J Boffelli

F Gauchet

D O Kashinski

D Talbi

A P Hickman

K Chakrabarti

E Bron

A Orbán

J Zs

Mezei

I F Schneider

Population of ground and lowest excited states of Sulfur via the dissociative recombination of SH + in the diffuse interstellar medium

Keywords: numbers: 33, 80, -b, 42, 50, Hz

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

SH + (sulfoniumylidene or sulfanylium) is ubiquitous in the Interstellar Medium (ISM). It has been detected in emission in W3 IRS 5, a region of high-mass star formation [1], in absorption in the diffuse interstellar medium, towards various distant star-forming regions [2,3] and in emission in the Orion Bar, a typical high UV-illumination warm and dense photon-dominated region (PDR) [4].

Thanks to this ubiquity, the SH + ion provides unique physical and chemical constraints on models that are applied to the environments where it is observed. SH + is suggested to form from the reaction of atomic S + with H 2 . However this reaction is highly endothermic by 0.86 eV (9860 K). To overcome this endothermicity in the diffuse ISM, turbulent dissipation, shocks, or shears are invoked. As a consequence, SH + is suggested as an important probe of turbulence [3,5] of the diffuse ISM. In photon dominated region where H 2 is vibrationally excited, it is suggested that this excess of vibrational energy allows the formation of SH + from S + and H 2 [6], providing information on the temperature of such environments. However, for SH + to be used as a tracer of the physical conditions of the media where it is observed, its chemistry needs to be known in detail and in particular its destruction mechanisms. SH + does not react quickly with H 2 [7] the most abundant interstellar molecule due to the endothermicity of the reaction, and therefore it is not severely depleted through this reaction. It is therefore considered that dissociative recombination (DR) of this ion with electrons (eq. ( 1)) is an efficient destruction pathway, and a rate constant of 10 -6 cm 3 •s -1 is assigned to this reaction in the KIDA and UMIST astrochemical data bases [8,9]. To validate this assumption we have started few years ago an extensive and accurate study of the DR of SH + using methods of theoretical chemistry and quantum dynamics [10]. The large variety of theoretical studies undertaken on SH + as well as on SH can be found in our previous papers [10,11].

In the present article, we aim to increase the accuracy of our previous computations [10] on the dissociative recombination of the ground-state SH + :

SH + (v + i ) + e -(ε) → S + H, (1)
taking into account the new molecular structure data characterizing the states of 4 Π symmetry of SH [11]. In addition, we calculate atomic yields produced via the DR process, resulting in the formation of the atomic sulphur in its ground state -3 P -and in its lowest excited state -1 D -and we produce cross sections and thermal rate coefficients for the vibrational excitation (VE) of the ion:

SH + (v + i ) + e -(ε) → SH + (v + f ) + e -(ε ). ( 2
)
in competition with its DR. Here v + i /v + f stand for the initial/final vibrational quantum numbers of the cation arXiv:2212.13538v1 [astro-ph.IM] 27 Dec 2022 and ε/ε the kinetic energy of the incident/scattered electrons.

The paper is organized as follows: Section II describes the MQDT method and the molecular data set used in the dynamical calculations. Section III presents the obtained dissociative recombination and vibrational excitation cross sections and thermal rate constants, as well as the estimated atomic yields and branching ratios. Section IV contains the concluding remarks.

II. THEORETICAL BACKGROUND

The MQDT approach has been proven to be a powerful method for the evaluation of the cross sections of the DR [12][13][START_REF] Jungen | Molecular Applications of Quantum Defect Theory[END_REF] and competitive processes like ro-vibrational and dissociative excitations. It was applied with great success to several diatomic systems like H + 2 and its isotopologues [START_REF] Giusti-Suzor | [END_REF][16][17][18][19][20][21][22], O + 2 [23,[START_REF] Guberman | Dissociative Recombination: Theory, Experiment and Applications IV[END_REF], NO + [25-29], CO + [30], N + 2 [31,32], BF + [33], triatomics like H + 3 [34][35][36], BF + 2 [37] and complex organic molecules [38].

A. MQDT method

The theoretical summary given below is limited to the account of the vibrational structure and couplings of SH + and SH, the rotational effects being neglected, and focuses on DR -equation (1). However, the reader should keep in mind that the other competitive processes (eq. ( 2)) -such as superelastic collision or vibrational deexcitation (SEC or VdE) (v + i > v + f ), and inelastic collision or vibrational excitation (IC or VE) (v + i < v + f )occur simultaneously and display quite similar features.

The DR results from the quantum interference between the direct mechanism, involving the doubly excited resonant states SH * * and the indirect one, occurring via Rydberg singly-excited predissociating states SH * .

The MQDT treatment of DR and VE requires the a priori knowledge of the potential energy curves (PECs) of the ion (ground and excited states), the relevant doubly excited dissociative states of the neutral molecule, and the series of mono-excited Rydberg states -of ground and excited ionic core -conveniently represented by their quantum defects. The driving forces of the DR and VE are the electronic couplings connecting the ionization continuum to the dissociation one.

A detailed description of our theoretical approach was given in [31,38], its main steps are the following:

i) Building of the interaction matrix V: For a given symmetry Λ of the neutral (electron + ion (core)) system and assuming that only one partial wave of the incident electron contributes to the relevant interactions, the geometry(R)-dependent electronic coupling of an ionization channel relying on the electronic-core state c β (β = 1 for the ground state (core 1) and β = 2 for the excited state (core 2)) with the dissociation channel d can be written:

V (e)Λ d,c β (R) = Φ d |H el |Φ el,c β , β = 1, 2, (3)
where V (e)Λ d,c β (R) is assumed to be independent of the energy of the external electron.

The integration is performed over the electronic coordinates of the neutral system. Here H el denotes the electronic Hamiltonian, Φ d is the electronic wave function of the dissociative state and Φ el,c β is the wave function describing the molecular system "Rydberg electron + ion in its c β electronic state".

Similarly, the electronic coupling between the two ionization continua is:

V (e)Λ c1,c2 (R) = Φ el,c1 |H el |Φ el,c2 . (4)
Integrating these couplings over the internuclear distance leads to the non-vanishing elements of the interaction matrix V(E):

V Λ d,vc β (E) = F d (E)|V (e)Λ d,c β (R)|χ vc β , β = 1, 2. (5) V Λ vc 1 ,vc 2 = χ vc 1 |V (e)Λ c1,c2 (R)|χ vc 2 . (6)
Here χ vc β (β = 1, 2) is the vibrational wave function associated with an ionization channel relying on the core c β , F d is the regular radial wave function of the dissociative state d and E is the total energy of the molecular system. This interaction is effective at small electron-ion and internuclear distances, in the reaction zone.

ii) Computation of the reaction matrix K: Using the second-order perturbative solution of the Lippmann-Schwinger integral equation [29,39,40], written in operator form as:

K = V + V 1 E -H 0 V, (7)
where H 0 is the Hamiltonian of the molecular system under study, with the inter-channel interactions neglected. The reaction matrix K in block form is:

K =   K d d K dvc 1 K dvc 2 K vc 1 d K vc 1 vc 1 K vc 1 vc 2 K vc 2 d K vc 2 vc 1 K vc 2 vc 2   , (8)
where the collective indices d, vc1 , vc2 span the ensembles of all individual indices d, v c1 and v c2 , which respectively label dissociation channels, ionization channels built on core 1 and ionization channels built on core 2. An extensive and rigorous derivation of the structure of each block of the K-matrix in second order for a multicore case was provided in our earlier work [41]. For SH + , with two attractive ion cores, a natural application of our earlier work leads to the following form of the K-matrix in second order:

K =    O V dvc 1 V dvc 2 V vc 1 d K (2) vc 1 vc 1 V vc 1 vc 2 V vc 2 d V vc 2 vc 1 K (2) vc 2 vc 2    , (9)
where the elements of the diagonal blocks of K are:

K Λ(2) vc β v c β = 1 W d χ Λ vc β (R)V (e)Λ c β ,d (R)F d (R < ) × G d (R > )V (e)Λ d,c β (R )χ Λ v c β (R ) dRdR . ( 10
)
Here W d is the Wronskian between the regular (F d ) and irregular (G d ) solutions at the origin of the nuclear Shrödinger equation,

R < = min(R, R ) and R > = max(R, R ), while β = 1, 2.
iii) Computation of the eigenchannel wave functions: It relies on the eigenvectors and eigenvalues of the reaction matrix K, i.e. the columns of the matrix U and the elements of the diagonal matrix tan (η) respectively:

KU = - 1 π tan (η)U , (11)
where the non-vanishing elements of the diagonal matrix η are the phase shifts introduced into the wave functions by the short-range interactions. iv) Frame transformation from the Born-Oppenheimer representation to the close-coupling one: It is performed via the matrices C and S, built on the basis of the matrices U and η and on the quantum defect characterizing the incident/Rydberg electron, µ Λ l (R). The elements of these matrices are:

C v + c β ,Λα = vc β U Λ vc β ,α χ v + c β (R) cos πµ Λ c β (R) + η Λ α χ vc β (R) , (12)
C d,Λα = U Λ d,α cos η Λ α , (13)
S v + c β ,Λα = vc β U Λ vc β ,α χ v + c β (R) sin πµ Λ c β (R) + η Λ α χ vc β (R) , (14)
S d,Λα = U Λ d,α sin η Λ α , (15)
where α denotes the eigenchannels built through the diagonalization of the reaction matrix K, while β = 1, 2. v) Construction of the generalized scattering matrix X , eventually split in blocks associated with energetically open and closed (o and c respectively) channels:

X = C + iS C -iS X = X oo X oc X co X cc . ( 16
)
vi) Construction of the physical scattering matrix S, whose elements link mutually the open channels exclusively, given by [13]:

S = X oo -X oc 1 X cc -exp(-i2πν) X co , (17)
µ 2 : R 2 (C 2 ) series R 1 -D 1 R 1 -D 2 R 1 -R 2 R 2 -D 1 R 2 -D 2 SH ** SH ** Internuclear distance (a 0 )
FIG. 1: Molecular structure data set: Left panels: 2 Π symmetry of SH [10], right panels: 4 Π symmetry of SH [11]. First row: PECs; Second row: Rydberg-valence and Rydberg-Rydberg electronic couplings; Third row: Quantum defects. Symbols stand for the quantum chemistry data points while solid and dashed lines represent the interpolated and extrapolated data.

where the matrix exp(-i2πν) is diagonal and relies on the effective quantum numbers ν v + associated to the vibrational thresholds of the closed channels.

vii) Computation of the cross-sections: Given the target cation on its level v + i , its impact with an electron of energy ε results in DR according to the formula:

σ diss←v + i = Λ,sym π 4ε ρ Λ,sym | S d,v + i | 2 , (18)
or results in VE following the formula:

σ v + f ←v + i = Λ,sym π 4ε ρ Λ,sym | S v + f ,v + i -δ v + f ,v + i | 2 , ( 19
)
where ρ Λ,sym stands for the ratio between the multiplicity of the involved electronic states of the neutral and that of the target ion.

