Electrochemical storage and conversion devices are in urgent need nowadays for the exploitation of energy generated from alternative but fluctuating sources, like wind and sun, in particular for employing them in emerging electrified systems, such as transport vehicles or advanced technological devices. At the core of these energy materials, such as batteries or supercapacitors, is typically the electrode/electrolyte couple, which strongly impacts the performance of the devices. Super-concentrated aqueous solutions recently emerged as promising electrolytes for high-performance energy storage systems due to their unique physico-chemical properties. Indeed, they differ markedly from conventional aqueous electrolytes. By dissolving salt at high concentrations in water, in which either the weight or volume ratios of salt-to-water exceed 1, a new family of electrolytes is classified as "water-in-salt". It was demonstrated that these water-in-salt electrolytes exhibit high electrochemical stability windows ( 3-4 V) far beyond that of pure water (1.23 V), making it possible to achieve high-voltage performance in batteries and supercapacitors. However, comprehensive studies aiming at understanding the microscopic mechanisms at play in water-in-salt electrolytes and their properties at the interface are needed to fully exploit their properties.

In this thesis, we have performed molecular dynamics simulations to systemically investigate the transport and structural properties of lithium bis(trifluoromethane sulfonyl)imide (LiTFSI) salt/water mixtures ranging from the dilute solution to the water-in-salt regime and the interfacial properties of a water-in-salt electrolyte at an extremely high concentration in supercapacitors. The thesis is divided into 5 chapters:

Chapter 1 starts with a brief introduction of the state-of-the-art concentrated elec-9 10 CONTENTS trolytes, in particular, water-in-salts and their applications in batteries and supercapacitors. As a complement of experiments, molecular dynamics simulation studies of water-in-salt electrolytes are emphasized in the last part and the current research status is summarized, along with the presentation of the motivation and objective of this thesis at the end of this chapter.

Chapter 2 recalls the general principle of molecular dynamics, the basic algorithm and the common ensembles used in molecular dynamics simulations. The constant potential electrode model and its implementation in our simulations are briefly introduced, and the importance of accounting for the surface polarization is illustrated.

Chapter 3 is dedicated to the study of i) the transport properties of LiTFSI and water mixtures in a wide range of salt concentrations; and ii) the force field dependence of the transport properties at high concentrations. The viscosity, diffusion coefficients, and conductivity are computed and analyzed for various concentrations.

Different parameterizations of force field are compared, which allows us to select the best parameters for further studies of highly concentrated water-in-salt.

Chapter 4 focuses on the structural properties of the water-in-salt electrolyte. The solvation property of lithium cations, such as the coordination number, the residence time of water in lithium's hydration shell, the potential of mean force for water molecules or TFSI anions escaping solvation shell of lithium, and the fraction of free water not bound to any lithium are computed and analyzed. The role of water in the water-in-salt electrolyte is analyzed based on the molecules local structural environments.

Chapter 5 presents the study of a super-concentrated water-in-salt electrolyte at the planar interface. The capacitive performance of a supercapacitor consisting of planar graphite electrodes separated by water-in-salt electrolyte is investigated. The evolutions of the interfacial structure at various applied potentials are analyzed to account for the non-trivial features of differential capacitance.

The last section summarizes all aforementioned aspects of this thesis and proposes some perspectives of future work.

I have immense gratitude to everyone in my life who has helped me and contributed to my thesis during the last three years. It is my pleasure to be able to thank them here.

First and foremost, I am forever indebted to my PhD advisor, Mathieu Salanne, who guided me with his great patience and profound knowledge through my PhD period. I would like to express my deep gratitude to him for his assistance at the beginning of my arrival in France. I greatly appreciated his enthusiasm, constant support and encouragement during the last three years. I benefited enormously from him about how to do science and communicate it in an effective way. I have also learned a great deal from his philosophy and innovation in doing scientific research. I would like as well to sincerely thank Olivier Fontaine at Institut Charles Gerhardt Montpellier. I am very grateful to have been able to collaborate with him and his experimental group. Thanks for their contributions to my thesis. Special thanks to my lovely friends in Paris for their help and encouragement. I am very thankful to have these friends who enrich my life with great happiness.

Finally, and most importantly, I am supremely thankful to my parents, my sister and my twin nieces for their unconditional love, unwavering support and understanding.

Solvent-in-salts

Liquid electrolytes can be classified according to their ionic concentrations. Two main families are generally used in electrochemical devices. In conventional electrolytes, the major species is a neutral solvent and a few, highly solvated ions are present; seawater is an archetypal example. On the contrary, ionic liquids are solvent-free electrolytes that have gained more and more attraction for energy storage applications over the past decade [START_REF] Douglas R Macfarlane | Ionic liquids and their solid-state analogues as materials for energy generation and storage[END_REF]. However, they suffer from a rather large viscosity, which hinders their use at relatively low temperatures.

Recently, a third class of liquid electrolytes was proposed, in which the ionic species are dissolved in large amounts inside the solvent [2], these are called "solventin-salts". As shown in Figure 1-1, the weight and volume ratios of salt-to-solvent are used to classify liquid electrolytes. The region C (both the weight and volume ratio are less than 1) covers most of the studied non-aqueous organic-based electrolytes, in which the salt concentration is generally limited in a range of 1-2 mol/L due to the solubility of the salt and optimal balance between viscosity and ionic conductivity.

The increase of the salt concentration by choosing proper salt/solvent couple moves an electrolyte into the region A, B, and D in Figure 1-1, in which the concept of "solvent-in-salts" (SIS) is proposed and to denote highly concentrated electrolytes.

Moreover, when the ratio is infinite (i.e., absence of the solvent), it is in the region of the above mentioned ionic liquids.

The synthesis of SIS electrolytes requires to find salts with a good solubility, which is generally the case when they are made of organic ions. However, Suo et al.

showed that such concentrated electrolytes could also involve inorganic cations by using Li[(CF 3 SO 2 ) 2 N] (LiTFSI). Due to the very low lattice energy of this salt, it can be mixed up to very large amounts with organic solvents. This work was extended to a series of other salts and solvents , which opens the way to explore new electrolytes for energy storage systems.

Water-in-salts

Among the potential solvents, water can be an attractive one due to its various advantages, such as non-toxic, high dielectric constant, and non-flammability, however, it is often discarded in electrochemical energy storage applications because of its narrow 1.1. CONCENTRATED ELECTROLYTES 13 electrochemical stability window (ESW) of 1.23 V, which allows neither high voltages nor high energies to be reached. Recently, this limitation was overcome through the introduction of a "water-in-salt" (WiS) electrolyte [27], for which the window could be extended to ≈ 4.0 V [28]. Such an important breakthrough leads to the development of aqueous-based electrolytes for energy storage systems.

Figure 1-2: Illustration of enhanced electrochemical stability window (ESW) when switching from "salt-in-water" to "water-in-salt". Adapted from chargedevs.com Specifically, the first "water-in-salt" electrolyte was reported by Suo et al. in 2015, where LiTFSI is dissolved in water at extremely high salt concentration of 21 m (m = mol/kg) [27]. A high-voltage aqueous lithium-ion battery was enabled through the formation of the solid-electrolyte interphase (SEI) during the first cycles, which prevents the water molecules from undergoing irreversible redox reactions, as shown in Figure 1-2. Further study demonstrated that the anodic dissolution of aluminum was suppressed in such super-concentrated WiS electrolyte, enabling the use of cost-effective aluminum current collectors for WiS-based aqueous lithium-ion batteries [29]. Apart from the formation of the SEI, the significant decrease of "free" water (i.e., water molecules that remain uncoordinated by any lithium cations) at super-concentrated WiS electrolytes also hinders the hydrogen and oxygen evolution 1.1. CONCENTRATED ELECTROLYTES involved in water hydrolysis at positive and negative electrodes. In the original work, the amount of free water molecules remains more than 15% of all water molecules at most concentrated status (21 m).

Considering that the maximum solubility of LiTFSI in water is 21-22 m at room temperature, it is thus not possible to further decrease of the portion of free water molecules. To overcome this limit, two main strategies were proposed: Firstly, by adding a second lithium salt into WiS electrolytes [30], it was reported that the fraction of free water was reduced to 11%, which further enhanced the redox stability of the so-called "water-in-bisalt" electrolyte, and thus leads to impressive performance in aqueous Li-ion batteries. Secondly, hydrate-melt lithium salt was reported as a promising electrolyte for high energy density aqueous batteries [31]. In this work, an eutectic composition of Li(TFSI) 0.7 (BETI) 0.3 •2H 2 O (where BETI denotes CF 5 SO 2 ) 2 N anion) is regarded as a lithium salt hydrate-melt, in which all water molecules are coordinated by lithium cations, i.e., without any free water. The water activity is further reduced compared to that of "water-in-salt" or "water-in-bisalt" electrolytes.

Moreover, regarding the transport properties of WiS electrolytes, the ionic conductivity of 21 m LiTFSI remains 8.2 mS/cm at room-temperature [27], which is close to that of non-aqueous solutions (9 mS/cm) used in commercial lithium batteries.

For the hydrate-melt electrolyte [31], though the viscosity is high (≈ 200 mPa•s), the ionic conductivity (3 mS/cm) is still comparable to that of Li-salt-based non-aqueous electrolytes. Furthermore, on the basis of the Walden plot, where electrolytes can be classified in terms of their performance as ionic conductors [32,33], the WiS (21 m LiTFSI) and hydrate-melt (Li(TFSI) 0.7 (BETI) 0.3 •2H 2 O) electrolytes can be regarded as good-ionic and super-ionic solutions, respectively [31]. The unexpectedly good performance of ionic conductivity for super-concentrated aqueous electrolytes, which is decoupled from the viscosity, is attributed to the water molecules that accelerate the cation's diffusion. As reported by Borodin et al., for WiS electrolyte (21 m LiTFSI) the liquid adopts a nano-heterogeneous structure with a 3D percolating lithium water network that promotes the cationic transport [34].

APPLICATION OF WATER-IN-SALTS IN BATTERIES

Application of water-in-salts in batteries

In 1994, the first aqueous Li-ion battery was proposed by Dahn and co-workers, providing an average operating voltage window of 1.5 V [35]. Since then, numerous efforts have been devoted to developments of aqueous rechargeable batteries in order to replace the flammable organic electrolytes. Significant improvements have been reached in this intriguing area with new battery chemistries explored [36][37][38][39][40][41]. However, as shown in Figure 1-3, the ESW for traditional aqueous electrolytes remains below 2 V. It is mainly limited by the hydrogen evolution at the anode, which is far above where most anode materials of lithium-ion batteries operate. As we discussed in the previous section, the use of WiS electrolytes enables a significant increase of the ESW allowing to reach high-voltage aqueous lithium-ion batteries [27].

Figure 123: Illustration of the evolution of electrochemical stability window for aqueous electrolytes ranging from pure water to water-in-salt [27].

The successful applications of LiTFSI-based WiS electrolytes in batteries have attracted much attention since 2015, and numerous efforts have been made to expand the family of WiS electrolytes to other alkali metal-based (Li + , Na + , K + ) electrolytes [28-30, 42-48, 48-54], multivalent metal-based (Mg 2+ , Ca 2+ , Zn 2+ ) electrolytes [START_REF] Wang | High-Voltage Aqueous Magnesium Ion Batteries[END_REF][START_REF] Lee | Modulating the hydration number of calcium ions by varying the electrolyte concentration: Electrochemical performance in a Prussian blue electrode/aqueous electrolyte system for calcium-ion batteries[END_REF][START_REF] Zhang | Cation-Deficient Spinel ZnMn 2 O 4 Cathode in Zn(CF 3 SO 3 ) 2 Electrolyte for Rechargeable Aqueous Zn-Ion Battery[END_REF][START_REF] Hu | Zn/V2O5 Aqueous Hybrid-Ion Battery with High Voltage Platform and Long Cycle Life[END_REF][START_REF] Zhang | Rechargeable aqueous zinc-manganese dioxide batteries with high energy and power densities[END_REF][START_REF] Li | Advanced Low-Cost, High-Voltage, Long-Life Aqueous Hybrid Sodium/Zinc Batteries Enabled by a Dendrite-Free Zinc Anode and Concentrated Electrolyte[END_REF][START_REF] Zhi | Acrylonitrile copolymer/graphene skinned cathode for long cycle life rechargeable hybrid aqueous batteries at high-temperature[END_REF][START_REF] Wan | Aqueous rechargeable zinc/sodium vanadate batteries with enhanced performance from simultaneous insertion of dual carriers[END_REF][START_REF] Wang | Highly reversible zinc metal anode for aqueous batteries[END_REF], and even metal-free electrolytes containing NH + 4 cation [START_REF] Holoubek | Amorphous titanic acid electrode: its electrochemical storage of ammonium in a new water-in-salt electrolyte[END_REF]. It was demonstrated by Suo et al. that an alternative cathode material (LiFePO 4 )

APPLICATION OF WATER-IN-SALTS IN BATTERIES

with larger electrochemical stability than the usual LiMn 2 O 4 , has durability against a wide range of temperatures and superior performances, making it become a promising candidate for large-scale electric energy storage applications [42]. Apart from the application in lithium-ion batteries, WiS as an electrolyte for cathodically stable Li-O 2 battery operations was also reported very recently [45]. In Li-O 2 batteries, no reported organic electrolytes fulfill the stability requirements due to the high reactivity of oxygen in the system. However, the use of WiS electrolytes (21 m LiTFSI) without any organic solvents overcomes this limits. The WiS electrolyte, which has low water activity owing to the lack of free water, exhibits little reactivity towards Li 2 O 2 or other oxygen species, leading to the stable operations of Li-O 2 battery. Moreover, successive attempts aimed at exploring new Li-based WiS electrolytes have been reported, among them adding a second composition in water-in-LiTFSI solutions gained significant success. Inspired by the study of "water-in-bisalt" electrolyte containing 21 m LiTFSI and 7 m LiOTf (OTf = trifluoromethane sulfonate) [30], a hydrophilic polymer polyvinyl alcohol (PVA) was introduced into such electrolyte to form an aqueous gel [43]. It was reported that in this super-concentrated aqueous electrolyte, the unique sulfur chemistry involving a phase change from high-order polysulfide to low-order polysulfide experienced by the lithiation of sulfur was observed, leading to the application of WiS electrolytes for beyond Li-ion chemistry in Li-ion/sulfur cells with an excellent performance. Furthermore, the use of the same WiS-based gel polymer electrolyte, along with an extra protective SEI layer formed by pre-coating the graphite anode with a prepared gel, made it possible to achieve a 4 V class aqueous Li-ion battery, whose energy densities approach those of state-of-the-art Li-ion batteries but with significantly enhanced safety [28]. Similar electrolyte, where a homogeneous aqueous gel polymer formed at high temperature (95 • C) by dissolving 25 m LiTFSI and 10 wt% PVA in water, was prepared by Yang et al.. The reported superior energy (141 Wh kg -1 ) and power (20.6 kW kg -1 ) density, along with the flexible and robust electrodes in the symmetric cell, opens the way to manufacture lithium-ion batteries on the materials level.

The abundant and readily accessible features of sodium (Na) make it be inves- 2.5 V, owing to the formation of a Na + -conducting SEI along with the reduced water activity that prevents the hydrolysis reactions [50]. The combined analysis of Raman spectra and molecular dynamics simulations revealed that the frequent contacts between Na + and F from the anions accompanied by a pronounced ion aggregation are mainly responsible for the formation of a stable SEI at much lower Na-salt concentration (9.3 m) than that of Li-salts discussed above. Kuhnel et al. reported a sodium bis(fluorosulfonyl)imide (NaFSI) based WiS electrolyte at super-concentration of 35 m (this results may be questioned since several groups did not report such a high solubility), in which the molar ratio of water-to-salt is less than 2:1, can extend the ESW up to 2.6 V [48].

