Linking the Performances of Li-O2 Batteries to Discharge Rate

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Linking the Performances of Li-O Batteries to Discharge Rate, Electrode and Electrolyte Properties Through the Nucleation Mechanism of LiO 2

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Yinghui Yin, Amangeldi Torayev, Caroline Gaya, Youcef Mammeri, and Alejandro A. Franco J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b05224 • Publication Date (Web): 14 Aug 2017 Downloaded from http://pubs.acs.org on August 14, 2017

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The Journal of Physical Chemistry

Linking the Performances of Li-O2 Batteries to Discharge Rate, Electrode and Electrolyte Properties through the Nucleation Mechanism of Li2O2 Yinghui Yin,1,2 Amangeldi Torayev,1,3 Caroline Gaya,1,4 Youcef Mammeri5 and Alejandro A. Franco1,2,3,6,* 1. Laboratoire de Réactivité et Chimie des Solides (LRCS), CNRS UMR 7314, Université de Picardie Jules Verne, 33 rue St. Leu, 80039 Amiens Cedex, France 2. Réseau sur le Stockage Electrochimique de l’Energie (RS2E), Fédération de Recherche CNRS 3459, CNRS FR 3459, 33 rue St. Leu, 80039 Amiens Cedex, France 3. ALISTORE-European Research Institute, CNRS FR 3104, Fédération de Recherche CNRS 3104, 33 rue Saint Leu, 80039 Amiens Cedex, France 4. IRT Saint-Exupery, 118 route de Narbonne, 31432 Toulouse, France 5. Laboratoire Amiénois de Mathématique Fondamentale et Appliquée (LAMFA), CNRS UMR 7352, Université de Picardie Jules Verne, 80039 Amiens Cedex, France 6. Institut Universitaire de France, 103 Boulevard Saint Michel, 75005 Paris, France

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ABSTRACT Li-O2 batteries have attracted a lot of attention because of their high theoretical capacity. Due to the high complexity of these systems, deep understanding of the discharge mechanism is still needed to push the state-of-art performance of Li-O2 batteries to the theoretical one. A universal multi-scale model combining nucleation theory, detailed reaction kinetics and mass transport is presented in this paper, which encompasses the impacts of discharge rate, electrolyte and electrode surface properties on the discharge capacity of Li-O2 batteries and on the morphology of the Li2O2 arising from its nucleation process.


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INTRODUCTION Due to its high gravimetric theoretical capacity up to ~3000 Wh/kg, the Li-O2 battery is regarded as a promising candidate to meet the demands of high endurance electrical vehicles.1,2 However, the practical discharge capacity of Li-O2 batteries in the state-of-the-art (about 500 Wh/kg)3 is still far from the theoretical value due to several performance limiting factors, such as the electrode surface passivation by the Li2O2 formed during discharge, the O2 diffusion in the electrolyte and the electrolyte stability.4–6 Moreover, it is found that the performance of a Li-O2 cell and the morphology of Li2O2 depend on multiple factors including the discharge rate, the type of electrolyte and the surface properties of the electrode.7–10 Besides, it has been reported that strategies like pre-seeding the electrode by adding seed crystals11 or pre-discharging the cell at low potential12 have significant impacts on the discharge capacity. More fundamental knowledge of the discharge mechanism is then required to enhance the performance of Li-O2 batteries and multiscale modeling is revealed as a useful tool to rationalize the experimental observations.13–16 However, mathematical models reported in literature consider oversimplified discharge mechanisms and therefore there is a lack of versatile models able to predict the discharge trends with respect to multiple experimentally-controllable parameters. In this paper, we present a Li-O2 battery model encompassing classical nucleation theory, detailed reaction kinetics and mass transport, which is able to simulate the discharge profiles and evolution over discharge of the Li2O2 particle size distribution as a function of the current density, electrolyte and electrode properties.