B. Molecular data

The molecular data required by MQDT method is as follows: the PECs of the ground and excited ion states (C 1 , C 2 and C 2 in Fig. 1), the PECs of the relevant dissociative autoionizing states of the neutral molecule (D 1 , D 2 and D 1 ), the quantum defects characterizing the different Rydberg series of bound predissociated states (R 1 , R 2 , R 1 and R 2 ), and the valence-Rydberg (R 1 -D 1 , etc.) and Rydberg-Rydberg (R 1 -R 2 , etc.) electronic couplings between the dissociation and/or the ionization channels of the neutral system. The DR cross section (Eq. 18) is extremely sensitive to the position of the crossing point between the PECs of the neutral dissociative states with respect to the PECs of the target ion. A slight change in the position of the crossing point can lead to a significant change in the predicted cross section. Furthermore, the PECs of the dissociative states must also converge to the correct asymptotic limits for large values of the internuclear distance in order to be able to clearly define them as either energetically open or closed channels. Thus special care need to be done calculating these data sets.

Only a few theoretical methods are able to provide all the necessary molecular data with the desired accuracy. Among these is the R-matrix theory [42], the complex Kohn variational method [START_REF] Rescigno | Computational Methods for Electron-Molecule Scattering[END_REF] and in the present case the block diagonalization method [START_REF] Pacher | [END_REF] combined with GAMESS suite [45].

The molecular data sets relevant for our DR and VE calculation are summarized in Fig. 1: On the left panels we present those calculated before for the 2 Π symmetry of SH [10], while on the right panel those obtained recently for the 4 Π symmetry [11]. The details for the 2 Π symmetry were given in [10] and, consequently, here we are focusing on the 4 Π symmetry. In the first row we displayed the PECs for the ground ion core (SH + X 3 Σ -: C 1 , green), for the excited ion core with 3 Π symmetry (C 2 , magenta) and for the dissociative state of SH having 4 Π symmetry (D 1 , dark green). In the second row we give the electronic couplings of the highly-excited Rydberg states (R 1 in black and R 2 in red) to the dissociative continuum (D 1 ). These coupling terms are V (e)Λ d,c β (R) defined in Eqs. (3). The terms of V (e)Λ c1,c2 (R) in Eqs. (4) representing the coupling between the two Rydberg series as a result of the diabatization procedure are zero [11]. In the third row we have the quantum defects: µ 1 (green) and µ 2 (magenta) that describe the infinite Rydberg series of PECs, converging to the ground core (C 1 ) and the excited core (C 2 ), respectively. The quantum defects were extracted from the Rydberg PECs, provided by the block diagonalization method.

The original diabatic potential energy curves are given by full symbols in Fig. 1. The ion and neutral PECs have been extended towards large internuclear distances by adding a D + C n /R n multipole term to the curves.

The details for each molecular state are summarised in table I. Moreover, in order to get the NIST atomic dissociation limits we have performed a global shift of ∆ NIST = 1.45708 Hartree for each of the PECs of the 4 Π symmetry set by preserving all other characteristics (e.g. ionization energies) of the electronic states.

The quantum chemistry electronic couplings were fitted with gaussian functions chosen to match their peak values. This procedure provides smooth functions on both ends, by considering the behaviour of the calculated couplings at small internuclear distances (left end) and by assuring a steep but continuous fall as soon as the resonant dissociative state crosses the electronic ground state of the ion (right end).

III. RESULTS AND DISCUSSION

The cross sections quantifying the major features of the DR of SH + are displayed in Figures 2 and4. Their corresponding thermal rate coefficients -Figures 3 and5 -are derived by convoluting the cross sections with the Maxwell distribution function for velocities v (related to incident energy of the electrons by ε = 1 2 mv 2 ) of the free electrons,

k(T ) = 8π √ m(2πk B T ) 3/2 +∞ 0 σ(ε) ε exp(-ε/k B T ) dε, (20)
where σ(ε) is given by (Eq. 18), k B is the Boltzmann constant and T is the absolute temperature of the electrons. Figure 6 gives the yields for the produced atomic fragments S ( 3 P)+H ( 2 S) and S ( 1 D) +H ( 2 S) via the DR process by considering the most relevant 2 Π and 4 Π symmetries of SH.

Finally, Figures 7 and8 present the vibrational excitation cross sections and rate coefficients respectively from the ground vibrational level of the ion to its two lowest excited vibrational levels, in comparison with those of the DR.

The calculations include 33 ionization channels in total corresponding to 18 vibrational levels belonging to the ground SH + X 3 Σ -state (C 1 in Figure 1) and 15 vibrational levels belonging to the excited SH + A 3 Π state (C 2 in Figure 1). For the incident electron we consider the p partial wave only. The calculations are performed in second order of the K-matrix and include both direct and indirect mechanisms of the studied processes. The explored range for the incident electron energy is 1 -500 meV (with a step of 0.01 meV) and the temperature range is 10 -1000 K.

A. Dissociative recombination

The calculated total (direct and indirect mechanisms) DR cross section for the 4 Π symmetry -blue curve in FIG. 3: Thermal rate coefficients calculated from the cross sections presented in Fig. 2.

Figure 2 -is presented and compared with the previously obtained cross sections for the 2 Π symmetry -red curve on the same figure, computed in our previous study [10].

One can clearly observe the 1/energy background behaviour of the DR cross sections at low collision energies for both molecular symmetries. Another typical characteristic of the total cross sections is the presence of resonance structures. They originate from the temporary capture of the incident electron into highly excited Rydberg states built on the ionic cores of PEC's C 1 and C 2 for the 2 Π symmetry and C' 1 for the 4 Π one (see Figure 1). One may notice that at low collision energies the contribution of the 4 Π symmetry is between three and four orders of magnitude smaller than that of the 2 Π symmetry, as illustrated in Fig. 3. Indeed, the 2 Π symmetry contributes with a rate around 10 -7 cm 3 •s -1 , while the 4 Π symmetry provides around a few 10 -11 cm FIG. 5: Thermal rate coefficients of the production of ground and excited sulfur atoms via DR, calculated from the cross sections presented in Fig. 4. The legend is the same as that in this figure .   100 K. This can be now -after performing our calculations -explained by the less favourable crossing of the dissociative state PEC with that of the target ion one -top right-hand side part of Fig. 1 -and the relatively small valence-Rydberg electronic couplings in the Franck-Condon region, middle right-hand-side part of the same figure.

One can conclude that the 4 Π symmetry states of SH are far less important than the 2 Π ones, contrary to our expectation [10], and they do not contribute significantly to a better agreement of our theoretical results with the storage-ring experiment at very low energy. FIG. 6: Yields for the production of ground and excited sulfur atoms via DR, calculated from the rate coefficients of Fig. 5 .The legend is the same as that in Fig. 4.

B. Branching ratios

In order to understand the Sulfur chemistry, besides the cross sections and thermal rate coefficients of DR, an important issue is the final state distribution of the S atoms resulting from this process.

According to Fig. 1, and neglecting -in a first stepthe possibility of re-distribution of the probability flux at the crossing between the PECs of the two dissociative paths, S atoms in their ground state 3 P are produced via the capture into D 2 2 Π and D 1 4 Π states, whereas the excited state 1 D is populated via the D 1 2 Π dissociative path.

Figs. 4 and 5 illustrate these branching ratios. One can notice that in the range 0.001-0.5 eV the cross section of generation of S( 3 P) atoms -green dashed lines with green circles -is overall smaller than the one obtained for S( 1 D) -violet dashed lines with violet circles -up to two orders of magnitude. As an exception, around 0.005 eV and around 0.09 eV collision energies, the DR cross section leading to S( 3 P) is higher than that of S( 1 D) by about one order of magnitude. The corresponding thermal rate coefficients are presented in figure 5, with the same color and symbol code. The generation of S( 3 P) atoms (green dashed line with green circles) has an average rate of 2 • 10 -8 cm 3 .s -1 in the temperature range 10 -200 K. It reaches its peak value of 4 • 10 -8 cm 3 .s -1 at about 40 K, having its origin in the behaviour of the cross section in the energy range 4 -10 meV. This rate is practically constant above 250 K. On the other hand, the rate of production of S( 1 D) atoms (violet line with violet circles) monotonically decrease from 2 • 10 -7 cm 3 .s -1 at 10 K to 3 • 10 -8 cm 3 .s -1 at 1000 K. Obviously, in this firststep approach, the production of S( 1 D) atoms dominates largely that of S( 3 P) atoms at low temperature.

To better compare the processes of populating the two lowest energy levels of the S atom, we present in Fig. 6 the yields resulting from the branching ratios from Fig. 5, calculated by dividing the corresponding thermal rate coefficients to the sum of both. In average, in the electron temperature range 10-1000 K, the DR process contributes to the generations of S( 3 P) atoms as much as 24%, and to that of S( 1 D) atoms with 76%.

In order to account for the flux redistribution at the crossing point (R 0 ∼ 8 a 0 ) between the PECs of the D 1 and D 2 dissociative states, we performed a Landau-Zener calculation [START_REF] Zener | [END_REF]49]. The probability of transition from one diabatic branch to the other -P 12 -is given by [START_REF] Larson | Dissociative Recombination, Theory, Experiment and Applications IV[END_REF]

P 12 (ε) = 1 -e -2πV 2 12 (R 0 ) av , (21)
where V 12 (R 0 ) = 0.0314 Hartree is the coupling element between the two dissociative states at their crossing point [10], a = dV1 dR -dV2 dR stands for the differences of PEC slopes at the crossing point and v is the relative collisional velocity [START_REF] Larson | Dissociative Recombination, Theory, Experiment and Applications IV[END_REF].

Consequently, starting from the dissociative states D 1 and D 2 (cf. the upper-left panel of Fig. 1), one obtain the cross sections σ 1 (ε) and σ 2 (ε) towards the S( 3 P)+H( 2 S) and S( 1 D)+H( 2 S) dissociation limits, respectively, according to the formulas:

σ 1 (ε) = (1 -P 12 )σ 1 (ε) + P 12 σ 2 (ε) σ 2 (ε) = (1 -P 12 )σ 2 (ε) + P 12 σ 1 (ε). (22)
Table II contains these Landau-Zener transition probabilities P 12 as function of the collision energy. Moreover, we display the branching ratios resulting from the cross sections convoluted with the anisotropic Maxwell distribution of the relative electron/ion velocities corresponding to longitudinal and transversal temperatures T = 0.025 meV and T ⊥ = 1.65 meV respectively, before and after performing the Landau-Zener calculation. This convolution allowed us to compare our branching ratios with those measured in the TSR storage ring for 1 meV collision energy [46,[START_REF] Becker | Imaging of Neutral Fragmentation Products from Fast Molecular Ion Beams: Paving the Way for Reaction Studies in Cryogenic Environment, Ph.D. thesis[END_REF].

The re-distribution of the flux of probability at the crossing between D 1 and D 2 results in the cross sections and yields illustrated in thick lines in Figs. 4, 5 and6, and in the yields displayed in Table II. One may notice in these figures an interchange of the populations in the ground and lowest excited state of the Sulfur atoms, due to this re-distribution. The good agreement with the TSR-measurements at very low energy supports this interchange, whereas the theoretically-computed yields at 1 meV without the Landau-Zener treatment disagree with the experimental ones.

