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Compactness of Lithium Peroxide Thin Film Formed in Li-O Batteries and Its Link to Charge Transport Mechanism: Insights from Stochastic Simulations Yinghui Yin, Ruijie Zhao, Yue Deng, and Alejandro A. Franco J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.6b02732 • Publication Date (Web): 12 Jan 2017 Downloaded from http://pubs.acs.org on January 12, 2017

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The Journal of Physical Chemistry Letters

Compactness of Lithium Peroxide Thin Film Formed in Li-O2 Batteries and Its Link to Charge Transport Mechanism: Insights from Stochastic Simulations Yinghui Yina.,b,‡, Ruijie Zhaoa,b,†,‡, Yue Denga,b,c and Alejandro A. Francoa,b,c,d* a

Laboratoire de Réactivité et Chimie des Solides (LRCS), Université de Picardie Jules Verne and CNRS, UMR 7314 – 33 rue St. Leu, 80039 Amiens, France

b

Réseau sur le Stockage Electrochimique de l'Energie (RS2E), CNRS FR3459, Amiens, France c

d

ALISTORE European Research Institute, CNRS FR3104, Amiens, France

Institut Universitaire de France, 103 Boulevard Saint-Michel, 75005 Paris, France

KEYWORDS. Energy Storage, Li-O2 Batteries, Stochastic Modeling, Kinetic Monte Carlo.

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ABSTRACT

We simulated the discharge process of Li-O2 batteries and the growth of Li2O2 thin film at mesoscale with a novel kinetic Monte Carlo model, which combined a stochastic description of mass transport and detailed elementary reaction kinetics. The simulation results show that the ordering of the Li2O2 thin film is determined by the interplay between diffusion kinetics and reaction kinetics. Due to the fast kinetics on the catalyst, the Li2O2 formed with the presence of catalyst (cat-CNF) shows a low degree of ordering and is more likely to be amorphous. Moreover, the mobility of the LiO2 ion pair, which depends largely on the nature of the electrolyte, also has some impacts on the homogeneity of the compactness of the Li2O2 thin film. These results are of high importance for the understanding of the role of catalyst and reaction kinetics in the Li-O2 batteries.

TOC GRAPHICS


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During the past decades Li-O2 batteries have been a research focus as regards energy storage devices due to their high theoretical capacity up to ~3000 Wh/kg.1,2 However, in the state of the art, the discharge capacity of a Li-O2 cell (about 500 Wh/kg3) is far behind the theoretical value and the insulating nature of the discharge product Li2O2 can be one of the main issues.4 Often the Li2O2 thin film is presumed to be crystalline and first-principle calculations indicated that the maximum distance for electron tunneling through this thin film is less than 10 nm.5 Nevertheless, Yang et al. recently found through experiments that the Li2O2 film formed during discharge could reach a thickness of ~40 nm, where carbon nanotubes incorporated with CeO2 nanoparticles are employed as the air electrode.6 The authors intended to attribute the unexpected thick Li2O2 film to the precipitation of solvated LiO2 ion pairs (LiO2(ip)) on the existing Li2O2 film, followed by the further disproportionation of LiO2. However, the morphology of Li2O2 in their experiments was not in agreement with the typical toroid morphology of Li2O2 formed through a solution-phase mechanism as reported in literature.7,8 It may imply that other factors could account for the thick Li2O2 film. A deeper investigation is lacking to provide insights into the impacts of the catalyst on the film thickness. Therefore, on the basis of a kinetic Monte Carlo (kMC) method, we developed an innovative three-dimensionally-resolved mesoscale model by combining stochastic descriptions of mass transport and the elementary reaction kinetics, to track the morphology evolution of Li2O2 formation and to investigate the impact of the catalyst.


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Figure 1. Schematic illustration of the two-step discharge mechanism in Li-O2 batteries with carbon nanofiber as air-electrode. Color code: yellow (Li+), pink (O2), purple (LiO2(ip)), orange (Li2O2). Theory and Methods The simulated system is a carbon nanofiber (CNF) embedded in a rectangular cell filled with electrolyte. For demonstration purposes, the diameter and the length of the fiber are 8 and 40 nm, while the dimensions of the cell are 30, 30 and 40 nm in height, depth and length. Catalysts nanoparticles are randomly distributed on the surface of the CNF. The nature of the catalysts could be noble metal9,10 or metal oxides,6,11 which promote the reaction kinetics without triggering side reactions in the system. There are five active species in total considered in the model, i.e., Li+, O2, solvated LiO2(ip), adsorbed LiO2(ad), and Li2O2. The two-step mechanism of Li2O2 formation is illustrated in Figure 1. The first step of discharge happens when the dissolved O2 molecule (pink) reacts with Li+ (yellow) on the electrode surface to form LiO2(ip) (purple in Figure 1, Eq.[1]), followed by the further reduction of LiO2(ip) to form Li2O2 (which can grow either directly from the CNF (orange) or on a catalyst (green)) with the presence of Li+ (Eq. [2]):

[1] [2]


