Prospect of Thermal Shock Induced Healing of Lithium Dendrite - ACS

Subscriber access provided by ALBRIGHT COLLEGE

Letter

Prospect of Thermal Shock Induced Healing of Lithium Dendrite Zijian Hong, and Venkatasubramanian Viswanathan ACS Energy Lett., Just Accepted Manuscript • DOI: 10.1021/acsenergylett.9b00433 • Publication Date (Web): 29 Mar 2019 Downloaded from http://pubs.acs.org on March 29, 2019

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Energy Letters

Prospect of Thermal Shock Induced Healing of Lithium Dendrite Zijian Hong and Venkatasubramanian Viswanathan∗ Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA E-mail: [email protected] Abstract Dendritic growth plagues the development of rechargeable lithium metal anodes. Recently, it has been reported that (Science 359, 15131516 (2018)) self-heating of the cell provides a mitigation strategy for suppressing dendrites. In order to study this phenomenon, we extend our recently developed nonlinear phase-field model to incorporate an energy balance equation allowing a full thermally-coupled electrodeposition model using the open-source software package MOOSE. In this work, we consider the interplay between ionic transport and electrochemical reaction rate as a function of temperature and explore the possibility of using thermal shock induced dendrite suppression. We discover that depending on the electrochemical reaction barrier and transport barrier, self-heating could accelerate (larger reaction barrier) or decelerate (larger diffusion barrier) dendrite formation. Given that the electrolyte constituents can be used to tune both barriers, this study could provide an important avenue to exploit the self-heating effect favorably through electrolyte engineering.

1

ACS Paragon Plus Environment

ACS Energy Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

There are increasing demands for high capacity, high energy density electrodes for applications of lithium batteries in heavy-duty transportation and aviation. 1–4 Among the many options, lithium metal anodes is a promising approach to improve the specific energy of the state-of-art battery systems. 5 However, despite decades-long effort, suppressing dendrites remains a challenge and numerous approaches have been proposed. Surface roughening, 6 mechanical stresses, 7–12 and plastic deformation of lithium 13,14 have been proposed as viable strategies for suppressing dendrites. Recently, Li et al., 15 showed that increasing the plating current density and thereby, increasing the self-heating of the cell due to parastic heat losses may provide another mitigation strategy to suppressing dendrites. High current/rate performance of lithium-metal batteries is a critical requirement for fast charging. 16,17 Some literature reports find support for shorter dendrites at higher rates, 18–20 while other reports suggest the opposite trend. 21–25 Similarly, increasing of temperature has shown to lead to the growth of longer dendrites or poor performance, 18,26–28 while others report an improved performance at higher temperature. 29–33 These studies indicate that the high current/rate and high temperature properties of the lithium battery is rather complicated which raises two key questions: (1) how to analyze the rate performance of a lithium-metal based battery (2) under what conditions will lithium metal anodes be stable against high rate cycling? Increase in the temperature of the cell leads to numerous changes that all have an effect on the electrodeposition process: increases in (i) diffusion coefficient of lithium ions in the electrolyte, (ii) electrochemical reaction rate and (iii) surface diffusion. It is worth highlighting that the electrochemical reaction barrier can be modified through tuning the SEI layer, desolvation energy of lithium ions in the electrolyte phase, 34–36 while the diffusion barrier can be modified by additives in the electrolyte. 37,38 In order to explore these competing effects and their effect on electrodeposition, a thermally coupled electrodeposition model is critical to model the thermal stability and the rate performance of lithium metal anodes. Phase-field simulation has emerged as a critical tool to the understanding of dendrite growth kinetics and underlying physics in lithium-ion batteries. 39–44 In an earlier work, we developed a hybrid grand-potential based nonlinear phase field model 41,45–47 within the fully open-source MOOSE (Multiphysics Object-Oriented Simulation Environment) framework. 48,49 This reaction-transport model did not account for thermal effects, as it did not solve an energy balance equation. A recent study has coupled the thermal generation and transport to the existing phase-field model, 50 however, it has ignored a key parameter (i.e., the electrochemical reaction barrier) that is critical to the understanding and designing of high rate/temperature stable lithium metal-based batteries. In order to fully reveal the thermal shock induced healing mechanism, we extend our phase-field model to build a thermally-coupled phase-field model that now couples an energy balance equation along with the reaction-transport model. Based on this model, we analyze the lithium electrodeposition kinetics under different applied overpotential and electrochemical reaction barrier. We identify that the electrochemical reaction barrier is a key parameter in determining the high rate/temperature dendrite growth mechanism. With a small electrochemical reaction barrier, the self-heating induces large increase in lithium ion transport which will suppress dendrite growth, leading to stable electrodeposition with small, compact filaments. While a large electrochemical reaction barrier will favor the growth of long dendrites due to largely increased electrodeposition 2