C. Vibrational excitation

In addition to the DR cross sections and rate coefficients we have calculated vibrational excitations (VE) of the relaxed (v + i = 0) molecular target into the lowest excited vibrational states (v + i = 1, 2) via the capture into states of both 2 Π and 4 Π symmetries of the neutral. 21)) for the transition between the two lowest dissociative 2 Π diabatic states of the SH molecule -D1 and D2 in the upper-left panel of fig. 1 -and corresponding branching ratios as function of the collision energy. Our MQDT/Landau-Zener results are compared with the TSR measured data, when available [46,[START_REF] Becker | Imaging of Neutral Fragmentation Products from Fast Molecular Ion Beams: Paving the Way for Reaction Studies in Cryogenic Environment, Ph.D. thesis[END_REF]. The cross sections over symmetries and the global thermal rate coefficients summed over all symmetries, can be seen in Figs. 7 and8 respectively, together with those obtained for DR.

MQDT-no LZ MQDT-LZ

TSR Energy P12 n( 3 P) n( 1 D) n( 3 P) n( 1 D) n( 3 P) n( 1 D) n(
According to Fig. 7 the VE cross sections show sharp thresholds corresponding to the excitation energies of the ion. Similarly to DR, they are driven by the Rydberg resonances and for this process too we found smaller cross sections for the 4 Π molecular symmetry. However the magnitude of the obtained difference for the two symmetries is different, while for the DR we get a difference of about two orders of magnitude, the VE cross sections differ only by one order of magnitude.

Figure 8 shows that while the DR rate coefficient is smoothly decreasing as a function of the temperature, the VE ones have a monotonically increasing behaviour due to the sharp thresholds. One can clearly see that the DR dominates over VE for all electronic temperatures up to 1000 K.

In order to facilitate the use of our recombination and excitation rate coefficients for kinetic modelling, we have fitted their temperature dependence by using the Arrhenius-type formula:

k(T ) = a 0 T 300 a1 e -a 2 T , (23)
where the temperature T is in Kelvin and the rate coefficient k in cm 3 s -1 . The fitting parameters for the DR of the ground vibrational state of the target and for the VE into the lowest two vibrationally-excited states are summarized in Table III. For all the processes, the fitted values reproduce well our MQDT rate coefficients, according to the RMS values given in the forth column of each table in the whole temperature range from 10 to 1000 K.

IV. CONCLUSIONS

In this paper we studied by MQDT the relevance of the 4 Π symmetry states of SH for the dissociative recombination of SH + at low energy/temperature. We have found that this symmetry has a far smaller contribution to the cross sections/rates than the 2 Π ones. Therefore, TABLE III: Fitting parameters for the formula (23), corresponding to the rate coefficients summed over 2 Π and 4 Π symmetries for dissociative recombination and vibrational excitation of vibrationally relaxed (v + i = 0) molecular cation. The fit applies for temperatures for which the rate coefficient is higher than 10 -16 cm 3 s -1 . v + i v + f Temperature range a0 a1 a2 RMS (K) (cm 3 s -1 K -A 1 ) (K) DR 0 10 ≤ T ≤ 1000 6.53104×10 -8 -0.348405 -2.59354 0.00855 VE 0 1 220 ≤ T ≤ 400 1.46041×10 -9 -0.432013 3535.88 0.00273 400 < T ≤ 1000 3.83266×10 -10 0.364274 3063.89 0.02488 VE 0 2 440 ≤ T ≤ 1000 8.44578×10 -10 0.464803 6941.58 0.01119 the comparison between theory and experiment did not change after the present study: an overall good agreement from 10 meV to 1 eV, and a disagreement increasing progressively up to one order of magnitude when the energy is decreased from 10 to 0.1 meV. We produced the branching ratios, and we took into account the redistribution of the probability fluxes at the crossing between the PECs of the two dissociative states. A spectacular inversion in the branching ratios takes place, resulting in a satisfactory agreement between our theoretical MQDT-Landau-Zener final results and those produced by the storage ring TSR at very low energy. More than two third of the recombination events result in ground state sulfur atoms.

We also computed vibrational excitation cross sections and rate coefficients. This process is largely dominated by the dissociative recombination below 1000 K.

Further studies will be devoted to the account of the rotational effects, which may result in a better agreement between theory and experiment, especially in the very low energy range.

  Population of ground and lowest excited states of sulfur via the dissociative recombination of SH+ in the diffuse interstellar medium J Boffelli, F Gauchet, D.O Kashinski, Dahbia Talbi, A.P Hickman, K Chakrabarti, E Bron, A Orbán, J.Zs Mezei, I.F Schneider To cite this version: J Boffelli, F Gauchet, D.O Kashinski, Dahbia Talbi, A.P Hickman, et al.. Population of ground and lowest excited states of sulfur via the dissociative recombination of SH+ in the diffuse interstellar medium. Monthly Notices of the Royal Astronomical Society, 2023, 522 (2), pp.2259-2266. 10.1093/mnras/stad1065. hal-04114590 I. INTRODUCTION

FIG. 2 :

 2 FIG.2: Cross section for SH + DR into the state of 4 Π symmetry (D 1 in Figure1, blue line) compared to that for DR into the states of 2 Π symmetry (D1 and D2 in Figure1, red line).

FIG. 8 :

 8 FIG.8: Vibrational excitation and dissociative recombination rate coefficients of the vibrationally relaxed SH + molecular cation: sum of the contributions via the SH states of 2 Π and 4 Π symmetries.

TABLE I :

 I Fitting parameters D and Cn used in the longrange multipole formula D+Cn/R n for the different molecular states.

	Molecular state n	D	Cn
	system		(Hartree) (Hartree×Bohr n )
	SH + 3 Σ -C1 4 -399.20323325	-16.769107
	SH + 3 Π	C 2 4 -399.13555828	-6.073002
	SH * * 4 Π	D 1 6 -399.58373325	89.132274
	SH * 4 Π	R 1 6 -399.29465171	-232.669573
	SH * 4 Π	R 2 6 -399.27473902	-146.713317

  3

  •s -1 at

		10 -13			2 Π,	4 Π → S(	3 P)
					2 Π → S(	1 D)
	) 2 Cross section (cm	10 -16 10 -15 -14 10	without LZ
		10 -17	without LZ with LZ
			with LZ
		0.001 -18 10	0.01		0.1	0.5
			Energy (eV)
	FIG. 4: DR cross sections contributing to the formation of
	S( 3 P)+H( 2 S) (green) and S( 1 D)+H( 2 S) (violet) atomic frag-
	ments. The dashed lines with circles stand for the results
	without the Landau-Zener (LZ) treatment, whereas the con-
	tinuous lines stand for the final results, obtained following the
	Landau-Zener treatment.
			2 Π,	4 Π → S(	3 P)	without LZ without LZ
	.s -1 )				with LZ with LZ
	Rate coefficient (cm 3	10 -7
		10 -8 10		100	1000
			Temperature (K)

2 Π → S( 1 D)

TABLE II :

 II Landau-Zener probabilities (eq. (

  Vibrational excitation and dissociative recombination cross sections of the vibrationally relaxed SH + molecular cation by considering both 2 Π and 4 Π symmetries of the formed molecular complex. The red and blue curves stand for DR, the dark green and cyan ones for 0 → 1 VE and those in turquoise and maroon give VE for 0 → 2. Finally, the thick curves correspond for the 2 Π while the thin curves for the 4 Π molecular symmetry of the neutral.

					1 S)
				(eV)
				0.001 0.99403 0.274 0.726 0.724 0.276 0.61 0.33 0.06
				0.01 0.99400 0.140 0.860 0.856 0.144 -	-	-
				0.1 0.99373 0.616 0.384 0.386 0.614 -	-	-
				0.5 0.99246 0.320 0.680 0.678 0.322 -	-	-
		10 10 -13 -14	DR	2 Π 4 Π
	Cross section (cm 2 )	10 -19 10 -18 10 -17 10 -16 -15 10
		10	-20
		0.1 -21 10	0 -> 1	0 -> 2	1
				Energy (eV)
	FIG. 7:

Acknowledgements

The authors acknowledge support from La Région Normandie, FEDER, and LabEx EMC3 via the projects PTOLEMEE, Bioengine COMUE Normandie Université, the Institute for Energy, Propulsion and Environment (FR-IEPE), the European Union via COST (European Cooperation in Science and Technology) actions TU-MIEE (CA17126), MW-Gaia (CA18104) and MD-GAS (CA18212). The authors are indebted to Agence Nationale de la Recherche (ANR) via the project MONA. This work was supported by the Programme National "Physique et Chimie du Milieu Interstellaire" (PCMI) of CNRS/INSU with INC/INP co-funded by CEA and CNES. J.Zs.M. thanks the financial support of the National Research, Development and Innovation Fund of Hungary, under the K 18 and FK 19 funding schemes with projects no. K 128621 and FK 132989, and it is very grateful for the hospitality of the Faculty of Physics of West University of Timisoara during his Visiting Professor Fellowship.

DATA AVAILABILITY

The data underlying this article will be shared on reasonable request to the corresponding authors.


Jordan François

Jordan Rio

Erwann Jeanneau

Marie-Ève L Perrin

Maïwenn Jacolot

Pierre- Adrien Payard

Florence Popowycz

Ir-Na Cooperativity Controls the Diastereoselectivity of Borrowing Hydrogen C-C Alkylation on Isosorbide: Synthesis Methodology and Mechanistic Investigation

The direct functionalization of isosorbide is a curent challenge of biomass valorisation due to the low selectivities usually obtained. Taking advantage of our preliminary observations concerning the diastereoselective Ir-catalyzed amination of isohexides we report the first direct C-C borrowing hydrogen direct functionalisation on isosorbide. The C-C alkylation was achieved with excellent diastereocontrol using an Ir-based organometallic homogeneous catalyst. The reaction sequence involves a catalytic dehydrogenation that converts the alcohol into a reactive ketone, the in situ aldol condensation / crotonisation, and a catalytic dehydrogenation leading to the homologated desired product. Once the parameters that control the reaction outcome were explored and optimized, the stereoelectronic effects from which the diastereoselectivity originates from have been investigated by means of a computional mechansitic performed at the DFT level. The roles played by the Na counter-cation to coordinate substrate's oxygen atoms and to guide hydride addition were evidenced allowing to rationalize the experimental selectivity at the molecular level.

