Christophe Coquelet
email: christophe.coquelet@mines-paristech.fr

Eric Auger

Alain Valtz

Density and excess volume for four systems involving eugenol and furan

Keywords:

Density and excess volume for four systems involving eugenol and furan

Christophe Coquelet, Eric Auger,

Introduction

Accurate predictions of the thermodynamic properties of multi-component fluid mixtures are essential for both the optimization of current industrial processes and the design of new ones.

Biomass is considered as the new source of raw material to produce new molecules and also energy (biofuels, biogas). In several operation, units like heat exchangers, liquid-liquid extraction and distillation columns require a good estimation of density, speed of sound and so excess volume for the mixtures concerned to design them. Among these systems, the second-generation biofuels or mixture of oxygenated compounds involve several molecules and mixtures whose such properties are unknown. Mixing of oxygenated compounds generally leads to solutions that do not behave ideally. The deviation from ideal behavior can be conveniently expressed by excess properties.

Excess properties are also very useful to understand the mixing state in terms of intermolecular interactions. The information concerning molecular interaction are required to the design of solvents for industrial applications. Solvents are designed to extract molecule of interest and to let the nondesirable molecules in the original media.

In this article, we will focus on two chemicals of interest furan and eugenol which are used as intermediate in chemistry or in medicine. Indeed, they are widely used in the production of the solvent tetrahydrofuran, as additives for detergents and herbicides, in dentistry applications, as antiseptic and anesthetic products in pharmacy and in aquaculture [1], [2]. Ethanol, 1-Octanol and nhexane are the studied solvents. Some volumetric properties of the systems Eugenol+Hexan, Eugenol+1-Octanol, Furan+Ethanol and Furan+1-Octanol are also presented.

First, new experimental measurements of density and excess volume for the binary mixtures Eugenol+n-hexan, Eugenol+1-Octanol, Furan+Ethanol and Furan+1-Octanol are presented. Then, these new experimental excess volumes are correlated by the Redlich-Kister correlation. Finally, the Prigogine-Flory-Patterson (PFP) Theory is applied to identify the most predominant molecular interaction.

Experimental details

Materials purities and suppliers

Table 1 presents the chemical species, suppliers, purity and refractive index. Compositions are prepared gravimetrically. given by Gladstone [3] at 290.33 K, GC: Gas Chromatograph

Experimental method

Density measurements have been all performed with the DSA5000M Anton Paar digital vibrating tube densimeter. The oscillating period or frequency, measured by the densitometer, is depending on the tube mass and therefore on the fluid density. Eq. 1 is used for relating the period of vibration, , to density, :

2   b a   (1)
where a and b are constants to be adjusted. For these purposes we have used bi-distilled and degassed water, and dry air, at 293.15 K. Uncertainty on measured density is estimated lower than 10 -5 g.cm -3 . One platinum resistance thermometer with 0.01 K accuracy is used for temperature measurements. The sample densities are then measured at thermal equilibrium for various temperatures. This densitometer permits also the measurement of speed of sound with an accuracy of 0.5 m.s -1 .

To prepare the mixtures, an empty 20 cm 3 glass bottle is air-tight closed with a septum and then put under vacuum using a vacuum pump where a needle is introduced through the septum. Empty bottle is weighed, and then the less volatile component, freshly degassed, is introduced by means of a syringe. After weighing the bottle loaded with the first component, the more volatile one is added similarly and then the bottle is weighed again. All weighing are performed using an analytical balance with 10 -4 g accuracy, correspondingly the uncertainty is estimated to be lower than 2x10 -5 for mole fractions. Maximum uncertainty resulting in the calculation of v E is estimated to be less than

2 x m u u u    u M M M M u M x M x M x M x u E                                                        (4)
With M i the molar mass of component i, m i the mass of component i,  i the density of component i,  m density of the mixture.

Results and Discussions

The density values of pure chemicals measured using the DSA 5000M Anton Paar densitometer are presented as a function of temperature in Table 2. Comparison with literature was done and presented in Supplementary Information. These data will be also considered to determinate the pure component parameters for the data treatment using PFP model (see section 3.2).

Table 2: Density of each pure component studied at atmospheric pressure (U p = ±0.03 kPa, U T =±0.01K, U  =±10 -5 g.cm -3 (k=2)).

Eugenol

Furan Ethanol 1-Octanol n-hexane

T / K
 exp / g.cm -3

T / K

 exp / g.cm -3

T / K

 exp / g.cm -3

T / K

 exp / g.cm -3

T / K

These data were used to calculate the excess volume. The excess molar volume v E , is calculated using Eq. 5.

* 2 2 * 1 1 v x v x v v E    (5)
where x 1 and x 2 represent mole fractions and * 1 v and * 2 v are the molar volumes of components 1 and 2 respectively. v stands for the molar volume of mixture. Using the measured density , Eq. 5 can be rewritten as:

* 2 2 2 * 1 1 1 2 2 1 1    M x M x M x M x v E           (6)
where 1 M and 2 M are the molar masses * 1  and * 2  are the densities of components ( 1) and (2) respectively.  stands for the density of the mixture.

Redlich Kister data treatment

Usually Redlich-Kister (RK) correlation [4] is chosen to correlate excess molar volume of binary systems. Eq. 6 presents the correlation.

     i i i E x x A x x v 2 1 2 1 (7)
The coefficients (A i ) have to be determined. The variance , corresponding to each fit, is calculated using Eq. 7.

 

            P N v v E cal E exp 2  ( 7
)
where P is the number of parameters (A n ) and N exp represents number of experimental data.

The main difficulty of the RK treatment is the selection of the number of parameter A i . In order to do that, it is recommended to investigate

2 1 x x v E
as a function of molar composition x 1 . This quantity gives us useful information concerning volumetric properties, particularly at low concentration as suggested by Desnoyers and Perron [5]. This term is directly related to the apparent molar volume and so can be assimilated to a thermodynamic property. Eq. 8 shows that

2 1 x x v E
is directly linked to the apparent molar volume.

2 * 1 , 1 1 * 2 , 2 2 1 x v v x v v x x v E       (8)
where  , i v is the apparent molar volume. Desnoyers and Perron indicates that the change of the slope can be attributed to various factor: first one, the size and shape of molecules, the second one the intermolecular interaction energy differences at dilution and the third one the formation of chemical complex containing unlike molecules. Also, at infinite dilution, The partial molar volume i v (cm 3 .mol -1 ) of each component i has been calculated using Eq. 9, with V, the volume of the mixture (cm 3 ).

j n P T i i n V v , ,            (9)
By differentiating Eq. 6 with respect to n i and combining the result to Eq. 9 leads to equations for the partial molar volumes of the different species (Eqs. 10 and 11).

P T E E x v x v v v , 2 2 * 1 1              (10) P T E E x v x v v v , 1 1 * 2 2              (11)
Using Redlich Kister equation, we can obtain the expression of partial molar volumes (Eqs. 12 and 13) with respect to x i . as a function of x 1 and v E as a function of x 1 , at 2 different temperatures.

               1 2 2 2 2 2 2 2 * 1 1 2 1 1 2 2 1 n n n n x nA x x x A x v v (12)                   1 2 2 2 2 2 2 2 * 2 2 2 1 1 2 2 1 1 n n n n x nA x x x A x v v (13)

a. Furan ethanol binary system

As we can see, excess molar volume is negative but becomes positive close to pure ethanol. The analysis of apparent molar volume does not reveal any original behavior. But we can see that for furan at infinite dilution, apparent molar volume decreases certainly due to the fact there are more H bonds between ethanol molecules who surround the furan molecule. Excess molar volume is positive when we approach pure furan and when we increase the temperature. There is less H-bond between the two chemicals and so as there is an importance difference between the two dipole moments (1.69D for ethanol and 0.66D for furan [6]), there is less cross interaction and so an increasing of excess volume.

Table 3: Densities () and excess molar volumes (v E ) for furan (1) + ethanol (2) binary system as a function of furan mole fraction at atmospheric pressure (U p = ±0.03 kPa, U x1 =±2x10 -5 , U T =±0.01K, U  =±10 -5 g.cm -3 , U VE =±0.003 cm 3 .mol -1 (k=2)).

x 1 d /g.cm -3 as a function of x 1 and v E as a function of x 1 at 2 different temperatures. We can observe that there is no specific behavior. We can consider that it is a mixture of two liquids with similar size. As we can see, excess molar volume is positive, it is certainly due the difference of polarity between the two chemicals (furan: 0.66 D and 1-Octanol: 1.66 D [6]). In comparison with ethanol, as associating effect is less important for 1-Octanol, it seems that there is no association between the two molecules.

V E /cm 3 .mol -1 d /g.cm -3 V E /cm 3 .mol -1 d /g.cm -3 V E /cm 3 .mol -1 d /g.cm -3 V E /cm 3 .mol -
Table 5: Densities () and excess molar volumes (v E ) for furan (1) + 1-Octanol(2) binary system as a function of furan mole fraction at atmospheric pressure (U p = ±0.03 kPa, U x1 =±2x10 -5 , U T =±0.01K, U  =±10 -5 g.cm -3 , U VE =±0.003 cm 3 .mol -1 (k=2)).

x 1 d /g.cm -3 In order to understand the difference between excess volumes of Furan-Ethanol and Furan -1-Octanol, we draw a parallel with the mixtures Benzene -Alcohols. First, we can consider that the presence of the oxygen atom in the aromatic ring is the major difference between Furan and Benzene. Excess Volume with Benzene is essentially positive and is increasing with the length of the 1-Octanol, probably because of steric considerations. Thus, we can conclude that negative excess volume of Furan-Ethanol is due to H-Bond between Ethanol and the oxygen atom of Furan. Indeed, the alkyl chain of 1-Octanol may hide the potential H-Bond, leading to positive excess volume of Furan-1-Octanol. This assumption is comforted by the increase of excess volume with temperature, traducing the H-bonding breaking when the temperature increases.

V E /cm 3 .mol -1 d /g.cm -3 V E /cm 3 .mol -1 d /g.cm -3 V E /cm 3 .mol -1 d /g.cm -3 V E /cm 3 .mol -1 d /g.cm -1 V E /cm 3 .mol - 1 d /g.cm -3 V E /cm 3 .

c. Eugenol 1-Octanol binary system

Table 7 presents the values of mixtures densities and excess volume. Table 8 presents our results.

Following Desnoyers and Perron's method we have considered 3 RK parameters. Figs 5-6 presents respectively,

2 1 x x v E
as a function of x 1 and v E as a function of x 1 , at 2 different temperatures. There is no particular behavior. We can consider that it is a mixture of two liquids with similar size. As we can see, excess molar volume is negative, it is certainly due to dipole-dipole interaction as the dipole moment of the two chemicals are quite similar (eugenol: 1.129 D [START_REF] Sharma | Study and Design of Eugenol Derivatives as Potent Antioxidant Using Quantum Mechanical Method[END_REF] and 1-Octanol: 1.66 D [6]).

