Maria Clara

Jesus Vieira

Luis Fernando Figueira Da Silva
email: luis-fernando.figueira-da-silva@ensma.fr

Luís Fernando Figueira Da Silva

Flame flashback critical Damköhler number for CO2 diluted CH4 and C3H8 mixtures with air

Keywords: Boundary layer flashback, Flashback propensity, Laminar, Premixed flames

The premixed laminar flame flashback phenomenon in tubes has been known and studied for several decades. However, the effect of the CO2 dilution has not been addressed, which is relevant for assessing the safety of oil-producing facilities. Furthermore, even if numerical studies have underscored the important role played by the mixture Lewis number (Le), these lack an experimental validation. For this reason, specific studies of premixed flame flashback in laminar flows have been undertaken. The objective is to assess the flame flashback critical conditions in mixtures of hydrocarbons -methane or propane diluted by various amounts of CO2 -with air. This is effected by determining the critical Damköhler number, which is computed using both experimental and numerical data. The former leads to the flashback critical velocity gradient, whereas the latter to a characteristic chemical time scale. The effect of different flame thickness definitions on the Damköhler Flame flashback critical Damköhler number number (Da) is examined, evidencing than an order of magnitude discrepancy may arise depending on the definition choice. For methane/air mixtures the critical Da increases with the equivalence ratio, whereas a decrease of nearly two orders of magnitude has been obtained for propane/air mixtures. The original results show that CO2 dilution increases Da only when the fuel dilution percentage is larger than 25% and 50%, for methane and propane, respectively, situations which correspond to flame extinction after flashback. The propane/air/CO2 mixture results exhibit a Da ∝ Le 5.06 dependency which closely follows the trend computed previously, whereas the methane/air/CO2 results evidence the thermal boundary condition at the tube wall influence.

Introduction

The flame flashback phenomenon in laminar flows has been known and studied for several decades [START_REF] Lewis | Combustion, Flames and Explosions of Gases[END_REF]. A significant amount of results is available, which demonstrate the influences exerted by fuel, dilution and tube diameter choices [START_REF] Kalantari | Boundary layer flashback of non-swirling premixed flames: Mechanisms, fundamental research, and recent advances[END_REF], for instance. However, a recent review of the state of the art [START_REF] Kalantari | Boundary layer flashback of non-swirling premixed flames: Mechanisms, fundamental research, and recent advances[END_REF] indicates that significant knowledge gaps remain, in particular with regard to the combustible mixture Lewis number influence, and the effect of fuel dilution by CO 2 . Indeed, concerning the latter, CO 2 is used to displace oil in mature reservoirs, and is naturally found in some geological formations, which leads to fuel gas produced with dilutions that may reach 75 %. Therefore, these knowledge gaps prevent the use of existing results for the prediction of flame flashback, in particular under the CO 2 -abundant gas production conditions of the Brazilian pre-salt offshore platforms. For this reason, specific experimental studies of CO 2 -diluted hydrocarbon/air premixed flames flashback in laminar flows are undertaken here.

Classically [START_REF] Lewis | Combustion, Flames and Explosions of Gases[END_REF], the flame flashback through the boundary layer is assumed to occur when the velocity of flow, u(y), is smaller than the local burning velocity, S 0 L , at some point near the wall, as seen in Fig. 1. The position at which the burning velocity is equal to the flow velocity is defined as the flame penetration distance, δ p . The flame is supposed to be extinguished at a certain distance from the wall, called the quenching distance (δ q ). When the flow velocity at y = δ p is equal to the local burning velocity the critical condition for flame flashback arises. This model further assumes that no flame/fluid interaction occurs and, therefore, that there are no disturbances in the laminar flow velocity upstream to the flame. More recent works determined that flow reversal may occur downstream the flames at the wall vicinity [START_REF] Gruber | Direct numerical simulation of premixed flame boundary layer flashback in turbulent channel flow[END_REF][START_REF] Eichler | Premixed flame flashback in wall boundary layers studied by long-distance micro-piv[END_REF].

During the past decades, the critical conditions leading to laminar boundary layer flashback in tubes have been subject of experimental and numerical studies. Pioneering experimental studies [START_REF] Lewis | Stability and structure of burner flames[END_REF] have identified the role of the flow velocity gradient at the wall on the flashback onset. The critical value of this gradient has been measured, for instance, as a function of the fuel type, mixture equivalence ratio and oxygen content, and summaries of these results are available [START_REF] Lewis | Combustion, Flames and Explosions of Gases[END_REF][START_REF] Kalantari | Boundary layer flashback of non-swirling premixed flames: Mechanisms, fundamental research, and recent advances[END_REF]. In particular, a decrease in oxygen dilution by nitrogen has been shown to significant increase the flame flashback propensity. Numerical studies of this phenomenon have extended the critical velocity gradient concept by means either of a Damköhler or a Karlovitz number [START_REF] Kurdyumov | Flame flashback and propagation of premixed flames near a wall[END_REF][START_REF] Kurdyumov | Lewis number effect on the propagation of premixed laminar flames in narrow open ducts[END_REF][START_REF] Kurdyumov | Experimental and numerical study of premixed flame flashback[END_REF][START_REF] Kalantari | Flashback propensity of turbulent hydrogen-air jet flames at gas turbine premixer conditions[END_REF]. The computed critical Damköhler number has been shown to be an increasing function of the Lewis number, and to decrease when the tube wall boundary condition changes from isothermal to adiabatic. To the best of our knowledge, a systematic experimental investigation of the Lewis number influence on the flashback propensity has not been performed, however. More recently, flame stretch effects were accounted for and shown to decrease the critical bulk velocity for flashback to occur for near-stoichiometry H 2 -air flames [START_REF] Hoferichter | Prediction of boundary layer flashback limits of laminar premixed jet flames[END_REF]. However, the stretch influence on flashback was found to be less pronounced for methane/air flames. Newly proposed Karlovitz number correlations incorporate the stretch effect on a premixed flame to predict the boundary layer flashback of turbulent swirling flames [START_REF] Ebi | Swirl flame boundary layer flashback at elevated pressure: Modes of propagation and effect of hydrogen addition[END_REF][START_REF] Novoselov | The effect of hydrogen addition on confined turbulent boundary layer flashback studied with a critically strained flame model[END_REF].

In order to further define the laminar boundary layer flashback controlling parameters, Fig. 1 shows a schematic model of this process, where a stabilised flame front can be seen inside a tube near the wall. On the right side of this figure, the velocity of the flow, u(y), is represented by a parabolic profile. On the left side of Fig. 1, which considers the stabilised flame front immediately upstream the edge of the tube, represents the three conditions conditions for flame/flow interaction. The horizontal axis, y, represents the distance from the tube wall, and the dashed lines 1, 2 and 3 symbolise different flow velocities. The solid curve represents the velocity of the laminar flame front near the wall. Note that, in this model, the laminar flame front velocity is zero within the quenching region, i.e., 0 < y < δ q . When the flow velocity is greater than the local burning velocity througout the flame front, the flame leaves the tube and stabilises on the outside, a situation which is represented by line 3. Line 2 indicates the critical condition for observing flame flashback, when the flow velocity is equal to the burning velocity at the flame penetration distance, y = δ p . If the flow velocity is reduced (line 1), the flame propagates into the tube. Given this picture, the velocity gradient used to characterise the flashback in the critical situation may then be defined as

g c = du dy y=δp = S 0 L δ p . (1)
In the classic premixed flame flashback model [START_REF] Lewis | Combustion, Flames and Explosions of Gases[END_REF][START_REF] Kalantari | Boundary layer flashback of non-swirling premixed flames: Mechanisms, fundamental research, and recent advances[END_REF], the local burning velocity at this critical condition is equal to that of a freely propagating one dimensional laminar premixed flame, and the flame penetration distance within the boundary layer, δ p , that controls the flashback phenomenon, is considered proportional to the laminar flame thickness, i.e., δ p = Kδ L , where K is assumed to be constant. This model further supposes that a developed laminar flow exists within the tube, which enables the critical condition for flashback to occur through the boundary layer to be expressed by equating the flow's and the modelled expressions of the critical velocity gradient, i.e., g c = (du/dy) y=δp = 8 Ū /D = S 0 L /(Kδ L ), where D is the tube diameter and Ū is the bulk flow velocity, both which stem from measurements here.

One should note that K may be interpreted as a Damköhler number [START_REF] Kurdyumov | Flame flashback and propagation of premixed flames near a wall[END_REF][START_REF] Kurdyumov | Lewis number effect on the propagation of premixed laminar flames in narrow open ducts[END_REF]. The critical Damköhler number for flashback to occur may then written as

Da = S 0 L g c δ L = DS 0 L 8 Ū δ L . (2)
An extra usual assumption concerns the definition of the laminar flame thickness, which is taken to be proportional to the mixture thermal diffusion coefficient, δ L = α/S L , thus leading to:

Da = (S 0 L ) 2 g c α = D(S 0 L ) 2 8 Ū α . (3)
However, such a flame thickness definition is known to under-predict the computed thermal thickness of premixed flames [START_REF] Grosseuvres | Combustion properties of H 2 /N 2 /O 2 /steam mixtures[END_REF]. Equations ( 2) and (3) suggest that, if the Damköhler number critical value is constant, the flashback propensity in terms of the critical velocity gradient should be reduced when S 0 L decreases, which is the case for hydrocarbon-air CO 2 diluted mixtures of interest to the present work. Note also that, under the assumptions leading to Eq. ( 3), the critical bulk velocity for flame flashback would be directly proportional to the tube diameter and the squared flame speed, i.e., Ū ∝ D(S 0 L ) 2 . As a consequence, the assumption of a constant Damköhler number could lead to an improper safety assessment, in terms of this velocity, if the actual Da value is larger than the presumed constant one.