Introduction

During the last decades, an effort has been made in order to promote the use of biobased feedstock instead of fossil resources. 1,2 Generally, they are constituted of carbohydrate products and give directly access to high-value products for a wide range of applications in fine chemistry. 3 Among them, isosorbide, a major product of the starch industry 4,5 has received particular attention by its use as a pharmaceutical product (e.g. isosorbide dinitrate: Isordil®) or as a solvent for cosmetic applications (e.g. dimethylisosorbide). 6 Conversion of isosorbide to high value added molecules has also attracted considerable interests both in academia and in industry for polymer applications [7][8][9] and for chiral induction purposes (chiral ligand, organocatalyst or auxiliaries). 10,11

Figure 1. Chemical structure of isohexides

Isosorbide is a chiral molecule featuring two secondary alcohols in C-3 endo and C-6 exo positions (Figure 1). Despite the expected difference between both hydroxyl groups, the reactivity balance between both positions is currently lesspronounced in practical, leading to limited selectivities in direct transformations. 12 Thus, the functionalization of isosorbide derivatives often requires a prior step of protection of one of the two hydroxyl group. 13 Although isosorbide functionalization into amines has been widely described using classical multisteps strategies (alcohol activation by a tosylate followed by a nucleophilic substitution with an amine), 13 greener alternatives must be considered nowadays. In this context, N-alkylation of ammonia with isohexides using the borrowing hydrogen (BH) methodology was successively reported by Beller, 14 Vogt 15 and Rose. 16 Although these procedures are very efficient, none of them is stereoselective and they provide a mixture of three stereoisomers. To complement, we have then developed the highly diastereoselective amination of isohexide derivatives with various primary amines using a cooperative catalysis between an Ir-based complex and a Brønsted acid (Scheme 1a). 17,18 Applying the C-C borrowing hydrogen methodology on isohexides would promote the synthesis of novel two-carbon homologated molecules that could find interesting applications in the polymer field amongst others (acids, esters and so on).

Please do not adjust margins

Please do not adjust margins Scheme 1. C-N and C-C functionalization on isosorbide using the BH methodology But, as far as we know, only few methodologies have been reported for the direct C-C homologation on isohexide derivatives. In 1998, Nair and coworkers reported the modification of C-6 protected isosorbide in a three-step sequence: oxidation of the alcohol on C-3 position, Wittig reaction and hydroboration. 19 More recently, a slight variation at the C-3 position was described via a reaction sequence involving successively an oxidation, the Horner Wadsworth Emmons reaction and an assisted metallic reduction. 20 In 2011, van Es reported the double functionalization of isomannide to afford the di-carboxylic acids through triflation, nucleophilic substitution followed by hydrolysis into acid. 21 Although effective, these syntheses have some limitations: toxicity of reagents, number of steps, low atom-economy, regio-and stereo-selective issues. The BH strategy thus appears as a promising alternative for the two-carbon elongation of isosorbide (Scheme 1b). This powerful tool indeed allows the direct activation of alcohols to form novel C-N and C-C bonds assisted by a metallic catalyst without the external use of molecular hydrogen. [22][23][24][25] Furthermore, this one-pot strategy promotes the atom economy, the reduction of waste and the generation of a stoichiometric amount of water as sole byproduct. In the case of the C-C bonds construction, the BH reaction consists in (i) a catalytic dehydrogenation that converts the secondary alcohol into a more reactive ketone, (ii) the in situ aldol condensation with a α-methyl ketone giving the corresponding a,b-unsaturated ketone, (iii) a catalytic dehydrogenation leading to the C-alkylated awaited compound (Scheme 2).

Scheme 2. General BH principle for the a-alkylation of ketones

The choice of the nucleophile was crucial for the exploration of this reaction. In 2017, Donohoe's group described the synthesis of α-alkylated ketones using secondary alcohols and pentamethylacetophenone (Ph*-methyl ketone). 26 Advantages of the Ph*-methyl ketone are multiple: it avoids self-condensation due to its steric hindrance, and the Ph* moiety can then be displaced via a retro Friedel-Crafts reaction to ultimately obtain the corresponding acid, ester, amide or alcohol. 27,28 Capitalizing on the success of Donohoe's group in the use of Ph*-methyl ketone as an ester (or acid or alcohol) surrogate, we envisioned to extend the C-C borrowing hydrogen methodology to the non-trivial isosorbide case.

Results and discussion

This study began by performing BH reaction with pentamethylacetophenone (1.1 eq.) and commercially available isosorbide (1.0 eq.) under Donohoe's classical conditions 26 in the presence of [Cp*IrCl2]2 (5 mol%) (Cp* = C5Me5) and NaO t Bu (2.0 eq.) in PhMe at 120 °C for 24 hours. Contrary to the conditions used commonly (2 eq. of primary or secondary alcohol), the use of only 1 eq. of isosorbide was another challenge to better valorize this biosourced alcohol. Despite a complete conversion (96%), the desired product was not detected. We presumed that isosorbide undergoes degradation during the reaction leading to volatile by-products that could not be detected by NMR. 29,[START_REF] Horton | Advances in Carbohydrate Chemistry and Biochemistry[END_REF] Indeed, a difficult balance was again pointed out in between selective functionalization and degradation pathways. To decrease the functional complexity of the substrate and to understand the formation of side products, the exo-monobenzylated isosorbide 1 was then considered as a model substrate (Scheme 3). The choice to protect the exo-position was made according to previously reported calculations mentioning that the oxidation of the hydroxyl group in the endo position is kinetically favored by a difference in energy barriers of 2 kcal.mol -1 . 31

Scheme 3. Base screening with 1

Reaction conditions: 1 (1.0 eq.), pentamethylacetophenone (1.1 eq.), [Cp*IrCl2]2 (5 mol%), base (2.0 eq.), toluene [1M], 120 °C, 24 h.; a 1,3,5-trimethoxybenzene as Please do not adjust margins Please do not adjust margins Pleasingly, when using the previously reported conditions, the expected C-C product 2 was formed but with a low yield of 13%. Noticeably, 17% of unexpected compounds 4/4' were detected in the crude 1 H NMR (Scheme 3). The formation of 4/4' may originate from the in situ formation of benzyl alcohol, raising from debenzylation of compound 1. Increasing the amount of NaO t Bu to 3 eq. did not increase the conversion, which only reached 30% after 24 hours. Switching to KO t Bu, the conversion was improved to 95%, but generated more degradation and enhanced quantities of additional side product 3. The isolation and characterization of the by-product 3 comforted our idea that one of the tetrahydrofuran cycles could be opened leading to volatile side-products and compound 3. This type of degradation was already reported under acidic conditions, pointing out once the selectivity challenge in functionalizing this substrate. 29,32 The cutting edge issue was to find the appropriate balance between conversion and degradation / selectivity on a substrate that is difficult to handle. The use of other strong bases such as KOH or KHMDS led to the same conclusion. Switching to carbonate bases or to Ag2O affected the conversion and only epimerized product 5 could be identified. Despite these moderate results, we decided to select NaO t Bu (2.0 eq) to pursue the methodological investigation by focusing on the screening of the catalyst (Table 1). First experiment was to run blank experiment without any catalyst (Table 1, entry 1) that led to almost complete recovery of the starting material, with only non-quantifiable traces of expected compound 2. Based on successful a-alkylation of secondary alcohols under metal-free conditions from Morrill's group, 33 the reaction was tested without any catalyst with an excess of alcohol (6.0 eq.): as well only traces of the expected compound were detected by The assessment of the influence of different protecting groups on the yield could help us (i) to understand the limitations encountered in isolating the compound of interest in high yield, (ii) to compare the influence of the exo-position in these two substrates. At this stage, the objective was twofold by trying to avoid by-products resulting from debenzylation process and to increase the selectivity in favour of the C-C borrowing hydrogen product. Nevertheless, the silane derivatives 6 and 7 led to complete degradation and/or deprotection. Ether 8 reacted similarly to compound 2, giving the expected compound 10 in a 13% NMR yield along with 1-(pentamethylphenyl)propanone 11 (17%) coming from the release of methanol in the reaction medium. In turn, ether 9 appeared as an interesting candidate because no such side product could be formed due to the quaternary carbon avoiding proton abstraction. Using the reaction conditions previously developed, the yield of C-C adduct 12 was evaluated around 40%, without any trace of side products (Scheme 4). Further optimization of the reaction conditions was then considered starting from substrate 9 (Table 2). Cp*Ir(Ts*dpen)(R,R) (Ir-2) appeared as the best catalyst for this transformation as other iridium catalysts (iridium dimer [Cp*IrCl2]2 or iridacycle Ir-2) led to the formation of the desired product with only 11% and 14% yield respectively (Table 2, entries 3-4). Pleasingly, we could decrease the amount of base to 1 eq. without any loss of reactivity (Table 2, entry 5). Also, when decreasing the catalyst loading to 5 or even 2 mol%, compound 12 could be isolated within similar yields (Table 2, entries 6 and 7). Time and temperature parameters were also investigated without any improvement (Table 2, entries 8-10). The best conditions were thus determined to be 2-5 mol% of iridium catalyst Ir-2 and 1.0 eq. of NaO t Bu giving 12 with a correct isolated yield of 47% (Table 2, entry 7). Even when increasing the amount of isosorbide derivative to 2.0 eq., the yield of the reaction did not exceed 50% (Table 2, entry 11). Applying Donohoe's conditions to isosorbide scaffolds proved to be quite challenging to reach high yields relative to simple substrates, but the perfect stereo-controlled C-C functionalization on isosorbide derivative is remarkable. As previously mentioned, a plausible pathway for this reaction, that does not involve change in oxidation state of the metal, would successively consist in (i) oxidation of the alcohol into ketone via a Ir(III)-catalysed dehydration, (ii) aldol condensation and (iii) enol reduction via hydrogenation (Scheme 5a). However, numerous previous mechanistic studies and reviews highlighted the diversity of factors such as catalyst, ligand, additives and / or solvent that control the reaction and its selectivity, making each catalytic system mechanistically unique. [34][35][36][37][38][39][40] To evidence the factors that guide the stereoselectivity under our reaction conditions, a combined experimental and theoretical mechanistic investigation was conducted. First, the role of the structure of the isohexide was experimentally addressed through a deconvolution strategy. Simplified substrates were tested to understand how the reactivity and selectivity were impacted by the steric hindrance and the functionalization of the substrate (Scheme 5b). 3-Hydroxytetrahydrofuran was first engaged in BH reaction using 5 mol% of iridium catalyst Ir-2 affording the expected compound 13 within excellent yield (96% NMR yield and 71% isolated yield), showing the robustness of the method. Adding a methyl group, either in β or α position led to compounds 14 and 15 with comparable yields (75 and 67% yield respectively). However, independently of the position of the methyl group, a moderate dr of 70:30 was measured, thus highlighting the importance of the coordinating group towards the selectivity of the reaction. A very similar trend was observed when replacing the methyl with a n Pr group: compound 16 was obtained in 70% yield and with a moderate dr of 70:30. On the contrary, the presence of a methoxy group in α position gave 17 in Please do not adjust margins Please do not adjust margins significantly lower amounts (30-40%, using either 1.0 or 2.0 eq. of base), but we were delighted to observe an enhanced dr of 99:1. The structure of 17 was confirmed by solid-state X-ray diffraction (XRD) analysis (Scheme 5b and SI).