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THEORY

Figure 1. Schematic illustration of the configuration and discharge process of a Li-O2 battery cell. As shown in Figure 1, the discharge of Li-O2 batteries starts with the formation of the LiO2 ion pair, noted as LiO2(ip), from the reduction of the O2 in presence of Li+:17,18 ↔

(1)

The formation of Li2O2 from both electrochemical reduction and disproportionation reaction involves desolvation and charge transfer. According to the reaction stoichiometry, twice the amount of energy is needed for ion pair desolvation in the disproportionation reaction compared to the electrochemical reduction. Moreover, the charge transfer between the electrode surface and the LiO2(ip) may be facilitated due to the partial desolvation of LiO2 under the electrostatic forces. Therefore, in the present model with DMSO as the reference solvent, the nucleation due to the electrochemical reduction (Eq.2) is considered to be favored over the nucleation from the disproportionation, thus

↔

(2)


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where n is the number of Li2O2 units in the nuclei. According to the classical nucleation theory the energy barrier of heterogeneous nucleation can be calculated from Eq. 3 6 (whose derivation is detailed in the Supporting Information) ∆ =

8

1

27 2!

(3)

where B is a geometrical factor with a value equaling 18 for a hemisphere, Ve is the molar

volume of Li2O2, is the specific surface energy of the Li2O2 surface exposed to the electrolyte, is the binding energy of Li2O2 on the electrode material, ! is the contact area between a

Li2O2 unit and the electrode material surface, ne is the number of electrons transferred and is the overpotential of the reaction in Eq. 2. Then the reaction kinetics of the nucleation reaction is given by # = $ !% exp −

∆

$ *

(4)

where knu is the kinetic rate constant for the nucleation reaction, Ac is the uncovered area of the electrode material surface, kb is the Boltzmann constant and T is the temperature. Furthermore, !+ =

/ -

5

5

6

6 5

!0 − 1 23 43 , !0 ≥ 1 23 43

. - 0 , !0 < 1 23 43 , 6

(5)

where A0 is the initial electrode material surface area, Nr is the number of particles with radius of r. The impact on the particle overlapping is not considered in the present model but a mathematical constrain is applied to prevent Ac to become negative. The formed Li2O2 nuclei can grow through both electrochemical and chemical pathways, which correspond to the so-called thin-film mechanism and solution-phase mechanism, respectively.9 In the thin-film mechanism, the reduction of LiO2 ion pairs and adsorbed LiO2(ad) take place on the surface of the Li2O2 particles as


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↔

9: ↔

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(6) (7)

However, due to its insulating nature, the thickness of the Li2O2 grown electrochemically is usually less than the maximum distance of electron tunneling (δe), which is around 10 nm according to DFT calculations.4 The same tunneling function as in our previous work13,19 is employed here to capture the electron tunneling effect ; < =

#= < 1 − 3> < − 7 = #= 0 2

(8)

where < is the Li2O2 layer thickness and #= < is the reaction rate on a Li2O2 layer with a thickness of < . For the sake of geometrical simplicity, we represent the Li2O2 particles as

hemispheres and we assume that the particles growth is isotropic. As a consequence, the difference of reaction rates at different parts of a single particle is ignored and < is represented

by the radius of a single particle. According to the Eq. 8, once the particle radius reaches 10 nm, the reaction rate of the electrochemical reduction (Eq.6) drops to zero. This assumption may lead to an underestimation of the growth rate of particles with a radius close to the tunneling distance, but for the large particles, the impact is negligible. In the solution-phase mechanism, the LiO2 ion pairs formed close to the electrode surface diffuse into the bulk electrolyte and become Li2O2 through a disproportionation reaction. However, it is difficult to have a direct formation of Li2O2 from the ion pairs as the interaction is weakened by the solvation shell. It is reported that the Li2O2 large particles formed from the solution-phase mechanism have an outer layer of LiO2-like component.20 Thus, we consider here that the LiO2 ion pairs are first adsorbed on the surface of Li2O2, followed by the further disproportionation of the adsorbed LiO2 (Eq. 9-10) ↔ 9:

(9)


6

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2 9: ↔

(10)

The kinetics of the chemical growth of a particle is described as #=% = $9:? !@ABC DE − $:? !F

(11)

where kads and kdes are the kinetic rate constants of adsorption and dissolution of superoxides,

@ABC DE is the concentration of the LiO2 ion pair, A is the surface area of the particles and γ is the

molar fraction of LiO2(ad). Moreover, the dissolution kinetics shows dependence on the particle radius according to21 $:? = $ H exp