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Both steps are electrochemical reactions, therefore their kinetics have a dependence on the overpotential as follows: = ° exp −

1 − − exp " #

[3]

where β is the charge transfer coefficient, η is the Butler-Volmer overpotential, ko is a pre-factor. Due to its insulating nature, the formation of Li2O2 passivates the electrode surface and lowers the reaction kinetics, thus here we approximate the reaction kinetics as a function of Li2O2 thickness with an error function as following: 1 − &' ( − )* [4] 2 where δ is the thickness of the Li2O2 film and dm is the maximum distance of the discharge $% =

reaction to be reactive. This relation was proposed in our previous work and has successfully reproduced the sudden death of a Li-O2 cell during discharge.12 After introducing the dependence on the Li2O2 thickness, the kinetics of the discharge reactions can be obtained as: = °

1 − 1 − erf ( − )* " exp − − exp − " # 2

[5]

Once δ ⩾ dm, Pt becomes zero, implying that there is no electrochemical event anymore. The value of the pre-factor ko strongly depends on the interaction between the reaction interface and the active species, especially the bonding energy or the adsorption energy. Due to a stronger bonding energy, the ko on the catalysts surface are higher than that on the carbon surface.6,13 By using noble metal (Ru and Pd) – catalyst-loaded carbon nanotubes as a cathode, Ma et al. have decreased the discharge onset overpotential by 0.2~ 0.3 V, which corresponded to an increase of ko value by 2 orders of magnitude.9 Thus, we adopted the same difference of ko value between the carbon fiber surface and the catalyst surface in the present model. Moreover, it is reported that Li2O2 could also be formed from the disproportionation reaction of LiO2(ip).14,15 However, this


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reaction has been overlooked in the model because the lifetime of LiO2(ip) (up to 20 h)16 is beyond the simulated time scale (10-5 s). To conduct the kMC simulation, the system was partitioned into cubic grids with a size of 0.5 nm, which corresponds to the size of solvated Li+ in organic electrolyte.17 Each of the active species (Li+, O2, Li2O2, LiO2(ad)) occupies one grid whereas the solvated LiO2(ip) takes two. This is due to the fact that LiO2(ip) is more likely to be a combination of solvated Li+ and O2- ions and it is relatively larger than the other species in the solvent. Catalysts are considered to occupy only one grid on the fiber surface. Besides, the solvent molecules are implicitly taken into consideration and their impacts are regarded to be mainly on the diffusion rates of the dissolved species as well as on the kinetic rates of the reactions. The electrolyte used in the model refers to DMSO with 1 M of Li+. The anion of the Li salt is not specified as its impacts are ignored in the model. The saturated concentration of O2 in the present system is about 1.6 mM according to experimental mesurement.18 The variation of the Li+ concentration, which is 2 to 4 magnitude higher than O2 concentration, is negligible during discharge. Thus, the value of Li+ concentration is kept constant. Besides, an isothermal condition is applied as the cell is assumed to be in contact with a thermal reservoir and the temperature fluctuation in the system is neglected. All the active species in the model are assumed to be mobile except for Li2O2 which tends to form a film on the electrode surface. The considered displacement events are of two types: translation and rotation. All the mobile species can move to the neighboring grids which are occupied by solvent and their corresponding kinetic rates of translation are described by a jumping frequency 12 which is obtained from the combination of the Einstein equation of random walk and the Stokes-Einstein equation (see Supporting Information):


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12 =

345&6

[6]

where 6 is the size of the grid, k is the Boltzmann constant, T is temperature, µ is the viscosity of the electrolyte and r is the hydrodynamic radius of the concerned particle. The calculated diffusion coefficients of all the mobile species are at the magnitude of 10-10 m2 s-1 which is similar to the values reported in literature.18,19 With the grid size of 0.5 nm in the model, the jumping frequency is set at the magnitude of 1010 s-1 according to Eq.[6]. LiO2(ip) is the only species for which the rotation is considered as an event of kMC, as it occupies two joint grids and the related rotation frequency is estimated to be at the same magnitude as that of the jumping frequency. To improve the calculation efficiency, the displacement of Li+ was described by collective motion as an alternative approach to individual jumping (see Supporting Information). The symbols and values of parameters used in the simulations are summarized in Table 1. Table 1. List of symbols and parameters values used in the model. Symbol

Parameter name

Unit

Jump frequency of Li+

s-1

Jump frequency of O2

s-1

Jump frequency of LiO2(ip)

s-1

Rotation frequency of LiO2(ip)

s-1

Kinetic constant pre-factor of carbon fiber

s-1

Kinetic constant pre-factor of defects

s-1

Saturated concentration of O2 from Ref.14

mol L-1

1.6 × 10 M

Concentration of Li+

mol L-1

1

F

Faraday constant

C mol-1

96500

R

Universal gas constant

J mol-1 K-1

8.314

78,:;< 78,AB

78,:;AB

7C,:;AB DE

DEF

GHIJ,AB G:;

Compactness of the Lithium Peroxide Thin Film ... - ACS Publications

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