Page 2 of 17

Page 3 of 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Energy Letters

rate. It is further shown that under high overpotential with relatively large electrochemical reaction barrier, “voids” can form during the electrodeposition process owing to the increase in both diffusivity and reactivity under increased temperature by self-heating, which could deteriorate the mechanical strength of the electrode and hence the battery performance. As we did in our earlier work and inspired by the feedback we received from the community, we make all the input files freely available to spur on follow-up studies and provide a pathway towards reproducible science in phase-field modeling. The detailed phase-field equations are taken from the previous literature, 47 which are given in the supplementary information. The local temperature distribution can be obtained by solving the energy balance equation: 50 Cp ρ

∂T = ∇κ∇T + Q ∂t

(1)

Where Cp , ρ, t and κ are the effective specific heat capacity, mass density, evolution time and effective thermal conductivity, which is related to the properties of the electrode and electrolyte phases through the partition function h(ξ), where ξ is the order parameter. The heat generation rate Q has mainly two contributions (the Ohmic heating and overpotential heating) if the entropy change during the reaction is ignored, given by, Q = QOhmic + Qop

(2)

The Ohmic heating can be expressed as: 51 QOhmic = σ(∇φ)2

(3)

while the overpotential heating can be written by: Qop = as

∂q φ ∂t

(4)

Here as is an empirical factor to scale the theoretical current density to the experimental current density to account for the fact that due to the limitation in the computational length scale, the calculated current density is larger than the experimental value. The charge flow rate can be estimated by: ∂q s ∂ξ = nF Cm (5) ∂t ∂t The equations above are solved using the open source MOOSE framework. All the parameters are similar to the previous report 47 with two major changes: first, the diffusion coefficient is dependent on the lithium ion concentration through an empirical exponential relationship, i.e., D0 = D00 exp(−k cc0 +k), with the prefactor k fitted to the experimental data, D0 is the diffusion coefficient at 300K, while D00 is the standard diffusion coefficient for 1 M electrolyte at 300 K, c and c0 are the local ion concentration and standard ion concentration; second, the exchange current density is increased by two orders of magnitude to match the experimental measured value. 52 It is shown from Figure S1 that the threshold dendrite nucleation overpotential decreases monotonically with the natural log of the exchange current density. This can be understood since the Bulter-Volmer type kinetic rate in Equation 1 is 3



directly related to the exponential of the overpotential while only linearly with the exchange current density. A more realistic threshold overpotential (∼50 mV) can be obtained by using the experimentally fitted exchange current density. The adaptive time step with a cutoff timestep interval of 0.002 s is used. The initial temperature is set as 300 K. The convection and radiation boundary conditions 50 are set at the left and right boundaries, i.e., κ(∇T )n = h(300 − T ) + R σR (3004 − T 4 ). n is the normal of the boundaries, h is the heat convection coefficient, R and σR are the emissivity and the Stefan-Boltzmann constant, respectively. This boundary condition specifies the heat exchange of the system with the surrounding (assuming a room temperature of 300 K), including both heat convection and heat radiation. The simulation parameters are listed in supplementary table. We start from the case where both the diffusion and electrochemical reaction rate are independent of temperature (i.e., both the diffusion barrier and the electrochemical reaction barrier are set to zero, referred as “barrier-less” case in the discussions below), the kinetic evolution results are shown in Figure 1. Figure 1(a)-(c) shows the dendrite growth kinetics under a relatively high overpotential of ∼200 mV, it can be seen that the dendrites nucleated after an average electrodeposition thickness of 45 µm. These nuclei grow rapidly upon longer time, first into compact filament, then into several needle-like long dendrites. The dendrite growth mechanism is similar to previous report, 47 which is completely due to the fact that the average reaction rate is larger than the transport rate, while the local uphill diffusion could lead to the drain of the local ion concentration in the concave regions. The formation of long dendrites will shorten the transport pathway which will further favor the growth of dendrites. The morphology evolutions under different overpotentials are given in Figure 1(d)-(f). It can be seen that generally, with larger overpotential, the dendrite is longer in length. This can be understood since the higher overpotential, the larger the growth velocity which leads to a higher imbalance of the reaction/transport ratio, leading to a depletion of lithium ions at the electrode/electrolyte interface. Interestingly, the vertical size of the dendrites decreases with increasing overpotential, which is consistent with previous experimental observations. 53 At higher overpotentials, the critical nuclei size will be smaller according to the nucleation theory since the driving force for nucleation is larger, which tends to decrease the vertical size. Having verified the consistency of the dendrite growth model, we now proceed to understand the influence of the self-heating on the dendrite growth kinetics under high overpotential (e.g. 200 mV), as depicted in Figure 2. The morphological evolution of the metal electrode with a diffusion barrier of 0.15 eV and a kinetic reaction barrier of 0 eV is shown in Figure 2(a)-(c). As compared to the “barrier-less” case shown in the previous figure, the onset dendrite formation time is greatly delayed, along with a spatially homogeneous interfacial growth speed. Even after an average deposition thickness of 80 µm, electrodeposition is compact and nuclei are small in size, indicating a great suppression for the dendrite growth. In order to reveal the underlying physics of the phenomenon, the average temperature is plotted versus the average deposition thickness in Figure 2(d). The average deposition thickness is directly related to the total current that has passed through the system. It can be seen that at an overpotential of 200 mV, the temperature can reach as high as ∼350 K, the 50 K temperature increase is consistent with the estimation from a previous report. 15 With this increase in temperature, the lithium ion mobility (calculated as the diffusivity times the 4


