Mesoscale Complexations in Lithium Electrodeposition - American

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Cite This: ACS Appl. Mater. Interfaces 2018, 10, 26320−26327

Mesoscale Complexations in Lithium Electrodeposition Feng Hao, Ankit Verma, and Partha P. Mukherjee* School of Mechanical Engineering, Purdue University, West Lafayette, Indiana 47907, United States

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S Supporting Information *

ABSTRACT: Mechanistic understanding of lithium electrodeposition and morphology evolution is critical for lithium metal anodes. In this study, we deduce that Li deposition morphology evolution is determined by the mesoscale complexations that underlie due to local electrochemical reaction, Li surface self-diffusion, and Li-ion transport in the electrolyte. Li-ion depletion at the reaction front for higher reaction rates primarily accounts for dendritic growth with needlelike or fractal morphology. Large Li self-diffusion barrier, on the other hand, may lead to the formation of porous Li film for lower reaction rates. Enhanced ion transport in the electrolyte contributes to homogeneous deposition, thereby avoiding nucleation for Li dendrite formation. This study also demonstrates that the substrate surface roughness strongly affects dendritic growth localization over the protrusive surface features. A nondimensional electrochemical Damkohler number is further proposed, which correlates surface diffusion rate and reaction rate and allows constructing a comprehensive phase map for lithium electrodeposition morphology evolution. KEYWORDS: electrodeposition morphology, self-diffusion rate, electrochemical reaction rate, electrolyte diffusion rate, Damkohler number

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INTRODUCTION The burgeoning demand for electrical energy storage has led to the resurgence of research efforts into utilizing Li metal as the anode in the Li-ion battery system. Commercial Li-ion battery systems utilizing intercalation chemistries, such as graphitic anodes, are reaching their upper limits of achievable capacity, thus paving the path for the recent revival of Li metal anode.1−7 Li-metal-based rechargeable batteries possess prominent advantages over state-of-the-art commercial Li-ion batteries, emanating from their high theoretical specific capacity (3860 mAh/g) and lowest negative electrochemical potential (−3.04 V vs the standard hydrogen electrode). The prospect of Li metal as the anode material also offers significant opportunities for sustainable battery systems beyond Li-ion chemistries, including Li−S batteries and Li−air batteries.8−10 Despite the remarkable progress, key challenges remain to the practical applications of Li-metal anodes, primarily related to battery safety and cyclability. Due to high chemical reactivity and large volumetric changes from repeated Li stripping and deposition during cycling, Li deposition tends to be in dendritic form, which decreases the cycling efficiency, eventually leading to exacerbated capacity fading effects and even short circuit.11,12 Extensive research efforts have been devoted to developing dendrite-free depositions, for instance, approaches are proposed to improve the uniformity of solid− electrolyte interphase (SEI)13−17 and increase dendrite growth resistance by using solid electrolytes.18−23 © 2018 American Chemical Society

Depending on the operating conditions, various morphologies of electrodeposited metal are observed in experiments.24,25 Imaging techniques like scanning electron microscopy, magnetic resonance imaging, tomography etc. have been used to capture the deposition process.15,26−34 In an earlier study, Yoshimatsu et al. found that particulate and needlelike Li were deposited on the Li electrode, and the needlelike Li was the dominant factor in creating “dead Li” that is responsible for the capacity loss.35 Using a glass capillary, Bai et al. visualized a transition from root-growing mossy lithium to tip-growing dendritic lithium.36 In addition to experiments, theoretical studies are focused on illuminating the growth mechanism of deposited metal,37−49 especially on dendrite growth. Since spherical diffusion conditions dominate at the hemispherical tips, the dendrite growth models by Barton and Bockris37 and Monroe et al.41 revealed that dendrites accelerate across cells. Li deposition encompasses a complex interplay between coupled physical phenomena associated with SEI microstructure, composition and concentration of Li salts, composition and concentration of solvents, Li wetting with substrate, and battery working conditions.5,50 Therefore, a comprehensive understanding of Li deposition mechanism is challenging, although essential in guiding material design for Received: May 28, 2018 Accepted: July 19, 2018 Published: July 19, 2018 26320