Multivalent metal-based batteries have attracted extensive interest as potential alternatives to lithium-ion batteries. Meanwhile, WiS electrolytes containing multivalent ions such as Mg 2+ , Ca 2+ , and Zn 2+ have already applied in the field of rechargeable batteries [START_REF] Wang | High-Voltage Aqueous Magnesium Ion Batteries[END_REF][START_REF] Lee | Modulating the hydration number of calcium ions by varying the electrolyte concentration: Electrochemical performance in a Prussian blue electrode/aqueous electrolyte system for calcium-ion batteries[END_REF][START_REF] Zhang | Cation-Deficient Spinel ZnMn 2 O 4 Cathode in Zn(CF 3 SO 3 ) 2 Electrolyte for Rechargeable Aqueous Zn-Ion Battery[END_REF][START_REF] Hu | Zn/V2O5 Aqueous Hybrid-Ion Battery with High Voltage Platform and Long Cycle Life[END_REF][START_REF] Zhang | Rechargeable aqueous zinc-manganese dioxide batteries with high energy and power densities[END_REF][START_REF] Li | Advanced Low-Cost, High-Voltage, Long-Life Aqueous Hybrid Sodium/Zinc Batteries Enabled by a Dendrite-Free Zinc Anode and Concentrated Electrolyte[END_REF][START_REF] Zhi | Acrylonitrile copolymer/graphene skinned cathode for long cycle life rechargeable hybrid aqueous batteries at high-temperature[END_REF][START_REF] Wan | Aqueous rechargeable zinc/sodium vanadate batteries with enhanced performance from simultaneous insertion of dual carriers[END_REF][START_REF] Wang | Highly reversible zinc metal anode for aqueous batteries[END_REF]. Among them, aqueous Zn-ion batteries have been developed in particular. Zhang et al. reported that a concentrated aqueous electrolyte of Zn(OTf) 2 , along with the cation-defected ZnMn 2 O 4 as a stable cathode material, exhibited not only a wide ESW of 2.5 V but also the high efficiency and long-term stability for aqueous Zn-ion batteries [START_REF] Zhang | Cation-Deficient Spinel ZnMn 2 O 4 Cathode in Zn(CF 3 SO 3 ) 2 Electrolyte for Rechargeable Aqueous Zn-Ion Battery[END_REF]. Apart from these, the application of WiS electrolytes in hybrid Zn-ion based batteries were reported, in which the electrolytes are mixtures of Zn salt and other salts. By adding a small amount of Mn(OTf) 2 salt into the concentrated Zn(OTf) 2 electrolyte, Zhang et al. reported a Zn-MnO 2 battery system with high energy and power densities [START_REF] Zhang | Rechargeable aqueous zinc-manganese dioxide batteries with high energy and power densities[END_REF] 3) that result in the absence of free water [47]. Moreover, aqueous Na-ion batteries with an inorganic electrolyte containing highly concentrated NaClO 4 salt dissolved in water were demonstrated to have high performances [49,[START_REF] Zhang | Towards High-Performance Aqueous Na-ion Batteries: Stabilizing the Solid/Liquid Interface for NASICON-Type Na2VTi(PO4)3 via the Use of Concentrated Electrolytes[END_REF]. Furthermore, an aqueous ammonium-ion (NH + 4 ) battery based on a novel WiS electrolyte of 25 m NH 4 CH 3 COO was reported by Holoubek et al. [START_REF] Holoubek | Amorphous titanic acid electrode: its electrochemical storage of ammonium in a new water-in-salt electrolyte[END_REF], which opens the way of exploring WiS electrolytes to the metal-free ones. Apart from these, a different battery utilizing all-organic (metal-free) electrodes together with WiS electrolyte (21 m LiTFSI) was reported by Dong et al., which can deliver a supercapacitor-like high power density (32 kW kg -1 ).

Application of water-in-salts in supercapacitors

Figure 1-4 shows the schematic of the Li-ion battery and supercapacitor. In contrast to batteries, supercapacitors rely on the highly reversible adsorption of ionic species at the electrode surfaces and the charging process is not limited by diffusion of ions in the bulk of the electrodes, allowing faster charging time, longer life cycles and higher power densities to be achieved but with a significantly lower energy delivery.

Therefore, supercapacitors can be regarded as promising energy storage systems that complement batteries or even replace them in high-power applications [START_REF] John | Electrochemical capacitors for energy management[END_REF][START_REF] Simon | Where Do Batteries End and Supercapacitors Begin[END_REF][START_REF] Salanne | Efficient storage mechanisms for building better supercapacitors[END_REF]. By investigating a wide range of salt molalities of LiTFSI as an aqueous electrolyte for supercapacitors, the operating voltage, power and energy densities, and electrochemical stability are compared by Lannelongue et al. [START_REF] Lannelongue | Water-in-Salt for Supercapacitors: A Compromise between Voltage, Power Density, Energy Density and Stability[END_REF], in which the 7 m LiTFSI WiS electrolyte was finally concluded to be the optimal one among them. A further study aimed at understanding the formation of SEI and eliminating its effects were reported. Coustan et al. investigated the electrochemical behavior of stainless steel electrode in 21 m LiTFSI WiS electrolyte, and pointed out that no SEI formed at potential cycling limited to a specific range, i.e., between 0 and -1.8 V, which gave new insight to design WiS-based electrolytes for supercapacitors [START_REF] Coustan | New insight in the electrochemical behaviour of stainless steel electrode in water-in-salt electrolyte[END_REF]. properties. Taking all these advantages, a model supercapacitor using the 5 m AWiS electrolyte displayed significant enhanced specific capacitance and high-rate capability, along with a wide operating voltage of 2.2 V.

Meanwhile the exploration of new

Motivation and objective

Computer simulation studies have played a crucial role in understanding the mechanisms at play for electrochemical systems, in particular, molecular dynamics (MD) has become the more widely used approach to obtain a realistic picture of the systems at the atomistic/molecular-scale. Among the studies of WiS electrolytes, especially their applications in batteries and supercapacitors, MD simulations have severed as important complements of experiments. In the original study of WiS electrolyte [27], the solvation property of Li cations was studied by MD simulations. The analysis of the coordination number of water molecules and TFSI anions in the first solvation shell of lithium and the fraction of free water, which illustrated the evolution of the Li cation primary solvation shell at salt concentration ranging from dilute (salt-in-water) to super-concentrated (water-in-salt). In Figure 1 cation was observed, along with a significant abatement of the fraction of free water up to 15%, while the number of TFSI anions participated in the lithium solvation shell was growing. As a consequence, the primary solvation shell of the lithium cation experienced tremendous changes as illustrated in Figure 1-5b when switching from low to high salt concentration regime. Moreover, MD simulations have applied in several other studies of WiS electrolytes, in which the other structure properties, such as radial distribution function (RDF), ion aggregations [30,31,50], were investigated, in addition to the solvation properties [47,[START_REF] Wang | Highly reversible zinc metal anode for aqueous batteries[END_REF]. Apart from these, a paramount study of the bulk WiS electrolyte was reported, in which not only the above-mentioned structure properties but also the transport properties (such as diffusion coefficient and ionic conductivity) were investigated by molecular dynamics simulations in combination with small-angle neutron scattering and a variety of spectroscopic techniques [34]. A liquid structure of nano-heterogeneous domains was adopted at concentrated LiTFSI WiS electrolytes (from 10 to 21 m) due to the presence of disproportionate cation solvation induced by solvent-separated lithium cations, in which the lithium-water domain (without TFSI) served as a 3D percolating channel accounting for the fast transport of lithium cation.

As demonstrated above that the utility of MD simulations in the study of WiS Thus, the first objective of this thesis is to comprehensive understanding the bulk properties of WiS electrolyte by performing MD simulations. To this end, the concentration dependence of the transport properties will mainly be discussed in chapter 3 and the detailed structural properties including analysis from the thermodynamic point of view, i.e., the strength of lithium solvation shell and water exchange rate inside which was seldom reported so far, will be discussed in chapter 4. However, an accurate MD simulation is entirely depended on a reliable model of the system to be investigated, i.e. the choice of an appropriate force field would determine the precision of the description of a given system. Diverse molecular dynamics simulations using either the classical force field [START_REF] Han | Dynamic features of water molecules in superconcentrated aqueous electrolytes[END_REF] (where the conductivity and diffusion coefficients are underestimated by more than one order of magnitude at 20 m compared with those reported experimentally [27,34]) or polarizable force field [27,30,34,50] have all been performed in the aforementioned studies, among which different force field parameters were used even for the same system with identical compositions [27,34], emphasizing the difficulty for precisely simulating WiS electrolytes. Thus, in this thesis, various transport properties including diffusion coefficient and viscosity, which are usually much more difficult to reproduce than the structural ones for concentrated electrolytes, are obtained using a set of different force fields in comparison to the experimental measurements and finally an optimum one is selected.

Interfaces between electrodes and electrolytes play a significant role in many processes for energy storage systems, such as electrochemical reactions in batteries and capacitance in supercapacitors. MD simulations have reported for the study of interfacial structures at electrode/WiS interfaces. As mentioned in the previous section where a 4 V aqueous Li-ion battery was reported [28], MD simulations were also Therefore, the second objective of this thesis is to fill the gap of quantifying the supercapacitor performance utilizing WiS electrolyte. To this end, the interfacial capacitance, which is one of the most important physical properties, intimately associated with the energy and power densities of supercapacitors, will be computed and analyzed in chapter 5 for a given WiS electrolyte (20 m LiTFSI) in supercapacitors. Moreover, its potential dependence behavior will also be discussed in light of the structural changes occurring inside the electric double-layer.

General principle of molecular dynamics

Computer simulations generate information at the microscopic level, i.e. atomistic or molecular positions, velocities, etc. it is then possible to convert this very detailed information into macroscopic quantities, such as pressure, internal energy, etc. The experimentally observable properties associated with these macroscopic terms are reasonably assumed to be given by the temporal average:

A obs = A (t) time = lim t obs →∞ 1 t obs t obs 0 A (t)dt (2.1)
where A obs is the macroscopic observable and the angle brackets denote the temporal average. The system is considered to obey to classical mechanics, so that the equations governing its time evolution are the well known Newton's equations of motion, which may be written:

m i ri = f i f i = - ∂ ∂r i U ({r i }) (2.2)
where m i , r i and ri are the mass of the particle i, its position coordinate and its acceleration. The total force f i acting on the particle i is the gradient of the total potential energy U ({r i }). Molecular dynamics (MD), which consists in modeling the evolution over time for an N-particle system therefore requires to solve the corresponding set of Newton's equation iteratively. With Equation 2.2, we immediately understand that the choice of the interaction potential U between the different particles, which is at the base of the computation of the forces f i , is of great importance for the reliability of the simulations. Since these forces are calculated at each step of the integration, the form of the interactions must be both sufficiently close to reality to correctly describe the evolution of the system and sufficiently simple for the computational cost of the forces to remain compatible with the current performance of computers.

So far as the calculation of the time averages is concerned, we clearly cannot hope to extend the integration of Equation 2.1 to infinite time, but might be satisfied to average over a long finite time, in which we solve Newton's equation for a given system until the properties of the system no longer change with time (i.e., equilibrate the system). After equilibration, the integration of Newton's equations makes it possible to generate a trajectory, i.e., a set of S configurations for the studied system.

These configurations, or micro-states, correspond to particular macroscopic quantities and are obtained in a given statistical set. The determination of the macroscopic observables is carried out considering that the set of S configurations extracted from the trajectory is equivalent to a large number of independent configurations, which is also called the 'ergodicity hypothesis'. During a molecular dynamics simulation, a magnitude A can take a multitude of discrete values A i . Under the ergodicity hypothesis, the average value of a macroscopic observable A equals to the overall average over the whole S configurations. Thus, the Equation 2.1 can be rewritten as:

A obs = A S = S i=0 p i A i (2.3)
where p i is the probability of observing the value A i for a given system.

Verlet algorithm

The algorithm used to integrate the equations of motion must be efficient and must make it possible to verify certainly important properties of Newton's equation: the conservation of the energy, the conservation of the total momentum, the conservation of the angular momentum and the reversibility of time. We will explain here as an example Verlet's algorithm [START_REF] Verlet | Computer" experiments" on classical fluids. i. thermodynamical properties of lennard-jones molecules[END_REF][START_REF] Michael | Computer simulation of liquids[END_REF]. The positions of a particle at time t ± ∆t, with ∆t the integration step, can be determined according to Taylor expansions:

r i (t + ∆t) = r i (t) + dr i (t) dt • ∆t + d 2 r i (t) dt 2 • ∆t 2 2 + d 3 r i (t) dt 3 • ∆t 3 6 + O(∆t 4 ) (2.4) r i (t -∆t) = r i (t) - dr i (t) dt • ∆t + d 2 r i (t) dt 2 • ∆t 2 2 - d 3 r i (t) dt 3 • ∆t 3 6 + O(∆t 4 ) (2.5)
The Verlet's algorithm is then obtained by summing these two equations:

r i (t + ∆t) = 2r i (t) -r i (t -∆t) + d 2 r i (t) dt 2 • ∆t 2 + O(∆t 4 ) = 2r i (t) -r i (t -∆t) + f i m i • ∆t 2 + O(∆t 4 ) ≈ 2r i (t) -r i (t -∆t) + f i m i • ∆t 2 (2.6)
Thus, the position of the particle i at time t + ∆t is calculated from its positions at times t and t -∆t, and the force acting on it at time t. We must keep in mind from this development that the calculated trajectory numerically depends on the chosen integration step. If the time step is too long, the properties of conservation and reversibility of time associated with the Newton's equation will no longer be verified and the trajectory will not be exploitable.

The trajectory is generated from an initial configuration, which must be originally built. The closer the initial configuration is to a realistic situation, the easier it will be to produce a workable trajectory. The representativity of the trajectory obtained for the N particles is extremely important because all the macroscopic properties that 2.1. MOLECULAR DYNAMICS we seek to study are statistical averages of microscopic properties. As a result, if the trajectory is not realistic, due to a poor choice of interaction potential between particles or a too large time step, all the estimated properties will be tainted with errors. For the rest of this thesis, it is thus important to choose the force field and the initial configuration correctly, i.e., the formulation of the interactions between particles (more details will be discussed later) and the geometry of different constituents, to describe the system in a way adapted to the properties we wish to study.

Ensembles

There are many statistical sets (ensembles) commonly sampled in molecular dynamics.

Firstly, the microcanonical ensemble corresponds to an evolution of the system during which the Hamiltonian H of the system, i.e the sum of the kinetic energy and the potential energy, is preserved. This set is also called N V E ensemble because the evolution of the system is made of fixed number of particles (N ), volume (V ) and constant energy (E). The microcanonical partition function may be written:

Q N V E = Γ δ(H (Γ) -E) = 1 N ! 1 h 3N drdpδ(H (r, p) -E) (2.7)
where Γ represents the set of particle positions (r) and momenta (p), H is the Hamiltonian, and δ is the delta function which is proportional to the probability density for this ensemble.

Secondly, it is possible to simulate a system in equilibrium with a thermostat at a temperature T . The corresponding statistical set is the canonical set (N V T ensemble). The canonical partition function is:

Q N V T = Γ exp(-H (Γ)/k B T ) = 1 N ! 1 h 3N drdp exp(-H (r, p)/k B T ) (2.8)
The appropriate thermodynamic function is the Helmholtz free energy

A A/k B T = -ln Q N V T (2.9)
In the canonical ensemble, all values of the energy are allowed and energy fluctuations are non-zero. In practice, the system is coupled to a thermostat that changes the equations of motion to maintain the temperature at a fixed value. An algorithm often used to perform this type of simulation is the algorithm of Nosé-Hoover [START_REF] William | Canonical dynamics: equilibrium phase-space distributions[END_REF][START_REF] Melchionna | Hoover npt dynamics for systems varying in shape and size[END_REF][START_REF] Glenn J Martyna | Nosé-hoover chains: The canonical ensemble via continuous dynamics[END_REF],

which is based on the addition of a term to the Hamiltonian:

H (r, p, p s , s) = i p 2 i 2ms 2 + 1 2 ij,i =j u(r i -r j ) + p 2 s 2Q + gkT ln (s) (2.10)
where g is the number of independent momentum degrees of freedom of the system, Q is an imaginary mass which should be chosen carefully along with systems. This additional term constrains the kinetic energy of the system to be equal to a chosen value. For simulating the bulk properties of WiS electrolyte in chapters 3 and 4, the N V T ensemble is used. Moreover, if we simulate a system using no external field and in which the center of mass is not fixed or if we have more than one conservation law, the Nosé-Hoover chains thermostat has to be employed to obtain the correct canonical distribution [START_REF] Frenkel | Understanding molecular simulation: from algorithms to applications[END_REF]. Other thermostats, such as velocity rescaling, the Andersen thermostat, the Berendsen thermostat and Langevin dynamics, can also be used to control temperature. Among them, Langevin thermostat is employed to simulate the WiS electrolyte at interfaces in Chapter 5. In this thermostat, the Newton's equations of motion are modified as:

mr = - ∂ ∂r U -γ ṙ + 2γk B T R(t) (2.11)
where γ is the viscosity and R(t) is a delta-correlated stationary Gaussian process

INTERACTIONS: THE FORCE FIELD

with zero-mean, satisfying:

R(t) = 0 R(t)R(t ) = δ(t -t ) (2.12)
Apart from the two ensembles as mentioned above, there are two other common statistical ensembles, i.e., the isothermal-isobaric constant-N P T ensemble and the grand canonical constant-µV T ensemble. The coupling of the system with a thermostat and a barostat makes it possible to carry out simulations in the N P T ensemble, in which the volume (V ) of the simulation box is then allowed to vary.