2ABC ,ABC

I*3

(12)

where $ H is a prefactor, ABC is the specific surface energy of free LiO2(ad), ,ABC is the molar volume of LiO2(ad) and r is the radius of a lithium oxides hemispherical particle. Since data for ABC and .ABC are not available, it is assumed that these parameters have the same values as for

Li2O2. From the disproportionation reaction stoichiometry in Eq. 9, a second order kinetics is expected with respect to the LiO2(ad) activity while the experimental measurement shows that the reaction order with respect to LiO2(ad) is 1.17 The reason of the inconsistency in the reaction order between theory and experiment is still unclear and first order kinetics is used in this model as a first approximation. The reaction rate of the electrochemical reaction j can be characterized by the local faradaic current density, iL

M95

= NOL

(13)

The addition of the local faradaic currents through the entire electrode gives the total current which equals the applied current under galvanostatic conditions, i.e. S

P Q = R 1 6

L

!L M95 i T L

(14)


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where Aj is the active surface area of the reaction j. For the reactions in Eq.1-2 , the active surface area refers to the area of the electrode that is not covered by Li2O2; while for the reactions in Eq. -7, the surface area refers to the area of Li2O2 surface exposed to the electrolyte. Except for the nucleation reactions, the reaction kinetics of the other electrochemical reactions can be described by L

M95

1 − Y N Z − L[ ?D,X = N U$M,L V W exp

−$ RT

,L

V W exp

?D,X

−Y N Z − L[

^ RT

(15)

where W D,X is the activity of species i (which refers to the dimensionless concentration for solute ?

in electrolyte or the molar faction for solids in solid mixtures), $M,L and $ ,L are

the

heterogeneous rate constants, Y is the charge transfer coefficient, Z is the electrostatic potential

of the electrode and L[ is the standard potential of the reaction j. For the reactions on the top of

the particle (Eq. 5-6), the active surface area as well as the local current density show dependence on the particle size, therefore, the total current through the entire electrode from reaction j is obtained from

243 M95 PL = R 1 25 i T 5,L 6 S

5

(16)

where Nr is the number of the Li2O2 particles having a radius r. As the result of the nucleation and growth process, the particle size distribution (PSD) of Li2O2 evolves with time. Within a continuum mathematical approach, the PSD evolution is governed by22

_> , ` _ _ a> , ` b = 0 _` _ _`

(17)

where f(L,t) is the number of particles with a size of L per unit of volume. The size of particle L can be described with either the particle radius or the volume of particles. However, the nucleation process is not considered in the above. A source term Snu is thus added to take into consideration the nucleation contribution as shown in Eq. 18


8

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_> , ` _ _ a> , ` b = c _` _ _`

(18)

Apart from the reactions, the mass transport of active species, especially that of O2, is of high importance for the performance of a Li-O2 batteries.5,23 In the present model, the mass transport of Li+, O2 and LiO2(ip) are solved along the thickness of the positive electrode and separator. It is assumed that the mass transport of species i in the porous mediator is mainly governed by diffusion as

_ d+ _ f _+ = ad g6, b c _` _e _e

(19)

where d is the porosity of the positive electrode or separator, h is the Bruggeman coefficient, g6, is the bulk diffusion coefficient of species i and Si is the source term, referring to the overall iA

consumption or formation rate of species i . Both Si and iQ can be calculated by summing up the consumption/formation rates of the species involved in each reaction c = 1 j,L OL L

_ = 1 1 j,L OL _`

L

(20)

(21)

In Eq.21, i stands for the component species of the particle, i.e. LiO2(ad) and Li2O2, si,j is the stoichiometric coefficient of species i in reaction j. RESULTS AND DISCUSSION In our model we assume a positive electrode made of a gas diffusion layer (GDL). We consider as electrolyte a 1 M LiClO4/DMSO solution. The parameters values used in the model are summarized in Table S1. It is commonly observed in literature that there is a potential dip at the initial stage of the galvanostatic discharge of a Li-O2 batteries, especially when the discharge rate is relatively low and when high donor number solvents such as DMSO are used.13,24–27 This behavior is well