Table 7: Densities () and excess molar volumes (v E ) for Eugenol(1) + 1-Octanol(2) binary system as a function of furan mole fraction at atmospheric pressure (U p = ±0.03 kPa, U x1 =±2x10 -5 , U T =±0.01K, U  =±10 -5 g.cm -3 , U VE =±0.003 cm 3 .mol -1 (k=2)).

x 1  /g.cm -3 v E /cm 3 .mol -1  /g.cm -3 v E /cm 3 .mol -1  /g.cm -3 v E /cm 3 .mol -1  /g.cm -3 v E /cm 3 .mol -1  /g.cm -3 v E /cm 3 .
x 1  /g.cm -3 v E /cm 3 .mol -1  /g.cm -3 v E /cm 3 .mol -1  /g.cm -3 v E /cm 3 .mol -1  /g.cm -3 v E /cm 3 .

d. Eugenol n-hexane binary system

Table 9 presents the values of mixtures densities and excess volume. Table 10 presents our results.

Following Desnoyers and Perron's method we have considered 5 RK parameters. Figs 7-8 presents respectively,

2 1 x x v E
as a function of x 1 and v E as a function of x 1 , at 2 different temperatures. There is no particular behavior. As we can see, excess molar volume is negative, it is a surprising result as the two dipole moments of the two chemicals are very different (eugenol: 1.129 D and no dipole moment for n-hexane [6]). Another type of molecular interaction must be predominant.

Table 9: Densities () and excess molar volumes (v E ) for Eugenol(1) + n-hexane (2) binary system as a function of furan mole fraction at atmospheric pressure (U p = ±0.03 kPa, U x1 =±2x10 -5 , U T =±0.01K, U  =±10 -5 g.cm -3 , U VE =±0.003 cm 3 .mol -1 (k=2)). In order to have a better evaluation of the molecular interactions involved in such mixtures, we have decided to use the PFP model.

x 1  /g.cm -3 v E /cm 3 .mol -1  /g.cm -3 v E /cm 3 .mol -1  /g.cm -3 v E /cm 3 .mol -1  /g.cm -3 v E /cm 3 .mol -1  /g.cm -3 v E /cm 3 .
x 1  /g.cm -3 v E /cm 3 .mol -1  /g.cm -3 v E /cm 3 .mol -1  /g.cm -3 v E /cm 3 .mol -1  /g.cm -3 v E /cm 3 .

e. Partial molar volume

Using the parameters fitted for each binary system, we can plot the partial molar of furan or eugenol as a function of the molar composition: Figs. 9-12. We have also plotted on the same figure  , 1

v the apparent molar volume for the furan and eugenol. Apparent molar volume is an important property as it is linked to the nature of the molecular interaction between the two molecules, herein the solute (furan or eugenol) and the solvent (n-Hexane, Ethanol and n-Octanol). The partial molar volume corresponds to the volume occupied by the solute in the solution and it depends to the nature of the surrounding molecules. Partial molar volume and apparent molar volume are linked by the equation 14.

i j TPx i i i i i n v x v v              , ,   (14)
At infinite dilution, these two quantities are identical. The deviations seem to be more important for solute composition close to 0. We can also mention that for the system Eugenol + n-Hexane some important deviations exist in the region rich in n-hexane (Fig. 12). The deviations are more important, particularly at the highest temperature, in comparison with the others binary systems studied. There are two possibilities: it is necessary to increase the number of parameters of the Redlich Kister correlation (it is difficult to do that considering the experimental uncertainty and the fact that the curve

2 1 x x v E
as a function of x 1 are well correlated) or it may be the sign that molecular interactions are different for eugenol + n-hexane binary system in comparison with the others studied systems.

Consequently, another model for the data treatment should be used in order to identify such kind of molecular interaction.

Prigogine-Flory-Patterson model

The Prigogine Flory Patterson model (PFP) [START_REF] Patterson | Corresponding states theories and liquid models[END_REF] was developed to analyze excess thermodynamic properties of polar mixtures (Gepert et al. [START_REF] Gepert | Is Flory's model the best tool for studying the thermodynamic properties of any kind of binary mixtures?[END_REF], Galvao and Francesconi [START_REF] Galvao | Application of the Prigogine -Flory-Patterson model to excess molar enthalpy of binary liquid mixtures containing acetonitrile and 1-alkanol[END_REF], Torres et al. [START_REF] Torres | Application of the Prigogine -Flory-Patterson theory to excess molar volume of binary mixtures of acetonitrile with 1-alkanols[END_REF]). On the same idea, in order to predict excess volumes, several authors [START_REF] Piñeiro | Re-examination and symmetrization of the adjustable parameters of the ERAS model[END_REF] use the Flory equation [START_REF] Flory | Statistical Thermodynamics of Liquid Mixtures[END_REF] while others [START_REF] Valtz | Volumetric Properties of Binary Mixtures of 1,2-Dichloroethane with Polyethers from[END_REF], [15] use the Prigogine-Flory-Patterson (PFP) theory, which is the Flory equation combined with the Prigogine corresponding states principle.

The equation of state used in PFP model is determined for pure liquid and mixtures. It is written using reduced quantities (Eq. 15). Eq. 16 presents the expression of the excess volume based on PFP theory. The PFP model describes the interaction between the chemical species. The physical interaction is the sum of 3 contributions:

T v v v T v p 1 1 ~~3 1 3 1    (
2 * 1 1 * 2 * 2 * 1 2 1 2 1 2 2 2 2 1 2 1 * 1 12 2 1 * 2 2 * 1 1 ) )( ( ~~       P P P P v v T v T v v v P T v T v x v x v E                           (16)
i. Interactional contribution. This contribution is proportional to the Flory parameter  12 . Flory parameter is also called cross parameter. It reflects the energy change during the formation of contacts between the unlike molecules. The  12 parameter can be calculated using solubility parameter defined by Hildebrand:

         2 2 1 12
RT v ( is an empirical constant equal to 0.34). This parameter can be also adjusted on experimental data. Volume v is the molar volume of the solvent. At the origin, the model was developed to study solubility of polymer in solvent. In our application, is it judicious to consider this molar volume independent of the composition?

ii. Curvature contribution or free volume contribution (link to configurational entropy). This contribution is due to the difference in the degree of thermal expansion between the molecules.

iii. P* contribution. This contribution takes into account the difference of internal pressure

( T v U          
) and reduced volume of components.

Here the tilde refers to an average reduced quantity, for example

2 2 1 1 ṽ v v     with 3 3 4 1 1 ~           T T v i i i  
and α i is the thermal expansion coefficient. Reduced temperature is obtained through PFP model by

3 / 4 3 / 1 ~1 ~v v T   and T T V      1 3 1 ~3 / 1 .
The characteristic pressure is given by

2 * ~i Ti i i v T P   
. Although, several authors consider α/κ as an adjustable parameter, the thermal expansion coefficient is

P T v v          1 
and the isothermal compressibility is

T T P v v           1  .
The contact energy fraction is

* 2 2 * 1 1 * 1 1 2 1 1 P P P          , the hardcore volume fraction is * 2 2 * 1 1 * 1 1 2 1 1 v x v x v x      
and the surface fraction is

2 2 1 1 2 2 2 s s s      
. s i being the molecular surface/volume ratios and s 1 /s 2 can be approximated by

3 / 1 * 1 * 2       v v
, the surface fraction is also expressed by:

3 / 1 * 1 * 2 2 1 2 1 1           v v    .
Consequently, using the PFP equation of state and the different defined variables, the expression of the excess volume can be determined (Eq. 17).

 

      2 1 2 * 1 1 * 2 * 2 * 1 2 1 2 1 3 / 1 3 / 1 2 2 1 * 1 12 2 1 3 / 1 3 / 2 3 / 1 * 2 2 * 1 1 ) )( ( 1 3 4 1 9 14 1 3 4 1 ~         P P P P v v v v v v v P v v v v x v x v E                (17)
Unity of v E is imposed by the choice of unity of v i * and v i . Temperature is in Kelvin. The choice of unity of pressure (among other P i * ) imposed the unity of χ 12 .

a. PFP Parametrization

For a pure component, the isothermal compressibility κ Ti is related to the isentropic compressibility  S via the Maxwell's relations (Eq. 18).:

p i S Ti C T v 0 2      (18)
where v i [m 3 /mol] is the molar volume of the compound i,  S is the isentropic compressibility . In order to estimate PFP parameters, densities and speed of sound data for furan, ethanol, n-hexane, Eugenol and 1-Octanol were used. Table 11 presents the speed of sound data for the concerned chemicals.

S S P v v           1  [Pa -1 ]
Concerning liquid heat capacity C p [J.mol -1 .K -1 ], we have used the data predicted by REFPROP [START_REF] Lemmon | NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP, Version 10[END_REF] for ethanol, the data from Guthrie et al. [START_REF] Guthrie | Thermodynamic properties of furan[END_REF] for furan, the data from Karabaev et al. [START_REF] Karabaev | Kinetische, thermische und kalorische Eigenschaften von fluessigen Eugenol[END_REF] for eugenol, the data from Melnikov et al. [START_REF] Mel'nikov | Complex Study of the Elastic and Thermal Properties of Hydrocarbons and Their Halogen Derivatives by the Acoustic Method[END_REF] for the n-hexane and the data from Rubini et al. [START_REF] Rubini | Excess molar enthalpies and heat capacities of dimethyl sulfoxide + seven normal alkanols at 303.15K and atmospheric pressure[END_REF] for the 1-Octanol. In order to calculate the molar volume, the thermal expansion, the isentropic compressibility and the isothermal compressibility, we have used the previous thermodynamic relations and considered in the concerned range of temperature, at atmospheric pressure that the mathematical relation for the different thermodynamic quantities were expressed by a second order polynomial expression with temperature (Eq. [START_REF] Mel'nikov | Complex Study of the Elastic and Thermal Properties of Hydrocarbons and Their Halogen Derivatives by the Acoustic Method[END_REF].

  c bT aT T F    2 (19)
The adjusted parameters a, b and c are presented in tables 12-16 for the different chemicals. Instead of providing the deviation with experimental data, we have indicated the standard deviation of each fitted parameter.

b. Results and Discussion

We have applied the PFP model for the 4 binary systems at 283, 293 and 303K. In order to adjust the  12 parameter, we have minimized the objective function (Eq. 20) using PFP parameters calculated using Eq. 19 for each pure component property.

  2 , exp,    i E i PFP E i v v OF (20)
Tables [START_REF] Guthrie | Thermodynamic properties of furan[END_REF][START_REF] Karabaev | Kinetische, thermische und kalorische Eigenschaften von fluessigen Eugenol[END_REF][START_REF] Mel'nikov | Complex Study of the Elastic and Thermal Properties of Hydrocarbons and Their Halogen Derivatives by the Acoustic Method[END_REF] presents the values of the parameters of each pure component at 283, 293 and 298K. The values of  12 parameters are presented in Table 20. This parameter is at the origin independent of the composition (Hansen [START_REF] Hansen | Hansen solubility parameters: a user's handbook[END_REF]) but it was used to represent the volumetric properties of binary systems involving polymer and solvent.  12 depends on molar volume of the solvent but our case of study considers the specie as the solvent, particularly if the molar composition is close to 0.5. So it can be not judicious to consider that  12 parameter is independent of volume fraction. In 1984, Mulder and Smolders [START_REF] Mulder | On the mechanisms of separation of ethanol/water mixtures by pervaporation. I. Calculations of concentration profiles[END_REF] have mentioned that excess functions are strongly concentration dependent. They have indicated that  12 parameter (a free energy parameter) can be expressed from the Excess Gibbs energy of mixing. They have studied the ethanol water binary system and show the evolution of  12 as a function of volume fractions. Also, Hansen [START_REF] Hansen | Hansen solubility parameters: a user's handbook[END_REF] has shown that the  12 parameter, originally calculated using Hildebrand solubility parameter, can be calculated by a  12 parameter which takes into account dispersive, polar and hydrogen bonding interactions. In consequence, we have decided to modify the cross parameter  12 by using Eq. 21. Results are presented in Table 20.