In general, the above mentioned thermodynamic variables are fixed for each ensemble, and other thermodynamic quantities must be determined by ensemble average. It is important to know in which ensemble the simulations are conducted to distinguish whether a macroscopic quantity is actually calculable from the trajectories.

Interactions: the force field

In molecular dynamics simulations, the formulation of interactions between particles involved in a system is diverse. Among them, the OPLS (or AMBER) force field is generally used in the classical molecular dynamics simulations when take into account all the atoms from the molecules as interaction sites. In OPLS [START_REF] William L Jorgensen | Development and testing of the opls all-atom force field on conformational energetics and properties of organic liquids[END_REF] (or AMBER [START_REF] Scott | A new force field for molecular mechanical simulation of nucleic acids and proteins[END_REF][START_REF] Cornell | A second generation force field for the simulation of proteins, nucleic acids, and organic molecules[END_REF]) force field, the total interaction potential is composed of bonded and non-bonded terms:

E total = E bonds + E angles + E dihedrals + E non-bonded (2.13)

Bonded interactions

The bonded (i.e., intramolecular) interactions include the first three terms, E bonds , E angles , E dihedrals , in Equation 2.13, which take the following forms:

E bonds = bonds ij k r ij 2 r ij -r eq ij 2 (2.14) 2.2. INTERACTIONS: THE FORCE FIELD 33 E angles = angles ijk k θ ijk 2 θ ijk -θ eq ijk 2
(2.15)

E dihedrals = dihedrals ijkl 4 m=1 V m ijkl 2 [1 + (-1) m cos mφ ijkl ] (2.16)
The sums respectively run over the full set of instantaneous bonds r ij , angles θ ijk and dihedrals φ ijkl , which must be defined prior to the simulations, i.e., the bonds are not allowed to break or form during the simulation. The quantities k r ij ,r eq ij ,k θ ijk ,θ eq ijk and V m ijkl are parameters of the force filed. Specifically, in Equation 2.14, the "bonds" typically involve the distance r ij = |r i -r j | of adjacent pairs of atoms in a molecular framework, and the form is assumed to be a harmonic with specified equilibrium bond distance r eq ij and spring constant k r ij . In Equation 2.15, the "bend angles" are between successive bond vectors involving three atom coordinates, and this bending term is taken to be quadratic in angular displacement from the equilibrium value. Finally, in Equation 2.16, the "torsion angles" are defined in terms of three connected bonds (i.e., four atom coordinates), and the torsion potential involves an expansion in periodic functions of order m = 1,2,3,4.

Non-bonded interactions

The last term in Equation 2.13 represents the non-bonded interactions, which is in principle composed of three contributions

E non-bonded = E repulsion + E dispersion + E electrostatic (2.17)
In some simulations of complex fluids, it is sufficient to use the simplest models that faithfully represent the essential physics. In this thesis, we use the Lennard-Jones potential form, which gathers both the repulsion and dispersion terms in Equa-34 2.3. SIMULATING CONSTANT POTENTIAL ELECTRODES tion 2.17 and is given by:

E Lennard-Jones = E repulsion + E dispersion = i j>i 4 ij σ ij r ij 12 - σ ij r ij 6 (2.18)
where r ij is the distance between particle i and j. σ ij and ij are the finite distance at which the inter-particle potential is zero and dielectric constant (i.e., the depth of the potential well), respectively, which are obtained using the geometric combining

rules σ ij = √ σ i σ i and ij = √ i j in OPLS-like force field.
The last term of electrostatic interactions in Equation 2.17 is represented by the usual Coulomb potential

E electrostatic = E Coulomb = 1 4π 0 i j>i q i q j r ij (2.19)
where 0 is the vacuum permittivity, and q i , q j are the charges of particles i and j. Note that an integer value of the total charge for a single ion is set in most of the simulations. However, the total charge of ion is smaller than its formal value due to polarization or charge transfer effects. Therefore, the reduced charge strategy is used to mimic the polarization effects. In this thesis, both the formal charge and reduced charge methods are taken into accounted when perform the molecular dynamics simulations.

Simulating constant potential electrodes 2.3.1 Fluctuating charges model and its implementation

In molecular dynamics simulations of supercapacitors, the choice of an appropriate model for the electrode presents a substantial challenge due to the difficulty in defining a consistent classical atomistic model for a metallic electrode. In the majority of the MD simulations, the charges carried by the electrode atoms are assumed to be constant during the simulation and homogeneously distributed on the surface of the electrode [START_REF] Pinilla | Polarization relaxation in an ionic liquid confined between electrified walls[END_REF][START_REF] Oliver | Screening at a charged surface by a molten salt[END_REF][START_REF] Feng | Microstructure and capacitance of the electrical double layers at the interface of ionic liquids and planar electrodes[END_REF][START_REF] Yang | Molecular simulation of electric double-layer capacitors based on carbon nanotube forests[END_REF]. While the fluctuations of the charge on the electrode, which is neglected in the constant charge method, contain information on the microscopic correlations within the adjacent electrolyte solution and their effect on the electronic properties of the electrode-electrolyte interface. Thus, it is important to take into account such fluctuations, which could be achieved by introducing a polarizable model involving fluctuating charges.

There are several ways to include polarization in classical MD simulations. In all cases, the introduction of polarizability induces an additional calculation cost.

However, in systems such as supercapacitors, where electrostatic interactions and electronic conduction play a crucial role in the determination of properties, it appears essential to represent this polarizability. The polarizability of atoms, ions or molecules is the ability of the electron cloud to deform under the effect of an electric field. For electrodes, we denote the polarizability as the ability of the material to conduct the current, i.e., the redistribution of the charges on different atoms constituting the solid electrode under the effect of an electric field. To take into account the polarizability of atoms, ions or molecules, several models exist. A first option is to assign the atoms a point dipole. The dipoles are then considered as additional degrees of freedom determined at each time step by a procedure for minimizing the total polarization energy [START_REF] Mathieu Salanne | From molten salts to room temperature ionic liquids: Simulation studies on chloroaluminate systems[END_REF]. A second option consists in assigning to each polarizable atom a Drude oscillator [START_REF] Iori | Including image charge effects in the molecular dynamics simulations of molecules on metal surfaces[END_REF], that is each atom/ion carries two point charges separated by a spring [START_REF] Lamoureux | Modeling induced polarization with classical drude oscillators: Theory and molecular dynamics simulation algorithm[END_REF]. A variant of this model is to consider a rigid "rod" of a certain length replace the spring. The rotation of the rod makes it possible to model the polarizability. This second approach has been successfully used to model the interface between an ionic liquid and a metal surface in order to study the stabilization of metal nanoparticles in an ionic liquid medium, the friction properties of these liquids or the structure of the liquid at the interface [START_REF] Alfonso | Solvation and stabilization of metallic nanoparticles in ionic liquids[END_REF][START_REF] Podgorsek | Interaction energies of ionic liquids with metallic nanoparticles: Solvation and stabilization effects[END_REF][START_REF] Mendonca | Nonequilibrium molecular simulations of new ionic lubricants at metallic surfaces: prediction of the friction[END_REF][START_REF] Mendonca | Interactions and ordering of ionic liquids at a metal surface[END_REF].

The main limitation of the two approaches described so far is the effective way to apply a potential difference between the electrodes. In molecular dynamics simulations, Siepmann and Sprik [START_REF] Ilja | Influence of surface topology and electrostatic potential on water/electrode systems[END_REF] have introduced a method for treating atomic charges 2.3. SIMULATING CONSTANT POTENTIAL ELECTRODES of the electrode as additional degrees of freedom. That is, the polarization is not represented by the assignment of a dipole to the atoms but by the fluctuation of the charge they carry. In the original work, the charges evolved following Car-Parrinello dynamics in order to maintain the electrode potential close to a target value. This model has been adapted by Reed et al. [START_REF] Reed | Electrochemical interface between an ionic liquid and a model metallic electrode[END_REF] in the case of Born-Oppenheimer dynamics for which it is assumed that the electronic degrees of freedom relax instantaneously relative to the movement of ions/molecules. In practice, the charges of the electrode atoms are represented by Gaussian charge densities centered on the atoms. They are calculated at each time step by minimizing the expression:

U = i q i (t) Ψ i ({q j }) 2 + q i (t)κ √ 2π -Ψ 0 (2.20)
where q i is the charge carried by the atom i, κ is the width of the Gaussian distributions, Ψ i ({q j }) is the potential at position i due to all other atoms and ions; the second term comes from the interaction of the Gaussian with itself and Ψ 0 is the applied potential. At each simulation step, all the charges must be determined in a self-consistent way by minimizing the Equation 2.20 using the conjugate gradient method. This methodology has been successfully applied to a number of electrodeelectrolyte interfaces [START_REF] Vatamanu | Ramifications of Water-in-Salt Interfacial Structure at Charged Electrodes for Electrolyte Electrochemical Stability[END_REF][START_REF] Reed | Electrochemical interface between an ionic liquid and a model metallic electrode[END_REF][START_REF] Reed | Electrochemical charge transfer at a metallic electrode: A simulation study[END_REF][START_REF] Michael A Pounds | Molecular aspects of the Eu3+/Eu2+ redox reaction at the interface between a molten salt and a metallic electrode[END_REF][START_REF] Vatamanu | Molecular insights into the potential and temperature dependences of the differential capacitance of a room-temperature ionic liquid at graphite electrodes[END_REF][107][START_REF] Vatamanu | Molecular Simulations of the Electric Double Layer Structure, Differential Capacitance, and Charging Kinetics for N -Methyl-N -propylpyrrolidinium Bis(fluorosulfonyl)imide at Graphite Electrodes[END_REF][START_REF] Burt | Capacitance of Nanoporous Carbon-Based Supercapacitors Is a Trade-Off between the Concentration and the Separability of the Ions[END_REF][START_REF] Pean | Confinement, Desolvation, And Electrosorption Effects on the Diffusion of Ions in Nanoporous Carbon Electrodes[END_REF][START_REF] Pean | Multi-scale modelling of supercapacitors: From molecular simulations to a transmission line model[END_REF][START_REF] Merlet | On the molecular origin of supercapacitance in nanoporous carbon electrodes[END_REF][START_REF] Merlet | Computer simulations of ionic liquids at electrochemical interfaces[END_REF][START_REF] Merlet | Influence of solvation on the structural and capacitive properties of electrical double layer capacitors[END_REF][START_REF] Merlet | Simulating supercapacitors: Can we model electrodes as constant charge surfaces?[END_REF][START_REF] Merlet | The Electric Double Layer Has a Life of Its Own[END_REF]. Compared with other faster methods [START_REF] Matt K Petersen | A computationally efficient treatment of polarizable electrochemical cells held at a constant potential[END_REF], this technique has the advantage of being directly applicable to the case of non-planar and irregular electrodes.

Importance of polarizability of electrode

During an electrochemical experiment, a potential difference is applied across the supercapacitor and the local charge, which fluctuates over time, depends both on the imposed potential and on the molecules surrounding the surface. Thus, modeling the electrodes in a polarizable way, i.e., allowing the fluctuations of charges on the electrode atoms as we discussed above, make MD simulations possible to become more reliable and comparable to the experiments. The first thing we notice during the simulations is the inhomogeneity of the charges on the surface of the electrode in It should be noted that the constant charge has been chosen such that the potential difference, reconstructed from the charge density, is equal to 1 V for a simulation at equilibrium. In Figure 2-2, we note that after 5 ps, the "pocket" (circled in red), which Temperature drift when a constant potential difference is suddenly applied (inset: when a constant charge is assigned to each carbon atom) [START_REF] Merlet | Simulating supercapacitors: Can we model electrodes as constant charge surfaces?[END_REF].

was empty in the initial configuration, is filled in the case of constant charge simulation and still empty in the case of constant potential simulation. This suggests that the use of constant charge accelerates the dynamics of the system. Moreover, in Figure 2-3, a temperature increase due to the Joule effect, is observed during the simulations. For constant potential simulation, the temperature gradient is consistent with a simple estimate based on Ohm's law [START_REF] Merlet | Simulating supercapacitors: Can we model electrodes as constant charge surfaces?[END_REF]. In contrast, for constant charge simulation, the temperature reaches 25,000 K in 1 ps, which is absolutely not realistic. This type of simulation should not be used to study dynamic phenomena. Therefore, it is conceivable to firstly impose a constant charge on the system to access a configuration close to equilibrium; the determination of the properties should be then performed at the constant potential. The MD simulations were performed using LAMMPS molecular dynamics simulation package [START_REF] Plimpton | Fast Parallel Algorithms for Short-Range Molecular Dynamics[END_REF]. The SPC/E water model was used in present systems [START_REF] Berendsen | The Missing Term in Effective Pair Potentials[END_REF]. An atomistic model of TFSI anion were considered. In a first step, a modified OPLS force field was used in case of this anion (here, we call this force field as FF1), where the parameters were taken from Ref [START_REF] Monteiro | Transport Coefficients, Raman Spectroscopy, and Computer Simulation of Lithium Salt Solutions in an Ionic Liquid[END_REF]. The simulations were conducted in the NVT ensemble, with the temperature set at 298.15 K. The simulation cells were cubic and constructed using experimental densities, and the details are provided in Table 3.1. For all of the simulations, the velocity-Verlet algorithm with a time step of 1 fs was used, the dynamics properties were obtained from the production runs with timescale over 60-110 ns after long equilibration runs (60 ns). The atomic coordinates were saved every 1 ps for post-analysis.

Viscosity

Methods

The shear viscosity of a liquid is calculated from the time integral of the shear stress autocorrelation function of the off-diagonal elements of the stress tensor. It is known as the Green-Kubo relation, which given by: where V and k B are the volume of the simulation cell and Boltzmann constant, respectively. σ αβ can be any of the five independent anisotropic components of the stress tensor(i.e. σ xy , σ xz , σ yz , σ xx-yy , σ 2zz-xx-yy ). To get better statistics, an average over these five components is used. As shown in Figure 34, the value of the integral in Equation 3.1 converges to a plateau after a certain time, which varies with the system molality -we will discuss this point later. For the dilute solutions, the integral converges in a few picoseconds, while it takes several hundreds of picoseconds to converge to a plateau at super-concentrated states. The viscosity can then be obtained by the plateau value of the running integral.

η = V k B T ∞ 0 σ αβ (0) • σ αβ (t) dt
The structural relaxation time, or Maxwell relaxation time τ Maxwell , measures the time taken by the fluid relax to a new configuration when it is sheared. This quantity can be extracted from the time for which the evolution of viscosity with respect to time (Figure 3-4) satisfies the following equation: In Figure 3-6, the simulated viscosities are plotted along with results from experimental measurements. The experimental results include both the measured values from our collaborators C. Rizzi and R. Bouchal and the values adopted from ref [27].

η(τ Maxwell ) = η(t → ∞)(1 - 1 e ) (3.2)

Results

As can be seen that the simulated viscosities are agreed well with both experimental results. The latter show a slight discrepancy for the larger concentration which may be due to difficulties for controlling the composition at large salt/water ratios.

Diffusion coefficient

Methods

The self-diffusion coefficient is computed from the slope of the mean-squared displacement average over the whole trajectory of individual species using the Einstein relation, which is defined as:

D α = lim t→∞ 1 6t |δR i (t)| 2 (3.3)
where D α is the self-diffusion coefficient of species α, the angle brackets denote average over all configurations, and δR i is the displacement of an individual ion i of species α.

