R Bois

I Pezron

A Nesterenko
email: alla.nesterenko@utc.fr

Dynamic interfacial properties of sugar-based surfactants: experimental study and modeling

Keywords: sugar-based surfactants, dynamics properties, surface tension, surface viscoelasticity

Careful investigation about dynamic adsorption properties of surfactant molecules has a tremendous interest for their practical applications. The intention of this article is to study the dynamic adsorption properties at air/water interface for 15 nonionic sugar-based surfactants with gradual structure variation. Based on obtained results the dynamic surface tension (DST) behaviour of glycolipids was found to depend on both hydrophobic chain length and bulk concentration of surfactant. Interestingly, the plot of the maximum rate of surface tension decrease against the surfactant bulk concentration showed a linear trend for all studied surfactants independently of their structure. Furthermore, it was confirmed that all molecules were gathered on one unique curve representing a plot of the limit elasticity versus the relative surface concentration of surfactant. The using approach provided further insight into the anticipation of the dynamic surface properties of sugar-based amphiphiles.

Introduction

Surfactants are large group of surface-active compounds using in various practical applications of everyday life. Due to their amphiphilic properties, they can be used as emulsifying, foaming, solubilizing, wetting or detergency agents in diversity of formulations.

A large part of the worldwide surfactant production is still synthetized from non-renewable materials, and thus cannot be considered as sustainable. Over the past decades, the development and the use of environmentally-friendly amphiphilic molecules have been intensively studied [START_REF] Bhadani | Current perspective of sustainable surfactants based on renewable building blocks[END_REF]. Natural-based surfactants can be produced from different fractions of agricultural biomass, such as peptides and amino acids [START_REF] Infante | Amino acid-based surfactants[END_REF][START_REF] Bordes | Amino acid-based surfactants -do they deserve more attention[END_REF], cellulose [START_REF] Xiao | Preparation of oligosaccharide surfactant based on cotton cellulose and application in hydrophilic modification of docetaxel[END_REF], sugars [START_REF] Ruiz | Sugar-Based Surfactants[END_REF], fatty acids and alcohols [START_REF] Johansson | Surfactants based on fatty acids and other natural hydrophobes[END_REF][START_REF] Dembitsky | Astonishing diversity of natural surfactants: 1. Glycosides of fatty acids and alcohols[END_REF].

2 Sugar-based surfactants consisted of a hydrophobic chain alkyl group and a hydrophilic carbohydrate head-group are the category of mild amphiphilics well known for their high wetting, foaming and emulsifying performances, reduced environmental footprint, good biodegradability, low toxicity and dermal tolerability [START_REF] Bhadani | Current perspective of sustainable surfactants based on renewable building blocks[END_REF][START_REF] Ruiz | Sugar-Based Surfactants[END_REF][START_REF] Gaudin | Investigating the impact of sugar-based surfactants structure on surface tension at critical micelle concentration with structureproperty relationships[END_REF][START_REF] Lourith | Natural surfactants used in cosmetics: glycolipids[END_REF][10][START_REF] Yoshimura | Equilibrium Surface Tension, Dynamic Surface Tension, and Micellization Properties of Lactobionamide-Type Sugar-Based[END_REF]. They are mainly produced from starch (glucose, galactose, mannose, xylose, sorbitol and lactose derivatives), sugar beet, sugarcane or carbohydrate-based residues of hemicellulose. Due to their mild character, biodegradability and functional properties, sugar-based surfactants have found applications in pharmaceutical formulations, cosmetic, food and personal care products [START_REF] Ruiz | Sugar-Based Surfactants[END_REF][START_REF] Hill | Sugar-based surfactants for consumer products and technical applications[END_REF][START_REF] Tesmann | Alkyl Polyglycosides in Personal Care Products[END_REF][START_REF] Rybinski | Alkyl Polyglycosides-Properties and Applications of a new Class of Surfactants[END_REF][START_REF] Zhao | Study on the synthesis and properties of an eco-friendly sugar-based anionic-nonionic surfactant[END_REF].

One of the essential functions of surface active molecules is the capacity to cover the newly created interface related to their non-equilibrium values of the interfacial tension. These dynamic surface properties of surfactants play an important role in various technological processes governed by non-equilibrium phenomena with continuous formation of new interfaces [START_REF] Aksenenko | Adsorption and surface dilational visco-elasticity of CnEOm solutions as studied by drop profile analysis tensiometry[END_REF][START_REF] Bastani | CFD simulation of bubble in flow field: Investigation of dynamic interfacial behaviour in presence of surfactant molecules[END_REF][START_REF] Kovalchuk | The effect of adsorption kinetics on the rate of surfactant-enhanced spreading[END_REF][START_REF] Pagureva | Surface properties of adsorption layers formed from triterpenoid and steroid saponins[END_REF]. For example, the rate of surfactant diffusion to a newly generated liquid/gas, liquid/liquid and liquid/solid interfaces has a direct bearing on respectively its foaming behavior, emulsifying capacity and wetting properties. Surfactant adsorption kinetic is the dominating factor controlling the interfacial film formation and stabilization. Furthermore, the film formation and resistance to rupture is often correlated to the viscoelasticity of the surface [START_REF] Champougny | Surfactant-induced rigidity of interfaces: a unified approach to free and dip-coated films[END_REF][START_REF] Lai | Interfacial dynamic properties and dilational rheology of mixed anionic and cationic Gemini surfactant systems at air-water interface[END_REF][START_REF] Noskov | Formation of protein/surfactant adsorption layer as studied by dilational surface rheology[END_REF]. The surface viscoelastic properties of adsorbed layer characterize the resistance of the interface to deformation. They affect strongly the stability of interfacial films and thus the properties of foams and emulsions [START_REF] Derkatch | Dynamic properties of gelatin/surfactant adsorption layers[END_REF][START_REF] Gadkari | Interfacial rheological behaviour of lentil protein isolate-fenugreek gum complex[END_REF][START_REF] Pepicelli | Characterization and modelling of Langmuir interfaces with finite elasticity[END_REF]. Thus, the optimal dosage of a surfactant needs the specific knowledge of dynamic adsorption properties. In the past years, in depth understanding the kinetics of surfactants adsorption and non-equilibrium surface properties have gained significant interest because of a direct relevance for their use [START_REF] He | Adsorption-desorption kinetics of surfactants at liquid surfaces[END_REF]. Additionally, the knowledge about dynamic properties can be useful to identify new molecules for potential applications and would be helpful to develop industrial formulations.

Regarding sugar-based surfactants, interfacial properties and particularly equilibrium properties, as the critical micellar concentration (CMC) or surface tension have been described previously. Several studies showed that even small changes in the molecular structure of glycolipids resulted in considerable differences in their physico-chemical properties [START_REF] Ruiz | Sugar-Based Surfactants[END_REF][START_REF] Gaudin | Investigating the impact of sugar-based surfactants structure on surface tension at critical micelle concentration with structureproperty relationships[END_REF][START_REF] Rosen | Surfactants and Interfacial Phenomena[END_REF][START_REF] Lu | Catalytic Synthesis of a New Series of Alkyl Uronates and Evaluation of Their Physicochemical Properties[END_REF][START_REF] Gaudin | New QSPR Models to predict the Critical Micelle Concentration of Sugar-Based Surfactants[END_REF][START_REF] Gaudin | Conformations of n-alkyl-α/β-dglucopyranoside surfactants: Impact on molecular properties[END_REF][START_REF] Gaudin | Impact of the chemical structure on amphiphilic properties of sugar-based surfactants: A literature overview[END_REF]. Gaudin et al [START_REF] Gaudin | Impact of the chemical structure on amphiphilic properties of sugar-based surfactants: A literature overview[END_REF] recently proposed a literature overview of structure effect on equilibrium surface properties. The CMC is strongly influenced by the hydrophobic chain while the polar head has a more significant effect on the value of surface tension at CMC. Furthermore established models based on quantitative structure-property relationship (QSPR) allow the prediction of the CMC of glycolipids according to the structure of the method represents an interesting approach for CMC estimation allowing to reduce both time and cost of experimental screening.

However, the experimental data on dynamic surface properties of sugar-derived surfactants are rare. For example, the dilatational viscoelasticity has been widely investigated for the dodecyl-β-maltoside solely [START_REF] Stubenrauch | Stability of Foam Films and Surface Rheology: An Oscillating Bubble Study at Low Frequencies[END_REF][START_REF] Grigoriev | Surface elasticities of aqueous β-dodecyl-d-maltoside solutions: A capillary wave study[END_REF][START_REF] Santini | A surface rheological study of non-ionic surfactants at the water-air interface and the stability of the corresponding thin foam films[END_REF][START_REF] Stubenrauch | Aqueous foams stabilized by n-dodecyl-[small beta]-d-maltoside, hexaethyleneglycol monododecyl ether, and their 1 : 1 mixture[END_REF][START_REF] Georgieva | Link between surface elasticity and foam stability[END_REF][START_REF] Stubenrauch | Mixtures of n-dodecyl-β-d-maltoside and hexaoxyethylene dodecyl ether -Surface properties, bulk properties, foam films, and foams[END_REF]. It was found that this alkylglucoside provides a higher surface elasticity compared to conventional ethoxylate derivatives surfactants. This particular property related to the film resistance properties and was shown to be closely correlated to foam stability [START_REF] Stubenrauch | Aqueous foams stabilized by n-dodecyl-[small beta]-d-maltoside, hexaethyleneglycol monododecyl ether, and their 1 : 1 mixture[END_REF][START_REF] Stubenrauch | Mixtures of n-dodecyl-β-d-maltoside and hexaoxyethylene dodecyl ether -Surface properties, bulk properties, foam films, and foams[END_REF]. Few studies describe the relationships between chemical structure and dynamic properties for conventional ethoxylates derivatives [START_REF] Hua | Dynamic surface tension of aqueous surfactant solutions: I. Basic paremeters[END_REF][START_REF] Hua | Dynamic surface tension of aqueous surfactant solutions: 3. Some effects of molecular structure and environment[END_REF][START_REF] Rosen | Dynamic Surface Tension of Aqueous Surfactant Solutions: IV Relationship to Foaming, in Surfactants in Solution[END_REF]. The results shown that the rate of surface tension reduction increases with an augmentation of the hydrophobic character of the surfactant. A predictive model for simulation of natural surfactants kinetic adsorption on solid surface was developed [START_REF] Faghihi | Modeling of kinetic adsorption of natural surfactants on sandstone minerals: Spotlight on accurate prediction and data evaluation[END_REF]. The results demonstrated that time parameter and surfactant concentration have the highest impact on the kinetic adsorption density. To our knowledge, there is currently no literature investigating the effect of chemical structure on dynamics of surface tension reduction for sugar-based surfactant.

The present study was conducted to analyse the dynamic adsorption properties of non-ionic glycolipids related to their applications. The effect of alkyl chain length, head group size, anomeric effect and concentration on the dynamic adsorption properties for a series of 15 nonionic sugar-derived surfactants was particularly examined. The adsorption kinetics at liquid/gas interface was studied. A comparison between experimental DST profiles and profiles calculated with empirical Rosen-model was performed. In addition, the numerical approach was employed to equilibrium surface tension data for calculating the limiting elasticity for different surfactants.

Materials and Methods

Materials

All commercial surfactants were used as received without further purification. Alkyl βglucosides as well as alkyl-α/β-maltosides (purity > 99%, HPLC) were purchased from Anatrace (Maumee, OH, USA). Octyl β-galactoside (purity > 99%, HPLC) was purchased from Carbosynth (Compton, Berkshire, UK). The synthesis of alkyl-uronates serie (purity > 99%, NMR spectroscopy) was described in previous study [START_REF] Lu | Catalytic Synthesis of a New Series of Alkyl Uronates and Evaluation of Their Physicochemical Properties[END_REF]. The same batch of synthetized surfactants was used in the present study.