The goal of this work is thus to determine the influence of the mixture composition and fuel dilution by CO 2 on the flame flashback limit, which is represented by a Damköhler number. This is effected by combining original experimental data of the critical flashback conditions with detailed chemical kinetics computational results to determine the flame speed and thickness. More specifically, the question of whether Da may be assumed to be constant is addressed, as is the influence of the mixture effective Lewis number. The extent to which different flame thickness definitions may change the critical Damköhler number values is examined also.

This paper is organised as follows: the experimental and computational methodologies used to determine the Damköhler and effective Lewis numbers for CO 2 -diluted methane and propane mixures with air are first presented. Then is assessed the influence on the Damköhler number of the flame thickness definition, of the mixture equivalence ratio and fuel CO 2 dilution, and of the effective Lewis number. Finally, the main conclusions of this work are presented.

Methodology

In this section are presented the experimental and computational methodologies adopted to characterise the flame flashback.

Experimental methodology

To study the boundary layer flashback phenomenon in laminar flows an experimental bench was set up, which is schematically shown in Fig. 2. Its dimensions were chosen based on data found in the literature [START_REF] Kalantari | Boundary layer flashback of non-swirling premixed flames: Mechanisms, fundamental research, and recent advances[END_REF], which indicated that determining the flashback limits throughout the flammability range of methane and propane mixtures with air should require tubes with different diameters and a wide range of flow meters. Accordingly, this bench consists of interchangeable D = 17, 6, 5, and 4 mm inner diameter quartz tubes, which are vertically mounted, the larger diameters being used to determine the flashback around stoichiometry, and the smaller for either fuel lean or fuel rich mixtures. These tube diameters are known with a 0.6 % accuracy. Note that for tubes with diameters smaller than 2 mm, extinction, instead of flashback, is expected to occur for undiluted mixtures [START_REF] Lewis | Combustion, Flames and Explosions of Gases[END_REF]. The tubes have a length L of 1 m, that ensures a fully developed laminar flow for all the Reynolds numbers considered, i.e., L/D > 0.05 Re. The maximum Reynolds number for all mixtures, flow rates and tube diameters considered is 1,250. This value correspond to an undiluted propane/air mixture, with equivalence ratio of φ = 1.25, flowing through the 17 mm diameter tube.

As shown in Fig. 2, Alicat Scientific flow controllers are used to measure the reactants flow rates prior to mixing. These MC-series controllers, with ranges of 0.5, 5, 50 and 500 SCCM, 5 and 20 SLPM, have a standard accuracy calibration of ±0.6 % of reading or ±0.1 % of full scale, whichever is greater. Throughout the experiments performed these flow controllers were used in different gas lines, so as to cover fuel/air mixtures from the lean to the rich flammability limit, and CO 2 dilution in the fuel stream up to 75 %. Mixing is effected in a 6 mm outer diameter tube which length is at least twice that required for obtaining a fully developed flow. The fuels studied here were methane and propane, which constituents are

C 3 H 8 /CH(CH 3 ) 2 (C 2 H 5 )/C 2 H 6 /1-C 4 H 8 /C 3 H 6 ,
and molar basis composition is (89.1, 4.16, 3.12, 2.94, 0.68) %.

Each experiment begins with the flame stabilised at the quartz tube rim for a chosen CO 2 dilution in the fuel stream. The air flow rate is then increased or decreased, so that the flame flashback arises either from the fuel rich or the fuel lean equivalence ratio, respectively. The steps with which the air flow rate is varied was adapted in order to achieve an adequate, repeatable, resolution of the flame flashback. Indeed, for each flow-meter, these steps are always smaller that 1 % of the corresponding full scale. The time interval between those flow rate steps was also larger for smaller flow rates, so that several flow residence times within the tube were allowed for before changing the flow rate. For a range of equivalence ratios at the vicinity of stoichiometry the flame may stabilise in a configuration in which a partial entrance in the tube is observed [START_REF] Lewis | Combustion, Flames and Explosions of Gases[END_REF]. In this work flashback is assumed to occur only when the flame visually propagates upstream in the tube, and such a partial entrance was not annotated. The set of experiments enables to determine the critical velocity gradient [g c = 32 V /(πD 3 ) = 8 Ū /D], where V and Ū are the measured mixture volume flow rate and the corresponding mean flow velocity when flashback occurs, which are functions of the equivalence ratio, φ, and fuel (methane or propane) dilution by CO 2 . All experiments have been conducted under ambient conditions, i.e., 1 atm and 25 C, and that the tube wall temperature was not measured.

Note that early studies [START_REF] Grumer | Temperature dependence of stability limits of burner flames[END_REF][START_REF] Dugger | Flame stability of preheated propane-air mixtures[END_REF] examined the influence on the flame flashback of preheating the fuel/air mixtures. The experimental conditions are such that the preheating temperature does not increase beyond 620 K, the fuels considered are methane and propane. These studies determined that the flame flashback critical velocity gradient increases with the mixture preheating, and that the penetration distance, obtained by dividing the flame speed by the critical velocity gradient, [Eq. ( 1)] decreases with preheating. More precisely, for a propane/air mixture temperature of 306 K, the penetration distance is 0.8 mm, 0.6 mm and 0.7 mm for the equivalence ratios of 0.8, 1.2 and 1.3, respectively, whereas for 617 K of initial temperature, the values of 0.6 mm, 0.4 mm and 0.5 mm were obtained for equivalence ratios of 0.9, 1.15 and 1.4 [START_REF] Dugger | Flame stability of preheated propane-air mixtures[END_REF].

Laminar flame properties determination

In order to determine Da via Eq. ( 2), S 0 L , the laminar flame front speed at which the flat, isobaric, adiabatic flame freely propagates must be provided. To this end, numerical calculations were performed using the Ansys CHEMKIN software, version 2020 R1. The chemical kinetic mechanisms adopted were: (1) the GRI-Mech 3.0 mechanism [START_REF] Smith | GRI-Mech 3.0[END_REF] for the methane/air/CO 2 mixtures, and (2) for propane/air/CO 2 mixtures the San Diego Mech [START_REF]Chemical-Kinetic Mechanisms for Combustion Applications, San Diego Mechanism web page[END_REF]. These mechanisms were chosen to represent the chemical kinetics of the studied mixtures based on their predictive ability demonstrated in previous review works [START_REF] Konnov | A comprehensive review of measurements and data analysis of laminar burning velocities for various fuel+air mixtures[END_REF][START_REF] Mendoza Orbegoso | On the predictability of chemical kinetics for the description of the combustion of simple fuels[END_REF], a brief analysis of the influence of different chemical mechanisms is given below. For the sake of conciseness the computed flame velocities are not reported here, but are given in the form of polynomial fits in the supplementary material file.

The classical flame flashback analysis defines the flame thickness, δ L , as the ratio of the fresh gases mixture thermal diffusion coefficient and the flame speed,

δ L,T = α S 0 L , (4)
thus leading from Eq. ( 2) to Eq. ( 3). In this work the computed flame thickness was also determined using a correction to δ L,T that accounts for variable thermal properties across the flame [START_REF] Blint | The relationship of the laminar flame width to flame speed[END_REF],

δ L,B = 2 α S 0 L T b T u 0.7 , (5)
and the temperature derivative maximum [START_REF] Poinsot | Theoretical and Numerical Combustion[END_REF], i.e,

δ L,max = T b -T u max (dT /dx) , (6)
where, T b and T u are the temperatures of the burned gases at equilibrium and of fresh mixture, respectively, and dT /dx was obtained from the premixed flame computations. When performing such flame computations care was taken to check for domain and mesh independence of the results for all studied fuel/dilutant/air mixtures.

In order to examine the influence of the chemical mechanism choice, the computed values of the S 0 L /δ L,max are compared in Fig. 3 for undiluted fuel/air mixtures as a function of the equivalence ratio. This inverse of a characteristic chemical time is given since it appears in Eq. ( 2). For methane-air mixtures were used the GRI 3.0 [START_REF] Smith | GRI-Mech 3.0[END_REF], San Diego Mech [START_REF]Chemical-Kinetic Mechanisms for Combustion Applications, San Diego Mechanism web page[END_REF], and USC II Mech [START_REF] Wang | USC Mech Version II. High-Temperature Combustion Reaction Model of H2/CO/C1-C4 Compounds[END_REF], whereas for propane/air mixtures the latter two have been considered only. Concerning the methane/air mixtures first, Fig. 3a shows that the agreement between the three examined mechanisms is very good for both lean and rich mixtures. The largest discrepancies arise at slightly fuel rich conditions. Indeed, the maximum value predicted with the GRI 3.0 is 905 s -1 , which may be compared to 830 and 810 s -1 for the San Diego and USC II mechanisms, respectively. These values correspond to 8% and 13% discrepancies between the GRI 3.0 and the two other mechanisms results. As it may be verified in Fig. 3b the discrepancies between the results obtained for propane/air mixtures are larger for lean and near stoichiometric values of φ, but very small for rich mixtures. More precisely, the maximum S 0 L /δ L,max value predicted by the San Diego mechanism is 1152 s -1 , whereas the USC II Mech yields 1058 s -1 , which represents an 11% difference. As a consequence, considering the fuel/air mixtures studied, the maximum discrepancy related to these chemical kinetic mechanism choices is of the order of 10%. L /δ L,max obtained for undiluted mixtures as a function of equivalence ratio. Comparison between chemical kinetic mechanism: GRI 3.0 [START_REF] Smith | GRI-Mech 3.0[END_REF] (solid line), San Diego Mech [START_REF]Chemical-Kinetic Mechanisms for Combustion Applications, San Diego Mechanism web page[END_REF] (dashed line) and USC II Mech [START_REF] Wang | USC Mech Version II. High-Temperature Combustion Reaction Model of H2/CO/C1-C4 Compounds[END_REF] (doted line).

