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Discharge Performance of Li-O Batteries Using a Multiscale Modeling Approach Jie Bao, Wu Xu, Priyanka Bhattacharya, Mark L. Stewart, Ji-Guang Zhang, and Wenxiao Pan J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b01441 • Publication Date (Web): 10 Jun 2015 Downloaded from http://pubs.acs.org on June 14, 2015

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The Journal of Physical Chemistry

Discharge Performance of Li-O2 Batteries Using a Multiscale Modeling Approach Jie Bao‡, Wu Xu‡, Priyanka Bhattacharya‡, Mark Stewart‡, Ji-Guang Zhang*‡, and Wenxiao Pan*† †

Fundamental and Computational Sciences Directorate, Pacific Northwest National Laboratory,

Richland, Washington 99352, United States ‡

Energy and Environment Directorate, Pacific Northwest National Laboratory, Richland,

Washington 99352, United States

ABSTRACT: To study the discharge performance of Li-O2 batteries, we propose a multiscale modeling framework that links models in an upscaling fashion from nanoscale to mesoscale and finally to device scale. We have effectively reconstructed the microstructures of a Li-O2 air electrode in silico, conserving the porosity, surface-to-volume ratio, and pore size distribution of the real air electrode structure. The mechanism of rate-dependent morphology of Li2O2 growth is incorporated into the mesoscale model. The correlation between the activesurface-to-volume ratio and averaged Li2O2 concentration is derived to link different scales. The proposed approach’s accuracy is first demonstrated by comparing the predicted discharge curves of Li-O2 batteries with experimental results at the high current density. Next, the validated modeling approach effectively captures the significant improvement in discharge capacity due to

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the formation of Li2O2 particles. Finally, it predicts the discharge capacities of Li-O2 batteries with different air electrode microstructure designs and operating conditions. KEYWORDS: Energy storage, multiscale modeling, porous air electrode, Li-O2 battery. 1. INTRODUCTION Rechargeable lithium-oxygen (Li-O2) batteries have been considered a promising battery technology to provide energy storage systems for next-generation electric vehicles, primarily because of their high theoretical specific energy that is about 5-10 times higher than that of stateof-the-art Li-ion batteries. However, development of rechargeable Li-O2 batteries is limited by many barriers.1 For non-aqueous Li-O2 batteries, one major challenge in designing air electrodes is the blocking of O2 and Li+ pathways by the precipitation of insoluble lithium peroxide (Li2O2) during battery discharge, thus limiting full utilization of the air electrode.1-4 In conjunction with experimental works,5-9 modeling offers useful insights into and provides quantitative understanding of the morphology and microstructure of the air electrode developed during the discharge process, which, in turn, can lead to a pathway that circumvents the drawbacks of current air electrode designs and improves battery performance. Several modeling studies have predicted the discharge performance of Li-O2 batteries via the continuum device-scale modeling approach.10-11 However, details regarding the real porous structure of the air electrode at finer scales were absent, limiting the reliability and accuracy of those models. Some improvements have been made by incorporating the actual pore size distribution into the device-scale model.4, 12-15

For example, Nimon et al. experimentally measured the pore size distributions both before

and at a few stages of discharge and input them into their device-scale model.12 Meanwhile, Xue et al. employed a bimodal log-normal function to mathematically describe the actual pore size distribution.13 In those works,4, 12-15 the air electrode structure was approximated by simplified


2

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pore geometries, such as spherical or cylindrical pores. Moreover, most past modeling studies, except for a recent work by Xue et al.,15 do not include both the surface-limited reaction and the solution-phase reaction mechanisms of Li2O2 growth. The surface-limited reaction requires surface adsorption of a thin Li2O2 film grown to cover the active electrode surface.11, 13, 16 Here, the electron tunneling limit through the film thickness (5‒10 nm) should be considered because of electrical passivation caused by the insulating nature of Li2O2.13,