Classic purification chain (Elga/Veolia, Wissous, France) was used to prepare aqueous solutions. Surfactant solution was prepared by dissolving a certain amount of each surfactant in water to obtain a desired concentration (between 0.001 and 1 C/CMC). All studied sugarbased surfactants were soluble in water at 25°C.

Equilibrium surface tension measurement

The measurement of surface tension at equilibrium (γeq) were obtained using K100 Krüss tensiometer (Hamburg, Germany) equipped with a Wilhelmy plate (length 10 mm, width 19.9 mm, thickness 0.2 mm) made of platinum. The tensiometer runs by holding a plate in a fixed vertical position attached to a microbalance. The microbalance measures the force acting on the plate, which is used for the calculation of surface tension. The sample solution was put in a glass vessel surrounded by thermostated system maintained at 25±1°C. Before each measurement, the plate was rinsed with ethanol and water, and burnt to red hot conditions in a blue flame to ensure perfect wetting (zero contact angle). The measurement of surface tension at the liquid/air interface was carried out by submerging a Wilhelmy plate in the solution during ten minutes, corresponding to the time required to reach an equilibrium surface tension (γeq). Each measurement was replicated three times. The Critical Micelle Concentration (CMC) of each surfactant was determined from the break point of concentration-surface tension curve.

Dynamic surface properties

In the present study, the maximal surfactant concentration for determination of all dynamic surface properties was fixed at the CMC. Below this value, surfactants are under a monomer form and higher adsorption at the air-water interface occurs at higher surfactant concentration [START_REF] Kovalchuk | The effect of adsorption kinetics on the rate of surfactant-enhanced spreading[END_REF]. Above CMC, surfactants aggregate as micelles, resulting in a different thermodynamic state that involves additional factors, such as the micelles stability. By limiting the study to concentrations below the CMC, all analyzed solutions will be considered at the same thermodynamic state. Solely the effect of surfactant concentration on dynamic surface properties will be investigated.

Dynamic surface tension measurement

The measurement of dynamic surface tension (DTS) of glycolipid solutions was realized using maximum bubble pressure method. This technique allows the measurement of surface tension at the newly formed surface of bubble in a surfactant solution. An inert gas (nitrogen) is bubbled continuously through a glass capillary. The maximum bubble pressure is directly related to the surface tension by the Laplace equation. Measurements of DST were performed using the BP2 Krüss tensiometer (KRUSS, Hamburg, Germany) at 25±1°C. Prior to each experiment, the capillary was rinsed with water and acetone, and oven dried. The time associated with the interface formation (surface age) was varied from 30 ms to 50 000 ms in every single experiment. Analyses were performed in triplicate.

Determination of limiting elasticity

The limiting elasticity or the high-frequency limit of the surface elastic modulus is defined by the expression of Equation 1 [START_REF] Lucassen | Dynamic measurements of dilational properties of a liquid interface[END_REF][START_REF] Lucassen-Reynders | Gibbs elasticity, surface dilational modulus and diffusional relaxation in nonionic surfactant monolayers[END_REF].

Eq. 1 E = -
With E0 the limiting elasticity (mN.m -1 ), γ the surface tension (mN.m -1 ) and Γ the surface concentration (mol.m -2 ).

From this equation, E0 can be determined using state equation of surfactants. For the present study, the value of limiting elasticity was calculated from experimental curve of surface tension versus concentration. First, the equation state based on Völmer isotherm (Eq. 2) was applied to calculate surface concentration, Γ [START_REF] Danov | Equilibrium and Dynamics of Surfactant Adsorption Monolayers and Thin Liquid Films[END_REF][START_REF] Kralchevsky | Chemical Physics of Colloid Systems and Interfaces[END_REF].

Eq. 2 γ = γ -RTΓ

where R is the universal gas constant (J.K -1 .mol -1 ), T is the temperature (K). Γ is the maximum (saturated) excess surface concentration (mol.m -2 ) obtained from Gibbs equation for concentrations close to CMC (Equation 3) [START_REF] Rosen | Surfactants and Interfacial Phenomena[END_REF][START_REF] Kralchevsky | Chemical Physics of Colloid Systems and Interfaces[END_REF][START_REF] Eastoe | Dynamic surface tension and adsorption mechanisms of surfactants at the air-water interface[END_REF][START_REF] Myers | Surfactant Science and Technology[END_REF]. Plots of surface tension versus concentration used for calculation of Γ are proposed in supplementary data (Figure SD1).

Eq. 3 Г = -

C is the concentration of surfactant (mol.m -3 ).

Then, the combination of equations 1 and 2 allowed to determine the final expression of E0 :

Eq. 4 E = RT ( )

Results and discussion

The CMC and the surface tension at CMC (γCMC) values for each series of surfactants with different alkyl chain length and different polar head structures were determined from the equilibrium surface tension isotherms. The maximum excess surface concentration Γ at the liquid/gas interface was calculated according to equation 3. The results obtained are presented in Table 1 and showed the same trends as already discussed in earlier studies from our group [START_REF] Gaudin | Investigating the impact of sugar-based surfactants structure on surface tension at critical micelle concentration with structureproperty relationships[END_REF][START_REF] Gaudin | Impact of the chemical structure on amphiphilic properties of sugar-based surfactants: A literature overview[END_REF].

Dynamic adsorption properties

Influence of surfactant structure on the kinetics of adsorption

The DST of surfactant solution depends on several factors: concentration of amphiphilic molecules, diffusion rate of surfactant monomer that can migrate and adsorb on the newly formed liquid/gas interface, stability of formed micelles, or phenomena that hinder adsorption (steric repulsions at interface or electrostatic interactions) [START_REF] Eastoe | Dynamic surface tension and adsorption mechanisms of surfactants at the air-water interface[END_REF]. The value of DST is also related to the surface age or rate of liquid/gas interface formation. The measured surface tension is lower at high surface age due to the time available for the surfactants to migrate to the newly created interface.

As a surface layer is directly connected with the bulk solution, the dynamic surface properties also strongly depend on molecular exchange processes. When the adsorption is driven by diffusion, the time to reach equilibrium strongly depends on the concentration of amphiphilic molecules. For the same amphiphilic molecule, the higher the surfactant concentration the faster the adsorption and desorption between bulk and surface, leading to lower DST.

For each series of glycolipids, DST was measured by maximum bubble pressure method. One example of comparison between alkyl-β-maltosides with different chain lengths is proposed in Figure 1. In this particular case, aqueous solutions were prepared at C = 0.2mM, corresponding to CMC of C12-βMalt. Thereby, no micelles were formed for none of the surfactant solutions. The DST of glycolipids decreased with the increase of surface age. This indicates that the amount of amphiphilic molecules onto the newly formed interface increases due to the lower rate of generation of a newly liquid/gas interface. Another observation made from these measurements is a remarkable decrease of the surface tension in the plateau region with the increase of the carbon number in hydrophobic chain.

The type of polar head showed slight effect on kinetics of surface tension reduction (Figure 2). For surfactants of alkyl chain with 10 carbons, surface tension reduction followed same mechanisms until of surface age around 1000 ms. For longer surface ages, surface tension of C10-βMalt approached its equilibrium value whereas surface tension of C10-βGlc kept decreasing. For shorter chain glycolipids, (C8-βGlc and C8-βGMalt), one could notice similar behaviour: at fixed concentration (C=0.2Mm), kinetics of adsorption are the same for the two surfactants. From Figure 2b, α/β anomer position has no significant influence on reduction of surface tension. More studies are needed with a greater number of glycolipid molecules to conclude on the effect of α/β position on DST reduction.

Dynamic surface tension curves for various concentrations of dodecyl-β-maltoside are plotted on Figure 3. Reduction in surface tension is faster when concentration increases. For example, considering 1000 ms of surface age, γ = 61 mN.m -1 for C = 0.2 mM while γ > 70 mN.m -1 for more diluted solutions.

Modeling of kinetic adsorption properties

The classical steps of surface tension reduction can be distinguished on Figure 1 and Figure 2 [27, [START_REF] Hua | Dynamic surface tension of aqueous surfactant solutions: I. Basic paremeters[END_REF][START_REF] Lin | Impact of surface dilation rate on dynamic surface tension[END_REF]. Firstly, an induction phase is observed, in which the surface tension remains elevated, close to that of pure water, as surfactants are diffusing from bulk to the interface.

This induction period is mainly related to the surfactant size and concentration. Once the adsorption has begun, surface tension rapidly decreases, followed by the meso-equilibrium that corresponds to a slower diminution. Finally, equilibrium is reached. For a same molar concentration, equilibrium surface tension reduces with an increase of hydrophobic chain length, due to a stronger adsorption [START_REF] Ruiz | Sugar-Based Surfactants[END_REF][START_REF] Rosen | Surfactants and Interfacial Phenomena[END_REF][START_REF] Lu | Catalytic Synthesis of a New Series of Alkyl Uronates and Evaluation of Their Physicochemical Properties[END_REF]. From Figure 1, induction phase is very similar for the three alkyl-β-maltosides. The next steps are more influenced by surfactant structure:

for C12-βMalt for example, surface tension is more reduced and on a longer time scale.

Meso-equilibrium and equilibrium are achieved faster for C8-βMalt. The same observations for the influence of hydrophobic chain length on DST are made for other series of glycolipids analyzed (see supplementary data, Figure SD2).

At long times, surface tension decreased towards its equilibrium value. To better describe kinetics of surface tension reduction, Rosen & al developed empirical model that showed consistent agreement with experimental data [START_REF] Hua | Dynamic surface tension of aqueous surfactant solutions: I. Basic paremeters[END_REF][START_REF] Hua | Dynamic surface tension of aqueous surfactant solutions: 3. Some effects of molecular structure and environment[END_REF][START_REF] Rosen | Dynamic Surface Tension of Aqueous Surfactant Solutions: 5. Mixtures of Different Charge Type Surfactants[END_REF]. This model (Equation 5) is generally employed to describe the first three stages of surfactant adsorption prior to equilibrium. Firstly, surface tension remained closed to that of pure water while surfactants are diffusing from the bulk (induction). Once they adsorbed at the air/water interface, surface tension goes with a fast decrease. When the surface tension varies more slowly, mesoequilibrium is reached.

Eq. 5 γ(t) = γ + ( * ) "

Where γ(t) is the dynamic surface tension at time t, γ0 surface tension of pure water (in the present study 72.8 mN.m -1 for air/water interface at 20°C), γm is the meso-equilibrium surface tension, often approximated to the equilibrium surface tension [START_REF] Kawale | The relation between the dynamic surface tension and the foaming behaviour in a sparger setup[END_REF], t* corresponds to the time needed to reduce by half the surface tension between γ0 and γm and n determines the rate of the surface tension reduction at t=t*. n and t* represent the constants that vary with surfactant concentration and structure. These parameters were determined from a fit of the measured data.

Comparison between the experimental data and the results of Rosen model is shown in Figure 3, for solutions of dodecyl-β-maltoside. These plots indicate that experimental and modelling results of kinetic adsorption exhibit good correlation. The same observations were made for other series of studied glycolipids (see supplementary data, Figure SD3).

Derivation of Eq. 5 gives the rate of surface tension reduction (Eq. 6).

Eq. 6

# $ # = n(γ -γ & ) ( * ) " $( ' * ( " )
Maximum value for rate of surface tension reduction (#

dγ dt # max
) is obtained at t=t*, corresponding to the inflection point of DST curve (Eq. 7) [START_REF] Tamura | Dynamic Surface Tension and Foaming Properties of Aqueous Polyoxyethylene n-Dodecyl Ether Solutions[END_REF][START_REF] Kanokkarn | Equilibrium and dynamic surface tension in relation to diffusivity and foaming properties: Effects of surfactant type and structure[END_REF].