The Damköhler number is determined here using both experimental and computed data as

Da = DS 0 L /(8 Ū δ L ) = πD 3 S 0 L /(32 V δ L ).
Therefore, the maximum experimental errors associated to Da are 2.4 % and 4.0 % for methane/air and propane/air respectively, whereas those corresponding to φ are 1.1 % and 1.8 %. These errors stem from those associated to the tube diameter and reactants flow rates measurements, which differ for methane and propane mixtures due to the different velocity gradients leading to flashback.

In order to recover either the critical velocity gradient, g c , or the bulk flow velocity, Ū , leading to flame flashback, the values of S 0 L and δ L must be known. Accordingly, are given as tables, in the supplementary material file, the polynomial coefficients corresponding to the fits of flame speed (S 0 L ) and thickness (δ L,max ) as a function of equivalence ratio and CO 2 dilution. These should enable a reconstruction of either the critical velocity gradient, g c , or the flow bulk velocity leading to flashback, Ū .

Concerning the mixture composition influence on Da, two different representations are adopted here, i.e., [START_REF] Lewis | Combustion, Flames and Explosions of Gases[END_REF] the equivalence ratio of the fresh gases, and (2) their effective Lewis number. The effective Lewis number is determined using a formulation [START_REF] Joulin | Linear stability analysis of two-reactant flames[END_REF] that relies on the Zel'dovich number to continuously vary between the fuel lean and fuel rich limits,

Le = Le 1 + H(Le 2 -Le 1 ), (7)
where Le 2 and Le 1 are the fuel-rich and oxidiser-rich Lewis numbers, which are defined as the ratio between the mixture thermal diffusivity, and the diffusion coefficient of the limiting reactant, i.e., fuel in the fuel-lean and oxygen in the fuel rich mixtures. The CO 2 dilution effect is thus accounted for in the thermal diffusion coefficient. These transport coefficients are determined using Flame flashback critical Damköhler number the classical formulations available in chemkin. In Eq. ( 7) H is given by:

H = n G(m, n -1, A) G(m, n, A) , G(m, n, A) = ∞ 0 ξ m (ξ + A) n exp(-ξ) dξ, (8)
m and n are the orders of reaction with respect to the deficient and abundant reactants, respectively, the normalised final concentration of the abundant reactant is either A = β(φ -1)/Le 2 or A = β(φ -1)/Le 1 , and

β = E a (T b -T u )/(RT 2 b
) is the Zel'dovich number. For the sake of simplicity it is assumed that m = n = 1; note that different reaction orders would lead to different slopes of the Le(φ) curve [Eq. [START_REF] Kurdyumov | Lewis number effect on the propagation of premixed laminar flames in narrow open ducts[END_REF]]. It should be stressed that this equation was derived on the basis of a single-step Arrhenius reaction, which in turn leads to the Eq. ( 8) reactant mass fraction dependency of the effective Lewis number. Therefore, when using such a formulation to determine Le, the detailed chemistry effects that may arise due to the CO 2 influence are not accounted for.

The Lewis number values for fuel lean (Le 1 , which corresponds to φ → 0) and fuel rich mixtures (Le 2 , which corresponds to φ → ∞) diluted by CO 2 are given in Tab. 1. In this table each column corresponds to a chosen CO 2 dilution in the fuel, ranging from 0% to 75%, and each line gives (Le 1 , Le 2 ) pairs for a given fuel/air mixture. These Lewis number limit values were computed using the transport properties obtained with the classical multi-component mixture formulas. In this table it may be verified that the CO 2 dilution in the fuel leads, in methane/air rich mixtures, to a decrease of the Le 2 values which is associated to the smaller thermal diffusivity of CO 2 . On the contrary, the propane/air mixtures are characterised by a Le 2 increasing trend with CO 2 dilution, which is due to the propane thermal diffusivity being smaller than that of the CO 2 . Since the CO 2 dilution is effected in the fuel, the lean limit values (Le 1 ) are unaffected, because the thermal diffusivity is that of the air. The Zel'dovich number is determined using a recently proposed methodology, which uses an extended Arrhenius expression that is optimally fitted to the computed premixed flame heat release rate [START_REF] De | Premixed flame heat release single-step chemistry for H 2 , CH 4 , and C 3 H 8 mixtures[END_REF]:

q(θ) ∝ {1 -exp[β (1 -1/θ)]} β exp β(θ -1) (1 + γθ)/(1 + γ) , (9)
where θ = (T -T u )/(T b -T u ) is the temperature based reaction progress variable, and γ = (T b -T u )/T u represents the thermal expansion across the flame. In this heat release rate expression, β and β control, respectively, the initial and the final q decrease towards equilibrium as θ → 1. For the sake of completeness, the Zel'dovich number correlations resulting from such a procedure that are used in Eq. ( 8) read: methane/air : β = 10.4 φ 4 -49.6 φ 3 + 98.7 φ 2 -90.7 φ + 33.4, [START_REF] Hoferichter | Prediction of boundary layer flashback limits of laminar premixed jet flames[END_REF] propane/air : β = -21.7 φ 4 + 106 φ 3 -164 φ 2 + 94.2 φ -12.3, [START_REF] Ebi | Swirl flame boundary layer flashback at elevated pressure: Modes of propagation and effect of hydrogen addition[END_REF] for which R 2 > 0.98.

Results and Discussion

The flame flashback results obtained for the methane and propane CO 2 diluted mixtures with air are now presented. These results considered dilutions ranging from 0% to 50% for methane, and from 0% to 75% for propane. In order to cover the equivalence ratio range between the lean and the rich flashback limits the tube diameters used are D = 4, 5, 6 and 17 mm. These lean and rich flashback limits are found for equivalence ratios of φ ≈ 0.7 and ≈ 1.3 and of φ ≈ 0.7 and ≈ 1.6 for methane and propane mixtures, respectively. Given these equivalence ratio ranges and tube diameters, the associated bulk flow velocities and total flow rates range from 0.025 < Ū < 1.47 m/s and 0.0192 < ∀t < 21.45 lpm, respectively. For a given tube diameter, the equivalence ratio range is typically covered by determining circa 500 critical flashback conditions. In what follows are examined the influences on the critical flashback Damköhler number of (i) the flame thickness definition, (ii) the mixture equivalence ratio and fuel dilution by CO 2 and (iii) the Lewis number.

Flame thickness definition influence

In this section is examined the influence of three different flame thickness definitions on the flame flashback critical Damköhler number, Eq. ( 2). More specifically, the considered flame thickness definitions are given by Eqs. ( 4), ( 5) and [START_REF] Kurdyumov | Flame flashback and propagation of premixed flames near a wall[END_REF]. Figure 4 shows the evolution with the mixture equivalence ratio of the computed flame thickness, as well as the corresponding critical Damköhler numbers, for methane/air and propane/air mixtures. This particular (φ, Da) representation was chosen due to its interest to process safety. For the sake of simplicity undiluted fuel mixtures results are given and discussed in this section only.

In Figs. 4a and 4b it can clearly be seen that the three flame thickness definitions lead to minimum values at equivalence ratios slightly larger than stoichiometry, which is related to the well-known rich shift of maximum S 0 L [START_REF] Law | On the off-stoichiometric peaking of adiabatic flame temperature[END_REF]. Indeed, regardless of the flame thickness definition chosen, both methane and propane mixtures with air exhibit a thickness increase for leaner and richer mixtures. For instance, the leanest methane/air flame thermal thickness is 3.3 times that of a stoichiometric flame, whereas this ratio is 2.2 when the maximum temperature gradient thickness is considered. Concerning lean propane/air flames, these ratios are somewhat smaller, i.e., 2.5 and 1.8, respectively. Rich fuel/air mixtures exhibit similar trends, albeit with larger absolute values for this thickness ratio. Moreover, at stoichiometry, the flame thickness values computed via Eqs. ( 4), ( 5) and ( 6), i.e., δ L,T , δ L,B , and δ L,max , are respectively 0.058, 0.47, and 0.43 mm for methane/air and 0.051, 0.42, and 0.36 mm for propane air mixtures. This reasonable agreement between δ L,max and δ L,B is verified throughout the considered equivalence ratio range, which confirms that the latter is a good approximation to the former. Furthermore, Figs. 4a and4b indicate that the choice of flame thickness definition should exert a significant impact on the Damköhler number computed via Eq. ( 2), since δ L,T δ L,max . Indeed, Figs. 4c and4d clearly show that the critical Damköhler number computed using the flame thermal thickness is an order of magnitude larger than that resulting from the two other formulations. For example, stoichiometric methane and propane air mixtures exhibit Damköhler number values of 1.97 and 2.06, respectively, when δ L,max is used, whereas the values corresponding to δ T are 0.43 mm and 0.37 mm. Nevertheless, the overall trend with the mixture equivalence ratio is independent of the flame thickness definition. For instance, examining first the computed Da values using δ L,max as flame thickness definition, for methane mixtures, Fig. 4c shows that the Damköhler number is practically independent of the equivalence ratio for 0.7 ≤ φ ≤ 1.1, that is, Da ≈ 2.5, when δ L,max is chosen. However, for φ > 1.1, an increase in the Damköhler number with equivalence ratio is observed. Using the same thickness definition for undiluted propane mixtures, as seen in Fig. 4d, the Damköhler number decreases steadily from ≈ 4 to ≈ 0.2 with φ, to 0.7 ≤ φ ≤ 1.5. These results confirm early numerical results [START_REF] Kurdyumov | Flame flashback and propagation of premixed flames near a wall[END_REF], which indicated that the constant Da assumption should not be used to describe flame flashback. However, methane/air and propane/air mixtures exhibit increasing and decreasing Da trends with φ, respectively, which discussion is deferred to section 3.3