16-17

In the solution-phase

reaction, Li2O2 is crystallized from the electrolyte solution, and particle deposition and growth of Li2O2 then occur on the electrode surface.15, 18 Likewise, several groups recently reported through experiments that the morphology of Li2O2 in a Li-O2 battery strongly depends on the discharge current density.19-21 In this work, we propose a multiscale modeling framework, where the mesoscale (10‒1,000 nm) and nanoscale (0.5‒100 nm) features of a real air electrode structure are captured by effectively reconstructing its porous structure in silico. Furthermore, our framework addresses the following mechanisms: the diffusion-limited transport of O2 across the porous structure of the air electrode, varying air electrode structures with different pore size distributions and surface-to-volume ratios, and the rate-dependent morphology of Li2O2 growth. Hence, we are able to predict the discharge performance of Li-O2 batteries based on the reconstructed electrode porous structure at different discharge current densities with varying air electrode microstructure designs. 2. MODELING METHODS 2.1 Governing Equations. Following the work by Xue et al.,13 the evolution of O2 concentration and Li2O2 concentration in an air electrode is governed by:


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∇ − = ∇ ∙

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and

= .

(1)

Here, and are the concentrations of O2 and Li2O2, respectively. is the faradaic current density. is the time-dependent active-surface-to-volume ratio of the air electrode. = 2 is the number of electrons involved in the reaction: 2Li + 2e! + O# → Li# O# . % is the Faraday is the effective diffusion coefficient of O2 in a porous media that can be constant, and

calculated from: /

= &'1 − ) , -. ,

*+

(2)

where is the diffusion coefficient of O2 in electrolyte; 0 and 1 denote the molar mass and density of Li2O2, respectively; - is the initial local porosity; and 2 is a parameter that depends on the tortuosity of the porous structure. in Eq. (1) is related to the electrochemical reaction forming Li2O2 and can be calculated from the Butler-Volmer equation:22 4!5

= %3 6exp 9−

5: ;
4!5?: ;
c!d? #

@ I .

(5)

In Eq. (6), I is the initial active-surface-to-volume ratio, erf is the error function, and g denotes )

the Li2O2 thickness that can be calculated from g = hI

+

di. Previous studies have

found that particle growth of Li2O2 is favored when the discharge current density is sufficiently low, if there is a small amount (between 30 ppm and 4000 ppm) of water in electrolyte,19, 21 or the donor-number of electrolyte is high.18 For example, Adams et al.’s experimental work19 shows that the Li2O2 morphology is toroidal at currents below 0.025 mA/cm2, while thin film growth dominates at currents above 0.04 mA/cm2. In recent theoretical work, Horstmann et al. incorporated a random term into the free surface energy calculation to relate the growth pattern with the current density in a 1D surface model based on phase-field theory.39 In our model, particle growth of Li2O2 is captured in the 3D open pores of the reconstructed mesoscale structure. Specifically, the void grids adjacent to solid grids are randomly selected as nucleation points for particles to grow at a given probability. Once

) +

= 1 in the selected void

grid, which indicates Li2O2 has filled up that grid, its neighboring void grids start to generate Li2O2. This process is not affected by the electron tunneling limit. We must point out that the void grid described herein is a numerical discretization of the open pores, instead of the pore itself, that cannot be completely filled. Moreover, the experimental measurement of the pore size distribution for KB carbon electrode shows a high peak in the range of 2‒5 nm.6 Such small pores are difficult to visualize in the SEM


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image (Figure 2 (b)), and they are not captured in the reconstructed mesoscale structure (Figure 2 (a) or Figure 3 (a) and (b)) due to the resolution. Therefore, to incorporate Li2O2 growth occurring in these small pores into the mesoscale model, we consider a finer-scale (i.e., nanoscale) structure to exist in the solid volumes (Figure 3 (a)) of the reconstructed mesoscale structure. Hence, in the mesoscale model, Eqs. (1)‒(3) also are numerically solved on the solid grids to model the O2 transport and Li2O2 growth in the nanopores. This requires the effective ) and the active-surface-to-volume ratio () on the solid grids to diffusion coefficient of O2 (