    2 1 0 12 12        b a (21)
The 0 12  parameter is determined by considering no composition dependency. a and b parameters are adjusted using objective function defined by equation 20 and taking 0 12  as a constant. (Supplementary information) show the results obtained at 298K. Tables S5-S9 (Supplementary information) show the results obtained at 283K. For the system furan ethanol, the main contribution to excess volume is attributed to the interactional contribution. It highlights the importance of the  12 parameter in the data treatment and the dependence to the composition of this parameter. It highlights the effect of polar and H-bonding interactions certainly linked to the composition of the mixture. For furan 1-Octanol, all the different types of interaction contribute at the same level to excess volume. For Eugenol 1-Octanol, the main contribution to excess volume is attributed to the interactional contribution. There is no effect of free volume. For the last binary system, eugenol nhexane, it seems that the main contribution to excess volume are free volume effect and internal pressure effect. On Figs. 17-18, we can see the most relevant contribution for the furan + ethanol and eugenol + n-hexane binary systems to excess molar volume. Figure 19 shows the evolution of  12 parameters with temperature. We can observe for each case a linear trend.

Conclusion

The densities of 4 binary mixtures (Eugenol + n-hexane, Eugenol + 1-Octanol, Furan + Ethanol and Furan + 1-Octanol) were measured over the temperature range T=(278.15 -323.15 K). Densities and speeds of sound were also measured for each pure component. Deduced from these properties, the excess molar volumes V E of these systems are well correlated by the Redlich-Kister correlation. Except for the furan + 1-Octanol binary systems, all the excess volumes are negative. Concerning the furan + ethanol binary system in the dilute region of ethanol, excess molar volume becomes positive when the temperature increases. The capability of the Prigogine-Flory-Patterson (PFP) model to predict the excess molar volume is tested on these binary mixtures. The PFP theory faces more difficulties in the restitution of the experimental V E for furan + ethanol binary system. For this system, it appears that the most relevant contribution is attributes to interactional interaction. A tentative of utilization of a χ 12 composition dependent was done and the results are better represented.

Density and excess volume for four systems involving eugenol and furan

Supplementary information 1. Comparison with literature data

We have compared our measured density data with literature data for 1-octanol, furan and eugenol.

We have also considered the DIPPR [1] correlation (equation n°105) (Eq. S1) available in Simulis™ Thermodynamics software from PROSIM France. For these three components, we have plotted a parity graph, experimental value vs calculated values.

                 E C T B A 1 1  (S1)
With A, B, C and D parameters and  the molar density in kmol.m -3 . It can be notified that parameter C corresponds to the critical temperature. Concerning eugenol, we have used boiling temperature. Table S1 shows the different parameters. We have adjusted the parameters using literature data for the furan and eugenol and applied the Eq. S1 with available parameters for 1-octanol. Concerning 1-Octanol, we have used the data from TDE (NIST) [2] available in ASPEN plus software [3]. Concerning furan we have used the data from Gunthrie et al. [4] and Timmermans and Hennaut-Roland [5]. Concerning eugenol we have used the data from Bingham and Spooner [6].

  mol -1 using Eqs. 2-4. Atmospheric pressure is measured by a GE Druck DPI 142 Barometric Indicator with an uncertainty

2

 2

  molar volume. There are two contributions for the apparent molar volume of a molecule: the volume of the molecule and the free volume space. By analysis the evolution of of x 1 we have selected the number of RK parameters for all the investigated binary systems.

1 Figure 6 :

 16 Figure 5:

1 Figure 9 : 1 Figure 10 :Figure 11 : 1 Figure 12 :

 1911011112 Figure 9: Calculated partial molar volume using Redlich-Kister correlation (solid line) and experimental apparent molar volume (symbols) of furan(1) + ethanol(2) system as a function of furan mole fraction at atmospheric pressure and 2 different temperatures: (○) 283.15 K, (×) 303.15 K.

.

  T*, p* and v* are the characteristics parameters obtained directly from the thermodynamic properties of the pure liquid.

  and is known thanks to the measurements of speed of sound c liquid [m/s] and density ρ [kg/m 3 ] reached in this work. Indeed, these three properties are linked in the liquid phase via:

Table 11 :

 11 Speed of sound data at atmospheric pressure (U p = ±0.03 kPa, U T = ±0.01K, U c = ±0.5 m.s -1 (k=2)).

Figure 13 :Figure 14 :Figure 15 :Figure 16 :Figure 17 :Figure 18 :

 131415161718 Figure 13 : Excess volumes for the furan(1) + Ethanol(2) binary system at 293.15 K as a function of molar composition. Symbols: experimental data, solid line: Calculated using PFP model with constant value of χ 12 , dashed line: Calculated with PFP model with constant χ 12 composition dependent.

Figure 19 :

 19 Figure 19: Evolution of χ°1 2 parameters as a function of temperature. (▲): furan + ethanol binary system, (+): eugenol + 1-Octanol binary system, (×): eugenol + n-hexane binary system, (•): furan + 1-Octanol binary system.

3 Figure S1 : 3 Figure S2 : 3 Figure S3 : 3 Figure S4 : 3 Figure S5 :

 3S13S23S33S43S5 Figure S1 : Parity graph concerning 1-Octanol. (×): literature data, red symbol: This work (Table2).

Figure S7 :Figure S8 :Figure S9 :Figure S10 :Figure S11 :Figure S12 :Figure S13 :

 S7S8S9S10S11S12S13 Figure S7: Excess volumes for the Furan(1) + 1-Octanol(2) binary system at 298K as a function of molar composition. Symbols: experimental data, solid line: Calculated using PFP model with constant value of χ 12 , dashed line: Calculated with PFP model with constant χ 12 composition dependent.

Table 1 : Chemical sample

 1

	Compound	CAS	Formula	Supplier	Purity	Refractive	nD
		Number			(GC)	index*	litt
						(293.15 K)
	Furane (stabilized) 110-00-9	C 4 H 4 O	SIGMA-ALDRICH	>99%	1.4215 6	1.41871 a
	n-Hexane	110-54-3	C 6 H 14	SIGMA-ALDRICH	>99%	1.3754 2	1.37226 a
	Eugenol	97-53-0	C 10 H 12 O 2	ACROS	>99%	1.5408 8	1.539 b
	1-1-Octanol	111-87-5	C 8 H 18 O	SIGMA-ALDRICH	> 99%	1.4292 1	1.4276 a
	Ethanol	64-17-5	C 2 H 6 O	FLUKA	> 99.8%	1.3614 8	1.35941 a

*: Apparatus; Anton Paar ABBEMAT 300 acuracy +/-0.0001, (a): Value from Component Plus (Prosim, France), (b):

Table 3

 3 presents the values of mixtures densities and excess volume. Table4presents our results.

	Following Desnoyers and Perron's method we have considered 4 Redlich Kister parameters. Figs. 1-2
	presents respectively,	v E
		1 x x	2

Table 4 : Redlich-Kister parameters and deviation for furan + ethanol binary system.

 4

						Variance
	T/K		Redlich Kister parameters		equation 7
		A 0	A 1	A 2	A 3
	278.15	-0.654	0.565	-0.114	0.223	0.003
	283.15	-0.617	0.578	-0.111	0.236	0.003
	288.15	-0.578	0.595	-0.098	0.269	0.004
	293.15	-0.534	0.610	-0.090	0.303	0.004
	298.15	-0.492	0.637	-0.070	0.312	0.004
	303.15	-0.431	0.639	-0.056	0.382	0.004

for furan(1) + ethanol(2) system as a function of furan mole fraction at atmospheric pressure and 2 different temperatures: (○) 283.15 K, (×) 303.15 K, solid line: Redlich Kister correlation.

		0.05
		0.00
	3 .mol -1	-0.05
	v E / cm	-0.10
		-0.15
		-0.20
		-0.25
		0.0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1.0
							x 1

Figure 2: Excess molar volume (v E ) for furan(1) + ethanol(2) binary system as a function of composition at atmospheric pressure and 2 different temperatures: (○) 283.15 K, (×) 303.15 K, solid line: Redlich Kister correlation.

  Table 5 presents the values of mixtures densities and excess volume. Table 6 presents our results.

	b. Furan 1-Octanol binary system
	Following Desnoyers and Perron's method we have considered 3 RK parameters. Figs 3-4 presents
	v E
	1 x x	2

Table 6 : Redlich-Kister parameters and deviation for furan + 1-Octanol binary system.

 6

						Redlich Kister parameters		Variance
				T/K								equation
						A 0		A 1			A 2	7
			278.15		1.318		0.512	0.095	0.002
			283.15		1.329		0.517	0.080	0.002
			288.15		1.341		0.518	0.087	0.002
			293.15		1.344		0.523	0.077	0.003
			298.15		1.341		0.515	0.072	0.002
			303.15		1.343		0.516	0.090	0.002
				1.4
				1.2
				1.0
			-1
			3 .mol	0.8
			/cm
			E /x 1 x 2	0.6
			v
				0.4
				0.2
				0.0
				0.0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1.0
									x 1
	Figure 3:	1 x x v E	2

for furan(1) + 1-Octanol(2) system as a function of furan mole fraction at atmospheric pressure and 2 different temperatures: (○) 283.15 K, (×) 303.15 K, solid line: Redlich- Kister correlation.

		0.40
		0.35
		0.30
	3 .mol -1	0.25
	cm	0.20
	v E /
		0.15
		0.10
		0.05
		0.00
		0.0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1.0
							x 1

Figure 4: Excess molar volume (v E ) for furan(1) + 1-Octanol(2) system as a function of furan mole fraction at atmospheric pressure and 2 different temperatures: (○) 283.15 K, (×) 303.15 K, solid line: Redlich Kister correlation.

Table 8 : Redlich-Kister parameters and deviation for eugenol + 1-Octanol binary system.

 8

	mol -1

Table 10 : Redlich-Kister parameters and deviation for eugenol + n-hexane binary system.

 10

	mol -1

hexane(2) system as a function of eugenol mole fraction at atmospheric pressure and 2 different temperatures

		0.0
		-0.2
		-0.4
	3 .mol -1
	cm	-0.6
	v E /
		-0.8
		-1.0
		-1.2
		0.0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1.0
							x 1

: (○) 283.15 K, (×) 303.15 K, (+) 323.15 K, solid line: Redlich-Kister correlation.

Figure 8: Excess molar volume (v E ) for eugenol(1) + n-hexane (2) system as a function of eugenol mole fraction at atmospheric pressure and 3 different temperatures: (○) 283.15 K, (×) 303.15 K, (+) 323.15 K, solid line: Redlich-Kister correlation.