Equivalence ratio and CO 2 dilution influence

The results of the critical Damköhler number for mixtures of methane/air/-CO 2 and propane/air/CO 2 are presented in Fig. 5, which depicts the Da values as a function of the equivalence ratio, for several tube diameters. Since the three flame thickness definitions examined in section 3.1 yielded analogous trends, the one adopted here is δ L,max only. Note that in the absence of detailed chemical kinetics computational results, which could be the case for fuel mixtures for which the combustion chemistry is unknown, using δ L,B instead seems fair. Figure 5 shows that, for moderate CO 2 dilutions, the overall trends of Da with φ are identical to those seen in Fig. 4 for undiluted mixtures, i.e., for methane/air mixtures a moderate Da increase with φ is seen, whereas propane/air mixtures exhibit a corresponding decrease that spans over more than an order of magnitude. Since the adopted model uses the assumption that Da = δ p /δ L , this suggests that, for a given δ L , flame penetration distance is relatively larger in leaner propane/air mixtures, when compared to richer ones, which is agreement with the early findings discussed in section 2.1 [START_REF] Grumer | Temperature dependence of stability limits of burner flames[END_REF][START_REF] Dugger | Flame stability of preheated propane-air mixtures[END_REF]. Concerning now the higher CO 2 dilutions, as seen in Fig. 5a, methane mixtures exhibit a Da increase as CO 2 is added beyond 30 %. For example, in the D = 17 mm tube, for stoichiometric methane/air mixtures, the Damköhler number is close to 2 and for methane/air/30%CO 2 mixtures it is nearly 3. As may be seen in Fig. 5b propane mixtures have a similar behaviour with respect to CO 2 dilution. Indeed, a stoichiometric propane/air mixture characterised by a Damköhler number of the order of 2, whereas a stoichiometric mixture of propane/air/75 % CO 2 is of the order of 4. It should be stressed that, in the particular case of those highest fuel dilutions, and for the smallest tube diameters, the flame flashback is followed by a nearly immediate extinction, i.e., the flame does not sustain stable propagation throughout the tube length. In this sense, these particular conditions do not strictly represent the flame flashback phenomenon. Thus, if those flame extinction results are discarded, Fig. 5 indicates that the critical Da value is independent of the tube diameter regardless the CO 2 dilution considered. As a consequence, for a given equivalence ratioand thus a Damköhler number -regardless the dilution by CO 2 , the flashback bulk velocity is such that Ū ∝ DS 0 L /(8δ L,max ). In order to further quantify the CO 2 dilution effect, Tab. 2 reports the critical Damköhler number values for stoichiometric fuel/air mixtures and the different dilutions used. The overall Da increasing trend with CO 2 fuel dilution is clearly seen. For instance, for methane and propane mixtures the critical Da value increases by 40% and 67%, when the respective dilutions are 30% and 75%. Note that the empty boxes in this table are dilutions for experiments have not been performed. number behaviour as a function of equivalence ratio is a classical one, tending to the value of the limiting reactant for very lean or very rich mixtures. Concerning fuel-rich mixtures first, the increase of CO 2 dilution in the fuel leads to a decrease of the effective Lewis number for methane mixtures, whereas an increase is observed for propane mixtures; these tendencies are related to the Le 2 values in Tab. 1. However, dilution by CO 2 exerts a less pronounced negligible influence on the effective Lewis number of lean propane mixtures, which is associated to the Le 1 values given in Tab. 1. Figure 7 depicts the critical Damköhler number as a function of the effective Lewis number for the different mixtures studied. The present results are shown as symbols, whereas the lines represent those of previous numerical studies [START_REF] Kurdyumov | Experimental and numerical study of premixed flame flashback[END_REF]. Again, each symbol represents a tube diameter, whereas the colours stand for different fuel dilutions by CO 2 . It is important to stress that these solid and dashed lines represent limiting cases of isothermal (300 K) and adiabatic boundary conditions at the tube wall, respectively, and that the Zel'dovich number used in the depicted computational results is β = 10 [START_REF] Kurdyumov | Experimental and numerical study of premixed flame flashback[END_REF]. Note that these computational results used Eq. (3) to define the Damköhler number. Therefore, in order to provide for a fair comparison with the present experimental values, these computed Da values were corrected using δ L,T /δ L,B = 1/7.55 from Eqs. ( 4) and [START_REF] Lewis | Stability and structure of burner flames[END_REF]. These computational results clearly show that the flame flashback Da increases with the Lewis number and decreases when the tube wall approaches an adiabatic condition: for instance, at stochiometry the computed Da is close to 12 when the tube wall is assumed to be isothermal, and ≈ .21 when an adiabatic surface is prescribed. The actual thermal boundary conditions prevailing at the experiments should lie between those limiting situations.

An increasing trend of Da(Le) was also observed in the present study for propane/air flames results, as may be verified in Fig. 7b, which closely follow the adiabatic boundary tendency, with the notable exception of those flashback cases that lead to flame extinction (solid symbols) -that are characterised by larger critical Damköhler number values. Indeed, within the range of the current measured data, the following correlation holds:

Da ∝ Le , with = 5.06, (12)
which may be compared with a previously determined value of = 1.68 [START_REF] Kalantari | Flashback propensity of turbulent hydrogen-air jet flames at gas turbine premixer conditions[END_REF] for turbulent hydrogen/air flames. Notice that close to the tube wall, near the flame base, non-unity Lewis number effects should influence the flame speed and thickness, which values could be different than those given by 1D planar freely propagating simulations. The critical Damköhler number correlation determined thus inherently incorporates such effect. Unfortunately the experimental techniques used do not permit to isolate curvature or stretch effects on Da, which can be done in detailed numerical simulations [START_REF] Howarth | An empirical characteristic scaling model for freely-propagating lean premixed hydrogen flames[END_REF][START_REF] Berger | Intrinsic instabilities in premixed hydrogen flames: Parametric variation of pressure, equivalence ratio, and temperature. part 1 -dispersion relations in the linear regime[END_REF][START_REF] Berger | Intrinsic instabilities in premixed hydrogen flames: parametric variation of pressure, equivalence ratio, and temperature. part 2 -non-linear regime and flame speed enhancement[END_REF].

The observed methane/air mixtures behaviour seen in Fig. 7a could seem, at first, to contradict that of the propane/air mixtures. However, for these mixtures, which are characterised by a rather small Lewis number variation, the effect dominating the critical Da seems to be that of the thermal boundary condition at the tube wall. Indeed, when using this (Le, Da) representation, Fig. 7a results indicates that smaller tube diameters tend to lead to larger Da values, which was not readily apparent in Fig. 5a, which used a (φ, Da) depiction. For these smaller tubes, the ratio between the quenched mixture region and flame surface area could be expected to increase, thus influencing the flashback conditions. These results underscore the need to include, in the Da model, a Péclet number, which could be modelled as [START_REF] Boust | A thermal formulation for single-wall quenching of transient laminar flames[END_REF] P e = δ q /δ L = 1/ϕ-1, where the quenching distance, δ q , is schematically shown in Fig. 1, and ϕ is the ratio between the measured flame heat transfer to the wall and the flame heat release. Developing a flame flashback model that accounts for flame quenching by the wall -via a Péclet number -should lead to better predictions, since it would involve the length scale corresponding to the quenching phenomenon which length scale (δ q ), as shown in Fig. 1, may be expected to be different from that of the flashback (δ p ). However, the present experimental apparatus does not enable a direct measurement of the former, and thus of ϕ. Therefore the development of a more general correlation, i.e, Da(Le, P e) is out of reach of the present endeavour. Another interesting avenue for such a development could be the use of artificial neural networks to avoid systematic measurements of the tube tip thermal boundary conditions [START_REF] Leask | Neural network prediction of boundary layer flashback[END_REF].

Conclusion

The critical Damköhler number for flame flashback to occur in CH 4 and C 3 H 8 mixtures was determined as a function of the fuel, the equivalence ratio and CO 2 dilution. To this end, measured flashback critical velocity gradient data, which provides a fluid time scale, was combined with detailed chemical kinetics simulation results of laminar one-dimensional, freely propagating premixed flames. These computations enabled to define the flame characteristic time scale using, together with the laminar flame speed, three different flame thickness definitions, i.e., (i) the classical thermal thickness, (ii) that based on the maximum temperature gradient, and (iii) one that corrects for temperature dependence of the thermal diffusion coefficient in (i) and thus approximates (ii). These length scales led to critical Damköhler numbers that exhibit a similar trend with equivalence ratio, but which value is nearly an order of magnitude larger when (i) is used. The critical Damköhler number definition eventually adopted is that based on the maximum temperature gradient, which has the advantage of accounting for detailed chemistry and transport formulations.

Methane/air/CO 2 flames exhibited an increasing Damköhler number with equivalence ratio. On the other hand, propane/air/CO 2 flashback is characterised by almost a two order of magnitude Damköhler number decrease as the equivalence ratio goes from 0.7 to 1.6. For both mixtures, CO 2 dilution results Flame flashback critical Damköhler number in a Damköhler number increase when flashback leads to flame extinction within the tube only.

The Lewis number influence on the critical Damköhler number of propane mixtures was found to follow existing numerical simulation results trends, leading to a Da ∝ Le 5.06 dependency. This good agreement between the present results and those numerical simulations suggest that the critical Damköhler number defined using the temperature gradient flame thickness is more suitable than the one that uses the thermal thickness. On the contrary, methane mixtures results showed a lesser sensitivity to Lewis number variations -which are rather small -but a seemingly larger one to tube diameter. Indeed, smaller tube diameters led to larger critical Damköhler number values, approaching those of the constant tube temperature simulations, which could be related to the thermal boundary conditions at the wall, that were not characterised in this study. Such a result indicates that the quenching region near the flame wall should be accounted for in a more general Damköhler number model, which could use a Péclet number, for instance.