be calculated from the nanoscale model. 2.5 Nanoscale Model. We first construct a nanoscale porous structure (see Figure 4 (a), top) using the particlepacking method according to the experimentally measured pore size distribution.6 Due to the pore size limitation, only thin film growth of Li2O2 is allowed in the nanopores. With Li2O2 growth on the pore surfaces, the active surface areas decrease as shown in Figure 4 (a) (bottom). Provided that varying thicknesses of Li2O2 cover the pore surfaces in the constructed nanoscale structure, the responsive curve of the active surface area is calculated as plotted in Figure 4 (b). The constitutive function obtained then is used to calculate in Eq. (1) in the mesoscale model for the solid grids with the porosity (-) in Eq. (7) equal to that of the nanoscale structure.


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(a)

(b)

Figure 4. (a): Cross-sectional images of the constructed nanoscale structure before discharge (top) and after 1-nm thin film growth of Li2O2 (bottom). (b): The calculated responsive curve of the active-surface percentage as a function of the thickness of Li2O2. 2.6 Multiscale Modeling Framework. The diagram shown in Figure 5 summarizes our multiscale modeling framework with different scales linked by an upscaling procedure. Specifically, the nanoscale model calculates the correlation between the active-surface percentage and the Li2O2 thin film thickness in the nanoscale structure, which is passed along to the mesoscale model to calculate the constitutive relation of as a function of the averaged Li2O2 concentration in the mesoscale structure. The result is then put into the device-scale model to calculate the battery’s discharge curves.


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Figure 5. Diagram of the developed multiscale modeling framework. To investigate the impact of the air electrode microstructure designs on the discharge performance of Li-O2 batteries, taking the constructed microstructure as a model for the real air electrode, we closely examined three different case structures with the following features: 1) (nominal case) the porosity of 0.887, surface-to-volume ratio of 3.90 W 10V cm!4, and pore sizes centered around 4 nm and 100 nm; 2) the porosity of 0.875, surface-to-volume ratio of 1.63 W 10V cm!4 , and pore sizes centered around 2 nm and 400 nm; and 3) the porosity of 0.879, surface-to-volume ratio of 2.85 W 10V cm!4 , and pore sizes centered around 30 nm. The features incorporate all of the pores and surfaces in both the mesoscale and nanoscale structures. Here, the nominal structure corresponds to the KB air electrode used in the experiments by Xu et al.5, 40 with the same porosity, surface-to-volume ratio and pore size distribution. Figure 6 compares the pore size distributions of the three constructed electrode structures and the KB electrode used in the experiments.5, 40


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Figure 6. Pore size distributions of the three air electrode structures. Case 1: pore sizes centered around 4 nm and 100 nm; Case 2: pore sizes centered around 2 nm and 400 nm; Case 3: pore sizes centered around 30 nm. 3. RESULTS AND DISCUSSION 3.1 Constitutive Relation. The mesoscale model yields the constitutive relation for the active-surface-to-volume ratio () as a function of the average concentration of Li2O2. The constitutive relation describes the variation of total active surfaces with the growth of Li2O2 during discharge and also predicts the total amount of Li2O2 to be generated after discharge. Figure 7 (a) shows the contours of Li2O2 concentration on a cross section (at y=1μm) of the mesoscale structure in Case 1 after partial discharge of 10%, 50%, and 90%, respectively, at a high current density (0.05 mA/cm2) without particle growth. For comparison, the same cross section of the clean electrode before discharge is also shown. During discharge, Li2O2 thin film (less than 10 nm thick) is gradually generated on the mesopore surfaces, as well as inside the solid volumes with nanopores, which are illustrated in Figure 7 (a) by the contour color of Li2O2 concentration gradually changing from blue to green from 10% to 90% partial discharge. Figure


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7 (b) depicts the evolution of Li2O2 concentration at a low (0.005 mA/cm2) current density with particles generated during discharge. Different from Figure 7 (a), large particles start growing in mesopores at nucleation points (light green dots on the slice of 10% partial discharge in Figure 7 (b)) and then gradually increase in size during discharge (red dots on the slice of 50% partial discharge and red patches on the slice of 90% partial discharge in Figure 7 (b)). Note that the exact particle shapes, such as toroidal,19-21, 41-43 are not addressed in this work. However, given the exact anisotropic surface energies to control the shape of particles, it can be incorporated into the mesoscale model in the future by coupling the phase-field equations.