Page 4 of 17

Page 5 of 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Energy Letters

Figure 1: Dendrite growth kinetics for the “barrier-less” case. (a)-(c) Morphological evolution after average Lithium electrodeposition depth of 45 µm, 60 µm and 80 µm under a large overpotential of 200 mV. (d)-(f) Morphology of the lithium electrode after average electrodeposition thickness of 105 µm under applied overpotential of 60 mV, 100 mV and 160 mV, respectively. local concentration under an ideal solution approximation) doubles, which largely increases the transport rate and delays the time for the drain of the local concentration (Figure 2e). Meanwhile, the interface velocity only increases by 4 times (Figure 2f) during the same time range, which can in part be compensated by the increasing of the local mobility. Thus, the dendrite growth can be largely delayed by the increased transport at elevated temperature through a self-heating process. The spatially resolved local interface velocity after an average electrodeposition of ∼80 µm for diffusion barriers of 0.15 eV and 0 eV (corresponding to Figure 2c and Figure 1c) are plotted in Figure 2(g)-(j). It is clearly demonstrated that with the 0.15 eV diffusion barrier, the variation of the interface velocity is small across the interface (the fluctuation is within 50 percent deviation from the mean average value). Meanwhile, with the growth of long dendrites when the diffusion barrier is 0 eV, the dendrite tip has orders of magnitude larger interface velocity as compared to the concave region, making the growth of dendrite even more favorable which cannot be stopped. This comparison clearly indicates that the self-heating induced increase in transport properties can homogenize the interface growth velocity leading to stable deposition at higher rates/temperature. The influence of the overpotential with the implementation of heat generation and transfer is further studied (with a diffusion barrier of 0.15 eV and electrochemical reaction barrier 5



Figure 2: Growth kinetics and underline physics under applied overpotential of 200 mV with a diffusion barrier of 0.15 eV and no electroreaction barrier. (a)-(c) Morphological evolution after average Lithium electrodeposition thickness of 45 µm, 60 µm and 80 µm, showing stable electrodeposition process (d)-(f) The evolution of temperature, local ion mobility and interface velocity along the middle of the cell. (g) Spatially resolved interface velocity after electrodeposition of 80 µm. (h) The maximum interface velocity (with varying X at each fixed Y position) as a function of the vertical position Y. Inset: the same plot with a linear vertical axis. (i) Similar plot of (g) but the diffusion barrier is zero. (j) The maximum interface velocity extracted from (i). 6


