. Besides the thermodynamics of the reaction, the metallic nature of the 1T' phase of MoS2 is expected to further improve the kinetics of the reaction and is responsible for the reduction of the overpotentials. Similar behavior has previously been reported in the case of the hydrogen evolution reaction on the 1T' phase of group-6 TMDs. 35 This is supported by the reduced Tafel slope of 75 mV dec -1 and the low charge transfer resistance RCT of 370 Ω.

Role of defects and crystallinity of MoS2 on the DMS oxidation

Defect engineering of MoS2 has been explored to trigger the electrocatalytic reactions such as the hydrogen evolution reaction or the splitting water. 43,44 To further understand the origin of the MoS2 activity toward the oxidation of DMS, we prepared electrodes with increasing density of defects. The defect concentration was tuned by thermally annealing MoS2 under hydrogen atmosphere at increasing temperatures in order to create point-defect vacancies (2H MoS2-Vs) and sulfur stripping defects (2H MoS2-Ss) corresponding to low and high defect densities respectively. 45 We also prepared amorphous MoS2 (A-MoSx) nanosheets grown under hydrothermal conditions in DMF (See details in Supporting Information). The structure and the composition of the MoS2 electrodes were analyzed by using Raman and XPS spectroscopy (Figure S16).

The sulfur-to-molybdenum ratios were estimated to 2.24, 1.79 and 0.63 for A-MoSx, 2H MoS2-VS and 2H MoS2-SS respectively. Figure 7a,b shows the DMS oxidation performance of the different electrodes compared with the 1T' and 2H phases of MoS2. We also estimated the electrochemically active surface area (ECSA) by measuring the electrochemical double layer capacitance. The corresponding ECSA-normalized polarization curves are presented in Figure 7c. The geometrical current density is found to be the highest for A-MoS2 along with 1T' MoS2, while the activity of the 2H phase increases with the concentration of sulfur vacancies. Conversely, JECSA sharply decreases for A-MoSx suggesting that the large geometrical current density is ascribed to the more porous or rough nature of the materials. Our results also demonstrate that the performance from defective 2H MoS2 is comparable to that of its pristine counterpart. We further calculated the binding energy of DMS on the basal plane of 1T' and 2H MoS2 with single sulfur vacancies (Figure S13, Table S2) and found that, for the same phase, the thermodynamics of the adsorption of DMS is virtually identical on defect-free MoS2 and MoS2-VS basal planes.

DMS oxidation mechanism from 1T' MoS2 nanosheets

Previous reports on the oxidation of DMS have suggested that the reaction proceeds through a one (DMSO) or two electrons (DMSO2) processes. 38,46,47 Instead, our results demonstrate that the DMS is selectively electrochemically oxidized into DMSO via a one-electron reaction on both Pt and MoS2. We anticipate that the oxidation of DMS involves the formation of a radical cation after the electron withdrawal from DMS: (𝐶𝐻 3 ) 2 𝑆 → (𝐶𝐻 3 ) 2 𝑆 •+ + 𝑒 -as proposed by Elinson and Simonet. 23 The first hint of the presence of radicals during the DMS oxidation is brought by the appearance of light-yellow color in the electrolyte in absence of oxygen during the reaction (Figure S17). Please do not adjust margins Please do not adjust margins reaction, we performed electron paramagnetic resonance (EPR) to detect the formation of sulfur radicals as reaction intermediates. The electro-oxidation of DMS was performed in the presence and in the absence of a radical trapping agent: 5,5-Dimethyl-1-pyrroline N-oxide, DMPO (See "EPR measurements" section in the Supporting Information). First, we performed the reaction in the absence of DMS and no free radical signals were detected. In the presence of DMS, clear EPR signatures are identified centered around 3510 G and the intensity of the signals increases with time (Figure 8a). The EPR measurements after 30 min revealed a six-line spectrum different from the spectrum of oxidized radical trapping agent ruling out any oxidation of DMPO. 48 The spectrum corresponds to hyperfine coupling constants of aN = 15.4 G, aH = 21 G (g = 2.0621) -close to the constants obtained when trapping 𝐶𝐻 3 𝑆 •-using DMPO: aN = 15.03 G and aH = 18 G. 49 Our EPR investigation thus points out that the oxidation of DMS involves the formation of an alkyl sulfur radical that further reacts with DMPO. The additional signals detected after 1h are attributed to the reduction of the DMPO (aN = 14.5 G, aH = 19.5 G, see details of the reaction mechanism in the Supporting Information). 50 The sulfur radical cations formed on MoS2 nanosheets thus act as a "cation pool" in the formation of DMSO as observed for other anodic oxidation reactions in electrosynthesis. 51,52 We propose that the sulfur radicals then reacts with the radical superoxide 𝑂 2 -• formed at the cathode as previously proposed for the oxidation of thioethers (Figure 8b and Figure S19). 53 To further confirm the role of oxygen in the reaction, we performed the same reaction under a flow of argon instead of oxygen. After 24 hours, the production rate of DMSO from the 1T' and 2H MoS2 nanozymes decreases from 680 and 71 L h -1 g -1 to only 213 and 38 L h -1 g -1 for the 1T' and 2H MoS2 respectively (Figure 8c). We also found that the Faradic efficiency decreased at higher applied potential (i.e. at higher current density) due to the limited concentration of O2 dissolved in the electrolyte. To generalize our approach, MoS2 nanosheets have been tested toward the oxidation of different alkyl and aryl sulfide molecules. Our investigations show that ethyl phenyl sulfide and diphenyl sulfide can be oxidized using 1T' MoS2 2D nanozymes and the onsetpotential associated with the reaction is found to increase when replacing alkyl chains for aryl groups revealing differences in term of reactivity (Figure 8d).