(a)

(b)

Figure 7. Contours of Li2O2 concentration on the cross section at y=1 μm of the mesoscale structure in Case 1, varying at different discharge stages. During discharge, Li2O2 is generated inside the solid volumes with nanopores, as well as on the mesopore surfaces (a) without particle growth or (b) with particle growth.


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Figure 8 presents the calculated responsive curves of from the mesoscale model as a function of averaged Li2O2 concentration (Figure 8 (a)) or effective Li2O2 thickness (Figure 8 (b)). The effective Li2O2 thickness provides an alternative scale for averaged Li2O2 concentration, and it is calculated from dividing the Li2O2 volume (G =

) +

) by the

initial surface areas of each structure. As shown in Figure 8, the obtained constitutive relation for is compared among the three different structures at a low current density (0.005 mA/cm2) with particle growth and a high current density (0.05 mA/cm2) without particle growth. Notably, in our mesoscale model, the surfaces of particles generated during discharge are counted into the total active surfaces. Thus, particle growth of Li2O2 at the low current density is found to create much more active surfaces.

(a)

(b)

Figure 8. The calculated responsive curves of the active-surface-to-volume ratio as a function of (a) averaged Li2O2 concentration or (b) effective Li2O2 thickness at a low current density (0.005 mA/cm2) with particle growth and a high current density (0.05 mA/cm2) without particle growth on the three different air electrode structures.


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In addition, the structure of Case 3—with a high pore size distribution around 30 nm—is optimal for the full use of pore volumes to deposit Li2O2 thin film.16 Thus, at the high current density, Case 3 produces the maximum amount of Li2O2 among the three cases, although it has a slightly smaller initial surface-to-volume ratio than Case 1. In contrast, Case 2 has the smallest initial surface-to-volume ratio. The large pores (>200 nm) cannot be fully used for thin film growth of Li2O2 at the high current density because of the electron tunneling limit. Hence, the least amount of Li2O2 is produced in Case 2 after active surfaces are completely depleted by the passive Li2O2 film. However, particle growth of Li2O2 at the low current density facilitates larger pores being better utilized. All three structures have similar porosities and total pore volumes. As such, no significant difference is expected among the three structures in the total amount of Li2O2 generated after discharge when particle growth occurs. Moreover, a sensitivity analysis concludes that the constitutive relation of (Figure 8) obtained in the mesoscale model is valid for a range of discharge current densities (0.001‒0.2 mA/cm2) and O2 concentrations ( ) specified in the boundary conditions of the mesoscale model (5 W 10!m − 5 W 10!V mol/cm3), shown in Figure 9 (a) and (b), respectively.

(a)

(b)


16

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Figure 9. Sensitivity analysis for the constitutive relation of as a function of averaged Li2O2 concentration obtained in the mesoscale model using the Case 1 (nominal case) air electrode structure. (a): Responsive curves calculated at different discharge current densities with and without particle growth of Li2O2. (b): Responsive curves calculated at different O2 concentrations ( ) specified in the boundary conditions without particle growth of Li2O2. 3.2 Discharge Capacity. Given the constitutive relation of calculated from the mesoscale model, Eqs. (1)‒(3) are closed and numerically solved using the implicit finite volume scheme in the 1D device-scale model, and hence the battery’s discharge performance can be predicted. In particular, the calculated discharge curves are compared with experimental measurements5, density of 0.05 mA/cm2. For consistency with the experiments,5,

