Keywords: Compréhension et modélisation du comportement et du Batteries à circulation, matériaux électroactifs organiques, modélisation, dégradations, stockage stationnaire Flow batteries, Electroactive organic materials, modelling, degradations, stationary storage

exemple des batteries à circulation

Table of contents

List of tables

List of figures

Introduction

While modern society tends to decrease its dependence on oil and fossil fuels by developing electric vehicles and increasing the share of renewable energy production, its electricity needs are constantly increasing. IEA predicts a doubling of electricity share in the global energy mix, from 27% in 2019 to 60% in 2030 to achieve the "Net Zero Emissions by 2050" scenario [1]. Electricity production and consumption have to be constantly balanced for the grid functioning, but this is harder and harder to achieve with an increasing share of renewable energies in the global electricity mix, as many of them are intermittent by nature (solar, wind) and cannot fit the demand curve. Also, fast response, stability and resilience are needed characteristics for the electricity grid. These characteristics are more difficult to achieve with the constant increasing in demand and the change in demand profiles which can eventually lead to power failures, as it happened in the United States in 2003 and 2011 [2]. Energy storage can help solving both issues, by creating a buffer between renewable generation of electricity and its consumption, and also by offering a flexible and fast responding resource to grid operators for a better fit of electricity needs.

Energy storage solutions are divided into four categories: mechanical, chemical, electrical and electrochemical storage. The main storage solutions deployed nowadays are mechanical, with pumped hydro and compressed air energy storage (CAES) representing more than 96% of the total installed storage capacity in terms of discharge power (175,000 MW) in 2018 [3]. Electrochemical energy storage comprises different types of batteries, which are a good choice for smaller applications due to their versatility of use, their high power to size ratio and their good efficiency. Furthermore, they do not need special terrain to be used, as do pumped hydro and CAES, and have a lower capital cost.

Figure 1 presents some of the existing storage systems and sort them regarding their usual power size (giving the corresponding application) and discharge time. electrodes. Redox flow battery performances are based on its energy, i.e., the amount of electrical energy that it can store -under chemical form -and deliver, and on its power, i.e., the maximum energy that it can deliver in a time unit. During the battery operation, performance losses cannot be avoided and must be minimized or at least controlled. They are the consequence of several phenomena including crossover, side reactions, degradation of the cell components, etc.

Understanding these phenomena is essential in order to mitigate them, but many of them are not suited to laboratory analysis because they appear on the course of long timescales. Modelling the system and its degradations is commonly used to explore these degradation reactions schemes in order to foresee the capacity or power fade of the battery, in combination with experimental work [5].

Redox flow batteries models already exist for inorganic technologies, and are based on other electrochemical devices models, such as PEMFC, lead-acid or lithium-ion. Several types of models exist, from empiric to physical-based, and can be applied at different scales.

This manuscript gathers the information and results obtained in the frame of a PhD entitled "Understanding and modelling the aging of organic electroactive species in redox flow batteries", During cycling, we also study the influence of the applied current density and the applied voltage on the aging of the cell. The electrolytes after aging (calendar and cycling) are characterized by 1 H NMR and cyclic voltammetry.

started
The fourth chapter presents the experimental results obtained and their analysis, as well as the calibration steps of the model. The calendar aging results obtained at 20°C and 40°C are compared.

Cycling results at 20°C and 40°C are also compared, to study the influence of temperature on aging in these conditions. The influence of current density and maximum cutoff voltage applied during cycling are also discussed. A part of these experimental results is used to calibrate the model. This calibration, done separately at 20°C and 40°C, is executed in 3 steps. First, a charge-discharge simulation is used to calibrate the diffusions and kinetic parameters of the main redox species, as well as the resistance of the cell. Then calendar aging results are used to calibrate the chemical degradation parameters.

Finally, we use cycling results to calibrate the parameters related to electrochemical degradations.

The fifth chapter answers the question whether the model is valid or not, under different conditions than the ones used for its calibration. For validation, we use the rest of the experimental results, which have not been used to calibrate the model. This helps to foresee the limits of the model, and in which conditions it can be applied. After the validation, we present some examples of extrapolation uses for this model. The model can help to characterize some capacity fade profiles, and to link them to specific degradations mechanisms. We also take a look at how the different degradations mechanisms developed here can compete between each other, on the basis of what we see in the model and especially in the evolutions of the concentrations of the different species at stake. The last section of this chapter is a sensitivity analysis made on the parameters related to the degradations implemented in the model. Finally, conclusions on the achieved work and perspectives for future work are drawn.

Aqueous redox flow batteries and their aging

Redox flow batteries (RFB) are energy storage systems which convert electrical energy into chemical energy during charging, and can deliver electrical energy back upon discharging, in controlled conditions (Figure 2). These batteries differ from conventional batteries (lead-acid, lithium-ion), because active material is dissolved in liquid electrolytes and not in the electrodes. These electrolytes flow from tanks through the electrodes with the help of a pumping system. This difference in architecture enables decoupling energy (linked to properties of the electrolytes and volume of tanks) from power (linked to the nature and surface of the electrodes).

From inorganic to organic flow batteries

In the first section, we give a general introduction on redox flow batteries. The macroscopic and microscopic parameters of importance in such batteries are presented and discussed. We talk about some inorganic technologies, which have been the first developed in the 60s. Then, we look at how organic species can help solving some of the issues encountered during the use of inorganic flow batteries.

Introduction to redox flow batteries

Redox flow batteries are electrochemical systems consisting of several flow reactors, the flow cells, and two tanks. Cells are placed in series electrically to form a stack, with bipolar plates between the cells. Within a stack, cells are placed in parallel regarding the electrolyte feed. Stacks are then mounted in series or parallel to give a module. Batteries are modules assembled in series/parallel and can then be employed as part of a process, for example combined with PV panels for storage.

Figure 2 Redox flow battery scheme

A unitary flow cell is composed of:

• Two electrodes, where electrochemical reactions take place at the interface with the liquid electrolyte,

• Current collectors or bipolar plates, where the electrons flow to and from the external electrical circuit,

• A membrane which separates the negative from the positive electrode, allowing the crossing of only certain ions,

• The electrolytes containing dissolved redox active species, which flow through the electrodes on each side of the membrane thanks to pumps.

Electrodes and current collectors

Electrodes in redox flow batteries are mostly carbon based. Depending on the cell design, it can be carbon felts (CF) or carbon papers [START_REF] Derr | Electrochemical degradation and chemical aging of carbon felt electrodes in all-vanadium redox flow batteries[END_REF]. The carbon felts, 3D porous materials, enable a high surface area for the electrochemical reactions and show a wide electrochemical stability window, good electrical conductivity, and decent resistance to corrosion, while being affordable. Electrodes undergo several activation processes before their use in a redox flow batteries, which can be oxidative or acidic attack, thermal treatment, metal doping, etc. [START_REF] Kabtamu | [END_REF]. The current collectors are made of graphite, for its low cost and good electrical conductivity. Copper or noble metals are avoided because they catalyze the hydrogen and oxygen evolution reactions, which are parasitic side reactions in aqueous redox flow batteries.

Membrane

The membrane assumes several functions in the cell. It must be a separator between the positive and the negative electrolyte to avoid any mixing, be electronically insulating so as not to allow short-circuits of the cell, but also be able to transfer ions through the membrane to ensure the global neutrality in the cell through conduction. The ions transport is one of the key elements for the choice of the membrane: it must be "selective" and let only certain types of ions across, usually either cations such as H + , K + , Na + or anions such as OH -or Cl -, but be impermeable to electroactive species so as to avoid "crossover", the phenomenon where electroactive species cross the membrane, thus resulting in a decrease of cell performance.

Membranes are characterized by several properties [8]:

• Ion exchange capacity (IEC), which is the ability of a membrane to allow the crossing of certain type of ions and prevent the crossing of the others,

• Water uptake, which refers to the ratio of maximum absorbed water weight to the dry membrane weight. The swelling ratio represents the ratio of length change between the dry and the wet membrane,

• Area resistance and ionic conductivity,

• Permeability, which is the rate of passive diffusion of species through the membrane, and ion selectivity.

Different types of membrane can be used, from the simple microporous membrane where a defined pore size prevents the crossing of big molecules, Cation Exchange Membrane (CEM) or Anion Exchange Membrane (AEM) where only cations or anions are allowed to go through, thanks to electrostatic attraction or repulsion by the membrane pendant chains [9], to amphoteric ion exchange membrane (AIEM), where positively and negatively charged species are grafted on the pendant chains, and both charged ions can be transported through the membrane [8].

CEM can be divided between the long side-chains (LSC) and the short side-chains (SSC) groups, the most common examples of each, being Nafion® for LSC and Aquivion® for SSC membranes [START_REF] Jones | Perfluorosulfonic Acid Membranes for Fuel Cell and Electrolyser Applications[END_REF]. These perfluorosulfonic acid (PFSA) cation exchange membranes rely on sulfonic acid groups, that allow the crossing of cations and prevents the crossing of anions. Nafion® is the most used CEM membrane and is also the main membrane used in PEMFC, due to its excellent properties: high water swelling ratio and proton conductivity, and excellent stability (both thermal, chemical and electrochemical) [START_REF] Mauritz | [END_REF]. Its main disadvantages are lowered proton conductivity at high temperature and/or low hydration, low ion selectivity and, mostly, high cost -between 500 and 1000 $.m -2 [12]. Aquivion® exhibit high thermal stability and higher proton conductivity at low water content, making them a good choice for high temperature applications. These perfluorosulfonic acid (PFSA) cation exchange membranes rely on sulfonic acid groups, that allow the crossing of cations and prevents the crossing of anions. They are currently the most stable membranes used for redox flow batteries, but ongoing research attempt to develop cheaper materials for the membranes.

AEM are also used in redox flow batteries, with the advantages of a lower crossover of cations due to the Donnan effect, especially useful in vanadium redox flow batteries. However, their conductivity is usually lower which results in a lower VE and a higher capacity fade rate [8]. AIEM combine both cations and anions exchange membranes properties, with both types of functional groups [13]. They potentially show high ionic conductivity (CEM property) with low permeability (AEM property), depending on the proportion of each functional group.

Some examples of cheaper microporous membranes exist, mostly when the electrolytes are polymers [14,15]. These microporous membranes prevent the crossover of big ions or molecules thanks to the size of their pores. Obviously, they usually possess higher permeability than ion exchange membranes, but are less expensive. Cross-linked or chemically modified membranes are promising membranes, with potentially improved mechanical strength and durability [16].

Electrolytes

Electroactive species are dissolved in the supporting electrolytes, called "posolyte" on the positive side and "negolyte" on the negative side of the cell. During charge and discharge where the electrolytes flow through the electrodes and electroactive species react, counter-ions travel through the membrane to maintain electroneutrality. In the charge process, the reduction of the negolyte and oxidation of the posolyte stores energy, which is subsequently distributed in the discharge process where the opposite reactions occur, as shown in Equation 1-1.

𝑂𝑥 + 𝑧𝑒 -+ 𝑥𝐻 + ↔ 𝑅𝑒𝑑 + 𝑦𝐻 2 𝑂 Equation 1-1
The choice of the solvent depends on several parameters. Some electroactive species are preferentially soluble either in acidic or basic conditions. Working in acidic or basic conditions provides a better conductivity, thanks to the Grotthus mechanism for the transport of H + and OH - [17]. For neutral solvents, employed for 2,2,6,6-Tetramethylpiperidinyl-1-oxyl (TEMPO) or viologens for example, a supporting electrolyte can be added to enhance the conductivity. It is typically based on the same ion than the counter ion of the electroactive material (for example KCl can be used associated with potassium ferrocyanide). Exotic supporting electrolytes are an interesting way of enhancing the solubility and conductivity of electrolytes, even though work is still needed to obtain better durability and power performances [18].

Key parameters in redox flow battery technology

Macroscopic parameters

Several parameters are used to describe the performances of a battery [17,19,20]. Table 1 describe the most common parameters used when it comes to evaluate the performances of aqueous redox flow batteries.

Table 1 Macroscopic key parameters for aqueous redox flow batteries operation

Physical parameter Formula

Nominal cell voltage (V) Levelized cost of energy storage -LCOEs

𝑈 𝑐𝑒𝑙𝑙 = 𝐸 𝑝𝑜𝑠 -𝐸 𝑛𝑒𝑔 -𝜂 𝑘𝑖𝑛𝑒𝑡𝑖𝑐𝑠 -𝜂 𝑟𝑒𝑠
(€.kWh -1 .cycle -1 ) 𝐿𝐶𝑂𝐸𝑠 = 𝐶𝐴𝑃𝐸𝑋 + 𝑂𝑃𝐸𝑋 𝑁. 𝜂
Theoretical cell voltage is the difference of potential between the positive 𝐸 𝑝𝑜𝑠 and the negative 𝐸 𝑛𝑒𝑔 electrodes, but the actual voltage 𝑈 𝑐𝑒𝑙𝑙 also includes inner resistance of the cell and kinetic overpotentials. Increasing cell voltage often comes at the expense of its lifetime, because of the limited window of stability of aqueous solvents. Some research teams play on electrodes' nature to have higher overpotentials for reduction or oxidation of water, which enables reaching cell voltages higher than 1.23 V.

Volumetric capacity of an electrolyte 𝑄 𝑣𝑜𝑙 is the amount of charge stored in the electrolyte, determined by the concentration of the electroactive species 𝐶 (mol.L -1 ) and the number of electrons exchanged in the redox reaction 𝑧. 𝐹 is the Faraday constant (C.mol -1 ), representing the amount of charge in one mole of electrons. Theoretical capacity of the cell 𝑄 𝑐𝑒𝑙𝑙,𝑡ℎ is equal to the lowest capacity between posolyte and negolyte. Energy density of a cell represents the amount of energy that can be stored in the entire cell [21]. It is homogeneous to a capacity density multiplied by the voltage of the cell. When estimating the energy density, the voltage Ucell (V) is usually the mean discharge voltage.

The product is divided by the sum of the two volumes, corresponding to the total electrolyte volume in the cell. This proposed way of calculating the energy density, is not always a consensus among researchers. Examples of calculations without taking into account the volume of both electrolytes are often found in the literature which, although not false, lead to overestimated energy density estimations at the process scale [17,22]. Energy density values between 40 -50 Wh.L -1 could theoretically be achieved according to measured solubilities and nominal cell voltage, however practical laboratory scale values are still far from theoretical, around 13 Wh.L -1 which is equivalent to 1 mol.L -1 electron concentration for each electrolyte and a cell voltage of 1 V [23,24]. Power density represents the maximum power per surface area of electrode that the battery can deliver. I is the current flowing through the external circuit (in A) and S the active surface area of the electrodes (in cm 2 ). Power density is mainly affected by the redox potentials, conductivities of the cell, kinetics of redox reactions and mass transport. Fischer et al. proposed a threshold value of 50 mW.cm -2 for industrial application [24].

Electrolyte Utilization is the ratio between experimental and theoretical capacity of a cell. This parameter, although important, is not yet systematically reported in scientific experiments [25]. The capacity fade rate of a battery is an essential parameter to estimate aging. It can be expressed in terms of capacity loss per cycle, per day, or "battery lifetime". A reasonable lifetime target for industrial development is between 6,000 and 20,000 cycles, with a goal of 10,000 cycles towards 2030 set by the European Commission [23,24,[START_REF]SET plan: Progress report[END_REF].

Coulombic efficiency (CE) is the ratio between the charge delivered during discharge and the charge accumulated during charging of the battery. Voltage efficiency (VE) is the ratio between the average charge voltage and the average discharge voltage. Energy efficiency (EE) is the ratio between the delivered energy during discharge and the stored energy during charge. EE is the product of CE with VE. At process scale, pumping losses, shunt currents as well as AC/DC conversion of electricity for the grid diminish the energy efficiency, which ranges between 50 to 90% depending on the calculation system. When comparing efficiencies from different sources, it is necessary to be careful about the method used to be relevant in the comparison. In fine, we must consider the global system, including the auxiliaries used to make the flow battery work as well as converters etc. to connect it with the grid.

Cost for energy storage systems can be assessed with the help of LCOEs, which is the Levelized Cost of Energy storage. This metric represents the cost of ownership relative to the energy delivered [START_REF] Pawel | [END_REF]. In the expression of LCOEs, CAPEX and OPEX are capital and operational costs for the installation, N is the cycle life and η the global efficiency of the installation. A target cost of 0.05 €.kWh -1 .cycle -1 has been set by the European Commission for stationary energy storage with batteries for 2030 [23,[START_REF]SET plan: Progress report[END_REF]. Toxicity must also be considered before industrial development of a chosen technology [24].

Microscopic properties

Macroscopic performances described above are governed by the microscopic physico-chemical properties of redox active materials, which will now be described.

Redox potential

Redox potential of active species dictates the voltage of the cell. Having a posolyte with high redox potential associated with a negolyte with low redox potential achieves a higher voltage, thus higher power and energy densities. For organic molecules, redox potential can be tuned through functionalization by electron-donating or electron-withdrawing groups, respectively to reduce or increase the redox potential value [18]. It is also necessary to consider the electrochemical stability window of the solvent, and redox potentials must be within these limits. That is why full-organic flow batteries are also very attractive, because the redox potential of a given molecule can vary a lot between aqueous and non-aqueous solvents, the latter enabling a much higher cell voltage.

Solubility

Solubility is the maximal concentration of a species in a solution before precipitation. It depends on the species and the solvent considered and is directly linked to capacity. To maximize the capacity of the electrolyte, the goal is to have the highest solubility of electroactive species in the electrolytes. To enhance solubility, it is possible to change the pH in aqueous media, or to use functionalization on organic species. Solubility is known for stable species only, and during the charge and discharge process, when the electroactive material is oxydized or reduced, solubility is different [19]. There is also a compromise to be done between the positive and negative side in terms of pH, ionic force of the solution etc: the solubility values obtained for active materials alone are overestimated when compared to actual values in a full cell. High solubility potentially means higher concentrations in active species thus higher energy density; but higher concentrations imply a higher risk of crossover between the electrolytes and a higher viscosity, thus a decreased mass transport of the species and a decrease in the overall energy efficiency [20].

Number of exchanged electrons

The number z used in the calculation of the capacity represents the number of electrons reversibly exchanged in a redox reaction. It is an important factor in the search for new molecules as redox active materials, as it can easily enhance by a factor of 2 or more the capacity and thus the energy density of the cell. However, finding molecules that can exchange 2 or more electrons with redox potential for these reactions within the stability window of the solvent is a challenging task.

Kinetic and transport parameters

Kinetic and transport coefficients are important for redox materials so as not to be limited either by diffusion or charge transfer processes. It is generally accepted that diffusion coefficient D 0 must be higher than 10 -6 cm 2 .s -1 , and kinetic constant k 0 must be higher than 10 -5 cm.s -1 [21]. These parameters are experimentally determined using Levich and Cottrell equations for diffusion processes, and Koutecky-Levich or Nicholson for kinetic constants [9].

Conductivity

Electrolyte's conductivity influences capacity utilization, power density as well as EE. A general trend is that charge-neutral active molecules decrease the polarity and then the conductivity of the solution.

A potential path to enhance conductivity is using a supporting electrolyte, which increases the concentration of ions in solutions and thus conductivity. Nevertheless, it is a compromise, as using a supporting electrolyte might decrease the solubility of electroactive species in solution. The supporting electrolyte nature and concentration much be chosen regarding the balance needed between energy and power density.

Stability

Stability of redox active molecules is an essential parameter in the overall durability of the flow battery.

They must be chemically stable in the electrolyte, meaning that they are not spontaneously degraded during calendar aging, which is the name for aging without charge or discharge or the battery. They must also be electrochemically stable, meaning that they are not degraded during cycling, where current flows through the battery and the redox state of the molecules change. For RFB applications, redox materials must be stable in both reduced and oxidized states at concentrations higher than 0.5 M, and in the operating temperature range of the battery (0 to 50 °C) [9].

Inorganic redox flow batteries

Historically, the first redox flow batteries were based on inorganic electroactive species [28]. First examples of flow batteries were patented by NASA, and the first prototype was presented in 1976 [START_REF] Thaller | Electrically rechargeable redox flow cell[END_REF].

It was the iron/chromium couple that seemed the most promising at that time, among other inorganic redox couples. In 1986, Skyllas-Kazacos et al. patented a redox flow battery based on vanadium couples on both sides [START_REF] Skyllas-Kazacos | All-vanadium redox flow battery[END_REF]. Vanadium redox flow batteries is the most used commercial technology among all redox flow batteries, thus is used as a reference.

Vanadium flow battery

Vanadium redox flow batteries (VRFB) have been the most studied system among redox flow batteries. This is mainly due to the simplicity of the system, its relatively low cost as well as its simplicity of operation [START_REF] Blanc | Paths to Sustainable Energy[END_REF]. The particularity of VRFB compared to other batteries are indeed that the same element, vanadium, is used as electroactive material on both sides of the cell, exploiting all its oxidation states. VO 2+ (V 4+ ) and VO2 + (V 5+ ) react at the positive electrode (Equation 1-2), V 2+ and V 3+ at the negative electrode (Equation 1-3).

𝑉𝑂 2+ + 𝐻 2 𝑂 ↔ 𝑉𝑂 2 + + 2𝐻 + + 𝑒 - Equation 1-2 𝑉 3+ + 𝑒 -↔ 𝑉 2+ Equation 1-3
The battery operates in acidic environment, typically concentrated sulphuric acid. The operating cell voltage is between 1.4 V and 1.6 V, with one exchanged electron [START_REF] Cunha | [END_REF]. The resulting typical energy density of such a cell is between 25-50 Wh/L [25]. A high power density and stable battery has been developed and can be cycled 20,000 times at 600 mA/cm², with an energy efficiency of 80%, and a maximal power density of 2.78 W/cm² [33]. The cost of all-vanadium batteries depends on several factors, and is estimated between 300 -700 $/kWh [START_REF] Cunha | [END_REF]. Several examples of demonstration systems have been developed (in the kW/kWh to MW/MWh range), some listed in a review about advances around vanadium batteries from Skyllas-Kazacos et al. in 2009 [34].

A known difficulty using vanadium species is the solubility of vanadium pentoxide V2O5, which can precipitate upon operating the battery and is quite hard to dissolve again [35]. Its main advantage is the use of the same material in both electrolytes: the impact of crossover is reduced because the electrolytes can be regenerated by remixing. This strategy allows for very long lasting electrolytes, but the remixing process results in an unavoidable punctual loss in efficiency [36].

Figure 3 presents the working scheme of a vanadium redox flow battery [START_REF] Pasquier | Ecole thématique Redox-flow 2019[END_REF].

Other inorganic technologies

The first flow battery to have been created is iron-chromium battery. In this battery, the ferric-ferrous couple is used in the positive electrolyte, along with the chromous-chromic in the negative side of the cell. Both half-cell reactions exchange one electron, and the standard cell voltage is 1.18 V. Electrolytes typically contain electroactive species at a 1M concentration, meaning a theoretical capacity of 26.8

Ah/L [START_REF] Thaller | Redox flow cell: Energy storage system[END_REF]. The chromium redox reaction is enhanced by small amounts of catalyst, namely lead or gold.

This technology is quite cheap as it uses abundant materials, but the crossover is pretty high due to the small size of the active materials, meaning a low current efficiency [START_REF] Weber | [END_REF]. There is also a risk of hydrogen evolution at the negative electrode if Fe 2+ is reduced to Fe 0 in case of overpotential at the negative.

Another well studied inorganic flow battery is polysulfide/bromide battery (PSB flow battery). The electrolytes are Br -/Br3 -in the positive tank, and S2 2-/S4 2-in the negative tank [40]. One electron per S2 2- or Br -species is exchanged during this reaction, and the standard voltage is 1.35 V. Power densities of up to 0.64 W/cm² were achieved at a practical voltage of 1.07 V and a temperature of 95°C. The pros for this technology are high efficiency, long life and low cost, and the cons are the need of operating at high temperatures to obtain good performances, along with the use of catalysts to enhance the reactions. Furthermore, formation of toxic gases H2S and Br2 needs to be avoided. This technology was commercially demonstrated by company Regenesys Ltd. (now VRB Power), with an energy efficiency around 75% [41].

Figure 4 presents a radar diagram comparing the macroscopic performances of the three inorganic technologies seen above (Vanadium, Fe/Cr and PSB). The criteria chosen are the following, rated qualitatively between 1 and 5:

• Energy density,

• Power density,

• Cost, which is a qualitative estimate of the cost for the technology looking at the material and species employed,

• Stability, which can be assessed with the loss of capacity per cycle of the batteries,

• Maturity, which is a qualitative estimate with the number of the industrial projects involving the technology.