Conclusions

Our findings reveal the potential of phase engineered TMDs as biomimetic electrocatalysts for the electrochemical oxidation of sulfide-based molecules. We identified the exfoliated MoS2 nanosheets as efficient two-dimensional electrocatalysts for the oxidation of alkyl and aryl sulfides. Remarkably, the metallic 1T' phase of MoS2 exhibits superior activity towards the production of DMSO from DMS compared to noble metals such as platinum nanoparticles and dirhodium complexes with reduced onset potential and lower Tafel slope. By carefully estimating the density of active sites, we determined that the TOF reaches 0.87 s -1 at a potential of 1400 mV vs. NHE, 30-fold larger than for polycrystalline platinum ( 0.03 s -1 ). The reaction proceeds via one-electron transfer and the Faradaic efficiency is found to be stable for at least 24 hours. We believe that our results open avenues for novel applications of TMDs towards electrochemical-assisted synthesis of organic molecules.

Figure 1 .

 1 Figure 1. Characterization of chemically exfoliated MoS2 nanosheets. (a) Structural model of DMSO reductase enzyme. (b) Structure of the active sites of the DMSO reductase showing the molybdenum atom coordinated with two pyranopterin dithiolene ligands. Color code for the atoms: grey: C, green: Mo, yellow: S, orange: P, red: O, blue: N. (c,d) 2H and 1T' phase of MoS2 with Mo atoms in a trigonal prismatic and octahedral coordination with sulfur atoms. (e) Mixed topographic and phase image obtained by using atomic force microscopy (AFM). Inset: height profile of an individual exfoliated MoS2 nanosheet deposited on 300 nm SiO2/Si wafer. (f) Length (orange) and width (blue) distributions of the exfoliated MoS2 nanosheets measured by AFM. The Gaussian fits of the length and width distribution are shown as dashed line. (g) X-ray photoelectron spectroscopy of the Mo 3d regions of as-exfoliated and 300°C-annealed MoS2 nanosheets. The raw and the fitted data are shown with open symbols and dashed lines respectively. From the deconvolution of the raw XPS signals, the metallic 1T' polymorph composes 70% of as-exfoliated nanosheets. At the opposite, the annealed nanosheets consist in 95% of the semiconducting 2H polymorph.

3

 3 This journal is © The Royal Society of Chemistry 20xx J. Name., 2013, 00, 1-3 |Please do not adjust marginsPlease do not adjust margins

Figure 2 .

 2 Figure 2. Characterization of the MoS2 electrodes. (a) Top view of the MoS2 electrodes observed under scanning electron microscope (SEM). (b,c) Cyclic voltammetry curves of the 1T' phase (b) and the 2H phase (c) of MoS2 nanosheets deposited on glassy carbon electrodes measured at increasing scan rates from 5 to 200 mV s -1 . (d) Corresponding evolution of ∆𝐽 0.05𝑉 with the scan rates for the 1T' and 2H phase MoS2. The slope gives access to the double layer capacitance (Cdl) of the MoS2 electrodes.

Figure 3 .

 3 Figure 3. Electrocatalytic behavior of MoS2 electrodes towards the oxidation of DMS compared with reference catalysts. (a) Polarization curves of 1T' and 2H MoS2 nanosheets in presence DMS compared to platinum nanoparticles, polycrystalline platinum, palladium nanoparticles, Rh2(esp)2 and glassy carbon. Inset: Magnification of the low potential region. Scan rate: 20 mV s -1 . (b) Corresponding Tafel plots from the different MoS2 electrodes compared to platinum. The smallest values of Tafel slopes are obtained for 1T' MoS2 nanosheets with 75 mV dec -1 .

2 - 4 |

 24 Figure 2

Figure 4 .

 4 Figure 4. Comparison of the electrochemical responses from MoS2 nanosheets and platinum. (a) ECSA-normalized polarization curves for the DMS oxidation on MoS2 nanosheets and polycrystalline platinum (Pt-PolyC). Inset: Comparison between the 1T' and 2H MoS2 nanosheets with supported Pt nanoparticles (Pt-NP). (b) Nyquist plots of the 1T' and 2H MoS2 nanosheets as well as Pt nanoparticles measured at 1350 mV vs. NHE.

Figure 5 . 5

 55 Figure 5. Production ratio of DMSO and determination of the reaction efficiency. (a) NMR spectra of the electrolyte during the reaction after 4, 8 and 24 hours. The DMSO and DMS signatures are visible at 2.1 ppm and 2.5 ppm respectively. (b) DMSO production from the 1T' and 2H MoS2 electrodes compared with supported Pt nanoparticles. Inset: Production rates of DMSO for the different electrodes averaged over 24 hours. (c) Ratio: ne -: nDMSO obtained from the NMR results and

Figure 6 .

 6 Figure 6. Estimation of the electrocatalytic performance of MoS2 nanosheets towards DMSO oxidation. (a) Evolution of the mass activity (in A g -1 ) with the increase of the applied potential for 1T' and 2H MoS2 electrodes compared to 20% Pt/C. The mass activity is normalized by the faradaic efficiency. (b) Evolution of the Turnover frequency (TOF) with the onsetpotential for 1T' and 2H MoS2 nanosheets and compared to polycrystalline Pt. (c) Binding energy of DMS on the surface of MoS2 and Pt (111) as a function of the coverage fraction. (d) Comparison between

6 |

 6 Figure 6

Figure 7 .

 7 Figure 7. Electrocatalytic behavior of amorphous MoSx and defective MoS2 electrodes towards the oxidation of DMS. (a,b) Polarization curves (a) and corresponding Tafel plots (b) of the different molybdenum sulfide electrodes. Scan rate: 20 mV s -1 . (c) ECSA-normalized (JECSA) polarization curves of amorphous MoSx and defective MoS2 electrodes toward the oxidation of DMS compared to the pristine 1T' and 2H phases of MoS2. Inset: Magnification of the low potential region.

Figure 8 .

 8 Figure 8. Mechanism of the electrochemical oxidation of DMS. (a) EPR spectra from the electrolyte in presence of radical trapping agent (DMPO) with absence of DMS (black, blank experiment) and after 30 min (orange), 1 h (blue) with presence of DMS. (b) Proposed mechanism for the reaction of DMS oxidation in O2 saturated solution. (c) Comparison of the DMSO production from 1T' and 2H MoS2 in presence or absence of O2 dissolved in the electrolyte.