Scheme 5. a) General mechanism proposed for the BH C-C alkylation. b) Extension to substituted tetrahydrofurans

Reaction conditions: hydroxy-THF derivative (1.0 eq.), pentamethylacetophenone (1.1 eq.), Ir-2 (10 mol%), NaO t Bu (2.0 eq.), toluene ([1M]), 120 °C, 24 h. 1 H NMR yields using 1,3,5-trimethoxybenzene as internal standard; a 2 Ir-2 and 1 eq. of NaOtBu were used; b 10 mol% Ir-2 was used; c obtained along with non-reduced product (10 to 20% yield)

Quite similar results were obtained with monodeoxyisosorbide, but surprisingly derivative 18 was obtained along with the non-reduced adduct 18' (see SI). The high stability of 18' with an endo-cycle saturation that is obtained by isomerization of the aldol product, is assumed to prohibit its reduction by the hydride. All in all, these experimental results suggest that the presence of a heteroatom at the C-4 position of the heterocycle benefits the selectivity, while its exact roleat the molecular scale -remained unclear.

The importance of considering solvation and ion-pairing effects in d 8 -or d 9 -metal catalyzed hydrogenations reactions has been outlined by several groups. [36][37][38][39] Since an excess of NaO t Bu was used, the catalyst [Cp * Ir(Ts*-dpen)(R,R)] (Ir-2) should exist under reaction conditions in its deprotonated state [Cp * Ir(Ts*dpen)(H)(R,R)] -Na + (Ir Na,H ) in which the sodium counter-ion comes from the base, and the hydride arises from alcohol-toketone oxidation. However, the role played by the sodium cation in the stereoselectivity of the reaction must be clarified.

To understand how the stereoselectivity of the reduction step (Scheme 5a, step iii) is influenced by the methoxy substituent and the counter-cation used, a theoretical mechanistic investigation has been performed at a DFT level using the M06 functional (detailed computational procedure in SI). 41 As a chemical model, the Ts*-dpen ligand has been simplified into the Ph-SO2-dpen one by removing the Me groups of the Ph ring. This structural simplification is supported by experimental evidences as using Ts-dpen or Ph-SO2-dpen instead of Ts*-dpen led to similar reactivity and diastereoselectivity but with a slight decrease in yield. No additional structural simplification has been done. As shown in Scheme 6, up to 8 stereoisomers of the conjugate ketone can be formed potentially by the aldol condensation and thus coexist under the reaction conditions as suggested by their relative stabilities (Scheme S1). As the reaction is not enantioselective, we have focused the mechanism investigation on the reduction of the most relevant (Z,S)-A isomer to restrict the number of substrate considered. Additional reduction mechanisms are available in SI (Schemes S3-S5). Among the Ir-complexes that could be formed between the reagents and the precursors under the experimental conditions, the deprotonated Ir-hydride complex Ir Na,H is the most stable one (detailed speciation is given in Scheme S2).

Thereof, in the energy profile presented in Scheme 6, Gibbs energies are relative to the ones of Ir Na,H and (Z,S)-A.

Ir Na,H is an octavalent heterobimetallic Ir/Na complex in which the nitrogen atoms N ). This transition state leads to the formation of (+/-)-(R,S)-17 product that is not observed experimentally.

Please do not adjust margins

Please do not adjust margins The overall Gibbs energy barrier of this pathway is computed to 31.0 kcal mol -1 , i.e. 2.0 kcal mol -1 higher than TS-re-(Z,S)-A-Ir H,Na . This trend is in good agreement with the experimentally observed dr ratio of 99:1, as the computed ∆∆G ≠ of 2.0 kcal mol - 1 would correspond to a dr ratio of 92:8. We have then further questioned the counter-intuitive preference for the MeO-Na coordination at the face opposite to the methoxy group. Interaction-Distortion Analysis (IDA) 42,43 reveals that the electronic energy required for substrate distortion is considerably lower when reduction occurs at the re face than at the si face (see Scheme S6). This confirms the crucial role played by the coordination of the methoxy group to Na to promote the diastereoselectivity of the reduction. All in all, the remarkable selectivity obtained for this reaction originates from the coordination of the methoxy group to the sodium cation. By favoring coordination of the substrate on its re face, Na favors the hydride addition to the face opposite to the methoxy group.

Conclusions

Direct or post-functionalization valorisation of isosorbide raises considerable interests both in academia and in industry. However, direct and selective functionalization of isosorbide is a challenge and most reported conditions suggest multi-steps strategies. Here we report the direct diastereoselective C-C alkylation on exo-protected isosorbide using pentamethylacetophenone. Protection of the exo-alcohol was required. The choice of NaO t Bu as a base and the protection of the exo-alcohol by a t Bu group enable us to isolate the desired product with yields up to 47% with an excellent diastereoselectivity of 99:1. A joint experimental and computational mechanistic study revealed the crucial role played by the Ir / Na heterobimetallic hydride complex as the active complex in the observed diastereocontrol. This joint methodology of synthesis and mechanistic reasoning study, not only illustrates the challenge in valorizing straightforwardly this biosourced alcohol, but also pave the way to further direct homologation and/or functionalization of polyfunctional bio-sourced compounds.

There are no conflicts to declare.

1 H

 1 NMR internal standard; values in parentheses indicate the yield of isolated product; b 3 eq.

  1 and N 2 of Ph-SO2-dpen ligand (Scheme 6), the hydride and the Cp* ligands coordinate the Ir(III) centre. In this complex, Ir and Na are bridged by the hydride, and by the N 2 and O 2 atoms of the Ph-SO2-dpen (Scheme 6). The reduction starts with the coordination of the catalyst Ir H,Na to either the re or the si face of (Z,S)-A substrate to give adducts re-(Z,S)-A-Ir Na,H or si-(Z,S)-A-Ir Na,H , respectively (Scheme 6). The formation of adduct re-(Z,S)-A-Ir Na,H is thermodynamically disfavoured by 7.0 kcal mol -1 . The oxygen atoms O 3 of the methoxy group and O 4 of the carbonyl groups of the complexed re-(Z,S)-A substrate chelates the sodium ion (Na-O 3 : 2.37 Å, Na-O 4 : 2.30 Å) within the plane defined by the π-system of the enone. Interestingly, the Na-H distance is not affected by the coordination of the substrate. The hydride transfer then occurs via transition state TS-re-(Z,S)-A-Ir Na,H (Scheme 6b), in which the hydride is approximatively at equal distance from Ir and C 1 . It is worth mentioning that at transition state TS-re-(Z,S)-A-Ir Na,H , the O 3 -Na interaction is lost. The overall Gibbs energy barrier for the reduction step at the re face is computed to 29.0 kcal mol -1 . The absolute configuration of the resulting product (+/-)-(S,S)-17 fits with the one experimentally observed after hydrolysis. When the addition is taking place at the si face, the catalyst approaches directly on the side of the methoxy group. Structure of adducts si-(Z,S)-A-Ir Na,H re-(Z,S)-A-Ir Na,H are similar, and the pre-complex si-(Z,S)-A-Ir H,Na is merely more stable than the re adduct re-(Z,S)-A-Ir H,Na by 1.3 kcal mol -1 . The associated transition state for the hydride transfer TS-si-(Z,S)-A-Ir H,Na is later than transition state TS-re-(Z,S)-A-Ir H,Na (Scheme 6d). It requires the Ir-H bond to be more elongated by 5% and the C 1 atom more pyramidalized than in TS-re-(Z,S)-A-Ir H,Na (see Scheme S6

Scheme 6 .

 6 Scheme 6. A) Free energy profile for hydride transfer from Ir H,Na at the re or si face of (Z,S)-A and B) associated structures of adducts (a) re-(Z,S)-A-Ir H,Na and (c) si-(Z,S)-A-IrH,Na and transition states (b) TS-re-(Z,S)-A-Ir H,Na and (d) TS-si-(Z,S)-A-Ir H,Na .

Table 1 . Catalyst screening with 1 Entry Catalyst (mol%) Conv. (%) [a] NMR yields (%) [a] 2 3 4/4' 5

 1 1 H NMR (Table1, entry 2). Different iridium-based catalysts were tested with enhanced catalyst loading of up to 10 mol% (Table1, entries 3-8). A good conversion of 77% was observed in the presence of 10 mol% of [Cp*Ir(Ts*-dpen)(R,R)] (Ir-2) (Table1, entry 7) leading to the formation of compound 2 within 30% NMR yield. Nevertheless, the side product 3 was still detected in a significant amount of 15%. When ruthenium-based catalysts (Table1, entries 8-12) were screened, no trace of expected compound was observed, mainly compounds 4/4' along with compound 3 were detected. Ferrocene carboxaldehyde led to complete recovery of the starting material (Table1, entry 13). The crucial observation at this stage of the study was the observed excellent diastereoselectivity of the reaction as compound 2 was isolated as a unique diastereoisomer. Whatever the nature of the catalyst (chiral or achiral), compound 2 was formed with an excellent dr > 99:1. The stereochemistry of 2 was determined through see SI) such as silanes ethers (6 and 7) or alkyl ethers (8 and 9) (Scheme 4). Compounds 7, 8 and 9 were synthesized from isosorbide while compound 6 was prepared from isomannide.

	1	None	traces	traces	-	-	-
	2 [b]	None	traces	traces	-	-	-
	3	[Cp*IrCl2]2 (5)	48	13 (8%)	n.d.	17	-
	4	[Cp*IrCl2]2 (10)	44	7	n.d.	16	-
	5	[Cp*IrI2]2 (5)	26	-	n.d.	14/11	-
	6	Ir-1 (10)	67	30 (30%)	n.d.	n.d./6	9 (12%)
	7	Ir-2 (10)	77	30 (18%)	15	n.d.	4
	8	[RuH2(CO)(PPh3)3 (10)	33	-	n.d.	10/12	-
	9	[RuHCl(CO)(PPh3)3 (10)	53	-	n.d.	18/15	-
	10	[Ru(p-cymene)Cl2]2 (5)	59	-	n.d.	28	n.d.
	11	Shvo's catalyst (5)	0	-	-	-	-
	12	RuCl2(DMSO)4 (10)	100	-	-	-	-
	13	Ferrocenecarboxaldehyde (10)	0	-	-	-	-

1

H NMR analysis based on the magnitude of the H3'a-H3' coupling constant. Indeed, on the isohexide skeleton, this 3 J constant that corresponds to a cis-coupling has a value of 4 Hz whereas the trans-coupling constant is around 0 to 1 Hz. H3'a appears as an apparent triplet considering the cis-coupling J(H3'a-H3') = J(H3'a-H6'a) = 4 Hz, while H6'a turns out to be a doublet of doublet because of the lower trans-coupling J(H6'a-H6') = 1.2 Hz. This observation was confirmed by NMR NOESY experiments (see SI). Considering the large amount of by-products detected that probably results from debenzylation, we decided to prepare different mono-protected isohexides using classical methods (

Table 2 . Optimization with 9

 2

	Entry	Cat. (mol%)	eq base	Conv. 9 (%) [a]	Yield 10 (%) [a]
	1 [b]	Ir-2(10)	2	77	30 (18%)
	2	Ir-2 (10)	2	100	44 (38%)
	3	[Cp*IrCl2]2 (5)	2	94	11
	4	Ir-1 (10)	2	100	14
	5	Ir-2 (10)	1	100	41 (41%)
	6	Ir-2 (5)	1	100	51 (37%)
	7	Ir-2 (2)	1	82	50 (47%)
	8 [c]	Ir-2 (5)	1	100	43 (40%)
	9 [d]	Ir-2 (5)	1	26	17
	10 [c,d]	Ir-2 (5)	1	77	40
	11 [e]	Ir-2 (2)	1	47	47

Reaction conditions: 1 (1.0 eq.), pentamethylacetophenone (1.1 eq.), catalyst (mol%), NaO t Bu (2.0 eq), toluene [1M], 120 °C, 24 h. a 1,3,5-trimethoxybenzene as 1 H NMR internal standard; values in parentheses indicate the yield of isolated product, b 6 eq of 1

Reaction conditions: 9 (1.0 eq.), pentamethylacetophenone (1.1 eq.), catalyst (mol%), NaO t Bu (eq), toluene [1M], 120 °C, 24 h. a 1,3,5-trimethoxybenzene as 1 H NMR internal standard; values in parentheses indicate the yield of isolated product, b reaction performed with 1, c 48 h, d 100 °C, e 2 eq. of 9 (conversion based on Ph*-methyl ketone)

This journal is © The Royal Society of Chemistry 20xx J. Name., 2013, 00, 1-3 | 6

Acknowledgements

The authors are grateful for the access to the MS analysis at the CCSM and NMR facilities at CCRMN at the Université Lyon 1. The CCIR of ICBMS is acknowledged for providing computational resources and technical support.