Table 12 : Values of the second order polynomial expression (Eq. 13) for 1-Octanol

 12

	Property/F	a	u(a)	b	u(b)	c	u(c )
	v/ cm 3 .mol -1	1.70E-04	2E-06	0.032	0.001	133.8	0.2
	 /K -1	-2.12E-09	1E-11	2.695E-06	6E-09	2.3E-04	9E-07
	Cp /J.mol -1 .K -1			1.07	0.03	-14.51	9
	S  /Pa -1	1.56E-14	4E-16	-5.3E-12	2E-13	8.7E-10	3E-11
	T  /Pa -1	1.5822E-14	1E-18	-4.9808E-12	7E-16	8.594E-10	1E-13

Table 13 : Values of the PFP parameters for n-hexane

 13

	Property/F	a	u(a)	b	u(b)	c	u(c )
	v/ cm 3 .mol -1	4.29E-04	1E-05	-0.0730	6E-03	115.1	9E-01
	 /K -1	-1.090E-08	1E-10	1.109E-05	6E-08	-9.48E-04	9E-06
	Cp /J.mol -1 .K -1	1.45E-03	9E-05	-4.93E-01	6E-02	213.40	9
	S  /Pa -1	7.45E-14	7E-16	-3.15E-11	4E-13	4.09E-09	6E-11
	T  /Pa -1	7.685E-14	6E-17	-2.929E-11	4E-14	3.604E-09	5E-12

Table 14 : Values of the PFP parameters for eugenol

 14

	Property/F	a	u(a)	b	u(b)	c	u(c )
	v/ cm 3 .mol -1	1.15E-04	5E-07	0.0601	3E-04	126.49	5E-02
	 /K -1	-1.267E-09	2E-12	1.551E-06	1E-09	4.830E-04	2E-07
	Cp /J.mol -1 .K -1			1.42E+00	4E-02	-74.59	9
	S  /Pa -1	1E-14	3E-17	-3.48E-12	2E-14	5.75E-10	3E-12
	T  /Pa -1	1.01237E-14	9E-19	-3.3423E-12	6E-16	6.1855E-10	9E-14

Table 15 : Values of the PFP parameters for Ethanol

 15

	Property/F	a	u(a)	b	u(b)	c	u(c )
	v/ cm 3 .mol -1	9.85E-05	9E-07	0.006	0.001	48.3	0.1
	 /K -1	-4.22E-09	2E-11	4.67E-06	1E-08	7.8E-05	1E-06
	Cp /J.mol -1 .K -1			0.35	0.00	8.8	0.7
	S  /Pa -1	2.70E-14	2E-16	-9.2E-12	1E-13	1.32E-09	2E-11
	T  /Pa -1	2.7408E-14	4E-18	-8.473E-12	2E-15	1.2527E-09	4E-13

Table 16 : Values of the PFP parameters for Furan

 16

	Property/F	a	u(a)	b	u(b)	c	u(c )
	v/ cm 3 .mol -1	2.47E-04	1E-06	-0.0388	8E-04	62.7	0.1
	 /K -1	-1.185E-08	3E-11	1.162E-05	2E-08	-9.24E-04	2E-06
	Cp /J.mol -1 .K -1	6.2E-04	2E-04	-1.59E-01	0.1	107.03	20
	S  /Pa -1	5.20E-14	3E-16	-2.25E-11	1E-13	2.92E-09	2E-11
	T  /Pa -1	5.473E-14	5E-17	-2.032E-11	3E-14	2.452E-09	5E-12

Table 17 : Physical constants of pure compounds at 283.15 K, used for calculations of Excess molar volume v E with PFP model: v i °: molar volume,  i coefficient of thermal expansion  T Isothermal compressibility, Reduction parameters of volume v i * and Pressure P i *.

 17

	Compound	v i °/ cm 3 .mol -1	10 3  i /K -1	10 3  T / MPa -1 v i * /cm 3 .mol -1	P i * / MPa
	Eugenol	152.728	0.818	0.484	127.280	689.143
	Furan	72.535	1.460	1.196	54.876	603.583
	n-hexane	128.814	1.319	1.470	99.309	427.080
	n-1-Octanol	156.514	0.822	0.717	130.344	467.630
	Ethanol	57.727	1.064	1.050	46.191	447.981

Table 18 : Physical constants of pure compounds at 293.15 K, used for calculations of Excess molar volume v E with PFP model: v i °: molar volume,  i coefficient of thermal expansion  T Isothermal compressibility, Reduction parameters of volume v i * and Pressure P i *. Compound v i °/ cm 3 .mol -1 10 3  i /K -1 10 3  T / MPa -1 v i * /cm 3 .mol -1 P i * / MPa

 18

	Eugenol	153.993	0.826	0.508	127.506	694.676
	Furan	72.535	1.460	1.196	54.516	633.197
	n-hexane	130.555	1.367	1.619	99.348	427.224
	n-1-Octanol	157.815	0.837	0.758	130.421	473.226
	Ethanol	58.350	1.086	1.123	46.261	450.833

Table 19 : Physical constants of pure compounds at 298.15 K, used for calculations of Excess molar volume v E with PFP model: v i °: molar volume,  i coefficient of thermal expansion  T Isothermal compressibility, Reduction parameters of volume v i * and Pressure P i *.

 19

	Compound	v i °/ cm 3 .mol -1	10 3  i /K -1	10 3  T / MPa -1 v i * /cm 3 .mol -1	P i * / MPa
	Eugenol	154.634	0.830	0.522	127.627	695.877
	Furan	73.073	1.483	1.257	54.575	630.661
	n-hexane	131.458	1.390	1.700	99.408	426.011
	n-1-Octanol	158.478	0.844	0.780	130.468	475.530
	Ethanol	58.669	1.097	1.162	46.300	451.726

Table 20 : χ 12 parameters used in the PFP theory

 20 Figs.[START_REF] Flory | Statistical Thermodynamics of Liquid Mixtures[END_REF][START_REF] Valtz | Volumetric Properties of Binary Mixtures of 1,2-Dichloroethane with Polyethers from[END_REF][15][START_REF] Lemmon | NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP, Version 10[END_REF] show the comparison between the two treatments with or without composition dependency of  12 parameter at 293.15 K. Figs. S6-S9 (Supplementary information) show the results obtained at 298K. Figs. S10-S13 (Supplementary information) show the results obtained at 283K. As we can see, we have a better correlation of the data when the  12 parameter is dependent of the composition. We have also evaluated the contribution of the different contribution of PFP model to excess volume at 293.15 K. For the 4 systems, the results are presented in Tables 21-24. Tables S2-S5

			283.15 K			293.15 K			298.15 K
	System	0 12 	a	b	0 12 	a	b	0 12 	a	b
	Furan + Ethanol	-33.97	1.0266	-0.4704	-30.14 1.0282	-0.5375	-27.98	1.034	-0.5817
	Furan + 1-Octanol	12.39	0.9051	-0.4545	5.68	1.0761	-0.5300	2.14	1.0761 -0.5300
	Eugenol + 1-Octanol	-38.82	1.0161	0.1728	-33.09 1.0181	0.1936	-30.38 1.0187	0.2003
	Eugenol + n-hexane	59.25	0.9872	-0.2000	62.36 0.9884	-0.1667	63.43 0.9892 -0.1501

Table 22 : Evaluation of the different contribution of the PFP model for the furan(1) + 1-Octanol(2) binary system at 293.15 K and comparison with experimental data. Experimental data Constant value of χ 12 χ 12 composition dependent x 1 v E / cm 3 .mol -1 Calculated contribution / cm 3 .mol -1 v E / cm 3 .mol -1 Deviation / cm 3 .mol -1 Calculated contribution / cm 3 .mol -1 v E / cm 3 .mol -1

 22

	Deviation

Table 23 : Evaluation of the different contribution of the PFP model for the Eugenol(1) + 1-Octanol(2) binary system at 293.15 K and comparison with experimental data. Experimental data Constant value of χ 12 χ 12 composition dependent x 1 v E / cm 3 .mol -1 Calculated contribution / cm 3 .mol -1 v E / cm 3 .mol -1 Deviation / cm 3 .mol -1 Calculated contribution / cm 3 .mol -1 v E / cm 3 .mol -1 Table 24: Evaluation of the different contribution of the PFP model for the Eugenol(1) + n-hexane(2) binary system at 293.15 K and comparison with experimental data. Experimental data Constant value of χ 12 χ 12 composition dependent x 1 v E / cm 3 .mol -1 Calculated contribution / cm 3 .mol -1 v E / cm 3 .mol -1 Deviation / cm 3 .mol -1 Calculated contribution / cm 3 .mol -1 v E / cm 3 .mol -1

 23

	Deviation

Table S1 : DIPPR correlation parameters for 1-Octanol, furan and Eugenol.

 S1

	Component	A	B	C	D	AAD :%
	1-Octanol*	0.0048979	0.24931	652.3	0.27824	0.44
	Furan	0.0015357	0.287097	490.2	0.303716	0.03
	Eugenol	0.0032754	0.638032	523	0.829143	0.19
	AAD: Average Absolute Deviation on literature data, * from Simulis™ Thermodynamics

Table 2 ).

 2

	According to Figs. S1 to S5, we can conclude that our pure component density data are in good
	agreement with literature data and consistent.
	2. Prigogine Flory Patterson (PFP) model
	In this part of the SI additional results concerning the modeling of the excess volume by using
	Prigogine Flory Patterson (PFP) model at 298 and 283K are presented (Figs. S6 to S13, Tables S2 to
	S9).

Excess volumes for the furan(1) + Ethanol(2) binary system at 298K as a function of molar composition. Symbols: experimental data, solid line: Calculated using PFP model with constant value of χ 12 , dashed line: Calculated with PFP model with constant χ 12 composition dependent.

		0.40
		0.35
		0.30
		0.25
	-1
	cm 3 .mol	0.20
	E /
	v
		0.15
		0.10
		0.05
		0.00
		0.0	0.2	0.4	0.6	0.8	1.0
				x1

Table S3 : Evaluation of the different contribution of the PFP model for the furan(1) + 1-Octanol(2) binary system at 298.15 K and comparison with experimental data. Experimental data Constant value of χ 12 χ 12 composition dependent x 1 v E / cm 3 .mol -1 Calculated contribution / cm 3 .mol -1 v E / cm 3 .mol - 1 Deviation / cm 3 .mol -1 Calculated contribution / cm 3 .mol -1 v E / cm 3 .mol -