  Figure 8

  To further point out the role of radicals during the

	a
	-2 ) Current density (mA cm		5 10 15 20 25		0 5 A-MoS X 1T' MoS 2H MoS 2 2 2H MoS 2 -V s 2H MoS s 2 -S J (mA cm -2 )	1,2 Pt. (V	vs.	1,4 NHE)
			0
			0,6	0,8		1,0	1,2	1,4	1,6
					Potential	(V	vs.	NHE)
	b
		1.6
	Potential (V vs. NHE)	1.3 1.4 1.5	1T' MoS 2 2H MoS 2		2H MoS 2 -S A-MoS 2 2H MoS 2 -V	S S
		1.2
			0.1			1	10
					Current		density	(mA	cm -2 Geom )
	c
	) -2 Current density (mA cm	0 1 2		0.0 0.3 0.6 A-MoS X -2 ) 1T MoS 2 2H MoS 2 2H MoS 2 -S s 2H MoS 2 -V s J (mA cm	1.2 Pot. (V vs. NHE) 1.4
			0.6 0.8 1.0 1.2 1.4 1.6
					Potential (V vs. NHE)

This journal is © The Royal Society of Chemistry 20xx J. Name., 2013, 00, 1-3 | 7

Acknowledgements D.V., L.M. and K.Q. acknowledge funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 804320). D.V. and Z.Q. acknowledge financial support from the US Army RDECom Grant N°W911NF-17-2-0033. H.E.M. acknowledges the French embassy in Egypt. N.O. thanks The Hong Kong Polytechnic University and the department of Applied Physics for the computational resources. L.L. acknowledges National Natural Science Foundation of China (21978111) and Zhejiang Provincial Natural Science Foundation of China (LY19B030005).

Conflicts of interest

There are no conflicts to declare.


J Bourgalais

O Durif

S D Le Picard

P Lavvas

F Calvo

S J Klippenstein

L Biennier
email: ludovic.biennier@univ-rennes1.fr

Propane Clusters in Titan's Lower Atmosphere: Insights from a Combined Theory/Laboratory Study

Keywords: planets and satellites: atmospheres, planets and satellites: individual: Titan, molecular processes

In spite of the considerable advances made by Cassini-Huygens in our understanding of Titan, many questions endure. In particular, the detailed processes that lead to the formation of haze aerosols in Titan's atmosphere, found in high concentrations at low altitudes, are not well identified. Hydrocarbons, which are abundant constituents of Titan's cold atmosphere originating from photochemical processes, may simultaneously condense on the surface of existing aerosols, nucleate and grow to generate new aerosol seeds. The relative importance of the various processes depends on several factors, including the saturation ratio. The dynamics of hydrocarbon condensation and nucleation in Titan's atmosphere remains poorly known. Aiming to progress on these issues, we investigate here the kinetics of propane dimer formation at low temperature through state-of-the-art laboratory experiments combined with theoretical calculations. Our results provide an estimate of the rate coefficients, which are then employed to evaluate the abundance of propane dimers in the lower atmosphere of Titan. The mixing ratios of propane dimers inferred, with a maximum abundance of 10 cm -3 near 100 km, is found to be under the detection limit of the Composite Infrared Spectrometer (CIRS) of the Cassini spacecraft. Based on our results, homogeneous nucleation of the most abundant species appears not to be relevant for the growth of aerosols. Future studies should focus on homogeneous nucleation of polar molecules or alternatively on heterogeneous processes, which are usually more efficient.

INTRODUCTION

A large variety of van der Waals complexes, in which molecules are bound by intermolecular dispersion forces, is expected in planetary atmospheres. The presence of such molecular complexes can affect both chemistry and climate, as the optical properties and reaction dynamics of the constituent monomers are altered by the intermolecular interactions at play (Vaida et al. 2003;Daniel et al. 2004). In particular, dimers as well as any other form of molecular structures whose interaction leads to symmetry breaking of isolated molecules, may cause an excess absorption and therefore play, a significant role in the greenhouse effect (Vigasin & Mokhov 2017). The first extraterrestrial dimer detected was H2-H2 in Jupiter's upper atmosphere at 120 K and in Saturn's atmosphere at 85 K, by Frommhold et al. (1984). In addition to their own role on radiative transfer in planetary atmospheres, the formation of molecular dimers is also believed to be the critical step for the onset production of larger clusters (Vehkamäki & Riipinen 2012) whose detailed growth processes are still relatively unknown. This was recently demonstrated in a kinetic study of water cluster formation at low temperature (Bourgalais et al. 2016). Such quantitative information is important for investigating condensation processes in cold planetary atmospheres through nucleation of molecular building blocks. Various theoretical methods were developed to estimate nucleation rates in order to characterize molecular growth. They are usually based either on thermodynamic (Diemand et al. 2013) or molecular (Schenter et al. 1999) approaches.

At the molecular level, nucleation is considered as a multistep process resulting from successive monomer addition reactions. Absolute nucleation rate predictions require rates for each elementary reaction step. However, detailed investigations of these elementary steps are scarce, essentially because such experimental measurements are challenging. A few works were devoted to a quantitative estimation of the formation kinetics of dimers, including benzene C6H6 [START_REF] Hamon | [END_REF] using laser-induced fluorescence, anthracene C14H10 (Biennier et al. 2011) and pyrene C16H10 (Sabbah et al. 2010) using photoionization at 157 nm coupled to mass spectrometry, and, more recently, water vapor (Bourgalais et al. 2016) using electron impact ionization coupled to mass spectrometry. All these experiments employed the so-called CRESU (French acronym standing for Kinetics of Reactions in Supersonic Uniform Flows) technique to generate continuous cold uniform supersonic flows through de Laval nozzles. Another approach for investigating cluster formation at low temperatures was adopted by Signorell and coworkers, using pulsed cold supersonic flows generated by de Laval nozzles, in which time evolution of propane (Ferreiro et al. 2016), toluene (Chakrabarty et al. 2017) and water [START_REF] Lippe | [END_REF] cluster distributions were monitored at temperatures ranging from 42 to 56 K for propane, 48 to 77 K for toluene, and at 47 and 87 K for water. In these studies, the evolution of cluster sizes was derived from mass spectrometry ion signals following single photon ionization at 118 nm (13.8 eV). Such detailed observations are valuable to understand the mechanisms involved in the growth of clusters. They notably allow the critical cluster size range for nucleation to be determined. Yet they require molecular-level simulations for more detailed and quantitative information to be extracted on the growth mechanisms, and do not provide any quantitative information on the rate coefficients of formation of dimers or larger clusters.