40

40

at the current

the nominal air electrode

structure (Case 1) is used in this comparison. We also consider that the air electrode is exposed to pure O2 at one atmospheric (1 atm) pressure. Figure 10 (a) shows very good agreement for two different electrolyte solvents, i.e., dimethyl sulfoxide (DMSO) and tetraethylene glycol dimethyl ether (TEGDME). Although the diffusion coefficient of O2 in DMSO is larger than that in TEGDME, the latter has a larger solubility of O2, which yields a higher discharge capacity for it. In addition, there are two small voltage drops on the calculated discharge curves in Figure 10 (a). The first one occurs at about 200 mAh/g, stemming from a significant reduction of O2 transport into the air electrode’s inner regions. The variation of cell voltage is determined mainly by the changes of the summation of the product of active-surface-to-volume ratio and O2 concentration over the whole air electrode, i.e., Φ = ∭ M dG. Figure 10 (b) shows the calculated O2 concentration distribution for DMSO solvent along the air electrode thickness (L) from the O2 inlet. We find that after 10% discharge, O2 can only transport into about half of the air electrode


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thickness, which implies that Φ decreases to about 15% of its initial value, leading to an observable increase in the absolute overpotential (|B|). A similar phenomenon was coined as “steady-state condition” by Read et al.44, who used it to describe the trade-off between O2 diffusion and consumption. The second small voltage drop takes place after about 80% discharge, which results from a significant decrease of the active-surface-to-volume ratio in the late stage of discharge (dash lines in Figure 8). Some previous experimental studies6,

40, 44

observed similar multiple plateaus in their discharge curves but did not explain the origin of such voltage drops. Our findings from simulations suggest a possible explanation and provide insights in understanding the underlying mechanisms for the observed phenomena.

(a)

(b)

Figure 10. (a) The calculated discharge curves for the nominal air electrode structure (Case 1) compared with the experimental data in different solvents at 0.05 mA/cm2 and 1 atm pure O2. (b) The calculated O2 concentration distribution along the thickness (L) of air electrode in DMSO solvent for 0.05 mA/cm2 at different discharge stages.


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After the model was validated, we compared the discharge curves for different air electrode structures in DMSO solvent at both the high (0.05 mA/cm2) and low (0.005 and 0.01 mA/cm2) current densities. We found that the formation of Li2O2 particles at the low current densities results in significant improvements in discharge capacity, which agrees with previous reports.19, 21

Our model satisfactorily captures this mechanism and provides quantitative comparisons.

Specifically, as illustrated in Figure 11 (a), the discharge capacity calculated with particle growth of Li2O2 at 0.005 mA/cm2 is more than six times as high as that without particle growth of Li2O2 at 0.05 mA/cm2, and similar trends were reported in experimental observations.19

(a)

(b)

Figure 11. (a): The calculated discharge curves for three different air electrode structures in DMSO solvent at 1 atm pure O2 and three different current densities: 0.05 mA/cm2 without particle growth of Li2O2 (dashed line), 0.01 (dash-dot line), and 0.005 mA/cm2 with particle growth of Li2O2 (solid line). (b): The calculated O2 concentration distribution along the thickness (L) of air electrode with the nominal structure (Case 1) at different discharge stages. For the low discharge current densities, O2 can transport into almost 100% thickness of the air electrode before partial discharge of 90%, depicted in Figure 11 (b). Moreover, the active-


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surface-to-volume ratio increases beyond its initial value with particle growth at the low current densities (shown in Figure 8, solid lines). This implies that Φ = ∭ dG decreases very slowly or even increases slightly during discharge. Therefore, the overpotential and consequent cell voltage are found to only slightly vary before 90% partial discharge, especially for 0.005 mA/cm2. The proposed model captures the cell voltage variation caused by the evolution of active-surface areas and O2 concentration distribution during discharge. Figure 11 (a) also demonstrates the impact of different air electrode microstructure designs on discharge capacity. At the high current density, Case 3 with pores centered around 30 nm affords optimal use of the pore volumes, which leads to the highest Li2O2 production in the mesoscale. However, it lacks larger pores that facilitate faster O2 transport in the device scale. In Case 1 with pores centered around 4 nm and 100 nm, the balance between the pore volume utilization in the mesoscale and O2 transport in the device scale offers an only slightly lower capacity than Case 3 (black and blue dashed lines in Figure 11 (a)). Conversely, although the large pores (>200 nm) in Case 2 allow for faster O2 transport in the device scale, the effect is overridden by its smallest initial surface-to-volume ratio and poorest use of the large pores for thin film growth of Li2O2, hence resulting in the lowest discharge capacity among the three cases (red dashed line in Figure 11 (a)). These findings detailing the impact of different air electrode structures on discharge capacity are consistent with a previously reported study.16 It concluded experimentally that for discharge involving only thin film growth of Li2O2, the air electrodes with a predominant pore size of 20−40 nm exhibited the highest discharge capacities. At low current densities, O2 transport in the device scale is less important in limiting the discharge capacity until the pore volumes significantly decrease at later discharge stages. When it occurs, the averaged Li2O2 concentration can be as high as 0.039 mol/cm3 near the O2 inlet.