Emergence of organic electroactive species for flow batteries

Inorganic electroactive materials have in common to be quite expensive, representing a large part in the overall battery cost. Moreover, the criticality of several inorganic materials is increasing, which dictates the resulting price due to finite reserves. Organic electroactive materials, employed in redox flow batteries since 2009, could potentially solve these problems while being non-toxic and environmentally benign [START_REF] Xu | World Non-Grid-Connected Wind Power and Energy Conference (WNWEC 2009)[END_REF]. The emergence of organic electroactive species is due to the great variety of possible structures, associated with the ability to functionalize them and thus enhance certain useful properties. They are used in multiple types of batteries, including lithium ion, solid state or aqueous batteries [START_REF] Cadiou | [END_REF]44]. In an ideal but realistic performance scenario, organic materials could theoretically function reversibly in batteries and have a great energy density of up to 210 Wh/L [45]. Furthermore, organic redox materials usually benefit from fast kinetics, thus enabling to dispense with the use of a catalyst as in some inorganic RFBs [17].

Initially developed in hybrid inorganic/organic batteries -combined with an inorganic material on the other side of the cell -, the use of organic electroactive materials on both sides gave birth to organic redox flow batteries (ORFBs). Active material in these batteries can be dissolved either in an aqueous water-based solvent, or in an organic solvent. In aqueous media, it is still challenging to combine high solubility of the materials and high cell voltage.

Developing "all-organic" redox flow batteries, meaning organic electroactive species in organic media, enables to access a higher cell voltage thanks to the wider electrochemical window of up to 5 V, as we would get rid of the water. However, severe drawbacks in terms of security of operation and power density, which are poor in these media, limit the development of all-organic redox flow batteries. The hurdles are to obtain decent conductivity, to lower the high resistance between electrolyte and separator and to enhance the chemical stability of species at a lower cost [46]. In this work we chose to focus on aqueous organic redox flow batteries (AORFBs), the reason being -at the time this work was written -their simplicity of use and better power and stability performances associated with increased safety.

Major families of organic molecules for aqueous RFBs are organometallics -mostly ferrocyanide and ferrocene -, quinones, viologens, (2,2,6,6-Tetramethylpiperidin-1-yl)oxyl (TEMPO), phenazines and alloxazines. These species, presented in Table 2, have been studied in RFBs applications for about a decade, and promising results have been achieved. Table 3 shows some key examples of performances for aqueous organic redox flow batteries, at laboratory scale.

Table 2 Main organic families used as electroactive species in ORFBs

Family Formula Characteristics

Ferrocyanide [47] • 1 e -transfer • E 0 = 0.5V vs. SHE • Light-sensitive Ferrocene [48] • 1 e -transfer • Stable • Low solubility Quinone [49] • 2 e -transfer • High solubility • Structural diversity (benzoquinones, naphthoquinones, anthraquinones)

Viologen [50] • Theoretical 2 e -transfer • Irreversible 2 nd e -transfer without functionalization • High solubility at neutral pH TEMPO [51] • 1 e -transfer • E 0 = 0.8 -1.1 V vs. SHE • Low solubility without functionalization Phenazine [52] • 2 e -transfer • Low solubility without functionalization • Easy synthesis • Structural diversity Alloxazine [53] • 2 e -transfer • Low solubility without functionalization • Ucell = 1V, j = 100 mA.cm -² • EU = 97%, CE > 99.9%

Table 3 Examples of aqueous organic redox flow battery full cell results

Negolyte

• Capacity retention: 99.83% after 480 cycles [56] Methyl viologen (0.5 M) 4-HO-TEMPO (0.5 M) 7

• Ucell = 1.25V, j = 60 mA.cm -² (0.5 M) 14

• Ucell = 1.1V, j = 40 mA.cm -2

• CE > 99%, EE = 84%

• Capacity retention: 96% after 180 cycles, more than 3000 cycles when the maximu voltage is lowered to 1.3V instead of 1.5V [60] The examples of full cell performances shown in Table 3 must be considered carefully, as the results depend a lot on experimental conditions. These include (but are not limited to) operating atmosphere (argon or nitrogen atmosphere vs. air), type of membrane used, reactants concentrations (which are sometimes much lower than their expected solubility), operating voltage window, current density, charge-discharge protocol (potential holds at the end of each phase or not) etc. The performances must also be compared with regards to the expected cost of each electrolyte, determining the viability of the redox flow battery. To give an idea of the state of the research in terms of durability of organic flow batteries in 2022, several research works are exhibiting good cycling performances for over 1,000 cycles (with a target of 10,000 cycles in 2030) [61][62][63].

Aging mechanisms of aqueous organic redox flow batteries

Performances' degradations in aqueous redox flow batteries are due to degradation of the cell internal components, namely electrodes, bipolar plates, and membrane, as well as aging of electroactive species. Aging mechanisms for the cell components of an ORFB are essentially the same than in traditional inorganic redox batteries and are quite well documented for the VRFB case. They are also largely inspired from the fuel cells aging literature. These degradations can occur at the electrodes or bipolar plates (similar degradations due to the same nature of materials used), or at the membrane.

Aging of electroactive organic species can be either of a chemical nature, usually explored with socalled "calendar aging" -aging without cycling -, or it can be electrochemical, resulting in a performance decrease upon cycling the battery.

Degradations of electrodes and bipolar plates

Mechanical degradation of the electrodes induces reduced active surface area or a change in the electrodes' porosity [64]. Derr et al. studied both the chemical [65] and electrochemical [66] degradation of carbon felt electrodes in a VRFB, using Electrochemical Impedance Spectroscopy (EIS)

and XPS [START_REF] Derr | Electrochemical degradation and chemical aging of carbon felt electrodes in all-vanadium redox flow batteries[END_REF]. They noted oxidation on both half cells, unexpectedly since the potential of the negative half-cell never exceeded the standard potential for carbon oxidation. The oxygen functional groups produced with oxidation of the electrodes had a significantly higher impact on the negative electrode.

Carbon corrosion induces a change in the electrode pore structure [67]. However, Nourani et al. stated that this corrosion overall enhances VRFB performance by increasing active surface area and hydrophilicity of the electrodes, acting like a surface treatment of the carbon electrode [68]. At the positive electrode, CO2 formation is a possible reaction to avoid in aqueous media. Current collectors, or bipolar plates, are mostly affected by the electrochemical corrosion due to the acidic electrolyte [69]. This corrosion can be neglected when operating in neutral or alkaline environment, conditions more and more frequently encountered thanks to the design of new organic species stable in these media.

Treatments are available to prevent several reactions or get the electrodes back to their pristine form.

These include ex-situ thermal treatments or reduction reaction for example. The use of noble metal catalysts, stable in acidic conditions, were also reported for the negative electrode. However, noble metals such as platinum or gold catalysts cannot be practically used because they catalyze hydrogen or oxygen evolution reaction, which are not desired in these redox flow systems [START_REF] Derr | Electrochemical degradation and chemical aging of carbon felt electrodes in all-vanadium redox flow batteries[END_REF].

Degradations of the membrane

Degradations of the membrane can be either mechanical, chemical, or electrochemical. Mechanical constraints are applied on the membrane if the pressure is too high, or in case of swelling of the membrane or the electrodes [70]. These constraints can lead to cracks or punctures in the membrane.

Hydrogen peroxide formation can be formed similarly as in fuel cells, with subsequent radical formation via Fenton reaction [71]. Such radicals can attack the membrane's polymer side-chains, provoking chemical degradation of the fuel cells membranes [72]. Chemical degradation also happens for vanadium redox flow batteries membranes, and is caused by oxidation of the membrane by catholyte species [69]. Ex-situ studies showed that SSC polymer membranes (e.g. Aquivion®) are less sensitive to radical attacks than LSC polymer membranes (e.g. Nafion®) [73]. Water transfer through the membrane is another issue, which can lead to precipitation of active species if their concentration exceed their solubility [74]. It has been demonstrated that the direction of the water flux depends on the SOC range of the study and the type of membrane used, AEM or CEM. This water transfer seems to be mainly caused by diffusion. The electro-osmotic drag of water and hydraulic permeation are considered negligible in the entire process, as the results modelled by Oh et al. suggest [75].

Crossover, although not being strictly a membrane degradation, is an aging mechanism partly related to the membrane properties. It is usually the predominant cause for performance degradation in inorganic RFBs but is lower in organic RFBs because of the higher steric hindrance of organic molecules compared to inorganic materials. Crossover of MV and TEMPO through different membranes by diffusion, migration and electroosmotic drag was studied [76]. They found that the diffusion rate in the membrane was not the main parameter for crossover, and the most diffusive membranes showed less crossover due to a reduced electroosmotic drag. Thus, the parameters to look for in a membrane along with diffusion coefficients of species are water uptake and ion exchange capacity, as the latter and a high water content mean both less electroosmotic drag and less crossover. Crossover can be reduced with modified operation parameters, such as increasing membrane thickness, operating at a higher current density or reducing the electrodes active area [20].

Side reactions occurring in redox flow batteries

In aqueous redox flow batteries, the main side reactions occurring are related to the electrochemical reactions of water. Oxygen evolution reaction (OER) and Hydrogen evolution reaction (HER) happen on the positive and negative electrode, respectively, when potentials approach the solvent's electrochemical stability limits. These reactions almost exclusively take place during the charging process, and induce a decrease in the active surface area [66]. For example, reactions are presented below at pH 14:

4𝑂𝐻 -⟶ 𝑂 2 + 4𝑒 -+ 2𝐻 2 𝑂 𝐸 𝑂𝐸𝑅 0 = 0.4 𝑉 Equation 1-4 2𝐻 2 𝑂 + 2𝑒 -⟶ 2𝑂𝐻 -+ 𝐻 2 𝐸 𝐻𝐸𝑅 0 = -0.8277 𝑉 Equation 1-5
These reactions are voltage-dependent, thus special care must be taken to stay within electrochemical stability window of water. Furthermore, oxygen and hydrogen evolution can induce pH fluctuations, which can lead to further degradation reactions for electroactive species [54].

Another side reaction observed in vanadium flow batteries is carbon oxidation to form CO2 [69]. This reaction not only decreases CE of the battery, but it also changes the electrode structure because of the oxygen reaction with carbon. However, this is known to happen in highly acidic environment and is therefore not a major degradation in most organic redox flow batteries.

Degradations of electroactive organic species

Aqueous organic redox flow batteries development is at an early stage, mainly because of the performance's losses occurring upon operation of the batteries. Losses can be attributed to several degradation factors, but the predominant are those directly concerning the use of new organic electroactive material. The degradations of quinones, organometallics, viologens and TEMPO have been explored for a few years now, but only few of these degradations have been studied in the frame of redox flow battery operation. This section will attempt to make a listing of the reported aging mechanisms in the literature for those organic molecules. Similar reports have been made by Liu et al.

[17] as well as Aziz et al. [77].

Ferricyanide/ferrocyanide

Several degradation reactions have been identified for ferrocyanide and are indicated in Figure 5 [ 47,78,79].

Figure 5 Ferrocyanide degradations reactions

Ferricyanide and ferrocyanide are known to be light-sensitive, and their degradation under the light is pH-dependent [78]. The reaction scheme is shown in Figure 5 a). The degradation rate is inversely proportional to the free cyanide concentration in solution. This rate thus is higher at the beginning and decreases over time [80]. Formation of Prussian Blue was also reported in situ, with the help of symmetric cell characterization [79,81,[START_REF] Cazot | Development of Analytical Techniques for the Investigation of an Organic Redox flow Battery using a Segmented Cell[END_REF]. It was detected on the membrane by FTIR-ATR analysis, after exposure to light in acidic conditions. The formation of Prussian Blue is a consequence of the presence of Fe(III) species in solution, with a reaction scheme shown in Figure 5 b). Ferrocyanide and ferricyanide species are also unstable under acidic conditions and generate toxic HCN as seen from ex situ studies, following the reaction scheme shown in Figure 5 c) [START_REF] Kolthoff | [END_REF]. As in acidic environment, the reduced form is unstable in alkaline media, as suggest the results shown in Figure 5 d) obtained in situ with half-cell configuration [47]. The conditions were the following: charge and discharge between -0.4/0.4 V, current densities from 40 to 100 mA/cm². The samples were studied after 300 cycles by 13 C NMR. Both decomposition products in acidic and alkaline media are different electroactive species.

However, Ventosa et al. recently reassessed the stability of ferrocyanide in alkaline media, and said that ferrocyanide was not degraded as proposed before with the release of CN -ion, but that the observed capacity fade was caused by OER [84].

Ferrocene

Dioxygen decomposition of ferrocenium in the presence of water was reported in acetonitrile [85].

The reaction scheme is exposed in Figure 6 a). The products are identified ex situ by CV, FTIR, GC-MS and electrochemical quartz micro balance (EQCM). There is precipitation of iron oxide, and formation of Fe 3+ , another electrochemically active species. Decomposition of ferricenium by nucleophilic attack in organic media, as represented in Figure 6 b), was reported in acetone, nitromethane or acetonitrile ex situ [86]. The reaction forms ferrocenium and another iron complex. The products are identified with ESR and electronic absorption and quantified via UV measurements. As far as we know, no decomposition reaction was proposed for ferrocene in aqueous media, suggesting a high stability of this component in the conditions encountered in AORFBs. The degradations paths have been more thoroughly explored for quinones than for other technologies.

They are especially sensitive to nucleophilic additions or substitutions [87]. Main reactions are summarized in Figure 7.

Figure 7 Quinone degradations reactions

Tabor et al. did a computational study of quinones stability vs. their structure using DFT coupled with semi-empirical calculations [88]. They found that as their reduction potential -hence their electron deficiency or Lewis acidity -increased, the species became more sensitive to nucleophilic additions, with a breaking point above 0.9V vs. SHE [77]. Benzoquinones are known to undergo a rapid nucleophilic attack in aqueous solution, called Michael addition. This reaction, shown in Figure 7 a), has been observed ex situ in several publications [54,89,90]. Reaction products were identified by 1 H NMR characterization experiments. The fully substituted benzoquinone formed is a redox active compound, but its potential is decreased of 100 mV for each added group, reducing the cell voltage.

Multi-hydroxylated compounds often show less reversible redox behavior [91]. Furthermore, an excess amount of the other side material is required to fully convert the benzoquinone during the first stages of operation, resulting in excess active material unutilized further during charge and discharge.

Incomplete utilization of this active material results in a reduced current density in the cell [54].

Authors thus designed a Michael addition-resistant molecule, dihydroxy dimethylbenzene sulfonic acid (DHDMBS) [89]. The strategy is to fully substitute the benzoquinone with methyl groups to avoid free sites for secondary reactions. A cell with AQDS and DHDMBS was cycled at 100 mA/cm², without capacity fade for 25 cycles. However, they started to notice capacity fade after further cycling.

DHDMBS, while being resistant to Michael reaction, is sensitive to another side reaction called "protodesulfonation" shown in Figure 7 b), observed in situ under acidic conditions. This reaction is quite slow compared to Michael addition, but not negligible, the capacity fade rate being 0.23% per hour (pseudo-first-order rate constant determined at 1 M sulfuric acid is 2.10 -6 s -1 ). Reaction rate increases with temperature and pH decrease (a dark precipitate rapidly forms in 4 M sulfuric acid).

Cycling degradation products were analyzed by 1 H-NMR, 13 C-NMR and Electrospray Ionization coupled with High resolution mass spectroscopy (ESI-HRMS) [92]. The formed 2,6-dimethylbenzene-1,4-diol is not very soluble in water, and precipitates when present with an excess of 10 -15%.

In mild basic solutions with the presence of H2O2, para-benzoquinone forms 2,3-epoxy-pbenzoquinone. The oxidation reaction by hydrogen peroxide shown in Figure 7 c) has been observed ex situ, and is usually followed by nucleophilic attack [93]. The reaction products were identified by HPLC, GC-MS, NMR and UV spectroscopy. The epoxide is formed with a second order rate constant of 0.77 M -1 .s -1 .

Anthraquinone, although being more stable and less prone to crossover than benzoquinones (but more than naphthoquinones, which are more substituted), were also reported to degrade in certain conditions. Brushett et al. studied the evolution of 9,10-anthraquinone-2,7-disulfonic acid both in acidic and mildly alkaline media (pH 9.76) [94,95]. They found that in both media, anthraquinone is prone to dimerization, with dimerization equilibrium constants of 5 and 8 M -1 in acidic and alkaline media respectively. The dimer formed is electrochemically inactive, and its concentration can be reduced by increasing temperature even though it is still present. They found that during cell operation, the dimer tends to disappear in favor of an electrochemically active quinhydrone, and the equilibrium constant shifts in favor of the monomer [95]. Unsubstituted anthraquinone produced anthrone in highly acidic conditions [96]. Similarly, a 2,6-DHAQ/Fe(CN)6 cell showed capacity fade of 5-8% per day at pH 14 [97]. DHAQ was cycled in a symmetric cell and decomposition products DHA (anthrone) and then (DHA)2 were identified in alkaline anaerobic conditions using MS, 1 H-NMR and HPLC compared to a pristine sample. Dianthrone formed as shown in Figure 7 d), despite still being redox-active, is impractical for a use in redox-flow batteries due to its higher potential and lower capacity. Furthermore, this product is unstable in strong alkaline conditions. However, the anthrone One strategy to mitigate the capacity fade is to limit the cutoff voltage in the cycling conditions [60].

As anthrone is formed at high SOC of the battery (i.e. when the negolyte is in its fully reduced form), limiting the cycling window results in less anthrone formation, and can decrease the capacity decay from 5.6%/day at a cutoff of 1.6V to 0.14%/day at a cutoff of 1.25V. However, the accessed capacity decrease from 99.9% to 88% of the theoretical capacity in these conditions. Another strategy is to modify the quinone by functionalization. 2,6-DBEAQ synthesized by Aziz et al. showed only slight degradation with 0.04% capacity fade per day at pH 14 [99]. However, 1 H RMN revealed that at higher temperature and even more in strong alkaline conditions, this species could undergo nucleophilic substitution as shown in Figure 7 e) [56]. The cleavage of both sides of the anthraquinone leads back to 2,6-DHAQ. An increase in temperature and pH increases the degradation rate of DBEAQ, even though it remains low compared to other quinone degradations reactions. The results were obtained with half-cell experiments, and led to the synthesis of 2,6-DPPEAQ, more stable at pH 12.

TEMPO

Several degradations reactions have been identified for TEMPO and are indicated in Figure 8.

Figure 8 TEMPO degradations reactions

In warm acidic aqueous solutions, TEMPO disproportionate into its oxoammonium salt and a nitroxyl anion. The anion is then protonated into TEMPOH, an inactive redox species. The TEMPOH formed can then form a dimer with TEMPO free radicals, shifting further the equilibrium of dismutation. The reaction steps are presented in Figure 8 a) [17]. TEMPO are known catalysts for alcohol oxidation [51].

The leading mechanism is presented in Figure 8 b), where TEMPO forms here again TEMPOH. The reaction can happen between two molecules of 4-HO-TEMPO, for instance. This loss of active material has been described ex situ from battery operation. TEMPO can be subject to a decomposition with opening of the aromatic ring, as presented in Figure 8 c). This degradation mode has been reported ex situ both in acidic and in basic media [100,101]. This reaction can be broadened to any TEMPO and ESI-MS. 4-oxo-TEMPO is another redox active species, with a slightly higher redox potential but lower solubilities of both oxidized and reduced form in water than 4-HO-TEMPO [103].

Viologen

Main identified viologen degradation reactions are indicated in Figure 9.

Figure 9 Viologen degradation reactions [17]

The radical MV +. formed upon reduction of MV 2+ is prone to dimerization, forming MV 0 and MV 2+ , as presented in Figure 9 a). In addition to the imbalance caused by the disproportionation reaction, the MV 0 formed is insoluble in water and can precipitate or be oxidized by protons leading to H2 evolution.

Substituted viologens like (NPr)2V or (SPr)2V are less sensitive to dimerization thanks to the repulsion between the pendant groups [104]. This different stability behavior observed in flow cells was explored ex situ, by isolating the molecules in an argon filled glovebox with UV measurements. MV +. is oxygen sensitive and can be oxidized to MV 2+ [17]. MV 2+ also reacts with oxygen to form active oxygen species such as hydrogen peroxide, that can further react with viologen to cause its oxidation and deprotonation of the viologen ring, following the scheme in Figure 9 b) [105]. These reactions have been observed ex situ, in the field of biochemistry, and form electrochemically inactive species.

Another degradation of MV 2+ reported ex situ is the reaction between hydroxide ions and viologen in basic solutions (pH > 12) [106]. The formed product, shown in Figure 9 c), is electrochemically inactive.

Summary of aging mechanisms

Table 4 sums up the major degradation mechanisms listed above for the electrodes and bipolar plates, the membrane, and the electrolyte. There is a detailed list of all the organic electroactive species families, with the corresponding aging phenomena as seen above. For each degradation, we propose a classification that is based on the corresponding microscopic physical phenomena as well as the effects expected on the performances of the battery (macroscopic) are detailed. Physical phenomena which happen at the microscopic scale are divided in four categories:

• Loss of active material (LossAM), which correspond to degradations of electroactive material in the posolyte or the negolyte, involving or not electrons. Loss of active material via an electrochemical reaction also produces unbalancing,

• Unbalancing of the electrolytes, which correspond to reactions or phenomena that utilize electrons -for example side reactions -, thus these electrons are not used in main reactions.

It then induces charge unbalancing and a decrease in faradaic efficiency,

• Change of active material (ChangeAM), which is the formation of new electroactive species in replacement of one of the reactants, for instance after a secondary electrochemical reaction.

The new active species will have different redox properties such as redox potential, diffusion coefficient, transfer kinetics etc. Its solubility must be high enough so that it does not precipitate, if not it corresponds to a LossAM,

• Internal resistance increase (R ++), which regroups all the phenomena that contribute to an increase in the resistance of the battery,

• Pressure drop increase (∆p ++), which corresponds to an increase in pressure drop caused by a change in fluidics.

Macroscopic effects on the battery, which can be measured, are the following:

• CE loss, which is a result of unbalancing or loss of active material,

• Energy fade, which also happens after unbalancing or loss of active material, as well as after a change in active material inducing a change in battery voltage,

• EE loss, resulting from an increase in resistance or in pressure drop,

• Catastrophic failure, which here refers to a sudden failure forcing the interruption of battery We can see that degradations of the electrodes or bipolar plates typically lead to EE loss, whereas degradations concerning the electrolyte and electroactive species mainly lead to energy fade and CE loss. Energy fade and CE loss occur typically when an electroactive species at the negolyte or the posolyte is transformed either into a non-electroactive specie or into a molecule with a sufficiently low solubility so that it precipitates, resulting in a loss of active material [77]. If the product is electrochemically active but its redox potential is different from the reactant's, the change in active Subsequently, physicochemical characterizations can be used to identify aging micro-phenomena. The latter characterizations are usually destructive and can give qualitative or quantitative results on degradation phenomena and products.

Performance evaluation methods

Different cell configurations are exploited to investigate degradations of the battery [20]. The cell can be either in flow mode or static. Static cell configuration can be used for initial stability tests, to detect major degradations, but is not suited to long-term analysis. In flow mode, the electroactive species are usually first tested in symmetric configuration, meaning that the same electrolyte is used on both sides of the membrane, thus eliminating crossover. If one side is in excess, it enables focusing on the degradations of the other side. Indeed, the capacity fade observed is then only related to degradations or side reactions of the limiting side.

When the stability has been studied in symmetric cell configuration, the next step is to challenge the electrolyte performance in asymmetric configuration, with different electrolytes on both sides of the battery. Here again, the electrolytes can be in a first step unbalanced, with an electrolyte in excess to focus on the degradations of the other side, and to study the stability depending on the SOC of this capacity limiting side [77]. Finally, the last step is doing cycling tests made in charge-balanced asymmetric cell configuration, with a stoichiometry in the concentration of electrons accessible on both sides. This is the closest configuration to the reality of operation but complicates the understanding and decorrelation of each degradation. Accelerated stress tests are widely used for other electrochemical storage systems, such as PEM fuel cells and Li-ion batteries [67,109,110]. An original two cells-in-series setup was developed by Mench et al. to study degradations of the electrodes and the membrane in a vanadium redox flow battery, in which degradations occurred seven times faster than in normal conditions [111].

Charge-discharge curves are the most widely used method for basic characterization of RFBs performances. Cycling tests can be performed in two different ways: potentiostatic or galvanostaticpotentiostatic. In potentiostatic cycling (Constant voltage or CV), charge or discharge is performed with a constant voltage instruction [112]. In galvanostatic-potentiostatic cycling (Constant current-constant voltage or CC-CV), charge or discharge is performed with at a constant current until the limit voltage is reached, followed by a constant voltage phase until the current has decreased below a stated value, usually a 20 th or a 50 th of the total cell capacity [55]. In the latter method, the constant voltage step enables accessing total available capacity in the electrolyte. Pauses at various SOC between the cycles, also called Current Interruptions, can provide information on the influence of SOC on the degradations [63]. Polarization curves as well as power density curves are mainly used for fuel cells performance evaluation [19,113]. Polarization curves give the relationship between cell voltage and current density.

Power measurements of a full cell can be performed by discharging the cell at various SOC and current densities. To evaluate the resistance of a redox flow battery, Electrochemical Impedance Spectroscopy (EIS) is a commonly used tool and the results' treatment and interpretation enable decoupling the different contributions to the global resistance. Hybrid pulse power characterization (HPPC) tests are widely used to determine internal resistance in lithium-ion batteries or other high-power systems, and can also be applied to evaluate redox flow battery resistance [114].