In fact, the use of periodic boundary conditions induces a box length dependence 3.3. DIFFUSION COEFFICIENT 47 of the measured diffusion coefficient due to the restriction of diffusion from long-range hydrodynamic interactions [START_REF] Dünweg | Molecular dynamics simulation of a polymer chain in solution[END_REF][START_REF] Yeh | System-size dependence of diffusion coefficients and viscosities from molecular dynamics simulations with periodic boundary conditions[END_REF]. The term of finite size correction (FSC) to the self-diffusion coefficient should be added to obtain the value of the diffusion coefficient finally, and this quantity is given by:

∆D F SC = 2.837k B T 6πηL (3.4)
where η is the viscosity as discussed in the previous section, and L is the length of the simulation periodic cell. than that for the Li cations. Therefore, it seems that the force field FF1 might not be applicable to precisely describe the transport in the super-concentrated systems above 12 m.

Results

Conductivity

Methods

The conductivity is obtained from the long-time slope of a plot of the mean-squared displacement of the charge density versus time:

λ = e 2 k B T V lim t→∞ 1 6t | i q i δR i (t)| 2 (3.5)
where q i and δR i are the charge and displacement of ion i, respectively. The sum runs over all cations and anions, which means that the mean-squared displacement in the brackets includes not only the self terms of an individual ion i but also the distinct terms (correlations between the displacements of different ions). Thus, the total conductivity can be decomposed to two parts (self and distinct). The Nernst-Einstein approximation for the conductivity can be obtained by neglecting the correlations of 3.4. CONDUCTIVITY 49 the distinct terms, i.e., δR i (t) • δR j (t) = 0, i = j, it is thus given by:

λ N E = N e 2 k B T V α q 2 α D α (3.6)
where q α is the charge of species α and D α is the diffusion coefficient of species α as defined in Equation 3.3. whose Walden plot lies much lower than the ideal line. The regions lie below the ideal line but close to it, corresponding to good-ionic electrolytes. The electrolytes are considered as super-ionic conductors whose Walden plots lie above the ideal line [32,33]. As shown in Figure 3-9, the plots of the systems at various concentration are locating at the good-ionic region, close to the ideal line when switching from low to super-concentrated states. Apart from these, the experimental results at 15 m and 20 m are on the ideal line, leading to even better performance as ionic conductors compared with the remaining concentrations. These could partially account for the high performance of using water-in-salt electrolytes in electrochemical storage devices, like lithium-ion batteries and supercapacitors.

Results

Comparison with other force fields 3.5.1 Type of force fields

As discussed above in this chapter, the simulated viscosities and conductivities can be well reproduced with experimental results for the whole studied concentrations by using the force field FF1. Also, the simulated diffusion coefficients of all the species agree well with the experimental measurements at concentrations below 12 m. However, the FF1 force field is failed to reproduce the value of diffusion coefficients at super-concentrated states (15 m and 20 m). The significant differences between the ratio of D W ater : D Li from experiment (≈ 2:1) and that from the previous simulations (≈ 1:1) at 15 m and 20 m would have significant effects on the structural properties, such as the property of solvation shell of Li and/or water molecules, which we will discuss in the next chapter. Therefore, we need to modify the force field, such as using reduced charge strategy to mimic polarization effects, or to chose another parameterization of the force field to improve the ability describing the electrolytes at super-concentrated states.

We implement three different sets of parameters for the force field to perform a new set of simulations at 15 m, in which the changes are as following:

1. FF2: Charges of Li cation and TFSI anion are uniformly scaled by a factor of 0.8 based on FF1, all the remaining parameters are the same as FF1;

2. FF3: Intermolecular parameters of TFSI anion are taken from ref [START_REF] José | Molecular force field for ionic liquids composed of triflate or bistriflylimide anions[END_REF] in which the charge of Li cation and TFSI anion are set to +1 and -1, respectively, the

Results

In Figure 3-10, the simulated viscosities obtained by using the different type of force fields are compared with the experimental value at 15 m. Largest value is given by FF3 force field, which is more than 2 times larger than the experimental measurement, compared with those from all the other type of force fields. The FF2 force field underestimates the viscosity showing a value only half of the experimental one, which is in contrast with the general fact that viscosity is often overestimated from simulations. This could be attributed to the excessive reduction of the charge in FF2. The

Conclusions

In this chapter, we studied the water and LiTFSI mixtures at various concentrations from dilute solutions to super-concentrated solutions, including the water-in-salt region. The dynamic properties, such as the viscosity, diffusion coefficient and conductivity, of the mixtures were computed and compared with experimental results.

The dependence of dynamic properties on concentrations is clearly found by using a uniform force field (FF1): the system becomes viscous with increasing viscosity and decreasing diffusivity when switching from low to high concentration regime, in which the drastic changes occur at concentrations above 12 m. These results are consistent with both the simulated and experimental values recently reported [34].

The extent of the decrease in diffusivity is similar to the case of all mixtures of ionic liquids with solvents, and the main consequence is that the choice of the optimal concentration for EDLC applications is likely to consist in a compromise between an 3.6. CONCLUSIONS 55 improved electrochemical stability window as reported [27] and a poorer diffusivity of the lithium ions (unlike batteries, for which the formation of a protective interphase at the surface of the electrodes is crucial [28]). This competition is also reflected on the electrical conductivity, which first increases to a maximum and then decreases at water-in-salt region. Based on analysis of the Walden plots, we confirm that the water-in-salt electrolytes at super-concentrated states have better performances as ionic conductors than the less concentrated systems.

In order to better reproduce the dynamic properties, especially the diffusion coefficients, with experiment at super-concentrate states, the different type of force fields are utilized to study the water-in-salt electrolytes at 15 m. The combined analysis based on both viscosity and diffusion coefficient shows that the FF4 force field can give results in good agreement with experimental measurements. Such transport quantities are usually much more difficult to reproduce than the structural ones for concentrated electrolytes, so their reproduction validates the use of FF4 force field to analyze the structure and the thermodynamics of the system. where r is the distance between A and B, g(r) is the radial distribution function of the A-B pairs, and ρ is the number density of particle B in the simulation cell. The g(r) between Li cation and water molecule obtained with the four force fields are shown in Figure 4-1a. In all cases, the first shell of tightly bound water molecules surround the Li cations with a distance around 1.8 Å (the first peak in Figure 4-1a) but with different peak values. We will discuss these peak values in the next section.

Moreover, all the force fields give almost the same position for the first minimum, located at around 2.57 Å and thus we take this value as the cutoff distance for the Li first solvation shell (i.e., hydration shell when the solvent is water). The hydration numbers of the Li are around 3.7 for FF1 and FF2 and 3.2 for FF3 and FF4. It is well established from the combination of experimental (neutron and X-ray diffraction) and simulation data that at infinite dilution the hydration number of lithium is 4, which means that some Li cations become under-hydrated at 15 m. Note that the charges of Li cation and TFSI anion are reduced in FF2 (FF4) compared with that in FF1 (FF3), but they have the same LJ parameters. Therefore, the hydration number of the Li first solvation shell seems to be nonsensitive to the Coulombic interactions but to be controlled by the Lennard-Jones terms.

Residence time of water

The first solvation shell is generally characterized by two main quantities: the average coordination number of the cation, which we have already discussed in the last section, and the mean residence time τ of a water molecule inside the shell.

The residence time, measuring the rate of the break-up of the first coordination shell of the lithium cations, is obtained by using the cage correlation function analysis [START_REF] Rabani | Calculating the hopping rate for self-diffusion on rough potential energy surfaces: Cage correlations[END_REF]. The instantaneous set of neighboring water molecules of any lithium ion i is defined by a neighbor list which is stored in a vector

I i (t) (i ∈ [1, N Li + ]).
n out i (t, t + δt) = |I i (t)| 2 -I i (t) • I i (t + δt) (4.2)
The cage-out correlation function for the Li + ions solvation shell then is given by

C out (t) = 1 N Li + N H 2 O i=1 Θ(1 -n out i (0, t)) (4.3)
where Θ is the Heaviside step function. So defined, the cage-out correlation function measures the rate at which a single molecule leaves the cage. Using similar definitions, it is also possible to calculate the correlation functions measuring rates for a molecule to enter into the cage (cage-in), but also for an ion to enter or to leave it (cage-in-orout).

Herein, the calculated cage-out correlation function and the corresponding residence time obtained from different type of force fields are shown in Figure 4-3 and of force fields, resulting in a residence time τ of 13.6 ns (Figure 4-4). Such a large residence time obtained from FF1 is associated with the large deviation of the diffusivity from experimental results (as discussed in Chapter 3), which makes the value unreliable. Apart from this, using FF4 force field, the given residence time (300 ps) is in agreement with reported results in the literature which are diverse (25-400 ps) depending on the simulation method [START_REF] Spångberg | Rate and Mechanisms for Water Exchange around Li + (aq) from MD Simulations[END_REF]. The FF2 force field, which uses modified Coulombic interactions from FF1 with reduced charges, gives a value of 600 ps, which is close to that from FF4. Finally the residence time (1 ns) is three times larger for FF3, in which the charges are not reduced, than that of FF4. Therefore, in contrast with the dependence of coordination numbers, the residence time is mainly affected by the Coulombic interactions rather than by the Lennard-Jones terms.

Potential of mean force

In order to analyze the thermodynamic aspect related to the Li solvation shell strength, we compute the potential of mean force (PMF) for the escape of water molecules (or TFSI anions represented by O atoms) from the solvation shell of Li cations, which is given by

PMF = -k B T ln g(r) (4.4)
where k B and T are the Boltzmann constant and temperature, respectively. 9.7 kJ/mol when entering this first solvation shell, a large number which is due to the small ionic radius and the large polarizing power of this cation. Moreover, the barrier height, E a , defined by the energy difference between the maximum and the minimum of PMF (in Figure 4-5a), can be obtained from the PMF as well. There is more discrepancy of this quantity since it ranges from 17 to 27 kJ/mol. Even though the reduction of charges in FF2 or FF4 decreases the barrier height compared with that without reduced charges (FF1 or FF3), it remains a high barrier for water molecules escaping from the first solvation shell of Li cations. This is due to the under-hydrated state of Li cation at 15 m, leading to the lack of free water molecules beyond the Li first hydration shell.

Considering that several TFSI anions are also involved in the Li first solvation shells, the PMFs for TFSI anions escaping from the solvation shell of Li cation is calculated as well as the corresponding energy differences (in Figure 456). Both the stabilization energy (∆E) and barrier height (E a ) of TFSI anions are much smaller than that of water molecules, which indicates that the former is much more loosely bound and more dependent on the force field.

Fraction of free water

Water molecules that do not belong to any Li first solvation shells are considered as free water in our work. The fraction of free water can then be obtained through the coordination analysis from the trajectory, the results for different force fields are shown in Figure 4567. The first two force fields (FF1 and FF2) show smaller fraction of free water molecules compared with the other two (FF3 and FF4). It is due to the larger average hydration number of water molecules observed in Figure 4-1b that requires more water in the presence of the Li first solvation shell, resulting in the decrease in the amount of free water. Moreover, it is clear that the FF1 gives a distinct value (0.6 %) compared with the others. Such a smaller value is also partially attributed to the absence of a second minima in the region around 4 Å in the Li-O(water) PMF (Figure 4-5a), which leads to an easier release of water molecules since they can access the adjacent lithium's first solvation shell. On the contrary, larger values of the fraction of free water are found for the rest of the force fields, owing to the valley appearing at around 4 Å in with that reported by Borodin et al. [27,34].

The fraction of free water is linked to the behavior of the diffusivity of water molecules and lithium ions. The limited fraction for FF1 (FF2) means that most water molecules are diffusing together with lithium ions resulting in similar values between water and lithium ions. In contrast, the relatively larger fraction of free water for FF3 (FF4) enables a portion of water molecules to diffuse with more freedom, which increases the average value of the diffusion coefficient of water molecules.

Lithium-lithium dimer

The first solvation shell of lithium ions is well understood based on the analysis in previous sections. In this section, we will discuss the structural properties beyond the first solvation shell of Li cations.

We calculate the radial distribution functions of lithium-lithium dimer for different force field as shown in Figure 45678. The first peak in g Li-Li (r) predicted by FF2 (FF4)

Competition between Li and TFSI

To understand whether the water molecules located in the vicinity of the TFSI (first peak of the g(r) shown in Figure 4-11a) are free or Li-bounded, the combined radial/radial distribution functions of the water-TFSI pair and water-Li pair are calculated for the different force fields. Figure 4-13 shows the results within the first solvation shell of lithium ions (r Ow-Li <2.4 Å). Similar as for the RDFs, two more likely regions (red or orange region) centered at around 2.8 Å and 5.5 Å are found for O atoms from TFSI surrounding water molecules within the first solvation shell of lithium ions, which shows that the water molecules can be bounded to both the lithium and the TFSI ions. Moreover, FF4 has the smallest value of intensity at short distances compared with the other force fields, which corresponds to the smallest probability of finding TFSI anion around water molecules. This shows that TFSI anions have a stronger hydrophobic character with this force field. On the contrary, the TFSI anions are more hydrophilic in FF1 compared with the other force fields.

Conclusions

In this chapter, we studied the structural properties of water-in-LiTFSI with the molality of LiTFSI at 15 m. The solvation shell of lithium ions was investigated in terms of the radial distribution function, coordination number, residence time of water molecule, and the potential of mean force for water molecules (TFSI anions) escaping from the solvation shell of Li cations. From the speciation point of view, the water/lithium ratio becomes lower than 4, which means that some Li + become under-hydrated, forming Li(H 2 O) + 3 and even Li(H 2 O) + 2 species. The missing water molecules are then replaced by the oxygen atoms of the TFSI anions, but the latter 4.3. CONCLUSIONS is much more loosely bound based on the PMF analysis. Moreover, the analysis of residence time and the fraction of free water suggest a high dependence on the choice of force fields. In particular, the larger fraction of free water with a relatively smaller residence time for FF4 compared with the others leads to the larger difference of diffusion coefficients between water molecules and Li + cations, which is in agreement with the experimental measurement. Apart from these, lithium-lithium dimers with short distance (r Li-Li < 3.8 Å) are found for FF4 and FF2, and these dimers are mostly coordinated by water molecules other than TFSI anions based on the analysis of combined radial/radial distribution functions.

The role of water molecules and their "solvation" properties were also investigated by the analysis of coordination number, combined distribution functions and so on.

A hydrophobic behavior of TFSI anions is found for FF4 while a more hydrophilic tendency is observed for FF1.

Chapter 5

Water-in-salt electrolyte at interface

The main physical property quantifying the performance of EDLCs for energy storage applications is the interfacial capacitance [START_REF] Salanne | Ionic Liquids for Supercapacitor Applications[END_REF][START_REF] Vatamanu | Capacitive Energy Storage: Current and Future Challenges[END_REF][START_REF] Vatamanu | Charge storage at the nanoscale: understanding the trends from the molecular scale perspective[END_REF]. This quantity is highly dependent on the electrode/electrolyte couple as reported in previous works [START_REF] Chmiola | Anomalous Increase in Carbon Capacitance at Pore Sizes Less Than 1 Nanometer[END_REF][START_REF] Haskins | Computational and Experimental Study of Li-Doped Ionic Liquids at Electrified Interfaces[END_REF]. In general, the main changes are attributed to the interfacial layer structure (or local structure) of the liquid electrolyte [START_REF] Merlet | On the molecular origin of supercapacitance in nanoporous carbon electrodes[END_REF][START_REF] Merlet | Highly confined ions store charge more efficiently in supercapacitors[END_REF]. Different pore sizes in nanoporous electrodes accompanying complex local structures have a large impact on the capacitance compared with non-porous electrodes. However, the capacitance can also take a wide range of values both in experiment and simulation even if the electrodes are planar [START_REF] Merlet | The Electric Double Layer Has a Life of Its Own[END_REF][START_REF] Friedl | Interface between an Au(111) Surface and an Ionic Liquid: The Influence of Water on the Double-Layer Capacitance[END_REF][START_REF] Su | Double Layer of Au(100)/Ionic Liquid Interface and Its Stability in Imidazolium-Based Ionic Liquids[END_REF][START_REF] Wen | Potential-dependent adlayer structure and dynamics at the ionic liquid/Au(111) interface: A molecular-scale in situ video-STM study[END_REF]. It is mainly the process of adsorption of cations and anions at the surface that controls the capacitance. The structure of the electrolyte at an interface differs from the bulk one, and it may change drastically when an electric potential is applied to the electrode. For example, Merlet et al. reported that the structure of an ionic liquid adsorbed on graphite electrodes can be either ordered or disordered depending on the applied voltage [START_REF] Merlet | The Electric Double Layer Has a Life of Its Own[END_REF]. In this study, the structural changes were explained by a substantial change in the charge distribution across the interfacial region that led to changes in the differential capacitance with applied voltage. Limmer performed systematic simulations for dense ionic solutions near charged planar electrodes and showed that first-order transitions and spontaneous charge density 74 5.1. MODEL AND COMPUTATIONAL DETAILS ordering at the interface might result in potential-driven anomalous differential capacitances [START_REF] Limmer | Interfacial Ordering and Accompanying Divergent Capacitance at Ionic Liquid-Metal Interfaces[END_REF]. More recently, Ma et al. reported that the differential capacitance might be strongly influenced by the charge-driven lateral structural evolution of the ions in EDLCs [START_REF] Jia | Charge driven lateral structural evolution of ions in electric double layer capacitors strongly correlates with differential capacitance[END_REF]. It is therefore very difficult to predict the interfacial structure without using complex simulation and/or experimental characterization techniques.