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captured by our model (Figure 2a) which correlates it closely to the nucleation process. According to the calculated evolution of the cell potential, the discharge processes can be divided into four stages: (I) LiO2(ip) accumulation; (II) nucleation; (III) Li2O2 growth and (IV) sudden death. As shown in Figure 2b, O2 reduction is the only reaction taking place during the stage I. LiO2(ip) is formed and accumulated in the electrolyte, leading to the decrease of the cell potential. Once the excess energy of the super-saturation overcomes the nucleation barrier, the stage II of nucleation is initiated along with a rapid decrease of the LiO2(ip) concentration (Figure 2c). The direct consumption of LiO2(ip) from the nucleation process is very limited, which can be seen from the reaction rate normalized to the rate of O2 reduction. However, the following chemical growth (adsorption of LiO2(ip)) and electrochemical growth (reduction of LiO2(ip) and LiO2(ad)) of Li2O2 consume the LiO2(ip) in the electrolyte, resulting in an increase of the cell potential and a decrease of the nucleation rate. During the stage III, there is no more new nuclei formed and the Li2O2 particles grow gradually mainly due to the chemical growth. With the increase of the particle size, on one hand, the active surface area for LiO2(ip) adsorption increases, leading to the gently decrease of LiO2(ip) concentration (Figure 2b) which results in the increase of the cell potential. On the other hand, the active surface area for O2 reduction, which refers to the surface area of the free electrode, decreases, leading to the increase of the local current density and to the decrease of the cell potential. The interplay between the two active surface areas gives rise to the bending shape of the potential profile (Figure 2a). At the end of this stage, the impact from the electrode passivation dominates in the system and the cell potential goes downhill until overcoming again the nucleation barrier, reaching stage IV. The remaining free surface of the electrode has been passivated quickly along with the drop of the cell potential, which corresponds to the phenomena known as “sudden death”. Similar bending shape of the potential


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curve has been reported with an analytical model fitted from experimental results by Rinaldi et al.28 A bimodal distribution of the particle size at the end of discharge process (Figure 2d) is observed from our simulation. Here the particles consist in a mixture of Li2O2 and LiO2(ad). Under the simulated conditions, the main part of the capacity comes from the particles with a radius of 90 nm, which are formed during the stage II. Moreover, though the size of large particles along the depth of the electrode remains the same, there are more particles formed close to the O2 inlet (depth of electrode = 0) than the separator side (depth of electrode = 235 µm). However, the gradient of the particle number is opposite for the small particles with a radius of 12 nm, which are formed during stage IV. This gradient is due to the higher LiO2(ip) concentration close to the separator side during stage IV as shown in Figure S1. The calculated particle size distribution from our model is in contrast with the simulation results reported by Lau et al.29 , where most of the capacity is credited to the small particles. This difference may result from the simplification of the discharge mechanism in Lau et al. model, where the impacts from the dynamic change of LiO2(ip) concentration on the nucleation process and the cell potential has been overlooked. As a result, the nucleation process happens continuously during the entire discharge and the cell potential decreases monotonously in their model. These trends are observed in our model when the discharge rate is very high (Figure S2) or the nucleation barrier is very low (Figure 4a and 5a).


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Figure 2. Simulation results for a Li-O2 battery with a GDL cathode: (a) the calculated potential profile during the discharge process and its four stages; (b) the reaction rate of O2 reduction (blue), electrochemical growth of Li2O2 (reduction of LiO2(ip) and LiO2(ad), red), chemical growth of Li2O2 (adsorption of LiO2(ip), yellow) and LiO2 disproportionation (purple); (c) the evolution of the nucleation rate and LiO2(ip) concentration during the discharge process; (d) the particle size distribution at the end of the discharge process. The reaction the (b) and (c) are normalized to the input current.