 S3

											1	Deviation
			Interactional Free volume	P* effect			Interactional Free volume P* effect		/ cm 3 .mol -1
	0.0134	0.010	0.001	-0.021	0.031	0.011	-0.001	0.002	-0.021	0.031	0.012	-0.002
	0.0256	0.022	0.002	-0.041	0.060	0.021	0.000	0.003	-0.041	0.060	0.022	-0.001
	0.0506	0.045	0.004	-0.079	0.116	0.042	0.003	0.006	-0.079	0.116	0.044	0.001
	0.0739	0.067	0.005	-0.113	0.168	0.060	0.007	0.008	-0.113	0.168	0.063	0.004
	0.0995	0.089	0.007	-0.149	0.222	0.081	0.008	0.011	-0.149	0.222	0.085	0.004
	0.1495	0.132	0.011	-0.213	0.322	0.119	0.013	0.016	-0.213	0.322	0.125	0.007
	0.1999	0.165	0.014	-0.272	0.415	0.157	0.008	0.021	-0.272	0.415	0.164	0.001
	0.2512	0.209	0.017	-0.324	0.500	0.193	0.016	0.025	-0.324	0.500	0.201	0.008
	0.3042	0.241	0.020	-0.370	0.578	0.228	0.014	0.029	-0.370	0.578	0.237	0.005
	0.3501	0.270	0.022	-0.403	0.636	0.255	0.015	0.032	-0.403	0.636	0.265	0.006
	0.4043	0.302	0.025	-0.432	0.692	0.285	0.017	0.034	-0.432	0.692	0.294	0.008
	0.4511	0.321	0.027	-0.449	0.729	0.306	0.015	0.035	-0.449	0.729	0.315	0.006
	0.5000	0.334	0.028	-0.459	0.756	0.325	0.009	0.036	-0.459	0.756	0.333	0.001
	0.5529	0.345	0.029	-0.460	0.770	0.339	0.006	0.036	-0.460	0.770	0.346	-0.001
	0.6016	0.349	0.030	-0.451	0.768	0.346	0.003	0.035	-0.451	0.768	0.352	-0.003
	0.6500	0.343	0.029	-0.433	0.750	0.346	-0.003	0.034	-0.433	0.750	0.350	-0.007
	0.7000	0.322	0.028	-0.405	0.714	0.338	-0.015	0.031	-0.405	0.714	0.340	-0.018
	0.7499	0.303	0.027	-0.365	0.658	0.319	-0.016	0.027	-0.365	0.658	0.320	-0.017
	0.8010	0.271	0.024	-0.314	0.578	0.288	-0.017	0.023	-0.314	0.578	0.287	-0.016
	0.8500	0.220	0.020	-0.253	0.478	0.245	-0.025	0.017	-0.253	0.478	0.242	-0.022
	0.9010	0.163	0.015	-0.179	0.346	0.183	-0.019	0.011	-0.179	0.346	0.179	-0.016
	0.9250	0.125	0.012	-0.139	0.274	0.147	-0.022	0.009	-0.139	0.274	0.143	-0.018
	0.9500	0.089	0.008	-0.096	0.191	0.104	-0.015	0.006	-0.096	0.191	0.101	-0.012
	0.9750	0.044	0.004	-0.049	0.100	0.055	-0.011	0.003	-0.049	0.100	0.053	-0.010

Table S7 : Evaluation of the different contribution of the PFP model for the furan(1) + 1-Octanol(2) binary system at 283.15 K and comparison with experimental data. Experimental data Constant value of χ 12 χ 12 composition dependent x 1 v E / cm 3 .mol -1 Calculated contribution / cm 3 .mol -1 v E / cm 3 .mol -1 Deviation / cm 3 .mol -1 Calculated contribution / cm 3 .mol -1 v E / cm 3 .mol -1

 S7

												Deviation
			Interactional Free volume	P* effect			Interactional	Free volume	P* effect		/ cm 3 .mol -1
	0.0134	0.013	0.005	-0.021	0.026	0.010	0.003	0.007	-0.021	0.026	0.012	0.001
	0.0256	0.023	0.010	-0.040	0.049	0.019	0.003	0.014	-0.040	0.049	0.023	0.000
	0.0506	0.043	0.020	-0.077	0.095	0.038	0.005	0.027	-0.077	0.095	0.045	-0.002
	0.0739	0.070	0.029	-0.110	0.137	0.056	0.014	0.039	-0.110	0.137	0.066	0.004
	0.0995	0.089	0.039	-0.146	0.181	0.075	0.014	0.052	-0.146	0.181	0.088	0.002
	0.1495	0.130	0.058	-0.210	0.263	0.112	0.019	0.075	-0.210	0.263	0.129	0.002
	0.1999	0.167	0.076	-0.268	0.340	0.148	0.020	0.097	-0.268	0.340	0.168	-0.001
	0.2512	0.205	0.093	-0.321	0.410	0.183	0.022	0.116	-0.321	0.410	0.206	-0.001
	0.3042	0.236	0.110	-0.367	0.475	0.217	0.019	0.134	-0.367	0.475	0.241	-0.005
	0.3501	0.269	0.123	-0.401	0.523	0.245	0.024	0.147	-0.401	0.523	0.269	0.001
	0.4043	0.298	0.137	-0.432	0.570	0.275	0.023	0.158	-0.432	0.570	0.297	0.001
	0.4511	0.316	0.147	-0.451	0.602	0.298	0.018	0.165	-0.451	0.602	0.316	0.000
	0.5000	0.333	0.156	-0.463	0.625	0.318	0.015	0.170	-0.463	0.625	0.332	0.001
	0.5529	0.342	0.162	-0.466	0.638	0.334	0.008	0.170	-0.466	0.638	0.342	0.000
	0.6016	0.346	0.165	-0.459	0.638	0.344	0.003	0.166	-0.459	0.638	0.345	0.002
	0.6500	0.340	0.165	-0.443	0.625	0.346	-0.006	0.158	-0.443	0.625	0.340	0.001
	0.7000	0.323	0.161	-0.416	0.596	0.340	-0.018	0.146	-0.416	0.596	0.326	-0.003
	0.7499	0.302	0.152	-0.378	0.551	0.324	-0.023	0.129	-0.378	0.551	0.302	0.000
	0.8010	0.269	0.137	-0.326	0.485	0.295	-0.026	0.108	-0.326	0.485	0.266	0.003
	0.8500	0.220	0.116	-0.265	0.402	0.253	-0.033	0.083	-0.265	0.402	0.220	-0.001
	0.9010	0.161	0.086	-0.188	0.293	0.190	-0.029	0.055	-0.188	0.293	0.159	0.002
	0.9250	0.123	0.069	-0.148	0.232	0.153	-0.030	0.041	-0.148	0.232	0.125	-0.002
	0.9500	0.086	0.049	-0.102	0.162	0.109	-0.023	0.027	-0.102	0.162	0.087	-0.001
	0.9750	0.042	0.026	-0.053	0.085	0.058	-0.016	0.013	-0.053	0.085	0.045	-0.003

Table S8 : Evaluation of the different contribution of the PFP model for the Eugenol(1) + 1-Octanol(2) binary system at 283.15 K and comparison with experimental data. Experimental data Constant value of χ 12 χ 12 composition dependent x 1 v E / cm 3 .mol -1 Calculated contribution / cm 3 .mol -1 v E / cm 3 .mol -1 Deviation / cm 3 .mol -1 Calculated contribution / cm 3 .mol -1 v E / cm 3 .mol -

 S8

Table S9 : Evaluation of the different contribution of the PFP model for the Eugenol(1) + n-hexane(2) binary system at 283.15 K and comparison with experimental data. Experimental data Constant value of χ 12 χ 12 composition dependent x 1 v E / cm 3 .mol -1 Calculated contribution / cm 3 .mol -1 v E / cm 3 .mol -1 Deviation / cm 3 .mol -1 Calculated contribution / cm 3 .mol -1 v E / cm 3 .mol -1

 S9

					Deviation
	Interactional Free volume	P* effect	Interactional	Free volume	P* effect

Acknowledgments

Financial support from the ANR of France through the project Memobiol (ANR-09-CP2D-10-04 MEMOBIOL) is gratefully acknowledged.


Anne-Laure Vallet

Emmanuel Lacôte
email: emmanuel.lacote@univ-lyon1.fr

Thiolation of NHC-Boranes: Influence of the Substitution at Boron

published or not. The documents may come

Several N-Heterocyclic Carbene (NHC)-boryl sulfides with Bsubstituents were prepared. The added steric hindrance leads to much improved selectivities as only the NHC-boryl mono-sulfides were obtained. The B-substituted NHC-boranes are also conducive to more selective S to N NHC-boryl shift, provided that the NHC used is not too sterically demanding.

The complexation of boranes with Lewis basic carbenes such as N-heterocyclic carbenes (NHCs), 1 mesoionic carbenes (MICs), 2 or cyclic alkyl amino carbenes (CAACs) 3 enables new reactivities owing to the stabilization by the carbenes of reactive intermediates, in particular boron-centered radicals.

4

As a consequence NHC-boranes and related structures have emerged as great tools for radical organic synthesis. [5][6][7][8] Thus, it is of primary importance to understand the reactivity of carbene boranes, so that one can discover new reactions they can be used in.

In particular, we showed that NHC-boryl radicals could undergo homolytic substitutions, thus leading to NHC-boryl sulfides and disulfides. 9 A likely ionic pathway was also evidenced, which delivered the same final products, via a hydride transfer from the NHC-boranes to the disulfides, followed by nucleophilic addition of the thiolate generated to the resulting borenium intermediates. 10 Most interestingly, the resulting NHC-boryl sulfides can be used as tin hydride surrogates in radical reactions 11 and Type I photo-initiators.

12 Both the ionic and radical reactions exhibit a large scope with regard to the NHCs and aryldisulfides, but we only considered BH 3 -adducts. Both the mono and bis-sulfides were generally observed. The reactions were optimized to deliver mostly one or the other of the products, but in some cases the adducts could not be separated, and the selectivities were not excellent. In this context, we decided to examine the influence of a pre-installed subtituent at boron. We reasoned that a steric lock could lead to more selective reactions. We report herein that this is indeed the case.

For this study we chose to work with aryl-substituted derivatives in order to have structurally similar groups. We thus selected four different aryl rings, with substituents ranging from strongly electron-withdrawing groups (4-CF 3 ) to strongly donating (MeO). Two NHCs were selected: the sterically demanding IPr and the smaller IMe. We examined two sets of conditions (see Table 1). In a typical thermal reaction, the NHC-(phenyl)borane was heated overnight at 45 °C in deoxygenated benzene in the presence of one equivalent of diphenyldisulfide (Table 1, Entry 1, conditions ).

In a typical photochemical reaction (Entry 2, h), the same reagents were irradiated at room temperature for 30 minutes using an OmniCure® S1000 apparatus. It is expected that the thermal reaction proceed via an ionic mechanism, 10 while the photochemical reaction proceeds via a radical mechanism.

9

The thermal reaction of the phenyl-substituted NHC-Borane DiMe-Imd-BH 2 Ph with diphenyl disulfide led to adduct 1a in 51% yield (entry 1). With di-(2-naphthyl) disulfide (resp. di-(4methoxy) disulfide), it delivered 1b (resp. 1c) in 80% (resp. 55%) yield (entries 3 and5). Noticeably, the corresponding photochemical reactions gave 1a and 1b in lower yields (19% vs. 51, entry 2; 30% vs. 80%, entry 4) but 1c was obtained in 72% yield, better than the thermal reaction (entry 6).

Considering that the thermal yields were on average better that the photochemical ones, we decided to examine the scope of the reaction only under thermal conditions. For DiMe-Imd-BH Several conclusions can be drawn from the previous study.

• The formation of NHC-boryl sulfides is sensitive to steric hindrance. The reactions require somewhat harsher conditions that the same ones using BH 3 -based Lewis pairs. There is a price to pay as the yields are smaller but there is a strong advantage, as only mono-adducts are obtained, under both thermal and photochemical conditions. The selectivity is better, which is especially interesting as the adducts obtained are those more difficult to isolate pure from the unsubstituted NHC-boranes.

• The homolytic reaction suffers more from steric hindrance than the (likely) ionic reaction. The radical reaction is a bimolecular homolytic substitution, which suffers strongly from steric congestion. The key elementary step in the thermal reaction is probably a hydride transfer from the NHC-borane.

This generates a borenium intermediate, which is intercepted by the thiolate generated. Our observations show that this suffers less from steric congestion than the S H 2.

• The nature of the substituent at boron has a stronger influence over reactivity than that of the disulfide. However, there is no clear relation between the electronic nature of the substituent at boron and the reactivity.