Notes and references

Author Contributions

The methodology of synthesis was designed by MJ and FP. Experimental work was performed by JF and molecular modelling by JR based on preliminary calculations from JF. The interplay between experiment and theory was supervised by PAP and MELP. XRD was performed by EJ. The manuscript was collegially written by all authors.

Conflicts of interest


Alexandre Gilet

Claude Quettier

Vincent Wiatz

Hervé Bricout

Michel Ferreira

Cyril Rousseau

Eric Monflier

Sébastien Tilloy

Synthesis of 2-Hydroxydodecyl Starch Ethers: Importance of the Purification Process

Keywords: Aqueous medium, Etherification, Starch modification

come   L'archive ouverte pluridisciplinaire

INTRODUCTION

Starch is one of the most abundant polysaccharides on earth and is found in cereals (wheat, corn, rice), legumes (pea) and tuber (potato, cassava) as semi-crystalline granules. [START_REF] Bemiller | Starch : Chemistry and Technology[END_REF][START_REF] Buléon | Starch Granules: Structure and Biosynthesis[END_REF] It is mainly composed of two polymers of D-glucose, which are amylose and amylopectin. The former is mainly linear with α-1,4 bonds while the latter is branched with 5% of α-1,6 bonds. Starch has been widely used in its native form (i.e. not chemically modified) or physically modified mainly for food applications. [START_REF] Bemiller | Starch : Chemistry and Technology[END_REF][START_REF] Bemiller | One Hundred Years of Commercial Food Carbohydrates in the United States[END_REF][START_REF] Ashogbon | Recent Trend in the Physical and Chemical Modification of Starches from Different Botanical Sources: A Review[END_REF][START_REF] Abbas | Modified Starches and Their Usages in Selected Food Products: A Review Study[END_REF] Starch derivatives have been developed to overcome some drawbacks of native starch used in food such as gel texture, retrogradation or syneresis. Such derivatives included starch esters (mainly phosphate, acetate and octenyl succinate), [START_REF] Landerito | Preparation and Properties of Starch Phosphates Using Waxy, Common, and High-Amylose Corn Starches. II. Reactive Extrusion Method[END_REF][START_REF] Ačkar | Starch Modification by Organic Acids and Their Derivatives: A Review[END_REF][START_REF] Sweedman | Structure and Physicochemical Properties of Octenyl Succinic Anhydride Modified Starches: A Review[END_REF] starch ethers (mainly hydroxyethyl, hydroxypropyl or carboxymethyl), [START_REF] Kaur | Factors Influencing the Properties of Hydroxypropylated Potato Starches[END_REF][START_REF] Pal | A Comparative Account of Conditions of Synthesis of Hydroxypropyl Derivative from Corn and Amaranth Starch[END_REF][START_REF] Spychaj | Medium and High Substituted Carboxymethyl Starch: Synthesis, Characterization and Application[END_REF] reticulated starch [START_REF] Ačkar | Starch Modification by Organic Acids and Their Derivatives: A Review[END_REF] and combination of these derivatizations. [START_REF] Ashogbon | Recent Trend in the Physical and Chemical Modification of Starches from Different Botanical Sources: A Review[END_REF][START_REF] Ačkar | Starch Modification by Organic Acids and Their Derivatives: A Review[END_REF][START_REF] Chen | Recent Progress in Chemical Modification of Starch and Its Applications[END_REF][START_REF] Masina | A Review of the Chemical Modification Techniques of Starch[END_REF][START_REF] Hong | Recent Advances in Techniques for Starch Esters and the Applications: A Review[END_REF][START_REF] Wilpiszewska | Ionic Liquids: Media for Starch Dissolution, Plasticization and Modification[END_REF][START_REF] Lewicka | Chemical Modifications of Starch: Microwave Effect[END_REF][START_REF] Tomasik | Chemical modification of starch[END_REF][START_REF] Gilet | Unconventional Media and Technologies for Starch Etherification and Esterification[END_REF] Due to the nature of the reagent that is employed and the used conditions, the granular structure of starch was usually preserved and the purification steps are fairly easy to proceed, the modified starch staying in suspension and thus being easily recovered by filtration. [START_REF] Bemiller | Starch : Chemistry and Technology[END_REF][START_REF] Kaur | Factors Influencing the Properties of Hydroxypropylated Potato Starches[END_REF][START_REF] Pal | A Comparative Account of Conditions of Synthesis of Hydroxypropyl Derivative from Corn and Amaranth Starch[END_REF][START_REF] Aminian | Preparation and Characterization of High Degree Substituted Sago (Metroxylon Sagu) Starch with Propylene Oxide[END_REF] Other methods including dry or semi-dry reactions [START_REF] Khalil | Preparation of Some Starch Ethers Using the Semi-Dry State Process[END_REF][START_REF] Khalil | Preparation of Some Cationic Starches Using the Dry Process[END_REF] and reactions in a medium where the starch did not swell (typically alcohols like ethanol or isopropanol, acetone or mixture of these solvents with water) [START_REF] Kooijman | Experimental Studies on the Carboxymethylation of Arrowroot Starch in Isopropanol-Water Media[END_REF][START_REF] Spychaj | Carboxymethyl Starch with High Degree of Substitution: Synthesis, Properties and Application[END_REF] led to a higher degree of substitution. [START_REF] Bemiller | Starch : Chemistry and Technology[END_REF] The synthesis of starch esters and ethers of high degree of functionalization and with different alkyl chain length allowed the obtainment of mechanical and thermal properties suitable for a plastic use [START_REF] Volkert | A Comparison of Different Synthesis Routes for Starch Acetates and the Resulting Mechanical Properties[END_REF][START_REF] Xu | Synthesis and Characterization of Starch Acetates with High Substitution[END_REF][START_REF] Junistia | Experimental and Modeling Studies on the Synthesis and Properties of Higher Fatty Esters of Corn Starch[END_REF][START_REF] Winkler | Thermal and Mechanical Properties of Fatty Acid Starch Esters[END_REF][START_REF] Funke | Effect of Reaction Conditions and Alkyl Chain Lengths on the Properties of Hydroxyalkyl Starch Research Paper[END_REF][START_REF] Bien | Hydrophobic Modification of Starch by Alkali-Catalyzed Addition of 1,2-Epoxyalkanes[END_REF][START_REF] Wesslén | Synthesis of Amphiphilic Amylose and Starch Derivatives[END_REF] but also implies the loss of the granular structure. [START_REF] Bemiller | Starch : Chemistry and Technology[END_REF] Purification process in that case was hindered due to the pastelike structure of the crude material and the difficulty of filtration of the product. Purification usually implied the use of mechanical energy to break the crude (like grinding or blending) or the dissolution in an appropriate solvent followed by precipitation. Works around starch etherification mainly concerned short chains where the granular structure was kept intact. Nevertheless, some publications described experiments with gelatinized/destructured starch and fatty epoxides in DMSO [START_REF] Wesslén | Synthesis of Amphiphilic Amylose and Starch Derivatives[END_REF][START_REF] Wesslén | Amphiphilic Graft Copolymers -Preparation and Interfacial Properties[END_REF] or in water. [START_REF] Funke | Effect of Reaction Conditions and Alkyl Chain Lengths on the Properties of Hydroxyalkyl Starch Research Paper[END_REF][START_REF] Bien | Hydrophobic Modification of Starch by Alkali-Catalyzed Addition of 1,2-Epoxyalkanes[END_REF][START_REF] Wokadala | Inducing PLA/starch Compatibility through Butyl-Etherification of Waxy and High Amylose Starch[END_REF] More precisely, in 2001 the groups of Lindhaueur and Warwel simultaneously described the production of higher starch ethers in an aqueous alkaline medium with 2-hydroxyalkyl chains possessing 8 to 18 carbons. [START_REF] Funke | Effect of Reaction Conditions and Alkyl Chain Lengths on the Properties of Hydroxyalkyl Starch Research Paper[END_REF][START_REF] Bien | Hydrophobic Modification of Starch by Alkali-Catalyzed Addition of 1,2-Epoxyalkanes[END_REF] The experimental conditions were relatively similar but the group of Warvel used in addition sodium sulfate as co-catalyst. Compared to the classical processes performed in organic solvent, water was considered as green solvent leading these two processes to ecological favorable experimental conditions. In both cases, the starch ethers were recovered by several washings in water and organic solvents (ethanol, isohexane or diethyl ether) or by Soxhlet extraction with petroleum ether. Nevertheless, there were no details on the purification conditions and on the nature of the impurities. In this context, we described in this article two detailed methods for the purification of 2-hydroxydodecyl potato starch ethers synthesized using alkaline conditions in water. 1,2-epoxydodecane was chosen for its industrial availability and its low price. In addition, to limit the quantity of co-products and so to reduce the environmental impact, the workup without sodium sulfate issued from the publication of Lindhauer was chosen. A special attention has been given to the optimisation of the purification conditions in order to facilitate this complicated step. That is why the impurities extracted from the medium were, as far as possible, quantified and identified.

MATERIALS AND METHODS

Materials

Potato starch with water content of about 16% was kindly supplied by Roquette Frères SA, Lestrem, France. 1,2-epoxydodecane (90% of purity) and potassium hydroxide (85% of purity; 15% w/w of water) were obtained from Aldrich and Merck respectively. Petroleum ether (boiling point: 40-60°C (> 90%)) and ethanol (99% of purity) were purchased from Aldrich and were used as supplied without further purification.