Eq. 7

# $ # &-. = n / 0$ *
This property gives a precise information about surface tension reduction. In the literature, one can also find the calculation of the surface tension fall rate (R1/2) that is of similar interest [START_REF] Hua | Dynamic surface tension of aqueous surfactant solutions: I. Basic paremeters[END_REF][START_REF] Kawale | The relation between the dynamic surface tension and the foaming behaviour in a sparger setup[END_REF]. For a high value of # dγ dt # max , or R1/2, the surfactant adsorption at the interface is fast and surface tension rapidly reaches its equilibrium value. This parameter depends on the surfactant mobility. In their study, Hua & Rosen [START_REF] Hua | Dynamic surface tension of aqueous surfactant solutions: I. Basic paremeters[END_REF] showed that an elevation of temperature accelerated the process of diffusion and adsorption : surface tension fall rate increased with temperature. The maximum rate of surface tension reduction is a property of interest as it could play a significant role in liquid film formation, for example during the foaming process [START_REF] Kawale | The relation between the dynamic surface tension and the foaming behaviour in a sparger setup[END_REF][START_REF] Tamura | Dynamic Surface Tension and Foaming Properties of Aqueous Polyoxyethylene n-Dodecyl Ether Solutions[END_REF][START_REF] Kanokkarn | Equilibrium and dynamic surface tension in relation to diffusivity and foaming properties: Effects of surfactant type and structure[END_REF][START_REF] Loubière | Influence of liquid surface tension (surfactants) on bubble formation at rigid and flexible orifices[END_REF].

The variation of # dγ dt # max for alkyl-β-maltosides at different concentrations is presented in arises with a concentration increase for different surfactants. For the same C/CMC ratio, alkyl-β-maltosides with higher CMC are more effective in increasing the adsorption rate at air/water interface corresponding

to higher # $ # &-.
values. Higher amount of surfactant molecules in solution results in greater rate of surface tension decrease. Furthermore, high rate of surface tension decrease is associated with shorter time t*. From the results obtained, the values of t* decrease with the increase in concentration and carbon chain length of surfactant. This observation is in accordance with literature [START_REF] Tamura | Dynamic Surface Tension and Foaming Properties of Aqueous Polyoxyethylene n-Dodecyl Ether Solutions[END_REF]. For a single surfactant, experimental points for different concentrations are aligned on a straight line.

An interesting observation can be made from Figure 4a, as all the data concerning alkyl-βmaltosides seemed to align on a same line. Figure 4b presents the results for all the surfactant of this study, at various concentrations. Experimental points of 15 surfactants were gathered on a same straight line, with correlation coefficient R²=0.93. These findings suggest that, for glycolipids studied, the evolution of kinetic of adsorption with solution concentration is independent of surfactant structure. This particular result differs from literature. For example, Tamura & al [START_REF] Tamura | Dynamic Surface Tension and Foaming Properties of Aqueous Polyoxyethylene n-Dodecyl Ether Solutions[END_REF] studied the kinetics of adsorption for ethoxylate derivatives. The results obtained showed that the curves intersection with the y-axis depend on number of ethylene oxide units in the surfactant structure. Thus, glycolipids behave very differently than ethoxylate derivatives regarding kinetics of adsorption at the interface. This could be attributed to the little variation in the polar head size and molecular weight of studied glycolipids compared to ethoxylate surfactants for the similar concentration range (0.002-150 mM and 0.01-30 mM respectively). Notably, for ethoxylate derivatives the molecular weight varies from 406 to 1551 g.mol -1 for molecules with fixed hydrophobic chain length and size of polar head changing from 5 to 31 ethylene oxide units [START_REF] Tamura | Dynamic Surface Tension and Foaming Properties of Aqueous Polyoxyethylene n-Dodecyl Ether Solutions[END_REF]. Whereas the molecular weight for the glycolipids of the present study is ranging from 264 to 510 g/mol -1 .

Therefore, results from property could be anticipated directly from the molar concentration, regardless the surfactant structure. It would be interesting to extend this study to more structures of surfactants in a wider concentration range.

Interfacial elasticity of surfactants

The mechanisms of liquid film formation, stabilization using surfactant and breakup are strongly linked to the viscoelastic properties of the films [START_REF] Georgieva | Link between surface elasticity and foam stability[END_REF][START_REF] Fainerman | Dilational surface visco-elasticity of CnEOm solutions under dynamic conditions[END_REF][START_REF] Pugh | Bubble and Foam Chemistry[END_REF][START_REF] Reichert | The importance of experimental design on measurement of dynamic interfacial tension and interfacial rheology in diffusion-limited surfactant systems[END_REF]. The dynamic properties of surfactants and stability of interfacial film could be characterised by using their viscoelasticity. This property depends on the concentration and the frequency of the disturbance of interfacial film [START_REF] Lai | Interfacial dynamic properties and dilational rheology of mixed anionic and cationic Gemini surfactant systems at air-water interface[END_REF][START_REF] Lucassen-Reynders | Gibbs elasticity, surface dilational modulus and diffusional relaxation in nonionic surfactant monolayers[END_REF][START_REF] Fainerman | Dilational surface visco-elasticity of CnEOm solutions under dynamic conditions[END_REF]. The rupture of liquid films stabilised by surfactants generally occurs on very short timescale corresponding to the high frequency surface elasticity. The properties of the interfacial film in this case can be characterized by the limiting value of elasticity (E0) or the high-frequency limit of the surface dilational elastic modulus. E0 was calculated for all studied glycolipids as detailed in Section 2. Values of surface concentration Γ and limiting elasticity E0 are summarised in Table II for alkyl-βmaltosides at various concentrations.

For the concentration of different glycolipids varying between 0.001 C/CMC and 1 C/CMC corresponding to a molar concentration range from 0.002 mM to 226.7 mM, the limiting elasticity E0 was found to vary from 1.9 mN.m -1 to 263.4 mN.m -1 (see supplementary data, Table SD1). The results reveal that E0 increases with an increase in surfactant concentration.

The same dependence of concentration and E0 was also found in the literature for other surfactants [START_REF] Stubenrauch | Stability of Foam Films and Surface Rheology: An Oscillating Bubble Study at Low Frequencies[END_REF][START_REF] Grigoriev | Surface elasticities of aqueous β-dodecyl-d-maltoside solutions: A capillary wave study[END_REF][START_REF] Santini | A surface rheological study of non-ionic surfactants at the water-air interface and the stability of the corresponding thin foam films[END_REF][START_REF] Boos | Dilational surface rheology studies of n-dodecyl-β-dmaltoside, hexaoxyethylene dodecyl ether, and their 1:1 mixture[END_REF]. For example, for C12-βMalt E0 calculated from Gibbs adsorption isotherm increased from 35 mN.m -1 to 71.5 mN.m -1 for concentration change from 0.01 mM to 0.069 mM respectively [START_REF] Grigoriev | Surface elasticities of aqueous β-dodecyl-d-maltoside solutions: A capillary wave study[END_REF]. Physically, the limiting elasticity is reached for very high frequency oscillations. In these conditions, oscillation is too fast to enable surfactants exchange with the bulk solution and the surfactant film behaves as an insoluble monolayer [START_REF] Lucassen-Reynders | Interfacial Viscoelasticity in Emulsions and Foams[END_REF]: film viscoelasticity equals the limiting elasticity E0. In addition, E0 is related to the surfactant surface concentration (Γ) that gives cohesion and rigidity to the film. Equation 4relating limiting elasticity with surface concentration demonstrates that the higher the value of E0, the more likely the film is to resist rupturing. Thus, the increase in value of limiting elasticity eventually provides better interfacial film stability and prevent coalescence [START_REF] Stubenrauch | Aqueous foams stabilized by n-dodecyl-[small beta]-d-maltoside, hexaethyleneglycol monododecyl ether, and their 1 : 1 mixture[END_REF][START_REF] Georgieva | Link between surface elasticity and foam stability[END_REF].

Limiting elasticity was put in regards with relative surface concentration (Г Г ⁄ ) for alkyl-β- Nevertheless, basic measurements could eventually help to predict various properties related to the interfacial film stabilization and to the limiting elasticity of surfactants, particularly in foam and emulsion formation [START_REF] Kawale | The relation between the dynamic surface tension and the foaming behaviour in a sparger setup[END_REF][START_REF] Kanokkarn | Equilibrium and dynamic surface tension in relation to diffusivity and foaming properties: Effects of surfactant type and structure[END_REF][START_REF] Nikseresht | Prediction of oil/water interfacial tension containing ionic surfactants[END_REF]. Thereby, the systematic characterization of dynamic properties brought better understanding on behaviours of sugar-based surfactants in solution. It would be of interest to expand the study to more structures of glycolipids and potentially surfactant mixtures. Surely, more complex systems involving addition of salt or ionic surfactants are to be investigated, as adsorption mechanisms can dramatically be modified.

Conclusions

Figure 4 .

 4 b involved the existence of correlation between # dγ dt # max and molar concentration of sugar-based surfactants. For glycolipids studied, this particular

maltosides (Figure 5

 5 .a). As expected, the figure indicates similar behaviours for the different molecules as surfactants seem to gather on one unique curve. The adsorbed surfactant layer can be described by the state equation based on Völmer model (Eq. 2). Thus, due to relatively little variation of Г values for studied glycolipids, experimental data points follow the same curve. The same methodology was applied for the determination of E0 for the 15 studied glycolipids. The global evolution with relative surface concentration is plotted in Figure5.b. results showed strong correlation (R²=0.98). This finding highlights the common behaviour of sugar-based surfactants at the liquid/air interface independently of their chemical structure as they follow a similar trend. Therefore, for studied glycolipids, the limiting elasticity could be anticipated directly from knowing the relative surface concentration, obtained from classical surface tension measurements. It should be noted that prediction accuracy of E0 is reduced for high Г Г ⁄ values (Г Г ⁄ >0.75).

  Dynamic surface properties of surfactants have a significant role in various technological processes involving the non-equilibrium phenomena with continuous formation of new interfaces. Many previous studies have shown that the maximum rate of surface tension reduction, , 52-54] and the limiting elasticity, E0,[START_REF] Stubenrauch | Aqueous foams stabilized by n-dodecyl-[small beta]-d-maltoside, hexaethyleneglycol monododecyl ether, and their 1 : 1 mixture[END_REF][START_REF] Georgieva | Link between surface elasticity and foam stability[END_REF][START_REF] Kawale | The relation between the dynamic surface tension and the foaming behaviour in a sparger setup[END_REF][START_REF] Pugh | Bubble and Foam Chemistry[END_REF] represent relevant dynamic properties, closely correlated to different applications of surfactant systems.In the present study, dynamic surface properties of 15 nonionic sugar-based surfactants with gradual structural variation were determined experimentally. In a first step, kinetics of surfactant adsorption were studied by maximal bubble pressure method. The dynamic surface tension was only marginally affected by the structure and anomery of sugar-derived polar head; however, results showed the significant increase in adsorption rate with the growth of carbon number in hydrophobic chain and concentration of surfactant. Fitting trials with Rosen empirical model allowed to calculate # dγ dt # max . In a second step, the limiting elasticity E0 was calculated for each glycolipid, from curve of surface tension versus concentration and use of Völmer isotherm. Experiments showed astonishing results for both dynamic properties. The maximum rate of surface tension reduction as found to be strongly correlated with the molar concentration of surfactant within the solution. More importantly, for studied glycolipids # dγ dt # max can be directly determined from knowing the solution system, independently on surfactant structure and without needing to perform characterization of dynamic surface tension. This result highlights that glycolipids behave differently than ethoxylate derivative surfactants regarding kinetics of adsorption at the interface[START_REF] Tamura | Dynamic Surface Tension and Foaming Properties of Aqueous Polyoxyethylene n-Dodecyl Ether Solutions[END_REF]. Furthermore, the limiting elasticity can be determined directly from the classical curve of surface tension versus concentration in two steps. The Gibbs equation allows the calculation of maximum excess surface concentration at CMC, Γ , whereas application of Völmer isotherm state equation enables to determine the relative surface concentration, Г Г ⁄ , for each concentration. Then, this two-step procedure is sufficient to estimate the limiting elasticity of surfactant. This workproposes a new way for the prediction of several properties of surfactants related to the dynamic of the interfacial film stabilization.