For the application of water-in-salt to EDLCs, several experimental works have been reported including some capacitance measurements [START_REF] Coustan | Electrochemical behavior of platinum, gold and glassy carbon electrodes in water-in-salt electrolyte[END_REF][START_REF] Gambou | Electrochemical characterization of MnO2-based composite in the presence of salt-in-water and water-in-salt electrolytes as electrode for electrochemical capacitors[END_REF][START_REF] Hasegawa | Hierarchically Porous Carbon Monoliths Comprising Ordered Mesoporous Nanorod Assemblies for High-Voltage Aqueous Supercapacitors[END_REF][START_REF] Lannelongue | Water-in-Salt for Supercapacitors: A Compromise between Voltage, Power Density, Energy Density and Stability[END_REF].In addition, a few studies have aimed at understanding the interfacial structure of these electrolytes near electrodes [START_REF] Vatamanu | Ramifications of Water-in-Salt Interfacial Structure at Charged Electrodes for Electrolyte Electrochemical Stability[END_REF][START_REF] Borodin | Modeling Insight into Battery Electrolyte Electrochemical Stability and Interfacial Structure[END_REF][START_REF] Wang | Hybrid Aqueous/Non-aqueous Electrolyte for Safe and High-Energy Li-Ion Batteries[END_REF], but their capacitive behavior has not been analyzed so far. Among the questions to be solved, an important one is whether water-in-salts behave as ionic solutions or ionic liquids. Thus, in this work, we performed molecular dynamics (MD) simulations at various applied potentials for an electrochemical cell consisting of a water-in-salt electrolyte at a concentration of 20 m (mol/kg) LiTFSI, placed between two planar graphite electrodes, in order to obtain a microscopic picture of the structure and the capacitive behavior on the interfaces and their dependence on the applied potentials. We discuss in particular the differential capacitances of either a single electrode or of the full electrochemical cell. We show the variation of the differential capacitance and relate them to structural changes at specific potential ranges.

Model and computational details

We use MD to simulate a cell consisting of 20 m LiTFSI placed between two graphite electrodes. The simulation box contains 255 Li cations, 255 TFSI anions and 707 water molecules (Figure 5-1). We use the FF1 force field described in Chapter 3 [START_REF] Berendsen | The Missing Term in Effective Pair Potentials[END_REF][START_REF] Monteiro | Transport Coefficients, Raman Spectroscopy, and Computer Simulation of Lithium Salt Solutions in an Ionic Liquid[END_REF]. As we discussed in chapter 3, the use of FF1 yields an electrical conductivity The carbon atom charges on the electrode were allowed to fluctuate by imposing a constant potential method implemented in LAMMPS code [START_REF] Ilja | Influence of surface topology and electrostatic potential on water/electrode systems[END_REF][START_REF] Reed | Electrochemical interface between an ionic liquid and a model metallic electrode[END_REF][START_REF] Plimpton | Fast Parallel Algorithms for Short-Range Molecular Dynamics[END_REF][START_REF] Wang | Evaluation of the constant potential method in simulating electric double-layer capacitors[END_REF], which ensured an adequate description of the surface polarization by ions and water during simulations. A vacuum region was added in the z-direction and the Yeh-Berkowitz condition for slab correction was used to mimic the 2D periodic boundary condition.

Its length was set to eight times L z , which was the minimal value to ensure that the calculated carbon atom charges were converged. Simulations were performed for 11 applied potential differences between the two electrodes, ∆Ψ, varying from 0 to 3 V in order to obtain good statistical properties. The simulations were conducted in the NVT ensemble with a time step of 1 fs at room temperature (298.15 K). The system was first equilibrated during 80 ns at zero constant charge on each electrode and followed by a 12 ns equilibration at the constant potential for each ∆Ψ. The data was then collected in a 25 ns production run at the constant potential with configurations saved every 1 ps for each simulation.

NUMBER DENSITY AND CHARGE DENSITY

Number density and charge density

For each simulation within the studied potential range, positive and negative electrodes were assigned equal but opposite potential, so that ∆Ψ follows the Equation 5.1:

∆Ψ = Ψ + -Ψ -= 2Ψ + = -2Ψ - (5.1)
The number densities are computed along the z-direction normal to the graphite At null potential difference (∆Ψ=0 V), layered structures of the water-in-salt electrolytes have already been observed (top of the Figure 5-2), reflecting the adsorption of all the species at electrode/electrolyte interface. The interactions in a given layer are dominated by the short-range repulsion and the Coulombic interaction, in which the former controls the packing of ions and the latter occur between the various ions.

Different sizes and shapes of the species lead to the variations in the distances between successive planes, and the bulk-like structure is then recovered after the density oscillations extend up to several tens of angstroms.

When a non-zero potential difference is submitted to the electrodes, as shown in the bottom of Figure 5-2 (∆Ψ =3 V), the electrolyte keeps layered structures at the interface. The peaks are more pronounced due to the accumulation of charge on the electrode surfaces compared with those at the null potential difference. Apart from these, segregations of the ionic species (Li + and TFSI -) appear on both the negative (left) and positive (right) electrodes, which is generally at the origin of the overscreening effect in ionic liquid electrolytes (more details of this effect will be discussed later in this section). In particular, on the negative electrode, water molecules approach to the electrode together with the increasing number of lithium cations while part of TFSI anions are excluded from the interfacial layers. In the meantime, on the positive electrode, most of the lithium cations and water molecules are rejected to enter the interfacial layer due to the domination of TFSI anions. The most pronounced features of the ions and water density are observed within 6-8 Å , which correspond to ion and water partitioning in the interfacial layers. At null potential difference (Figure 5-3b), TFSI anions and water have similar peaks located at 3 Å , which is slightly higher than those in bulk. Though no lithium ion approaches the electrode surface closer than 3.4 Å , the first peak of Li cations appearing at 4.2

Å is the highest one observed in the interfacial layers. The overall peaks alternate between cations and anions indicating a typical picture of ionic liquid-like charge ordering at the interface.

Upon charging of the electrode up to ∆Ψ equals 3 V, i.e., 1.5 V and 1.5 V on the negative and positive electrodes, respectively, a significant increase of the cation (anion) and water adsorption at the interface is observed. On the negative electrode, the highest peaks of Li cations and water molecules increase up to values that are 7 and 5 times higher than their bulk ones, respectively (Figure 5-3a). The Li cations and water molecules have their first peaks located at the same distance to the electrode (2 Å), while different positions of their second peaks are observed (4 Å for Li and 3 Å for water). This indicates a change in the orientation of water molecules with respect to the electrode surface as reported by Vatamanu et al. [START_REF] Vatamanu | Ramifications of Water-in-Salt Interfacial Structure at Charged Electrodes for Electrolyte Electrochemical Stability[END_REF]. On the positive electrode, the interfacial layers within 2-6 Å are dominated by TFSI anions with three observed peaks, while the water molecules and Li cations are screened from direct interaction with the electrode surface. Moreover, the highest peak within 6 Å is around 3 times higher than the bulk one for predominant species which is smaller than the ones on the negative electrode. The difference of the distributed features for all the species between negative and positive electrode surfaces has significant impact on the charge density distributions at interfacial layers.

In Figure 5-4, the charge density profiles are obtained by combining the contributions from both the electrodes and electrolytes, in which the relation ρ q = ρ α • q α (ρ α and q α are number density and charge for species α) is used to calculate the charge density of the electrolyte. Similarly to the number density profiles in Figure 5- The total surface charge on the negative/positive electrode is the sum of the charges of the individual electrode atoms, which is linked to the capacitive performance of supercapacitors. As shown in Figure 5-5, the total charge, Q tot (t), fluctuates with respect to the time in constant potential simulations. After a long equilibration for a fixed applied potential difference ∆Ψ, the average total charge Q tot ∆Ψ estimated from their fluctuations reaches a converged value. The latter can then be used to quantify the capacitance of a supercapacitor.

Integral capacitance of full electrochemical cell

The capacitance is one of the most important physical properties for the performance of EDLCs. However, one can define it in several ways. The integral capacitance of the full electrochemical cell, C int , is defined as (for ∆Ψ = 0):

C int (∆Ψ) = σ ∆Ψ ∆Ψ (5.2)
where σ ∆Ψ is the average surface charge density of the positive electrode given by Qtot ∆Ψ S

(with S the surface area). Note that most of the charge is accumulated on the two graphene planes located closer to the liquid, for example at the largest applied potential, the average charge within the three graphene layers are 0.21, -2.01 and 9.66 electrons, respectively. In the present work, the calculated C int ranges from 3.5 to 4.3 µF/cm 2 depending on ∆Ψ. This quantity is regularly used in applied studies to estimate the energy density of the EDLCs.

Calculation of differential capacitance of single

electrode based on potential drop

Poisson potential

The electrostatic potential profile across the EDLC cell determines the potential drop for each interface, and is obtained by solving Poisson's equation:

ϕ(z) = ϕ q (z 0 ) - 1 0 z z 0 dz z -∞ dz ρ q (z ) (5.3)
where ρ q (z) is the average charge density profile across the cell, as shown in Figure 5- potential drop across each interface is then given by ∆Ψ ± = Ψ ± -Ψ bulk and is used to characterize the interfaces.

Differential capacitance of single electrode

The differential capacitance, C diff , is defined by

C diff = ∂ σ ∆Ψ ∂∆Ψ (5.4)
which measures the response of the average surface charge density to changes in the applied potential difference and provides much more information on the physicochemical processes than the integral capacitance. The single electrode differential capacitances can also be defined by splitting the applied potential difference, ∆Ψ, between the two electrodes into two potential drops, ∆Ψ ± , at the electrode/electrolyte interface for both positive and negative electrodes.

The average surface charge as a function of the potential drop across each interface

C s diff = ∂ σ ∆Ψ ∂∆Ψ ± (5.5)
As shown in Figure 5-8, the curve may be fitted by many polynomial functions, leading to very different shapes for the capacitance. We therefore limit ourselves to two linear fits, for ∆Ψ ± positive and negative, respectively. As shown in Figure 5-7, the negative electrode has a larger capacitance (10.1 µF/cm 2 ) than the positive electrode (5.6 µF/cm 2 ). Such a difference is in agreement with the results reported in planar graphite electrodes and pure RTILs [START_REF] Merlet | Influence of solvation on the structural and capacitive properties of electrical double layer capacitors[END_REF][START_REF] Merlet | Imidazolium Ionic Liquid Interfaces with Vapor and Graphite: Interfacial Tension and Capacitance from Coarse-Grained Molecular Simulations[END_REF][START_REF] Xing | Electrode/Electrolyte Interface in Sulfolane-Based Electrolytes for Li Ion Batteries: A Molecular Dynamics Simulation Study[END_REF], and it can be attributed to the different shapes or sizes of ions. The larger difference in capacitive behaviors between positive and negative electrodes compared with reported results in BMIM-PF 6 system (3.9 µF/cm 2 and 4.8 µF/cm 2 for positive and negative electrode, respectively [START_REF] Merlet | Imidazolium Ionic Liquid Interfaces with Vapor and Graphite: Interfacial Tension and Capacitance from Coarse-Grained Molecular Simulations[END_REF])

arises from the much larger asymmetry between the Li cation (1.8 Å in radius) and the TFSI anion [START_REF] Uysal | Structural origins of potential dependent hysteresis at the electrified graphene/ionic liquid interface[END_REF] (which has dimensions of 10.9×5.1×4.7 Å3 ). The differential capacitances can be computed more reliably using the importance sampling method [START_REF] Merlet | The Electric Double Layer Has a Life of Its Own[END_REF][START_REF] Limmer | Charge Fluctuations in Nanoscale Capacitors[END_REF][START_REF] Betul Uralcan | Concentration Fluctuations and Capacitive Response in Dense Ionic Solutions[END_REF][START_REF] Ray | Importance sampling large deviations in nonequilibrium steady states[END_REF]. Compared to previous equation, single electrode capacitances cannot be obtained (the full cell one C diff is calculated instead), but the method is much more converged statistically. This approach also allows studying microscopic properties, such as the number of ions close to the interface, as a continuous function of the applied potential difference. While for the standard approach these quantities are only available at the simulated potentials. Here, the total charge Q tot of the electrode is utilized to determine the weight of configurations at an arbitrarily applied potential by using the weighted histogram analysis method involved in importance sampling [START_REF] Ferrenberg | Optimized Monte Carlo data analysis[END_REF][START_REF] Tan | Theory of binless multi-state free energy estimation with applications to protein-ligand binding[END_REF]. As shown in Figure 5-9,

0 2 4 6 8 Q tot (e) -6 -5 -4 -3 -2 -1 0 1 2 ln
P (Q tot ) 0 V 0.3 V 0.5 V 0.7 V 1 V 1.2 V 1.5 V 2 V 2.4 V 2.7 V 3 V

CALCULATION OF DIFFERENTIAL CAPACITANCE OF FULL CELL FROM FLUCTUATION OF SURFACE CHARGE

there is a good overlap between histograms of Q tot obtained from the eleven performed simulations, which fulfills the requirement for correct histogram reweighting.

To obtain the probability distribution of any other property, A, as a function of ∆Ψ, we just need to integrate Q tot from the joint distribution of Q tot and A as

P (A|∆Ψ) = dQ tot P (Q tot , A|∆Ψ) (5.6)
Specifically, in this chapter, we consider below as the observables A: the surface charge density σ, the numbers of ions and water in the interfacial layers adsorbed on both negative and positive electrodes. more likely values of surface charge (red region), which are located at ∆Ψ ∼ 0, 0.35, 0.9, 1.2, 1.6, 1.8, 2.6, and 3 V. These applied potentials correspond to a more effective balance between the interfacial electrolyte and the surface charge on electrodes.

Distribution of surface charge and differential capacitance

The intermediate states between these points show large distributions of σ, which correspond to the large fluctuations regions where structural changes occur as we will discuss later.

In constant potential simulations, the differential capacitance (in Figure 5-10b) is proportional to the variation of surface charge density on the electrode as defined by

C diff = S k B T (δσ) 2 ∆Ψ (5.7)
It can be obtained directly from the probability distribution of σ in Figure 5-10a.