Synthesis of starch hydroxydodecyl ethers

To a suspension of potato starch (2.14 g of starch containing 16% (w/w) of water i.e. 11.1 mmol of anhydroglucose unit (AGU)) in water (4.0 g) in a 25 mL autoclave with a mechanical stirring, potassium hydroxide (0.58 g of potash containing 15% (w/w) of water i.e. 8.9 mmol, 0.8 eq. mol/AGU) dissolved in water (0.9 g), was added at room temperature (Figure 1). The thick and clear starch gel obtained was stirred for 15 minutes. To this gel was added the 1,2epoxydodecane (6.80 g, purity (90%), 33.3 mmol, 3 eq. mol/AGU). The autoclave was closed and the medium was then heated at 140°C for 6h under stirring. At the end of the reaction, the autoclave was cooled down to room temperature. The solid reaction product (a beige pasty crude product named crude) was extracted from the autoclave. Note that no liquid phase was present. As described in detail afterwards in this publication, the isolation of the starch product was performed by the following procedures (Figure 1). Pre-purification steps were done on the crude product by several washings by a mixture of water/ethanol (1/2). The product purified by this pre-purification

Characterisation

Elemental analysis was used to determine the molar substitution (MS) of the product and was carried out on a Thermo Scientific FlashEA 1112. The samples were oven-dried at 100°C for 24h before the analysis to remove water.

NMR analyses were recorded on a Bruker DPX300 Avance spectrometer. [START_REF] Bemiller | Starch : Chemistry and Technology[END_REF] H-NMR and [START_REF] Masina | A Review of the Chemical Modification Techniques of Starch[END_REF] C-NMR analysis were recorded at 25°C at 300.13 MHz and at 75.5 MHz respectively. The sample was dissolved in an appropriate solvent (CDCl3 or DMSO-d6, purchased from Eurisotop (99.5% and 99.8% of isotopic purity, respectively)).

Infrared spectra were recorded on a Bruker Vector 22 FTIR spectrometer with a diamond/Zr crystal under attenuated total reflectance. The spectra were recorded by the accumulation of 100 scans between 700 and 4000 cm -1 at a resolution of 4 cm -1 .

MALDI-TOF spectra were realized with a Bruker DaltonicsUltraflex II spectrometer in the positive reflectron mode.

RESULTS AND DISCUSSION

2-Hydroxydodecyl ethers of starch were synthesized from potato starch and 1,2-epoxydodecane in alkaline medium. The isolation of starch products was performed in two steps: (i) a prepurification procedure followed by a purification by grinding in ethanol or by Soxhlet in petroleum ether.

The pre-purification procedure of the crude was performed as described in the Figure 2. This step consisted in neutralising the alkaline medium with aqueous HCl solution and then to remove the created potassium chloride. The crude extracted from the autoclave (14.42 g) was put in 50 mL of water and grinded by the mean of an Ultra-Turrax® (1 min) until only small particles could be observed. The alkaline medium was neutralized with 1 M aqueous hydrochloric acid under stirring by an Ultra-Turrax® (1 min). 100 mL of ethanol was then added (giving a ratio 2:1

C C C

14.42 g to water). This mixture of water/ethanol (1/2) was used to solubilize KCl and the potential organic impurties. The suspension was grinded for 1 min by Ultra-Turrax® and centrifuged. The solid and liquid phases were separated by centrifugation. The liquid phase containing impurities was evaporated for identification and a mass of 2.71 g was extracted. The solid phase was washed by grinding in 75 mL of a mixture of water/ethanol (1/2) and recovered by centrifugation. This step was repeated once. After evaporation of the two liquid phases, masses of 0.40 g and 0.19 g were extracted. The solid phase recovered after the third centrifugation was dried under vacuum and a PPP mass of 6.20 g was obtained. In order to optimize the purification, the three extracted solids obtained during the pre-purification step were analysed. The two first solids contained KCl as demonstrated by formation of a AgCl precipitate by addition of aqueous AgNO3. So, KCl was extracted during the two first washings. A sample of each solid was dissolved in CDCl3 and analysed by 1 H NMR (Figure 3). The spectra of 1,2-epoxydodecane and 1,2-dodecanediol were presented as reference (Figure 3, spectra 1 and 2). No traces of 1,2-epoxydodecane was observed in the three filtrates, confirming its total consumption. The presence of 1,2-dodecanediol, as hydrolysis product of the epoxide, was clearly showed in the three filtrates (Figure 3, spectra 3, 4 and 5). However, some peaks in these spectra did not match with the 1,2-epoxydodecane (black dots on spectra 4 and 5 in Figure 3). To determine the nature of the residual impurities, the solids issued from the washings 2 and 3 were gathered and washed with small quantities of ethanol to remove the 1,2-dodecanediol. Indeed, the solubility of 1,2-dodecanediol in ethanol at 25°C was determined to be 300 g/L. The washing left an insoluble product after solubilisation of 1,2-dodecanediol. This insoluble product was dried, dissolved in CDCl3 and analysed by [START_REF] Bemiller | Starch : Chemistry and Technology[END_REF] H NMR (Figure 3, spectrum 6), [START_REF] Masina | A Review of the Chemical Modification Techniques of Starch[END_REF] C NMR, 2-dimensional NMR experiments and MALDI-TOF-MS (see supporting information; Figures S1, S2 andS3).

Bis-(2-hydroxydodecyl)oxide was clearly identified. This dimer was issued from the reaction of 1,2-dodecanediol on 1,2-epoxydodecane. The symmetry of the obtained oxide was probably due to the preference of the less hindered primary alcohol of 1,2-dodecanediol to attack the less substituted site of the epoxide. It seemed important to notice that this kind of by-product was never reported during the synthesis of 2-hydroxyalkyl starch ethers.

To resume, at the end of the pre-purification steps and after drying under vacuum, PPP was recovered (m(PPP) = 6.20 g). So, from a crude mass of 14.42 g (containing 5.33 g of an initial mass of water), 6.20 g of PPP was obtained by having removed 3.30 g of impurities. The observed enhancement of 0.41 g (14.42 g -5.33 g -3.30 g -6.20 g) was attributed to the medium neutralisation by KOH (the weight of KOH was replaced by the weight of KCl formed) and to the consumption of water in the formation of 1,2-dodecanediol. PPP was not totally soluble in classical NMR solvents preventing analysis. However, when CDCl3 was added on PPP, the NMR analysis clearly showed the presence of soluble impurities such as 1,2-dodecanediol and dimer. In addition, the last purification by the mixture water/ethanol (1/2) allowed to only extract 6% (=0.19/3.30x100) of impurities (compared to the values of 82% (=2.71/3.30x100) and 12% (=0.40/3.30x100) extracted during the first and the second washings, respectively). So, the impurities seemed deeply included inside the modified starch and so an enhanced purification was necessary. So, to be further purify, PPP was submitted to two different subsequent treatments either by an Ultra-Turrax® apparatus (Grinding) or by a Soxhlet extraction (Soxhlet). The treatment by an Ultra-Turrax® allowed to stir, disperse, homogenize and grind the modified starch in order to remove impurities by further washings. The extraction by Soxhlet allowed to remove impurities from modified starch by repeated washings with an organic solvent at higher temperature. In order to obtain two samples of PPP (one for the purification by grinding and another for the purification by Soxhlet; 2 x 6.20 g), the synthesis and the pre-purification steps were performed twice with high reproducibility.

In order to remove the residual impurities, the first choice felt on a purification by further grinding on PPP. To find the best solvent to extract the impurities, the solubility of 1,2-dodecanediol and bis-(2-hydroxydodecyl)oxide was determined in various solvents at 25°C (table 1). According to these results, heptane, petroleum ether or water were inappropriate solvents since the impurities were insoluble. The impurities were only slightly soluble in isopropanol, diethyl ether, acetone or ethyl acetate. The best options appeared to be available for chloroform or THF since both impurities were highly soluble. Unfortunately, the crude product swelled in those solvents and cannot be recovered afterwards, either by filtration or by centrifugation. Ethanol is therefore the best solvent among the remaining solvents to extract these impurities by considering their solubility. PPP (6.20 g) was grinded for 1 minute in pure ethanol (75 mL -Figure 4). The solid and the liquid phase were separated by centrifugation. The liquid phase was evaporated and the residual solid (0.87 g) was analysed by 1 H-NMR. The presence of 1,2-dodecanediol and bis-(2hydroxydodecyl)oxide was demonstrated. This procedure was repeated twice and 0.41 g and 0.25 g of residual solids containing 1,2-dodecanediol and bis-(2-hydroxydodecyl)oxide were respectively obtained. At the 3 rd extraction, 1 H NMR analysis demonstrated that the dimer was more and more difficult to extract. The dimer has a limited solubility in ethanol at room temperature (15 g.L -1 ) but its solubility in ethanol at 50°C was higher (300 g.L -1 ). Therefore, to extract the remaining impurities, the solid was grinded in 50 mL of ethanol and then the suspension was heated at 50°C under stirring. The solid did not stay in this dispersed form when heating but became soft and sticky. The warm solvent is thus removed by transfer. The product needed to be

Solvent

C C C

cooled down with cold ethanol (50 mL) to make it hard enough to be again grinded. This process was repeated until no impurity was observed in the filtrate (five times). At the end, the final product SE-G was obtained after drying under vacuum (m(SE-G) = 3.50 g). Some assays were performed to determine the molar substitution (MS). MS was defined as the molar ratio of 2-hydroxydodecyl substituents to anhydroglucose units of the starch molecules. The first attempts for its determination were realized by NMR but unfortunately this modified starch was not soluble in the traditional solvents (water, chloroform, DMSO, acetone, pyridine, methanol or ethanol) even after being heated for 24h. Hence, the molar substitution was determined by the mean of elemental analysis (Table 2, entry 1-see supporting information). The MS value for SE-G was equal to 1.11.

A reaction efficiency of 37% and a yield of 85% were also determined. The FT-IR spectra of native starch and SE-G were shown in supporting information (Figure S5). The structure of etherified starch was mainly confirmed by the intensity increase of the carbon-hydrogen bonds elongation bands (C-H) compared to native starch. To find the best way for the purification, another method was performed to extract the impurities.

Thus, a Soxhlet extraction was performed on PPP (6.20 g) with petroleum ether (40-60°C fraction)

as solvent since this one is usual to purify modified starch (Figure 5). 28 Note that other solvents (such as ethanol, chloroform) were assayed but they were inappropriate for a purification by Soxhlet (product stuck on the cartridge, leak across the cartridge). After 24 h of extraction with petroleum ether, the product in the cartridge was found as an aggregated uniform solid instead of its initial powder form. The liquid phase (solution in petroleum ether) was evaporated leading to a residual solid (3.59 g). The analysis by 1 H-NMR allowed to identify the presence of 1,2-dodecanediol and bis-(2-hydroxydodecyl)oxide. A second Soxhlet was performed and no supporting impurities were extracted. After drying under vacuum, the final product SE-S was obtained (m(SE-S) = 2.60 g). The MS, reaction efficiency and yield were equal to 1.12, 37% and 63%, respectively (Table 2, entry 2). As already described in the case of SE-G, the FT-IR spectrum of SE-S showed the intensity increase of the carbon-hydrogen bonds elongation bands (C-H) compared to native starch (see supporting information; Figure S5).