Table II and

 II Fig. 4a. The obtained results show that # $ # &-.

Acknowledgements

This work was performed, in partnership with the SAS PIVERT, within the frame of the French Institute for the Energy Transition (Institut pour la Transition Energétique (ITE) P.I.V.E.R.T. (www.institut-pivert.com) selected as an Investment for the Future ("Investissements d'Avenir"). This work was supported, as part of the Investments for the Future, by the French Government under the reference ANR-001-01.


Rémi Beucher

Claudia Cammarano

Enrique Rodríguez-Castellón

Vasile Hulea
email: vasile.hulea@enscm.fr

Direct conversion of ethylene to propylene over Ni-and W-based catalysts: An unprecedented behaviour

Keywords: Tandem catalysis, Heterogeneous catalysis, Metathesis, Ethylene, Propylene, KIT-6

A new ethylene to propylene catalytic process based on cascade reactions, with two catalysts and two reactors, has been explored in this study. In the first reactor loaded with Ni-AlKIT-6 catalyst, at 60-120 °C and 3 MPa, part of ethylene has been selectively transformed into 2butene. In the second reactor, loaded with WOx/KIT-6 catalyst, 2-butene reacted with the unconverted ethylene at 450 °C and 0.1 MPa. Unprecedented results in terms of catalytic activity, selectivity towards the formation of propylene and stability against deactivation were achieved under these conditions. More precisely, an ethylene conversion of ~85% and a selectivity to propylene of 55% and butenes of 30% remained unchanged during 24 h on reaction stream.

Introduction

Propylene, a major chemical intermediate, is usually produced from fossil-based feedstock, using highly efficient processes, such as fluidized catalytic cracking and steam cracking of saturated hydrocarbons. Owing to the strong demand for polypropylene during the last years (average annual demand growth of 4.5%), the supply of propylene is of great concern because the traditional sources will not be sufficient to cover the demand. Research efforts have been made to develop alternative routes to propylene production based on accessible raw materials, such as propane, ca. propane dehydrogenation [START_REF] Lavrenov | Propylene production technology: Today and tomorrow[END_REF], methanol, ca. methanol to olefins process [START_REF] Tian | Methanol to olefins (MTO): From fundamentals to commercialization[END_REF], and ethylene.

One of the most exciting methods is the conversion of ethylene to propylene (ETP) without the addition of other hydrocarbons [START_REF] Hulea | Toward platform chemicals from bio-based ethylene: Heterogeneous catalysts and processes[END_REF][START_REF] Ghashghaee | Heterogeneous catalysts for gas-phase conversion of ethylene to higher olefins[END_REF][START_REF] Blay | Converting olefins to propene: Ethene to propene and olefin cracking[END_REF][START_REF] Hulea | Direct Transformation of butenes or ethylene into propylene by cascade catalytic reactions[END_REF]. The sustainability of this technology is guaranteed by the fact that the ethylene production by dehydration of bioethanol has become economically feasible [START_REF] Sun | ACS Catal. Recent advances in catalytic conversion of ethanol to chemicals[END_REF][START_REF] Zhang | Dehydration of ethanol to ethylene, bioethylene production from ethanol: A review and techno-economical evaluation[END_REF][START_REF] Mohsenzadeh | Bioethylene production from 1 st and 2 nd generation ethanol: A mini review and techno-economical evaluation[END_REF]. The ETP process consists of catalytic cascade reactions, including either (a) oligomerization/cracking or (b) dimerization/isomerization/metathesis chemical steps. Typically, oligomerization/cracking is catalyzed by acidic microporous materials like zeolites and SAPOs [START_REF] Oikawa | Highly selective conversion of ethene to propene over SAPO-34 as a solid acid catalyst[END_REF][START_REF] Dai | Verifying the mechanism of the ethene-to-propene conversion on zeolite H-SSZ-13[END_REF][START_REF] Jun | Conversion of Y into SSZ-13 zeolites and ethylene-to-propylene reactions over the obtained SSZ-13 zeolites[END_REF] or by multifunctional Ni-mesoporous materials [START_REF] Iwamoto | Selective conversion of ethylene to propene and butenes on nickel ion-loaded mesoporous silica catalysts[END_REF][START_REF] Frey | Comparison of differently synthesis Ni(Al)MCM-48 catalysts in the ethene to propene reaction[END_REF][START_REF] Perea | Alumino-mesostructured Ni catalyst for the direct conversion of ethene to propene[END_REF][START_REF] Stoyanova | The role of speciation of Ni 2+ and its interaction with the support for selectivity and stability in the conversion of ethylene to propene[END_REF], at temperatures higher than 350 °C. Generally, mixtures of saturated and unsaturated hydrocarbons of low selectivity to propylene, were produced in such ETP processes.

The processes based on the dimerization/isomerization/metathesis chemical steps are operated at lower temperature (50-150 °C) in the presence of transition metal-based catalysts [START_REF] Taoufik | Direct transformation of ethylene into propylene catalyzed by a tungsten hydride supported on alumina: Trifunctional single-site catalysis[END_REF][START_REF] Li | Conversion of ethene to propene by a dual function NiSO4/Re2O7/γ-Al2O3 catalyst[END_REF][START_REF] Buluchevskii | One-stage synthesis of propylene from ehylene using Pd-Re2O7/B2O3-Al2O3 catalyst[END_REF][START_REF] Ghashghaee | Nanostructured hydrotalcite-supported RuBaK catalyst for direct conversion of ethylene to propylene[END_REF][START_REF] Andrei | Ethylene to propylene by one-pot catalytic cascade reactions[END_REF][START_REF] Andrei | Nickel and molybdenum containing mesoporous catalysts for ehylene oligomerization and metathesis[END_REF][START_REF] Beucher | Selective production of propylene and 1-butene from ethylene by catalytic cascade reactions[END_REF]. Three consecutive reactions and three catalytic sites are involved in these processes:

(i) dimerization of ethylene to 1-butene, (ii) isomerization of 1-butene to 2-butene, and (iii) metathesis reaction of 2-butene with unreacted ethylene to propylene, as described below.

(i) Ethylene dimerization As shown in several studies [START_REF] Taoufik | Direct transformation of ethylene into propylene catalyzed by a tungsten hydride supported on alumina: Trifunctional single-site catalysis[END_REF][START_REF] Li | Conversion of ethene to propene by a dual function NiSO4/Re2O7/γ-Al2O3 catalyst[END_REF][START_REF] Buluchevskii | One-stage synthesis of propylene from ehylene using Pd-Re2O7/B2O3-Al2O3 catalyst[END_REF][START_REF] Ghashghaee | Nanostructured hydrotalcite-supported RuBaK catalyst for direct conversion of ethylene to propylene[END_REF], the catalytic sites involved in these reactions could coexist on a single support. Basset and co-workers [START_REF] Taoufik | Direct transformation of ethylene into propylene catalyzed by a tungsten hydride supported on alumina: Trifunctional single-site catalysis[END_REF] used a trifunctional WH3/Al2O3 catalyst at 150 °C and 0.1 MPa for the above processes. Li et al. [START_REF] Li | Conversion of ethene to propene by a dual function NiSO4/Re2O7/γ-Al2O3 catalyst[END_REF] used a single bimetallic supported catalyst, NiSO4/Re2O7/γ-Al2O3 in an ETP process operated at 50 °C and 0.1 MPa.

Catalysts like MeO/Re2O7/B2O3-Al2O3 (Me = Pd or Ni) have been also designated by Buluchevskii et al. [19] for the one-stage ETP process performed at 80 °C and 0.1-1 MPa.

More recently, Ghashghaee and Farzaneh [START_REF] Ghashghaee | Nanostructured hydrotalcite-supported RuBaK catalyst for direct conversion of ethylene to propylene[END_REF] developed a nanostructured Ru-Ba-K-MgO-Al2O3 catalyst able to convert ethylene into propylene and butenes at 70 °C and 0.1 MPa.

These studies showed that using a single catalyst, which provides different active sites, is a challenging concept. In practice, it is very difficult to balance the catalytic functions involved in the ETP process. Consequently, over these catalysts undesired reactions could occur, causing a decrease in propylene selectivity. Additionally, the catalysts rapidly deactivated.

These weaknesses could be circumvented by distributing the different catalytic sites on two catalysts. Our group developed an original ETP process based on two robust and highly active solid catalysts [START_REF] Andrei | Ethylene to propylene by one-pot catalytic cascade reactions[END_REF][START_REF] Andrei | Nickel and molybdenum containing mesoporous catalysts for ehylene oligomerization and metathesis[END_REF]. In a single reactor operated at 80 °C and 3 MPa, ethylene was first converted over a Ni-AlSBA-15 catalyst into 2-butenes, which then reacted with the unconverted ethylene over a MoO3-SiO2-Al2O3 catalyst to produce propylene. More recently, we proposed a new efficient heterogeneous catalytic system associating Ni-AlKIT-6 and ReOx/γ-Al2O3 [START_REF] Beucher | Selective production of propylene and 1-butene from ethylene by catalytic cascade reactions[END_REF][START_REF] Beucher | Direct transformation of ethylene to propylene by cascade catalytic reactions under very mild conditions[END_REF]. Under identical mild conditions (60 °C, 3 MPa), ethylene was very selectively converted into high added value molecules, i.e. propylene and 1-butene. Despite their remarkable initial performance (the initial ethylene conversion was higher than 70%), the supported MoOx and ReOx catalysts suffered from significant deactivation after 5 h on reaction stream. Working at low temperature, the loss of catalytic activity was most probably due to the poisoning of active centers by strongly adsorbed products.

Beside the Re-and Mo-based catalysts, W-supported oxides are also well-known metathesis catalysts [START_REF] Lwin | Olefin metathesis by supported metal oxide catalysts[END_REF]. It should be noted that a WOx/SiO2 catalyst is used in industrial metathesis processes for converting ethylene and 2-butene to propylene [START_REF] Mol | Industrial applications of olefin metathesis[END_REF]. While ReOx and

MoOx catalysts operate at low temperatures, i.e. 20-80 °C or 80-250 °C, WOx catalyst is active only at temperatures higher than 400 °C. The long catalyst lifetime compared to MoOx or ReOx, the easy and efficient regeneration and the resiliency to oxygenate molecules in the feed are the major advantages of supported WOx catalysts [START_REF] Lwin | Nature of WOx sites on SiO2 and their molecular structure-reactivity/selectivity relationships for propylene metathesis[END_REF].

In the present study, we prepared and characterized two mesoporous functionalized materials, i.e. Ni-AlKIT-6 and WOx/KIT-6. They were evaluated as catalysts in the ETP process based on cascade reactions: dimerization/isomerization over Ni-AlKIT-6 and metathesis over WOx/KIT-6. The catalytic sites have been probed by ammonia temperatureprogrammed desorption (NH3-TPD), hydrogen temperature-programmed reduction (H2-TPR), X-photoelectron spectroscopy (XPS) and 27 Al MAS NMR.

KIT-6 is a mesoporous material, possessing a bicontinuous cubic structure with Ia3d symmetry and an interpenetrating cylindrical pore system [START_REF] Kleitz | Cubic Ia3d large mesoporous silica: synthesis and replication to platinum nanowires, carbon nanorods and carbon nanotubes[END_REF]. It is a suitable support for the present catalysts, thanks to its high surface area and large interconnected mesopores, which are key factors for high mass transport properties. As known, these properties are crucial for processes that involve reactive olefins [START_REF] Hulea | Toward platform chemicals from bio-based ethylene: Heterogeneous catalysts and processes[END_REF][START_REF] Hulea | Direct Transformation of butenes or ethylene into propylene by cascade catalytic reactions[END_REF].