The discharge rate is a key parameter for the discharge performance and product morphology of a Li-O2 batteries.7,26,30 Figure 3a shows the simulated discharge curves at the rate of 0.1, 0.5 and 1 A/m2, respectively. It is observed that with the increase of discharge rate, the potential dip


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becomes shallower but wider, which is correlated to the extension of nucleation period. At very high current density, where the consumption rate of LiO2(ip) is all the way lower than the its formation rate, the cell potential continuously decreases and the final particle size becomes close to the electron tunneling distance. As a consequence, there are more particles formed during the nucleation process at high current density and the electrode surface is passivated faster, ending up with a lower discharge capacity. Though the experimental reference is not the same, the simulated discharge curves is in good qualitative agreement with the experimental result reported by Girishkumar et al (Figure 3b).2 Also, the final particle size distributions of the simulated discharge curves (Figure 3c) vary with the change of discharge current density. The peak of particle size at higher radius in the bimodal distribution located at 125, 50 and 20 nm at the rate of 0.1, 0.5 and 1.0 A/m2, respectively. Besides, it is reported that the morphological transition of Li2O2 from thin film, which is represented by small particles, to large toroidal particles, took place at a narrow current range.7,30 This has also been observed in the model as the nucleation rate has an abrupt increase in concentration-potential zone as shown in the Figure S4 and S5. The above interplay between discharge rate, discharge capacity and particle size is not only in a good agreement with, but also shed a light on experimental results reported in the literature.26,30 Moreover, it is revealed that the capacity fraction from the smaller particle increases with the rising of discharge capacity. As the charge mechanism depends on the size of Li2O2 particles,19 different shapes of charge curves are expected for the Li-O2 batteries with different charge rate, which has already been observed by Zhai et al.20


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Figure 3. (a) Calculated discharge curves of Li-O2 batteries at 0.1 (blue), 0.2 (red), 0.5 (yellow); (b) Experimental discharge curves for an aprotic Li-O2 cell (based on a Ketjenblack cathode) at 0.1, 0.5 and 1 mA/cm2(c) Simulated final particle size distribution corresponding to the discharge curves in (a). Figure 3(b) is reprinted with permission from Ref. 2. Copyright (2017) American Chemical Society.

As the surface energy of the Li2O2 in the electrolyte plays an important role in the nucleation process, it shows a strong impact on the discharge process of Li-O2 batteries. The average surface energy of Li2O2/O2 is calculated to be 0.77 J/m2.31 However, this value for Li2O2 in the electrolyte is expected to be lower considering the stabilization effects of the solvent. A set of simulations has been run with different values of surface energy: the results indicate that when the surface energy decreases from 0.75 to 0.65 and 0.55 J/m2, the discharge capacity drops from


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38 to 20 and 10 mAh/gGDL, respectively (Figure 4a). At the same time, it is observed that with the decrease of the surface energy, the potential dip related to the nucleation becomes shallow and even disappears as in the case where the surface energy equals 0.55 J/m2. This variation could be ascribed to the decrease of the nucleation barrier as a result of the decrease of surface energy according to Eq. 3. Consequently, the nucleation process can take place at lower concentration of LiO2(ip) with higher kinetics. The fast nucleation results in a fast passivation of the electrode, leading to a sloppy shape of the discharge curve and a limited discharge capacity. The corresponding final PSD also confirms the above explanations (Figure 4b-d). The radius peaks are located at 90, 50 and 27 nm for the cases with surface energy of 0.75, 0.65 and 0.55 J/m2, respectively. The decreasing trend of large particles size along with the increased capacity fraction of small particles is an evidence of fast passivation due to the decrease of the Li2O2/electrolyte surface energy, which depends mainly on the electrolyte property. In the literature, it is widely found that the Li2O2 morphology and discharge capacity depend on the type of electrolyte, which is mainly discussed from the viewpoint of the donor number and the capability to stabilize the ion pair.9,18 Here we propose a complementary explanation from the perspective of nucleation process to give more insight to the impact of electrolyte on the discharge mechanism. Moreover, a potential oscillation is observed in the discharge curve in the case with surface energy of 0.55 J/m2 (Figure 4a and Figure S3). This potential oscillation is closely related to the nucleation process and is mainly due to the nonlinear character of the Li-O2 battery system. Similar phenomenon has been already reported in other nonlinear chemical systems,32,33 but to the best of our knowledge, this is the first time that this behavior is reported for Li-O2 batteries.