DOI: 10.1021/acsami.8b08796 ACS Appl. Mater. Interfaces 2018, 10, 26320−26327

Research Article

ACS Applied Materials & Interfaces

Figure 1. (a) Li deposition morphology map in terms of local overpotential and Li surface self-diffusion barrier, consisting of four regions: dense Li film, needlelike Li (dendrite), fractal Li (dendrite), and porous Li film. High reaction rates and self-diffusion barrier exacerbate dendritic growth. Morphologies of fractal Li at the local overpotential of 0.3 V, with Li surface self-diffusion barriers of (b) 0.5 eV and (c) 0.6 eV. As the self-diffusion barrier increases, slenderness of the dendritic branches increases (see region enclosed by dashed circles). (d) Porosity map for Li films.

atoms, more and more vacancies are produced inside the metal film. In contrast to the film formation at low reaction rate, dendritic Li grows on the substrate at high local reaction rate. Interestingly, depending on Li surface self-diffusion kinetics and local overpotential, Li can grow as a needlelike structure or fractal (treelike) structure. When Li self-diffusion barrier is small, Li atoms diffuse very fast and fill the vacancies on the metal surface, resulting in a dense needlelike Li. In Figure 1a, as the local overpotential continues to increase, needlelike Li can transform to fractal Li. The results are consistent with previous experiments, where smooth needlelike Li was found.40 It should be stressed that needlelike Li is observed under lower currents in batteries, which could be caused by large local overpotential.2,51 In this work, the focus is on the initial Li deposition at the local overpotential, which could be very large due to surface inhomogeneity, even during low-rate battery charge. Alternatively, the dendrite is highly branched (fractal Li) even at a moderate reaction rate when the surface selfdiffusion barrier is large. Under these circumstances, Li surface self-diffusion is hindered and surface defects cannot be selfhealed by new deposited Li atoms. Synergizing with the high local reaction rate, it generates fractal Li, which is also widely observed in experiments.3,36 The characteristics of individual regimes in Figure 1a are related to the local overpotential and self-diffusion barriers. For fractal Li, Li self-diffusion barriers are 0.5 and 0.6 eV in Figure 1b,c, respectively. Contrasting the two morphologies, we can see that decreasing Li self-diffusion rate tapers the Li dendrite,

good battery performance. In this regard, we aim to address the mechanism of Li electrodeposition morphologies using a mesoscale model capable of bridging multiple length and time scales. In particular, we focus on the roles of local overpotential, Li surface self-diffusion kinetics, and Li-ion transport in the electrolyte (see the details in Supporting Information). The influence of substrate surface roughness on Li deposition is also revealed.

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RESULTS AND DISCUSSION Impact of Reaction Kinetics and Surface Diffusion Characteristics. Primarily, the effects of electrochemical reaction rate (overpotential) and Li surface self-diffusion kinetics (self-diffusion barrier) are incorporated to explore Li deposition behavior. Figure 1a illustrates the morphology map, which is roughly divided into four regions: dense metal film, needlelike Li, fractal Li, and porous metal film. It contrasts the dependence of the four different morphologies on the relative dominance of electrochemical reaction and self-diffusion rates. Metallic Li forms a dense film when the local reaction rate is low and Li surface self-diffusion barrier is small. In this regime, Li reduction becomes the rate-determining step and thus it allows sufficient time for Li surface diffusion, which leads to a uniform Li deposition. As Li self-diffusion barrier increases, formation of porous Li film is observed. Although low local reaction rate ensures homogeneous Li deposition, large Li selfdiffusion barrier suppresses Li diffusion on the metal surface, and the sluggish Li diffusion could not smoothen the rough surface. As the uneven surface is covered by new deposited Li 26321