Acknowledgments

This work was performed while L.F. Figueira da Silva was on leave from the Institut Pprime (UPR 3346 CNRS, France). This work was supported by Petrobras contract no. 5900.0111688.19.9 under the technical monitoring of Dr. P. R. Pagot. Support was also received from Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq, Brazil) under the Research Grant No. 304444/2018-9. This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior -Brasil (CAPES) -Finance Code 001.

Ethical statement

Fig. 1 :

 1 Fig. 1: Schematic model of the interaction between flame and boundary layer that leads to the concept of the critical velocity gradient. Velocity profiles of the laminar flow and flame front under the flashback condition.

Fig. 2 :

 2 Fig. 2: Experimental apparatus scheme, showing the fuel (CH 4 or propane), air, and CO 2 mass flow controllers, mixing tubes, vertical quartz tube, and flame position prior to flashback.

Fig. 3 :

 3 Fig. 3: Inverse of the flame characteristic chemical time scale S 0L /δ L,max obtained for undiluted mixtures as a function of equivalence ratio. Comparison between chemical kinetic mechanism: GRI 3.0[START_REF] Smith | GRI-Mech 3.0[END_REF] (solid line), San Diego Mech[START_REF]Chemical-Kinetic Mechanisms for Combustion Applications, San Diego Mechanism web page[END_REF] (dashed line) and USC II Mech[START_REF] Wang | USC Mech Version II. High-Temperature Combustion Reaction Model of H2/CO/C1-C4 Compounds[END_REF] (doted line).

Fig. 4 :

 4 Fig. 4: Flame thickness and Damköhler number as a function of the equivalence ratio for undiluted fuel/air mixtures, δ L,T : blue, δ L,B : red, δ L,max : black. The symbols correspond to different tube diameters, i.e., D = 4 ( ), 5 ( ), 6 (•) and 17 ( ) mm.

Fig. 5 :

 5 Fig. 5: Flashback Damköhler number for methane and propane/air flames diluted with CO 2 as a function of the equivalence ratio for mixtures in tubes of D = 4 ( ), 5 ( ), 6 (•) and 17 ( ) mm. The symbols colours are organised such as: black -undiluted, green -10 %, yellow -15 %, red -25 %, blue -30 %, cyan -50 % and magenta -75 %. The filled symbols represent the highest dilution percentage.

Fig. 6 :

 6 Fig.6: Computed effective Lewis number as a function of the mixture equivalence ratio for different CO 2 dilutions in the studied fuels. The symbols colours are organised such as: black -undiluted, red -25 %, cyan -50 % and magenta -75 %.

Fig. 7 :

 7 Fig.7: Flashback Damköhler number for methane and propane/air flames diluted with CO 2 as a function of the effective Lewis number for mixtures in tubes of D = 4 ( ), 5 ( ), 6 (•) and 17 ( ) mm. The symbols colors are organized such as: black -undiluted, green -10 %, yellow -15 %, red -25 %, blue -30 %, cyan -50 % and magenta -75 %. The filled symbols represent the highest dilution percentages. The lines correspond to the previously computed results[START_REF] Kurdyumov | Experimental and numerical study of premixed flame flashback[END_REF]: dashed -adiabatic, solid -isothermal (300 K) tube wall.

Table 1 :

 1 Lewis number values for fuel lean (φ → 0) and rich (φ → ∞) mixtures, noted (Le 1 , Le 2 ), for different CO 2 (%) dilutions.

			CO 2 (%) in fuel
		0	25	50	75
	Methane/air (0.997, 1.09) (0.997, 1.01) (0.997, 0.92)	-
	Propane/air	(1.93, 0.82)	(1.93, 0.85)	(1.93, 0.97)	(1.93, 1.14)

Table 2 :

 2 Damköhler number values for stoichiometric fuel/air mixtures and different fuel dilutions. Lewis number and CO 2 dilution influence In order to address the relation between the Lewis number and the critical flashback conditions, Fig. 6 depicts the effective Lewis number for the different combustible mixtures studied. This figure shows that the effective Lewis

					CO 2 in fuel
		0	10	15	25	30	50	75
	Methane 1.97 2.20	-	2.35 2.75	-	-
	Propane	2.06	-	2.41 2.42	-	2.56 3.45

•

  Funding: Maria Clara de Jesus Vieira received funding from Petroleo Brasileiro SA (grant 5900.0111688.19.9) and from Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Finance Code 001. Luis Fernando Figueira da Silva received funding from Petroleo Brasileiro SA (grant 5900.0111688.19.9), from Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Finance Code 001 and from Conselho Nacional de Desenvolvimento Científico e Tecnológico, (grant 304444/2018-9). • Conflict of Interest: The authors have no competing interests to declare that are relevant to the content of this article. • Ethical approval: not applicable. • Informed consent: not applicable. • Author contribution: All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Maria Clara de Jesus Vieira and Luis Fernando Figueira da Silva. The first draft of the manuscript was written by Luis Fernando Figueira da Silva and Maria Clara de Jesus Vieira, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.


H Porthault

G Piana

J M Duffault

S Franger

Influence of Ionic Interactions on Lithium Diffusion Properties in Ionic Liquid-Based Gel Polymer Electrolytes

Keywords: Lithium metal batteries, Gel polymer electrolytes, photo-initiated reticulation, ionic liquids, lithium transport

In this study, we characterize a ternary gel polymer electrolyte (GPE) composed of bisphenol A ethoxylate dimethacrylate (BEMA) and N-propyl-N-methylpyrrolidinium bis(trifluoromethanesulfonyl)imide (PYR13TFSI) ionic liquid and we particularly study the influence of salt content and polymer network composition. The effect of salt concentration in liquid solutions (1-x)Pyr13TFSI-xLiTFSI (molar ratio R = x/(1-x)) is finely characterized by Arrhenius measurements, PFG-NMR and Raman spectroscopy. They highlight ions interactions evolution with the salt content. For lower salt concentrations, ions pairs with bidentate coordinations [Li(TFSI)2] -are preferentially formed. A salt content rise leads to the formation of ionic aggregates where several Li + are bound by TFSI -to form [Liz(TFSI)y] (z-y)

large clusters. These ionic arrangements changes modify the mean charge of the complexes involving Li. It leads to better cycling performances with higher salt concentration contrary to the ionic conductivity evolution. When the binary solution is added to the GPE, a dual transport mechanism, by diffusion in the liquid phase and hops assisted by segmental

Introduction

The internet of things (IOT) is experiencing a huge development since the 2000s. New objects emerged in everyday life applications like wearables for healthcare or fashion (medical ships, functionalized clothing, etc.) and securing of personal data (secured smart cards, etc.). These applications require new needs like high temperature ability to be compatible with smart cards selling process, flexibility to be mechanically compliant for wearables applications, limited thickness (< 500 µm) to be easily integrated etc. However, the main aspect remains the safety from a physiological aspect for healthcare applications (low toxicity, bio-compatibility, etc.) and a physicochemical feature (low flammability, no leakage concerns, etc.) [1][START_REF] Zopf | CHAPTER 14 Wearable Energy Storage Based on Ionic Liquid Gels, in Polymerized Ionic Liquids[END_REF][3]. Many studies are then carried out to substitute the classical liquid electrolyte with a solid one. Considering the flexibility and mechanical requirements of these new applications, solid polymer electrolytes (SPE) [4] or ceramic electrolytes [5] cannot be considered. Gel polymer electrolytes (GPE), where a solvent and/or a liquid plasticizer is incorporated into the polymer network-salt system, turns out to be a good alternative material [6][7][8][9]. This concept is developed from the 1975 by Feuillade et al [10] and applications in lithium ion batteries are reported since the 1990s by Tarascon et al [11] with solid polymer matrixes encompassing solution of carbonates (EC:DMC) and LiPF6 salt.

The use of unstable liquids reduces the safety beside the SPE. Hence, since the 2000s, many teams added ionic liquids as solvent due to their high thermal stability and low vapor pressure [12][13][14]. Main ionic liquids reported in the literature as electrolytes are initially based on imidazolium cations because of their high conductivity and low viscosity.

Nevertheless, quaternary ammonium, like pyrrolidinium or piperidinium, are now widely used due to their higher electrochemical stability and compatibility with Li metal anodes [15]. Furthermore, in addition to the smart choice of the ionic liquid, the lithium salt also has a main influence on the battery performance as it insures the lithium ionic conductivity. The almost exclusively salt used in commercial Li-ion batteries is the lithium hexafluorophosphate LiPF6 that exhibits high ionic conductivity, good electrochemical stability and prevents the corrosion of the aluminum current collector. However, its high moisture sensitivity (forming HF) and low thermal stability (< 55 °C) make it not consistent with new applications. More promising salts are currently developed to substitute LiPF6 and among them, lithium bis(trifluoromethanesulfonyl)imide LiTFSI and lithium bis(florosulfonyl)imide LiFSI seem to be the best candidates. TFSI -anion is chosen in this study regarding its better thermal stability despite its lower conductivity [15]. Nevertheless, salt concentration also greatly influences performances. Hence, even if low salt concentrations are considered favorable for many years (higher conductivity at low temperature related to lower viscosity) [16,17], increasing number of studies report positive impact of higher salt concentration [18], going up to ''superconcentrated electrolyte'' [19], namely concentrations higher than 3 mol L -1 . The choice of the polymer matrix containing the liquid solution is also essential. In many works, GPE is formed by solvent evaporation.

The polymer chains (typically linear PEO or PVDF compounds) are linked by weak Van der Waals and hydrogen bonds [6]. It results in low mechanical properties particularly for samples with high liquid proportion. On the other hand, a crosslinked host polymer creates a chemical gel with the formation of strong covalent bonds. It leads to higher mechanical properties and better liquid retention [20]. Crosslinking can be achieved by thermal curing [21,22] or photo-initiated processes [23][24][25][26][27][28][29]. The structure of the polymer network plays an important role on the electrochemical performances and some groups tune the transport properties by mixing different polymers for example by adding pending linear chains [30].