Although the masses of PPP were the same at the beginning of both further purifications (6.20 g for each), each method of purification gave a different quantity of final product. Indeed, the purification by grinding and Soxhlet gave 3.50 g and 2.60 g, respectively. Note that a same value of MS (around 1.1) was determined for the two products (SE-G and SE-S). In order to ensure of the specificity of each purification method, the samples SE-G and SE-S were purified by Soxhlet (Figure 6) and grinding (Figure 7), respectively. SE-G was suspended in petroleum ether and a Soxhlet extraction was performed during 24 h. The liquid phase (solution in petroleum ether) was evaporated leading to a residual solid (0.63 g). A second Soxhlet extraction was performed and no supporting solid was extracted (< 0.01 g). After this purification, the MS and the reaction efficiency remained constant whereas the overall yield decreased to 70% ( For the same purpose, by following a similar procedure than SE-G, SE-S was grinded twice in 50 mL of ethanol and then the suspension was heated at 50°C under stirring (Figure 7). The warm solvent is then removed by transfer. It is important to underline that no impurity was extracted.

Logically, the values of the MS, reaction efficiency and yield remained constant (1.12, 37% and 63%, respectively -Table 2, entry 4).

In order to understand this difference in behavior between SE-G-S and SE-S-G samples, we noticed that the solid (0.63 g) extracted during the Soxhlet treatment of SE-G (Figure 6) was perfectly soluble in chloroform, contrary to all the obtained starch ethers samples. This unexpected property permitted to obtain a 1 H-NMR spectrum in CDCl3 which showed the absence of 1,2dodecanediol and of bis-(2-hydroxydodecyl)oxide but the presence of peaks relative to 2hydroxydodecyl chains and to glucose units (see supporting information; Figure S4). Because of its solubility in chloroform and of the observed NMR signals, we think that this extracted solid was probably composed of low molecular weight starch ethers. This interpretation was confirmed by elemental analysis. Indeed, the extracted solid gave a MS value of 1.09, compared to 1.11 and 1.10 for SE-G and SE-G-S respectively, showing that the major difference of solubility observed came probably from smaller molecular sizes in the extracted solid and not from a possible higher degree of etherification.

The structural changes producing these low molecular weight starch ethers probably occurred during the synthesis at high temperature in strong alkaline conditions. Indeed, some publications described the degradation of starch chains in alkaline conditions. [START_REF] Han | Structural Changes in Corn Starches during Alkaline Dissolution by Vortexing[END_REF][START_REF] Lee | Effect of pH on Aqueous Structure of Maize Starches Analyzed by HPSEC-MALLS-RI System[END_REF][START_REF] Jackson | Characterization of Starch Cooked in Alkali by Aqueous High-Performance Size-Exclusion Chromatography[END_REF][START_REF] Igura | Effect of Longer Heating Time on Depolymerization of Low Moisturized Starches[END_REF] To give a global overview of the synthesis, figure 8 Masses extracted (solids): and SE-S-G. The process by Soxhlet extraction compared to the process by grinding required less steps for the purification (1 vs 8) but a longer time (24h vs 80 minutes). It can be noted that whatever the method of purification, the values of the MS were around 1.1. However, there is a gap in the recovery yield of the products by comparing SE-G, SE-S, SE-G-S and SE-S-G (85%, 63%, 70% and 63%, respectively). The difference was probably due to the extraction of low molecular weight starch ethers when the treatment by Soxhlet was performed. Finally, it would be very interesting to find a method to determine a potential degradation of the starch molecular structure during the synthesis. Unfortunately, classical methods required a solvent to solubilize the modified starch but, in our case, 2-hydroxydodecyl starch ethers of were insoluble in usual solvents.

CONCLUSIONS

2-hydroxydodecyl starch ethers were synthetized by reaction of 1,2-epoxydodecane with potato starch in aqueous alkaline medium. A careful attention has been given to the purification steps and, more precisely, to the identification and the quantification of the co-products. In addition to classically observed 1,2-dodecanediol, bis-(2-hydroxydodecyl)oxide was extracted from the crude. This dimer issued from the reaction of the diol on the epoxide has never been described during the synthesis of 2-hydroxyalkyl starch ethers. The purification by Soxhlet extraction compared to the process by grinding required less steps but a longer time. The values of the MS were always around 1.1 in the used conditions, but the recovery yields were higher for the treatment by grinding compared to Soxhlet (85% vs 63%). Finally, in term of industrial Jérémy Ternel, Nicolas Kania and Dominique Prévost are acknowledged for NMR analysis and technical assistance.

Figure 1 :

 1 Figure 1: 2-hydroxydodecylstarch synthesis and purification modes conducted after etherification

Figure 2 :

 2 Figure 2: Pre-purification steps of the 2-hydroxydodecylstarch from the crude reaction product

Figure 3 :

 3 Figure 3: 1 H-NMR spectrum of (1) 1,2-epoxydodecane, (2) 1,2-dodecanediol, (3) first solid issued

  of bis-(2-hydroxy-dodecyl)oxide in ethanol at 50°C is equal to 300 g.L -1

Figure 4 :

 4 Figure 4: Further washings done by Grindings of the pre-purified product (PPP) and leading to a

  Pre-Purified Product (prepurified starch ether); G: grinding step by using an Ultraturrax grinder, at 20°C, during 1 min; C: centrifugation step at 4000 rpm, 20°C and during 5 min (sol.=solid; liq.=liquid); E: evaporation of the ethanol by a rotary vacuum evaporator; 50°C: heating of the suspension at 50°C under stirring and until the particules gather together into a soft and sticky solid (2 min are needed); T: removal of the liquid around the sticky solid by simple Transfer into another flask (the sticky solid turns to a hard solid by cooling); V: drying under vacuum; SE-G: Starch Ether purified by Grinding.

Figure 5 :

 5 Figure 5: Further washings done by Soxhlet extractions on the pre-purified product (PPP) and

Figure 6 :

 6 Figure 6: Further washings done by Soxhlet extractions on the 2-hydroxydodecylstarch obtained

Figure 7 :

 7 Figure 7: Further washings done by Grindings of the 2-hydroxydodecylstarch obtained after

Figure 8 ::::

 8 Figure 8: Mass follow-up done during the purification of the 2-hydroxydodecylstarch and

140°C, 6 h Crude product

  . . . . . . . . . . . . . . . .

	Potato Starch (16% w/w of H 2 O) . . . . . . . . . . 2.14 g . . . . . . . (11.1 mmol of AGU)
	1,2-Epoxydodecane (90% of purity) . . . . . . . 6.80 g . . . . . . . (33.3 mmol of epoxide; 3 eq. mol. /AGU)
	KOH (85% of purity; 15% w/w of H 2 O) . . . . . 0.58 g . . . . . . . (8.9 mmol; 0.8 eq. mol. /AGU)
	Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.90 g . . . . . . . (5.33 g for the overall water; 3 g/g of dry starch)

14.42 g (overall mixture obtained as a beige paste) Further purification by Grinding EtOH SE-G Further purification by Soxhlet

	step was named PPP (pre-purified product). After this step, the remaining solid was purified either
	by grinding in ethanol or by Soxhlet in petroleum ether. The products purified by Soxhlet or
	grinding were named SE-S (Starch Ether -Soxhlet) and SE-G (Starch Ether -Grinding),
	INITIAL MEDIUM:
	respectively.
		HCl aq. / H 2 O / EtOH
	CRUDE	Pre-purification	PPP
			Petroleum ether
			SE-S

Table 1 :

 1 Solubility of the two impurities in different solvents at 25°C

Table 2 :

 2 Experimental results obtained for the synthesis of 2-hydroxydodecylstarch

	Entry	Product	MS a	MS b	MS c	RE d (%)	Yield (%)
	1	SE-G	1.13	1.09	1.11	37	85
	2	SE-S	1.15	1.08	1.12	37	63
	3	SE-G-S	1.12	1.09	1.10	37	70
	4	SE-S-G	1.15	1.08	1.12	37	63
	a calculated from the percentage of C determined by elemental analysis; b calculated from the percentage of H
	determined by elemental analysis; c Mean of the two values; d RE (reaction efficiency) = experimental MS / theoretical
	MS

Table 2 ,

 2 entry 3).

		Petroleum		Petroleum
		ether		ether
	SE-G	S	sol.			S	sol.	V	SE-G-S
	3.50 g	E	liq.	Petroleum ether	liq.	E		Petroleum ether	2.86 g
	Masses extracted (solids):	0.63 g		< 0.01 g
	SE-G: Starch Ether purified by Grinding; S: Soxhlet extraction done with petroleum ether (40-60°C) during 24 h; E: evaporation of the
	solvents by a rotary vacuum evaporator; V: drying under vacuum; SE-G-S: Starch Ether purified by Grinding and then by Soxhlet.

  lists the various purification steps.

		+ 50 mL EtOH	+ 50 mL EtOH
	SE-S	G	C	sol.	G	50°C	T	sol.	V	SE-S-G
	2.60 g		liq.					liq.		2.59 g
		EtOH	E		EtOH	E
			< 0.01 g				< 0.01 g

SE-S:

Starch Ether purified by Soxhlet; G: grinding step by using an Ultraturrax grinder, at 20°C, during 1 min; C: centrifugation step at 4000 rpm, 20°C and during 5 min (sol.=solid; liq.=liquid); E: evaporation of the ethanol by a rotary vacuum evaporator; 50°C: heating of the suspension at 50°C under stirring and until the particules gather together into a soft and sticky solid (2 min are needed); T: removal of the liquid around the sticky solid by simple Transfer into another flask (the sticky solid turns to a hard solid by cooling); V: drying under vacuum; SE-S-G: Starch Ether purified by Soxhlet and then by Grinding.

Funding Sources

IFMAS (Institut Français des Matériaux Agro-Sourcés / ANR-10-IEED-0004-01) is acknowledged for the financial support of Alexandre Gilet's thesis.

Synthesis of 2-Hydroxydodecyl Starch Ethers:

Importance of the Purification Process Alexandre Gilet, ‡, † , Claude Quettier, ※ Vincent Wiatz, ※ Hervé Bricout, ‡ Michel Ferreira, ‡ Cyril Rousseau, ‡ Eric Monflier, *, ‡ Sébastien Tilloy, ‡ development, the recycling of the washing solvents is possible in the both cases. Nevertheless, the technologies available at industrial scale are more in line with the transposition of the grinding process that can provide better productivity through the use of existing and scalable equipment to handle both grinding of the crude product and extraction of soluble by-products in relevant solvent.

Supporting Information.

The characterizations of bis-(2-hydroxydodecyl)oxide and the determination of the molar substitution (MS) of the 2-hydroxydodecyl potato starches by elemental analysis were presented.

AUTHOR INFORMATION

Corresponding Author

*Telephone: +33 3 21 79 17 72. E-mail: eric.monflier@univ-artois.fr

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. ACKNOWLEDGMENT