Degradations' diagnostic

In order to determine if there is a change in the concentration of the electrochemical species or new electrochemical products, a common electrochemical method is cyclic voltammetry [108].

Electrochemical reaction mechanisms can be studied with Rotating Disk Electrode (RDE) voltammetry.

When degradations of the performances are observed, the investigation of the degradation phenomena involved is made with the help of physical characterizations. The most used are spectroscopy techniques (UV-vis, IR, Raman) for assessing electrolyte stability and redox reaction reversibility, and microscopy analysis (Scanning electron microscopy, Transmission electron microscopy) to explore surface changes, for example on the membrane or the electrodes. NMR spectroscopy is widely used to study the evolution of electrolytes' composition. Mass spectroscopy is also used to detect new products in the electrolytes and can be coupled to chromatography techniques. XPS, X-ray tomographic microscopy (XTM) and XRD are commonly used to study electrode morphology degradations. Electron spin resonance (ESR) spectroscopy is used to study crossover and transport of water through the membrane in VRFBs [108].

Online measurements of the active species concentrations have been explored in certain cases. an online NMR setup for studying the degradations in redox flow batteries [117].

Chosen approach in the thesis

As mentioned, organic molecules are subject to several degradations mechanisms which are not completely understood or quantified nowadays. Modelling tools are interesting when coupled with experiments to gain a better understanding of the degradation phenomena and how they affect the performances. The goal of this PhD is to employ modelling tools to explore and gain better understanding of degradation mechanisms occurring in new aqueous organic flow batteries. To address the challenge of ORFB modelling, we decided to implement a dedicated scientific approach based on a combined experimental and modeling study of this phenomenon as described in Figure 12.

This approach has been chosen generic enough so that it can be adapted to other organic redox flow batteries, with different active molecules.

Figure 12 Scientific approach scheme

Establishing a thorough review on organic redox flow batteries, their modelling and aging was the first step of the PhD. For the choice of the redox couples, the specifications were that the molecules undergo degradations that were well-studied in the literature. Cheaper systems have also been prioritized. Fe(CN)6 4-/Fe(CN)6 3-redox couple dissolved in 1 M KOH was chosen for the posolyte, and 2,6-DHAQ 2-/2,6-DHAHQ 4-redox couple dissolved in 1M KOH was chosen for the negolyte. These couples have been extensively studied by several research groups, and hypotheses for their possible degradations are known [55,97,98,117]. Half-reactions and the corresponding redox potentials are given in Equation 1-6 and Equation 1-7 [55].

𝐷𝐻𝐴𝑄 2-+ 2𝑒 -↔ 𝐷𝐻𝐴𝐻𝑄 4- E 0 = -680 mV vs SHE Equation 1-6 [𝐹𝑒(𝐶𝑁) 6 ] 3-+ 𝑒 -→ [𝐹𝑒(𝐶𝑁) 6 ] 4- E 0 = +510 mV vs SHE Equation 1-7
According to the studies already performed on this flow battery chemistry, degradations are mainly attributed to the degradation of 2,6-DHAQ. Two mechanisms are proposed in the literature for the degradation of the reduced form of 2,6-DHAHQ 4-, presented in Equation 1-8 and Equation 1-9 [96][97][98]117]. These mechanisms differ in that the first reaction proposed is chemical, whereas the second is electrochemical.

2𝐷𝐻𝐴𝐻𝑄 4-+ 2𝐻 2 𝑂 → 𝐷𝐻𝐴𝑄 2-+ 𝐷𝐻𝐴 3-+ 3𝑂𝐻 - Equation 1-8 𝐷𝐻𝐴𝐻𝑄 4-+ 2𝐻 2 𝑂 + 2𝑒 -→ 𝐷𝐻𝐴 3-+ 3𝑂𝐻 - Equation 1-9
Chapter 2 is dedicated to the description of the model built during this PhD, with explanations of starting hypotheses and conditions as well as how the different degradations are described. Based on the example of DHAHQ 4-degradations, chemical as well as electrochemical degradations have been implemented in the physical model. Chapter 3 describes the experimental setup developed for calendar and cycling aging of the batteries, as well as the experimental protocols for aging and characterization of the electrolytes. Chapter 4 presents the main experimental results used for model calibration. Chapter 5 describes model validation and some extrapolations that can be made with it.

In the end, this approach delivers an extended model of ORFB which considers aging, calibrated with experimental data and then validated against other experimental data. The model will be used to assess the effect of the main degradations' parameters on battery performances, and to give general guidelines on capacity fade profiles depending on the nature of the degradation. We make the hypothesis of an isothermal model, we do not consider temperature variations in the battery.

Modelling the degradations in aqueous redox flow batteries 2.1 Generalities about battery modelling

The modelling of a battery gives useful insights on performance prediction of the battery operation at different scales. Modelling has been thoroughly developed for different technologies such as Li-ion and PEMFC, and has been easily transposed, with minor changes, to vanadium redox flow batteries [118,119]. For instance, modelling the OCV and SoC of a redox flow cell is essentially the same as in a

Li-ion battery, while the species transport in the fluid circuit, the porous electrodes and the membrane are modelled based on PEMFC models [120].

The different scales of complexity for models are the following:

• Electrical equivalent circuits (EEC),

• Physics-based models (0D, 1D, 2D or 3D),

• Ab initio models.

The simplest models are empirical electrical equivalent circuits, which reproduce the behaviour of cells with the help of electrical components [121][122][123]. The first is RC circuit, and the circuit can be improved by adding resistances, capacitors, Warburg diffusion elements etc. The EEC models are parameterized with the help of EIS measurements, and they are very fast to compute, allowing the modelling of large timespans in decent computing time.

Up next are physical models, based on equations describing the behavior of the battery. In the case of redox flow batteries, the main equations describe the electrochemical part (Butler-Volmer, Nernst), as well as the mass transport of water and charged species in the cell (Nernst-Planck, Darcy) and the electrical phenomena (Ohm's law). Obviously, the physical equations include some approximations to

give an accurate representation of the reality. The accuracy and complexity of the chosen assumptions result in different computing times. The parameters' values used in the modelling are either defined in the literature, calculated experimentally or fitted, by trying to reproduce the tendency of experimental data [124] The fitting of parameters is often far from being straightforward as the problems aren't linear and phenomena are coupled. Physics-based models mesh is also important: a 0D model considers no space variation of any parameters in each component, while 1D, 2D or 3D models take into account spatial variation along one, two or three dimensions [5,81,[125][START_REF] Petit | The International Flow Battery Forum[END_REF][127]]. Among these three last approaches, finer meshes lead to better accuracy but higher computing time.

Finally, the highest complexity level models are ab-initio models, which exploit the first principles without additional assumptions. Ab-initio model can be used for exploring new tailored molecules, or predicting the solvation of molecules in different solvents [128][129][130].

The model complexity is chosen accordingly to the pursued objectives, the modelled scale, and the computation power. Indeed, building an EEC model on the material scale makes no sense as the information obtained and the accuracy would be irrelevant, as well as choosing a 3D model or ab initio model to represent the battery at the process scale: the computing time would be too large, and the level of details too fine.

Redox batteries can be modelled at different scales: materials, component, cell, stack, battery, or process. Some studies modelled only the organic redox molecules very precisely, in order to predict their physicochemical properties [49,131]. Many authors focused on only one component of the redox flow cell: the membrane and the porous electrodes being the most studied [132,133]. Several models exist for an entire redox flow cell [124,134]. Finally, the largest scale for models includes several cells in series or parallel, with the associated tanks and fluid circuit [START_REF] Blanc | Modeling of a vanadium redox flow battery electricity storage system[END_REF]. These different scales are dependent on each other: indeed, larger modelling scales require a certain quantity of data. This data is accessible from smaller scales modelling results.

As explained above, the scale and complexity of models are chosen regarding the intended use [136].

Physical models at cell or stack level can help, for instance, to investigate the effect of microstructure [137,138] or the influence of crossover [124,133,[139][140][141][142][143], but also more generally operational conditions [5,120,[144][145][146][147][148][149]. Larger scale models (process or energy management system) often use integrated empirical models because of their simplicity and thus reduced computing time [121,123,[START_REF] Clemente | Costa-Castelló[END_REF][151][152][153]. Most of the existing models for redox flow batteries are dedicated to vanadium flow batteries, with only a few physical models considering organic active species [136, [154][155][156][157][158]. In this PhD work, we chose to develop and use a physical model in 0D, which is a good compromise between physical meaning and computing time, and to study organic species with it.

0D modelling of a redox flow cell

The 0D physical model used as a basis in the PhD has been described elsewhere [136]. This first section 2.1 describes the basic model, and sections 2. 1. Concentration of each species is considered homogeneous in the tanks, in the electrodes and in the membrane, i.e., there is no spatial variation of the concentrations (0D model),

2. The cell is in adiabatic conditions, 3. Dilute solution theory is applied, which is equivalent to considering that there is a relatively small quantity of solute compared with solvent [START_REF] Al-Fetlawi | Modelling and simulation of all-vanadium redox flow batteries[END_REF]. This approximation means that every component diffuses independently, and that activity is equal to concentration for each species.

This approximation is subject to debate considering the relatively high concentrations for active species (0.5 M and 0.4 M) [158].

4. Ohmic losses in both solid and electrolytic phases are neglected, 5. Resident time in tubing is also neglected, 6. Losses due to crossover are neglected in comparison with HER/OER as well as chemical and electrochemical secondary reactions, due to the size and negative polarization of the active species [77,99].

The choice of a 0D model is made in this thesis because of the interesting ratio between computing time and physical accuracy. In order to simulate aging experiments of several weeks or months in a reasonable timescale (in a first approach), it is necessary to have simple enough conditions so that calculations are easily made, and computing divergence issues are avoided as much as possible.

Evaluation of the cell voltage

The cell voltage is the difference potential between positive and negative collectors' solid potentials 𝜙 𝑠 + and 𝜙 𝑠 -. This difference can then be distributed among several characteristic quantities which are related to specific phenomena occurring into the battery. It is expressed following Equation 2-1.

𝑈 𝑐𝑒𝑙𝑙 = 𝜙 𝑠 + -𝜙 𝑠 -= ∆𝜙 + + 𝜂 𝑜ℎ𝑚 𝑠+ + 𝜂 𝑜ℎ𝑚 𝑒+ + 𝜂 𝑚𝑒𝑚 -∆𝜙 --𝜂 𝑜ℎ𝑚 𝑠--𝜂 𝑜ℎ𝑚 𝑒- Equation 2-1
In this equation, Δ𝜙 + and Δ𝜙 -are the differences between solid and electrolytic potentials in respectively the positive and negative electrodes, 𝜂 𝑜ℎ𝑚 𝑠+ (respectively 𝜂 𝑜ℎ𝑚 𝑠-) is the ohmic overpotential due to the mean ohmic drop between the positive collector (respectively negative collector) and the membrane, 𝜂 𝑜ℎ𝑚 𝑒+ (respectively 𝜂 𝑜ℎ𝑚 𝑒-) the overpotential between the mean electrolyte potential between the positive (respectively negative current collector) and the membrane, and 𝜂 𝑚𝑒𝑚 the membrane electrolytic overpotential. The terms used in the calculation of the global cell voltage can be expressed following Equation 2-2 to Equation 2-5.

Calculation of reference potentials

Reference potentials of each main reactions are calculated with Equation 2-6 and Equation 2-7, based on the half-reactions given in equations 1-6 and 1-7. Reference potentials 𝐸 𝑟𝑒𝑓 1 (for posolyte) and 𝐸 𝑟𝑒𝑓 2 (for negolyte) are calculated with a Nernst law, which is valid because there is no mixed potential, and both reductor and oxidant are present in solution for each couple. Because dilute solution theory is applied, activity is approximated to concentration in the calculations. Standard potentials 𝐸 1 0 and 𝐸 2 0 are obtained from literature. As these reactions take place in alkaline media at pH 14, negolyte species are fully deprotonated, meaning no water or H + ions are involved in the calculation of reference potentials. 𝑅 and 𝐹 are respectively molar gas constant and Faraday constant, while 𝑇 is the temperature.

Table 6 Calculation of reference potentials

𝐸 𝑟𝑒𝑓 1 = 𝐸 1 0 + 𝑅𝑇 𝐹 𝑙𝑛 ( [𝐹𝑒(𝐶𝑁) 6 3-] [𝐹𝑒(𝐶𝑁) 6 4-] ) Equation 2-6 𝐸 𝑟𝑒𝑓 2 = 𝐸 2 0 + 𝑅𝑇 2𝐹 𝑙𝑛 ( [𝐷𝐻𝐴𝑄 2-] [𝐷𝐻𝐴𝐻𝑄 4-]
) Equation 2-7

Redox reaction kinetics

Equations representing redox reactions kinetics and how they are computed in the model are presented in Table 7. is 0.5.

Electrolytic overvoltages in the membrane

The fourth overvoltage expressed in the calculation of global cell voltage is related to losses in the membrane, detailed in Table 8. This overvoltage has two contributions, as expressed in Equation 2-13.

The first loss is due to a discontinuity in ionic concentrations of charge carriers in the membrane (here H + and K + only) between the membrane and the electrodes. The resulting Donnan potential is expressed with a Nernst-like equation as shown in Equation 2-14 [START_REF] Knehr | [END_REF]. The second contribution is related to ohmic losses in the membrane.

Modelling capacity fade due to HER/OER side reactions

HER and OER modelling were described in several works [120,136,149]. Here, additions made to the model for HER/OER modelling are the calculation of reference potentials and the calculation of redox kinetics for side reactions. Equations related to this addition are gathered in Table 10.

Oxygen and hydrogen evolution reactions occur as represented in Equation 2 Some works also studied the formation of gas bubbles associated with HER and OER, and how they impact the transport of the electrolyte [120,149,[START_REF] Al-Fetlawi | Modelling and simulation of all-vanadium redox flow batteries[END_REF]. When formation of oxygen and hydrogen occurs, the liquid phase of the electrolyte is in equilibrium with a gas phase (gaseous O2 or H2

Modelling of chemical degradations

Electroactive species degradation reactions have been widely modelled for other battery technologies, such as lithium-ion [162]. If the effect of the degradation on the overall cell performance -in terms of coulombic efficiency loss, energy efficiency loss or capacity fade -can be assessed, then the modelling of the phenomena and their impact becomes easier. A hypothesis to classify the degradations happening to electroactive species is the one described in section 1.2.5, which correlates the macroscopic effect on the cell performance and the microscopic phenomena occurring -loss of active material, unbalancing of the electrolytes or pressure drop increase -. Such microscopic phenomena can be incorporated in physics-based models by adjusting the species concentrations (active material loss), velocity of the fluid (pressure drop increase) [163], the redox potentials (unbalancing) etc. This modelling scheme is inspired from similarities between these electroactive material transformations and the ones taking place in lithium-ion batteries, giving namely loss of lithium inventory, positive or negative electrode material loss [164].

Kwabi and Modak developed and validated an electrochemical model for a symmetric aqueous organic flow cell including some active reactant degradations [157]. They modelled, for instance, the rate of reactant decay 𝑅 𝑑𝑒𝑐𝑎𝑦 (mol.L -1 .s -1 ) of species 𝐴 by a chemical degradation:

𝑅 𝑑𝑒𝑐𝑎𝑦 = 𝑑[𝐴] 𝑑𝑡 = -𝑘 𝑐ℎ𝑒𝑚 [𝐴] 𝛼 𝑐ℎ𝑒𝑚 Equation 2-24
Here, 𝑘 𝑐ℎ𝑒𝑚 (s -1 ) is the reaction constant and 𝛼 𝑐ℎ𝑒𝑚 is the decay reaction order. Diffusion-driven crossover can be modelled in the same way. As this mechanism is SOC-dependent, the authors studied the influence of the cycling protocol on the evolution of the capacity fade rate. They showed that the capacity fade rate is strongly correlated with the degradations mechanism but also with the cycling protocol described in section 3.3.2 (CC, CV or CCCV cycling, symmetrical or asymmetrical voltage limits, etc.). Their model can be adapted to several cycling conditions as well as to different supposed degradations paths.

We used this method to model chemical degradations involving redox species such as seen in Equation 1

Modelling of electrochemical degradations 2.4.1 Electrochemical degradations producing non redox active species

Non-reversible electrochemical reaction -gas, insoluble product, or non-electroactive species formation for example -can be modelled with a new current density via Tafel producing a decrease in the reactant concentration and in current efficiency. In this study, the reaction in Equation 1-9 can be active species. Degradation product (𝐷𝐻𝐴) 2 4-is supposed to have poor redox properties; we chose in a first approximation to consider it redox inactive, meaning that this reaction is irreversible. If we want to model this as a new redox active species however, we need to calibrate or experimentally determine its diffusion coefficient, the standard potential associated to the new redox reaction, the kinetics etc.

Numerical details and parameters

State variables, which are the variables describing the physical state of the system, are the following in this model:

• Concentrations of the 9 species in the positive and negative tanks,

• Cell voltage,

• Cell current,

• Positive and negative overvoltages ηpos (or Δ𝜙 𝑝𝑜𝑠 ) and ηneg (or Δ𝜙 𝑛𝑒𝑔 ),

• The discrete state in which the system is, which can be either charge, discharge, floating after charge (constant voltage charge), floating after discharge, rest (open circuit voltage) after charge, rest after discharge, or power profile. These states are numbered from state 1 (constant current charge) to state 7 (power profile). The operating conditions for each state as well as the triggering conditions for the end of each event are given in Table 11 [136].

Specific changes to the model for calendar aging

In order to properly model calendar aging, we made several changes to the model we use for cycling.

These changes are in the event conditions, that trigger the change of state in the model (ocv, constant current charge or discharge, constant voltage charge or discharge). At the beginning of the simulation, we perform 2 complete charge-discharge cycles, then a complete charge. After this charge, the cell is in an ocv state; we thus impose an ocv time of 7 days (which is the average time of calendar aging between two check-ups), before starting again with 2 charge-discharge cycles. This whole operation is then repeated, for as long as the calendar aging lasts.

Numerical implementation

We chose lsodar solver in R, that enables automatical changes between stiff and non-stiff resolution methods. Furthermore, this solver takes into account root functions that we use to drive the model.

The resolution algorithm is presented in Figure 13. It is composed of 3 main functions:

• Initialization defines calculation conditions as well as initial values,

• Calculation function, whose role is to evaluate temporal derivatives of the parameters to be calculated by the solver, • Root function which acts as an event trigger, by calculating the moments when the solver must stop to change the state of the system (for example, when switching from charge to discharge). This function also enables different scenarios, such as regular charge-discharge cycling, calendar aging with periodic check-ups, as well as the implementation of a typical power profile representative of a real use case.

After the calculations, results are post-treated in order to extract and draw capacity, voltage or concentrations curves, for instance.

Figure 13 Scheme of the model resolution algorithm

Initial and boundary conditions

At the beginning of simulation, the cell is in a constant current charge (state 1), starting from a nearly fully discharged cell. Initial concentrations, negative and positive overpotentials as well as voltage and current are given in Table 15. Negative and positive overvoltages equal equilibrium potentials of main redox reactions calculated via Nernst. Initial voltage equals the difference between these overvoltages, and initial current equals charging current. Concentrations of minor species in the compartments are not null, to avoid computing issues related to dividing by 0 in Nernst equation.

Table 15 Initial values for state variables in the model

Parameter Posolyte Negolyte

[𝑂𝐻 -] 0 1000 𝑚𝑜𝑙 ⋅ 𝑚 -3 1000 𝑚𝑜𝑙 ⋅ 𝑚 -3 [𝐷𝐻𝐴𝑄 4-] 0 10 -1 𝑚𝑜𝑙 ⋅ 𝑚 -3 1 𝑚𝑜𝑙 ⋅ 𝑚 -3 [𝐷𝐻𝐴𝐻𝑄 2-] 0 10 -1 𝑚𝑜𝑙 ⋅ 𝑚 -3 500 𝑚𝑜𝑙 ⋅ 𝑚 -3 [𝐹𝑒(𝐶𝑁) 6 3-] 0 400 𝑚𝑜𝑙 ⋅ 𝑚 -3 10 -1 𝑚𝑜𝑙 ⋅ 𝑚 -3 [𝐹𝑒(𝐶𝑁) 6 4-] 0 1 𝑚𝑜𝑙 ⋅ 𝑚 -3 10 -1 𝑚𝑜𝑙 ⋅ 𝑚 -3 [𝐾 + ] 0 2600 𝑚𝑜𝑙 ⋅ 𝑚 -3 2000 𝑚𝑜𝑙 ⋅ 𝑚 -3 [𝑂 2 ] 0 0 𝑚𝑜𝑙 ⋅ 𝑚 -3 1 𝑚𝑜𝑙 ⋅ 𝑚 -3 [𝐻 2 ] 0 0 𝑚𝑜𝑙 ⋅ 𝑚 -3 1 𝑚𝑜𝑙 ⋅ 𝑚 -3 [𝐷𝐻𝐴 3-] 0 10 -1 𝑚𝑜𝑙 ⋅ 𝑚 -3 10 -1 𝑚𝑜𝑙 ⋅ 𝑚 -3

Materials and methods

This section describes experimental tools and setups used for aging studies. At first, a single flow cell was used for cycling experiments. Later, we developed a test bench enabling the cycling of up to 8 flow cells in parallel, in different current and voltage conditions.

Single flow cell experimental setup

Cycling experiments are performed in a Pinflow® flow cell setup, presented in Figure 14. A picture of the global setup is shown in Figure 15 along with a scheme showing the different parts. A zoom on the negative side of the cell setup is shown in Figure 16. The electrolytes are fueled from the tanks to the cell using peristaltic pumps. The nominal flowrates of electrolytes are 10 mL/min on the negative side and 16 mL/min on the positive side, which ensure a resident time in the tubing low enough and can be changed if needed. Pipes and connections are in PTFE. N2 circulates in the electrolyte tanks to ensure that no interaction between electroactive species and oxygen occurs.

Nitrogen is saturated in humidity by bubbling in a water container, so that it doesn't dry the solutions which could lead to precipitation of active species.

Electrolytes also circulate through an ocv cell, which is basically a cell where the electrolytes flow from Adding an ocv cell to the global setup caused some problems, mainly related to leakages in the pipes around the reference electrode. For that reason, we gave up using an ocv cell later in the experiments, since it complicates the setup. We chose to simplify the flow circuit at the price of not being able to always access electrolytes' potentials.

Building of an 8-cells test bench

In order to perform more aging experiments in the time allocated to the PhD, a new test bench was built. It enables cycling up to 8 Pinflow® cells at the same time, in a parallel setup as shown in Figure 17. Each cell in the new bench is in a similar configuration than the single cell described above: the global cell architecture, membrane and electrodes are the same, inputs and outputs of electrolytes to/from the tanks are the same, there is also N2 flowing, etc.

Cells are on the bottom of the picture, placed on a retention bin. Each cell is electrically connected to a potentiostat BioLogic MPG205, which has 8 channels and can power up to 5 A each [168]. Electrolyte is fueled to cells from tanks thanks to peristaltic pumps. Tanks are tinted glass vials of 80 mL and 200 mL for negolyte and posolyte respectively. Electrolyte tanks are kept at a given temperature thanks to a cryothermostat which is connected to a retention container filled with distilled water (black box on top of the picture). We assume that temperature inside of the cells is equal to the temperature measured in the retention container (due to the small transit time of the electrolytes out of the tanks), which is a few degrees less than the temperature imposed by the cryostat. The temperature of the experiments stated from now on (20 or 40 °C) is the water temperature measured in the container.

Nitrogen flows through each tank to ensure an inert atmosphere, with no oxygen interaction. It flows through water first to humidify the gas (as in the precedent experiment setup). Nitrogen then goes through tanks and are, afterwards, bubbling in water so that we can visually approximately control nitrogen fluxes going out of the tanks. Nitrogen fluxes are controlled to a minimum to ensure inert atmosphere but not to waste gas. Electrolyte flow rate is fixed to 18 mL.min -1 for each electrolyte.

Here, flow rates are the same for each electrolyte because we use a restricted number of peristaltic pumps, thus we cannot use two different flow rates for each posolyte and negolyte circuit.

Figure 18 shows electrolyte tanks in the thermostatic container, each tank having one input of electrolyte, one output of electrolyte, one input of gas and one output of gas. Before starting experiments, nitrogen is bubbled through the electrolytes for 30 min, then pipes are removed from the liquid and set above it to create a nitrogen sky on top of the liquid in each tank.

Calendar aging campaign

Calendar aging experiments are performed in thermostatic chambers. Electrolytes are stored into tinted glass tanks, which are put into climatic chambers and left for 50 days. In addition to these glass tanks, smaller electrolyte samples (20 mL) are also put in sealed vials. The electrolytes in glass tanks are periodically put into a flow battery and cycled for 2 complete charge-discharge, in order to assess the battery capacity (which is related to the degradation state of the electrolytes). This protocol is detailed further. In parallel, a small quantity (350 µL) of negolyte stored in sealed vials is occasionally taken for 1 H NMR analysis. For each electrolyte -posolyte and negolyte -solution, 4 samples are taken for calendar aging in different conditions:

• Electrolyte totally charged (SOC 100%) at 20°C, • Electrolyte totally charged (SOC 100%) at 40°C, • Electrolyte totally discharged (SOC 0%) at 20°C, • Electrolyte totally discharged (SOC 0%) at 40°C.