In a previous work [31], we have already reported on the influence of the UV-curing on the electrochemical properties. In the present work, we focus on the effect of the salt concentration, mainly in high concentration range ( ≥ 1 mol L -1 ), and the polymer network composition on the GPE properties. A special interest is dedicated to the influence of ionic interactions in the binary solution (lithium salt and ionic liquid) and between the liquid phase and the polymer network. This results in an optimization strategy by linear polymer addition.

Experimental

Materials and samples preparation

Bisphenol A ethoxylate dimethacrylate (BEMA, Mn~1700, EO/phenol 15), Darocur® 1173 (97 %), poly(ethylene glycol) methyl ether methacrylate (me-PEGMA, Mn~500), and bis(trifluoromethane)sulfonimide lithium salt (LiTFSI, 99.95 %) are purchased from Sigma Aldrich. N-propyl-N-methylpyrrolidinium bis(trifluoromethanesulfonyl)imide (PYR13TFSI, 99.9 %) is purchased from Solvionic (Figure 1). The binary solution composing the GPE is defined as (1-x) Pyr13TFSI : x LiTFSI where x is the molar content of LiTFSI and R, the molar ratio, is defined in eq.1. The corresponding values in mol L -1 are given in supporting file, Table S1.

(eq.1)

The GPE electrolyte is composed of this binary liquid solution with various R and BEMA as host polymer in an initial 70:30 wt % ratio. The synthesis procedure is the same than the one described in our previous study [31] and is reminded in the supporting file. The influence of the UV-curing parameters being described previously [31], the curing conditions are fixed here at 3 min at 3 mW cm -2 . Depending on the characterization, GPE membrane can be selfstanding or directly realized on a substrate as shown in Figure 2a andb.

Characterizations

Thermogravimetric (TGA) and Differential Scanning Calorimetric (DSC) analyses are carried out using a Q500 Model (TA Instruments). For TGA, samples are heated at 5 °C min -1 up to 600 °C under argon atmosphere. For DSC analyses, samples are at first cooled down to -40 °C and then heated up to 150 °C at 10 °C min -1 under nitrogen atmosphere.

Mechanical properties are determined using Dynamic Mechanical Analysis (DMA) under shearing (Dynatest Metravib VA 2000 instrument) as previously described [31] and reminded in supporting file. Measurements are carried out with a dynamic displacement of 5 µm at 0.1 Hz frequency between -120 °C and 150 °C with a temperature control of 2 °C min -1 .

Viscosity determination is done under shearing stress using a Bohlin CVO rheometer (Malvern) with a plan-cone configuration. Values are determined at 25 °C with a shearing rate of 100 s -1 (150 µm gap).

Electrochemical Impedance Spectroscopy (EIS) is used to determine ionic conductivity (Biologic VMP3, 100 mHz-1 MHz, 10 mV) in a symmetric Pt-Pt Biologic HTCC-conductivity cell (k = 1.0 cm -1 ) for both liquid binary solutions and GPE. For the GPE study, the liquid precursors solution is put in the conductivity cell glass vial, electrodes are dipped into the solution and the cell is closed under argon atmosphere. The solution is then directly UVpolymerized through the glass. The electrolyte resistance is considered to be the high frequency one, assuming that the connection resistances are negligible. Arrhenius measurements are then carried out between 25 and 80 °C (298-353 K).

Considering the high ionic liquid content media, the most popular Bruce & Vincent or

Watanabe electrochemical techniques [32][33][34][35] to determine the Li transference number, where the assumptions are for dilute solutions, are hardly applicable. Therefore, in this work, as it was done in our previous study, we chose to evaluate the transference number by PFG-NMR technique from the diffusion coefficients determination ( [31,36], supporting file). As a reminder, this technique takes into account all mobile species, including those that do not contribute to the current transport, leading to a slight overestimation of the TLi value.

Raman spectroscopy is carried out using a Renishaw inVia equipment with a 785 nm laser in the 200-1800 cm -1 range. For binary solutions, spectra are normalized in regards to the 1240 cm -1 peak assigned to the TFSI --CF3 group which is not affected by ionic interactions [37].

The focus is then done on the 700-800 cm -1 area.

Cycling performance are evaluated using CR2032 coin cells sealed under argon. To avoid limitation by the electrode (porosity soaking, composition influence, etc.), we chose to work on a ''model'' electrode material. Currently, there is many various cathodic materials, mainly intercalation ones like LiCoO2 or the high voltage LiNixMnyCozO2 group [3,38]. In this paper, we choose to test our GPE with the well-known LiCoO2 cathodic material. The positive electrode is thus a pure LiCoO2 material deposited by sputtering process on titanium foil substrate. The deposit thickness is about 1 µm and the material is thermally treated for 2h at 600°C to obtain the desired R-3m phase [39]. 16 mm diameter discs are then cut to obtain cathodes (S = 2.01 cm²). The capacity observed with standard liquid electrolyte (EC:PC:DMC 1:1:3 1 M LiPF6) is 65.6 µAh cm -2 or 130 mAh g -1 . 16.5 mm discs of Whatman GF/A are used as glass fiber separator for tests with liquid binary solution. For cycling with gel polymer electrolyte, a Celgard 2400 ring (14 mm internal diameter) is used as shim (18 µm thickness) instead of the Whatman separator, the active surface is then 1.54 cm². 20 µL of liquid GPE precursor solution are deposited on the cathode material by drop casting and directly cured by UV-irradiation process. The system is then put into the CR2032 coin cell with Li metal foil (Albemarle, 135 µm) as anode. The electrochemical stability window of a GPE with a molar ratio R of 0.3 is 1.5-4.25V vs Li + /Li considering a degradation current density lower than 2 µA cm -2 (Supporting file, Figure S2). This anodic stability enable the galvanostatic cycling between 3.0 and 4.2 V vs Li + /Li done at 25 °C under various current (from 15 to 60 µA).

Results and Discussion

Influence of the salt content in liquid binary solutions

DSC thermograms (Supporting file Figure S3) of the neat Pyr13TFSI exhibits an endothermic melting peak at 13.30 °C, close to the value reported in the literature (10 °C [40]). When the Li salt is added, two endothermic peaks appear at 3.47 °C and 18.79 °C showing two distinct transitions characteristic of a solid solution. This result is consistent with the phase diagram of the LiTFSI-Pyr13TFSI system reported in the literature [41]. According to this phase diagram, this solid solution is liquid at 25 °C up to x = 0.33 (R=0.5). However, the solution is visually still liquid up to x = 0.375 (R = 0.6) at 25 °C and becomes solid around 20 °C. This concentration is then considered in this study as the maximum quantity of salt dissolved in the ionic liquid.

The solution viscosity (Figure 3a) increases exponentially with the salt content. As expected, the ionic conductivity at 25 °C (Figure 3a) decreases with salt content inversely to the viscosity, from 4.12 to 0.25 mS cm -1 for R = 0 and 0.6 respectively. The Walden plot (Figure 3b) exhibits a linear evolution of log Λm (the molar conductivity in S cm 2 mol -1 ) vs log (1/η) (the viscosity in P). The curve is slightly below the ideal one obtained with a liquid KCl solution (black line). MacFarlane et al [42] reported the same tendency for the neat ionic liquid (Pyr13TFSI, pink line reported in the insert). This deviation from the Walden rule (Λmη= constant) is attributed to ionic associations, mainly the strong Li + -TFSI -interactions occurring in this system as previously reported by Giffin et al [43]. This leads to an increase of the solution viscosity and its glass transition temperature. The Arrhenius plots of these compositions are shown in Figure 3c. The ionic conductivity increases with temperature due to the viscosity decrease. Measurements cannot be done below 25 °C for R = 0.6 due to the liquid to solid-like conversion of the system leading to a very high resistance. For the R = 0.3 solution, a slope discontinuity is observed between 15 °C and 20 °C also due to the liquid to solid transition as observed in DSC thermograms with a melting temperature of 18.8 °C.

Above these transition temperatures, the evolution of the conductivity curves can be fitted by the Vogel-Tammann-Fulcher (VTF) equation [44,45] with good correlation parameters (R² > 0.999) (Table 1):

√ • ( ) (eq.2)
With A (S cm -1 K -1/2 ) a pre-factor correlated to the charge carriers numbers, B (J) the pseudoactivation energy, T0 (K) the theoretical glass transition temperature Tg and kB the Boltzmann constant (1.3806 J K -1 ). Used for ionic liquids or polymer electrolytes, this model assume that species motion is governed by the free volume redistribution and not the thermal activation.

The temperature rise leads to the material expansion and the free volume increase. The B constant is called ''pseudo-activation energy'' since it is not really related to an activation mechanism but depends on the species motion resulting from the free volume ordering. This parameter is inversely proportional to the liquid fragility index m, directly related to the ionic conductivity and depending on the liquid ionicity and the anion size. Sippel et al [46] showed that highest ionic conductivities are achieved by liquids combining low glass temperature and high fragility index, thus low pseudo-activation energy B. This B parameter is low for studied solutions (Table 1) and values are close to the toluene one (1/m ~ 5.6 [47]) which means that solutions can be considered as a fragile material. B parameter increases with salt content meaning that required energy for species motion rises, which is in good accordance with the viscosity evolution. In this VTF model, the theoretical glass transition temperature T0 represents an ideal temperature from which polymer chains of the system start to be mobile. This T0 is systematically lower than the glass transition temperature Tg and the approximation T0 = Tg -50 K is usually used [48,[START_REF] Bresser | Molecular Systems Design & Engineering[END_REF]. This T0 parameter increases with molar ratios R meaning that species are less mobile. For R = 0, the calculated T*g temperature is -53.6 °C. This value is hard to compare to the literature considering that besides MacFarlane et al. [START_REF] Macfarlane | [END_REF] who reported a Tg of about -90 °C, most of other groups [51,52] do not detect any glass transition for the neat Pyr13TFSI. However, the reported experimental Tg values for others alkyl pyrrolidinium chains [52,53] seems to be lower than T*g calculated in our study but its evolution (increase with salt content) is the same [54]. When the lithium salt is added, the A parameter, referring to charge carriers number, slightly decreases with salt molar ratio.