Experimental

Catalysts preparation

The dimerization/isomerization Ni-AlKIT-6 catalyst has been prepared in three successive steps, as shown in Fig. S1 Al-containing material (sample AlKIT-6) was obtained from KIT-6 and sodium aluminate (99%, Carlo Erba) according to the procedure developed by our group [START_REF] Andrei | Heterogeneous oligomerization of ethylene over highly active and stable Ni-AlSBA-15 mesoporous catalysts[END_REF]. The solid (2 g of Na-AlKIT-6) was then converted into NH4-AlKIT-6 by ionic exchange (2 h, 30 °C, and 100 mL of 0.5 M NH4NO3 aqueous solution). The sample was subjected to nickel-ion exchange with a 0.5 M aqueous solution of Ni(NO3)2 obtained from hexahydrate nickel(II) nitrate (98%, Alfa Aesar), following the same procedure as described above. The exchanged sample was dried and then calcined for 5 h in air-flow at 550 °C to achieve the catalyst denoted as Ni-AlKIT-6. A portion of NH4-AlKIT-6 was calcined for 5 h in airflow at 550 °C to obtain the H-AlKIT-6 sample.

WOx-based metathesis catalysts, containing 4 and 8 wt% W were prepared by the incipient wetness impregnation method using an aqueous solution of ammonium metatungstate (99%, Honeywell) and KIT-6, Na-AlKIT-6 or H-AlKIT-6 as supports. Before impregnation, the exact amount of water required to fill the support pores was determined.

The proper amount of ammonium metatungstate for achieving the requested tungsten loading was dissolved in an appropriate amount of distilled water. This solution was added to the support dropwise. The wet material was dried at 80 °C for at least 6 h and calcined in static air at 550 °C for 8 h. These materials will be denoted as X-W-KIT-6, X-W-Na-AlKIT-6 and X-W-H-AlKIT-6 (where X = 4 or 8 represents the W loading, wt%).

Catalysts characterization

The powder XRD measurements were performed on a Bruker AXS D8 diffractometer.

The solid textures were evaluated by nitrogen adsorption/desorption at -196 °C, using a

Micrometrics ASAP 2020 analyzer. 27 Al MAS NMR spectra of the calcinated samples were obtained as previously reported [START_REF] Andrei | Heterogeneous oligomerization of ethylene over highly active and stable Ni-AlSBA-15 mesoporous catalysts[END_REF] Kα radiation (100 µm, 100 W, 20 kV, 1486.6 eV) and a dual-beam charge neutralizer. The procedure has been previously described [START_REF] Beucher | Direct transformation of ethylene to propylene by cascade catalytic reactions under very mild conditions[END_REF].

The acidity of Ni-AlKIT-6 was explored by temperature-programmed desorption (TPD) using ammonia as probe molecule (Micromeritics AUTOCHEM 2910). H2-TPR measurements were performed using the same apparatus. The sample (~40 mg) was pretreated for 6 h in air-flow at 550 °C, and then cooled down to room temperature in Ar gas flow. The reduction of the sample was carried out while heating from room temperature to 1100 °C with a ramp of 10 °C min -1 using a certified gas mixture of 2 vol% H2 in Ar (Air Liquide) with a flow rate of 20 mL min -1 . Hydrogen concentration at the reactor outlet was measured by thermal conductivity detector (TCD) after removing water by a cooling trap.

Nickel content in the catalyst was measured by atomic absorption spectrometry using a

Varian Spectra 220 apparatus and a source emitting monochromatic radiation with a wavelength of 232 nm. The sample (~40 mg) is dissolved in 100 mL of 2 mol L -1 sodium hydroxide solution. Tungsten content measurements were performed on a PANanalytical Axios max device with an X-ray source (4 kW rhodium tube). A 100 mg sample was used for analysis.

Catalytic tests

The performances of the catalysts were evaluated in a laboratory-scale unit (Fig. S2

Results and discussion

Characterisation of catalysts and supports

The powder XRD results showed that all samples prepared in this study were wellorganized mesoporous materials. Thus, the small-angle XRD patterns (Fig. S3) showed a diffraction peak d211 (2θ = 0.97°) and a peak d220 (2θ = 1.12°) characteristic of the cubic Ia3d symmetry of KIT-6 materials [START_REF] Kleitz | Cubic Ia3d large mesoporous silica: synthesis and replication to platinum nanowires, carbon nanorods and carbon nanotubes[END_REF]. No signal was observed in the powder XRD patterns recorded at 2θ > 5°, confirming the absence of crystalline NiO or WOx species (Fig. S4).

Additionally, the nitrogen adsorption-desorption isotherms were of type IV, with a sharp capillary condensation step, characteristic of high-quality materials with homogeneous mesopores (Fig. S5,ESI). The main textural properties, calculated from sorption data, as well as the composition and acidity of different samples are summarized in Table 1.

Table 1.

The 27 Al MAS NMR spectrum of Ni-AlKIT-6 (Fig. S6, ESI) shows a major signal at about 55 ppm, corresponding to the tetrahedrally-coordinated aluminum species. Such a result confirms that the post-synthesis alumination with sodium aluminate at room temperature is an efficient method to incorporate aluminum into the silica matrix.

Ni-AlKIT-6 had a Si/Al ratio of 11.0 and a Ni content of 2±0.2 wt% (Table 1). The corresponding Ni/Al ratio is 0.25 (mol/mol), indicating an exchange level of NH4 + ions with

Ni 2+ of about 50%. During the calcination at 550 °C (see the experimental section), NH4 + ions are decomposed into ammonia and H + , generating the Brönsted acidic sites associated to aluminum atoms. Note that the acid sites are useful for the 1-butene isomerization in the ETP process [START_REF] Andrei | Ethylene to propylene by one-pot catalytic cascade reactions[END_REF][START_REF] Beucher | Selective production of propylene and 1-butene from ethylene by catalytic cascade reactions[END_REF].

The oxidation state of Ni and Re sites in the catalysts was examined by XPS. The deconvoluted spectrum of the Ni-AlKIT-6 catalyst in the Ni 2p region is shown in Fig. 1. The main signal with a binding energy of 857.7eV is attributed to isolated Ni(II) species [START_REF] Moussa | Nature of active nickel sites and initiation mechanism for ethylene oligomerization on heterogeneous Ni-beta catalysts[END_REF], and more precisely to tetrahedrally coordinated Ni(II). This result is confirmed by the presence of its primary satellite peak at 863 eV. The weaker signal at 854.2 eV reveals the presence of NiO, which was not detected by XRD because of its small amount. It is commonly accepted that only the isolated Ni species are precursors of the catalytic dimerization/oligomerization sites [START_REF] Andrei | Heterogeneous oligomerization of ethylene over highly active and stable Ni-AlSBA-15 mesoporous catalysts[END_REF][START_REF] Moussa | Nature of active nickel sites and initiation mechanism for ethylene oligomerization on heterogeneous Ni-beta catalysts[END_REF].

Figure 1.

Fig. 2 shows the deconvoluted XP spectra of the fresh 4-W-KIT-6 and after reaction (24 h) catalyst samples in the W 4f region. Four contributions at 35.0, 36.5, 37.2 and 38.6 eV can be distinguished in the spectra. According to the literature, the doublet W 4f7/2-W 4f5/2 recorded at 35.0 and 37.2 eV can be assigned to W 5+ oxidation state, while the second and more intense doublet at 36.5 and 38.6 eV corresponds to W 6+ [START_REF] Lallemand | Continuous stirred tank reactor for ethylene oligomerization catalyzed by NiMCM-41[END_REF][START_REF] Bazarjani | Visible light photocatalysis with c-WO3-x/WO3×H2O nanoheterostructures in situ formed in mesoporous polycarbosilane-siloxane polymer[END_REF]. The XPS W 4f core level spectrum of the spent catalyst also shows two doublets, but the relative intensity of the doublet at high binding energy assigned to W 6+ is much higher than in the case of the fresh catalyst sample.

Figure 2.

The total acidity of W-based catalysts was evaluated by ammonia TPD. As expected, the TPD profiles shown in Fig. 3 and the amount of adsorbed/desorbed ammonia (Table 1) strongly depends on the composition of catalytic materials. Both Al and W generated acid sites when added to the parent KIT-6 silica (4-W-KIT-6, Na-AlKIT-6 and 4-W-Na-AlKIT-6, Fig. 3). For these materials, ammonia desorbed at T < 300 °C, which is typical for the weak acid sites. The number and strength of acid sites increased when the sodium ions are replaced by protons (H-AlKIT-6 and 4-W-H-AlKIT-6 samples). The large desorption trace up to 450 °C indicates the presence of medium strength acid sites.

Figure 3.

The reducibility of W species has been examined by temperature-programmed reduction with hydrogen (H2-TPR). The TPR profiles of 4-W-KIT-6, 4-W-Na-AlKIT-6 and 4-W-H-AlKIT-6 revealed a first H2 consumption signal at ∼825 °C and a second one at 1000, 975 and 1025 °C, respectively (Fig. S7, ESI). The two reduction bands can be assigned to the reduction of W 6+ and W 5+ isolated species into metallic W in a two-steps process: W 6+ /W 5+ → W 4+ → W 0 [START_REF] Vermaire | The preparation of WO3TiO2 and WO3Al2O3 and characterization by temperature-programmed reduction[END_REF][START_REF] Kourieh | Investigation of the WO3/ZrO2 surface acidic properties for the aqueous hydrolysis of cellobiose[END_REF]. The differences in high-temperature reduction domains could be attributed to the different interactions between W species and the supports.

The absence of bulky WO3 was demonstrated by X-ray diffraction and H2-TPR analyses.

The latter analysis showed an interaction between the support and tungsten. W 6+ and W 5+ are thus most probably found as isolated WOx species on the surface of silica. According to the literature [START_REF] Lwin | Olefin metathesis by supported metal oxide catalysts[END_REF], two isolated W 6+ species have been identified. The W 5+ reflects probably the same species but bearing a hydroxyl (see Scheme 1).

Scheme 1.

To summarize, all synthesized catalysts are well organized mesoporous materials with high surface area, pore volume and pore diameter of 7.4-8 nm. Ni-AlKIT-6 contains Ni 2+ and H + sites, while metathesis catalysts contain W 6+ and W 5+ -species.

ETP on Ni-W catalysts

In order to produce propylene from ethylene, two catalytic beds consisting of Ni-AlKIT-6

and W-based materials were placed in two consecutive reactors. The dimerization/isomerization reactions occurred in the first reactor in the presence of 0.2 g of Ni-AlKIT-6 operated at 60 °C and 3 MPa. The feed consisted of 2 L h -1 of ethylene-nitrogen mixture (1/1, v/v). The choice of these parameters was based on our previous studies [START_REF] Andrei | Ethylene to propylene by one-pot catalytic cascade reactions[END_REF][START_REF] Andrei | Heterogeneous oligomerization of ethylene over highly active and stable Ni-AlSBA-15 mesoporous catalysts[END_REF][START_REF] Lallemand | Continuous stirred tank reactor for ethylene oligomerization catalyzed by NiMCM-41[END_REF] and dimerization experiments performed over Ni-AlKIT-6 (results are shown in ESI).

The complete effluent gas stream from the first reactor, containing the unreacted ethylene and the oligomers (mainly butenes), was directed to the second reactor, where the metathesis step occurs. The second reactor contained 0.5 g of W-based catalyst and was operated at 450 °C and 0.1 MPa. In the first reactor, over Ni-AlKIT-6, ethylene was mainly converted to butenes. Coupling the two reactors, the main product was propylene, but some amounts of pentenes and heptenes were formed. These results indicate that the W-based catalyst also is able to catalyze metathesis reactions involving olefins higher than C4. Typical chromatograms obtained in the ethylene dimerization over Ni-AlKIT-6, and dimerization-metathesis over Ni-AlKIT-6 + 4-W-KIT-6 are given in Fig. S8 (ESI).