The formation of dimers and their subsequent growth into larger clusters is of particular interest for Titan's atmosphere, where a rich organic inventory, as well as thick organic hazes are observed (Vuitton et al. 2019;[START_REF] West | Titan Haze[END_REF]. Organic dimers may form in this atmosphere, however, no study thus far has attempted to evaluate the abundance and potential impact of such components. Cassini IR observations do reveal features that have not been interpreted by regular gas molecules but are considered to be an unknown condensate (Anderson & Samuelson 2011;Jennings et al. 2015), and their potential interpretation through dimer formation needs to be evaluated. Moreover, as temperature decreases rapidly in Titan's lower atmosphere, most of the formed photochemical products condense below ∼150 km, suggesting that larger clusters should readily form. However, this homogeneous nucleation mechanism would have to compete with the typically faster heterogeneous nucleation on the surface of the haze particles (Lavvas et al. 2011), and it is important to evaluate if cluster formation can provide a significant additional component to the haze population. Although the details of haze formation are unknown, it is well-established that ion-neutral chemical reactions in Titan's upper atmosphere allow for the rapid formation of macromolecules that subsequently nucleate, thus initiating the haze formation (Waite et al. 2007;Lavvas et al. 2013). If cluster formation can proceed fast enough to compete with the heterogeneous nucleation on the surface of the falling haze particles, then an additional formation mechanism has to be considered in the microphysics models of Titan's haze (Lavvas et al. 2010;[START_REF] Rannou | [END_REF].

In this study we experimentally investigate the formation kinetics of propane dimers at 23, 36 and 49 K, and use the derived rate coefficients to calculate the association and evaporation rates in order to estimate the abundance of propane dimers in Titan's lower atmosphere. Propane, originating from the methane photochemistry (Vuitton et al. 2019) is of special interest as it is at the crossroad of mass and abundance: smaller mass photochemical products (e.g. ethane) are more abundant but their binding energy would be too weak to support the formation of dimers at the conditions under investigation, while larger mass photochemical products (e.g. C4H10) are less abundant. Nitrile species are also produced in Titan's atmosphere (e.g. HCN, HC3N, etc) and could more efficiently form dimers due to their polar nature. This could be the subject of future studies.

The experimental methods are described in Section 2. In Section 3 the various processes through which the propane clusters go before being detected in their ionized form in the present experiments are investigated in order to give a representative picture of the neutral clusters distribution in the cold supersonic flows. Estimated dimerization rate coefficients are given and discussed in Section 4. Theoretical determination of association and dissociation rate coefficients and their comparison with experimental data are presented in Section 5. In Section 6, the results are implemented in a photochemical model to perform a detailed evaluation of the dimer abundance in the low (< 200 km) atmosphere of Titan. Our conclusions are finally given in Section 7.

EXPERIMENTAL METHODS

Laboratory experiments were carried out using a CRESU machine developed in Rennes (Dupeyrat et al. 1985). The CRESU method has been previously employed to investigate the kinetics of homogeneous nucleation of condensable species [START_REF] Hamon | [END_REF]Sabbah et al. 2010;Bourgalais et al. 2016) and only a brief overview with some details specific to this study are outlined here. A comprehensive description of the current setup is provided in the Supporting Information of Bourgalais et al. (2016). In this work, we have explored the formation of propane clusters in cold and dense uniform supersonic helium flows, in which a small (< 1% of total flow density) and controllable amount of propane was introduced. Three different Laval nozzles with temperature, density and pressure characteristics given in Table 1, were employed to cover the 23-49 K temperature range. The time evolution of the propane cluster densities in the flow was monitored by coupling the CRESU reactor with a time-of-flight mass spectrometer combined with an electron gun to ionize the clusters in an intermediate low-pressure chamber. Electron impact ionization and the detection of the propane clusters are discussed below. 1. Experimental conditions for the three supersonic uniform flows used in this work; tmax corresponds to the flow hydrodynamic time. The errors on the temperature, the total flow density and the pressure chamber are under 5% at the level of the two standard deviations from the mean and are calculated from separate measurements of the impact pressure using a Pitot tube as a function of distance from the Laval nozzle.

IONIZATION AND DETECTION OF PROPANE CLUSTERS

Sampling, ionization and mass-selective detection

After a controllable reaction time, the cold and thermalized uniform flow is sampled to generate a molecular beam in which reactions are essentially stopped since the mean duration between successive collisions soars up to the microsecond scale. Propane clusters formed in the molecular beam are submitted to a transverse flux of 70 eV electrons, leading to a fraction of them being ionized. Immediately after ionization, the charged species are guided into the extraction zone after a short travel time that depends on their mass (∼ (m/amu) 1/2 microseconds). From there the clusters are injected into the flight tube where they fly for tens of microseconds before impacting a multichannel plates detector.

Impacting ions lead to a signal that is related to the ion population. The cluster content of the flow is inferred from the analysis of the mass spectra, which provide an image of the cluster population albeit with some distortion. Cluster ions are visible on mass spectra of He flows seeded with propane, as displayed for instance in Fig. 1 for the low temperature of 23 K. At short flight times, i.e. below 15 µs, the mass spectra show two groups of peaks assigned to C2 and C3 hydrocarbons. This mass pattern originates from sequential decay reactions of ionized propane (e.g. C3H + 8 -→ C3H + 7 , etc.). At longer flight times, the mass spectra reveal a series of peaks that are assigned to stoichiometric propane clusters, i.e. of the (C3H8)n type. In order to reconstruct a faithful image of the neutral clusters distribution, it is necessary to identify and quantify the respective importance of the various possible processes that they go through before being detected in ionized form.

Dynamical aspects and fragmentation pattern

Various aspects of the fragmentation dynamics of ionized molecular clusters have been explored in the past, in particular for propane (Foltin et al. 1992), but many pieces of the puzzle are still missing. We provide below some elements on the the energetics and the dynamics of the processes involved.