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Around this concentration value, the order of cases in terms of the active-surface-to-volume ratio from largest to smallest is Case 2> Case 1> Case 3 (shown in Figure 8 (a)). This high concentration of Li2O2 first appears near the O2 inlet of the air electrode. A larger active-surfaceto-volume ratio leads to a higher local reaction rate and, thereby, more Li2O2 accumulation near the O2 inlet, which hinders O2 propagation from the inlet to the battery interior regions and limits discharge capacity. In consequence, the order of cases in terms of the discharge capacity at the low current densities is Case 2< Case 1< Case 3 as shown in Figure 11 (a) (dash-dot and solid lines). Thus, the microstructure design in Case 3 outperforms the other two cases and provides the highest discharge capacity at the low current densities with particle growth of Li2O2. Therefore, our multiscale modeling framework offers quantitative prediction of the relationship between the discharge performance and microstructural details of the air electrode for Li-O2 batteries. Our model indicates that pore sizes in the air electrode structure and discharge current densities are closely correlated for a Li-O2 battery to deliver high capacity. A porous air electrode with pore sizes centered around 30 nm favors the low current density (0.005 mA/cm2) for achieving higher capacity (i.e., ~8300 mAh/g carbon). At the high current density (0.05 mA/cm2), this electrode leads to a slightly higher capacity (i.e., ~1300 mAh/g carbon) than the one with pore sizes centered around 4 nm and 100 nm. The effect of O2 pressure on the discharge capacity of Li-O2 batteries also is investigated. Previous experimental studies have reported that an increase in O2 pressure increases O2 solubility in electrolyte following Henry’s law,45-46 thus enhancing the discharge capacity.44 Figure 12 shows the calculated discharge curves when a Li-O2 battery with the Case 1 air electrode structure is discharged in a pure O2 pressure of 1 or 2 atm. The battery uses DMSO solvent and is discharged at 0.005 and 0.01 mA/cm2, respectively, with the formation of Li2O2


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particles. The O2 saturated concentration at 2 atm was calculated from Henry’s law given its value at 1 atm. A higher O2 pressure present in the O2 inlet greatly enhances the discharge capacity of a Li-O2 battery, which increases from 8300 to 11700 mAh/g carbon at 0.005 mA/cm2 and from 4960 to 8526 mAh/g carbon at 0.01 mA/cm2 when the O2 pressure increases from 1 to 2 atm.

Figure 12. The calculated discharge curves for DMSO solvent at 0.005 and 0.01 mA/cm2, respectively, in 1 or 2 atm pure O2 with particle growth of Li2O2 using the Case 1 air electrode structure. Moreover, an increase in temperature from 248 K to 323 K slightly decreases the O2 solubility in organic solvents by about 5%.47 However, an increase in temperature can significantly increase O2 diffusivity in electrolytes. For example, it has been reported that the O2 diffusivity

in

TEGDME

solvent

follows

the

relationship

to

temperature

as:

< = #mpq r−0.0185>s − 298? + 1t!4.48 Here, #mpq is the O2 diffusivity at 298 K, and < is the O2 diffusivity at temperature s. Figure 13 shows the calculated discharge curves for TEGDME solvent at four different temperatures: 283, 298, 323, and 343 K, respectively. The discharge capacity is significantly enhanced with increasing temperature because of the increase in O2 diffusivity, which is consistent with experimental observations.16, 48 Previous studies49 also


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have reported that high temperature might favor charge transport through Li2O2, especially at low current densities, and yield high discharge capacity. Although this mechanism is not addressed in the present work, it can be incorporated into our mesoscale model in the future by coupling the appropriate governing equations for charge transport through Li2O2.