Effect of support and W loading

4-W-KIT-6, 4-W-Na-AlKIT-6 and 4-W-H-AlKIT-6 metathesis catalysts with 4 wt % W have been coupled with Ni-AlKIT-6 to perform the ETP reactions. Table 2 summarizes the most relevant results in terms of product distribution obtained at a similar overall ethylene conversion of ∼50%. For these tests, ethylene conversion in the first reactor was about 35%.

The results obtained on a catalytic system containing 8 wt % W (8-W-KIT-6) are also included in Table 2.

Table 2.

The effect of support on the amount of each ETP product is noticeable. First, the amount of propylene (which is the main product for all catalytic systems) decreased from 59.4% over the 4-W-KIT-6 catalyst with an Al-free support to 44.0 and 36.1% over the 4-W-Na-AlKIT-6 and 4-W-H-AlKIT-6 catalysts, respectively. On the other hand, the concentration of the C4+ hydrocarbons increased in the opposite way for the three catalysts. The selectivity in (C3 + C4) hydrocarbons considered as useful products in the ETP process, was very high for all catalysts, but some differences are apparent. For example, 85, 79.8 and 66.7% selectivity was obtained over 4-W-KIT-6, 4-W-Na-AlKIT-6 and 4-W-H-AlKIT-6, respectively. Additionally, the 1-C4/2-C4 ratio in butenes significantly decreased (Table 2). In our opinion, the acidity of the catalyst supports can be considered as the main parameter responsible for these differences. First, the WOx species catalyse the metathesis reactions between butenes and ethylene (Scheme 2). However, at 450 °C, the acid sites of the aluminated metathesis catalysts (i.e. 4-W-Na-AlKIT-6 and 4-W-H-AlKIT-6) can activate a series of undesirable reactions, e.g. oligomerization, isomerization, and cracking, which involve the primary products (propylene, 1-butene).

Scheme 2.

To conclude, in the ETP process carried out under the present conditions and with metathesis catalysts based on KIT-6 materials, a non-acid pure silica is more efficient as support than the silica-alumina supports. According to Le Roux et al. [START_REF] Le Roux | Silica-alumina-supported, tungsten-based heterogeneous alkane metathesis catalyst: Is it closer to a silica-or an alumina-supported system?[END_REF], the acidity of the support improved the self-metathesis of propylene with a tungsten catalyst. In our study, this effect is manifested by an over-activity of the most acidic catalyst leading to a decrease of propylene selectivity.

To establish the role of W loading, the ETP process has been carried out in the presence of Ni-AlKIT-6 and 8-W-KIT-6 catalysts. By comparing the catalysts with 4 and 8% W (Table 2), it can be seen that the product distribution depends on the W amount in the catalyst. Thus, the amount of propylene and useful molecules (C3 + C4) is decreased when W loading increased from 4 to 8%, and that in favour of the heavier molecules. These results suggest that at a higher concentration of W sites, the catalyst exhibits an over activity in metathesis, and thus the C3 and 1-C4 primary products are consumed in subsequent reactions with other olefins. This means that a perfect balance between the amount of Ni and W sites in the ETP process is required to efficiently convert ethylene to propylene.

Evaluation of catalyst deactivation

The stability against deactivation of the 4-W-KIT-6 metathesis catalyst was examined in a long-term (24 h on reaction stream) catalytic test. To increase the total ethylene conversion, the first reactor containing the Ni-Al-KIT-6 catalyst was operated at 120 °C and 3

MPa. To ensure a quantity of ethylene sufficient for the metathesis reaction in the second reactor, the conversion of ethylene in the first reactor was kept ∼50%. The ethylene conversion, as well as the amount of C3 and C4 among the ETP products as a function of time on stream are given in Fig. 4.

The initial conversion of ethylene was 72%, but it increased during the first 4 h to reach a plateau at ∼85%. The molar selectivity to propylene decreased progressively. A 65% initial selectivity is noticed which drops to 51% after 5 h on reaction stream, and then remains stable. The selectivity to butenes remains constant at ∼27% during 24 h on reaction stream.

The average concentration in C5, C6, C7 and C8 was 9, 4, 3 and 4 vol%, respectively. The yield in propylene (ethylene conversion x propylene selectivity) corresponding to the plateau was ∼45%, while the productivity in propylene was 39 mmol g -1 h -1 .

Figure 4.

To check whether the catalysts suffered from any modification after 24 h on reaction stream, these were analysed by powder XRD, TGA and XPS. The analysis of the catalysts diffractograms before and after reaction (Fig. S9) indicates no major structural deterioration of the KIT-6 support after deposition of nickel and tungsten metals. The TGA profiles of the spent nickel-based catalyst showed a weight loss of 55% (Fig. S10, ESI). The signal derivative shows three distinctive mass-loss peaks centred at ∼275, 330 and 500°C. The relatively large mass loss on this catalyst is related to its dimerization role. Heavier products formed by oligomerization can be trapped in the pores and this confirms the need of using a support with an adequate pore size and pore volume. The TGA profile of the spent tungsten catalyst showed a weight loss of about 2.5% between 450 and 500 °C, proving that under the present reaction conditions, only a small amount of heavy carbonaceous species were adsorbed on the metathesis catalyst. The XP spectra of the fresh and used Ni-AlKIT-6 and 4-W-KIT-6 catalysts are given in Fig. 1 and Fig. 2, respectively. The XP spectrum of the nickel catalyst after reaction shows little change in the surface composition of nickel species (Fig. 1).

The tetrahedrally coordinated Ni(II) species are still the majority species. However, the 854.2

eV signal (highlighting the presence of NiO species) is higher on the spent than the fresh catalyst. Thus, there is degradation of a small part of nickel sites.

As for the fresh sample, W 6+ and W 5+ species are still present on the spent catalyst (Fig.

2

), but their ratio (W 6+ /W 5+ ) appears increased compared to that before the reaction, ca. 61-39 (at.%) before the reaction to ca. 82-18 (at%) after the reaction. We have shown that W 6+ can represent isolated WOx sites on the surface of the solid and W 5+ might represent the same species but with hydroxyl attached (Scheme 1). This decrease in the amount of W 5+ can thus reflect a decrease in the hydroxyl concentration on the surface of the tungsten-based catalyst.

It is speculated that the proportion of hydroxyl might be reduced during activation under air prior to the reaction.

Comparison with the literature

As stated in the Introduction section, various catalytic systems and procedures were used for converting ethylene into propylene without adding other hydrocarbons in the process.

Inhomogeneous results were obtained, depending on the catalyst (see Table S1, ESI). Over

Ni-MCM-41 and Ni-MCM-48 catalysts, the specific activity in propylene was 0.8-3.1 mmol gcatal -1 h -1 at 350-400 °C [START_REF] Iwamoto | Selective conversion of ethylene to propene and butenes on nickel ion-loaded mesoporous silica catalysts[END_REF][START_REF] Frey | Comparison of differently synthesis Ni(Al)MCM-48 catalysts in the ethene to propene reaction[END_REF][START_REF] Perea | Alumino-mesostructured Ni catalyst for the direct conversion of ethene to propene[END_REF]. Using W-H3/γ-Al2O3, Taoufik et al. [START_REF] Taoufik | Direct transformation of ethylene into propylene catalyzed by a tungsten hydride supported on alumina: Trifunctional single-site catalysis[END_REF] obtained 9.6 mmol gcatal -1 h -1 at 150 °C. Over polymetallic NiSO4/Re2O7/γ-Al2O3 [START_REF] Li | Conversion of ethene to propene by a dual function NiSO4/Re2O7/γ-Al2O3 catalyst[END_REF] and MeO/Re2O7/B2O3-Al2O3 (Me = Pd or Ni) [START_REF] Buluchevskii | One-stage synthesis of propylene from ehylene using Pd-Re2O7/B2O3-Al2O3 catalyst[END_REF] catalysts, the specific activity of propylene was 12.6 and 2.8 mmol gcatal -1 h -1 , respectively. The best results were obtained by combining two distinct dimerization/metathesis catalysts in a single reactor: 48 mmol gcatal -1 h -1 over Ni-AlSBA-15 + MoO3-SiO2-Al2O3 [START_REF] Andrei | Ethylene to propylene by one-pot catalytic cascade reactions[END_REF], 28 mmol gcatal -1 h -1 over Ni-AlSiO2 + MoOx/(Al)SiO2 [START_REF] Andrei | Nickel and molybdenum containing mesoporous catalysts for ehylene oligomerization and metathesis[END_REF], and 26 mmol gcatal -1 h -1 over Ni-AlKIT-6 + ReOx/γ-Al2O3 [START_REF] Beucher | Selective production of propylene and 1-butene from ethylene by catalytic cascade reactions[END_REF]. In this study, using two catalysts (Ni-AlKIT-6 + WOx/KIT-6) and two reactors, we were also able to obtain a high ethylene productivity, i.e. 40 mmol gcatal -1 h -1 . Moreover, these catalysts showed very high stability against deactivation (Fig. 4). Note that the catalytic systems previously evaluated in all ETP processes suffered from significant deactivation [START_REF] Iwamoto | Selective conversion of ethylene to propene and butenes on nickel ion-loaded mesoporous silica catalysts[END_REF][START_REF] Frey | Comparison of differently synthesis Ni(Al)MCM-48 catalysts in the ethene to propene reaction[END_REF][START_REF] Perea | Alumino-mesostructured Ni catalyst for the direct conversion of ethene to propene[END_REF][START_REF] Stoyanova | The role of speciation of Ni 2+ and its interaction with the support for selectivity and stability in the conversion of ethylene to propene[END_REF][START_REF] Taoufik | Direct transformation of ethylene into propylene catalyzed by a tungsten hydride supported on alumina: Trifunctional single-site catalysis[END_REF][START_REF] Li | Conversion of ethene to propene by a dual function NiSO4/Re2O7/γ-Al2O3 catalyst[END_REF][START_REF] Buluchevskii | One-stage synthesis of propylene from ehylene using Pd-Re2O7/B2O3-Al2O3 catalyst[END_REF][START_REF] Ghashghaee | Nanostructured hydrotalcite-supported RuBaK catalyst for direct conversion of ethylene to propylene[END_REF][START_REF] Andrei | Ethylene to propylene by one-pot catalytic cascade reactions[END_REF][START_REF] Andrei | Nickel and molybdenum containing mesoporous catalysts for ehylene oligomerization and metathesis[END_REF][START_REF] Beucher | Selective production of propylene and 1-butene from ethylene by catalytic cascade reactions[END_REF]. Fig. 5 compares the yield in propylene vs. time on stream for the dual catalytic system, Ni-AlKIT-6 + 4-W-KIT-6 with the yields obtained over Ni-AlSBA-15 + MoO3-SiO2-Al2O3 [START_REF] Andrei | Ethylene to propylene by one-pot catalytic cascade reactions[END_REF] and Ni-AlKIT-6 + ReOx/γ-Al2O3 dual catalytic systems reported [START_REF] Beucher | Selective production of propylene and 1-butene from ethylene by catalytic cascade reactions[END_REF]. Undoubtedly, the W-based catalytic system is more efficient and much more stable than the other ones.

Figure 5.

The direct conversion of ethylene to propylene has been investigated using two dual catalytic systems and two reactors in series. The cascade reactions involved in the process, i.e. dimerization/isomerization/metathesis were catalyzed by Ni 2+ , H + (both delivered by Ni-AlKIT-6 catalyst) and W (from WOx/KIT-6 catalyst), respectively. Even if the ETP process was governed by the metathesis step, a perfect balance between the amount of Ni and W sites is essential to efficiently convert ethylene to propylene. For the W-based metathesis catalysts, the support consisting of a non-acid pure KIT-6 silica was more efficient than the silicaalumina supports. Unlike catalytic systems based on MoOx and ReOx, those based on WOx were highly active and stable over a long reaction period. Thus, the ethylene conversion (~ 85%), as well as the yield in propylene (45%) remained unchanged during 24 h on reaction stream.