Page 6 of 17

Page 7 of 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Energy Letters

of 0 eV), as given in Figure 3. It is demonstrated that the vertical length of the dendrite/filament also decreases with increasing overpotential, similar to the “barrier-less” case studied previously. Interestingly, the length of the dendrite does not monotonically increase with increasing overpotential. Instead, the dendrite length is slightly longer under an overpotential of 100 mV as compared to 60 mV and 160 mV. This can be understood since the electrodeposition rate under 100 mV is much lower than under applied overpotential of 160 mV, which gives a longer electrodeposition time to reach the same average deposition thickness, hence a longer dendrite growth time. Whereas under an small applied overpotential of 60 mV, the dendrite nucleation time is much longer since it needs a larger interfacial perturbation to overcome the nucleation barrier to form dendrites (hence the larger vertical length). The temperature evolution, mobility and interface velocity are further calculated, shown in Figure 3(d)-(f). It is demonstrated that below 100 mV, the increase in temperature is minimal (e.g., within 20 K), while the temperature increases rapidly at higher overpotential (as high as 35 K for 160 mV and 50 K for 200 mV). With the increase in temperature, the self-diffusion mobility increases by ∼40 percent from 100 mV to 160 mV. Even larger increase in ion transport properties (which includes both diffusion and migration) can be expected under 160 mV as compared to the case with smaller overpotential, since the ion migration depends on both mobility and electric field which both increases under higher overpotential. The maximum interface velocity along the metal/electrolyte surface is plotted for different overpotentials, it can be seen that the perturbation in interface velocity is mostly within 50 percent, showing good surface stability during electrodeposition when the overpotential is below 200 mV. In a short summary, the self heating induced dendrite suppression at large overpotential can be realized when the electrochemical reaction barrier is much smaller than the diffusion barrier, i.e., the increase in the transport during heating is much larger than the increase in the the electrochemical reaction. This can be part of the mechanism for the experimental observation in the previous report in addition to the surface diffusion mechanism suggested. 15 It should be noted here that in the current model the electrolyte is simplified by its physical properties such as diffusivity, diffusion barrier and heat conductivity, etc. Other properties such as boiling point, side reactions and corrosion to the current collectors, etc. should also be taken into consideration in practice. We further investigate the growth dynamics with a large electrochemical reaction barrier, i.e., 0.3 eV, as shown in Figure 4. Under large overpotential (e.g., 200 mV), the dendrites nucleated much earlier than the previous cases. After an average deposition thickness of 45 µm, various compact dendrite nuclei can be observed, which grow rapidly into long dendrites thereafter (Figure 4a-c). The length and the quantity of the dendrites are even larger than the “barrier-less” case under the same growth condition. This can be explained that in the current case, the ion mobility is larger, which gives larger lithium ion transport rate that can supply more lithium to form more dendrites. With the increasing of temperature, the increase in electrodeposition rate exceeds the increase in lithium ion transport, giving rise to the large increase in dendrite length. The dependence of the overpotential is also studied (Figure 4d-f) which shows longer dendrites under higher overpotential, similar to the “barrier-less” case. This is to be expected as the benefit of increasing ionic transport at elevated temperatures under higher overpotential is surpassed by the increasing of lithium plating rate. One interesting feature to note here is the formation of “voids” (Figure 4c). They can form 7



Figure 3: Influence of the applied overpotential with a diffusion barrier of 0.15 eV and electrochemical reaction barrier of 0 eV. (a)-(c) The interface morphologies after electrodeposition thickness of 105 µm under applied overpotential of 60 mV, 100 mV and 160 mV, respectively. (d) Average cell temperature during electrodeposition under different applied overpotential. (e) Line plot of the local mobility after electrodeposition thickness of 105 µm cutting along the middle of the cell. (f) Line plot of the maximum interface velocity along the electrode/electrolyte interface.

8


Page 8 of 17

Page 9 of 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Energy Letters

Figure 4: Dendrite growth kinetics with large electrochemical reaction barrier and dendrite length with different electrochemical reaction barrier and overpotential. (a)-(c) Morphological evolution after average Lithium electrodeposition thickness of 45 µm, 60 µm and 80 µm under large overpotential of 200 mV. (d)-(f) The morphologies after electrodeposition thickness of 105 µm under applied overpotential of 60 mV, 100 mV and 160 mV, respectively. (g)Dendrite length as a function of average electrodeposition length with different lithium electrochemical reaction barrier. (h) Dendrite length after an average electrodeposition of 90 µm under different overpotential with different electrochemical reaction barrier. 9



when both the electrochemical reaction barrier and the applied overpotential are relatively high (i.e., the electrochemical reaction barrier is equal to or greater than the diffusion barrier). The void formation dynamics are depicted in Figure S3. The dendrites nucleated shortly after an electrodeposition time of 60 s. Unlike the previous report where only few dendrites can grow due to the limitation of ion transport, in this case, with the thermally boosted lithium ion self-diffusion and migration, the dendrites are rather compact and dense which not only grow laterally, but also expand horizontally to form a wedge shape. After ∼80 s, the two neighboring dendrites merge at the “bottle-neck” of the dendrites to form an inclusion where the bottom of dendrites merely grow. The formation of the inclusion blocks the ion transport path further. The void no longer grows after the depletion of the lithium ion inside. The interface velocity is plotted in the vicinity of the void, as shown in Figure S5. Initially, the interface velocity is very large in the boundaries of the two neighboring dendrites. While since the formation of the inclusion, the interface velocity quickly decays due to the depletion of the lithium ion concentration. Eventually, as the transport path is closed and the lithium ions have been drained, the interface velocity surrounding the void region becomes negligible. The formation of the voids in the lithium electrode could deteriorate the performance of the battery leading to dead lithium, causing capacity fade for the battery. 54–56 To further study the influence of the lithium electrochemical reaction activation barrier, the dendrite length is plotted as a function of the average deposition thickness (which is directly related to the total current) under various overpotential (Figure 4g-h). It is clearly demonstrated that the dendrite length increases rapidly with increasing deposition thickness (total current) with a high electrochemical reaction activation barrier (i.e., the electrochemical reaction activation barrier is above the diffusion barrier). While the dendrite growth is largely delayed with a smaller electrochemical reaction activation barrier. This can be understood since in this case the temperature increases rapidly during the deposition which leads to largely increased ion transport while the electrochemical reaction rate is insensitive to the temperature change, resulting in a delay for the dendrite growth. Interestingly, the dendrite length is much shorter even when the electrochemical reaction activation barrier is equal to the diffusion barrier as compared to the barrier-less case where the reaction rate and diffusion rate is independent of temperature. This is due to the fact that although the self diffusion rate increases in the same speed as the electrochemical reaction rate, the increasing of the reaction rate would lower the deposition time which decreases the dendrite growth time. Meanwhile, the dendrite length under different overpotential after an electrodeposition of 90 µm is plotted in Figure 4h. It can be clearly seen that the dendrite length is very similar under different electrochemical reaction activation barrier when the overpotential is below 120 mV. While above this value, the length of the dendrite increases dramatically with increasing eleectrochemical reaction barrier. Interestingly, under lower overpotential (e.g., from 40 mV to 120 mV), the dendrite length is even slightly longer at 60 mV for most of the cases, which is due to the largely increased deposition time to pass the same total current, which gives rise to a longer dendrite growth time. To discuss, the self heating at high overpotential which increases the ion transport rate could suppress the dendrite growth when the electrochemical reaction barrier is smaller than the diffusion barrier. While in the case where the electrochemical reaction barrier is much larger than the diffusion barrier, the increase in temperature would lead to a largely increased dendrite growth rate. Here in this study we demonstrated the complexity of the problem and 10