We recall here that the relation between the response to voltage and the equilibrium fluctuations of the surface charge is not limited to a typical linear response approximation [START_REF] Limmer | Charge Fluctuations in Nanoscale Capacitors[END_REF][START_REF] Rotenberg | Structural Transitions at Ionic Liquid Interfaces[END_REF]

Conclusions

In this chapter, the aim was to explore the capacitive performance of water-in-LiTFSI electrolyte in supercapacitors. We performed molecular dynamics simulations of 20 m

LiTFSI placed between two planar graphite electrodes at various applied potentials ranging from 0 to 3 V. The integral capacitance of the full electrochemical cell, as well as the single electrode capacitances, were computed. Using importance sampling methods, the differential capacitance was investigated as a continuous function of the applied potential difference ∆Ψ. The differential capacitance displays a number of non-trivial features which we explained by investigating the structural evolutions of the interfacial electrolytes. Contrarily to previous works on conventional aqueous or organic electrolytes [START_REF] Burt | Capacitance of Nanoporous Carbon-Based Supercapacitors Is a Trade-Off between the Concentration and the Separability of the Ions[END_REF][START_REF] De-En | Solvent effect on the pore-size dependence of an organic electrolyte supercapacitor[END_REF][START_REF] Jiang | Unusual effects of solvent polarity on capacitance for organic electrolytes in a nanoporous electrode[END_REF][START_REF] Jiang | Molecular dynamics simulations of the electric double layer capacitance of graphene electrodes in mono-valent aqueous electrolytes[END_REF][START_REF] Yang | Molecular Origin of Electric Double-Layer Capacitance at Multilayer Graphene Edges[END_REF][START_REF] Bo | Design of Supercapacitor Electrodes Using Molecular Dynamics Simulations[END_REF], the water molecules do not play a direct role on the variation of the capacitance because most of them are strongly bound inside the first hydration shell of the lithium ions, so that the capacitive behavior overall displays similar features as in the case of pure ionic liquids. This work is a first step toward understanding the capacitive behaviors of water-in-salt electrolyte in supercapacitors from simulations, in particular, the structural driven potential dependence of differential capacitance, which still requires more experimental explorations. The results could provide useful information for the understanding and development of new water-in-salts electrolytes and their applications in both supercapacitors and batteries.

General conclusions

The aim of this work was to investigate the water-in-salt electrolytes and their performance in supercapacitors. We performed molecular dynamics simulations for: i) bulk LiTFSI and water mixtures at various salt concentrations; and ii) interface of the LiTFSI-based water-in-salt electrolyte at high concentration in contact with planar graphite electrodes.

Firstly, the dynamic properties including viscosity, diffusion coefficient and conductivity were systemically investigated for systems of LiTFSI and water mixtures in a wide range of salt concentrations from 0.3 m to 20 m using a first parameterization of the force field (FF1). There is an apparent dependence of dynamic properties on salt concentrations. The system becomes viscous with increasing viscosity and decreasing diffusivity when switching from low to high concentration regime. The ionic conductivity first increases to a maximum (at 3.5 m) and then decreases at water-insalt region. However, on the basis of Walden plot, where the molar conductivity is shown as a function of fluidity, the super-concentrated water-in-salt electrolytes exhibited even better performance as good-ionic solutions than those with smaller salt concentrations. Therefore, it seems that the conductivity of water-in-salt solutions at high concentration was decoupled from its viscosity, making it possible to be a promising electrolyte for both batteries and supercapacitors from the dynamic point of view.

Moreover, the dependence of diffusion coefficients on force field parameters, especially the ratio of water-to-lithium at super-concentrated water-in-salt electrolytes, are observed in our simulations, emphasizing the difficulty for precisely describing the water-in-salt electrolytes from simulations. Based on the modification of the parame-

94

GENERAL CONCLUSIONS ters from FF1, we re-computed the dynamics properties using four different force field and compared the results with experimental measurements. An optimized force field was ultimately proposed, which can be able to reproduce all the dynamic properties with experiments.

Apart from the dynamics of LiTFSI and water mixtures, the structural properties of the system at a specific concentration, i.e., 15 m LiTFSI dissolved in water, were also studied to have a deep understanding of the microscopic pictures of water-in-salt electrolytes at super-concentrated states. On the one hand, the solvation property of lithium ions was investigated in terms of the coordination number, residence time of water and potential of mean force. From the speciation point of view, the water/lithium ratio becomes lower than 4 due to the insufficient amount of water at 15 m, which leads to the under-hydration of Li + that forms Li(H 2 O) + 3 or even Li(H 2 O) + 2 . The missing water molecules are then replaced by oxygen atoms from TFSI anions, but the latter is much more loosely bound based on the potential of mean force analysis. The analysis of residence time of water and fraction of free water strongly associated with the potential of mean force and exhibited a high dependence on the choice of force field. Moreover, the formation of some lithium-lithium dimers was observed at short distances (r Li-Li < 3.8 Å), which were mostly coordinated by sharing water molecules rather than TFSI anions. On the other hand, the analysis of the solvation property of water molecules indicated that the hydrophobic behavior of TFSI anions also depends on the choice of force field.

Secondly, the study of 20 m LiTFSI aqueous solutions placed between two planar graphite electrodes was performed, in order to explore the double-layer structure of water-in-salt electrolyte, and its consequence for the interfacial capacitance. The results showed that many structural changes occur in the layer of adsorbed liquid when the potential of the electrode is changed. Fluctuations in the two ions (Li + and TFSI -) concentrations as well as in the water distributions are observed. We also see substantial reorientations of the anionic species. All these structural changes, which were studied using importance sampling methods, are linked to peaks in the differential capacitance, which shows that the free energy landscape of this system is

Confinement Effects on an Electron Transfer Reaction in Nanoporous Carbon Electrodes

Zhujie Li, †, ‡, ¶ Guillaume Jeanmairet, ‡, ¶ Trinidad Meńdez-Morales, †, ¶ Mario Burbano, †, ¶ Matthieu Haefele, † and Mathieu Salanne* , †, ‡, ¶ † Maison de la Simulation, CEA, CNRS, Univ. Paris-Sud, UVSQ, UniversitéParis-Saclay, F-91191 Gif-sur-Yvette, France ‡ Sorbonne Universiteś, UPMC Univ Paris 06, CNRS, Laboratoire PHENIX, F-75005 Paris, France ¶ Reśeau sur le Stockage E ĺectrochimique de l'E ńergie (RS2E), FR CNRS 3459, 80039 Amiens Cedex, France * S Supporting Information ABSTRACT: Nanoconfinement generally leads to a drastic effect on the physical and chemical properties of ionic liquids. Here we investigate how the electrochemical reactivity in such media may be impacted inside of nanoporous carbon electrodes. To this end, we study a simple electron transfer reaction using molecular dynamics simulations. The electrodes are held at constant electric potential by allowing the atomic charges on the carbon atoms to fluctuate. We show that the Fe 3+ /Fe 2+ couple dissolved in an ionic liquid exhibits a deviation with respect to Marcus theory. This behavior is rationalized by the stabilization of a solvation state of the Fe 3+ cation in the disordered nanoporous electrode that is not observed in the bulk. The simulation results are fitted with a recently proposed two solvation state model, which allows us to estimate the effect of such a deviation on the kinetics of electron transfer inside of nanoporous electrodes.

N anoconfinement effects strongly impact many liquid properties, such as transport, diffusion coefficients, phase transitions, and solvation structures. 1-4 They are particularly important for supercapacitors, which have emerged as a complementary energy storage solution to batteries. 5 This is due to the fact that supercapacitors display faster charging times and consequently higher power deliveries than batteries while attaining longer life cycles. However, the energy density of batteries is higher. In supercapacitors, energy storage is realized through the adsorption of ions at the surface of two oppositely polarized electrodes, forming a so-called electrical double layer. 6 Nanoconfinement has been observed to have a significant influence on the performance of supercapacitors, as has been demonstrated by experiments 7,8 and simulations, 9-12 where it was shown that the use of materials with subnanometric pores as electrodes greatly increases the capacitance of these devices.

Within the realm of electrochemical applications, roomtemperature ionic liquids (RTILs) have attracted considerable attention. 13,14 In principle, the properties of RTILs are tunable due to the wide variety of cations and anions from which they can be prepared. Because RTILs are solely made of charged species, it would have been expected that using them to replace standard electrolytes would increase the performance of supercapacitors. Yet, the interfacial capacitance of RTILs and acetonitrile-based electrolyte supercapacitors remains somewhat similar. This rather disappointing observation has been attributed to the more important correlations between ions in RTILs, which is due to the absence of electrostatic screening by the solvent. 15 An alternative could be to take advantage of the tunability of RTILs to develop new storage concepts. Recently, Mourad et al. reported a large enhancement of the energy stored due to simultaneous capacitive and Faradaic processes when biredox RTILs are used as electrolytes in a supercapacitor. 16 Among the various questions raised by this study, the most important ones are the following: How is the electron transfer rate affected by confinement? Does the charging of such a supercapacitor remain dominated by the ionic diffusion?

From the theoretical point of view, electron transfer reactions in solution are usually studied in the framework of Marcus theory, which aims at accounting for the influence of solvent fluctuations on the rate of electron transfer. 17 Marcus theory has been widely used to interpret experiments and simulations with undeniable success. However, some systems exhibiting a deviation from Marcus linear behavior have been reported. 18,19 Several extensions to the theory were proposed to account for them. 20,21 A reason why Marcus theory might fail arises from the fact that one of its key assumptions is that the fluctuations of the solvent around the reactant and the product are similar. Yet, if the solvation states of the two species are structurally different, this hypothesis can be wrong, as evidenced by the use of density functional theory-based molecular dynamics (MD) simulations of aqueous copper and silver ions. 19,21 In experiments as well, introducing asymmetry in Marcus theory 22 was necessary to fit the voltammetric data of various RTILs. 23 Finally, in the case of interfacial systems, several studies have underlined the importance of field penetration into the metal and of solvent spatial correlations. 24,25 Confinement might have a drastic influence on the solvation shell of the adsorbed species. 26,27 Thus, it is worth investigating this effect on the electron transfer rate. 28 We report here a MD study of the Fe 3+ /Fe 2+ electron transfer reaction, which has already been proposed in previous redox supercapacitor concepts. 29,30 The experimental studies involve complex species, so that we focus on a simplified system in order to gain a first insight into electron transfer reactions in carbon nanopores. In particular, our study corresponds to infinite dilution because it is known that inorganic salts have low solubilities in imidazoliumbased RTILs. 31 The studied ionic liquid is 1-ethyl-3-methylimidazolium tetrafluoroborate (EMIM-BF 4 ), which is put in contact with model carbide-derived carbon (CDC) nanoporous electrodes. We show that the free-energy profiles for the electron transfer reaction strongly deviate from Marcus theory due to the presence of two solvation states for the Fe 3+ species.

We build on previous work by using a simulation cell similar to the one that we used to investigate the origin of increased capacitance in nanoporous carbon-based supercapacitors (see Figure 1). 10 We employ a coarse-grained model of EMIM-BF 4 with, respectively, 3 and 1 interaction sites for the cation and the anion, 33 to which we add one iron ion and the appropriate number of chloride counterions. We keep the electric potential inside of the electrodes constant and equal to 0 V by using the procedure developed by Siepmann and Sprik, 34 which allows the charge on the electrode to adjust in response to the local electric potential due to the electrolyte ions. Each electrode is represented by a model of CDC containing 3821 carbon atoms. 35 To address the effect of the local environment experienced by the redox species, we run several simulations in which the initial position of the iron ion is set in different pores of the disordered carbon material. In order to study the following redox half-reaction

→ + + + - Fe Fe e 2 3
we perform simulations of the reduced species Fe 2+ and of the oxidized one Fe 3+ . It has been shown by Warshel 36,37 that a relevant reaction coordinate to study the electron transfer reaction is the vertical energy gap ΔE, which is defined as

Δ = - E E E R R R ({ }) ({ }) ({ }) N N N 1 0 (1)
where E 1 and E 0 are the instantaneous potential energies of a system with either the reduced or the oxidized state of the redoxactive species for a given microscopic configuration {R N }. We recall here that in the linear response assumption in Marcus theory, 17,38 the distribution of the order parameter is Gaussian, 39 and in particular, the shape of the distribution of ΔE obtained by performing simulations with the Hamiltonian of the reactant or the product should be identical. As shown in Figure 2a, this is clearly not the case, the distribution for the Fe 2+ being almost Gaussian while the one for the Fe 3+ is not. This is a first indicator that this system does not follow a Marcus theory picture. In order to increase the statistical accuracy, we use the freeenergy perturbation method. This variant of umbrella sampling introduces a coupling parameter (η) between the reduced and oxidized states. 40 The simulations are then performed with an intermediate Hamiltonian associated with the potential energy surface E η defined as the linear superposition

A direct consequence of the linear assumption of Marcus theory is that E η should vary linearly with η. 40 To test this, we carried out simulations with different values of the coupling parameter η = 0, 0.25, 0.5, 0.75, 0.8, 0.9, and 1.0. It is clear for Figure 2b that the Marcus picture is violated because the corresponding vertical energy gaps do not follow the expected linear variation. As pointed out in the introduction, discrepancy with Marcus theory often originates from strong changes in the solvation shell between the reduced and oxidized states. To investigate if that is indeed the case here, we examine the coordination number (CN) of the iron cation along the simulations. The radius of the first solvation shell is taken equal to the first minimum of the Fe-BF 4 radial distribution function in the absence of electrodes (3.8 Å). We observe that the CN of the Fe 3+ cation fluctuates between values of 4 and 6 during the simulation. This is clearly an effect of the confinement because the cation remains close to the carbon electrode and the corresponding CN is 4 in the pure RTIL. In contrast, the Fe 2+ cation has a CN that remains equal to 4 during the whole simulation, as shown in Figure S1.

The distances between Fe 3+ and the six nearest anions along a representative trajectory are displayed in Figure 3a; the other simulations display similar variations. The alternation between two coordination environments is confirmed by the fact that during some parts of the simulations we detected that four anions are closely coordinated to the Fe 3+ with a Fe-BF 4 distance of 2.8 Å, the two remaining anions being located farther away from the iron with a distance greater than 4 Å, while in other parts, the six anions are coordinated with Fe 3+ with metal-ligand distances fluctuating between 2.6 and 3.8 Å. Figure 3c,d shows representative snapshots of the two coordination states, which appear to be tetrahedral and octahedral, respectively. The corresponding fluctuations of the vertical energy gap are shown in Figure 3b. Sudden changes occur concomitantly with the jumps in CN in Figure 3a, which shows that the confinement effect on the solvation of Fe 3+ is at the origin of the departure from Marcus theory discussed above.

Among all models available in the literature to extend Marcus theory to nonlinear behavior, 41 we use the one proposed by Vuilleumier et al. 21 In particular, we employ their two-Gaussian solvation (TGS) state model, which allows the reactant and product to experience two different solvation states (S 0 and S 1 ). This leads to four (two pairs) diabatic free-energy parabolas instead of two in the case of Marcus theory. For each of the states S 0 or S 1 , the Landau free energy is assumed to be quadratic, which corresponds to a Gaussian probability distribution P η . The authors also derived the necessary equations to compute the average energy gap ⟨ΔE⟩ η and the Landau free energies.

Marcus theory involves only two parameters: ΔA measures the relative position of the two parabolas, while λ is the reorganization energy of the solvent, which fixes the curvature of the parabola and also the width of the Gaussian distribution of the reaction coordinate. In the TGS model, four parameters are required, one reorganization energy for each state λ S 0 and λ S 1 and the relative positions of the two parabolas for each solvation state ΔA S 0 and ΔA S 1 . Moreover, a fifth parameter is necessary to set the relative position of the two pairs of parabolas, for instance, the difference in free energy between the two solvation states of the reduced species Δ S A 0 = A S 1 Fe 2+ -A S 0 Fe 2+ . The effect of the confinement was not investigated by the authors of the TGS model because they only carried out simulations in bulk. However, it has been shown from simulation

The Journal of Physical Chemistry Letters

Letter studies of the Eu 3+ /Eu 2+ redox couple in potassium chloride molten salt at a fcc metallic electrode that the reorganization energy strongly depends on the distance between the ion and the electrode. 42 This reorganization energy is expected to decrease when the redox species get closer to the electrode. We mention that this behavior had previously been predicted theoretically by Marcus for perfect conductors, 38,43 but this effect should decrease if the role of field penetration into the metal electrode was accounted for. 24,25 To quantify this effect in our system, we performed additional simulations with planar graphite electrodes. They confirm the dependency on the distance to the electrode of the reorganization energy, as shown in Figures S2-S4. In nanoporous electrodes, it is not possible to define a simple distance to the electrode; the fit of the TGS model should therefore yield an averaged contribution of all of the possible distances. However, we observed that the iron does not go into contact with the carbon during the entire simulation, regardless of the iron solvation state, the nature of the pore in which it is solvated, or its CN. For this reason and for the sake of simplicity, we made the additional assumption that the reorganization energies should be equal for both states, turning the original five-parameter model TGS into a four-parameter one. The different parameters obtained by fitting the simulation data are given in Table 1. The diabatic free-energy curves for the reduced and oxidized species in Fe 3+ /Fe 2+ predicted by the TGS model with the parameters of Table 1 are plotted in Figure 5. The two parabolas for the reduced or oxidized state (η = 0 or 1) correspond to a given solvation state. The free-energy difference (Δ S A 0 ) between the hexacoordinated and the tetracoordinated forms of Fe 2+ is large (0.52 eV) with respect to the thermal energy k B T (34.5 meV at T = 400 K). The hexacoordinated state is therefore very unlikely, which explains why it is never observed in our equilibrium simulations. On the other hand, the free energies of the two coordination states are very close to each other for Fe 3+ .