Calendar aging experiments serve the purpose of decoupling degradations happening during battery operation (i.e., under current load) and those happening without external current (i.e., which happen during calendar storage). The next sections present the exact formulation steps and the experimental protocol used to assess calendar aging.

Electrolytes' formulation

The following steps are done for each electrolyte, at 20 -in a standard full cell cycling setup as seen above. Though the electrolytes are supposed to be in the discharge state when dissolved into KOH, this complete discharge is made for caution and ensuring that electrolytes really are fully discharged, and have not been oxidized by any means before storage.

20 mL of each discharged electrolyte (at SOC 0%) are collected and put into a sealed vial, kept under argon atmosphere to ensure as much as possible that no air degradation will occur during aging. 50 mL of each charged negolyte and 200 mL of each charged posolyte are also collected and put into separate tinted glass tanks, for further capacity evolution check-ups. SOC100 samples are prepared by totally charging a full DHAQ/ferrocyanide cell with a CC-CV charge, in the same standard cell cycling conditions. 20 mL of each charged electrolyte (at SOC 100%) are collected and put into a sealed vial under argon atmosphere. 50 mL of each charged negolyte and 200 mL of each charged posolyte are also collected and put into separate tinted glass tanks, for further capacity evolution check-ups.

Experimental conditions

Tinted glass tanks were regularly check the discharge capacity of the solutions. To do so, negolytes (50 mL) are put into a full cell against 200 mL of the corresponding (same SOC) ferrocyanide aged electrolyte. We perform two complete CC-CV charge and discharge cycles in the regular conditions of cycling aging (see section 1.3.2): Umax = 1.6 V, Umin = 0.6 V, and j = 37.5 mA.cm -2 . After two cycles, the electrolytes are charged (resp. discharged) for 100% SOC electrolytes (resp. 0% SOC electrolytes), and put back into the tinted glass tanks in thermostatic chambers. Such capacity measurements are performed on electrolytes at 20°C and SOC100, and on both SOC0 and SOC100 samples at 40°C. The reason behind that is we performed the measurements at 40°C first, and wanted to assess if the SOC at which the electrolytes were stored had an effect on the resulting capacity evolution. At 20°C, we only performed capacity measurements at SOC100 because of a lack of time for making other experiments at SOC0. In parallel, 1 H NMR analysis are performed on SOC0 and SOC100 negolytes stored at 20°C, after 50 days of storage (without cycling).

Table 16 establishes a sum up of every experimental condition tested. These calendar aging experiments are used for calibrating the model. Each experiment is named -Calendar20 #1 and #2 for 20°C calendar aging and Calendar40 #1 and #2 for 40°C calendar aging -and we will refer to these names in the chapter 4, when presenting experimental results.

20 °C 0% SOC X Calendar20 #1 100% SOC X X Calendar20 #2 40 °C 0% SOC X Calendar40 #1 100% SOC X Calendar40 #2

Cycling aging campaign

In parallel to calendar aging tests, cycling experiments are performed in order to investigate degradations due to electrochemical aging, as well as the influence of several parameters on aging which can be temperature, current, voltage, concentrations of active species, pH, etc.

Formulation of the electrolytes

Cycling conditions

The regular cycling protocol combines cycle aging phases and characterization cycles. The cycling begins with 5 charge-discharge cycles, so that the cell reaches its "normal-use" capacity and current efficiency. Then a check-up phase is done, consisting in characterization techniques such as Hybrid pulse power characterization (HPPC) test profile, Electrochemical impedance spectroscopy (EIS) and capacity measurement, to assess the battery state of health. After that, cycling resumes with a CC-CV (Constant Charge -Constant Voltage) protocol, an example of which is given in Figure 19. It consists in the subsequent steps detailed hereafter:

• Constant current charge at a current density j until the cell voltage reaches a fixed upper limit Umax,

• Constant voltage charge at a voltage Umax to fully charge the cell, until the absolute current value has decreased under a fixed limit Ilim,

• Relaxation phase with no current nor voltage applied for 30 minutes,

• Constant current discharge at a current density -j until the cell voltage reaches a fixed lower limit Umin,

• Constant voltage discharge at a voltage Umin to fully discharge the cell, until the absolute current value has decreased under a fixed limit,

• Relaxation phase with no current nor voltage applied for 30 minutes.

This CC-CV protocol is repeated for the desired number of cycles. Every 40 cycles, characterizations are made under the same protocol as in the beginning, to assess capacity and resistance of the cell.

Figure 19 Example of a charge-discharge in CC-CV mode, with voltage in blue and current in red

The electrolytes are also characterized at the beginning and at the end of the cycling, with electrochemical characterizations such as cyclic voltammetry, as well as physico-chemical characterizations such as proton NMR, in protocols detailed further. Results of these characterization serve the purpose of determining the degradation products.

Starting experiments were made in standard cycling conditions, following the protocol developed by Cacciuttolo et al. [55,136]. Electrolytes are cycled following the CC-CV protocol described at the beginning of the section. Lower voltage limit Umin is 0.6 V, upper voltage limit Umax is 1.6 V, and current density is j = 37.5 mA.cm -2 . The limiting current signaling the end of the constant voltage phase Ilim is equal to 2 mA.cm -2 .

Temperature is known to usually have an impact on battery's aging in most systems. To assess the effect of temperature on our cell's aging, we performed cycling experiments both at 20 °C and at 40

°C. Temperature is controlled by using a cryostat, which feeds a bath into which electrolyte tanks are plunged. The bath is covered to avoid as possible evaporation of water, and the level of water is regularly controlled to ensure electrolyte tanks are still covered by water. The temperature in the cell is approximated as being the temperature in the tanks, meaning we assume no heat losses in the pipes and the cell. The resulting data are used to calibrate or validate the model, by introducing a temperature dependency of several parameters.

Another factor that has a great impact on batteries performances is the current density. To evaluate how it can affect flow battery aging, we also performed different experiments with a current density variation, from 37.5 mA.cm -2 to 75 mA.cm -2 . We also studied the influence of cut-off voltages for the end of galvanostatic cycling. In a previous work by Cacciuttolo et al. [136], model suggests that upper voltage limit Umax had a greater impact on aging than Umin. For studying the impact of Umax on electrolytes' aging, we performed cycling experiments in the same conditions as before but with different values for Umax: 1.5 V, 1.6 V and 1.7 V.

Cycling with a power profile

Finally, a realistic power profile is also used for validation. Specific power profiles are profiles where the flow cell is power monitored, as it would be in a real application. Those used for validation of the model are imported from .txt files. The power profile we chose for experiments is representative of a real case use of the flow battery in stationary storage conditions. It is imported from a Pacific

Northwest National Laboratory study [START_REF] Conover | Protocol for Uniformly Measuring and Expressing the Performance of Energy Storage Systems[END_REF]. Before applying a duty cycle from the power profile (7 200 s), the battery is set at a medium-high SOC by a constant current phase, with a voltage limit at 1.4 V.

After a relaxation phase of 30 min, 10 duty cycles from the power profile (72 000 s) are applied in a row, followed by a capacity check-up with two CC-CV charge and discharge cycles in standard cycling conditions, and a charge back to medium SOC. This operation is then repeated several times, while we follow the evolution of the capacity.

Characterization of the electrolytes

For identifying the degradation products of either cycling or calendar aging, specific characterizations are made. In our case study, it consists in NMR spectroscopy (mainly 1 H NMR with a few attempts of 13 C NMR), and cyclic voltammetry essentially.

1 H NMR spectroscopy

NMR characterizations are made with a Brüker NMR spectrometer, at a frequency of 300 MHz.

Samples are diluted in deuterium oxide D2O, and for each sample 200 µL of electrolyte are mixed with 300 µL D2O. 16 scans are done for each spectrum.

Cyclic voltammetry

Cyclic voltammetry experiments are performed on each aged electrolyte after cycling experiments.

The results of these experiments are interpreted qualitatively in comparison with fresh electrolytes voltammograms. We looked for disappearance of existing peaks and/or appearance of new ones, which could assess for the degradation of existing redox active materials and formation of new redox inactive or redox active species.

We also explored the occurrence of crossover by sweeping potential in a global range including both negolyte and posolyte species redox activity curves. Thus, if a signal is detected in negolyte sample, for instance, corresponding to posolyte reduction or oxidation range of potential, it means that posolyte species crossed the membrane to enter negolyte tanks.

Preparation of samples and setup

Cyclic voltammetry experiments were usually performed on 100 mL of sample, diluted to 0.1 M. Some experiments were made on sample at a concentration of 1 mM, but without great success because of the low signal to noise ratio at such concentrations. Aged electrolytes samples are taken directly from tanks after cycling, with a volumetric pipette, and mixed into a volumetric flask of 100 mL with KOH 1 M. After mixing, the resulting solution is used for voltammetry.

The experimental setup is a three-electrodes system, pictured in

Experimental results

Calendar aging results

For determining the rate of capacity fade due to chemical degradations (in the absence of a current source), we use calendar aging experiments. Electrolytes are stored in thermostatic chambers, respectively at 20°C and 40°C, and from time to time "check-ups" are performed on the electrolytes to determine the capacity of a full cell working with the electrolytes. For each check-up, 50 mL of negolyte and 200 mL of posolyte are put in tinted glass tanks, then deaerated by bubbling nitrogen in the solution for about 30 minutes. After that, nitrogen only flows above the liquid in the tank, to avoid contact between oxygen and the solution. 3 charge-discharge cycles are done according to the described protocol (section 3.2), then electrolytes are pumped back into their tanks, which return in thermostatic chamber for the rest of calendar aging. Pipes are rinsed with water thoroughly after each check-up, and specific pumping pipes (those connected to peristaltic pumps) are changed after each time because otherwise it could lead to leakages because of the high pressure applied on those pipes.

We chose not to change the components of the cell (carbon felts, membrane or collectors) between the experiments, as only a few cycles are done each time so it should not cause too much wear on the cell components. A little quantity of electrolyte is lost in the pipes after each check-up, which is considered negligible but is a source of uncertainty.

Figure 23 shows the evolution of the capacity of electrolytes stored at 20°C and 40°C, measured in a standard cell. There are samples of electrolytes are kept at SOC0 and SOC100 at 40°C (Calendar 40 #1 in green and #2 in blue), and a sample at SOC100 at 20°C (Calendar20 #2 in red). The capacity is measured with the fresh electrolytes -point at time = 0 days -, then a second measurement is made after around 10 days, a second after around 25 days and a third after around 40 days. We performed linear regression on the results for all the samples (dashed curves). We make the hypothesis that the measured capacity fade is mainly due to the chemical degradation of DHAHQ 4-, producing DHA 3-.

Figure 23 Evolution of the capacity during calendar aging with electrolytes stored at 20°C SOC100 (red), 40°C SOC0 (green) and 40°C SOC100 (blue)

The coefficients obtained from the linear regression models are summarized in Table 18. The capacity fade rate is comprised between -16 to -20 mAh/day during the calendar aging for all 3 samples.

According to our results, storing at SOC0 seem to lead to more linear capacity fade, with a R² value of 0.999 and a standard error on the slope of ±0.3 mAh/day, which gives a capacity fade rate comprised between -19.9 and -20.5 mAh/day. Results with calendar aging at 40°C and SOC100 are not linear at all, with a R² value of 0.932. Looking at the chart, the second capacity check-up after 8 days gives a much lower capacity value than for the 2 other samples. The standard error on the slope is ±3.2 mAh/day, which gives a capacity fade rate comprised between -13.4 and -19.8 mAh/day. The first comment to make on these results is that there seem to be a greater capacity fade for SOC0 samples, though our analysis is not sufficient to conclude on a definite influence of the SOC on the capacity fade rate in calendar aging. This is quite unexpected since the hypothesis is that chemical degradation occurs when SOC is high, because it degrades DHAHQ 4-. Thus, electrolytes at high SOC should undergo more degradations than electrolytes at low SOC. However, we must note that storage conditions were not precisely controlled. Apart from temperature, no parameter (atmosphere, presence of oxygen, precise state of charge) was measurable/controllable, meaning that the real SOC is not always known. We can however get an idea of the SOC of the electrolytes when measuring the open circuit voltage (ocv) of the cell right before a check-up. We did that and measured an ocv for electrolytes in Calendar40 #1 of 0.5V before the first check-up, 0.78V at t=14 days and 0.96V at t=21 days. For electrolytes in Calendar40 #2, we measured ocv values of 1.46V before the first check-up,

1.30V at t=8 days, 1.27V at t=27 days and 1.29V at t=42 days. The fact that ocv values increase for SOC0 sample and decrease for SOC100 sample indicate that there is indeed some charging (respectively discharging) for the samples at SOC0 (respectively SOC100). This is expected because of the uncontrolled atmosphere during aging and check-ups. Aziz et al. evidenced that aeration of a negolyte DHAQ solution could restore capacity by oxidating DHA 3-back to DHAQ 2- [97], which could happen in our experimental conditions.

The second result arising from these figures is that temperature does not seem to have an impact on the capacity fade during calendar aging. For samples at 20°C and SOC100 -we did not perform studies on samples at 20°C and SOC0 because of a lack of time -, the capacity fade rate is comprised between -16.0 and -19.6 mAh/day. These values are totally in range with the values obtained at 40°C. With a R² value of 0.980, we can say that our results are not linear.

Overall, our results do not indicate a potential influence of the SOC nor the temperature on capacity fade during calendar aging. Further tests at different SOC and temperatures for longer calendar aging times should be launched to get a better understanding of whether these parameters influence or not the capacity evolution. Since the SOC does not have that big of an impact on the results, measurements made on electrolytes at SOC 100 only will be used for model calibration at 20°C and 40°C.

Figure 24 shows the evolution of the voltage (left) and current (density) of the electrolytes at 20°C and SOC0 throughout aging. The curves for fresh electrolytes are in red, after 14 days in green, after 21 days in blue and after 28 days in purple. In every voltage graph, we see a constant current charging (resp. discharging) part, and a constant voltage charging (resp. discharging) part. The repartition of the constant current and constant voltage part differs between the data considered. Current and voltage profiles of the check-up after 14 days of calendar aging are very different from the three other points.

The constant current part is nearly absent, and there is only a constant voltage contribution to the charge, which takes a longer time than usual (here more than 4 hours instead of 30 min, compared to the fresh cell). The disappearance of the constant current charging and discharging means that the resistance increased a lot. This could be attributed to a radical change in the redox species that play a part during charging, or anything else that can cause a tremendous increase of the cell resistance, such as precipitation in the cell, or clogging of the pores, etc. This behavior disappears in the subsequent check-ups, so it could either be a transient phase linked to the transformation of active species, or an experimental flaw due to a bad rinsing of the cell, for instance.

Apart from the graph at 14 days, we can see that constant current charging and discharging goes faster as the cell ages, which is in agreement with the increase in resistance throughout aging, due to several factors. Another thing to be mentioned is the appearance of a slight bump on the current profile during floating in discharge, on the blue curve after 21 days. This bump at j = -20 mA.cm -2 (t = 3h) is characteristic of the formation of a new redox species. We see that this bump disappears from the graphs after 28 days. This could be an intermediate degradation product such as DHA 3-, but we do not have enough information to conclude here on the exact nature of this specie appearing around 0.8V. The curves for fresh cell are in red, after 8 days in purple, after 27 days in green and after 40 days in blue. Here, the profiles of voltage and current are similar throughout aging. The constant current charge (respectively discharge) time decreases over aging, which is coherent with the capacity loss observed and is the sign of greater ohmic losses throughout aging, due to the different degradations occurring. The green curve after 27 days shows a longer constant voltage charge than the others, and the associated floating current is noisy. The noise in the current can be due to several factors, such as bubbles formed in the flow or a flaw in electrical connection. The noise in the current prevents it from reaching the minimum fixed limit of 40 mA, which implies a longer constant voltage charging. Since we do not notice this behavior in the following discharge, it is most likely an experimental error which is not significant. We also clearly notice a bump appearing at the end of constant current discharge on the voltage profile in every test on aged samples, for instance at t = 2h for the blue curve. This is probably the sign that new redox species are being formed, around 0.7V. The nature of this specie is uncertain at this point, but it could be DHA 3-. Post-mortem characterizations will help to confirm this hypothesis or not.

Cycling experiments results

This section presents the main experimental results obtained from cycling studies. We performed different batches of experiments in order to study the influence of temperature, current density and maximum cut-off voltage on the cell's performances during time. The last experiments are duty cycles, thanks to imported power profiles.

Figure 26 Capacity fade curves of cycling experiments, at 20°C and 40°C

This figure gives a first look into the difference in capacity fade between 20°C and 40°C experiments.

We will go into further details in the following sections 4.1.2.2 and 0, but we can already see that the capacity fade profiles are very different depending on the temperature. The capacity fade at 40°C is much faster, at least in the first 25 cycles. When considering all the experiments, the capacity fade at 20°C is between -4.5 and -8 mAh per cycle, whereas at 40°C it is comprised between -25 and -85 mAh per cycle. For cycling experiments at 40°C, the capacity goes from between 1250 and 1600 mAh, depending on the experiment, to 750 mAh (60% of initial capacity) in 15 to 25 cycles. For 20°C experiments, this decrease from 100% to 60% occurs within at least 40 cycles, for the experiments with the highest capacity fade rate (Cycling20 #3, #4 and #5), and such a decrease in capacity is not even seen for experiments Cycling20 #2, which are cycled with a lower Umax. Another interesting thing that can be seen on every Cycling40 graph is an increase in capacity in the second and third cycle compared to the initial value, before a decrease as usually observed during aging. This behavior, that is not observed on any 20°C cycling experiment, will be discussed in more details after, in section 4.1.2.2.

Unfortunately, due to electronical issues on the pumps and an electrical shutdown, 40°C cycling studies did not last for as long as we had planned at the beginning. Due to increased degradations because of the temperature, it was enough to obtain tendencies from the generated capacity fade curves.

However, longer experiments at 40°C would be needed in order to confirm the long-term behavior of cells cycling at 40°C.

Influence of the current density

Several current densities are used for the experiments. Lower current experiments are performed at 37.5 mA.cm -2 , medium current experiments at 50 mA.cm -2 and high current experiments at 75 mA.cm -

2

. The aim is to study the influence of the current on capacity fade profiles.

Figure 27 shows experimental results obtained during a same experimental batch on the 8-cells bench, at 20°C (left) and 40°C (right). In each temperature set, wo cells are cycled at 37.5 mA.cm -2 (Cycling20 #1 and Cycling 40 #1), two at 50 mA.cm -2 (Cycling20 #4 and Cycling40 #3), and two at 75 mA.cm -2 (Cycling20 #5 and Cycling40 #4), following the standard CC-CV protocol described in section 3.3.2. In general, the capacity fade graphs have the same profile for a given temperature, and we cannot see any obvious influence of the current regime on the capacity fade. forced us to stop these experiments, and to resume the day after. We can see that this pause in cycling comes with a small increase in capacity for the next cycles, meaning that a part of the capacity was restored. This is in good agreement with the findings of Aziz et al. in their research [97], that demonstrated that oxygenation of the solutions enables restoring some of the capacity lost, by reversing some DHA 3-into DHAQ 2-. Even though we try to limit oxygen interactions in this setup via flowing nitrogen through the tanks, we cannot totally prevent oxygenation of the solutions because we are not in controlled atmosphere (i.e., aqueous glovebox).

At 40°C, the starting capacities measured for every experiment are more dispersed, ranging from 1250 to 1600 mAh. At cycle 2 in every experiment, the capacity rose by more than 10% of its initial value (from 1250-1600 to 1700-1800 mAh, depending on the conditions), before decreasing as it was expected. This behavior could be attributed to the formation of new redox active species in a first time, before their consumption after the first few cycles. For example, if some DHAQ 2-is produced by a chemical or an electrochemical degradation of DHAHQ 4-, this can shift the equilibrium of the cell and produce an increase in capacity. However, this is not clear yet and is only a suggestion; further tests of cycling and characterization of the electrolytes after a few cycles are needed to explore the possible degradation pathways of the electrolytes. After this increase, there is a fast decrease in capacity during about 5 cycles, before slowing around 900 mAh. The capacity fade rate changes from around -75 mAh/cycle between 1500 and 900 mAh, to about -20 mAh/cycle between 900 and 750 mAh. These capacity fade rates are still greater than the ones measured at 20°C.

As we performed two experiments for each condition in these current density experiments, we were interested in how our experiments can be reproductible or not. In order to investigate the reproducibility, we calculate the mean squared error (MSE) of the capacity measurements, which is the sum of the square differences values of the capacities measured for two experiments in the same conditions. It is calculated as described in Equation 4-1 for the experiment 𝑘, with 𝐶𝑎𝑝 𝑘.1,𝑖 the capacity measured at cycle 𝑖 in the first experiment, and 𝐶𝑎𝑝 𝑘.2,𝑖 the capacity measured at cycle 𝑖 in the second experiment.

MSE 𝑘 = ∑ (𝐶𝑎𝑝 𝑘.1,𝑖 -𝐶𝑎𝑝 𝑘.2,𝑖 ) 2 𝐶𝑎𝑝 𝑘.1,𝑖 2 𝑖 Equation 4-1
We obtained the following values for the current density experiments:

• MSE 𝐶𝑦𝑐𝑙𝑖𝑛𝑔20 #1 = 0.15, • MSE 𝐶𝑦𝑐𝑙𝑖𝑛𝑔20 #4 = 3.64, • MSE 𝐶𝑦𝑐𝑙𝑖𝑛𝑔20 #5 = 4.43, • MSE 𝐶𝑦𝑐𝑙𝑖𝑛𝑔40 #1 = 0.19, • MSE 𝐶𝑦𝑐𝑙𝑖𝑛𝑔40 #3 = 0.03, • MSE 𝐶𝑦𝑐𝑙𝑖𝑛𝑔40 #4 = 0.04.
The experiments Cycling20 #4 and Cycling20 #5 have huge quadratic errors, compared to Cycling20 #1.

As we can see on the charts of Figure 27-a), the blue and green curves are not quite superimposable. Same goes for experiment Cycling40 #1, with a quadratic error 5 to 6 times higher than Cycling40 #3 and Cycling40 #4. In general, the quadratic errors for cycling experiments at 40°C are lower than those at 20°C, because there are fewer capacity measurements (10 to 25 cycles vs 80 to 120 cycles), thus the sum of the errors is lower.

Influence of the cut-off voltage

After studying the influence of temperature and current density on the capacity fade profiles during cycling, we decided to change the maximum cutoff voltage. This is done at 20°C only because we lacked time for more experiments at 40°C. Figure 28 shows the results obtained with this set of experiments.

7V in blue

It can be observed from this chart that the capacity fade profile looks the same for each value of Umax, however the capacity decrease is slower when Umax = 1.5V. There is apparently no significant difference between the capacity fade at Umax = 1.6V and Umax = 1.7V, which could indicate that the maximum degradation level has already been reached at 1.6V. Also, repeatability of the experiment Cycling20 #3 is not really good: another set of experiments should be made in these conditions to confirm the capacity evolution. Cycling at Umax = 1.5V thus enables a longer lifetime for the battery, with a decrease in capacity of 35% of its initial value in 120 cycles, whereas when Umax = 1.6 or 1.7V the battery loses 45% of its initial capacity in 90 cycles. The mean squared error values obtained for these experiments are: MSE 𝐶𝑦𝑐𝑙𝑖𝑛𝑔20 #2 = 0.39, and MSE 𝐶𝑦𝑐𝑙𝑖𝑛𝑔20 #3 = 6.40. The two experiments with Umax 1.7V give different results, thus caution must be taken with the interpretation of these results.

To give an idea of the difference in the electrochemical nature of species between the beginning and the end of a cycling experiment, we plotted in Figure 29 voltage curves, at the 2 nd cycle -a) and b)and the 80 th cycle -c) and d) -. We did not take the first cycle as an example since the profile is not representative of the following cycles, due to the different phenomena taking place in the first charge and the first discharge of the battery. In each graph, a charge-discharge curve is shown for Umax = 1.5V in green, Umax = 1.6V in red, and Umax = 1.7V in blue. For fresh cells, those charge-discharge curves at nearly superimposable, in particular when looking at the constant current charging when the voltage rise from 0.6 to Umax. For aged cells however, we can see several differences. First, there are obvious differences between aged and fresh cells curves: we can see the apparition of bumps on constant current charge and discharge curves, indicating changes in active redox species. Also, there are differences between the aged curves, depending on the corresponding maximum cutoff voltage. For Umax = 1.5V, we can see a bump during charging at U = 1.4V, whereas for Umax = 1.6 and 1.7V, the charge-discharge curves look similar. For the latter, we observe a bump during charging around U = 1.3V, and a smaller bump during discharge around U = 0.8V.