Energy deposition in the dimer following ionization

For a neutral propane cluster, the sequence starts with electron impact ionization:

(C3H8)n + e --→ (C3H8)n + * + e -+ e - (1)
Ionization itself occurs extremely fast upon electron impact as the time needed for an electron of 70 eV to travel 1 Å through a molecule is only about 2 ×10 -17 s. The molecule being hit by the electron can be considered to be at rest because its thermal velocity of a few hundreds of m•s -1 is negligible compared to the speed of the electron rushing through [START_REF] Gross | Mass spectrometry: a textbook[END_REF]). In terms of energetics, firstly only a fraction of the energy of the impinging electron will contribute to ionize and heat the cluster as most of it is carried away with the electron itself after the collision. Secondly, the ionization process will take away the amount of energy corresponding to the adiabatic ionization potential of the dimer, which is 10.7 eV (See Sec. 3.2.2). Then, the minimum amount of excess energy remaining in the cationic dimer following ionization of the neutral dimer can be evaluated by performing electronic structure calculations. A realistic geometry for the neutral dimer was first obtained from classical simulations using the Amber ff94 force field. Density-functional theory calculations were then carried out using the double hybrid functional M06-2X and the aug-cc-pVDZ basis set for the cation in the doublet state, followed by a local optimization. The absolute vertical and adiabatic energies thus obtained are -237.7450 and -237.7745 Hartree, or a difference exceeding 0.8 eV or 18 kcal/mol. Qualitatively, this sets a lower bound to the excess energy deposited in the cationic cluster. Weak intermolecular energies and any moderate redistribution will facilitate the evaporation of individual monomers, possibly before statistical equilibrium is established (Abdoul-Carime et al. 2015). The observation of stoichiometric cationic propane clusters in the mass spectra thus suggests that monomer evaporation is an important decay channel after ionization, even if a fraction of the energy deposited is sufficient to induce intramolecular covalent bond breaking. The energy deposited in the clusters that do not undergo intramolecular dissociation can be roughly evaluated as not exceeding a few eV per molecule. Those findings are in agreement with recent studies of Irikura (2017) which combined experimental breakdown data from photoelectron-photoion-coincidence measurements and the Binary-Encounter Bethe (BEB) theory. These authors found that for tetrahydrofuran C4H8O and methane CH4 the energy deposited by energetic electrons (> 25 eV) was below 20 eV. Assuming a complete relaxation to the electronic ground state of the ion and taking into account the adiabatic ionization energy, a corresponding energy deposited under 5 eV as vibrational excitation was estimated.

Dissociation lifetime of the cationic dimer

The structure of the cationic monomer was presumed to be that obtained by relaxation from the neutral geometry. The structure of the dimer cation was obtained via random sampling over the relative orientations of the two monomers. Higher level energies were determined from single point CCSD(T)-F12/cc-pVTZ-F12 calculations (Knizia et al. 2009;Peterson et al. 2008) at the MP2/cc-pVTZ optimized geometries. The CCSD(T)-F12/cc-pVTZ-F12//MP2cc-pVTZ calculated zero-point corrected binding energy for the cationic dimer is -11.30 kcal/mol. The corresponding adiabatic ionization energies for the monomer and dimer are 11.0 and 10.7 eV, respectively. The microcanonical dissociation rate coefficient for the cationic dimer was predicted with RRKM theory. The longrange transition state flux was evaluated with VRC-TST (Klippenstein 1992) employing direct MP2/cc-pVDZ determinations of the interaction energies. The reaction coordinate was presumed to be the distance between the two centers-of-mass. Rigid-rotor harmonic-oscillator (RRHO) approximations were used in the evaluation of the state density, but with one torsional mode treated as a free rotor. Such RRHO assumptions may introduce modest errors in the predicted rate (e.g., a factor of 3), but the predicted magnitude and energy dependence of the dissociation rate should be at least qualitatively correct. The high internal energy of the cluster leads to the rapid evaporation of a monomer, which is the lowest energy dissociation channel. According to calculations performed for the dimer, displayed in Fig. 2, evaporation will proceed very fast, on the ps time scale, as the estimated internal energy (a few eV) is off the chart. We will assume here as a reasonable hypothesis that only one monomer is evaporated after ionisation under the accessible laboratory time frame (a few tens of microseconds). For clusters larger than the dimer (n ≥ 3) this means that the (C3H + 8 )n-1 ion images the (C3H8)n neutral population (cf. Figure 3).

Fragmentation pathways of the cationic dimer

The key question is then to distinguish the monomer ion fragments (C2H +

x , C3H + y ) tracing the neutral monomer C3H8 from those tracing the dimer (C3H8)2. As far as we are aware, no electron-impact ionization mass spectrum for the propane dimer (C3H8)2 is available in the literature. Fortunately some clues can be gathered from the monomer studies. In the 70-eV electron impact ionisation mass spectrum of the propane monomer, the two-carbon group dominates over the three-carbon group, with the C2H + 5 ion being the most abundant fragment (Linstrom & Mallard 2005). As was discussed at length above, the fragmentation pattern is tightly linked to the internal energy of the ion, and therefore to the impacting electron energy. The energy left in the remaining ionized monomer after evaporation of one unit from the dimer (secondary product) is lower than the energy deposited in the monomer directly, at least by an amount corresponding to the dissociation energy (a few kcal/mol). Consequently, the fragmentation pattern is likely to differ. In particular, the lower internal energy is expected to change the branching into the various exit channels (Chupka & Kaminsky 1961). In the study of Denifl et al. (2005) it was shown that it requires more energy to form C2H + 5 and C2H + 4 than C3H + 7 via electron impact ionization of neutral propane. Accordingly, the distribution of the fragments is expected to shift towards the C3 group as the internal energy decreases (cf. Fig. 4).