Page 10 of 17

Page 11 of 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Energy Letters

the possibility of deteriorated/better performances at higher temperature/rate depending on the relative magnitude of the barriers. The lithium electrochemical reaction activation barrier can be divided into three parts: 57 1, the desolvation barrier, where the lithium ions come out of the solvation complex; 2, the plating barrier, the barrier for the lithium ion to attach to the metal surface; 3, the charge transfer barrier, where electrons transfer to the surface of the electrode. These three barriers depend largely on the electrolyte composition and concentration, the surface roughness and surface defect/impurity concentration, the formation of solid electrolyte interface (SEI) between the electrode and the electrolyte (which could modify both the plating barrier and charge transfer barrier), etc. which can be rather complex. In particular, the formation of SEI could in general increase the electrochemical reaction activation barrier, but it also depends on the composition of the SEI components, cracks and grain boundaries in SEI, etc. Thus, it is not surprising to find contradictory experimental results regarding the influence of the high rate, high overpotential and high temperature on the battery performance. Also note here that for the simplicity of the model, some other factors are neglected such as the formation of SEI, side reaction/decomposition of electrolyte at elevated temperature, etc. More follow up works could be done to reveal the key parameters to electrolyte/electrode engineering to enable high rate charging. In conclusion, we identified an important parameter, the lithium electrochemical reaction barrier, that governs the high overpotential/current stability of the lithium battery. Generally, when this barrier is small as compared to the diffusion barrier, the self heating at high overpotential/current would lead to largely increased ion transport, which can slow down the growth of the dendrites, as has been observed experimentally. While with a large electrochemical reaction barrier, the increase in the reaction rate surpasses the increase in ion transport, which will drastically increase the dendrite growth rate. Similarly, this parameter also governs the high temperature performance of a lithium metal anode. It is also shown that in the case with medium to large barrier and large overpotential/high rate, “voids” can form due to the side growth of the neighboring dendrites, which is not easy to capture without a thermally-coupled model. The formation of the “voids” can deteriorate the mechanical properties of the electrode and lead to the formation of “dead lithium”. We hope that this study could spur further experimental/theoretical studies on the heat generation and systematic measurements of the electrochemical reaction and diffusion barriers.

Acknowledgement Z.H. and V.V. would like to acknowledge the support from the U.S. Department of Energy, Energy Efficiency and Renewable Energy Vehicle Technologies Office (Award No. DEEE0007810).

Supporting Information Available The Supporting Information is available free of charge on the ACS Publications website at DOI: XXXX. All MOOSE input files are made freely available. Contents in the supporting information: Phase-field model; Influence of the exchange current density;Fitting of the diffusion barrier;Parameters used in the simulation;Bubble formation dynamics;Dendrite growth 11



kinetics with electrochemical reaction barrier of 0.15 eV;Concentration and temperature distribution under applied overpotential of 200 mV with electrochemical reaction barrier of 0 eV;Concentration and temperature distributions with electrochemical reaction barrier of 0 eV under different overpotentials;Influence of the electrochemical reaction barrier on the concentration and temperature distributions.