• In all cases, steric hindrance at the NHC part of the Lewis pair is a very strong factor. It totally shuts down the ionic reaction.

The radical substitution goes on somewhat, but is very low yielding, and it is accompanied by a lot of degradation. Our next step was to examine whether the 1,3 NHC-boryl shift from sulfur to nitrogen we discovered (12) would still be operant. Indeed, on the unsubstituted NHC-boranes, the bulky NHC IPr prevented the shift to take place. We selected two disulfides suitable with the rearrangement, bis(mercaptobenzothiazolyl) disulfide and bis(1phenyltetrazolyl) disulfide. The reaction of variously substituted B-aryl NHC-boranes derived from the IMe carbene and bis (mercaptobenzothiazolyl) disulfide proceeded at 65°C in benzene (Scheme 1). Gratifyingly, in all cases the monosubstituted B-amino NHC-borane was isolated in modest (23% for 2b, 34% for 2c) to good yields (62% for 2a, 67% for 2d). In the case of the p-trifluoromethyl substituted aryl borane derivative, 8% of monosulfide were also isolated, and not in the other cases. This again suggests that the B-N products come from rearrangement of the corresponding B-S adducts initially formed.( 12) Adducts 2a-d are the first examples of Bsubstituted amino NHC-boranes. The reactions worked slightly less efficiently in the case of bis(1-phenyltetrazolyl) disulfide (Scheme 2). Despite the average yields (23-58% for 3a-d), only the corresponding mono-substituted amino NHC-boranes were again isolated except for 3b where a minor amount (10%) of the mixed bisadduct was also isolated. The rearrangement is not limited to imidazolydinene-boranes, as triazolylidene-borane 3e was obtained in 56%. Note that all derivatives 3a-e have a high number of nitrogen atoms, which makes them potentially pyrotechnic. We however experienced no problem in handling them. Despite the high nitrogen (and boron) content, there are enough heavier atoms to prevent Please do not adjust margins Please do not adjust margins explosions. Nonetheless, adequate care should always be exercised when handling these products. Finally, the presence of the very congested IPr on the borane blocked the rearrangement, in both the benzothiazole and the mercapto tetrazole series (Scheme 3). In both cases, the NHCboryl monosulfides (4a and 4b) were obtained respectively in 42% and 64% yields. Overall, the NHC-boryl shift is also very selective. That supports the hypothesis that the NHC-boryl sulfides are formed first selectively, and rearrange (or not) in a consecutive mechanistical step.

Conclusions

To conclude, we could extend the synthesis of NHC-boryl sulfides to B-substituted boranes. The added steric hindrance at the boron atom makes the reactions more difficult and slightly lower yielding. However it allows much improved selectivities as only the NHC-boryl mono-sulfides are obtained. When the disulfide employed are suitable to S to N NHC-boryl shift, i. e. when they have an -C=N bond in a 5-membered ring, the corresponding amino NHC-boranes are formed, except when a highly congested carbene is present, which shuts down the rearrangement but not the thiolation. All NHCboranes isolated are new. They are all stable despite the steric hindrance around the boron atom, which could lead to frustrated Lewis pairs. 13 We are now focusing on studying the reactivity of the compound, in particular the influence of the aryl group on the strength of the B-S bond, and its ability to be an antenna for photochemical cleavage of the same bond. Finally, the NHC-boranes obtained are stereogenic at boron, 14 which might be interesting for stereochemical applications.

  Scheme 1. 1,3-NHC boryl shift with B-substituted NHC-borane and bis(mercaptobenzothiazolyl) disulfide

Scheme 2 . 1 , 3 -

 213 Scheme 2. 1,3-NHC boryl shift with B-substituted NHC-borane and bis(1phenyltetrazolyl) disulfide.

Scheme 3 .

 3 Scheme 3. Absence of 1,3-NHC boryl shift with B-substituted IPr-boranes

Table 1 .

 1 were obtained in rather poor yields (29%, 27% and 8%, respectively, entries10-12). We next varied the NHC and chose the bulky IPr to replace the small IMe (entries 16-20). No reaction took place under the thermal conditions (entries 16 and 18). Scope of the Preparation of NHC-Boryl Sulfides from B-Substituted NHC-Boranes.

	2 [(4-CF 3 )-C 6 H 4 ] the NHC-boryl sulfides were
	obtained in yields similar to those obtained with the phenyl-
	substituted substrate (44% for 1d, entry 7; 82% for 1e, entry 8;
	44% for 1f, entry 9). and electron-donating (4-OMe)
	substituents at boron are compatible with the reaction.
	Alternatively, the electron-donating-substituted NHC-borane
	DiMe-Imd-BH

2 [(4-OMe)-C 6 H 4 ] delivered adducts 1j-l in 62% yields (resp. 42%, 75%, entries 13-15). Curiously, the m-Br substituted NHC-Borane DiMe-Imd-BH 2 [(3-Br)-C 6 H 4 ] was a This journal is © The Royal Society of Chemistry 20xx Please do not adjust margins Please do not adjust margins poor substrate, as 1g-i a Conditions: 45°C; PhH, overnight () or PhH, rt, Omnicure® irradiation (h); b Carbene is Dipp-(Imd); c no reaction; d degradation

This journal is © The Royal Society of Chemistry 20xx

† This work was supported by CNRS. A.-L. V. thanks ICSN for a doctoral stipend.

Conflicts of interest

There are no conflicts to declare.

Notes and references


domain: chim chim.orga sdv

text:
Melisa Del Barrio

Matteo Sensi

Christophe Orain

Carole Baffert

Sébastien Dementin

Vincent Fourmond

Christophe Léger
email: leger@imm.cnrs.fr

Electrochemical Investigations of Hydrogenases and Other Enzymes That Produce and Use Solar Fuels

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

Introduction

The activation of small molecules is a key aspect of renewable energy research. The reactions of water electrolysis and H 2 oxidation could serve for storing and returning to the grid the energy that is intermittently produced from renewable sources such as sunlight. Recent concerns about climate change have also boosted the research on CO 2 reduction to various synthetically valuable organic molecules. Nature is an expert in chemical energy conversion, and at a time when we are endangering the planet by recklessly using fossil and nuclear energies, a rightful giving-back would be to seek inspiration from the strategies that have proved effective since the origin of Life. The study of enzymes that use and produce small biological fuels should be very informative in this respect.

Living organisms store energy in the form of small molecules that are continuously produced and recycled (fig. 1). Sunlight is used by photosynthetic organisms to produce energy (in the form of ATP) and biomass. Dioxygen, the byproduct of oxygenic photosynthesis, is reduced in the respiratory chains of plants, mammals and aerobic microorganisms in relation to ATP synthesis. Most microorganisms also use H 2 as an energy vector: it is evolved (by fermentation, mainly, and as a byproduct of nitrogen fixation) and re-oxidized (using dioxygen, sulfate or other electron acceptors) as part of the bioenergetic metabolism of either the organism where dihydrogen is produced or a distinct bacterium that shares the same ecosystem. Some bacteria grow using CO as an energy source: they may use e.g. O 2 or nitrate to oxidize the CO from natural sources into CO 2 , which is fixed either by the enzyme Many of these reactions are catalyzed by large enzymes that use one or several inorganic cofactors based on transition metals. Neither the active site nor its conserved proteic environment fully determine the enzyme's catalytic properties, and structural elements such as accessory clusters, substrate channels or residues involved in proton transfer, which are remote from the active site, play a decisive role. More than one hundred years after Michaelis and Menten initiated the research on enzyme mechanisms by defining the methodology for the analysis of enzyme reactions, enzyme kinetics has become the poor cousin of enzymology and modern methods such as crystallography and spectroscopy, often aided by computational chemistry, 1 have taken over. However, regarding the investigation of the finest details in the catalytic cycle, these experimental methods do have a weakness: they rely on the assumption that the forms of the enzyme that are stable enough to be trapped and detected are actually catalytic intermediates. But catalytic intermediates are elusive and many metalloenzymes reversibly or irreversibly convert into stable forms that are inactive (i.e. not part of the catalytic cycle). In the particular case of hydrogenases, which catalytically evolve H 2 , another level of difficulty is that the Author version of: Acc. Chem. Res. 51 769 (2018) http://dx.doi.org/doi:10.1021/acs.accounts.7b00622 substrate proton cannot be removed from the buffer, and therefore catalytic H 2 evolution competes with the reduction of the enzyme; this implies that the catalytically-competent reduced states of hydrogenase cannot be stabilized. At the other end of the redox scale, the same is true for the S4 state of the oxygen-evolving manganese cluster of Photosystem II.

There are therefore various reasons why certain catalytic intermediates cannot be isolated and inactive species may sometimes be mistaken for catalytic intermediates. Kinetics, by focusing on activity and changes in activity, is required to identify the experimental conditions that favor the accumulation of catalytic intermediates. [START_REF] Jacques | Kinetics of substrate inhibition of periplasmic nitrate reductase[END_REF] Figure 2: Typical electrochemical set-up used to measure the activity of an enzyme adsorbed onto a rotating-disk graphite "working" electrode, and to expose it to various potential steps and sweeps, substrates, inhibitors and light.

In Marseille, our interest has been mostly in using enzyme kinetics: we believe that designing experiments where the enzyme is actually catalyzing a reaction is a condition for learning about how this enzyme works. The method that we favor is direct electrochemistry (or "protein film voltammetry"). when one changes the electrode potential, the temperature, the concentration of activator, inhibitor or substrate, or shines light on the adsorbed enzyme.

This electrochemical method has disseminated from the group of Fraser Armstrong through a significant number of research groups worldwide over the last 15 years. The combination of dynamic electrochemistry and spectroscopy is a recent development. [START_REF] Sensi | New perspectives in hydrogenase direct electrochemistry[END_REF] Several principles have guided our own contribution. First, we have been interested in steps in the catalytic cycles that take place far from the active site (e.g. along the ET chain or in the tunnels that guide the substrate and inhibitors, or inter-domain movement); these steps may limit the rate of catalysis and determine the global catalytic properties of the enzyme.

This complexity poses a challenge to experimental and computational mechanistic studies of metalloenzymes and to the biomimetic approaches to catalysis. Second, our objective has always been to quantitatively interpret the data by developing and using various kinetic models and free softwares. [START_REF] Fourmond | QSoas: A Versatile Software for Data Analysis[END_REF] In an effort to promote this approach, we shall describe in fig. S1 a few useful procedures. Last, collaborations with theoretical chemists have allowed us to establish quantitative relations between kinetic measurements and molecular mechanisms. This approach contrasts with, and complements, traditional strategies which all aim at seeing catalytic intermediates using methods that exploit the interactions between light and matter: crystallography, spectroscopy. Here we shall describe results representative of our work, hopefully inspiring further research in this field.