As cells with Umax = 1.6V and 1.7V undergo more degradations in total, we can think that the voltage curve during charging for Umax = 1.5V, with a bump at U = 1.4V, is an intermediate degradation state.

After that, another redox species is formed at U = 1.3V, and in discharge around U = 0.8V. This is just a hypothesis, but the conclusion here is that several redox processes are probably happening either at the same time or one after another, and if we cannot conclude on what exactly happens, we can at least say that more experimental tests and characterizations would be interesting for getting more information on the degradations steps and formed products.

.4 PNNL power profiles representing real use conditions

Finally, the last experiments done on redox flow cells are to drive them with a power profile input, which is representative of a realistic usage of the cell. Left chart on Figure 30 shows the evolution of the voltage during this power profile input. The power profile we use is a "normal" power profile,

where the cell stays around a medium SOC -here, the voltage during a duty cycle ranges between 1.2 and 1.5V. There are more "aggressive" power profiles, where the cell can be driven to low or high SOC, which we did not try in this work. We will see in chapter 5 if the built model can replicate this kind of profile.

Figure 30 a) Evolution of the voltage during a power profile, and b) capacity fade throughout a PNNL test consisting of several consecutive power profiles with capacity measurements in between

Every 10 duty cycles (which takes about a day), the capacity of the cell is measured with a simple charge-discharge test, in standard conditions. Right chart on Figure 30 shows the evolution of the cell capacity during its operation. Compared to previous experiments, the capacity fade is much lower. This is explained by the fact that during these power profiles tests, the cells are kept at medium SOC, whereas degradations usually take place at extreme SOC. If our experiments are indeed representative of the reality, we can infer that flow batteries lifetime during real usage are longer than predicted lifetime by laboratory standard tests, i.e., charge and discharge cycling experiments.

Characterization of aged electrolytes

Experiments used to characterize the electrolytes are cyclic voltammetry and 1 H NMR. Some 13 C NMR tests were also conducted, but the results are non-exploitable because of too much noise in the signals.

We present here the results of cyclic voltammetry in section 4.1.3.1, then 1 H NMR results in section 4.1.3.2. These results are presented and analyzed qualitatively, since the characterizations are not the main purpose of this work. In-depth analysis coupled to other characterizations are needed to conclude on the exact nature of the formed degradation products.

Cyclic voltammetry

We performed cyclic voltammetry on electrolytes before and after cycling. We present in Figure 31 the results of cyclic voltammetry at Vb = 100 mV.s -1 on both fresh and aged posolytes and negolytes, after the first set of experiments at 20°C. Different sweeping rates, from 20 to 100 mV.s -1 , were also tested; the results are not different from those presented below, so we chose to only put graphs at 100 mV.s - 1 for clarity and cycle number 2 out of the 3 we did for every voltammetry experiment. We only present cyclic voltammetry for these experiments since the resulting data is representative of every cyclic voltammetry result performed on aged samples (at 20°C or 40°C).

Figure 31 Cyclic voltammetry on aged posolytes at 20°C, compared to new electrolytes (dashed curve). Top chart is for negolytes and bottom chart is for posolytes

Cyclic voltamograms for fresh posolyte and fresh negolyte are purple dashed curves. We can see that the curves for all aged posolyte samples (bottom) are superimposable and in line with the fresh posolyte curve, with a small shift that is due to a change in the baseline, which could be a consequence of a pH change for instance (we did not investigate further this shift). This is in agreement with our hypothesis that no significant degradation occurs on the positive side of the cell.

Unlike the bottom chart however, aged negolytes (top chart) are quite different from the voltammogram for fresh negolyte. For every aged electrolyte except Cycling20 #2.1, we cannot distinguish redox peak anymore, neither in oxidation nor in reduction. The khaki green curve, corresponding to the experiment where Umax = 1.5V, is indeed different from other aged samples: here, the signal is the same as for fresh 2,6-DHAQ but the intensities of the peaks in oxidation and reduction are lower than for the fresh sample. It means that the electrolyte, in the conditions of our experiment, is not in the same degradation state than the others.

For all the other aged negolytes, we zoomed on the voltammogram in order to see peaks. The zoomed graphs are displayed in Figure 32 a), and compared to a voltammogram issued from literature for (DHA)2 in b). We have small peaks on the curve between -1.1V and -0.5 vs. SHE (at -0.95, -0.7 and -0.4V vs. SHE in oxidation, and -1.1, -0.9 and -0.7V vs. SHE in reduction). We also see a peak around 0.2V vs.

NHE in oxidation, which disappear in the subsequent reduction signal. Even though the potential is near from the potential of ferrocyanide, the fact that we don't see a peak in reduction indicates that it is probably not the sign of crossover. We actually see the same peak on fresh negolyte, just shifted of a few hundreds of mV (Figure 31 top). Overall, the peaks that we find in the zoomed voltammograms for aged negolytes are very similar to the peaks found for (DHA)2. This is coherent with our assumption that, ultimately, (DHA)2 is formed during aging. Because of the volume of solution required for cyclic voltammetry studies (at least 20 mL for an experiment), we did not perform it on electrolytes during calendar aging so as not to change the volume of electrolyte (and thus the capacity) used in the Pinflow cell during check-ups. Cyclic voltammetry studies on calendar aging electrolytes would be useful, in particular to determine if the degradation products formed are the same in the different calendar aging conditions (20°C/40°C, and SOC0/SOC100).

1 H NMR results

We performed 1 H NMR on both calendar and cycling aged samples, at 20°C. Figure 33 shows the results on calendar samples after 50 days, with measurements made on initial negolyte diluted in D2O (blue spectrum), and on aged negolytes diluted in D2O, at SOC 0 (red spectrum) and SOC 100 (green spectrum). The 3 spectra are shifted so that the reference peak of water is at the same place (this peak is not visible in the figure because the chemical shift is lower than the ones considered here). We only consider the aromatic peaks since we have water in the samples, rendering other peaks invisible. On the reference spectrum, we see peaks at 6.7, 7.0 and 7.8 ppm, characteristic of 2,6-DHAQ. Those peaks are also found on the other spectra, but the chemical shifts are shifted towards lower ppm. Since the peaks are the same, this shift can be attributed to a change in the experimental settings under which are done 1 H NMR studies. Indeed, 2,6-DHAQ is diluted in KOH, and 350 µL are collected and mixed with 250 µL of D2O: there are still water and hydroxide ions in the mix. A more accurate way to perform NMR analysis could have been to dry thoroughly the sample, then dilute only the powder in D2O. In our case, the resulting shifted spectra can be caused by a change in pH, for instance.

The 3 samples have been prepared in the exact same conditions. The spectra taken on TopSpin™ are zoomed at the same scale, yet the intensities of the peaks for the sample at SOC0 and for the sample at SOC100 are lower. This indicates that there is less 2,6-DHAQ in the aged samples than in the reference electrolyte. On the green spectra which is the aged electrolyte at SOC 100, in addition to the standard peaks corresponding to 2,6-DHAQ, we can see other small peaks whose chemical shifts are close to the initial ones: 6.7 and 7.4 ppm. They may correspond to some of the peaks of DHA, as we can see from Figure 34, taken from Aziz et al. [97]. We remind that these electrolytes (SOC 0 and SOC 100) were kept in sealed vials and did not undergo any cycling: thus, no (DHA)2 shall be formed. We also performed NMR analysis on cycling aged negolytes at 20°C diluted in D2O, taken after cycling at different current densities (37.5, 50 and 75 mA.cm -2 ) and different Umax values (1.5, 1.6 and 1.7V).

Figure 35 shows the results on cycling aged samples, with measurements made on initial negolyte diluted in D2O (blue spectrum). voltage. For this one, the red curve shows lower intensity of the peaks corresponding to the initial spectrum, which is again in agreement with the corresponding voltammogram. However, unlike for calendar aged sample stored at SOC 100, we do not observe new peaks in the red spectrum, which would indicate that no DHA 3-was in the solution at the time where NMR studies were achieved. This is in line with our hypothesis of degradation mechanism, where DHA 3-is chemically formed at high SOC (and we see it on the calendar aging spectrum) and is then electrochemically and irreversibly dimerized into (DHA)2 4-, a poor redox active species. This hypothesis, however, does not explain why we do not observe any proton signal in the NMR spectra of the cycled electrolytes. Further studies need to be done to explore the exact mechanism happening in our study, and why our NMR results are different from those found in the literature [97,98,117].

The intensity of the peaks is lower than for the fresh 2,6-DHAQ, meaning that some of the DHAQ has been transformed into another species. On the sample at SOC100, we find small peaks at 6.7 and 7.4 ppm, which are comparable to the peaks found in DHA spectrum, but not exactly at the same chemical shifts. Our hypothesis to explain these results is that only a bit of DHA was formed during calendar aging, by a way of chemical degradation. Further studies would be needed in order to be sure of the nature of the formed product and on the conditions where it is formed (for example if we find the same peaks at 40°C).

• We did cycling experiments at 20°C and 40°C, at different current densities and different cutoff voltages. The capacity fade rate during cycling depends on the temperature (the higher the temperature, the higher the capacity fade). It depends on the voltage in a certain extent (lowering the cut-off voltage to 1.5V substantially reduces the capacity fade but increasing it to 1.7V does not seem to have a notable effect), but does not depend much on the applied current density, neither at 20°C nor at 40°C.

• The electrolytes that undergo cycling experiments at 20°C are then characterized post-mortem with cyclic voltammetry and 1 H NMR. The cell cycled with Umax = 1.5V shows the same peaks, both on voltammograms and NMR spectra, than fresh 2,6-DHAQ. Every other cycled cell shows no more peaks in their NMR spectrum, and multiple peaks of small intensity on their voltammograms. These peaks, seen in cyclic voltammetries, are similar to the ones seen on the voltammogram of (DHA)2. These observations lead us to the conclusion that the sample cycling at a lower Umax did not age in the same way as the others, in which 2,6-DHAQ was degraded, probably into (DHA)2. In all the samples except for Cycling20 #2, all the 2,6-DHAQ signal disappeared both in NMR and in voltammetries studies. However, we still have capacity remaining in the battery. This is probably the signature of another redox species forming, with poor redox properties (low peaks in CV) but still enough capacity to enable cycling of the battery.

• We also used the cells in power duty cycles corresponding to a realistic usage. The resulting measure capacity fade rate is lower than the capacity fade rate measured during a simple charge-discharge operation.

Calibration of the model

This last section describes how the model is calibrated, based on the experimental results exposed above. The calibration of our model took place in 3 major steps:

1) The first step to ensure is that it simulates well enough a simple charge-discharge experiment.

For this, we calibrate some parameters of the original model, which are subject to changes and are related to the experiment. The parameters are the main reactions kinetics 𝑘 𝐷𝐻𝐴𝑄 2-/𝐷𝐻𝐴𝐻𝑄 4-and 𝑘 𝐹𝑒(𝐶𝑁) 6 3-/𝐹𝑒(𝐶𝑁) 6 4-, diffusion coefficients of the considered species 𝐷 𝐷𝐻𝐴𝑄 2-, 𝐷 𝐷𝐻𝐴𝐻𝑄 4-, 𝐷 𝐹𝑒(𝐶𝑁) 6 3-and 𝐷 𝐹𝑒(𝐶𝑁) 6 4-, which are known for glass carbon but have to be calibrated for carbon felts in this experiment as they depend on several parameters such as compression of the felt. Another important parameter to calibrate is the membrane resistance 𝑅 𝑚𝑒𝑚 , which depends on geometric parameters of the membrane 𝛿 𝑚𝑒𝑚 and 𝐴 𝑚𝑒𝑚 , and on the membrane conductivity 𝜎 𝑚𝑒𝑚 , which can vary depending on the experimental setup. The last important parameter to consider in the model in order to fit a voltage curve is the amount of unbalancing in the cell at the beginning. Indeed, we prepared the solutions for cycling in uncontrolled environment (i.e., not in aqueous glovebox), so oxidation by the atmosphere is unavoidable between the preparation and the beginning of cycling. Since it is a major parameter, its value was calibrated (we did not find a way to accurately measure it experimentally). The value ∆ 𝑐𝑜𝑛𝑐 is used to describe unbalancing: it is the amount (in %) of initial Fe(CN)6 4-that has been oxidated to Fe(CN)6 3-by the air, and is thus not accessible for cycling anymore,

2) After calibrating the values for global parameters of the model, the second step is to calibrate the parameters characteristic of the chemical degradation as hypothesized in section 1.2.3.

We simulated calendar aging experiments and compared the results to experimental calendar aging data. The parameters 𝑘 𝑐ℎ𝑒𝑚 and 𝛼 𝑐ℎ𝑒𝑚 are calibrated so that simulated capacity fade fits experimental capacity fade experienced during calendar aging,

3) To finish calibration, electrochemical parameters are calibrated to fit experimental cycling results. We calibrate the values of 𝑖 0 𝐷𝐻𝐴 and 𝛽 𝐷𝐻𝐴 , which correspond to the parameters related to the electrochemical dimerization of DHA 3-in (DHA)2 4-, to fit experimental cycling curves. If the fitting is not satisfactory enough, we can implement another electrochemical equation, for example an electrochemical degradation of DHAHQ 4-into DHA 3-as hypothesized in the work of Zhao et al. [98,117]. However, this equation brings the model to another level of complexity, and calibration of the parameters is usually more difficult as interdependency between all the degradations has to be taken into account.

This calibration work is done at 20°C and at 40°C. Indeed, diffusion or kinetics parameters as well as resistance related to the membrane can vary significantly with a change in temperature. The unbalancing value ∆ 𝑐𝑜𝑛𝑐 is calibrated for each simulation, to best fit the first cycle capacity of the related experiment. The set of parameters obtained is not necessarily unique, so when in doubt we choose the parameters that are the closest to measurements found in the literature and, for each parameter, we ensure that the solution is physically possible.

20°C

In this section, the results of calibration at 20°C are presented. The simulation fits quite well the experimental curve, except for some slope changes that are not well mimicked by the simulation.

Calibration of the parameters related to chemical degradation 𝒌 𝒄𝒉𝒆𝒎 and 𝜶 𝒄𝒉𝒆𝒎

After calibrating the values for global parameters of the model, the second step is to calibrate the parameters characteristic of the degradations at 20°C. We simulated calendar aging experiments and compared the results to experimental calendar aging data. The results in simulation are pretty good, with the simulated capacity corresponding to the experimental capacity measured with the check-ups. We did try several sets of parameters, with different values for 𝛼 𝑐ℎ𝑒𝑚 (0.5, 1 and 2). For each value, there was a corresponding 𝑘 𝑐ℎ𝑒𝑚 that would make the simulation fit the experiment. We chose to go with alpha = 1 so as not to overcomplicate the model, since we did not think that the physics required to consider a second order for the chemical reaction. A limit of the calibration is that we did not achieve to get anything else than a linear capacity fade (with the three points considered here), no matter which 𝛼 𝑐ℎ𝑒𝑚 value we chose.

Calibration of the parameters related to electrochemical degradations 𝒊 𝟎 𝑫𝑯𝑨 and 𝜷 𝑫𝑯𝑨

After calibrating the chemical degradation, the last step is to modify the values of the electrochemical degradation's parameters, so that simulation curves can fit experimental cycling curves. At 20°C, we performed cycling experiments at different current densities, and with different maximum cutoff voltage values. We chose to calibrate the model thanks to the experiments at low and high current densities (j = 37.5 and 75 mA.cm -2 ) and the experiments at medium and high cutoff voltage values (Umax = 1.6 and 1.7V) and to use the remaining results (j = 50 mA.cm -2 and Umax = 1.5V) for the validation.

Figure 38 shows the results of the simulation for cycling in standard conditions. The simulated capacity is in blue, and the experimental data corresponding in red. The simulation fits quite well the experiment; however, we did not achieve to replicate the logarithmic shape of the experimental curve, with the capacity fade rate decreasing when the concentration (thus the capacity) decreases.

Figure 38 Simulated (blue) vs. experimental (red and green) capacity evolution during cycling in standard conditions

Figure 39 shows the simulated capacity (blue curve) corresponding to cycling at a high current density, with j = 75 mA.cm -2 , Umin = 0.6V and Umax = 1.6V. The experimentally measured capacity during cycling is represented by the red curve. The simulation is close to the experimental curve; however, the starting capacity in the simulation is higher than the experimental capacity. Also, there is a change in the experimental capacity fade profile with 3 sections: before cycle 15, the capacity fade rate is low; then it increases between cycle 15 and cycle 50, before decreasing until the end. We were not able to model these slope changes with our model, which is probably not complex enough for that.

Figure 40 shows the simulated capacity (blue curve) corresponding to cycling with a higher voltage limit, with j = 37.5 mA.cm -2 , Umin = 0.6V and Umax = 1.7V. The experimental curve is in red. Here also, even though the simulation fits quite well the experimental capacity, we did not achieve to represent the starting capacity nor the changes in slopes.

These simulations have been obtained with 𝑖 0 𝐷𝐻𝐴 = 1.10 -7 A and 𝛽 𝐷𝐻𝐴 = -11.5. We can see from the simulation results that the capacity fade profile does not rely much on the applied current, which is coherent with the experiment. It also does not seem to vary a lot when changing the maximum cutoff voltage, which is in line with the experiment at 1.7V. We will check if this behavior still applies at Umax = 1.5V during the model validation, in chapter 5. 19 summarizes the value of every calibrated parameter in section 4.2.1, at 20°C. species. Modelling this phenomenon requires a higher level of complexity in the model, this is another limit of our model.

Calibration of the parameters related to chemical degradation 𝒌 𝒄𝒉𝒆𝒎 and 𝜶 𝒄𝒉𝒆𝒎

After calibrating the model parameters without degradation of active species, we calibrate the chemical degradation forming DHA 3-. Figure 42 presents the results of simulations (blue) with values of 𝑘 𝑐ℎ𝑒𝑚 = 1.10 -7 m.s -1 and 𝛼 𝑐ℎ𝑒𝑚 = 1, after calendar aging at 40°C for 40 days, compared to the experimental results (red).

Figure 42 Simulated capacity loss (red) compared to experimental capacity loss (blue) for samples stored at 40°C in calendar aging

Here, the simulated fit is not very good. We did achieve to obtain a logarithmic shape for the capacity fade, but the values obtained with the simulation are quite far to the experimental values, and the model overestimates the capacity fade compared to the reality. A point that could be of importance is that our model for calendar aging differs a bit from reality. Indeed, it considers that everything is done at 40°C, whereas, experimentally, the electrolytes are stored at 40°C but the capacity check-ups (that can take 2 to 3 days each) are done at ambient temperature, so closer to 20°C. Thus, the simulated capacity fade is overstated compared to the reality.

Calibration of the parameters related to electrochemical degradations 𝒊 𝟎 𝑫𝑯𝑨 and 𝜷 𝑫𝑯𝑨

After calibrating the chemical degradation parameters, we calibrate the degradation parameters 𝑖 0 𝐷𝐻𝐴 and 𝛽 𝐷𝐻𝐴 . Figure 43 presents the results of the simulation (blue curve) with the fitted parameters, in standard conditions: j = 37.5 mA.cm -2 , Umin = 0.6V and Umax = 1.6V, vs. the experiment (red and green points). With only these degradation phenomena (chemical and irreversible electrochemical degradation) and in such a short cycling time, we achieved to obtain a logarithmic shape for the capacity fade. Furthermore, we achieved to simulate an increase in the capacity observed in the second cycle experimentally, which is the consequence of the long floating time in charge and discharge at the beginning of cycling (as time goes on, this constant voltage cycling time decreases). However, we only achieved to simulate this increase in capacity by increasing the value of ∆ 𝑐𝑜𝑛𝑐 to 40%, thus the starting capacity is lower than the experimental capacity measured at the first cycle. the values obtained at 20°C, the main reactions kinetics and diffusion coefficients are overall higher by 1 to 2 orders of magnitude, while the kinetics of OER and HER are way higher (by 2 and 4 orders of magnitude, respectively). The resistance of the membrane is approximately 3 times lower, and the fitted unbalancing is also lower (even though we do not think that this is an effect of the temperature; it could just be that the experiments started right after the preparation of the solutions, thus they did not have time to undergo much unbalancing). Finally, the chemical kinetics of the degradation is the same, but the electrochemical degradation happens at a 5-time faster rate.

Conclusions on experimental results and model calibration

To summarize this chapter, here are the key results obtained experimentally and linked to the model calibration:

• We performed calendar aging at 20°C and 40°C and measured the capacity fade linked to chemical degradation thanks to these tests. The measured capacity fade does not depend much on the SOC at which the electrolyte is stored, nor on the temperature,

• We did cycling experiments at 20°C and 40°C, at different current densities and different cutoff voltages. The capacity fade rate during cycling depends on the temperature (the higher the temperature, the higher the capacity fade). It depends on the voltage in a certain extent (lowering the cut-off voltage to 1.5V substantially reduces the capacity fade but increasing it to 1.7V does not seem to have a notable effect), but does not depend much on the applied current density, at least in these experiments,

• We also used the cells in power duty cycles corresponding to a realistic usage. The resulting measure capacity fade rate is lower than the capacity fade rate measured during a simple charge-discharge operation,

• We used 1 H NMR and cyclic voltammetry to characterize the aged electrolytes. The results obtained show that we still find 2,6-DHAQ in the samples during calendar aging at 20°C, but there is another species being formed at high SOC that could be DHA 3-. For the electrolytes after cycling aging, the signal corresponding to 2,6-DHAQ disappears from voltammograms and NMR spectra after aging, except for the electrolyte cycled with a lower voltage limit. This is in line with the measured capacity during cycling and indicates that cycling at a maximum voltage of 1.5V significantly reduces the capacity fade,

• We observed many signs of different degradations occurring during aging. We did not investigate these degradations in depth, thus further experiments and analysis would be needed to conclude and be sure of what exactly happens in the cell during aging,

• Finally, we use all these results to calibrate the model presented in chapter 2. It is a 3-steps calibration, with the first being the calibration of the diffusion coefficients and kinetics related to the main reactions and to OER/HER, as well as the resistance of the cell. After that, we calibrate the chemical degradation parameters so that the simulation fits the experimental capacity fade during calendar aging. The last step of the calibration is to fit the parameters corresponding to the electrochemical degradation which is, in our case, the dimerization of DHA 3-into (DHA)2 3-. This calibration method is applied at 20°C and 40°C.

• The resulting calibrated model fits well the charge-discharge curves at 20 and 40°C. It fits reasonably well the capacity fade due to calendar aging and the capacity fade due to cycling aging at 20°C. It has trouble fitting the capacity fade during cycling at 40°C, and this last point could be improved by performing longer cycling experiments at 40°C, as well as sampling electrolytes at the beginning of cycling to elucidate the phenomenon happening in the first few cycles that causes the capacity to increase.

Model validation and extrapolation

In chapter 4, we described the calibration of the model on several operating points thanks to

Cycling experiments for validating the model

Cycling experiments at different operating points than those dedicated to calibration are used for asserting whether the model is valid on those operating points or not and its ability of interpolation.

For each experiment, the other parameters are standard; for instance, if the current density is changed then the maximum cutoff voltage Umax is 1.6V, and if the maximum voltage is changed then the current density is 37.5 mA.cm -2 . The conditions for cycling experiments for model validation are:

• 20°C cycling at medium (50 mA.cm -2 ) current density (Cycling20 #4),

• 40°C cycling at medium (50 mA.cm -2 ) and high (75 mA.cm -2 ) current densities (Cycling40 #3 and Cycling40 #4),

• 20°C cycling with lower maximum cutoff voltage (Umax = 1.5V, Cycling20 #2),

• 40°C cycling with lower maximum cutoff voltage (Umax = 1.5V, Cycling40 #2)).

Cycling at different current densities

This section describes how the model is working out at different -medium and high -current densities.

Figure 44 shows simulation results at 20°C, with Umax 1.6V and j = 50 mA.cm -2 (experimental conditions of Cycling20 #3). Simulation curve is in blue, while experimental points of Cycling20 #3.1 are in red and Cycling20 #3.2 in green.

Figure 45 shows simulation results at 40°C, with Umax 1.6V and j = 75 mA.cm -2 (experimental conditions of Cycling40 #4). Simulation curve is in blue, and experimental points are in red for Cycling40 #4.1 and green for Cycling40 #4.2.

Figure 46 shows simulation results at 40°C, Umax 1.6V and j = 50 mA.cm -2 (experimental conditions of Cycling40 #3). Simulation curve is in blue, and Cycling40 #3.1 is in red while Cycling40 #3.2 is in green. the value is correct correct. The logarithmic tendency is the same as in the experiments. Throughout the 100 simulated cycles, the capacity starts from 1600 mAh and ends at 620 mAh (62% capacity loss in total). In the experiments, the capacity goes from 1400 mAh to between 550 and 650 mAh (between 55 and 60% capacity loss). There is a difference between simulated and experimental capacity at the first cycle, with an overestimation of the starting capacity by the model. This difference between simulation and experiments stays pretty much the same throughout cycling, but longer simulations and cycling could lead to different results since the experimental capacity fade rate tends to decrease faster than for the simulation.