This decrease is attributed to the viscosity increase and is probably amplified by the formation of neutral ion pair associations or ionic complex [Li(TFSI)n+1] n-limiting the number of charge carriers [48,54]. To elucidate the contribution of each ion to the global conductivity, NMR spectroscopy is conducted on the three nuclei 1 H, 7 Li and 19 F. The salt molar ratio increase induces a peaks broadening on NMR spectra (not shown here) reflecting the restriction of molecules mobility which is consistent with viscosity increase. Likewise, all diffusion coefficients of each nucleus, measured by PFG-NMR spectroscopy and reported in Figure3a, decrease with salt content.

In all tested samples, the Pyr13 molecules diffuse faster than TFSI and Li is consistently slower than both of them: > ≫ !" . This result is in good accordance with the literature [41,55] but not consistent with the Stokes-Einstein diffusion law prescribing that smaller particles diffuse faster. As NMR technique detects the nucleus signal, there is no distinction between ions and neutral species. Therefore, measured diffusion coefficients represent an average value of ions and its complexes. This low diffusion coefficient of lithium can then be attributed to the strong interactions with TFSI -anions creating large [Li(TFSI)n+1] n-complexes as previously suggested by VTF results. The Li transference number (inset Figure 4a) increases with LiTFSI molar ratio while TH and TF slowly decrease. The TLi transference number and the total ionic conductivity allow the determination of the apparent lithium conductivity (Figure 4b), that gives an approximation of the current fraction that would be transported by lithium species under an electrical field. Consequently, it is possible to calculate an apparent lithium conductivity, slightly overestimated as it takes into account ionic complexes and neutral species. Interestingly, the lithium conductivity exhibits a bell shape evolution with a maximum around R = 0.25. Beyond this salt content, the viscosity increase becomes the limiting phenomenon and lithium species are less mobile. A theoretical conductivity can be calculated though the Nernst-Einstein equation assuming that ion activity is equal to 1 without ionic associations (eq.3). For each ion, the charge is equal to 1 (Pyr13 +1 , TFSI -1 and Li +1 ), the conductivity can then be expressed as follows:

" ² % " & " ' " ( (eq.3)

)*% ∑ " , % - & + & + !" & !" / (eq.4)
As previously stated, the calculated conductivity (eq.4, Figure 4c), taking into account all species, is always higher than the experimental one and therefore, it is possible to define a degree of ionic association, estimating the neutral species ratio: (eq.5)

∆ )*% 1 -
For the neat PYR13TFSI, the association degree is 24 %, which means that 76 % of ions are dissociated (Figure 4c). When the molar ratio increases (up to 0.25), the association degree slightly decreases indicating that Li-TFSI interactions are stronger than PYR13-TFSI ones.

When the salt content is higher, the presence of neutral complexes rises. This trend is in good accordance with results reported by Nicotera et al [41].

Figure 4: NMR diffusion coefficients of each nuclei for various binary solutions with the associated transference numbers (inset) (a); evolution of the total and lithium ionic conductivity for various LiTFSI molar ratios (b), evolution of the experimental and NMR calculated ionic conductivities and derived association degree for various R molar salt ratios at 25 °C (c) (dash lines for eye guidance only).

The interactions between TFSI -and Li + can be deeper characterized by Raman spectroscopy [56]. All spectrum are normalized in regards to the peak of the -CF3 vibrational stretching mode around 1240 cm -1 which is not modified by ionic interactions [37]. The more intense Raman signal is localized in the 800-700 cm -1 range due to the overall TFSI -expansioncontraction. It is then usually studied to investigate the lithium solvation in ionic liquid. TFSI - anion presents two conformers (C1 cisoid cis and C2 transoid trans) but the high conformal flexibility leads to a small energy barrier (< 3.5 kJ mol -1 ) [57,58] only detectable in the gas state (peak splitting < 3 cm -1 ). In the liquid state, this conformal effect only leads to the broadening of the most intense peak at 740-742 cm -1 , sum of C1 and C2 contributions [59].

Moreover, the negative charge of TFSI -is highly delocalized leading to a weak coordination ability with Pyr13 + cation [57] already noticed with NMR spectroscopy. Hence, both dissociated and poorly coordinated TFSI -thereafter to ''free'' TFSI -and are evidenced by the Raman peak around 741 cm -1 visible in the neat ionic liquid signal (R = 0, Figure 5a).

When the molar salt content increases, this peak intensity decreases and slightly drifts towards 743 cm -1 with the gradual appearance of a new mode around 748 cm -1 . This new mode, referring to the ''coordinated'' TFSI -, evidences the restrained expansion-contraction of anions coordinated with Li + . They are coordinated in tetrahedral geometry by four oxygen of the -SO2 groups of TFSI -molecules [60][61][62]. Raman spectra can then be convoluted with two functions (mix of Gaussian and Lorentzian) centered on 741 and 748 cm -1 corresponding to the ''free'' and ''coordinated'' TFSI -anions respectively (fit example for R = 0.6 in Figure 5a). The integration of fitted peaks allows to calculate the fractions of ''free'' and ''coordinated'' TFSI -(Figure 5b). In the neat ionic liquid, the association degree ∆NMR previously determined is about 24 % whereas less than 3 % are coordinated in Raman results. This difference is attributed to the weak interactions between TFSI -and PYR13 + , neglected in Raman calculations (hardly discriminating) and taking into account as neutral Pyr13TFSI species in the NMR association degree calculation. In binary solutions, when the salt content increases, the ''free'' TFSI -ratio decreases for the benefit of the ''coordinated'' TFSI -. A mean coordination number n can then be calculated describing the average number of TFSI -molecules coordinated with Li + cations. For the very low salt ratios (R < 0.1), n > 2 which means that Li are mainly part of anionic complexes with monodentates coordinations [Li(TFSI)4] 3-, each TFSI -providing one oxygen atom. When the molar ratio R increases, the mean coordination number n decreases due to the rise of bidentates complexes [Li(TFSI)2] - where each TFSI -provided two oxygen atoms. Above a critical molar ratio of 0.25, n seems to slightly rise again. This could be explained by the formation of aggregates network [Liz(TFSI)y] (z-y) where each Li shares several TFSI -with its Li neighbors though the O=S=O groups. These aggregates are reported to occur when the Li---Li distances are less than 5Å [59,63]. The modification of ionic arrangements is clearly evidenced in battery cycling results (Figure 6). Galvanostatic curve of mean salt content (R = 0.3, Figure 6a) at low current (15 µA) exhibits an initial polarization higher than those with standard electrolyte which leads to a lower initial discharge capacity (39 µAh cm -1 ie 60 % of the capacity obtained with standard liquid electrolyte). Cycling ability is improved when salt content increase, with few improvements beyond R = 0.4. The high current ability (Figure 6c) is clearly improved for the higher salt content (R = 0.6). These results are consistent with previous assumptions established from NMR and Raman spectroscopy. For the lower salt contents (R < 0.2), the mean coordination number (1 < n < 3) corresponds to complex charges between 0 and -2.

Above this concentration (R > 0.2), the total complex charge varies between 0 and -0.25. The absolute value is then lower which means that higher salt content are beneficial under an electric field. This trend is accentuated for higher currents that is clearly seen in Figure 6c.

Wang et al [64] observed the same trends and conclude to a reinforced 3D network of Li + coordinated with anions (FSA -in their study) whereas bidentate complexes and free solvent divide the solution in small size areas with the lower concentration. In all cases, it demonstrates that a lower ionic conductivity does not necessarily degrades the electrochemical performances and the rate capability.

Influence of the salt content in gel polymer electrolyte (GPE)

The binary solution is associated with a polymer to form the GPE. The initial GPE composition is 70 wt % of liquid binary solution and 30 wt % of BEMA polymer. For the salt content R = 0.3, the integration of the binary solution in the GPE leads to a decrease of about 52 % of the ionic conductivity (0.489 mS cm -1 for the GPE versus 0.93 mS cm -1 for the corresponding liquid binary solution). The Arrhenius plots (not shown here) exhibit a VFT behavior typical of amorphous materials. B and T0 parameters are higher than those of the binary solution are (7.12 kJ mol -1 and 190.3 °C) which evidences the confinement of the liquid phase and its interactions with the polymer. NMR measurements are done at 25 °C for the lower salt content while 60 °C are necessary for the higher salt content (R = 0.6) to be able to detect Li diffusion. When the salt ratio increases (Figure 7a), the diffusion coefficients of H and F decrease as expected due to the viscosity increase. This evolution is the same as the one reported in binary liquid (Figure 4a) evidencing the low interaction of the polymer network with the ionic liquid as reported by Sotta et al [21] for the percolating part of the liquid phase. By contrast, the diffusion coefficient of Li drastically decreases in the GPE. This drop is accentuated by the salt content increase up to 0.3. Beyond this concentration, the diffusion coefficient of Li remains quite stable while those of H and F continue to decrease.