References (1) Sripad, S.; Viswanathan, V. Evaluation of Current, Future, and Beyond Li-Ion Batteries for the Electrification of Light Commercial Vehicles: Challenges and Opportunities. J. Electrochem. Soc. 2017, 164, E3635–E3646. (2) Sripad, S.; Viswanathan, V. Performance Metrics Required of Next-Generation Batteries to Make a Practical Electric Semi Truck. ACS Energy Lett. 2017, 2, 1669–1673. (3) Guttenberg, M.; Sripad, S.; Viswanathan, V. Evaluating the Potential of Platooning in Lowering the Required Performance Metrics of Li-Ion Batteries to Enable Practical Electric Semi-Trucks. ACS Energy Lett. 2017, 2, 2642–2646. (4) Fredericks, W. L.; Sripad, S.; Bower, G. C.; Viswanathan, V. Performance Metrics Required of Next-Generation Batteries to Electrify Vertical Takeoff and Landing (VTOL) Aircraft. ACS Energy Lett. 2018, 3, 2989–2994. (5) Kerman, K.; Luntz, A.; Viswanathan, V.; Chiang, Y.-M.; Chen, Z. Practical Challenges Hindering the Development of Solid State Li Ion Batteries. J. Electrochem. Soc. 2017, 164, A1731–A1744. (6) Tikekar, M. D.; Choudhury, S.; Tu, Z.; Archer, L. A. Design principles for electrolytes and interfaces for stable lithium-metal batteries. Nat. Energy 2016, 1, 16114. (7) Monroe, C.; Newman, J. Dendrite Growth in Lithium/Polymer Systems: A Propagation Model for Liquid Electrolytes under Galvanostatic Conditions. J. Electrochem. Soc. 2003, 150, A1377–A1384. (8) Monroe, C.; Newman, J. The Effect of Interfacial Deformation on Electrodeposition Kinetics. J. Electrochem. Soc. 2004, 151, A880–A886. (9) Monroe, C.; Newman, J. The Impact of Elastic Deformation on Deposition Kinetics at Lithium/Polymer Interfaces. J. Electrochem. Soc. 2005, 152, A396–A404. (10) Tikekar, M. D.; Archer, L. A.; Koch, D. L. Stabilizing Electrodeposition in Elastic Solid Electrolytes Containing Immobilized Anions. Sci. Adv. 2016, 2, 1600320. (11) Ahmad, Z.; Viswanathan, V. Stability of Electrodeposition at Solid-Solid Interfaces and Implications for Metal Anodes. Phys. Rev. Lett. 2017, 119, 056003.

12


Page 12 of 17

Page 13 of 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Energy Letters

(12) Barai, P.; Higa, K.; Srinivasan, V. Effect of Initial State of Lithium on the Propensity for Dendrite Formation: A Theoretical Study. J. Electrochem. Soc. 2017, 164, A180– A189. (13) Ferrese, A.; Newman, J. Mechanical Deformation of a Lithium-Metal Anode Due to a Very Stiff Separator. J. Electrochem. Soc. 2014, 161, A1350–A1359. (14) Barai, P.; Higa, K.; Srinivasan, V. Lithium dendrite growth mechanisms in polymer electrolytes and prevention strategies. Phys. Chem. Chem. Phys. 2017, 19, 20493– 20505. (15) Li, L.; Basu, S.; Wang, Y.; Chen, Z.; Hundekar, P.; Wang, B.; Shi, J.; Shi, Y.; Narayanan, S.; Koratkar, N. Self-heating–induced healing of lithium dendrites. Science 2018, 359, 1513–1516. (16) Morrissey, P.; Weldon, P.; OMahony, M. Future standard and fast charging infrastructure planning: An analysis of electric vehicle charging behaviour. Energy Policy 2016, 89, 257 – 270. (17) Burnham, A. et al. Enabling fast charging Infrastructure and economic considerations. J. Power Sources 2017, 367, 237 – 249. (18) Nishida, T.; Nishikawa, K.; Rosso, M.; Fukunaka, Y. Optical observation of Li dendrite growth in ionic liquid. Electrochim. Acta 2013, 100, 333 – 341. (19) Nishikawa, K.; Mori, T.; Nishida, T.; Fukunaka, Y.; Rosso, M. Li dendrite growth and Li+ ionic mass transfer phenomenon. J. Electroanal. Chem. 2011, 661, 84 – 89. (20) Brissot, C.; Rosso, M.; Chazalviel, J.-N.; Baudry, P.; Lascaud, S. In situ study of dendritic growth inlithium/PEO-salt/lithium cells. Electrochim. Acta 1998, 43, 1569 – 1574. (21) Nishikawa, K.; Mori, T.; Nishida, T.; Fukunaka, Y.; Rosso, M.; Homma, T. In Situ Observation of Dendrite Growth of Electrodeposited Li Metal. J. Electrochem. Soc. 2010, 157, A1212–A1217. (22) Nishikawa, K.; Naito, H.; Kawase, M.; Nishida, T. Morphological Variation of Electrodeposited Li in Ionic Liquid. ECS Trans. 2012, 41, 3–10. (23) Lu, Y.; Tu, Z.; Archer, L. A. Stable lithium electrodeposition in liquid and nanoporous solid electrolytes. Nat. Mater. 2014, 13, 961. (24) Rosso, M.; Gobron, T.; Brissot, C.; Chazalviel, J.-N.; Lascaud, S. Onset of dendritic growth in lithium/polymer cells. J. Power Sources 2001, 97-98, 804 – 806. (25) Bai, P.; Li, J.; Brushett, F. R.; Bazant, M. Z. Transition of lithium growth mechanisms in liquid electrolytes. Energy Environ. Sci. 2016, 9, 3221–3229.