Figure 47 shows the evolution of the concentrations during cycling at 20°C, with j = 50 mA.cm-2; this concentrations profile throughout cycling is typically the same for every experiment at 20°C. We can see that during cycling, the posolyte is dictating the end of charging (when the concentration in Fe(CN)6 4-falls to zero), whereas the negolyte is limiting at the end of discharge (when the concentration of DHAHQ4-, in red, falls to zero). During cycling, there is formation of DHA3-, in khaki green, that is responsible for the capacity fade. There is also formation of DHAQ2-(golden curve) along with the formation of DHA3-, which explains why the concentration of DHAQ2-decreases more slowly than that of DHAHQ4-in red.

The validation results at 40°C are the same when the model is run in conditions Cycling40 #3 and Cycling40 #4. For these two sets of experimental conditions, the starting capacity is lower than the experimental capacity, as it was the case for the validation of the model. The model replicates the increase in capacity in the first 3 cycles, as the experiments. This behavior is explained by Figure 48, which shows the evolution of the concentration in the tanks during simulation. In the first few cycles, we notice an increase in the concentration of DHAHQ 4-, in red in the top chart. This "increase" is in fact a consequence of the unbalance at the beginning; the concentration of DHAHQ The increase in capacity in the first cycles can be explained thanks to Figure 48, which shows the evolution of the concentration in the tanks during simulation at 40°C, with j = 50 mA.cm-2. In the first few cycles, the posolyte is limiting the end of charge, and the negolyte the end of discharge. As kinetics are faster at 40°C than at 20°C, the battery stays at a higher voltage for a longer time, thus there is formation of O2 (pink curve). This oxygen formation allows a higher conversion of DHAHQ 4-in the negolyte. At the end of the charge, the negolyte is more reduced compared to what would happen without O2 formation. As can be seen in the graph, the amount of negolyte which is transformed is getting higher during the first 4 cycles when discharge is limited by the negolyte and charge by the posolyte. However, from cycle 5, the negolyte becomes limiting for both charge and discharge and O2 formation is not visible anymore, leading to a fast capacity fade. Overall, the simulations are quite good, both at 20 and 40°C, when current is increased in the experiments. The tendencies are well replicated by the model, and the percent of capacity loss is close between simulations and corresponding experiments. The biggest difficulty of the model here is to be close to the experiments in the first few cycles, since the simulated capacity is either overestimated (at 20°C) or underestimated (at 40°C). This difference could be the consequence of an unbalance in the state of charge of the electrolytes, that we cannot reproduce in the model; we tried changing ∆ 𝑐𝑜𝑛𝑐 but it leads to a change in the whole capacity fade profile, which does not suit the experimental capacity fade anymore. We can see that the simulations are not very affected by the current density, so are the experiments.

Cycling with a lower voltage limit

This section presents the simulation results obtained when the cell is cycled with a lower maximum cutoff voltage Umax. Figure 49 shows simulation results at 20°C, Umax 1.5V and j = 37.5 mA.cm -2 (Cycling20 #2). Simulation curve is in blue, and experimental points are in red for Cycling20 #2.1 and in green for Cycling20 #2.2.

Figure 50 shows simulation results at 40°C, Umax 1.5V and j = 37.5 mA.cm -2 (Cycling40 #2). Simulation curve is in blue, and experimental points are in red.

At 20°C, with a current density of j = 37.5 mA.cm -2 and a maximum cutoff voltage Umax = 1.5V, the model gives a result quite far from the experiments, with a mean squared error of MSE 𝐶𝑦𝑐𝑙𝑖𝑛𝑔20 #2,𝑚𝑜𝑑𝑒𝑙 = 10.5. We saw in chapter 4 that in these conditions, the capacity fade was much lower than for any other experiment. This tendency is not reproduced by the model, which gives a capacity fade profile very close to those obtained with higher Umax. This is definitely one limit of our model at 20°C: it does not reproduce the behavior of the experimental battery when cycling with a lower voltage limit. The simulated capacity fade has a much higher slope than for the experiments. It starts from a higher capacity value (1580 mAh vs. 1380 mAh), and reaches after 120 cycles a lower capacity value (500 vs. 900 mAh). The capacity loss is of approximately 0.58% per cycle in the simulation, against 0.29% for the experiments. The inability to properly simulate the aging with a lower maximum cutoff voltage is a big flaw of our model. The reason why is that it does not take into account one or several phenomena, that have a big impact on capacity fade and are highly dependent on the voltage of the cell. For example, if an electrochemical degradation occurs when the cell is at high voltage -between 1.5V and 1.6V -but is not considered in the model, it could induce a big difference like we see here. Our hypothesis is thus that some electrochemical degradation happens here, but we failed in modelling it for the reasons described in section 5.3.1. The profiles of concentration provided by the model are the same than those seen in Figure 47, and they probably don't match the actual evolution of the concentrations. The modelling results at 40°C, unlike those obtained at 20°C, are very close to the experiment. For this simulation, we changed the value of ∆ 𝑐𝑜𝑛𝑐 compared to the other experiments: indeed, taking a ∆ 𝑐𝑜𝑛𝑐 value of 40% led to very highly underestimated capacity at the beginning (about 50% less than the actual experimental capacity). We took ∆ 𝑐𝑜𝑛𝑐 = 0% for this simulation; this assumption is realistic since ∆ 𝑐𝑜𝑛𝑐 can be very different between two experiments, depending on how much care was taken in the preparation of the electrolytes. The starting capacity is close to the experimental capacity (1400 vs. 1300 mAh), and the profile of the capacity fade is well replicated by the model. After the first 3 cycles, both experimental and modelled capacity decrease with a logarithmic tendency and a high slope. For the experiment, the capacity fade rate is of about -6.6% per cycle between cycle 4 and cycle 10, before reaching after 10 cycles a much lower capacity fade rate of about -1.4% per cycle (here, this value is rounded because we lack of enough experimental data). In the model, the same tendency is found, only with a slope break at 15 cycles instead of 10. The mean squared error is the lowest for this simulation: MSE 𝐶𝑦𝑐𝑙𝑖𝑛𝑔40 #2,𝑚𝑜𝑑𝑒𝑙 = 0.38. Overall, the simulation results are very close to the experiment for a lower maximum cutoff voltage at 40°C, except for the capacity increase found at the beginning of cycling, which we could not simulate. because the potential of the positive electrode is higher after the 15th cycle than before, and kinetics of OER are favored from this point on. As we saw previously for the first cycles at 40°C, a part of the electrons is used for the formation of oxygen, less electrons are used for the main reactions in the posolyte and allows a bigger charge of the negolyte before reaching the end of constant voltage criterion. As a consequence, the available species for discharge in the negolyte is higher leading to a decrease of the capacity fade rate. This result gives a good example of competition and interplay between different degradations (in this case, chemical degradation and oxygen formation).

Specific power profile representative of real use conditions

The last simulation test we make to assess the validation of the model is simulating the conditions of a realistic use, which are represented by the specific power profile described in section 4.2.4. This simulation compared to experimental results is shown in Figure 52. The simulation results are close to experiments, which means that the dynamic behavior of the flow cell represented by the model is accurate. In order to fit the voltage at the beginning of the simulation, we modified the triggering of the event that starts the power profile in the model. The model loses its accuracy between 0.4 and 0.8h, where the profile tends to be more dynamic with very short charge and discharge times. It also overestimates the voltage when a peak of charge occurs, and predicts voltage values of up to 1.8V which are outside of the usual voltage window for an aqueous flow cell based on 2,6-DHAQ/ferrocyanide. When the voltage is close to the extreme voltage (maximum and minimum), its evolution is exponential. That is why only a small error in the calculation can lead to a big difference in the resulting voltage, as we see for example around 0.7h.

To go further, longer simulations that reproduce the behavior of the cell during several power profile sets, with capacity check-ups interspersed in between those power profiles are needed. Unfortunately, due to the long simulation time needed for that (here, it took 20 minutes to simulate 2 hours of power profile), we did not have time or calculation power to perform such simulations. These results thus validate the nominal model, but are not enough to validate the degradation model.

Model extrapolation

Adding an electrochemical degradation to the model

Literature suggests another degradation path for DHAHQ 4-, proposed by Zhao et al. [98,117]. They reported an electrochemically triggered decomposition of DHAHQ 4-into a mix of DHA 3-and DHAL 3-.

We wanted to incorporate this electrochemical degradation into the model, with a simplified Butler-Volmer law for the produced current, Nernst equations for the reaction potential and the formation of DHA 3-, which is the same species as what is produced by the chemical degradation already considered in the model. Taking into account this degradation in the model would result in 3 degradations paths in total: chemical degradation of DHAHQ 4-into DHA 3-and DHAQ 2-, electrochemical degradation of DHAHQ 4-into DHA 3-, and ultimately dimerization of DHA 3-into (DHA)2 4-. Another reaction to take into account could be the spontaneous reoxidation of DHAHQ 4-into DHAQ 2-with the production of H2, as hypothesized by Zhao et al. [117].

We tried calibrating the model with these degradations, without success. This is due to several factors: first, the number of degradations parameters to calibrate increases from 2 to 4, and these parameters are interdependent. The parameters characteristic of the reversible electrochemical degradation are the kinetics of the degradation 𝑘 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑐ℎ and the reference potential of the electrochemical reaction 𝐸 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑐ℎ . We found that the simulation results are highly dependent on the value of 𝐸 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑐ℎ , and had trouble running the model with the correct parameters; 𝐸 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑐ℎ was either too low and we did Such degradations lead to different profiles in the evolution of active species concentrations, which in turn lead to different capacity fade profiles. Figure 53 shows the results of a cycling experiment conducted at 40°C under standard conditions, with only a chemical degradation (here, we took kchem = 5.10 -5 and αchem = 1). Figure 54

Conclusions

Aqueous redox flow batteries are an efficient way to store electrical energy under its chemical form.

The architecture of the battery enables to decouple energy from power, allowing for good versatility along with safety of operation when operated in aqueous media. Inorganic redox flow batteries, which have been developed for the past 50 years, are gradually giving way to organic electroactive materials.

The properties of those can be efficiently tuned via functionalization, and they are potentially cheaper and less harmful for the environment. The main families of electroactive species were presented, with a discussion about advantages and drawbacks of each. The performances are promising but still far from reaching those of inorganic based (vanadium mostly), due to the difference in maturity between the technologies.

In the course of this thesis, we chose to focus on organic redox couples in aqueous media, because they are easier to work with and overall cheaper. Degradations occurring on the cell physical components such as membrane or electrodes for vanadium redox flow batteries are quite well reported in the literature and transcribe easily to organic flow batteries. Degradations of the organic electroactive materials are, on the other hand, not thoroughly understood and there are only a few papers taking interest in describing the degradation reactions. Some of these degradation schemes were found to take place during battery operation and are associated to a decrease in power or energy.

In order to gain a better understanding of such degradations, we developed an experimental method to study aging, along with a degradation model for a redox flow battery. We chose to work with the redox couples 2,6-DHAQ/2,6-DHAHQ and ferrocyanide/ferricyanide, because their degradations are among the most documented in the literature.

The model developed here has the same basis than an already developed model. The cell voltage is estimated by the decomposition into several overpotentials, associated respectively to the electrode, the membrane, as well as a solid and an electrolytic ohmic potentials. To this model were previously added water splitting reactions, forming hydrogen and oxygen. Our contribution to this model is the addition of several degradation reactions. We added a chemical reaction, which consumes DHAHQ 4- and produces DHA 3-as well as DHAQ 2-. Then we added an irreversible electrochemical degradation which is the dimerization of DHA 3-into (DHA)2 4-. This irreversible electrochemical degradation is modelled with a Tafel law. These reactions are generic mechanisms, and can be applied to other degradation mechanisms such as crossover, or any other mechanism that consumes a reactant. It is calibrated and validated with the help of dedicated experimental work.

The experimental work is carried out to calibrate and validate the simulation results. At first, an organic flow cell has been set up, with 2,6-DHAQ as negolyte and Ferrocyanide as posolyte. The flow cell configuration is made so as to have a limiting side, and the degradation measured (capacity fade) on the global cell can be attributed only to this limiting species' degradations: in our case, it is 2,6-DHAQ.

The first experimental setup was then enhanced by building a test bench, so that up to 8 cells can be cycled at the same time. This setup enables a real comparison between the different conditions of current, voltage etc. applied to the batteries, since the exterior atmosphere parameters are the same for each cell in the test bench. The temperature is controlled thanks to a cryostat, and we perform experiments at 20 and 40°C to assess the influence of the temperature on the results. The established cycling protocol is a CC-CV protocol, with an applied current density j and voltage limites Umin and Umax.

We perform cycling experiments at different j values (37.5, 50 and 75 mA.cm -2 ) and different Umax values (1.5, 1.6 and 1.7V). In parallel with this cycling work, a calendar aging campaign of both electrolytes is launched at two different temperatures -at 20 and 40°C -and two different states of charge -0% and 100% -for each electrolyte. Periodical check-ups of the capacity during calendar aging are done. We performed NMR analysis and cyclic voltammetries on the aged electrolytes, in order to gain a better understanding of their aging. The last experiment performed was an importation of a power profile representative of a real use of the battery, which is a dynamic profile where the battery is power-monitored, at 20°C.

The experimental results obtained from calendar aging samples is that neither temperature nor SOC seem to have an impact on the aging in the conditions of our test (so, according to our hypotheses, on the chemical degradation rate). We observe a small amount of charge (respectively discharge) occurring in the electrolytes at SOC0 (respectively SOC100), which is the consequence of the uncontrolled atmosphere in the storage tanks, with the presence of oxygen. The results obtained from cycling experiments show that temperature has a big influence on the capacity fade (so, according to our hypotheses, on the irreversible electrochemical degradation rate). The maximum cutoff voltage also impacts the capacity fade, especially when the value is lowered from 1.6 to 1.5V. It means that some phenomena are taking place at 1.6V and not at 1.5V. The capacity fade rate with Umax = 1.7V is not statistically differentiable from the capacity fade rate with Umax = 1.6V. From these results, it seems that cycling this system up to Umax = 1.5V is better for longevity of the battery, and is not detrimental for the overall resulting capacity. It also limits the formation of hydrogen or oxygen. The applied current density does not seem to have an impact on the resulting capacity nor on the capacity fade rate, in the conditions of our experiments. Also, we notice an increase of the capacity in the first 2 cycles on every experiment at 40°C, which we do not see at 20°C. This could be caused by the temporary production of a redox species -for instance, DHAQ 2--that induces an increase in the capacity, before being consumed. The results of the power profile are that the capacity fade is lower in such a utilization of the battery than when it is simply charged and discharged. The reason behind this is that degradations usually appear at extreme SOC values, whereas the power profile keeps the battery at a medium SOC for most of the time. Finally, post-mortem characterizations of the aged electrolytes showed that, during calendar aging at 20°C or 40°C, no visible degradation is seen in NMR spectra for electrolytes at SOC0, whereas new peaks arise for electrolytes at SOC100. 1.5V at 20°C and 40°C, and the power profile at 20°C). The results of the validation show that the model is unable to correctly predict the evolution of the capacity when Umax = 1.5V at 20°C, whereas it is very accurate in the same conditions but at 40°C. This is probably due to the fact that it is incomplete, and adding other degradation mechanisms (a reversible electrochemical degradation, for instance), could help improve the model on this precise operating point. The dynamic behavior of the model is pretty good, and the simulated voltage during the power profile is very accurate except when the profile gets too dynamic, with very short charge and discharge periods.

Different perspectives arise from this work:

• Adding a reversible electrochemical reaction to the model. This electrochemical degradation can be modelled with a Butler-Volmer law and its potential determined with a Nernst equation,

• The model can be transposed to other redox couples, provided that the degradation mechanisms for these species are known. The degradations can be modelled either with a chemical reaction that consumes the reactant, with a Tafel law for irreversible electrochemical reactions or with a Butler-Volmer law for a reversible electrochemical reaction,

• The built model can help identifying specific capacity fade profiles (logarithmic, linear etc.) and associate these with one of the degradation mechanisms seen above,

• The simulation of power profiles was used in this work, but not to its full potential. Indeed, it would be interesting to simulate long duty cycles representative of a real use, with check-ups to measure the capacity in between these power profiles. This would enable validating the aging model on a realistic use, since our present work only validate the nominal model on a realistic use.

• Another perspective in terms of modelling would be to build a 2D model of the same flow battery, in order to explore heterogeneities inside the components of the cell [127]. This is important in order to ensure that the hypotheses taken in the 0D model are valid,

• To gain a better understanding of what is happening in the redox system at rest, longer calendar aging tests can be carried out, with different variations of the SOC. Keeping the electrolytes in a controlled atmosphere such as an aqueous glovebox would also be very handy to make sure that no parasitic interaction with oxygen occurs during calendar aging,

• More cycling experiments can also be performed, but an important point for exploring the degradations during the aging is to periodically sample some of the electrolytes during cycling, to do NMR or cyclic voltammetry analysis on them. This would greatly help for observing the degradations occurring in the course of the aging, instead of just post-mortem analysis when, in our case, most of the signal has disappeared and is not exploitable anymore.

  OF CONTENTS .................................................................................................................... LIST OF TABLES .............................................................................................................................

Figure 1

 1 Figure1General comparison of different energy storage technologies, in terms of their discharge time vs. power rating, from[2] ...................................................................................................................................................... Figure 2 Redox flow battery scheme ..................................................................................................................... Figure3Working scheme of the traditional vanadium flow battery, from[START_REF] Pasquier | Ecole thématique Redox-flow 2019[END_REF] ................................................... Figure 4 Radar diagram for inorganic flow batteries ............................................................................................ Figure 5 Ferrocyanide degradations reactions ...................................................................................................... Figure 6 Ferrocene degradations reactions ........................................................................................................... Figure 7 Quinone degradations reactions ............................................................................................................. Figure 8 TEMPO degradations reactions ............................................................................................................... Figure 9 Viologen degradation reactions [17] ....................................................................................................... Figure 10 Main degradation mechanisms in aqueous organic redox flow batteries ............................................ Figure 11 Performances' degradations and their causes in aqueous organic redox flow batteries ...................... Figure 12 Scientific approach scheme ................................................................................................................... Figure 13 Scheme of the model resolution algorithm ........................................................................................... Figure 14 Flow cell setup, a) exploded view and b) assembled cell ....................................................................... Figure 15 Overview of the experimental setup of a redox flow cell (picture and corresponding scheme) ............ Figure 16 Focus on the negative side of the cell (negolyte) .................................................................................. Figure 17 Picture of the 8-cells test bench ............................................................................................................ Figure 18 Inputs and outputs of electrolyte to the tanks (front), with N2 flowing (back) ..................................... Figure 19 Example of a charge-discharge in CC-CV mode, with voltage in blue and current in red ..................... Figure 20 Reference 1 H NMR spectrum for fresh 2,6-DHAQ/KOH electrolyte diluted in D2O ................................Figure 21 Cyclic voltammetry setup with 3 electrodes .......................................................................................... Figure 22 Example of cyclic voltammogram, on fresh electrolytes (DHAQ in red and ferrocyanide in blue ......... Figure 23 Evolution of the capacity during calendar aging with electrolytes stored at 20°C SOC100 (red), 40°C SOC0 (green) and 40°C SOC100 (blue) .................................................................................................................. Figure 24 a) Voltage and b) current density measured throughout calendar aging at 20°C: new electrolytes in red, after 14 days in green, after 21 days in blue and after 28 days in purple ............................................................. Figure 25 a) Voltage and b) current density of the cell stored at SOC100 measured throughout calendar aging at 40°C, at t=0, 8, 27 and 40 days ............................................................................................................................. Figure 26 Capacity fade curves of cycling experiments, at 20°C and 40°C ............................................................ Figure 27 Evolution of the capacity a) at 20°C and b) at 40°C, at various current densities: j = 37.5 mA.cm -2 in red, 50 mA.cm -2 in green and 75 mA.cm -2 in blue ........................................................................................................ Figure 28 Evolution of the experimental capacity when maximum cutoff voltage varies, at 20°C: ...................... Figure 29 Evolution of a charge-discharge curve between fresh and aged cell, at different maximum cutoff voltage values: Umax = 1.5V in green, Umax = 1.6V in red and Umax = 1.7V in blue. Chart a) is the voltages for new cells, b) the current for new cells, c) the voltage after 80 cycles and d) the current after 80 cycles .................................. Figure 30 a) Evolution of the voltage during a power profile, and b) capacity fade throughout a PNNL test consisting of several consecutive power profiles with capacity measurements in between ................................. Figure 31 Cyclic voltammetry on aged posolytes at 20°C, compared to new electrolytes (dashed curve). Top chart is for negolytes and bottom chart is for posolytes ................................................................................................ Figure 32 a) Zoom on experimental cyclic voltamograms obtained for aged cells a), compared to b) a voltamogram obtained with (DHA)2, from ref. [97] ..................................................................................................................... Figure 33 NMR spectra of calendar aged samples after 50 days at 20°C: Calendar20 #1 (red), Calendar20 #2 (green) vs. reference (blue) ................................................................................................................................... Figure 34 1 H NMR spectra of DHA (top) and (DHA)2 (bottom) in D2O, from ref [97]............................................. Figure 35 NMR spectra of cycling aged samples at 20°C: reference (blue), Cycling20 #2.1 (red) and the others cells (Cycling20 #1.1 in green and Cycling20 #4.1 in purple are shown as representative examples) .......................... Figure 36 Simulated cell voltage (blue) compared to actual cell voltage (red) in standard conditions, at 20°C ...Figure 37 Simulated capacity loss (blue) compared to experimental capacity loss (red) for samples stored at 20°C and SOC100 in calendar aging .............................................................................................................................. Figure 38 Simulated (blue) vs. experimental (red and green) capacity evolution during cycling in standard conditions ............................................................................................................................................................ Figure 39 Simulated (blue) vs. experimental (red) capacity evolution during cycling at high current density ....

Figure 37

 37 Figure1General comparison of different energy storage technologies, in terms of their discharge time vs. power rating, from[2] ...................................................................................................................................................... Figure 2 Redox flow battery scheme ..................................................................................................................... Figure3Working scheme of the traditional vanadium flow battery, from[START_REF] Pasquier | Ecole thématique Redox-flow 2019[END_REF] ................................................... Figure 4 Radar diagram for inorganic flow batteries ............................................................................................ Figure 5 Ferrocyanide degradations reactions ...................................................................................................... Figure 6 Ferrocene degradations reactions ........................................................................................................... Figure 7 Quinone degradations reactions ............................................................................................................. Figure 8 TEMPO degradations reactions ............................................................................................................... Figure 9 Viologen degradation reactions [17] ....................................................................................................... Figure 10 Main degradation mechanisms in aqueous organic redox flow batteries ............................................ Figure 11 Performances' degradations and their causes in aqueous organic redox flow batteries ...................... Figure 12 Scientific approach scheme ................................................................................................................... Figure 13 Scheme of the model resolution algorithm ........................................................................................... Figure 14 Flow cell setup, a) exploded view and b) assembled cell ....................................................................... Figure 15 Overview of the experimental setup of a redox flow cell (picture and corresponding scheme) ............ Figure 16 Focus on the negative side of the cell (negolyte) .................................................................................. Figure 17 Picture of the 8-cells test bench ............................................................................................................ Figure 18 Inputs and outputs of electrolyte to the tanks (front), with N2 flowing (back) ..................................... Figure 19 Example of a charge-discharge in CC-CV mode, with voltage in blue and current in red ..................... Figure 20 Reference 1 H NMR spectrum for fresh 2,6-DHAQ/KOH electrolyte diluted in D2O ................................Figure 21 Cyclic voltammetry setup with 3 electrodes .......................................................................................... Figure 22 Example of cyclic voltammogram, on fresh electrolytes (DHAQ in red and ferrocyanide in blue ......... Figure 23 Evolution of the capacity during calendar aging with electrolytes stored at 20°C SOC100 (red), 40°C SOC0 (green) and 40°C SOC100 (blue) .................................................................................................................. Figure 24 a) Voltage and b) current density measured throughout calendar aging at 20°C: new electrolytes in red, after 14 days in green, after 21 days in blue and after 28 days in purple ............................................................. Figure 25 a) Voltage and b) current density of the cell stored at SOC100 measured throughout calendar aging at 40°C, at t=0, 8, 27 and 40 days ............................................................................................................................. Figure 26 Capacity fade curves of cycling experiments, at 20°C and 40°C ............................................................ Figure 27 Evolution of the capacity a) at 20°C and b) at 40°C, at various current densities: j = 37.5 mA.cm -2 in red, 50 mA.cm -2 in green and 75 mA.cm -2 in blue ........................................................................................................ Figure 28 Evolution of the experimental capacity when maximum cutoff voltage varies, at 20°C: ...................... Figure 29 Evolution of a charge-discharge curve between fresh and aged cell, at different maximum cutoff voltage values: Umax = 1.5V in green, Umax = 1.6V in red and Umax = 1.7V in blue. Chart a) is the voltages for new cells, b) the current for new cells, c) the voltage after 80 cycles and d) the current after 80 cycles .................................. Figure 30 a) Evolution of the voltage during a power profile, and b) capacity fade throughout a PNNL test consisting of several consecutive power profiles with capacity measurements in between ................................. Figure 31 Cyclic voltammetry on aged posolytes at 20°C, compared to new electrolytes (dashed curve). Top chart is for negolytes and bottom chart is for posolytes ................................................................................................ Figure 32 a) Zoom on experimental cyclic voltamograms obtained for aged cells a), compared to b) a voltamogram obtained with (DHA)2, from ref. [97] ..................................................................................................................... Figure 33 NMR spectra of calendar aged samples after 50 days at 20°C: Calendar20 #1 (red), Calendar20 #2 (green) vs. reference (blue) ................................................................................................................................... Figure 34 1 H NMR spectra of DHA (top) and (DHA)2 (bottom) in D2O, from ref [97]............................................. Figure 35 NMR spectra of cycling aged samples at 20°C: reference (blue), Cycling20 #2.1 (red) and the others cells (Cycling20 #1.1 in green and Cycling20 #4.1 in purple are shown as representative examples) .......................... Figure 36 Simulated cell voltage (blue) compared to actual cell voltage (red) in standard conditions, at 20°C ...Figure 37 Simulated capacity loss (blue) compared to experimental capacity loss (red) for samples stored at 20°C and SOC100 in calendar aging .............................................................................................................................. Figure 38 Simulated (blue) vs. experimental (red and green) capacity evolution during cycling in standard conditions ............................................................................................................................................................ Figure 39 Simulated (blue) vs. experimental (red) capacity evolution during cycling at high current density ....