Figure 13. The calculated discharge curves for TEGDME solvent at different temperatures and 0.01 mA/cm2 in 1 atm pure O2 with particle growth of Li2O2 using the Case 1 air electrode structure. Finally, in this proposed model, Li+ is assumed to be adequate and to transport much faster than O2. Hence, consumption and transport of Li+ in the air electrode have no effects on the predicted discharge capacity. However, a lower Li salt concentration can significantly increase O2 solubility and diffusivity in some electrolytes.44 The present model can examine the effect of Li+ concentration on discharge capacity through corresponding variations in O2 solubility and diffusivity. For example, assuming an increase in O2 solubility and diffusivity caused by a decrease of Li+ concentration, the calculated discharge capacity increases according to our model. Whereas, as noted by others,15 Li+ in air electrode may be depleted at very high discharge rates, which will result in an overestimate of discharge capacity by the present model. We will further investigate Li+ transport and its effect on discharge capacity in future work.


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4. CONCLUSION In conclusion, we present a multiscale modeling framework that predicts the discharge performance of Li-O2 batteries by incorporating the nanoscale and mesoscale details of the air electrode structure and the reaction mechanisms occurring at those scales. In particular, the real air electrode microstructure of a Li-O2 battery was modeled and reconstructed via the particlepacking method. With that, we directly simulated the rate-dependent morphology of Li2O2 growth on 3D pore surfaces, which are assumed to be a close approximation of the real air electrode pore surfaces. Moreover, derivation of the constitutive relations for the active-surfaceto-volume ratio allows for building the seamless link of scales all the way from nanoscale to device scale. A good agreement was found in the discharge behaviors for different solvents between simulations and experiments at the high current density. Also, the significant improvement in discharge capacity due to the formation of Li2O2 particles was effectively captured. In addition, the proposed modeling approach not only provides quantitative understanding about the mechanisms that may affect the discharge performance of Li-O2 batteries but also offers reliable guidance to determine optimal air electrode microstructure designs with pre-set power rating targets. Furthermore, the established modeling framework can be extended to include other mechanisms that may affect the discharge performance of Li-O2 batteries and be applied to other metal-air batteries, with metals such as Zn, Na, and Mg, as well as be adapted to investigate other new energy storage techniques and materials. AUTHOR INFORMATION Corresponding Authors * Wenxiao Pan, PO Box 999, MSIN K7-90, Richland, WA, 99352, USA, 509-375-6686, [email protected].


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* Ji-Guang Zhang, PO Box 999, MSIN K2-44, Richland, WA 99352, USA, 509-372-6515, [email protected]. Notes The authors declare no competing financial interests. ACKNOWLEDGMENTS W. Pan and J. Bao were supported by the Applied Mathematics Program within the U.S. Department of Energy (DOE), Office of Advanced Scientific Computing Research (ASCR) as part of the Collaboratory on Mathematics for Mesoscopic Modeling of Materials (CM4). W. Xu and J.-G. Zhang acknowledge financial support from the Assistant Secretary of DOE’s Energy Efficiency and Renewable Energy, Office of Vehicle Technology. P. Bhattacharya is grateful for support from a Linus Pauling Distinguished Postdoctoral Fellowship at Pacific Northwest National Laboratory (PNNL). PNNL is operated by Battelle for the DOE under Contract DEAC05-76RL01830. The finite volume code was adapted from the massive parallel computational fluid dynamics (CFD) program, ParaFlow, developed and provided by David Rector and Mark Stewart. W. Pan additionally thanks Xiaoliang Wei and Eduard Nasybulin for their valuable advice and helpful discussions about this work. SUPPORTING INFORMATION AVAILABLE The particle-packing method, numerical details, and model parameters discussed in this work are fully described in the Supporting Information. This information is available free of charge via the Internet at http://pubs.acs.org.


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