This trend is more significant on the transference numbers evolution in Figure 7b. The transference number TH steadily decreases while the TF increases due to the increase of TFSI - concentration with salt content. On the contrary, the Li transference number sharply decreases up to R = 0.3 where it reaches a minimum before a slight increase for higher salt content. Considering the diffusion evolution of F and Li, we can assume that bellow R = 0.3, Li + are no more solvated by TFSI -as previously observed in binary solutions (Figure 4) and [Liz(TFSI)n] z-n complexes are dissociated in the presence of BEMA. This assumption is confirmed by Raman spectra (supporting file Figure S4) showing that the only remaining band corresponds to the ''free'' TFSI. In the case of GPE, Li + are complexed to PEO groups of BEMA polymer though about five oxygens forming a crown around the cation [65,66]. Li + transport mechanism is then a mix between hopping among complexation sites assisted by polymer segmental motion. In this type of amorphous material, segmental motion is strongly dependent of the system viscosity. Hence, a salt ratio increase induces an increase of the viscosity and thus limits the motion of lithium ions. Above 0.3, the viscosity still increases but lithium diffusion is stable. It shows that beyond a critical salt concentration, the transport mechanism is more complex. We can imagine that the majority of PEO complexation sites is occupied or the steric hindrance of PEO chains does not allow more complexation of added Li + . Hence, a part of Li + is no more solvated by PEO chains but remains as ionic complexes in the liquid phase. Li + ions can then move either by ionic migration among the liquid phase or by hops assisted by the PEO segmental motion. This assumption is strengthen by Raman spectra (supporting file Figure S4) where a slight shoulder around 742 cm -1 appears for the higher salt content. This phenomenon induces a slight increase of the Li transference number for the higher salt content. However, most of Li being solvated by PEO chains, we can imagine that ionic complexes with TFSI -will be preferentially monodendate forming [Li(TFSI)4] 3-with high negative charge. Galvanostatic cycling, presented in Figure 7c, shows that cycling ability is improved by increasing salt content. Cycling performance are poor for the lower salt contents (R < 0.2) and greatly improved above R = 0.3. This concentration corresponds with the slope change on the transference number evolution as reported above (Figure 7b). According to previous results and interpretations, cycling performances can be limited by restricted segmental motion, which limits Li transfer by hopping. When the salt content increases beyond R = 0.3, a part of the Li transport is ensured by ionic migration in the liquid phase which can explain the better cycling ability. Thus, the limiting factor appears to be the segmental motion of the polymer network. The explored strategy is to enhance segmental motion by introducing a linear polymer that decreases the crosslinking density of the polymer network. 19 F and 7 Li nuclei determined by NMR measurements at 25°C (solid lines) and 60°C (dash lines); Galvanostatic cycling at various currents for GPE integrating various salt content binary solutions (c).

Influence of the linear polymer content

The chosen linear polymer is a monomethacrylate, the polyethylene glycol methacylate (PEGMA). To avoid the stability limitation in reduction (~2.5V vs Li + /Li), -OH pending functions are replaced by methoxide groups (poly(ethylene glycol) methyl ether methacrylate (me-PEGMA)). The synthesis protocol is the same (70 wt% of liquid binary phase, 30 wt% of polymer) except that a proportion of BEMA is replaced by me-PEGMA which leads to a decrease of the ratio Li/(crosslinking points, CP). The number of crosslinking points CP is determined such as 1 mol of BEMA equals 2 mol of crosslinking points considering the two methacrylate functions and 1 mol of me-PEGMA corresponds to 1 mol of crosslinking points. Considering the previous results, the salt content is fixed at R = 0.6.

The addition of linear me-PEGMA directly affects the GPE mechanical properties. The theoretical crosslinking density of the polymer can be determined by the following equation [START_REF] Pascault | Thermosetting Polymers[END_REF]:

: ; < =% (eq.6)
Where νe is the crosslinking density (mol m -3 ), R the perfect gas constant (8.314 J mol -1 K -1 ) and T the temperature (K). Theoretical crosslinking density is close to the expected one, i.e.

2×[BEMA] considering the presence of two methacrylate functions per BEMA molecule. The Young's modulus decreases linearly with νe and thus with the BEMA concentration and me-PEGMA addition (Table 2). This lower mechanical strength comes with an increase of the ionic conductivity up to 0.26 mS cm -1 for the higher content (0.14 mS cm -1 without me-PEGMA). This value is close to the binary liquid solution one (Table 1).The diffusion coefficients of H and F (Figure 8a) slightly increase with me-PEGMA ratios but transference numbers (not shown here) remains quite constant. The increase of chain polymer mobility enhances the diffusion in the liquid phase illustrating the interpenetrated morphology of the GPE. The Li transport, assuming to be mostly provided by hops assisted by segmental motion, doubles with me-PEGMA addition. The increase is significant with 9 wt% me-PEGMA but remains quite limited with higher me-PEGMA content. This is consistent with previous results assuming a complex mechanism with hops assisted by segmental motion and ionic diffusion in the liquid phase. The addition of me-PEGMA increases segmental motion leading to a rise of Li diffusion. No obvious improvement is observed with higher me-PEGMA content considering that the limiting phenomenon is the viscosity of the binary solution, amplified by the high salt content R = 0.6. Considering the increase of the total ionic conductivity and the evolution of Li transference number, best cycling results are expected with the higher me-PEGMA content (15B-85P, 25.5 wt%). Galvanostatic cycling (Figure 8c) shows that polarization is lower with the addition of me-PEGMA. Discharge capacity values (Figure 8b) are quite similar for the lower current (< 15 µA) but high current ability is greatly improved with me-PEGMA addition. This result is in good accordance with previous measurements that show an increase of the Li conductivity with me-PEGMA content.

Conclusion

Pyr13TFSI and LiTFSI are chosen for their good thermal stability fitting with new emerging applications. When the salt content increases, the total ionic conductivity severely drops (up to -95 %) due to the large viscosity rise. NMR spectroscopy shows that apparent transference number of lithium is boosted by the salt addition with an optimum of Li conductivity around R = 0.3 (0.08 mS cm -1 ). The evolution of the dissociation ratio ∆NMR

shows that the quantity of neutral species increases (up to 60 %) with the salt content as also predicted by the evolution of the prefactor A in VTF fittings. By combining these results

with Raman spectroscopy, we can assume that for the lower salt concentration, monodentate complexes [Li(TFSI)4] 3-are formed. With salt addition, these complexes are converted into bidentate coordinated complexes [Li(TFSI)2] -with a low mean negative charge. With higher salt concentration, large clusters (Liz[TFSI]y) z-y , binding several Li together, are formed. These complexes and aggregates present mean negative charges that greatly influence cycling performances. Hence, monodentate complexes exhibit a high negative charge that seems to be detrimental for galvanostatic cycling. The increase of salt content, decreasing the mean charge of complexes involving Li, improves the cycling performances despite the ionic conductivity drop (60 % remaining discharge capacity at C).

The integration of binary solution in GPE generates an additional transport mechanism by hops assisted by segmental motion due to the Li coordination by oxygen of PEO chains.

When salt concentration increases, TLi is enhanced by adding migration in the liquid phase to hopping transport. This leads to a great improvement of electrochemical performances above R = 0.3. The addition of linear polymer (me-PEGMA) limits mechanical properties of the GPE but significantly improves ionic conductivity (close to the liquid one) by enhancing segmental motion. Hence, the Li transference number is multiplied by two and discharge capacity is close to 70 % of the theoretical one at 25 °C. This study showed that a deep understanding of ionic interactions can help putting forward further optimizations especially on the choice of components nature in electrolytes (acrylate functions substitution, cation choice, etc.).

Figure 1 :

 1 Figure 1: Chemical Structures of BEMA and me-PEGMA host polymer, Darocur1173 photo-initiator, Pyr13 + cation (with 1 H NMR assignments) and LiTFSI salt.

Figure 2 :

 2 Figure 2: Optical view of self-standing GPE membranes (a) and SEM cross section view of a GPE directly deposited and cured on a substrate (b).

Figure 3 :

 3 Figure 3: Ionic conductivity and viscosity measurements at 25 °C for various LiTFSI molar ratios (a), Walden plot (Pyr13TFSI reported from [42]) (b) and associated Arrhenius plots (c).

Figure 5 :

 5 Figure 5: Raman spectra of various salt content solutions in the 770-725 cm -1 range (a); coordinated or free TFSI -ratios and associated mean coordination numbers of various salt contents (pink dot lines for eye guidance only) (b).

Figure 6 :

 6 Figure 6: Galvanostatic curves for R = 0.3 and standard carbonates electrolyte LP100 at 15µA, 25°C (a), Galvanostatic cycling at 25 °C for various salt contents: at constant current (15µA) (b), and for various currents, 10 cycles of each current (c).

Figure 7 :

 7 Figure 7: Evolution of the diffusion coefficients (a) and apparent transference number (b) of 1 H, 19 F and 7 Li nuclei determined by NMR measurements at 25°C (solid lines) and 60°C (dash lines); Galvanostatic cycling at various currents for GPE integrating various salt content binary solutions (c).

Figure 8 :

 8 Figure 8: Evolution of the diffusion coefficients of H, F and Li and apparent transference number of Li at 60°C (a); Galvanostatic cycling of LiCoO2/GPE/Li coin cells integrating 100 wt% BEMA or 15-85 wt% BEMA:me-PEGMA polymer for various current at 25°C (b) and corresponding cycling curves (c).

Table 1 :

 1

	13

Ionic conductivity at 25°C, VTF fitting parameters and theoretical glass transition temperature T*g extrapolated from T0 values for each R molar ratio solution.

Table 2 :

 2 Various physico-chemical properties of GPE containing R = 0.6 PYR13TFSI-LiTFSI binary solution at 70 wt% and 30 wt% of polymer consisting of X wt% of BEMA and (1-X) wt% of me-PEGMA. B =BEMA, P= me-PEGMA, CP = crosslinking point.

Acknowledgements

The authors thank P.A. Bayle (Univ. Grenoble Alpes, CEA, INAC-MEM, LRM, MINATEC Campus) for helpful discussions and technical expertise on PFG-NMR measurements.

This study was founded through the EnSO European project. EnSO has been accepted for funding within the Electronic Components and Systems For European Leadership Joint Undertaking in collaboration with the European Union's H2020 Framework Program (H2020/2014-2020) and National Authorities, under grant agreement n° 692482.