Figureη

  Figure Simulated (blue) vs. experimental (red) capacity evolution during cycling with a higher maximum cutoff voltage ................................................................................................................................................................ 102 Figure Simulated cell voltage (blue) compared to actual cell voltage (red) in standard conditions, at 40°C . 103 Figure Simulated capacity loss (red) compared to experimental capacity loss (blue) for samples stored at 40°C in calendar aging ................................................................................................................................................. 104Figure 43 Simulated (blue) vs. experimental (red and green) capacity evolution during cycling in standard conditions, at 40°C. ............................................................................................................................................. 105 Figure Simulated capacity (blue) vs. experimental capacity with j = 50 mA.cm -2 at 20°C .............................. 109 Figure Simulated capacity (blue) vs. experimental capacity with j = 75 mA.cm -2 at 40°C .............................. 109 Figure Simulated capacity (blue) vs. experimental capacity with j = 50 mA.cm -2 at 40°C .............................. 110 Figure Evolution of the concentrations during cycling at 20°C, with j = 50 mA.cm -2 ...................................... 112 Figure Evolution of the concentrations with j = 50 mA.cm -2 at 40°C .............................................................. 112 Figure Simulated capacity (blue) vs. experimental capacity with Umax = 1.5V at 20°C ................................... 114 Figure Simulated capacity (blue) vs. experimental capacity (red) with Umax = 1.5V at 40°C .......................... 115 Figure Evolution of the concentrations with U = 1.5V at 40°C ....................................................................... 116 Figure Simulation of the voltage evolution during a power profile (blue), compared to the experimental signal (red) ..................................................................................................................................................................... 116 Figure Simulation results with only a chemical degradation (blue curve) ...................................................... 119 Figure Simulation results with only an irreversible electrochemical degradation .......................................... 120 Figure 55 Example of competition between the chemical and irreversible electrochemical reactions: top chart shows the evolution of the concentrations in negolyte and posolyte, and the bottom graph the evolution of the capacity troughout aging .................................................................................................................................... 121

Figure 1 2 ]

 12 Figure 1 General comparison of different energy storage technologies, in terms of their discharge time vs. power rating, from [2]

  in December 2019 at the Institut Français du Pétrole et des Energies Nouvelles (IFPEN) under the supervision of Dr. Martin PETIT, in collaboration with FEMTO-ST under the direction of Pr. Marie-Cécile PERA. This PhD falls within the research on organic redox flow batteries as novel stationary energy storage systems, performed at IFPEN. Its aim is to study the degradations occurring in a wellknown system in an aqueous organic flow battery, with a combined modelling and experimental approach to study aging. The first chapter gives an overview of redox flow technologies, degradations, and modelling approaches. General principles and properties associated to redox flow batteries are first presented, with a focus on organic active materials in aqueous media and the degradations associated to the operation of such batteries. After describing the degradations, different modelling approaches such as empirical models, physical models and ab-initio calculations are described. Finally, the chosen approach in the thesis is presented.The second chapter describes the modelling work developed during the PhD, with the IDE Rstudio. The model is constructed from the basis of another model built by IFPEN colleagues, which has been explained in the literature[START_REF] Derr | Electrochemical degradation and chemical aging of carbon felt electrodes in all-vanadium redox flow batteries[END_REF]. This starting point is a 0D physical model which incorporates electrochemical reactions and the associated redox kinetics, electrolytic overvoltages and mass balance equations for the species. Water splitting parasitic reactions are also taken into account in this model. The challenge of this thesis is to understand the degradation modes of organic electroactive materials in redox flow batteries and incorporate them into physical models in order to be able to predict future cycling of the battery. In this perspective, we added to the model degradations of different natures, which are based on the literature on the studied electrochemical system: chemical degradations, irreversible electrochemical degradations and reversible electrochemical degradations.The parameters related to these degradations are calibrated thanks to experiments; all of this is presented in chapter 4.The third chapter presents the experimental setup which is used during the thesis, to study aging at the cell level in a laboratory. Aging experiments performed in this thesis are of two kinds: calendar aging and cycling. During calendar aging, the electrolytes are aged in separate tanks, without any flow cell nor current flowing. Cycling is the standard protocol to study aging in batteries, during which the electrolytes are incorporated into a flow cell setup, and cycled under a variety of experimental conditions such as different current densities, voltage, concentrations etc. First cycling experiments were done with a single Pinflow® flow cell, then a test bench was built in order to cycle up to 8 cells in parallel, with different cycling conditions but under the same atmosphere. Both calendar aging and cycling experiments are performed at 20°C and 40°C, to explore the influence of temperature on aging.

Figure 3

 3 Figure 3 Working scheme of the traditional vanadium flow battery, from [37]

Figure 4

 4 Figure 4 Radar diagram for inorganic flow batteries

Figure 6

 6 Figure 6 Ferrocene degradations reactions

  produced can be oxidized back to DHAQ by aeration, restoring the battery capacity. Another study uses online Electron Spin Resonance (EPR) and NMR to track the concentration of the radical intermediate DHAQ 3-.[98]. They revealed formation of both DHA and 2,6-dihydroxyanthranol (DHAL) during high SOC (1.6 or 1.7V) potential holds. Formation of such degradation products is concentration dependent, increasing with DHAQ concentration as DHAQ 3-. concentration decreases.

  derivative with an electron withdrawing group in ortho-position of the N=O link. Another degradation mechanism reported for 4-HO-TEMPO (TEMPOL) is its self-oxidation with hydroxyl radicals, to form 4oxo-TEMPO (TEMPONE)[102]. The scheme proposed by Marshall et al. is presented in Figure8 d). The reaction products and intermediates were observed by electron spin resonance spectroscopy (ESR)

  material causes energy fade. If one side is capacity limiting, the conclusions may differ, as it is the case in the study by Aziz et al. of the quinone-bromide flow battery[107]. A change in the electrolyte flow -caused by precipitation, gas evolution or degradation of the electrode for example -causes a change in the pressure drop, leading to an increase of the global resistance and thus EE loss or, ultimately, catastrophic failure. Figure10presents a scheme for describing the main degradations taking place in an organic redox flow battery. Figure11is a summary of the performances' degradations and their proposed causes, making a link between macroscopic and microscopic scale.

Figure 10

 10 Figure 10 Main degradation mechanisms in aqueous organic redox flow batteries

  3 and 2.4 describe the additions made to the model during this PhD.The different species taken into account in the physical model are OH -, 2,6-DHAQ 2-, 2,6-DHAHQ 4-, Fe(CN)6 4-, Fe(CN)6 3-, K + , H2, O2, and DHA 3-. The following hypotheses are assumed:

  -19 and Equation 2-20. Redox potentials are calculated in Equation 2-21 and Equation 2-22, via Nernst equation as for main redox reactions. Unlike main reactions however, the current arising from these reactions is modelled with a Tafel kinetic (Equation 2-23), because of the irreversible nature of the reaction.

Figure 14 Flow

 14 Figure 14 Flow cell setup, a) exploded view and b) assembled cell

  each side of the separating membrane, without current input or output. The potential of each electrolyte is measured with a graphite electrode, by measuring a difference in potential between this graphite electrode and a reference electrode placed further in the flow circuit. The reference electrode used is a Hg/HgO electrode, in a salt bridge containing KOH at 1 M concentration. This cell enables a constant access to the cell's open circuit voltage, and thus ohmic losses and resistance associated can be easily calculated.The electronic device used to induce power profiles to the cell is a Biologic® SP-300 potentiostat, along with a 10 A booster. It enables different control modes, the ones used here being galvanostatic or potentiostatic. It can also perform Electrochemical Impedance Spectroscopy, with frequencies ranging between 7 MHz to 10 µHz. Cycling experiments are performed with EC-Lab software.

Figure 15 Figure 16

 1516 Figure 15 Overview of the experimental setup of a redox flow cell (picture and corresponding scheme)

Figure 17 Figure 18

 1718 Figure 17 Picture of the 8-cells test bench

  and 40°C. Potassium hydroxide (KOH analytical grade, VWR), potassium ferrocyanide trihydrate (99+%, ThermoScientific) and 2,6-DHAQ (anthraflavic acid 96%, MuseChem) are used as received. K4Fe(CN)6 (concentration 0.4 M) posolyte solutions are prepared by dissolving solid potassium ferrocyanide in KOH 1 M, while 2,6-DHAQ (concentration 0.5 M) negolyte solutions are prepared by dissolving anthraflavic acid in KOH 2 M. One mole of KOH is necessary to fully deprotonate DHAQ, thus the resulting solution is at pH 14. SOC0 samples are prepared by totally discharging a full DHAQ/Ferrocyanide cell with a constant current-constant voltage (CC-CV) discharge protocol -which will be presented in detail in section 3.3.2

  Potassium hydroxide (KOH analytical grade, VWR), potassium ferrocyanide trihydrate (99+%, ThermoScientific) and 2,6-DHAQ (anthraflavic acid 96%, MuseChem) are used as received. K4Fe(CN)6 (concentration 0.4 M) posolyte solutions are prepared by dissolving solid potassium ferrocyanide in KOH 1 M, while 2,6-DHAQ (concentration 0.5 M) negolyte solutions are prepared by dissolving anthraflavic acid in KOH 2 M. One mole of KOH is necessary to fully deprotonate DHAQ, thus the resulting solution is at pH 14. Both electrolytes are prepared and stored in tinted glass, to protect them from UV and light (ferro/ferricyanide are sensitive to photochemical degradation). The volume of liquid in each negolyte tank is V-= 60 mL, and in each posolyte tank V+ = 200 mL, ensuring an excess of ferrocyanide compared to DHAQ. Indeed, we chose to focus on DHAQ degradations based on literature results as seen in section 1.4, which suggest that ferrocyanide degradations are negligible compared to DHAQ degradations in such a flow battery.

  Figure 20 presents an example of NMR spectrum for fresh negolyte (2,6-DHAQ at 0.5 M concentration in KOH 1 M, diluted in deuterium oxide). Spectrum is zoomed on interesting peaks that are characteristic of 2,6-DHAQ molecule.

Figure 20

 20 Figure 20 Reference 1 H NMR spectrum for fresh 2,6-DHAQ/KOH electrolyte diluted in D2O

Figure 21 .

 21 Working electrode is a graphite disk of 0.196 cm² surface, plunged into the solution. It comes from a spinning electrode but is used in static mode. Counter electrode is a platinum square, of about 1 cm² and is directly plunged into the solution. Reference electrode is Hg/HgO, into KOH 1 M solution in a salt bridge, which is itself in the solution. Before voltammetry experiments, nitrogen bubbles in each solution for about 30 min to deoxygenize the mixture.

Figure 21 Cyclic voltammetry setup with 3 electrodes 3 . 4 . 2 . 2

 213422 Figure 21 Cyclic voltammetry setup with 3 electrodes

Figure 22

 22 Figure 22 Example of cyclic voltammogram, on fresh electrolytes (DHAQ in red and ferrocyanide in blue

Figure 24 a

 24 Figure 24 a) Voltage and b) current density measured throughout calendar aging at 20°C: new electrolytes in red, after 14 days in green, after 21 days in blue and after 28 days in purple

4.1. 2 . 1

 21 Influence of the temperature As presented earlier, several sets of experiments are performed at 2 different controlled temperatures: 20 and 40°C. Figure 26 presents the evolution of measured capacity in the different experiments carried out, at 20°C (Cycling20) and 40°C (Cycling40). For more clarity in the chart, we put in the same color experiments made under the same conditions (for instance, Cycling20 #1.1 and Cycling20 #1.2 are the red curves labeled Cycling20 #1).

Figure 27

 27 Figure 27 Evolution of the capacity a) at 20°C and b) at 40°C, at various current densities: j = 37.5 mA.cm -2 in red, 50 mA.cm -2 in green and 75 mA.cm -2 in blue

Figure 28

 28 Figure 28 Evolution of the experimental capacity when maximum cutoff voltage varies, at 20°C: Umax = 1.5V in green, Umax = 1.6V in red, and Umax = 1.7V in blue

Figure 29

 29 Figure 29 Evolution of a charge-discharge curve between fresh and aged cell, at different maximum cutoff voltage values: Umax = 1.5V in green, Umax = 1.6V in red and Umax = 1.7V in blue. Chart a) is the voltages for new cells, b) the current for new cells, c) the voltage after 80 cycles and d) the current after 80 cycles 4.1.2.4 PNNL power profiles representing real use conditions

Figure 32 a

 32 Figure 32 a) Zoom on experimental cyclic voltamograms obtained for aged cells a), compared to b) a voltamogram obtained with (DHA)2, from ref. [97]

Figure 33 NMRFigure 34 1

 3334 Figure 33 NMR spectra of calendar aged samples after 50 days at 20°C: Calendar20 #1 (red), Calendar20 #2 (green) vs. reference (blue)

Figure 35 NMR

 35 Figure 35 NMR spectra of cycling aged samples at 20°C: reference (blue), Cycling20 #2.1 (red) and the others cells (Cycling20 #1.1 in green and Cycling20 #4.1 in purple are shown as representative examples)

4. 2 .

 2 Figure36presents the simulated charge-discharge curve after calibration (blue), vs. the experimental curve (red). The charge-discharge curve considered here is from the second cycle of the experiment at 20°C in standard conditions: j = 37.5 mA.cm -2 , Umax = 1.6V and Umin = 0.6V.

Figure 36

 36 Figure 36 Simulated cell voltage (blue) compared to actual cell voltage (red) in standard conditions, at 20°C

Figure 37

 37 Figure 37 presents the results of a calendar aging simulation at 20°C for 20 days (in blue), with values of 𝑘 𝑐ℎ𝑒𝑚 = 2.10 -6 m.s -1 , 𝛼 𝑐ℎ𝑒𝑚 = 1. The experimental data points, corresponding to the capacity measured via check-ups seen in Figure 23, are the red triangles.

Figure 37

 37 Figure 37 Simulated capacity loss (blue) compared to experimental capacity loss (red) for samples stored at 20°C and SOC100 in calendar aging

Figure 39 Figure 40

 3940 Figure 39 Simulated (blue) vs. experimental (red) capacity evolution during cycling at high current density

  Further experiments are needed to understand what can happen in the first hours of cycling, such as sampling negative and positive electrolyte after the first cycle and performing analysis on it to detect the active species in the solution.Overall, the value of simulated capacity after 15 cycles is quite close to the experimental capacity, but the linear capacity fade rate may probably lead to an overstatement of the capacity fade over longer times. Longer cycling experiments at 40°C are required for an overall better calibration of the model.

Figure 43

 43 Figure 43 Simulated (blue) vs. experimental (red and green) capacity evolution during cycling in standard conditions, at 40°C.

  experimental results. Now, we are investigating whether this model can work on other operating points, and exploring the limits of the model. The validation work is described in sections 5.1 and 5.2, with regular cycling experiments and with the simulation of specific power profiles representative of a real use. Section 5.3 is focused on exploring possible extrapolations of the presented model: they include the addition of new electrochemical degradations, and the identification of typical capacity fade profiles in respect to the related degradation mechanism, and how the degradations can compete between each other.

Figure 44 Figure 45 Figure 46

 444546 Figure 44 Simulated capacity (blue) vs. experimental capacity with j = 50 mA.cm -2 at 20°C

Figure 47 2 Figure 48

 47248 Figure 47 Evolution of the concentrations during cycling at 20°C, with j = 50 mA.cm -2

Figure 49

 49 Figure 49 Simulated capacity (blue) vs. experimental capacity with Umax = 1.5V at 20°C

Figure 50

 50 Figure 50 Simulated capacity (blue) vs. experimental capacity (red) with Umax = 1.5V at 40°C

Figure 51

 51 Figure 51 Evolution of the concentrations with U = 1.5V at 40°C

Figure 52

 52 Figure 52 Simulation of the voltage evolution during a power profile (blue), compared to the experimental signal (red)

  presents the results obtained with only an irreversible electrochemical degradation of the same species, in this case with 𝑖 0 𝐷𝐻𝐴 = 1.10 -5 and 𝛽 𝐷𝐻𝐴 = 11.5. The resulting capacity fade profiles are very different in the two simulations performed. When only a chemical degradation occurs, the capacity fade is high in the first cycles, then tends to decrease and is nearly null after a few cycles in the conditions of our simulation. For an irreversible electrochemical reaction, the behavior is quite the opposite: the capacity fade is slower on the first few cycles, then only increases towards the end of the simulation. These results give just a qualitative view of how a type of degradation can impact the capacity fade, and give ideas on what kind of degradation can take the lead during aging by looking at the capacity fade. If the capacity fade profile is logarithmic, this could be in favor of a chemical degradation, and if it is increasing as the concentration in reactant decreases it could be in favor of an electrochemical mechanism.

Figure 53 Figure 55

 5355 Figure 53 Simulation results with only a chemical degradation (blue curve)

  For cycled electrolytes, all the signals except for the electrolyte cycled at Umax = 1.5V at 20°C show no 2,6-DHAQ signal left (both in NMR and cyclic voltammetry). In cyclic voltammetries, we find irregular peaks and bumps on the signals when we zoom, which are very close to the voltammogram of (DHA)2 obtained in the literature.A part of these results is used for calibrating the model. Calendar aging at 20 and 40°C at SOC100 help calibrating the values of the chemical degradation kinetics, whereas cycling aging at 37.5, 75 mA.cm-2 and with Umax = 1.7V are used for the calibration of the irreversible electrochemical degradation kinetics, at 20°C. Cycling results at 37.5 and 75 mA.cm -2 are used for the calibration of the irreversible electrochemical degradation kinetics, at 40°C. The model is quite predictive in these conditions, even though we have difficulties to reproduce the behavior of the capacity at 40°C, especially in the first few cycles. The rest of the experiments are used for validating the model (j = 50 mA.cm -2 and Umax =

TABLE

Table 1

 1 Macroscopic key parameters for aqueous redox flow batteries operation .............................................. Table 2 Main organic families used as electroactive species in ORFBs ................................................................. Table 3 Examples of aqueous organic redox flow battery full cell results ............................................................. Table 4 Reported degradation mechanisms in the literature, along with their effects on performances and diagnostic tools ..................................................................................................................................................... Table 5 Detailed contributions to the overall cell voltage ..................................................................................... Table 6 Calculation of reference potentials ........................................................................................................... Table 7 Redox reactions kinetics equations........................................................................................................... Table 8 Electrolytic overvoltages computation ..................................................................................................... Table 9 Mass balance in the compartments and the tanks .................................................................................. Table 10 Equations describing HER and OER modelling ........................................................................................ Table 11 Different operating states of the cell ...................................................................................................... Table 12 Geometric parameters of the model ...................................................................................................... Table 13 Charge and mass transport parameters ................................................................................................. Table 14 Reactions and kinetics parameters ......................................................................................................... Table 15 Initial values for state variables in the model ......................................................................................... Table 16 Summary of calendar aging experiments for model calibration ............................................................ Table 17 Summary of cycling test conditions ........................................................................................................ Table 18 Coefficients of the linear regression models ........................................................................................... Table 19 Calibration of model parameters at 20°C ............................................................................................. Table 20 Calibration of model parameters at 40°C .............................................................................................

Table 4 Reported degradation mechanisms in the literature, along with their effects on performances and diagnostic tools

 4

	Component		Reported degradations	Microscopic	Macroscopic	Diagnostic tools
	Electrodes Bipolar plates	&	Thermal & Mechanical Chemical aging	R ++ R ++	EE loss EE loss	Visual inspection, EIS, XPS, Electrochemical techniques, SEM, MS
	Membrane		Water transfer Chemical degrad. Mechanical degrad.		LossAM R ++ ∆p & R ++	Energy & CE loss EE loss Catastrophic failure	Visual inspection, Spectroscopy, FTIR, SEM, 1 H NMR, Visual inspection
			Leakage/clogging		∆p ++	Catastrophic failure
	Electrolyte (general)		Precipitation Crossover		∆p ++ & LossAM Unbalancing &	Catastrophic failure Energy & CE loss	Visual examination, Spectroscopy, 1 H NMR,
					LossAM
			Side reactions		∆p ++ & unbalancing	Energy & CE loss
	Ferrocyanide		Photodegradation HCN formation (acidic) Degradation (basic)	LossAM ChangeAM ChangeAM	Energy & CE loss Energy fade Energy fade	CV, LSV, UV-vis spectro., IR spectro., 13 C NMR
	Ferrocene		Decomposition organic media	in	LossAM & unbalancing Energy & CE loss	CV, LSV, FTIR, GC-MS, EQCM, ESR, UV-vis spectro.
	Quinone		Nucleophilic attack Protodesulfonation Dimerization Anthrone formation		ChangeAM & LossAM Unbalancing & LossAM	Energy & CE loss	1 H NMR, 13 C NMR, UV-vis spectro., MS, HPLC, EPR
			Disproportionation -	LossAM
	TEMPO		dimerization Ring opening Alcohol oxidation		LossAM Unbalancing &	Energy & CE loss	CV, LSV, 1 H NMR, IR, UV-vis spectroscopy, ESR, ESI-MS
			Oxidation (basic)		ChangeAM
	Viologen		Dimerization Alkaline degradation		LossAM	Energy & CE loss	UV-vis spectroscopy, CV, LSV,
			Oxygen degradation		LossAM & Unbalancing

1

H NMR,

13

C NMR

  Tong et al. reported in situ UV-vis spectrophotometry for concentration monitoring in a quinone based redox flow battery [115]. Similarly, Schubert et al. developed an approach based on IR spectroscopy,

which provides real time data concerning electrolyte SOH in a redox flow cell

[116]

.

Zhao et al. used

Table 5 Detailed contributions to the overall cell voltage

 5 The calculation of each of the overpotentials presented from Equation 2-2 to Equation 2-5 is detailed in the next sections (2.2.1.1 to 2.2.1.4). Among these overvoltages, 𝜂 𝑜ℎ𝑚

	Electrode overpotential	Δ𝜙 = 𝜙 𝑠 ̅̅̅ -𝜙 𝑒 ̅̅̅	Equation 2-2
	Solid ohmic overpotential	𝜂 𝑜ℎ𝑚 𝑠	= 𝜙 𝑠 ± -𝜙 𝑠 ̅̅̅ ≈ 0	Equation 2-3
	Electrolytic ohmic overpotential	𝜂 𝑜ℎ𝑚 𝑒	= 𝜙 𝑒 ̅̅̅ -𝜙 𝑒 ± ≈ 0	Equation 2-4
	Membrane overpotential	electrolytic	𝜂 𝑚𝑒𝑚 = 𝜙 𝑒 𝑚𝑒𝑚 + -𝜙 𝑒 𝑚𝑒𝑚 -	Equation 2-5
				𝑠	and 𝜂 𝑜ℎ𝑚 𝑒	are neglected as
	explained in hypothesis 4.