The encouraging results obtained in the present work about the catalytic conversion of ethylene into propylene could create the basis for new research focused on the conversion of non-oil-based sources into low-carbon olefins. Thus, the ETP process could be incorporated as a second stage into an integrated system, including the bio-ethanol dehydration to ethylene and its conversion into propylene.

Figure captions

  , ESI) equipped with two stainless steel fixed-bed reactors (i.d. = 6 mm, length = 150 mm) coupled in series. The mass flows of gases were monitored by thermal mass flow control valves (Brooks 5850S HP). Before each test, the catalysts (particle size ranging from 0.15 to 0.25 mm) were activated in-situ for 8 h at 550 °C under a nitrogen gas flow. The catalytic measurements have been realized at constant temperature and pressure, using a feed gas stream consisting of C2H4 and N2 (1:1 v/v). The products have been analyzed online by GC (Varian CP-3800, FID), using a CP-PoraPLOT Q capillary column (25 m, 0.53 mm, 20 µm) and an auto-sampling valve. Ethylene conversion (X) was calculated from the respective concentrations at the inlet (Ci) and outlet (Co) of the reactor (X = 1 -Ci/ Co). Product selectivity for the molecule i was Si = y/2 × xi /∑ xj, where x stands for mole fraction and y is a coefficient equal to C atoms in the respective molecule. The amount of products confined in the catalyst during the tests was evaluated by TGA using a NETZSCH TG 209C apparatus (20 mg catalysts, 20 mL min -1 air, temperature ramp of 10 °C min -1 up to 800 °C).

Fig. 1 .

 1 Fig. 1. Ni 2p3/2 X-ray photoelectron spectra recorded on Ni-AlKIT-6 sample before (fresh) and after 24 h of reaction (aged).

Fig. 2 .

 2 Fig.2. W 4f X-ray photoelectron spectra of 4-W-KIT-6 sample before (fresh) and after 24 h of reaction (aged).

Fig. 3 .

 3 Fig. 3. Ammonia TPD profiles of the supports alone and the various catalysts.

Fig. 4 .Fig. 5 .Scheme 1 .Scheme 2 .

 4512 Fig. 4. Ethylene conversion (○), C3 (□) and C4 (◊) selectivity vs. time on reaction stream. Reaction conditions: Feed = 2 L h -1 of ethylene-nitrogen mixture (1/1, v/v); Dimerization reactor: Ni-AlKIT-6 (0.5 g), T = 120 °C, P = 3.0 MPa; Metathesis reactor: 4-W-KIT-6 (0.5 g), T = 450 °C, P = 0.1 MPa.

a

  Me = Ni or W, b BdB pore diameter (DP), total pore volume (VP), BET specific surface area (SBET). c from NH3-TPD.

6 a

 6 Reaction conditions: Feed = 2 L h -1 of ethylene-nitrogen mixture (1/1, v/v); First reactor: 0.2 g of Ni-AlKIT-6, 60 °C, 3 MPa; Second reactor: 0.5 g of W-based catalyst, 450 °C, 0.1 MPa; b after the second reactor.

Figure 1 .

 1 Figure 1.

Figure 2

 2 Figure 2.

Figure 3 .

 3 Figure 3.

Figure 4

 4 Figure 4.

  on a Varian 600 MHz WB Premium Shielded spectrometer, equipped with 3.2 mm o.d. ZrO2 rotors at a rotation speed of 20 kHz. The fresh and spent catalysts were characterized by X-ray photoelectron spectroscopy (XPS). The spent

catalyst, carefully recovered from the reactor was kept under a nitrogen atmosphere before characterization. The measurements were performed on an ESCALAB 250 (Thermo Electron) spectrometer equipped with an Al Kα source (1486.6 eV), and on a Physical Electronics spectrometer (PHI Versa Probe II Scanning XPS Microprobe with monochromatic X-ray Al

Table 1 .

 1 Composition, textural properties and surface acidity of catalysts.

	Sample	Si/Al	Me a
		(mol mol -1 )

Table 2 .

 2 Ethylene conversion and product distribution in the ETP process: effect of support used in the metathesis catalysts a .

Acknowledgments

ERC thanks for financial support project RTI2018-099668-BC22 of Ministerio de Ciencia, Innovación y Universidades and FEDER.


Léo Barassin

Elodie Gabali

Barbara Jammes

Julie Renault

Mohamed Bekhtaoui

Céline Bonnyaud
email: célinebonnyaud@aphp.fr

Case of an elderly patient in acute hospitalization for severe COVID-19: Motor Aspects

Keywords: COVID-19, Evaluation, Fonction motrice, Grand âge, Hospitalisation aiguë Assessment, Acute hospitalization, COVID-19, Motor function, Older

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

Introduction

Depuis mars 2020, les services hospitaliers rencontrent une recrudescence de patients qui présentent des troubles respiratoires et physiques liés au COVID-19. Les personnes âgées sont fortement touchées par cette pandémie et sont plus à risque de développer une forme grave. D'après les dernières données épidémiologiques (23 avril 2020), les personnes âgées de 65 ans et plus représentent 72% des patients hospitalisés et plus de 93% des décès [START_REF] Chêne | COVID-19 : point épidémiologique national du 23[END_REF]. Depuis le 1er mars 2020, l'âge médian au décès est de 84 ans. Les conséquences liées à la symptomatologie de l'atteinte virale et à l'hospitalisation sont nombreuses. Parmi celles-ci, on observe une dégradation des capacités motrices, a fortiori chez les personnes de grand âge.

Cette étude de cas retrace l'évolution des capacités motrices et des constantes cardiorespiratoires d'une patiente de grand âge atteinte d'une forme sévère du COVID-19 en hospitalisation aiguë. Ce cas apparaît atypique par son évolution, d'un pronostic initial très grave à une récupération respiratoire et motrice. L'approche des capacités motrices observées parallèlement aux capacités respiratoires apparaît également singulière. Ce projet relate les données du dossier de la patiente, dans le cadre d'une prise en soins courante. Le consentement libre et éclairé de la patiente a été recueilli.

Antécédents et histoire des problèmes de santé

Madame P. est une patiente de 86 ans, mesurant 1,50 m pour 47 Kg (IMC 20.9, à la limite de la minceur et du poids normal). Elle a été hospitalisée le 23/03/2020, suite à une asthénie qui durait depuis une semaine. Elle a, par ailleurs, comme antécédents médicaux, de l'asthme, de l'hypertension artérielle et une dégénérescence maculaire liée à l'âge. La patiente est arrivée aux urgences avec une tension à 157/110 mmHg, une fréquence cardiaque (FC) de 87 battements par minutes (Bpm), une température de 38°C, une fréquence respiratoire (FR) de 29 cycles par minutes (Cpm) et une saturation en oxygène (Sa02) de 98%. Elle a été hospitalisée en service de médecine interne, avec un scanner thoracique typique du COVID-19 qui présentait de probables foyers surinfectieux aux deux bases. Devant la dégradation de l'état de la patiente au cours de la nuit, une oxygénothérapie à 4L/min a été mise en place. En Le TUG consiste à se lever d'une chaise standard, de marcher 3 m pour contourner un plot et revenir s'asseoir, à vitesse confortable [START_REF] Podsiadlo | The timed "up & go": A test of basic functional mobility for frail elderly persons[END_REF][START_REF] Steffen | Age-and Gender-Related Test Performance in Community-Dwelling Elderly People: Six-Minute Walk Test, Berg Balance Scale, Timed Up & Go Test, and Gait Speeds[END_REF]. Ce test est recommandé chez les personnes âgées ; sa fiabilité est excellente pour cette population [START_REF] Siggeirsdóttir | The timed "Up & Go" is dependent on chair type[END_REF]. Trois essais sans canne sont réalisés et la moyenne des 3 essais est retenue.

Le 5STS consiste à se lever et s'asseoir sur une chaise standard cinq fois de suite en un temps minimal. Ce test permet une évaluation des capacités motrices fonctionnelles des membres inférieurs et du système cardio-respiratoire. Il présente une excellente fiabilité chez les personnes âgées [START_REF] Kendrick | Usefulness of the modified 0-10 Borg scale in assessing the degree of dyspnea in patients with COPD and asthma[END_REF].

Dans ce contexte d'atteinte essentiellement respiratoire, un recueil des constantes a été fait après le 5STS et la durée de retour à la SaO2 initiale (au repos) a été relevée. D'autre part, la patiente devait évaluer son ressenti d'essoufflement après le test grâce à l'échelle verbale de Borg modifiée (score entre 0, pas d'essoufflement et 10, essoufflement extrême) ; cette variante de l'échelle de Borg est validée et plus simple pour les patients gériatriques [START_REF] Kendrick | Usefulness of the modified 0-10 Borg scale in assessing the degree of dyspnea in patients with COPD and asthma[END_REF][START_REF] Morris | Verbal numerical scales are as reliable and sensitive as visual analog scales for rating dyspnea in young and older subjects[END_REF].

Il n'a pas été possible d'effectuer un test de marche (un test de marche de 6 minutes aurait été pertinent), pour respecter les consignes de service ainsi que par manque de matériel d'oxygénation portable permettant la déambulation dans le service.

Une évaluation de la qualité de vie a également été effectuée au moyen du questionnaire EQ-5D [START_REF] Group | EuroQol -a new facility for the measurement of health-related quality of life[END_REF][START_REF] Brazier | Testing the validity of the Euroqol and comparing it with the SF-36 health survey questionnaire[END_REF] ; il évalue 5 dimensions : la mobilité, les activités quotidiennes, les activités courantes (loisir, travail), les douleurs ou l'inconfort et l'anxiété ou la dépression, ainsi que la perception de l'état de santé sur une échelle visuelle analogique de 0 à 100 (100 étant le meilleur état de santé imaginable).

La patiente a été évaluée quotidiennement pendant 7 jours, avec deux jours de repos (J4-J5) correspondant au week-end. Au cours de cette période, la rééducation a été essentiellement motrice et fonctionnelle à raison de 30 min / jour.

Résultats

Suivi longitudinal

Les évaluations se sont déroulées de J1 à J3, puis de J6 à J7, à la suite du week-end. Les valeurs des constantes au repos et les performances aux tests sont reportées dans le tableau I, avec les normes pour la catégorie d'âge de la patiente [START_REF] Steffen | Age-and Gender-Related Test Performance in Community-Dwelling Elderly People: Six-Minute Walk Test, Berg Balance Scale, Timed Up & Go Test, and Gait Speeds[END_REF][START_REF] Desrosiers | Normative Data for Grip Strength of Elderly Men and Women[END_REF][START_REF] Bohannon | Five-repetition sitto-stand test performance by community-dwelling adults: A preliminary investigation of times, determinants, and relationship with self-reported physical performance[END_REF]. Selon l'avis médical, les valeurs des constantes au repos ne contre-indiquaient pas la rééducation motrice.

Sur le plan ventilatoire, l'amélioration de la patiente a permis un sevrage en 02 le 19 avril, à J6.

La figure 3 montre l'évolution des paramètres respiratoires mesurés au repos (FC, FR, SaO2) et du temps au Timed up and go au cours de la rééducation.

La figure 4 montre l'évolution du temps de réalisation au 5STS, du temps de récupération après le test ainsi que de l'apport en O2 au cours du traitement.