13



(26) Ishikawa, M.; Takaki, Y.; Morita, M.; Matsuda, Y. Improvement of ChargeDischarge Cycling Efficiency of Li by LowTemperature Precycling of Li. J. Electrochem. Soc. 1997, 144, L90–L92. (27) Inaba, M.; Tomiyasu, H.; Tasaka, A.; Jeong, S.-K.; Ogumi, Z. Atomic Force Microscopy Study on the Stability of a Surface Film Formed on a Graphite Negative Electrode at Elevated Temperatures. Langmuir 2004, 20, 1348–1355. (28) Ruiz, V.; Kriston, A.; Adanouj, I.; Destro, M.; Fontana, D.; Pfrang, A. Degradation Studies on Lithium Iron Phosphate - Graphite Cells. The Effect of Dissimilar Charging Discharging Temperatures. Electrochim. Acta 2017, 240, 495 – 505. (29) Mistry, A.; Fear, C.; Carter, R.; Love, C. T.; Mukherjee, P. P. Electrolyte Confinement Alters Lithium Electrodeposition. ACS Energy Lett. 2019, 4, 156–162. (30) Yang, H.; Guo, C.; Chen, J.; Naveed, A.; Yang, J.; Nuli, Y.; Wang, J. An Intrinsic Flame-Retardant Organic Electrolyte for Safe Lithium-Sulfur Batteries. Angew. Chem. Int. Ed. 2019, 58, 791–795. (31) Aryanfar, A.; Brooks, D. J.; Colussi, A. J.; Merinov, B. V.; Goddard III, W. A.; Hoffmann, M. R. Thermal relaxation of lithium dendrites. Phys. Chem. Chem. Phys. 2015, 17, 8000–8005. (32) Aguesse, F.; Manalastas, W.; Buannic, L.; Lopez del Amo, J. M.; Singh, G.; Llords, A.; Kilner, J. Investigating the Dendritic Growth during Full Cell Cycling of Garnet Electrolyte in Direct Contact with Li Metal. ACS Appl. Mater. Interfaces 2017, 9, 3808– 3816, PMID: 28055178. (33) Mogi, R.; Inaba, M.; Iriyama, Y.; Abe, T.; Ogumi, Z. In Situ Atomic Force Microscopy Study on Lithium Deposition on Nickel Substrates at Elevated Temperatures. J. Electrochem. Soc. 2002, 149, A385–A390. (34) Tang, M.; Newman, J. Electrochemical Characterization of SEI-Type Passivating Films Using Redox Shuttles. J. Electrochem. Soc. 2011, 158, A530–A536. (35) Cheng, X.-B.; Zhang, R.; Zhao, C.-Z.; Wei, F.; Zhang, J.-G.; Zhang, Q. A Review of Solid Electrolyte Interphases on Lithium Metal Anode. Adv. Sci. 2016, 3, 1500213. (36) Chen, S.; Zheng, J.; Yu, L.; Ren, X.; Engelhard, M. H.; Niu, C.; Lee, H.; Xu, W.; Xiao, J.; Liu, J.; Zhang, J.-G. High-Efficiency Lithium Metal Batteries with FireRetardant Electrolytes. Joule 2018, 2, 1548 – 1558. (37) Zhang, S. S. A review on electrolyte additives for lithium-ion batteries. J. Power Sources 2006, 162, 1379 – 1394. (38) Cheng, L.; Curtiss, L. A.; Zavadil, K. R.; Gewirth, A. A.; Shao, Y.; Gallagher, K. G. Sparingly Solvating Electrolytes for High Energy Density LithiumSulfur Batteries. ACS Energy Lett. 2016, 1, 503–509.