The thermodynamic and kinetic information extracted from Figure 5 is summarized in a mechanistic diagram in Figure 6. We 1. "CN4" and "CN6" labels refer to the tetra-and hexacoordinated solvation states and correspond to S 0 and S 1 , respectively. Black numbers: free-energy differences; red numbers: activation energies (labeled ΔA 1 † and ΔA 2 † in Figure 5).

The Journal of Physical Chemistry Letters

Letter can see that the electron transfer from tetracoordinated Fe 2+ to hexacoordinated Fe 3+ is as likely as the transfer to the tetracoordinated Fe 3+ from a thermodynamic point of view because the corresponding free-energy differences are very similar, 0.25 and 0.24 eV, respectively. From a kinetic point of view, the picture is completely different because the corresponding activation energy, taken at the intersection between the two parabolas, is much higher (0.55 vs 0.39 eV). As a consequence, the effect of the confinement is likely to have a negative impact on the kinetic rate of the electron transfer reaction. Indeed, it allows for the existence of hexacoordinated Fe 3+ , which is not stable in the bulk liquid in our simulations. The electron transfer from Fe 2+ to this chemical species has a very large activation energy barrier, making such events unlikely to occur. This result contrasts with the observation of Remsing et al., who observed enhancement of the electron transfer due to the confinement 44 in a very different system. This is easily explained because in their work both the reduced and oxidized species were desolvated with respect to the bulk, while we observe the opposite behavior.

In conclusion, the aim of this work was to investigate the freeenergy properties of an electron transfer reaction in a nanoporous carbon electrode. We performed MD simulations of the Fe 3+ /Fe 2+ redox couple dissolved in EMIM-BF 4 RTIL in contact with CDC electrodes. The latter were maintained at a constant potential of 0 V during the simulations. The vertical energy gap between the redox species was used as the reaction coordinate, which enabled us to interpret the microscopic solvent fluctuation properties. The computed probability distribution of the vertical energy gaps and the equilibrium value of energy gaps do not follow the linear response approximation of standard Marcus theory. We demonstrated the strong influence of the nanoconfinement effect on the solvation shell of the iron cations, which is the main reason for this departure from Marcus theory. In particular, the Fe 3+ cation, which is tetracoordinated in the bulk, admits two stable solvation states in the nanoporous material: tetracoordinated and hexacoordinated. To account for this deviation, we used the TGS model, 21 from which the free-energy curves for all of the redox species in their various solvation states were extracted. This allowed us to qualitatively analyze the effect of confinement on the electron transfer reaction. The fluctuations in the structure of the solvation shell of Fe 3+ were shown to have a negligible effect from a thermodynamic point of view. Rather, it was shown that the activation energy of the associated electron transfer process is much higher for the hexacoordinated form. It is therefore likely that the stabilization of this solvation state will result in a slow down of the electron transfer reaction kinetics. This work is a first step toward a deeper understanding of the influence of the confinement on electron transfer in redox supercapacitor devices, 29 which will be extended in future years to promising systems such as biredox RTILs. 16 To this end, it will be necessary to simulate more complex redox probes and to account systematically for the various complexation states. Another important aspect will be to decouple the contribution of the electron transfer event from the work term that controls the approach of the ion to the interface in nanoconfinement. 28 The techniques developed in this work could also provide useful information for the development of ionic-liquid-based thermoelectrochemical cells. 45

■ METHODS

We performed MD simulations of the present systems using coarse-grained force fields. The nonbonded interactions are represented using Lennard-Jones and Coulomb potentials, and the corresponding parameters for carbon atoms and EMIM-BF 4 interaction sites that we used herein are obtained from our previous work. 32,46 The parameters for the chloride and the iron ions are respectively taken from refs 47 and 48 (the chloride anions were added in order to maintain the electroneutrality of the simulation cell; however, their effect on the vertical energy gap was not studied because we focused on infinite dilution conditions). The simulations were conducted in the NVT ensemble, with the temperature set at 400 K using a Nose-Hoover thermostat (relaxation time: 10 ps). The simulation cell was orthorhombic, with x = y = 4.37 nm and z = 14.86 nm, which reproduced the density of the RTILs compared with experimental results. Periodic boundary conditions were employed along x and y directions only through the use of a 2D Ewald summation. 49 For all of the simulations, the time step was 2 fs, and the time scales of production runs were over 500 ps after equilibration. The electrodes were maintained at a constant potential (0 V in our present study) during the production runs. The vertical energy gap was sampled every 1 ps during the simulation. Following our previous work, a constant was added to the energies calculated in the simulation to represent the (gasphase) ionization potential of Fe 2+ and the work function of the metal; 42 in practice, the value (15.78 eV) was chosen to bring the calculated redox potential close to the typical experimental values for the Fe 3+ /Fe 2+ couple in RTILs. 50 ■ ASSOCIATED CONTENT * S Supporting Information

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.7b00458.

Distance between the anions and Fe 2+ inside of the CDC electrode, snapshot of the simulated graphite-based electrochemical cell, potentials of mean force with respect to the distance to the graphite, and corresponding reorganization energies (PDF)

■ AUTHOR INFORMATION

Corresponding Author *E-mail: mathieu.salanne@upmc.fr.

ORCID

Mathieu Salanne: 0000-0002-1753-491X

Notes

The authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

This work was supported by the French National Research Agency (Labex STORE-EX, Grant No. ANR-10-LABX-0076). We acknowledge support from EoCoE, a project funded by the European Union Contract No. H2020-EINFRA-2015-1-676629, from the DSM-eńergie programme of CEA, and from the Eurotalent programme. We are grateful for computing resources on OCCIGEN (CINES, French National HPC) and CURIE (TGCC, French National HPC) obtained through the project x2016096728.

■ REFERENCES

I

  feel so lucky to work under his supervision. I would like to sincerely thank Benjamin Rotenberg, Mario Burbano, Guillaume Jeanmairet, Trinidad Méndez-Morales and Matthieu Haefele for their fruitful discussions and contributions to my research. I would like to thank also my colleagues from both Maison de la Simulation and Laboratoire PHENIX.

I

  have been privileged to have visits with David Limmer at University of California, Berkeley, and Vladislav Ivanistsev at University of Tartu. I would like to thank them for sharing their knowledge and I have benefited from the fruitful discussion with them.

Figure 1 - 1 :

 11 Figure 1-1: Distribution map of liquid electrolytes with weight and volume ratio of salt-to-solvent [2].

1. 2 .

 2 APPLICATION OF WATER-IN-SALTS IN BATTERIES tigated as an alternative ion of Li when targeting more economically competitive rechargeable batteries. Meanwhile, the development of aqueous sodium-ion batteries utilizing WiS electrolytes has made significant progress. Suo et al. demonstrated that a Na-ion WiS electrolyte containing 9.3 m NaOTf in water could expand the ESW to

  . Hu et al. report that a formulated novel WiS electrolyte of 21 m LiTFSI and 1 m Zn(OTf) 2 enabled great improvements in both voltage platform and cycling stability for Zn/V 2 O 5 aqueous hybrid-ion battery [58]. Moreover, a hybrid-Zn battery was reported by Wang et al. through the use of WiS electrolyte containing 1 m Zn(TFSI) 2 and 20 m LiTFSI [63]. 1.3. APPLICATION OF WATER-IN-SALTS IN SUPERCAPACITORS The Zn metal anode combined with either LiMn 2 O 4 or O 2 cathodes exhibited a high Zn reversibility along with high energy densities. Aqueous hybrid Zn/Na batteries were also reported by Li et al. very recently [62], in which 8 m NaClO 4 + 0.4 m Zn(OTf) 2 WiS electrolyte was used. So far, most reported WiS electrolytes including those above utilize fluorinated anions except for a few studies. However, Leonard et al. reported that the use of potassium acetate (KAc) aqueous solution at 30 m as a WiS electrolyte could provide an ESW of 3.2 V, broadening the exploration of new electrolytes for high-performance aqueous K-ion batteries [54]. Lukatskaya et al. reported that a mixed cation acetate WiS electrolyte (32 m KAc + 8 m LiAc) could be utilized to achieve high voltage (3 V) aqueous batteries, which has the reported lowest amount of water-to-salt ratio (1.

Figure 1 - 4 :

 14 Figure 1-4: Schematic of (a) supercapacitor and (b) Li-ion battery.

NaClO 4

 4 WiS electrolytes have been reported by Reber et al. and Zhang et al. [72, 77], where Na-ion based WiS electrolytes for supercapacitors were proposed. The former group demonstrated that an 8 m NaTFSI solution exhibited a high ionic conductivity of 5 S/m, along with enhanced ESW, which had better capacitive performances using AC-based electrodes than that of 21 m LiTFSI electrolyte. Upon adding a redox additive (0.5 m KI) into 8 m NaTFSI, the AC/AC full cell can deliver a high energy density of 37.8 Wh kg -1 with the operating voltage up to 1.8 V, which is comparable to the state-of-the-art non-aqueous supercapacitors. The latter group Zhang et al. reported that a MnO 2 -based supercapacitor using 17 m WiS as electrolyte displayed high energy and power densities and excellent cycle performance [77]. Moreover, a potassium acetate aqueous solution of 75 wt.% KAc (molar ratio of water-to-salt is 1.8) as WiS electrolyte was studied by Tian et al. [71]. The supercapacitor cell combined this electrolyte with AC/AC symmetric electrodes exhibited a high operating voltage of 2.0 V, along with enhanced energy densities compared with that of the normal concentration of the electrolyte. Apart from these, Zhang et al. demonstrated that the use of a protected lithium 1.4. MOTIVATION AND OBJECTIVE 21 negative electrode and MO 2 or AC electrodes combined with WiS electrolyte (21 m LiTFSI) could expand the maximum cell voltages (4.4 V or 4 V) and operating voltages (1.5 V or 1.8 V), making them become high-performance hybrid supercapacitors [79]. Dou et al. developed a hybrid organic/aqueous electrolyte by introducing a co-solvent-in-salt system, i.e., acetonitrile was added into 21 m LiTFSI WiS electrolyte yielding a "acetonitrile/water-in-salt" (AWiS) hybrid electrolyte [74]. The optimal AWiS hybrid electrolyte with a salt concentration of 5 m provided improved conductivity, decreased viscosity and lowered freezing temperature compared with 21 m LiTFSI WiS while inherited the featured advantages of WiS electrolyte, i.e., moisture-tolerant, non-flammable, wide ESW of 3 V. The presence of acetonitrile molecules separates the Li cations and TFSI anions, and thus weakens the electrostatic cation-anion attractions, which ultimately results in the enhanced transport

Figure 1 - 5 :

 15 Figure 1-5: Solvation property of Li cations obtained from MD simulations. (a) Coordination number of O(water) and O(TFSI) in the first solvation shell of Li + and the fraction of free water not coordinated by any Li + . (b) Illustration of the evolution of the lithium primary solvation shell in dilute and water-in-salt solutions. Adapted from Suo et al. [27].

1. 4 .

 4 MOTIVATION AND OBJECTIVE 23 electrolytes enables a deep understanding of the bulk structure, and thus leading to a better design of new electrolytes for energy storage systems with enhanced electrochemical performances. While the microscopic picture of WiS electrolytes remains lack of information on the nature and characterization of the solvation complexes, motivating us to further investigate various properties of such systems in a wide range from diluted to super-concentrated solutions.

1. 4 .

 4 Figure 1-6: Snapshots of the interfacial layer for "water-in-Bisalts" electrolyte containing 21 m LiTFSI and 7 m LiOTf at planar graphite electrode surface (top) and the corresponding density profiles normalized by bulk density as a function of distance from the electrode (bottom) at -2, 0, and 2 V vs the potential of zero charge [81].

Figure 2 - 1 :

 21 Figure 2-1: (a) Illustration of electric double layer capacitors with two electrodes maintained at constant potential difference. The atoms of the electrode are colored according to the instantaneous charge q i they carry, with the corresponding scale shown at the graphite electrode (b) a representative configuration of the first adlayer of the 1.5M 1-butyl-3-methylimidazolium (red) hexafluorophosphate (green) in acetonitrile (blue) solution in contact with it and the 111 crystal facet of a platinum electrode (c) a representative configuration of the first adlayer of the water in contact with it [118].

Figure 2 -

 2 Figure 2-1 shows the instantaneous atomic charges of a carbon electrode of the graphitic structure in contact with liquid electrolytes. In this figure, we see that the charges are not homogeneously distributed on the surface of the electrode. The charge carried by an electrode atom depends both on the imposed potential difference and the electrolyte present in the vicinity. Thus, each positive (respectively negative) charge is observed near an anion (or a cation, respectively). Taking polarizability into account thus modifies the representation of electrostatic interactions at the electrode-

Figure 2 - 2 :Figure 2 - 2 )

 2222 Figure 2-2: Evolution of the structure inside a positive nanoporous carbon electrode upon application of a constant charge (top) or a constant applied potential (bottom)simulation. The initially empty pore region is highlighted with a red circle[START_REF] Merlet | Simulating supercapacitors: Can we model electrodes as constant charge surfaces?[END_REF]. Green spheres: anions; red spheres: cations.

Figure 2 -

 2 Figure 2-3:Temperature drift when a constant potential difference is suddenly applied (inset: when a constant charge is assigned to each carbon atom)[START_REF] Merlet | Simulating supercapacitors: Can we model electrodes as constant charge surfaces?[END_REF].

Figure 3 - 1 :

 31 Figure 3-1: Structure of the mixture of water molecule, Li cation, and TFSI anion.

Figure 3 - 2 :

 32 Figure 3-2: Simulation cells of water and LiTFSI mixtures at 0.3 m (left), 3.5 m (middle), and 15 m (right). Same color labels as in Figure 3-1 except that the water molecules are shadowed for clarity.

Figure 3 - 3 :

 33 Figure 3-3: Simulated and measured densities at various concentrations.

Figure 3 - 4 :

 34 Figure 3-4: Evolution of viscosity data calculated by Equation 3.1 as a function of time at various concentrations. The final value of viscosities are given by the plateaus.

Figure 3 - 5 :

 35 Figure 3-5: Calculated viscosities (a) and Maxwell relaxation times (b) at various concentrations.

Figure 3 - 6 :

 36 Figure 3-6: Comparison of the calculated and experimental viscosities. The circles, stars, and triangles represent the calculated results by our simulations, measured results by our collaborators, and experimental results from ref [27], respectively.

Figure 3 - 7 :

 37 Figure 3-7: Simulated and measured diffusion coefficients for the water molecule, Li cation, and TFSI anion at various concentrations. Experimental results were obtained by A.-L. Rollet and R. Bouchal using pulse-field gradient NMR.

Figure 3 - 8 :Figure 3 - 9 :

 3839 Figure 3-8: Simulated and experimental conductivities at various concentrations. Experimental results were obtained by R. Bouchal.

3. 5 .