Évaluations finales

Le dernier jour de traitement correspond à la sortie de la patiente vers un service de soins de suite (le sevrage en oxygène étant un des principaux critères de sortie). Ce jour-là, elle était sevrée d'O2. Au repos, la FC était de 94 Bpm, la FR de 34 Cpm et la SaO2 de 92%. Le temps moyen du 5STS était de 26,1 ± 2 s. En fin de test, la SaO2 était de 92%, la FC de 92 Bpm et la patiente estimait son essoufflement à 8/10. Le meilleur score de la force de serrage maximal était de 6,6 kg à la main droite et 9,4 kg à la main gauche. Le TUG n'a pas été réalisé car la patiente se sentait « trop fatiguée ». Concernant la qualité de vie, la patiente a évoqué des problèmes à la marche, pour se laver et s'habiller, accomplir ses activités courantes (loisirs) ; elle présentait des gênes ou des douleurs modérées et se disait modérément anxieuse ou déprimée. Enfin elle évaluait son état de santé actuel à 70/100. Elle estimait sa peur de chuter à 8/10 (avec une dernière chute 2 jours avant son hospitalisation, dans sa salle de bain).

Discussion

L'objectif de cette étude de cas était d'observer l'évolution motrice d'une patiente de grand âge (86 ans) à la suite d'une atteinte sévère de COVID-19. Les constantes au repos apparaissent relativement stables malgré un sevrage en oxygène, à l'exception de la fréquence respiratoire qui augmente dès le jour du sevrage. Les capacités locomotrices montrent une amélioration (diminution de presque 5 secondes au TUG). Cette amélioration est supérieure à la valeur minimale détectable de changement qui est de 4,09 secondes chez une population gériatrique [START_REF] Ries | Test-retest reliability and minimal detectable change scores for the timed "up & go" test, the six-minute walk test, and gait speed in people with Alzheimer disease[END_REF]. Cette amélioration locomotrice s'accompagne d'une stabilisation de la SaO2 malgré un sevrage en oxygène. Ces résultats suggèrent que les améliorations respiratoires de la patiente s'accompagnent d'une récupération notable de la performance locomotrice, avec une augmentation des fréquences respiratoire et cardiaque.

Les données du 5STS montrent une variation des performances : une amélioration entre J1 et J3, une diminution entre J3 et J6, puis une amélioration entre J6 et J7, pour obtenir une performance en fin de traitement proche de celle de la valeur initiale. A noter que cette relative stabilité de la performance chronométrique entre J1 et J7 est accompagnée d'un sevrage en oxygène. Après une journée d'adaptation à ce nouveau contexte en air ambiant, on note une faible amélioration de la performance, mais surtout un gain notable en temps de récupération de la SaO2. Ces résultats suggèrent que l'aspect respiratoire et moteur sont étroitement liés. Ce lien entre capacités fonctionnelles et capacités respiratoires et musculaires a déjà été établi dans d'autres pathologies respiratoires comme la bronchopneumopathie chronique obstructive (BPCO) [START_REF] Mansour | Pulmonary function and functional capacity cut-off point to establish sarcopenia and dynapenia in patients with COPD[END_REF]. Cet objectif d'homéostasie au cours d'un exercice passe par un ajustement de la performance physique à l'effort, régulé par le système nerveux autonome qui produit un ajustement cardio-respiratoire selon les informations perçues pendant l'exercice (hypoxie, hypercapnie). La performance à l'exercice oscille donc comme résultat d'interactions entre les organes [START_REF] Noakes | From catastrophe to complexity: A novel model of integrative central neural regulation of effort and fatigue during exercise in humans: Summary and conclusions[END_REF][START_REF] Noakes | From catastrophe to complexity: A novel model of integrative central neural regulation of effort and fatigue during exercise in humans[END_REF]. L'observation d'une relative stabilité de la performance aux passages assis-debout dans un contexte de sevrage en oxygène et de gain de temps de récupération après l'effort apparaît comme un résultat plutôt positif d'évolution chez cette patiente. Ce test du 5STS rapide sollicite davantage le système cardio-respiratoire que la locomotion à vitesse spontanée (TUG), moins coûteuse énergétiquement, ce qui peut expliquer l'écart de résultats entre ces deux aspects de la fonction motrice (gain notable pour le TUG, relative stabilité pour le 5STS).

Les résultats de la force maximale de serrage des mains montrent une diminution bilatérale.

Celle-ci peut s'expliquer par les jours d'alitement et d'arrêt des activités manuelles de la patiente, ce qui n'est pas favorable au maintien de la force musculaire [START_REF] Méan | Alitement en milieu hospitalier: la mobilisation peut-elle préserver la personne âgée hospitalisée du déclin fonctionnel?[END_REF]. Ces résultats peuvent aussi s'expliquer par la rééducation qui ne ciblait pas spécifiquement un travail de renforcement musculaire, mais plutôt une approche fonctionnelle. Par ailleurs, cette diminution ne peut pas s'expliquer par le sevrage en oxygène, l'effort réalisé (de 5 secondes environ) utilise l'ATP stocké dans les muscles comme substrat énergétique et non l'énergie issue de l'oxygène (filière aérobie).

Légende des figures :

  présence d'une aggravation des symptômes, une augmentation de cet apport en 02 (6 L/min) et un traitement par hydroxychloroquine ont été instaurés le 25/03/2020. Ce traitement a été suspendu deux jours après pour cause de dégradation cardiaque (allongement de l'intervalle QT). Devant l'augmentation des besoins en 02 (9L au masque le 30/03/2020), des corticoïdes ont été introduits le 31/03/2020 dans l'objectif de réduire la supplémentation en 02. Ce contexte de dégradation mené à aborder une exclusion d'une réanimation intensive et d'une intubation, en accord avec la famille. Le 08/04/2020, dans les suites d'une oxygénodépendance réduite à 2L/min d'02, la patiente a été transférée en gériatrie aiguë. Dans ce contexte de stabilisation, une rééducation a été initiée avec mise au fauteuil et sollicitation motrice douce. La figure 1 illustre l'évolution des constantes respiratoires pendant la phase qui a précédé la rééducation. La figure 2 présente la frise chronologique des événements marquants de l'hospitalisation de la patiente. Autonomie avant l'hospitalisation Âgée de 86 ans, Mme P. était autonome avant son hospitalisation pour les gestes du quotidien comme la toilette et l'habillage, mais avait besoin d'une aide-ménagère pour les courses, le ménage et la préparation des repas qu'elle réchauffait. D'autre part, elle marchait seule quotidiennement, avec une canne à l'extérieur. Son niveau d'activités physiques antérieur a été évalué par le questionnaire de Ricci et Gagnon. Avec 1 h de gymnastique et 2 séances de 30 minutes de sollicitation musculaire par semaine avec un masseur-kinésithérapeute, Mme P. obtenait un score de 27/45. Elle était donc considérée comme une personne active. Évaluations du suivi rééducatif Le suivi des capacités motrices de cette patiente de grand âge qui avait présenté une forme sévère du COVID-19 a démarré le 15/04, en phase stabilisée, après 23 jours d'hospitalisation. Au niveau cognitif, la Mini Mental State Examination (MMSE) a été réalisée. C'est un test de grande fiabilité et recommandé chez la personne âgée [2]. Le volume d'oxygène et les constantes cardio-respiratoires au repos (SaO2, FC et FR) étaient recueillis quotidiennement. L'évaluation des capacités motrices comprenait un test de force de serrage maximal (test de préhension ou grip test), le test du Timed Up and Go (TUG) et le test du Five sit-to-stand (5STS). Ces évaluations correspondent aux outils de référence recommandés chez la personne âgée et en pratique conventionnelle d'après « Réponse rapide dans le cadre COVID-19 » publiée par la Haute Autorité de Santé [3]. L'évaluation de la force de serrage maximal est réalisée au moyen du dynamomètre numérique (EH101, Deyard), dans une position standardisée, coude fléchi à 90°, avant-bras posé, poignet en position neutre et dynamomètre en position verticale. Trois essais sont réalisés de chaque côté, avec une pause d'une minute entre chaque essai ; le meilleur score est retenu. Ce test présente une excellente fiabilité chez les personnes âgées [4]. La latéralité a été notée.

  point de vue cognitif, la patiente avait un score de 22/30 au MMSE, avec une bonne orientation temporo-spatiale, de bonnes capacités d'apprentissage et praxiques, mais des difficultés pour le calcul et la mémoire de travail. Les normes établies pour les plus de 79 ans se situent entre 20 et 26 selon le niveau de scolarité[START_REF] Kalafat | Standardisation et étalonnage français du "Mini Mental State" (MMS) version GRÉCO[END_REF].Le premier jour de traitement, la patiente était sous deux litres d'02. Elle avait une FC au repos de 84 Bpm, une FR à 20 Cpm et une SaO2 à 92 %. La moyenne du TUG était de 27,6 ± 2,2 s. Le temps moyen au 5STS était de 25,6 ±3 ,4 s. Après le test, la SaO2 était à 92 % et la FC à 83 Bpm. La perception de l'essoufflement était cotée à 6/10.

  Au final, bien que les performances de Mme P. aux tests chronométriques soient diminuées par rapport à la norme chez des sujets du même âge, la patiente a progressé sur le plan locomoteur et est restée relativement stable au test assis-debout, dans un contexte de sevrage en oxygène.Ce suivi présente certaines limites dont la constance dans les horaires des évaluations. Les fluctuations de la fatigue de la patiente ont parfois nécessité des interventions fractionnées dans la journée. L'absence de sollicitation des fonctions motrices par les rééducateurs le week-end (J4 et J5), avec éducation de la patiente à la réalisation d'exercices en autonomie, est aussi à signaler ; cela peut avoir impacté les données.ConclusionMme P. fait partie d'une minorité de patients très âgés qui présentent une atteinte sévère de Covid-19 à avoir récupéré d'un point de vu respiratoire et fonctionnel. En effet, au 23 avril 2020, les personnes âgées représentaient 93% des décès (1). Le suivi quotidien des performances motrices de la patiente nous a permis d'observer l'interaction entre les aspects respiratoire et moteur d'une patiente gériatrique atteinte du COVID-19.

Figure 1 :Figure 2 :Figure 3 :Figure 4 :Figure 1 -Figure 3 -

 123413 Figure 1 : Constantes respiratoires de la patiente au cours de son hospitalisation *Introduction de l'hydroxychloroquine **Arrêt de l'hydroxychloroquine, *** introduction des corticoïdes (BL je ne vois pas à quoi correspondent les * sur le schéma) Figure 2 : Frise chronologique des évènements marquants de l'hospitalisation de Madame P. (BL : rajouter un « e » à « arrivée ») Figure 3 : Evolution des paramètres respiratoires mesurés au repos (FC, FR, saturation en O2) et du temps au time-up-and-go au cours de la prise en charge rééducative (BL : rajouter «des, au et en » dans le titre et enlever les « s » à Jour 2, Jour 3….) Figure 4 : Evolution des paramètres mesurés au 5STS et de la délivrance en O2 au cours de la fin d'hospitalisation

Figure 4 -

 4 Figure 4 -Évolution du 5STS et de la délivrance d'O 2 au cours du suivi

  Tableau I-Constantes et moyenne (+/-écart-type) pour les tests chronométriques, ou maximum pour test de la force maximaleJour 1 Jour 2 Jour 3 Jour 6 Jour 7 Normes

								(> 80
								ans)
	Fréquence cardiaque au repos (Bpm)	84	78	81	85	94	80
	Fréquence respiratoire au repos (Cpm)	20	24	15	25	30	12-20
	Saturation au repos (%)	92	93	92	92	92	95-100
	O2 (L)		2	2	2	0	0	0
	Timed up and go (s)	27,6	26,7	25	22,7	-	11±3
	Grip Test main droite (Kg)	-	14,2	8,2	7,2	6,6	20±5,8
	Grip Test main gauche (Kg)	-	11,3	9,9	9,5	9,4	19±5,5
		Temps (s)	25,6	19,2	23	27,9	26,1	10,6±3,4
		Saturation en fin de test (%)	93	93	92	90	92	95-100
		Fréquence cardiaque fin de test	83	75	79	71	92	-
	5 sit to stand	(Bpm)
		Borg modifiée fin de test	6	6	6	5	8	-
		Temps de retour à la saturation	-	35	75	81	30	-
		de repos (s)

de participer à cette étude, ainsi que Hervé Chanut, cadre de