The earlier investigation of Buck et al. (1988) on electron impact induced fragmentation of size selected ethylene clusters (C2H4)n at an electron energy of 100 eV hints towards such a behavior. In that work, the dimer (C2H4)2 shows a fragmentation pattern in which the product size distribution is clearly shifted towards the higher masses of the C2 group with e.g. the absence of C2H. In our experiments, the C3/(C2+C3) ratio derived from the mass spectra for different initial propane concentrations is not constant (Fig. 5) but appears to scale with propane concentration and is affected by the presence of cluster ions. Propane dimers are likely to be the main source of the excess of C3 hydrocarbon ions. In the work of Buck et al. (1988) on ethylene clusters, the trimer and tetramer also produced some C2 ions, however this channel amounts to a branching ratio of at most 46%, which contrasts with a value of 89% for the dimer. Here, the first stages of nucleation are probed on the microsecond time scale and at low initial propane fractions. As a result, the size distribution is tilted towards low masses. By considering that in our case too, the fragmentation after evaporation will be limited to successive H loss channel (leading to C3 hydrocarbons) with marginal C loss channel (decomposing into C2 hydrocarbons), the dimer fraction defined by:

ζ = [(C3H8)2] [C3H8] (2)
can then be in principle expressed as:

ζ(t) C3 C3 + C2 (t) n n min →0 • σ C 3 H 8 i σ (C 3 H 8 ) 2 i (3)
where n is the propane concentration, C2 and C3 represent the ion signals into the respective channels, σi the ionisation cross sections, and

C3 C3 + C2 n n min →0
(4) the difference between the ratio at a given propane concentration n and at the lowest measured concentration nmin for which a signal can still be extracted, but in which aggregation is absent. Following the work of Deutsch et al. (2000) on small size clusters, we adopt an additivity rule in which the electron impact ionization cross section of the neutral cluster of size m is about m times that of the neutral monomer:

σ (C 3 H 8 )m i = m • σ C 3 H 8 i (5)
Unfortunately, the extraction of the dimer fraction rests on a non-background-free approach. As a consequence the associated noise gets very high and, in practice and despite our efforts, it should be considered as a qualitative tracer.

DIMER FORMATION RATE COEFFICIENT

The first step of these experiments was to determine the onset of propane nucleation. For this purpose, the time profile of the propane monomer concentration [C3H8](t) was plotted at each flow temperature employed and for different initial densities (see Fig. 6 for an example at 23 K). At low initial propane monomer concentrations [C3H8](t = 0), no cluster ion peaks are seen and [C3H8](t) is constant along the reaction time, indicating the absence of nucleation. When the initial concentration [C3H8](t = 0) increases, the propane monomer time profile [C3H8](t) decays with time with a rate that scales with the initial concentration. This loss of monomer is due to the onset of propane nucleation. Cluster formation is initiated by dimerization, which is considered as a critical step conditioning the growth of clusters (Bourgalais et al. 2016;Vehkamäki & Riipinen 2012). Once formed, dimers go on to react rapidly with others monomers to form trimers and larger oligomers, as evidenced by mass spectra shown in Fig. 1. The onset of propane nucleation was obtained over the narrow range of 23-49 K under our experimental conditions, but not above, due to the limited initial reactant concentration (below 1%) allowed to maintain the uniformity of CRESU flows. Our measurements are also constrained by the short flow hydrodynamic time (100-200 µs). The propane dimer grows from monomers, stabilized notably through collisions with He atoms to evacuate the energy acquired during the formation of the pair. The whole process can be summarised as:

C3H8 + C3H8 k 1,1 --→ (C3H8)2 (6)
which can be generalized for larger clusters to:

(C3H8)i + (C3H8)n+1-i k i,n+1-i ------→ (C3H8)n+1 (7)
From the listed reactions and considering the growth to be irreversible, we can write down the equations which govern the time evolution of the various species. In the most general way for the n th cluster:

d[(C3H8) n ] dt = i≤ n 2 ki,n-i[(C3H8) i ][(C3H8) n-i ] - i≥1 (δn,i + 1) kn,i[(C3H8) n ][(C3H8) i ] (8)
where δn,i is the Kronecker symbol. Basically, the first term is a production term, coming from smaller molecules while the second term is a consumption term forming larger clusters. For instance, the differential equation governing the evolution of the monomer is written:

d[C3H8] dt = - i≥1 (δ1,i + 1) k1,i[C3H8][(C3H8) i ] (9)
which gathers only loss terms. We go on with a similar equation for the dimer:

d[(C3H8)2] dt = +k1,1[C3H8] 2 - i≥1 (δ2,i + 1) k2,i[(C3H8)2][(C3H8) i ] (10) T k 1,1 [C 3 H 8 ] 0 [He] ζ (K)
(10 -13 cm 3 s -1 ) (10 14 cm -3 ) (10 16 cm -3 ) 22.9 2 -10 and for the trimer:

d[(C3H8)3] dt = +k1,2[C3H8][(C3H8)2] - i≥1 k3,i[(C3H8)3][(C3H8) i ] ( 11
)
From there, we build a simple kinetic model with the above equations to reproduce the time evolution of the clusters up to the tetramer. The ultimate objective is to derive the k1,1 reaction rate, which can be considered at low temperature as the nucleation bottleneck, i.e. the rate governing the kinetics of the whole process since it is the slowest. The procedure consists in numerically solving a set of four coupled differential equations. The dimer time evolution is considered only qualitatively as the non-background-free method employed to extract the data (see Sec. 3.2.3) leads to strong uncertainties. In spite of this missing piece of information, the output data remain consistent and robust. Ingredients in the model are kept simple. The rates ki,j for forming clusters larger than i + j ≥ 4 are allowed to only vary in a 3-5×10 -10 cm 3 s -1 window for all flow temperatures considered. In addition, the inequality k1,1 < k1,2 < k1,3 is enforced since adding a monomer to a dimer (trimer) is more efficient than adding a monomer to a monomer (dimer). The calculated time-evolutions obtained with the model are displayed in Fig. 7 for an He flow at 22.9 K and for an initial monomer concentration [C3H8](t = 0) = 2.63×10 14 cm -3 as an illustration. The set of results for the dimerization rate coefficient k1,1 are gathered in Table 2. The derived rates exhibit large uncertainties with typically a factor of 5 between the lowest and the highest values. They nevertheless provide reasonable orders or magnitude.