14


Page 14 of 17

Page 15 of 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Energy Letters

(39) Liang, L.; Qi, Y.; Xue, F.; Bhattacharya, S.; Harris, S. J.; Chen, L. Q. Nonlinear Phase-field Model for Electrode-electrolyte Interface Evolution. Phys. Rev. E 2012, 86, 1–5. (40) Liang, L.; Chen, L.-Q. Nonlinear Phase Field Model for Electrodeposition in Electrochemical Systems. Appl. Phys. Lett. 2014, 105, 263903. (41) Chen, L.; Zhang, H. W.; Liang, L. Y.; Liu, Z.; Qi, Y.; Lu, P.; Chen, J.; Chen, L.-Q. Modulation of Dendritic Patterns During Electrodeposition: A Nonlinear Phase-field Model. J. Power Sources 2015, 300, 376 – 385. (42) Yurkiv, V.; Foroozan, T.; Ramasubramanian, A.; Shahbazian-Yassar, R.; Mashayek, F. Phase-field Modeling of Solid Electrolyte Interface (SEI) Influence on Li Dendritic Behavior. Electrochim. Acta 2018, 265, 609 – 619. (43) Guyer, J. E.; Boettinger, W. J.; Warren, J. A.; McFadden, G. B. Phase field modeling of electrochemistry. I. Equilibrium. Phys. Rev. E 2004, 69, 021603. (44) Guyer, J. E.; Boettinger, W. J.; Warren, J. A.; McFadden, G. B. Phase field modeling of electrochemistry. II. Kinetics. Phys. Rev. E 2004, 69, 021604. (45) Cogswell, D. A. Quantitative Phase-field Modeling of Dendritic Electrodeposition. Phys. Rev. E 2015, 92, 011301. (46) Plapp, M. Unified Derivation of Phase-field Models for Alloy Solidification from A Grand-potential Functional. Phys. Rev. E 2011, 84, 031601. (47) Hong, Z.; Viswanathan, V. Phase-Field Simulations of Lithium Dendrite Growth with Open-Source Software. ACS Energy Lett. 2018, 3, 1737–1743. (48) Gaston, D.; Newman, C.; Hansen, G.; Lebrun-Grandi, D. MOOSE: A Parallel Computational Framework for Coupled Systems of Nonlinear Equations. Nucl. Eng. Des. 2009, 239, 1768 – 1778. (49) Tonks, M. R.; Gaston, D.; Millett, P. C.; Andrs, D.; Talbot, P. An Object-oriented Finite Element Framework for Multiphysics Phase Field Simulations. Comput. Mater. Sci. 2012, 51, 20 – 29. (50) Yan, H.; Bie, Y.; Cui, X.; Xiong, G.; Chen, L. A computational investigation of thermal effect on lithium dendrite growth. Energy Convers. Manag. 2018, 161, 193 – 204. (51) Srinivasan, V.; Wang, C. Y. Analysis of Electrochemical and Thermal Behavior of LiIon Cells. J. Electrochem. Soc. 2003, 150, A98–A106. (52) Shi, F.; Pei, A.; Vailionis, A.; Xie, J.; Liu, B.; Zhao, J.; Gong, Y.; Cui, Y. Strong texturing of lithium metal in batteries. Proc. Natl. Acad. Sci. 2017, 114, 12138–12143. (53) Pei, A.; Zheng, G.; Shi, F.; Li, Y.; Cui, Y. Nanoscale Nucleation and Growth of Electrodeposited Lithium Metal. Nano Lett. 2017, 17, 1132–1139. 15



(54) Shi, F.; Pei, A.; Boyle, D. T.; Xie, J.; Yu, X.; Zhang, X.; Cui, Y. Lithium metal stripping beneath the solid electrolyte interphase. Proc. Natl. Acad. Sci. 2018, 115, 8529–8534. (55) Devaux, D.; Harry, K. J.; Parkinson, D. Y.; Yuan, R.; Hallinan, D. T.; MacDowell, A. A.; Balsara, N. P. Failure Mode of Lithium Metal Batteries with a Block Copolymer Electrolyte Analyzed by X-Ray Microtomography. J. Electrochem. Soc. 2015, 162, A1301–A1309. (56) Lin, D.; Liu, Y.; Li, Y.; Li, Y.; Pei, A.; Xie, J.; Huang, W.; Cui, Y. Fast galvanic lithium corrosion involving a Kirkendall-type mechanism. Nat. Chem. 2019, 11, 382 – 389. (57) Xu, K.; von Cresce, A.; Lee, U. Differentiating Contributions to Ion Transfer Barrier from Interphasial Resistance and Li+ Desolvation at Electrolyte/Graphite Interface. Langmuir 2010, 26, 11538–11543.

16


Page 16 of 17

Page 17 of 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Energy Letters

Graphical TOC Entry

17


Prospect of Thermal Shock Induced Healing of Lithium Dendrite - ACS

Recommend Documents