Diffusion along gas channels: new methods and functional implications

In NiFe hydrogenase, a "tunnel" guides the substrate/product H 2 and inhibitors such as CO Electrochemistry can be used to measure the rates of diffusion within hydrogenase. The method consists in examining the kinetics of binding and release of the competitive inhibitor CO in a very simple electrochemical experiment where one measures the H 2 -oxidation current at a constant potential and monitors the change in activity that results from a transient exposure to the inhibitor CO (fig. 3). When the experiment is performed with e.g. WT Df NiFe hydrogenase, the change in turnover rate closely follows the change in CO concentration in the cell (fig. 3DE), showing that CO diffuses very quickly in and out of the enzyme. In contrast when the side chains of the position 122 and 74 amino acids are modified (fig. 3C), the change in turnover rate occurs with a delay (fig. 3F) that results from the slow diffusion of CO along the modified tunnel. The data can be analyzed by assuming bimolecular binding and 1st order release of the ligand,

E k in × [CO] ---------------- k out ECO (1)
to measure the rates of diffusion in either direction (fig. S1 CD). The meaning of these rate constants depends on the relative rates of intramolecular diffusion and bond breaking/formation at the active site; in NiFe hydrogenase, the rate of inhibition by CO, k in , is a good proxy of the rate of intramolecular diffusion, k 1 (cf SI section S1).

In figure 4B shows the good agreement between the calculated diffusion rates (k 1 ) and the experimental CO-binding rates for several NiFe hydrogenase site-directed mutants. [START_REF] Greco | Combining experimental and theoretical methods to learn about the reactivity of gas-processing metalloenzymes[END_REF] Intramolecular diffusion partly determines the global properties of hydrogenase. For example, slowing down diffusion along the gas channel of NiFe hydrogenase slows the rate of inhibition by O 2 (fig. 4A andsection S1), but if the reaction with O 2 is irreversible, the only consequence is to postpone the moment the enzyme becomes fully inactive. However, some mutations in the gas channel of NiFe hydrogenase significantly increase the resistance to O 2 of Df NiFe hydrogenase, [START_REF] Hamdan | Relation between anaerobic inactivation and oxygen tolerance in a large series of NiFe hydrogenase mutants[END_REF] independently of any effect on diffusion. In hydrogenases that are "naturally" O 2 -resistant, this property is given by a particular FeS cluster in the electron transfer chain. [START_REF] Lukey | Oxygen-Tolerant [NiFe]-Hydrogenases: The Individual and Collective Importance of Supernumerary Cysteines at the Proximal Fe-S Cluster[END_REF] The second example is related to the reasons why certain hydrogenases are better cata-Author version of: Acc. Chem. Res. 51 769 (2018) http://dx.doi.org/doi:10.1021/acs.accounts.7b00622 lysts (in terms of v max ) in one particular direction of the reaction. Mutations that selectively slow the diffusion of H 2 in Df NiFe hydrogenase decrease the activity for H 2 production because H 2 exit is slow and determines the rate of H 2 production. [START_REF] Abou Hamdan | Understanding and Tuning the Catalytic Bias of Hydrogenase[END_REF] In contrast, H 2 oxidation in solution is limited by ET to the redox partner, and indeed the mutations of the surface exposed cluster of NiFe hydrogenase that slow intermolecular ET slow down H 2 -oxidation more than H 2 -production. [START_REF] Dementin | Changing the Ligation of the Distal [4Fe4S] Cluster in NiFe Hydrogenase Impairs Inter-and Intramolecular Electron Transfers[END_REF] Modifying either the gas channel or the ET chain tunes the catalytic bias of a hydrogenase by slowing a step that is limiting in only one direction of the reaction.

Intramolecular mass transport is an important aspect of the reactivity of CO-dehydrogenases (CODHs), the enzymes that convert CO and CO 2 . In the bifunctional enzyme where the CODH subunit is associated with an acetyl-coA synthase (ACS) subunit, a dynamically formed gas channel transports CO from the production site in the CODH subunit to the utilization site in the ACS subunit. [START_REF] Wang | Uncovering a Dynamically Formed Substrate Access Tunnel in Carbon Monoxide Dehydrogenase/Acetyl-CoA Synthase[END_REF] The pathways used by CO in the CODH dimer are still elusive, but intramolecular transport is likely to be very fast, based on the observations that these enzymes react with O 2 and CO very quickly (> 10 7 s -1 M -1 ) [START_REF] Merrouch | O 2 Inhibition of Ni-Containing CO Dehydrogenase Is Partly Reversible[END_REF][START_REF] Domnik | A High Efficiency CO-Scavenging CO Dehydrogenase with Resistance to O 2[END_REF] and some CODHs have a Michaelis constant in the nM range [START_REF] Domnik | A High Efficiency CO-Scavenging CO Dehydrogenase with Resistance to O 2[END_REF] (fig S1 EF).

Interpreting catalytic wave shapes

Understanding the dependence of turnover rate on electrode potential is the most important goal in direct electrochemistry. Different situations must be distinguished, depending on whether or not the response reaches steady-state (fig. 5). If the potential is swept, the scan rate ν defines the time scale τ = RT /F ν of the experiment. A departure from steadystate occurs when this time scale matches that of a redox transformation of the enzyme.

Redox driven (in)activations are often slow (time constants in the range 5-500 s), and are therefore manifested in a hysteresis in the voltammograms recorded at slow scan rates (10 -4 -10 -2 V/s). Redox transformations between catalytic intermediates occur on the time scale of Author version of: Acc. Chem. Res. 51 769 (2018) http://dx.doi.org/doi:10.1021/acs.accounts.7b00622 turnover (10 -4 s-10 -2 s), and making the system depart from catalytic steady-state requires scan rates in the range 0.5-50 V/s. [START_REF] Zeng | Transient Catalytic Voltammetry of Sulfite Oxidase Reveals Rate Limiting Conformational Changes[END_REF] At even faster scan rates catalysis does not proceed during the potential sweep and the catalytic signal vanishes. [START_REF] Jones | Interruption and Time-Resolution of Catalysis by a Flavoenzyme Using Fast Scan Protein Film Voltammetry[END_REF] By changing the scan rate, one can therefore turn on and off (and learn about) some of the redox reactions that affect the catalytic response.

We have discussed how slow redox transformations between active and inactive forms result in a strong hysteresis in the voltammetric wave-shape. [START_REF] Fourmond | Modelling the voltammetry of adsorbed enzymes and molecular catalysts[END_REF] Here we focus on two other aspects of the interpretation of voltammetric signals.

Figure 5: How scan rate (ν) affects the catalytic response. Actual (solid lines) or simulated (dotted lines) voltammograms of a film of Aquifex aeolicus hydrogenase at scan rates ranging from very slow (for which both catalysis and the anaerobic inactivation are at steady-state) to very fast (for which they are both outrun).

How the kinetics of intramolecular ET affects steady-state catalytic wave shapes

To describe a voltammetric response, an important phenomenological parameter is the "catalytic potential", i.e. the mid-point potential of the sigmoidal catalytic signal, whose value defines the catalytic "overpotential" (and thus, the driving force required to trigger catalysis) and the "catalytic bias" (the relative magnitude of the current in the two directions).

A simple model of catalytic cycle (fig. 6), which depicts a two-electron active site "A" wired to the electrode by a relay "R," shows how the catalytic potentials depend on the properties of the enzyme (redox potentials, intramolecular ET rate constants). The model assumes that the active site exists in three redox states (oxidized, intermediate and reduced) characterized by the two potentials E 0 OI and E 0 IR . E 0 R is the potential of the relay. The ratio k 2 /k -2 defines whether the active site works one-way or both ways.

Intramolecular ET is defined by the rate constants k ±1 and k ±1 , and the parameter λ = k 1 /k 2 describes whether intramolecular ET is fast or slow compared to active site chemistry.

Depending on the parameters of the model, four distinct wave-shapes are predicted (circled numbers in fig. 7) and two one-electron catalytic potentials are defined (marked by blue and red vertical lines): the signal may consist of two broad (one-electron) waves each centered on one of the two catalytic potentials, 1 ; or a single, sharp (two-electron) wave centered on their average value, 2 and 4 ; or a single one-electron wave centered on one of the two catalytic potentials, 3 . These catalytic potentials depart from E 0 OI and E 0 IR (just like Michaelis constants are not true thermodynamic parameters).

Figure 7 shows the changes in apparent catalytic potentials against λ = k 1 /k 2 (fast intramolecular ET being on the right of each X-axis), for irreversible or reversible catalysis (left or right panels, respectively), assuming that the active site potentials are crossed or uncrossed (E 0 OI greater or smaller than E 0 IR , top and bottom panels, respectively). Each panel shows the continuous change from the situation intramolecular ET is slow in both directions of the reaction (λ small) and one of the two catalytic potential equates E 0 R , to the situation where intramolecular ET is fast (rightmost) and the catalytic potentials match the active site potentials. In contrast to a common assumption, the situation where the signal is a single wave at E 0 R can occur only when catalysis is irreversible (wave 3 ).

Fast scan catalytic voltammetry

Figure 1 :

 1 Figure 1: The biological cycling of solar fuels.

and O 2

 2 in and out of the enzyme. The narrow end of this tunnel, near the active site, is shaped by the side chains of two conserved amino-acids (L122 and V74 in D. fructosovorans (Df ) NiFe hydrogenase) as shown in fig. 3. Much effort has been put in testing Volbeda's initial Author version of: Acc. Chem. Res. 51 769 (2018) http://dx.doi.org/doi:10.1021/acs.accounts.7b00622 assumption 7 that these side-chains determine O 2 access to the active site of hydrogenase and O 2 sensitivity.

  Df NiFe hydrogenase, certain point mutations slow the rate of binding of CO one thousand fold (fig. 4). As discussed in ref 9, the relations between the rate of CO binding and the Michaelis constant for H 2 (fig. 4b in ref 9) or the rate of inhibition by O 2 (fig. 4A) demonstrate that the mutations have the same effect on the rates of diffusion of these three molecules, which take the same path inside the enzyme. (Similar experiments could identify amino acids that determine the diffusion rates in FeFe hydrogenases. 10 ) Crystallography and molecular dynamics calculations had long been used to identify Author version of: Acc. Chem. Res. 51 769 (2018) http://dx.doi.org/doi:10.1021/acs.accounts.7b00622

Figure 3 :

 3 Figure 3: Electrochemical estimation of the kinetics of substrate/inhibitor diffusion within Df NiFe hydrogenase. Change in activity upon exposure to CO (panel D) of the WT enzyme (left) and the L122F-V74I mutant (right). The structures in panels ABC were drawn using the pdb files 1YQW and 3CUS. Adapted with permission from ref. 8 copyright 2008 Natl. Acad. Sc. USA.

Figure 4 :

 4 Figure 4: Plots of the rate of inhibition by O 2 (Panel A) and the calculated rate of diffusion k 1 (Panel B) against the rate of inhibition by CO. Each data point corresponds to one mutant of Df NiFe hydrogenase. Adapted with permission from ref. 9 copyright 2010 NPG and ref. 11 copyright 2014 RSC.

Figure 6 :

 6 Figure 6: A reversible catalytic cycle that takes into account two-electron redox chemistry at the active site "A" in three redox states, oxidized O, intermediate I, and reduced R (potentials E 0 O/I and E 0 I/R ) and intramolecular ET via an oxidized or reduced relay "R" (potential E 0 R ). Steps 2 and -2 include substrate binding and release, and k 2 and/or k -2 may depend on substrate concentrations. Reproduced with permission from ref. 22 copyright 2013 ACS.

4 λFigure 7 :

 47 Figure7: The shapes of the steady-steady-state voltammograms predicted from the scheme in fig.6(left panels and circled numbers) and the changes in the values of the two one-electron catalytic potentials versus the potential of the relay (also indicated by vertical lines on top of the voltammograms) as a function of the parameter λ, which is large when intramolecular ET is fast (panels abcd); the dotted lines show the position of the observed wave(s) (SI section S2). The left (ac) and right (bd) panels are for k 2 /k -2 = 0.5 and ∞ (hence bi-or uni-directional catalysis, respectively), and the top (ab) and bottom (cd) panels show the situations where the active site potentials are uncrossed, or crossed over, respectively.