THEORETICAL EVALUATION OF ASSOCIATION AND DISSOCIATION RATES

The rovibrational properties of the reactants and the complexes were determined at the MP2/cc-pVTZ level. For the dimer complex, the optimized structure was again obtained by further optimizing the lowest energy geometry obtained in a random sampling over interfragment orientations. Higher level energies were determined from single point CCSD(T)-F12/cc-pVTZ-F12 calculations at the MP2/cc-pVTZ optimized geometries. The zero-point corrected dimer binding energy is predicted to be -1.33 kcal/mol. Thermal kinetic predictions were obtained from a master equation treatment implementing VRC-TST fluxes for the transition states, simple rigid rotor harmonic oscillator estimates for the partition functions and state densities of the complexes, Lennard-Jones collision cross sections, and exponential down energy transfer probabilities. The long-range transition state flux was evaluated with VRC-TST (Klippenstein 1992) employing direct MP2/cc-pVTZ determinations of the interaction energies. The reaction coordinate was presumed to be the distance between the two centersof-mass. The lack of prior studies of the effective size for a van der Waals dimer (here the Lennard Jones collision cross section is estimated from σ dimer =10 Å, ε dimer =400 cm -1 and σHe=2.55 Å , εHe=7 cm -1 ), and of the temperature dependence of the average downwards energy transfer at low temperatures [here set as 200 (T /298 K) 0.5 cm -1 ], leads to considerable ambiguity in the final rate estimates. Finally, we employ a correction factor of 3.3 to account for anharmonicities on the vibrational density of states for the complex, with this last factor obtained from a fit to experimental data. While all these values are reasonable, their ambiguity leads to significant uncertainties in the final rate estimates (e.g., perhaps a factor of 4 or more). Despite the aforementioned limitations, as seen in Fig. 8, this master equation-based model is able to quantitatively reproduce the full set of experimental observations, which lends some credence to both the theoretical model and the experimental analysis.

PROPANE DIMER FORMATION IN TITAN'S LOWER ATMOSPHERE

In Titan's atmosphere, Cassini observations reveal that the highest propane density lies between 100 and 150 km, before the onset of condensation at lower altitudes (Vinatier et al. 2010). Therefore, we anticipate that the propane dimer density will be maximum near this range as well. The local atmospheric conditions (∼ 120-170 K, 1-10 mbar) at this altitude range are different from those for the retrieved as- sociation and dissociation rates, thus an extrapolation in temperature is required. Moreover, in order to evaluate the dimer population with a photochemical model we need to transform the above derived rates into a temperature-and pressure-dependent form that will allow to represent the dimer formation and loss rates at all required conditions. For the association reaction we use the standard Troe formula (Troe 1979) where the reaction rate at temperature T and atmospheric density [M] is described as:

k(T, [M]) = k0[M] 1 + k0[M]/k∞ F (1+log(k 0 [M]/k∞) 2 ) -1 c (12) with k0[cm 6 s -1 ] = 10 -25 T K -3.31
exp(-14.5 K/T ) (13)

for the low pressure limit, k∞[cm 3 s -1 ] = 1.9 × 10 -10 T K 0.146 exp(-2.1 K/T ) (14)

for the high pressure limit, and Fc = 0.4. For the dissociation rate we use the formula:

k diss = k δ [M] (15) with k δ [cm 3 s -1 ] = 7839 T K -5.27
exp(-765.9 K/T ) ( 16)

to describe the dimer dissociation rate at different conditions. We use these rates in a photochemical model to evaluate the abundance of propane dimers (Lavvas et al. 2008a,b). The model solves the continuity equation for the main hydrocarbon species, taking into account atmospheric mixing and molecular diffusion, as well as the condensation of the species once their individual saturation limits are reached. The model is updated with the latest chemical networks for Titan's atmosphere from Vuitton et al. (2019) where further information for the processes leading to the formation of C3H8 and other photochemical products in Titan's atmospheres can be found. Our simulated propane mixing ratio (Fig. 10) is consistent with the Cassini/CIRS observations in the lower atmosphere (Vinatier et al. 2010), which reveal a quasi-constant mixing ratio of ∼10 -6 . Our simulated profile rapidly decreases below 100 km altitude as the local drop in Titan's atmospheric temperature leads to the rapid condensation of most photochemical products, including propane. In these calculations, condensational loss is treated in terms of the super-saturation of each species evaluated based on the saturation vapour pressure of each gas at the temperature of each altitude, i.e. the system relaxes to the saturation limit of each component (Lavvas et al. 2008a).

At these conditions, our calculations demonstrate that the corresponding (C3H8)2 mixing ratio remains small at all altitudes and reaches a maximum mixing ratio of ∼10 -17 near 100 km (Fig. 10). At lower altitudes the condensation loss of propane monomers limits the abundance of dimers. This abundance, corresponding to a maximum density of ∼10 dimers cm -3 , is too small to be detected in the Cassini/CIRS data. Although the detection limit of each species can vary depending on its spectroscopic properties, a typical mixing ratio detection limit for the latter instrument is at the ppb (10 -9 ) range (Nixon et al. 2010). Therefore we can conclude that propane dimers will not have significant implication in the radiation transfer in Titan's atmosphere considering their predicted low abundance.

The population of dimers before the onset of condensation constrains the population of nuclei that will rapidly grow to larger clusters once super-saturation conditions are reached. Our simulated density of dimers is larger than the density of haze particles in Titan's lower atmosphere (∼1cm -3 according to Tomasko et al. 2008;Doose et al. 2016). However, we need to consider that heterogeneous nucleation is faster than homogeneous nucleation. Classical nucleation theory [START_REF] Pruppacher | Microphysics of Clouds and Precipitation[END_REF] indicates that at the conditions under investigation heterogeneous nucleation is many orders of magnitude more efficient than homogeneous nucleation (Fig. 11). Our calculations suggest that irrespective of the particle size (in the range of 0.1-1 µm) and for various values of the contact angle between the propane condensate and the haze particle surface, heterogeneous nucleation starts at super-saturation values that are more than 50 times lower than the super-saturation required for the onset of homogeneous nucleation (∼nucleation rate of 1 cm -3 s -1 ). The simulations show that the higher abundance of dimers compared to haze particles will not compensate for the difference in the rates of the two mechanisms and that propane molecules will more efficiently condense on the surface of the falling haze particles than form new pure-condensate particles.