 5 COMPARISON WITH OTHER FORCE FIELDS intramolecular parameters are the same as FF1;3. FF4: Scaled charges of Li cation and TFSI anion with a factor of 0.8 based on FF3, all the remaining parameters are the same as FF3.Note that the water molecule is always without scaled charges; we keep using SPC/E model during all the simulations. Each of the simulations with new force fields is performed with equilibration runs for 60 ns, followed by 60 -90 ns production runs for data collections. The specific charges of Li cation and TFSI anion for the four force fields are listed in

FF1Figure 3 - 10 :Figure 3 - 11 :

 310311 Figure 3-10: Calculated viscosities from the different type of force fields compared with the experimental result.

  water-in-salt electrolyteAs discussed in chapter 3, the dynamic properties significantly change with the increase of concentrations, which could be attributed to the variation of structural properties, such as the solvation shell and speciation. Therefore, the structural properties of water-in-salt electrolytes at 15 m are discussed in this chapter not only to account for the dynamical performances but also to have deep understandings of the microscopic pictures of water-in-salt electrolytes at super-concentrated states. Although the FF4 has proven to be the best choice describing the systems at 15 m among the four studied force fields, it is also interesting to compare them when studying the structural properties. The results from this comparison are expected to shed new light on influence/role of the salt and water correlations.

4. 1 58 4. 1 .

 1581 Solvation shell of Lithium 4.1.1 Coordination number of Lithium The average coordination number of a reference particle A, i.e. the number of observed particles (B) surrounding each A on average, is calculated by integrating the radial 57 SOLVATION SHELL OF LITHIUM distribution function (RDF) of the A-B pairs through n(r ) = 4πρ r 0 r 2 g(r)dr (4.1)

Figure 4 - 1 :

 41 Figure 4-1: (a) Radial distribution functions of Li-water pair, and (b) corresponding coordination numbers as a function of Li-water distance.

Figure 4 -

 4 Figure 4-1b shows the corresponding coordination numbers (hydration numbers) of water molecules surround the Li cation. The plateau ranging from 2.1 Å to 3-3.5 Å for each of the force fields corresponds to the boundary between the Li first hydration shell and the second solvation shell, which is much more loosely bound.

Figure 4 - 2 :

 42 Figure 4-2: (a) Radial distribution functions of Li-O(TFSI) pair, and (b) corresponding coordination numbers as a function of Li-O(TFSI) distance.

Figure 4 - 4 ,Figure 4 - 3 :

 4443 Figure 4-4, respectively. The decay rate of the cage-out correlation function using FF1 (blue line in Figure 4-3) is extremely slow compared with the other three type

Figure 4 - 4 :

 44 Figure 4-4: Residence times obtained from cage-out correlation functions for which the function equals 1/e (dashed line in Figure 4-3).

Figure 4 -Figure 4 - 5 :

 445 Figure 4-5a shows the PMFs for water molecules escaping from the solvation shell of Li cations. The first minimum corresponding to the first peak in Figure 4-1a, indicates the strength of the Li-water interaction, which is represented by the energy gap (∆E) between the first minimum and the reference value (arbitrary fixed at 0 kJ/mol). The energy gaps (stabilization energies), ∆E, extracted from Figure 4-5a are shown in Figure 4-5b. We can see that the water molecules are stabilized by 8.8 to

Figure 4 - 6 :

 46 Figure 4-6: (a) Potential of mean forces for breaking of a Li-O(TFSI) "bond". (b) Stabilization energies (∆E) and barrier heights (E a ) calculated from the corresponding PMFs.

Figure 4 -Figure 4 - 7 :

 447 Figure 4-5a. In Particular, the FF3 and FF4 give similar value which is in agreement

Figure 4 - 8 :Figure 4 - 9 :Figure 4 -Figure 4 - 10 :

 48494410 Figure 4-8: Radial distribution functions of lithium-lithium pair.

4. 2 . ROLE OF WATER 69 4. 2 Figure 4 -

 26924 Figure 4-11: (a) Radial distribution functions of Hw(water)-O(TFSI) pair, and (b) Corresponding coordination numbers as a function of Hw(water)-O(TFSI) distance.

Figure 4 -

 4 Figure 4-12: (a) Potential of mean forces for breaking of a Hw(water)-O(TFSI) "bond". (b) Stabilization energies (∆E) and barrier heights (E a ) calculated from the PMFs.

Figure 4 - 13 :

 413 Figure 4-13: Combined radial/radial distribution functions for the Ow(water)-O(TFSI) pair (x axis) and Ow(water)-Li pair (y axis). The color bars represent the intensity of the contour plots, in which the values are shown in logarithmic scale for clarity.

  of 0.79 S/m a viscosity of 46.1 mPa•s, which are in good agreement with experimental results of Suo et al. (0.82 S/m and 36.2 mPa•s, respectively, albeit for a slightly larger concentration in salt of 20.8 m) [27]. The electrodes consist of three fixed graphene layers on each side (Figure 5-1) with in-plane dimensions of L x = 32.25 Å and L y

Figure 5 - 1 :

 51 Figure 5-1: The snapshot of simulation cell consisting of 20 m LiTFSI confined between two three-layered graphite electrodes, in which the all-atom model of electrolyte is shown at the interfaces with H (white), O (red), Li (green), F (orange), C (cyan), S (yellow), and N (blue) atoms, respectively. The TFSI anions beyond interfaces are represented by isosurface instead. The carbon walls are shown in side views.

Figure 5 - 2 :

 52 Figure 5-2: Number density profiles of Li cations, water molecules, and TFSI anions at applied potential differences ∆Ψ = 0 V (top) and 3 V (bottom). Note that the density profiles of water and TFSI are represented by the average densities of atoms in their molecules, respectively, for better comparison.

Figure 5 - 3 :

 53 Figure 5-3: Normalized density profiles of Li cation, water molecule, and TFSI anion with respect to their bulk density, as a function of distance to the positive/negative electrode at applied potential Ψ -= -1.5 V (a), Ψ ± = 0 V (b), and Ψ + = 1.5 V (c).

Figure 5 - 4 : 5 . 3 Figure 5 - 5 :

 545355 Figure 5-4: Charge density profiles across the simulation cell at applied potential difference ∆Ψ = 3 V (a), 1.5 V (b), and 0 V (c).

5. 4 .

 4 CALCULATION OF DIFFERENTIAL CAPACITANCE OF SINGLE ELECTRODE BASED ON POTENTIAL DROP 81

4 ,Figure 5 - 6 :

 456 Figure 5-6: Poisson potential across the simulation cell calculated using Equation 5.3 at ∆Ψ= 3 V.

5. 4 . 83 - 1 2 )C 2 Figure 5 - 7 :

 48312257 Figure5-7: Surface charge density as a function of the potential drop across each interface. Linear fits are shown in dotted and dashed lines for negative (σ < 0) and positive electrodes (σ < 0), respectively. The corresponding differential capacitances are given by the slope of the two curves.

5. 4 . 16 C (µF /cm 2 ) local 2 nd order global 5 th order global 8 th orderFigure 5 - 8 :

 416258 Figure5-8: Fitted results of single electrode differential capacitance using different orders of polynomial fit. The σ = f (∆Ψ ± ) plot in Figure5-7 is fitted in different ways: first locally fits using 2nd order of polynomial for each three neighbored points; and then global fits using 5th and 8th orders of polynomial for the whole set of data. The differential capacitances are obtained by the derivative of each polynomial functions at specified potential drops.

5. 5 . 85 5. 5

 5855 CALCULATION OF DIFFERENTIAL CAPACITANCE OF FULL CELL FROM FLUCTUATION OF SURFACE CHARGE Calculation of differential capacitance of full cell from fluctuation of surface charge 5.5.1 Fluctuation of surface charge

Figure 5 - 9 :

 59 Figure 5-9: Distributions of total surface charge (Q tot ) at various applied potential difference, in which the distributions are shown in logarithmic scale. The points are the simulated results, and the corresponding line in same color represents the plot fitted by Gaussian distribution.

Figure 5 -

 5 Figure 5-10: (a) Contour plot of the probability distribution of surface charge density on the electrodes. The probability is indicated by the color bar shown on the right. (b) Differential capacitance as a function of the applied potential difference.

5 . 6 Figure 5 - 89 Figure 5 - 11 :Figure 5 - 12 : 3 V

 565895115123 Figure 5-12, respectively. On the negative electrode, the number of Li cations increases with |Ψ -|, and the probability distribution becomes narrower at large negative potential (Figure 5-11a). The number of water molecules smoothly increases together with Li cations at low negative potentials (Figure 5-11b), but fluctuates more at large negative potentials.This may be attributed to the overlap of the Li ion solvation shells competing to include the water molecules in the presence of a large number of Li cations, and also accompanied by the change in the number of O from TFSI (Figure5-11c). The first notable change occurs at -0.075 V (dashed lines with label 1 ) where the most probable number of F (Figure5-11d) drops while the one of O from TFSI increases (Figure5-11c). This indicates a reorientation of the TFSI anions. At the same time, the probability distribution of the number of Li cations becomes different at this region. This structural change could be related to the first peak (label 1 ) of full cell differential capacitance in Figure5-10b since the potential at negative electrode (Ψ -=-0.075 V) exactly matches the potential difference, ∆Ψ, at which the first peak

Figure 5 -

 5 Figure 5-13: (a) Density profiles of O and F from TFSI anions as a function of distance from the positive electrode at Ψ + = 0.75 and 1.0 V (∆Ψ = 1.5 and 2 V). Grey and light-blue background represent the first and second adsorbed layers, respectively. (b) and (c) are the typical snapshots close to the positive electrode (grey slab on the bottom) from simulations at Ψ + = 0.75 and 1.0 V, respectively.

Figure 1 .

 1 Figure 1. Simulation cell composed of two porous electrodes held at constant potential (cyan: C atoms). The electrolyte is composed of a FeCl 3 or FeCl 2 unit dissolved in EMIM-BF 4 , modeled using a coarse-grained force field 32 (red: the three interaction sites of EMIM + ; green: the single site of BF 4 -; blue: Fe (III) cation; violet: Cl -anions).

Figure 2 .

 2 Figure 2. (a) Probability distribution of the vertical energy gap in reduced and oxidized states. (b) Average vertical energy gap for Fe 3+ /Fe 2+ in RTILs with various coupling parameters η.

Figure 3 .

 3 Figure 3. (a) Distance between Fe 3+ and the six closest anions. (b) Vertical energy gaps of the oxidized state Fe 3+ . (c,d) Snapshots of the two different solvation structures.

Figure 4

 4 Figure 4 compares the results obtained by simulations to the TGS model with the parameters given inTable1. The left-hand panel shows the probability distribution of the vertical energy gap for the simulations realized with different values of the η parameter. The fitted TGS model agrees well with the whole set of distributions. The right-hand panel reproduces the data of Figure2, that is, the vertical energy gap as a function of η. While those data could not be well reproduced by assuming linear response, the use of the TGS model allows an almost perfect fit to the data.The diabatic free-energy curves for the reduced and oxidized species in Fe 3+ /Fe 2+ predicted by the TGS model with the parameters of Table1are plotted in Figure5. The two parabolas

Figure 4 .

 4 Figure 4. (a) Probability distribution of the vertical energy gap as a function of the coupling parameter η. Points are the simulation data, and lines are the TGS model with the parameters from Table 1. (b) Comparison between the simulated average vertical energy gap for Fe 3+ /Fe 2+ in RTILs with various coupling parameters η (points) and the TGS model (red line).

Figure 5 .

 5 Figure 5. Diabatic free-energy curves of the reduced and oxidized species obtained by the TGS model with the parameters of Table1. "CN4" and "CN6" labels refer to the tetra-and hexacoordinated solvation states and correspond to S 0 and S 1 , respectively.

Figure 6 .

 6 Figure 6. Mechanistic diagram of the electron transfer reaction under confinement. Black numbers: free-energy differences; red numbers: activation energies (labeled ΔA 1† and ΔA 2 † in Figure5).

( 1 )

 1 Alba-Simionesco, C.; Coasne, B.; Dosseh, G.; Dudziak, G.; Gubbins, K. E.; Radhakrishnan, R.; Sliwinska-Bartkowiak, M. Effects of Confinement on Freezing and Melting. J. Phys.: Condens. Matter 2006, 18, R15-R68. The Journal of Physical Chemistry Letters Letter 108 BIBLIGRAPHY THIS PAGE INTENTIONALLY LEFT BLANK

Table 3 .

 3 1: Simulation cell parameters for water and LiTFSI mixtures Molality (mol/kg) Cell size 1 ( Å) Number of LiTFSI Number of water

	0.3	35.88	8	1480
	3.5	28.38	32	507
	7.0	31.34	64	507
	12.0	29.16	64	296
	15.0	35.57	128	473
	20.0	34.70	128	355

1. The cell size is calculated based on the experimental density.

Table 3

 3 .2.

Table 3 .

 3 2: Charges of Li cation and TFSI anion

	Force field Li	C	F	O	S	N
	FF1	1.0 0.2988	-0.1176	-0.3588 0.4845 -0.4258
	FF2	0.8 0.23904 -0.09408 -0.28704 0.3876 -0.34064
	FF3	1.0	0.35	-0.16	-0.53	1.02	-0.66
	FF4	0.8	0.28	-0.128	-0.424	0.816	-0.528

Table 1 .

 1 TGS Model Parameters for Fe 3+ /Fe 2+ Obtained by Fitting Simultaneously on P η (ΔE) and ⟨ΔE⟩ η

	TGS parameters	λ S0	ΔA S0	λ S1	ΔA S1	Δ S A 0
	(eV)	1.11	0.24	1.11	-0.27	0.52

2.3. SIMULATING CONSTANT POTENTIAL ELECTRODES THIS PAGE INTENTIONALLY LEFT BLANK

J. Phys. Chem. Lett. 2017,8,[1925][1926][1927][1928][1929][1930][1931]

Acknowledgements

In summary, the comprehensive studies of water-in-salt electrolyte and its applications in supercapacitors provided beneficial microscopic pictures and mechanisms at play at the interface, leading to better understanding of these systems and the development of new water-in-salt electrolytes for electrochemical storage systems.

As perspective, on the one hand, the ion correlations and collective dynamics [START_REF] Mcdaniel | Ion Correlation and Collective Dynamics in BMIM/BF 4 Based Organic Electrolytes: From Dilute Solutions to the Ionic Liquid Limit[END_REF] in current LiTFSI-based water-in-salt electrolytes will be studied soon to fully understand the conductive behaviors of these systems, which are important for tuning new similar electrolytes towards optimal performance in their numerous applications. On the other hand, the study of Li-based water-in-salt electrolytes with various anion components is also deserved for ascertaining the role of anions plays in such systems.

Furthermore, extending of the study to other salts-based, such as Na + , K + , Mg 2+ , Zn 2+ , etc. water-in-salt systems would also be interesting. In this work, we have performed MD simulations of the Fe 3+ /Fe 2+ redox couple dissolved in 1-ethyl-3-methyl-imidazolium tetrafluoroborate (EMIM-BF 4 ) roomtemperature ionic liquid (RTIL) in contact with carbide-derived carbon (CDC) nanoporous electrodes. We investigated the free energy properties of an electron transfer reaction in a nanoporous carbon electrode. The electrodes were maintained at a constant potential of 0 V by allowing the atomic charges on the carbon atoms to fluctuate during the simulations, and it is thus a polarizable electrode model.

The vertical energy gap between the redox species was used as the reaction coordinate, which enabled us to interpret the microscopic solvent fluctuation properties.

The computed probability distribution of the vertical energy gaps and the equilibrium value of energy gaps do not follow the linear response approximation of standard Marcus theory. We demonstrated the strong influence of the nanoconfinement effect on the solvation shell of the iron cations, which is the main reason for this departure from Marcus theory. In particular, the Fe 3+ cation, which is tetracoordinated in the bulk, admits two stable solvation states in the nanoporous material: tetracoordinated and hexacoordinated.

To account for this deviation, we used the Two-Gaussian solvation model, from which the free energy curves for all the redox species in their various solvation states were extracted. This allowed us to qualitatively analyse the effect of the confinement on the electron transfer reaction. The fluctuations in the structure of the solvation shell of Fe3+ were shown to have a negligible effect from a thermodynamic point of view. Rather, it was shown that the activation energy of the associated electron transfer process is much higher for the hexacoordinated form. It is therefore likely that the stabilization of this solvation state will result in a slow down of the electron transfer reaction kinetic. This work is a first step towards a deeper understanding of the influence of the confinement on the electron transfer in redox supercapacitor devices, which will be extended in future years to promising systems such as biredox RTILs. The techniques develop in this work could also provide useful information for the development of ionic liquids-based thermo-electrochemical cells.

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