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Figure 4. a) Simulated discharge curves of Li-O2 batteries with surface energies of Li2O2/electrolyte equaling to 0.75 (blue), 0.65 (red), 0.55 (yellow) J/m2 and their final particle size distribution (b-d). Another parameter related to the nucleation barrier is the binding energy (Eb) between Li2O2 and the electrode material, which depends mainly on the surface property of the electrode material. It is reported that the binding energy of Li2O2 on the defective site of graphene is -0.7~0.9 eV, which double or even triple the value on perfect graphene of -0.26 eV.34 The impact of the binding energy on the discharge process has also been investigated with the present model. As showed in Figure 5a, when the binding energy of Li2O2 on the carbon electrode decreases from -0.26 to -0.50 and -0.70 eV, which refers to the increase of the interaction between Li2O2


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and the electrode material, the discharge capacity drops from 38 to 24 and 12 mAh/gGDL, respectively, accompanied by the reduction of the width of the potential dip. Correspondingly, the peak radius from the calculated final particle size distribution shrinks with the decrease of the binding energy. The dependence of the discharge capacity on the surface property of electrodes has been observed experimentally by Wong et al., which reported that with the increase of O/C ratio on a carbon nanotube surface, the discharge capacity decreases (Figure 5b) and the particle size of Li2O2 also reduces.10 According to the present model, the above phenomenon is also originated from the change of nucleation barrier. As the stronger binding between the electrode material and Li2O2 favor the formation of nuclei, faster nucleation takes place at the electrode with the lowest binding energy, resulting in faster passivation and lower capacity. Moreover, the binding energy of Li2O2 on the surface of catalyst (Pt, Au, TiO2, etc.) is usually much higher than that on carbon surface,35–37 leading to a preferential nucleation on the surface of the catalyst. The catalyst is thus expected to be quickly inactive due to the surface passivation. The observed improvement in the catalyst-loaded system is more likely to be accredited to the pre-seeding effects. The Li2O2 formed on the catalyst surface retards the LiO2(ip) accumulation in the electrolyte and delays the passivation of the carbon surface, resulting in an improvement of the discharge capacity.


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Figure 5. a) Calculated discharge curves of Li-O2 batteries with a binding energy of Li2O2/electrode equaling to -0.26 (blue), -0.50 (red), -0.70 (yellow) eV; (b) Calculated discharge and charge profiles of Li-O2 batteries with electrodes of different O/C ratio, which implies different binding energies of Li2O2/C; (c) Calculated final particle size distributions corresponding to the discharge curves in (a). Figure 5(b) is reprinted with permission from Ref. 10. Copyright (2017) American Chemical Society. CONCLUSION In summary, a comprehensive and innovative multi-scale model was built by combining the classical nucleation theory and detailed mathematical descriptions of the mass transport and the discharge mechanism in a Li-O2 battery. The simulation results from the proposed model reproduces the typical shapes of discharge curve of Li-O2 batteries, which are characterized by a potential dip at the beginning and potential drop at the end of the discharge process. This


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potential evolution reflects the dynamic change of the LiO2(ip) concentration and the surface coverage of the electrode material by Li2O2. Moreover, the proposed model merges in a single cohesive theory the Li-O2 battery performance dependence on the discharge rate, electrolyte property and electrode surface property due to the nucleation process, providing deep insights into the discharge reaction mechanism of the Li-O2 batteries. ASSOCIATED CONTENT Supporting Information. The Supporting Information is available free of charge. Supplementary Calculation Results, Heterogeneous nucleation theory, Table of parameters, Method to describe the evolution of particle size distribution, Finite volume method for the mass transport and Kinetics of LiO2(ip) adsorption/desorption (PDF). AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] Notes The authors declare no competing financial interest. ACKNOWLEDGMENT The authors are grateful to the Conseil Régional des Hauts de France and the European Regional Development Fund for the funding support through the project MASTERS. Prof. Dominique Larcher (LRCS) and Prof. Ezequiel P.M. Leiva (University of Cordoba, Argentina, visiting scientist at LRCS) are acknowledged for helpful discussions. The authors also thank Mrs. Carine Lenfant for English proofreading.


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TOC GRAPHICS


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Linking the Performances of Li-O2 Batteries to Discharge Rate

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