Table 7 Redox reactions kinetics equations

 7 𝑖 0 𝑖 is the standard current for reaction 𝑖, explained in Equation 2-10. It considers kinetic constant 𝑘 𝑖 , charge transfer coefficient 𝛼 𝑖 and 𝑐 𝑂 and 𝑐 𝑅 , which are bulk concentrations for oxidizer and reducer respectively. Felt surface concentrations are considered in this Butler-Volmer form, here represented by 𝑐 𝑅 𝑠 and 𝑐 𝑂 𝑠 for reducer and oxidizer. Surface concentrations are more representative of the physical reality of electrochemical phenomena; they are calculated thanks to Equation 2-11, which involves charge transfer coefficient 𝑘 𝑚𝑙 , defined here as the ratio between species diffusion coefficient 𝐷 𝑖 and standard pore size 𝑑 𝑓 (Equation 2-12) [160]. In the calculation of surface concentrations, 𝜈 𝑗,𝑟𝑒𝑑

				𝑑Δ𝜙 𝑑𝑡	=	1 𝑎 𝑠 𝐶 𝑑𝑙	(	𝐼 𝑉𝑜𝑙 𝑐𝑜𝑚𝑝 𝜀	-∑ j 𝑓 𝑖 𝑖	)	Equation 2-8
	j 𝑓 𝑖 = 𝑎 𝑠 𝑖 0 𝑖 [	𝑐 𝑅 𝑠 𝑐 𝑅	exp (	𝛼 𝑖 𝐹(∆𝜙 -𝐸 𝑟𝑒𝑓 𝑖 ) 𝑅𝑇 ) -	𝑐 𝑂 𝑠 𝑐 𝑂	exp (-	(1 -𝛼 𝑖 )𝐹(∆𝜙 -𝐸 𝑟𝑒𝑓 𝑖 ) 𝑅𝑇	)]	Equation 2-9
						𝑖 0 𝑖 = 𝐹𝑘 𝑖 𝑐 𝑅 𝛼 𝑖 𝑐 𝑂 1-𝛼 𝑖	Equation 2-10
			𝑎 𝑠 𝐹𝑘 𝑚𝑙 (𝑐 𝑗 𝑠 -𝑐 𝑗 ) = ∑ 𝜈 𝑗,𝑟𝑒𝑑 𝑖 𝑖	𝑗 𝑓 𝑖	-∑ 𝜈 𝑗,𝑜𝑥 𝑖 𝑗 𝑓 𝑖 𝑖	Equation 2-11
						𝑘 𝑚𝑙 =	𝐷 𝑖 𝑑 𝑓	Equation 2-12

The first overpotential Δ𝜙 given in Equation 2-2 represents the charge transfer between solid and electrolyte phase. In this model, we chose to compute this overpotential using a double layer capacitance 𝐶 𝑑𝑙 (Equation 2-8), whose charging depends on the balance between input current 𝐼 and the sum of current densities j 𝑓 𝑖 for each electrochemical reaction 𝑖. 𝑎 𝑠 is the specific area of an electrode, 𝜀 its porosity and 𝑉𝑜𝑙 𝑐𝑜𝑚𝑝 the compartment volume. Charge transfer currents are calculated for each reaction. For main redox half reactions given in Equations 1-6 and 1-7, charge transfer currents are computed with Butler-Volmer kinetics in a simplified form shown in Equation 2-9.

Here,

  These losses depend on membrane conductivity 𝜎 𝑚𝑒𝑚 , membrane area 𝐴 𝑚𝑒𝑚 , membrane thickness 𝛿 𝑚𝑒𝑚 and the global electrolytic current 𝐼 𝑒𝑙𝑒𝑐 . This overpotential value has been calibrated before, because 𝛿 𝑚𝑒𝑚 and 𝜎 𝑚𝑒𝑚 can vary depending on water swelling, thus their values are difficult to estimate [136].

Table 8 Electrolytic overvoltages computation

 8 𝑛 𝑒 𝑖 is the number of exchanged electrons by the reaction 𝑖, and 𝑄 𝑐𝑜𝑚𝑝 is the compartment flow rate so that

	𝜂 𝑚𝑒𝑚 = 𝜂 𝑜ℎ𝑚 𝑚𝑒𝑚 + 𝜂 𝐷𝑜𝑛𝑛𝑎𝑛	Equation 2-13
	𝜂 𝐷𝑜𝑛𝑛𝑎𝑛 =	𝑅𝑇 𝐹	𝑙𝑛 (	[𝐾 𝑝𝑜𝑠 + ] [𝐾 𝑛𝑒𝑔 + ]	)	Equation 2-14
	𝜂 𝑜ℎ𝑚 𝑚𝑒𝑚 =	𝛿 𝑚𝑒𝑚 𝜎 𝑚𝑒𝑚 𝐴 𝑚𝑒𝑚	𝐼 𝑒𝑙𝑒𝑐 = 𝑅 𝑚𝑒𝑚 𝐼 𝑒𝑙𝑒𝑐	Equation 2-15

2.2.1.4 Mass balance equations

Table

9

presents equations that describe mass balance both in the compartments and in the tanks. In the compartments, the concentrations of species change during cycling due to electrochemical reactions. In the 0D representation we chose, there is no difference in species concentrations in the compartments. As proposed in Equation 2-16, it is possible to estimate the output concentrations 𝐶 𝑜𝑢𝑡 𝑗 based on the currents issued from each reactions involving the considered species j and on the input concentrations in the compartments, which are equal to tanks concentrations 𝐶 𝑡𝑎𝑛𝑘 𝑗 assuming a perfect mix in the tanks. Here,

Table 9 Mass balance in the compartments and the tanks

 9 As said above, tanks are considered as perfectly stirred reactors. Species concentrations in the tanks are, in a first approximation, only affected by the feeding rate of products coming from the compartments, and the output concentrations calculated above. Thus, Equation 2-18 enables estimating temporal variation of tanks concentrations in species j, labeled 𝐶 𝑡𝑎𝑛𝑘

	𝐶 𝑜𝑢𝑡 𝑗	= 𝐶 𝑡𝑎𝑛𝑘 𝑗	+	𝜀 𝑐𝑜𝑚𝑝 𝑉𝑜𝑙 𝑐𝑜𝑚𝑝 ℱ𝑄 𝑐𝑜𝑚𝑝	∑ 𝑖	𝑖 𝜈 𝑗 𝑛 𝑒 𝑖 𝑗 𝑓 𝑖	Equation 2-16
		Δ𝐶 𝑜𝑢𝑡 𝐾 + = ∑ 𝑧 𝑗 𝐶 𝑜𝑢𝑡 𝑗 𝑗		Equation 2-17
	𝑑𝐶 𝑡𝑎𝑛𝑘 𝑗 𝑑𝑡	=	𝑄 𝑉 𝑡𝑎𝑛𝑘	(𝐶 𝑜𝑢𝑡 𝑗 -𝐶 𝑡𝑎𝑛𝑘 𝑗	)	Equation 2-18

𝑗

, which depends on the electrolyte flow rate 𝑄, the tank volume 𝑉 𝑡𝑎𝑛𝑘 and the output concentrations from compartments and bulk concentrations in the tank.

Table 10 Equations describing HER and OER modelling

 10 presented above. For redox kinetics, 𝑖 0 𝑂𝐸𝑅/𝐻𝐸𝑅 is the exchange current density of the OER or HER reaction and 𝛽 𝑂𝐸𝑅/𝐻𝐸𝑅 the associated Tafel slope.

	4𝑂𝐻 -⟶ 𝑂 2 + 4𝑒 -+ 2𝐻 2 𝑂	Equation 2-19
	2𝐻 2 𝑂 + 2𝑒 -⟶ 2𝑂𝐻 -+ 𝐻 2	Equation 2-20
	𝐸 𝑟𝑒𝑓 𝑂𝐸𝑅 = 𝐸 𝑂𝐸𝑅 0	+	𝑅𝑇 4ℱ	ln (	[𝑂 2 ] [𝑂𝐻 -] 4 )	Equation 2-21
	𝐸 𝑟𝑒𝑓 𝐻𝐸𝑅 = 𝐸 𝐻𝐸𝑅 0	+	𝑅𝑇 2ℱ	ln ( [𝑂𝐻 -] 2 [𝐻 2 ] 1 )	Equation 2-22
	j 𝑓 𝑂𝐸𝑅/𝐻𝐸𝑅 = 𝑖 0 𝑂𝐸𝑅/𝐻𝐸𝑅 exp (𝛽 𝑂𝐸𝑅/𝐻𝐸𝑅 (∆𝜙 -𝐸 𝑟𝑒𝑓 𝑂𝐸𝑅/𝐻𝐸𝑅 ))	Equation 2-23

  ). Al-Fetlawi et al. focused on the influence of electrolyte flow rate, bubble diameter and operating temperature on OER, and the influence of flow rate, bubble diameter and current on HER. In both cases, bubbles formation reduces the active surface area of the carbon felts, as well as the effective diffusion coefficient of vanadium species by modifying the electrolyte flow. The impact is stronger for OER than HER because the volume of formed oxygen is greater than that of formed hydrogen in applied conditions. Increasing flow rate decreases gas volume fraction in the electrodes, thanks to the greater convection that removes bubbles from electrodes. As bubble diameter increases, slip velocity increases and gas volume fraction decreases because gas bubbles are removed quicker. OER reaction

rate increases exponentially with temperature, thus provoking a decrease in current efficiency. An increasing applied current produces an increase in HER reaction rate and higher gas volume fraction in the electrode. Produced bubbles can be removed faster by increasing the electrolyte flow rate. In this work, the impact of bubbles formation is neglected.

Table 11 Different operating states of the cell

 11 In the table, 𝐼 𝑐ℎ and 𝐼 𝑑𝑐ℎ are charge and discharge currents respectively, while 𝑈 𝑚𝑎𝑥 and 𝑈 𝑚𝑖𝑛 are maximum and minimum cutoff voltages for the end of constant current charge and discharge respectively. 𝑡 𝑠𝑡𝑎𝑡𝑒 is the time spent in the current state, 𝑡 𝑟𝑒𝑠𝑡 the duration of the rest period and 𝑡 𝑝𝑟𝑜𝑓𝑖𝑙𝑒 the duration of the imported power profile, while 𝜏 is the typical time step for calculating the current during a constant voltage phase. It is here fixed to 0.01 s.

	State number	Physical state	Operating condition	End condition
	1	Constant current charge			𝐼 = 𝐼 𝑐ℎ	𝑈 = 𝑈 𝑚𝑎𝑥
	2	Constant current discharge			𝐼 = 𝐼 𝑑𝑐ℎ	𝑈 = 𝑈 𝑚𝑖𝑛
	3	Floating after charge	𝑑𝐼 𝑑𝑡	=	1 𝜏	(𝑈 𝑚𝑎𝑥 -𝑈)	|𝐼| < 𝐼 𝑙𝑖𝑚
	4	Floating after discharge	𝑑𝐼 𝑑𝑡	=	1 𝜏	(𝑈 𝑚𝑖𝑛 -𝑈)	|𝐼| < 𝐼 𝑙𝑖𝑚
	5	Rest after charge			𝐼 = 0	𝑡 𝑠𝑡𝑎𝑡𝑒 > 𝑡 𝑟𝑒𝑠𝑡
	6	Rest after discharge			𝐼 = 0	𝑡 𝑠𝑡𝑎𝑡𝑒 > 𝑡 𝑟𝑒𝑠𝑡
	7	Power profile		𝐼 = 𝑓(𝑡 𝑠𝑡𝑎𝑡𝑒 )	𝑡 𝑠𝑡𝑎𝑡𝑒 > 𝑡 𝑝𝑟𝑜𝑓𝑖𝑙𝑒

or obtained from literature. Table

12

gathers geometric parameters of concern for compartments and felts. Charge and mass transport parameters are presented in Table

13

; they have been calibrated in a precedent work by

Cacciuttolo et al. [136]

, but are calibrated again in this work with the help of chargedischarge curves. In Table

14

, reactions parameters values are given. These values are taken from literature for standard redox potentials and charge transfer coefficients of main reactions, or have been calibrated or experimentally determined in

[136]

for kinetic constants, standard current densities as well as Tafel coefficients. New degradations parameters in this model will be calibrated thanks to experiments, in chapter 4.

Table 12 Geometric parameters of the model

 12

	𝑉 𝑐𝑜𝑚𝑝	40 x 50 x 3 mm 3	Measured
	𝜀 𝑐𝑜𝑚𝑝	0.93	Manufacturer
	𝑑 𝑓	10 µm	Manufacturer
	𝑎 𝑠	35000 m 2 /m 3	Manufacturer
	𝛿 𝑚𝑒𝑚	125 µm	Manufacturer
	𝐴 𝑚𝑒𝑚	20 cm²	Measured

Table 13 Charge and mass transport parameters

 13

	𝐷 𝐷𝐻𝐴𝑄 2-	Unknown	To calibrate
	𝐷 𝐷𝐻𝐴𝐻𝑄 4-	Unknown	To calibrate
	𝐷 𝐹𝑒(𝐶𝑁) 6 3-	Unknown	To calibrate
	𝐷 𝐹𝑒(𝐶𝑁) 6 4-	Unknown	To calibrate
	𝑅 𝑚𝑒𝑚	Unknown	To calibrate

Table 14 Reactions and kinetics parameters

 14

	𝐸 𝐷𝐻𝐴𝑄 2-/𝐷𝐻𝐴𝐻𝑄 4-0	-0.684 V vs SHE	[55]
	𝐸 𝐹𝑒(𝐶𝑁) 6 3-/𝐹𝑒(𝐶𝑁) 6 4-0	0.516 V vs SHE	[55]
	𝐸 𝑂 2 /𝐻𝑂 -0	0.4 V vs SHE	[166]
	𝐸 𝐻 2 𝑂/𝐻 2 0	-0.8277 V vs SHE	[166]
	𝐸 𝐷𝐻𝐴𝐻𝑄 4-/𝐷𝐻𝐴 3-0	-0.2 V vs SHE	[98]
	𝛼 𝐷𝐻𝐴𝑄 2-/𝐷𝐻𝐴𝐻𝑄 4-	0.5	[55]
	𝛼 𝐹𝑒(𝐶𝑁) 6 3-/𝐹𝑒(𝐶𝑁) 6 4-	0.5	[55]
	𝛼 𝑐ℎ𝑒𝑚	Unknown	To calibrate
	𝑘 𝐷𝐻𝐴𝑄 2-/𝐷𝐻𝐴𝐻𝑄 4-	7.0•10 -5 m.s -1	Calibrated [136]
	𝑘 𝐹𝑒(𝐶𝑁) 6 3-/𝐹𝑒(𝐶𝑁) 6 4-	3.3•10 -5 ms -1	Calibrated [136]
	𝑘 𝑐ℎ𝑒𝑚	Unknown	To calibrate
	𝛽 𝑂𝐸𝑅	13.6 Vdec -1	Experimentally determined [136]
	𝛽 𝐻𝐸𝑅	-12.0 Vdec -1	Experimentally determined [136]
	𝛽 𝐷𝐻𝐴	Unknown	To calibrate
	𝑖 0 𝑂𝐸𝑅	3.1•10 -5 A/carbon felt	Experimentally determined [136]
	𝑖 0 𝐻𝐸𝑅	2.6•10 -8 A/carbon felt	Experimentally determined [136]
	𝑖 0 𝐷𝐻𝐴	Unknown	To calibrate

Table 16 Summary of calendar aging experiments for model calibration

 16

	Operating conditions Temperature (°C) State of Charge (%)	NMR spectroscopy	Capacity measurements	Experiment name

Table 17

 17 establishes a sum up of cycling conditions for every experiment. Here, several experiments[START_REF] Derr | Electrochemical degradation and chemical aging of carbon felt electrodes in all-vanadium redox flow batteries[END_REF] are used for calibrating the model, while others (5) are used for validating the model.

Table 17 Summary of cycling test conditions

 17

	Operating conditions
	Temperature T (°C)	Current density j (mA.cm -2 )	Upper voltage limit Umax (V)	Calibration or validation?	Experiment name
			1.6 V	Calibration	Cycling20 #1.1 and #1.2
		37.5 mA.cm -2	1.5 V	Calibration	Cycling20 #2.1 and #2.2
	20 °C		1.7 V	Validation	Cycling20 #3.1 and #3.2
		50 mA.cm -2	1.6 V	Calibration	Cycling20 #4.1 and #4.2
		75 mA.cm -2	1.6 V	Calibration	Cycling20 #5.1 and #5.2
			1.6 V	Calibration	Cycling40 #1.1 and #1.2
		37.5 mA.cm -2
			1.5V	Validation	Cycling40 #2
	40 °C
		50 mA.cm -2	1.6 V	Validation	Cycling40 #3.1 and #3.2
		75 mA.cm -2	1.6 V	Calibration	Cycling40 #4.1 and #4.2
	Specific power profile	Validation	PNNL #1.1 and #1.2

Table 18 Coefficients of the linear regression models

 18

	Sample	Intercept	Slope	R²	Standard error on the slope
	Calendar20 #2	1220	-17.8	0.980	1.8
	Calendar40 #1	1227	-20.2	0.999	0.3
	Calendar40 #2	1181	-16.6	0.932	3.2

Table 19 Calibration of model parameters at 20°C

 19

	Parameter	Value at 20°C
	𝑘 𝐷𝐻𝐴𝑄 2-/𝐷𝐻𝐴𝐻𝑄 4-	3.6.10 -7 m.s -1
	𝑘 𝐹𝑒(𝐶𝑁) 6 3-/𝐹𝑒(𝐶𝑁) 6 4-	2.4.10 -5 m.s -1
	𝐷 𝐷𝐻𝐴𝑄 2-	5.3•10 -11 m².s -1
	𝐷 𝐷𝐻𝐴𝐻𝑄 4-	1.4•10 -8 m².s -1
	𝐷 𝐹𝑒(𝐶𝑁) 6 3-	2.3•10 -11 m².s -1
	𝐷 𝐹𝑒(𝐶𝑁) 6 4-	8.4•10 -10 m².s -1
	𝑖 0 𝑂𝐸𝑅	4.3.10 -6 A/carbon felt
	𝑖 0 𝐻𝐸𝑅	8.2.10 -8 A/carbon felt
	𝑅 𝑚𝑒𝑚	2.2•10 -1 Ω
	∆ 𝑐𝑜𝑛𝑐	27%
	𝑘 𝑐ℎ𝑒𝑚	2.10 -6 m.s -1
	𝛼 𝑐ℎ𝑒𝑚	1
	𝑖 0 𝐷𝐻𝐴	1.10 -7 A
	𝛽 𝐷𝐻𝐴	-11.5

Table 20

 20 summarizes the values of each calibrated parameter of the model at 40°C. In comparison to

Table 20 Calibration of model parameters at 40°C

 20

	Parameter	Value at 40°C
	𝑘 𝐷𝐻𝐴𝑄 2-/𝐷𝐻𝐴𝐻𝑄 4-	1.6.10 -4 m.s -1
	𝑘 𝐹𝑒(𝐶𝑁) 6 3-/𝐹𝑒(𝐶𝑁) 6 4-	5.10 -5 m.s -1
	𝐷 𝐷𝐻𝐴𝑄 2-	3.0.10 -10 m².s -1
	𝐷 𝐷𝐻𝐴𝐻𝑄 4-	3.0.10 -6 m².s -1
	𝐷 𝐹𝑒(𝐶𝑁) 6 3-	2.3.10 -11 m².s -1
	𝐷 𝐹𝑒(𝐶𝑁) 6 4-	6.4.10 -6 m².s -1
	𝑖 0 𝑂𝐸𝑅	1.3.10 -4 A/carbon felt
	𝑖 0 𝐻𝐸𝑅	1.8.10 -2 A/carbon felt
	𝑅 𝑚𝑒𝑚	8.1.10 -2 Ω
	∆ 𝑐𝑜𝑛𝑐	18-40%
	𝑘 𝑐ℎ𝑒𝑚	1.10 -7 m.s -1
	𝛼 𝑐ℎ𝑒𝑚	1
	𝑖 0 𝐷𝐻𝐴	1.1.10 -5 A
	𝛽 𝐷𝐻𝐴	-11.5

  4-should be higher in the first cycles, but is limited because a portion of this species is chemically degraded and transformed into DHA 3-(green) and DHAQ 2-(golden). The tendency after that increase is close to the experiments, with a logarithmic profile for the capacity fade. The simulated capacity fade in 20 cycles is of around 40% in both simulations, against 45 to 55% in the experiments. As in 20°C experiments, the capacity fade rate seems to decrease faster for the experiments than for the simulation, which could lead to an underestimation in longer experiments: this could be explored with longer cycling experiments.

	MSE 𝐶𝑦𝑐𝑙𝑖𝑛𝑔40 #3,𝑚𝑜𝑑𝑒𝑙 = 0.43 and MSE 𝐶𝑦𝑐𝑙𝑖𝑛𝑔40 #4,𝑚𝑜𝑑𝑒𝑙 = 0.44.

modelled via this mechanism, if we consider that DHA 3-

Formation of new redox active couples

If we follow the hypothesis made by Aziz et al. on subsequent oxidation of 𝐷𝐻𝐴 3-in highly alkaline conditions, new redox active species are produced [97]. They proposed the oxidation of DHA followed by a radical dimerization, forming (𝐷𝐻𝐴) The capacity fade rate is lower for every 20°C cycling experiment compared to the 40°C cycling experiments, with the lowest reported when cycled with Umax = 1.5V. The experiments with Umax = 1.7V (Cycling20 #3), j = 50 mA.cm -2 (Cycling20 #4) and j = 75 mA.cm -2 (Cycling20 #5) are the least reproductible (highest quadratic errors between the 2 experiments performed in each of these conditions).

The results obtained from the experiments performed in calendar and cycling aging are the following:

• We did calendar aging studies at 20°C and 40°C, with sets of electrolytes stored at SOC0 and SOC100 for both. We followed the capacity fade throughout aging for the samples at SOC100 20°C, and the samples at SOC0 and SOC100 at 40°C. Overall, the capacity fade measured for these 3 samples is statistically non differentiable, and we cannot conclude on a potential effect of either the SOC or the temperature on the capacity fade in calendar aging. Further measurements (for longer time, and at different SOC) are needed. Overall, it seems that the rate of chemical degradation is quite independent of the temperature.

• Post-mortem 1 H NMR studies have been done on calendar aged samples at 20°C. We find the same peaks than for the new electrolyte, characteristic of 2,6-DHAQ. These peaks are shifted of 0.3-0.5 ppm, which is probably a consequence of a change in the experimental environment.

40°C

In this section, the calibration results at 40°C are presented.

Calibration of the model parameters (with only HER/OER as aging)

Based on the same principle than at 20°C, the values of the model parameters with only HER/OER as aging (as well as the unbalancing amount ∆ 𝑐𝑜𝑛𝑐 ) are optimized with a Levenberg-Marquardt algorithm so that the simulated charge-discharge curve fits the experimental, with the result shown in Figure 41.

The blue curve corresponds to the simulated voltage, and the red curve corresponds to the experimental voltage of the second cycle.

Figure 41 Simulated cell voltage (blue) compared to actual cell voltage (red) in standard conditions, at 40°C

Here, we can see that the simulated charge-discharge curve does not fit exactly the experiment.

Several parameters explain that result, the first one being the long floating time between t = 2h and t = 8h. This unusually long floating, which can be due to the formation of hydrogen during charging, or of another redox species with the production of current, is simulated by artificially fixing a minimum time of 6 hours of floating. This modelling trick does not represent the physical reality of floating, but it was the best we found to try and have similar cycling times in the simulation and in the experiment.

The second thing that we did not model is the bump on the discharge curve at about 0.7V, which has been seen in many experimental results after some aging and is characteristic of a change in the redox not see any capacity fade, or too high (even when we increased it by a little bit) and the simulation crashed, because of a divergence in the model calculations.

Also, the calibration is done with several experimental data obtained from calendar aging and cycling aging in different experimental conditions: the calibrated simulations must fit in every experimental conditions. Furthermore, adding an electrochemical reaction to the model adds to its complexity, and thereby increases computing time. Thus, the time needed for calibration is increased because of the complexity of the model and its computing time.

While we believe adding these electrochemical degradations would enable a better fitting between the simulations and the experimental work, we could not prove it by getting a model that would properly work with these 3 degradations. An alternative would be either to dedicate more time to the calibration, with a computing cluster and/or optimization algorithms, or to try running this model into another software than R more suited to such low dimension physical modelling, such as Simcenter Amesim™.

Modelling the reversible capacity fade: oxidation of DHA 3-into DHAQ 2-

Another perspective of this model is the addition of an oxidation reaction that converts the DHA3-back into DHA Q 2-. This mechanism has been proposed by Aziz et al. [98] for explaining the ability to restore the lost capacity in the battery when exposed to air, or when oxygen was bubbled in the solution. This phenomenon could be modelled by adding an electrochemical reaction between DHA 3-and O2, producing DHAQ 2-. With this addition to the model, there would then be a competition between two reactions, that use DHA3-as a reactant: on one side there is the dimerization of DHA 3-into (DHA)2 4-, and on the other side the oxidation of DHA 3-into DHAQ 2-. We could then properly calibrate the dimerization reaction -which has not been the case in the present model, since the dimerization in our model had no impact on other species than DHA 3-, and thus we could not measure its effect on the cell capacity, for instance -. Thanks to this, we could measure the part of capacity that is irreversibly lost (through dimerization) and the part that is reversibly lost (DHA 3-that did not undergo dimerization, and that can be oxidated back to DHAQ 2-).

Identification of typical capacity loss profiles corresponding to specific degradations mechanisms

In this section, we present general capacity fade profiles representative of a degradation mode. For a reminder, we studied in this work 2 main degradation paths:

• A chemical degradation,

• An electrochemical degradation producing a redox inactive species (the reaction is thus irreversible).