  Jones et al. have shown that fast scan rates can outrun catalysis by fumarate reductase:the fast-scan voltammetric response consists of pairs of peaks, as observed in the absence of substrate.[START_REF] Jones | Interruption and Time-Resolution of Catalysis by a Flavoenzyme Using Fast Scan Protein Film Voltammetry[END_REF] Slower scan rates result in a transient catalytic response which can also be interpreted.[START_REF] Zeng | Transient Catalytic Voltammetry of Sulfite Oxidase Reveals Rate Limiting Conformational Changes[END_REF]

Figure 8 :

 8 Figure 8:The active site H-cluster of FeFe hydrogenase and its reactions with H 2 , CO, 24,28 O 2 10,29 and light.[START_REF] Sensi | Photoinhibition of FeFe Hydrogenase[END_REF]

Figure 9 :

 9 Figure 9: The effect of CO (left) and O 2 (right) on the H 2oxidation activity of FeFe hydrogenase. The enzyme was exposed to CO and to the light of a 450 nm laser beam as shown in panel A. The catalytic response (panel B) was used to measure the CO in/out rate constants plotted against light power in panels CD. Panel F shows the response of C. acetobutylicum and C. reinhardtii FeFe hydrogenases exposed to O 2 as indicated in panel E. The rate constants of reactivation (k a in eq. 3) are plotted against electrode potential in panel G. Adapted with permission from ref. 28 copyright 2016 ACS and ref. 10 copyright 2017 NPG.

  Author version of: Acc. Chem. Res. 51 769 (2018) http://dx.doi.org/doi:10.1021/acs.accounts.7b00622

	3-5 A redox enzyme is adsorbed as a submonolayer film
	onto the surface of a rotating disc electrode (fig 2) and electron transfer (ET) between the
	enzyme and the electrode is direct. In the presence of the substrate, electron transfer to/from
	the electrode continuously regenerates the redox state of the enzyme that is competent
	for catalysis. The resulting current is proportional to the turnover frequency and to the
	electroactive coverage. The latter is most often unknown but provided it is constant much
	information can be gained by analyzing the relative changes in current that are observed

  Author version of: Acc. Chem. Res. 51 769 (2018) http://dx.doi.org/doi:10.1021/acs.accounts.7b00622

Acknowledgement

Our work is supported by CNRS, Agence Nationale de la Recherche (ANR-12-BS08-0014, ANR-14-CE05-0010, ANR-17-CE11-0027) and the Excellence Initiative of Aix-Marseille University -A*MIDEX, a French "Investissements d'Avenir" programme (ANR-11-IDEX-0001-02). The authors are part of the French bioinorganic chemistry network (www.frenchbic. cnrs.fr).

Author version of: Acc. Chem. Res. 51 769 (2018) http://dx.doi.org/doi:10.1021/acs.accounts.7b00622

The enzyme human sulfite oxidase consits of a catalytic domain, containing the mononuclear molybdenum active site, and an ET domain, whith a heme cofactor. The two are linked by a flexible hinge. The enzyme can adopt an open conformation, in which the heme domain can interact with redox partners but not with the molybdenum site, and a closed conformation, in which intermolecular ET is blocked but electrons can be exchanged between the heme and the molybdenum. By recording catalytic voltammograms at various scan rates, we could observe and interpret the deviation from steady-state catalysis, up until very fast scan rates where catalysis is outrun. [START_REF] Zeng | Transient Catalytic Voltammetry of Sulfite Oxidase Reveals Rate Limiting Conformational Changes[END_REF] Only a model which takes into account conformational changes can reproduce the data, showing that conformational changes still occur when the enzyme is adsorbed onto the electrode. This conclusion could not be reached from the examination of data recorded under steady state conditions. Interpreting this type of signals is difficult because it must rely on numerical simulations but we believe that this effort will eventually prove as significant as the historical step from steady-state enzyme kinetics to stopped flow.

In an alternative approach, Parkin and coworkers have also recently taken advantage of the possibility to mute the catalytic response by modulating the potential at high frequency, and recording concomitantly the steady-state catalytic response and the high frequency harmonics. The latter embed the information about non-catalytic ETs. They used this strategy to explore the relation between the properties of the ET chain and the catalytic bias in E. coli hyd-1 WT and various mutants. [START_REF] Adamson | Retuning the Catalytic Bias and Overpotential of a [NiFe]-Hydrogenase via a Single Amino Acid Exchange at the Electron Entry/Exit Site[END_REF] 4 Combining kinetics and theory to understand the reaction of the H-cluster with small ligands To illustrate the approach that combines electrochemical kinetics and theoretical calculations, we discuss a few reactions of the active site H-cluster of FeFe hydrogenase (fig. 8).

The inhibition of the enzyme by CO

(At very low potential, the affinity of the H-cluster for CO is so low that neither binding nor damage occurs.) The dependence of k in and k 3 on the electrode potential (fig. 2A in ref 24) shows that the species that reacts irreversibly with CO is one-electron more reduced than the resting state "Hox" ([4Fe4S] 2+ Fe II Fe I ). According to DFT, Hred has the electronic structure [4Fe4S] 2+ Fe I Fe I , in which the iron atoms already fulfill the 18-electron rule. Upon CO binding to Hred, a bond must be cleaved: either the exogenous CO ligand is released or the bond between the proximal Fe and the cysteine that bridges the [4Fe4S]

subcluster breaks, giving the inactive, inert compound

all FeFe hydrogenases inactivate under these conditions. [START_REF] Ceccaldi | The hydrogen dependent CO 2 reductase: the first completely CO tolerant FeFe-hydrogenase[END_REF] A recent FTIR investigation of the enzyme from D. desulfuricans showed that the binuclear cluster is indeed released upon reduction of the HoxCO state, [START_REF] Rodríguez-Maciá | Spectroscopic Evidence of Reversible Disassembly of the [FeFe] Hydrogenase Active Site[END_REF] but the spectroscopists believe that this follows the reduction to [4Fe4S] 1+ Fe I Fe I . When the disruption of the H-cluster occurs in a closed FTIR cell, the binuclear cluster can rebind under oxidizing conditions. [START_REF] Rodríguez-Maciá | Spectroscopic Evidence of Reversible Disassembly of the [FeFe] Hydrogenase Active Site[END_REF] All this is relevant to the biological maturation of the H-cluster. [START_REF] Megarity | Electrochemical Investigations of the Mechanism of Assembly of the Active-Site H-Cluster of [FeFe]-Hydrogenases[END_REF] That CO binding to the H-cluster is weakened by irradiation can be observed in electrochemical experiments where the enzyme is adsorbed on an electrode and simultaneously irradiated by the light beam of e.g. a laser diode (fig 2). Under these conditions, the larger the power and the shorter the wavelength, the lower the magnitude of the inhibition. Fig. 9 CD clearly reveals that the illumination has an effect only on k out , which increases with the power density of the incident light. From the value of the slope (155 cm 2 /s/W at 450 nm, converted into ≈ 18mM -1 cm -1 ) and the molar absorption coefficient of the H-cluster, we concluded that most of the absorbed blue photons lead to photo-dissociation of the apical CO. This is consistent with the results of TDDFT calculations, which show that the excitations that involve the dinuclear subcluster occur in the high energy part of the visible spectrum and identify a barrierless relaxation pathway that dissociates the exogenous, apical CO. [START_REF] Sensi | Reactivity of the Excited States of the H-Cluster of FeFe Hydrogenases[END_REF] TDDFT calculations also helped us understand the molecular basis of the photoinhibition of FeFe hydrogenase. [START_REF] Sensi | Photoinhibition of FeFe Hydrogenase[END_REF] The FeFe hydrogenases from C. acetobutylicum and C. reinhardtii are irreversibly damaged by UVB; this results from the photodissociation of one of the intrinsic CO ligands, followed by rearrangement of the binuclear cluster. This photoinhibition reaction prevents the use of the full solar spectrum to drive artificial photocatalytic dyads where either an enzyme or a bacterium receives electrons from a photosensitizer. Some FeFe hydrogenases are destroyed even by visible light, [START_REF] Rodríguez-Maciá | Electrochemical Investigations on the Inactivation of the [FeFe] Hydrogenase from Desulfovibrio desulfuricans by O2 or Light under Hydrogen-Producing Conditions[END_REF] and the possibility of irreversible photoinhibition will have to be considered to optimize H 2 photoproduction systems where a particular FeFe hydrogenase is wired to a light-harvesting systems.

An obstacle to using FeFe hydrogenases is also their sensitivity to O 2 . Figure 9F shows that their activity decreases following each transient exposure to O 2 , after which a partial reactivation is observed. The change in activity over time is again consistent with eq 3, where the active enzyme reacts with O 2 to form an inactive O 2 -adduct that can either give back the active form (rate constant k a ) or be irreversible transformed into a dead-end.

The rate of inhibition involves the diffusion of O 2 through the protein matrix (forward and backward rate constants k 1 and k -1 ) followed by the formation of a Fe-O 2 bond (rate constants k 2 and k -2 ). The measured inhibition rate k in is a combination of all the corresponding rate constants (section S1):

Molecular dynamics calculations could be use to elucidate the intramolecular diffusion pathways and to predict the rates of diffusion to and from the active site: and k -1 = 8×10 7 s -1 . The rate of O 2 binding to the H-cluster has been calculated by DFT. [START_REF] Kubas | Aerobic damage to [FeFe]-hydrogenases: activation barriers for the chemical attachment of O 2[END_REF] The values of the rate constants (k 2 = 2×10 3 s -1 and k -2 = 1.4×10 -2 s -1 , k 2 k -1 ) suggest that most O 2 molecules leave the enzyme without binding to the H-cluster. Combining all calculated rate constants gives k in = 9 × 10 -2 s -1 /mM, which is only one order of magnitude smaller than the experimental value (k in = 1 s -1 /mM). The agreement is fair, considering that each of the contributing calculated rate constants includes systematic errors.

The reactivation that is seen in fig. 9F when O 2 is flushed away from the electrochemical cell is not just the unbinding of O 2 . Indeed, k a is very dependent on pH and isotope-exchange and increases exponentially as the electrode potential decreases: the reactivation is actually the reduction of the O 2 -bound adduct (this reduction is a negligible contribution to the faradaic current). According to DFT calculations, the reduction product is H 2 O.

The calculations also suggest that under certain conditions (high pH, high E) a hydroxyl ligand formed at the H-cluster en route to H 2 O may react with a nearby cysteine; indeed, this cysteine was found oxidized in a structure of the enzyme [START_REF] Swanson | FeFe]-hydrogenase oxygen inactivation is initiated at the H cluster 2Fe subcluster[END_REF] and its replacement with aspartate decreases k 3 ten-fold. [START_REF] Kubas | Mechanism of O 2 diffusion and reduction in FeFe hydrogenases[END_REF] This reaction may explain that the inhibition by O 2 is not fully reversible.

Biographical Information

Supporting Information

The Supporting Information is available free of charge on the ACS Publications website. Supporting Information Available: the meaning of the experimental binding/release rate constants; the apparent potentials plotted in fig. 7; a few examples of quantitative data analysis.