CONCLUDING REMARKS

Owing to a diversity of processes occuring simultaneously, the chemical and physical pathways leading to the formation and growth of particles in Titan's low atmosphere provide a wide open field of investigation. In this study we considered the propensity of propane to form homogeneous clusters through nucleation. Our work was motivated by the large abundance of neutral hydrocarbons in Titan's atmosphere and their high level of saturation. Propane, initially detected and identified in Titan's atmosphere after the Voyager 1 flyby (Hanel et al. 1981;Maguire et al. 1981) shows a constant uniform abundance at the ppm level throughout the stratosphere in recent analyses (Vinatier et al. 2015;Coustenis et al. 2018;Lombardo et al. 2019). The results of the photochemical model used in this study display a consistent maximum of 10 -6 in the stratospheric mixing ratio above 100 km. Below this altitude, the abundance starts to decrease drastically due to the expected onset of propane condensation (Lavvas et al. 2011). The model output predicts a maximum propane dimer density near 100 km but below the ppb detection limit of the CIRS instrument. Moreover, the difference between the monomer and the dimer mixing ratios is quite significant (∼10 orders of magnitude around 60 km) and shows that condensates coming from homogeneous nucleation of the most abundant alkanes appear to be irrelevant for the formation of new particles, while the possible implications of dimer formation on the atmospheric properties seems negligible. However those investigations should be extended to other abundant species that carry dipoles, often N-bearing atoms, which could thus form stronger intermolecular bonds.

The current work has also exposed some limits of electron-impact ionization mass spectrometry for the study of quantitative cluster formation in the case of multiple overlapping ionization product channels. We were in particular unable to identify a reliable tracer of the dimer, but had to rely on a number of assumptions (evaporation pattern, ionization cross sections...), and the derived rates were tainted with large uncertainty. Future studies will be performed with a tunable photon energy source (provided e.g. by synchrotron radiation) for threshold ionisation to limit evaporation and fragmentation. Such an experiment combining uniform supersonic flows and time-of flight mass spectrometry with photoionization, dubbed CRESUSOL, has recently been designed and is now operational.

Figure 1 .

 1 Figure 1. Time-of-flight mass spectra of helium uniform flow at 23 K seeded with propane with an initial density of 3.22 × 10 14 cm -3 and for different reaction times in the 0-90 µs window.

Figure 2 .

 2 Figure 2. Calculated absolute evaporation rate (i.e. loss of a monomer) vs. excess energy for the cationic propane dimer (C 3 H 8 ) + 2 .

Figure 3 .

 3 Figure 3. Dissociation dynamics of propane clusters (C 3 H 8 )n following electron impact ionization.

Figure 4 .

 4 Figure 4. Fragmentation pathways for a propane molecule and a propane dimer ionized by an energetic electron

Figure 5 .

 5 Figure 5. Evolution of the fragmentation pattern as indirect evidence of the presence of dimers. The experimental C 3 /(C 2 +C 3 ) ratio shows some dependence on the flow temperature and initial propane fraction for reaction times above 40 µs. The dimer fraction ζ can be derived from the C 3 /(C 2 +C 3 ) ratio assuming that the change in this ratio is mainly assigned to dimer fragments.

Figure 6 .

 6 Figure 6. Propane monomer density vs time in a 22.9 K flow derived from time-of-flight mass spectrometry measurements. The He flow density is 4.75×10 16 cm -3 . For initial propane fractions exceeding 0.5%, the monomer signal decays with time as monomers are consumed at the benefit of clusters.

Figure 7 .

 7 Figure 7. Calculated and experimentally measured time evolution of propane monomer and small clusters up to tetramer (n = 4). Flow conditions: T = 22.9 K and [He]=4.75 ×10 16 cm -3 . Intial propane monomer density: 2.63×10 14 cm -3 . The calculated and measured monomer signals (n = 1) have been scaled for illustrative purpose by a factor of 0.01. Only the calculated profile is displayed for the dimer (n = 2) as the time evolution derived from experiments remains qualitative (see Sec. 3.2.3).

Figure 8 .

 8 Figure 8. Calculated and experimental C 3 H 8 + C 3 H 8 association rates vs. temperature and pressure.

Figure 9 .

 9 Figure 9. Calculated (C 3 H 8 ) 2 → C 3 H 8 + C 3 H 8 dissociation rates vs. temperature and pressure.

Figure 10 .

 10 Figure 10. Simulated propane C 3 H 8 and propane dimer (C 3 H 8 ) 2 abundances in Titan's lower atmosphere. Black lines represent the mixing ratios and blue lines the corresponding number densities of each component. The gray and black curves with error bars correspond to the retrieved C 3 H 8 stratospheric abundance from Cassini observations at mid latitudes (30N and 39N, respectively, from Vinatier et al. 2010), which are more representative of our disk-averaged simulations.

Figure 11 .

 11 Figure 11. Predictions of classical nucleation theory for the homogeneous (black line) and heterogeneous (red and blue lines) nucleation rates of C 3 H 8 . Different colours present evaluations of heterogeneous nucleation rates at different radius spherical particles, while different broken lines reveal the dependence of the heterogeneous rate on the contact angle between the condensate and the substrate.

Table

	T /K	[He]/10 16 cm -3	p/mbar	tmax/µs
	22.9	4.75	0.18	103
	36.1	5.26	0.29	140
	49.1	10.45	0.78	92

Table 2 .

 2 Experimental rate coefficients for the dimerization of propane monomer at temperatures between 23 and 49 K derived from a kinetic model. ζ denotes the maximum calculated dimer fraction.

			1.73 -2.63	4.75	0.09
	36.1	0.7 -3.5	2.17	5.26	0.008
	49.1	0.2 -1	6.55	10.45	0.002

c 2019 The Authors

MNRAS 000, 1-10 (2019)

This paper has been typeset from a T E X/L A T E X file prepared by the author.MNRAS 000, 1-10 (2019)

ACKNOWLEDGEMENTS This work was supported by the CNRS-INSU Programme National de Planétologie (PNP). LB thanks Paul Scheier and Musahid Ahmed for helpful discussions regarding the ionized cluster fragmentation dynamics. The contribution from SJK is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences under Contract No. DE-AC02-06CH11357 (BES Gas Phase Chemical Physics Core Program).