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barriers of Li-ion transport in the electrolyte are 0.3, 0.4, and 0.5 eV in Figure 3a−c, respectively. The deposition morphologies obtained illuminate the critical role of ion transport in the electrolyte. In Figure 3b, the morphology is a combination of Li film and Li dendrites. Reducing the energy barrier enables fast transport of Li ions to the reaction zone. Consequently, the deposited Li forms a film in Figure 3a. In contrast, increasing the energy barrier weakens Li-ion transport in the electrolyte, which leads to the growth of Li dendrites in Figure 3c. Thus, the morphology experiences a transition from Li film to Li dendrite with varying energy barriers in Figure 3. The aforementioned results can be explained from a discussion on the effect of electrolyte ionic diffusivity on the concentration of Li+ ions near the metal−electrolyte interface. An increase in the transport diffusion barrier leads to amplified transport resistance accelerating depletion of available Li+ ions near the interface. This generates lesser random seed points for initiation of deposit. Once the initial preferential deposit of Li occurs, reaction occurs exclusively on top of this existing Li because of the curtailed diffusional transport length. To verify this, Figure 3d presents Li-ion content profiles quantified through Li-ion occupation ratio in the electrolyte, corresponding to the systems in Figure 3a−c. For dendritic morphology, Li ions are depleted at the reaction front, leading to a large concentration gradient, which is in good agreement with previous studies.39,54 The onset time for the depletion is termed as Sand’s time τ, which reads τ = πD(eC0/2Jta),2 where D is the ionic diffusivity, C0 is the bulk concentration, J is the current density, and ta is the transference number.4,32 For the formation of Li dendrite, the limiting current density is written as J* = 2eC0D/taL, where L is the distance between the electrodes.4,32 It can be seen that the diffusivity D plays a critical role. The diffusivity decreases with increasing Li-ion diffusion barrier in the electrolyte, which shortens Sand’s time and reduces the limiting current density. As demonstrated in Figure 3, a relatively high diffusion barrier could initiate Li dendrite growth after the concentration at the reaction front decreases to zero. On the basis of analysis, it can be concluded that high local overpotential and sluggish Li-ion transport generate a Li-ion-depleted zone that accounts for dendritic Li growth. Moreover, it implies that dendrite formation could be alleviated by enhancing Li-ion transport in practical batteries, such as elevating the operating temperature, adding electrolyte additives to increase ion mobility, and improving the wettability of separators to enhance the holdup of electrolyte.22,55−60 Impact of Substrate Geometry. The influence of substrate surface roughness on Li morphology at high local overpotential is explored. The horizontally aligned ridge has a width of 0.1L (L is the system width) and a height of 0.1H (H is the system height). For the two dendritic morphologies, Figure 4 shows that Li dendrite prefers to grow on the ridge. In the early stage, Li is deposited over the entire substrate due to initially uniform Li-ion distribution. However, as the deposition proceeds, Li-ion concentration is substantially reduced at the reaction front. Because of the concentration gradient, the deposition rate on the ridge is slightly higher than that in the valley. As metallic Li on the ridge grows upward, the dendrite could propagate faster and faster because of more Li ions available around the dendrite tips, resulting in few Li ions toward the base of the dendrite (see Movie S1). For a relatively low-rate deposition, Figure S3 indicates that surface roughness aggravates uneven Li deposition (Supporting Information).

exemplified by the deposit regions enclosed in circles. Tapering is evident from increase in slenderness of the dendritic branches as the self-diffusion barrier is increased from 0.5 eV (Figure 1b) to 0.6 eV (Figure 1c). At high diffusion barriers, Li diffusion is too slow to homogenize the structure before the subsequent deposition of new incoming Li atoms on the metal surface at high electrochemical reaction rate. For the metal film, Figure 1d depicts its porosity map, indicating that increasing the local overpotential and surface self-diffusion barrier facilitates the growth of porous Li film. Conversely, Li self-diffusion barrier smaller than 0.5 eV can reduce the porosity below 1%. As a result, enhancing Li surface selfdiffusion is of great importance to achieve a densely packed Li deposition layer. In fact, our simulations indicate that the porosity is nonzero even for the morphologies in the region of dense Li film (with a porosity less than 5%). For instance, the structure with the local overpotential of 0.1 V and Li selfdiffusion barrier of 0.3 eV has a porosity of 0.1%. To explore substrate effect on Li morphology, the reaction kinetics of substrate/Li+ is changed by modifying the exchange current density of substrate/Li+ in Figure 2, while the reaction

Figure 2. Effect of substrate exchange current density on deposition morphology. Exchange current densities of substrate/Li+ are (a) 1, (b) 0.1, and (c) 0.05 mA/cm2. Lower Li affinity to substrate as compared to itself can lead to the formation of spheroidal Li islands.

rate on Li metal is the same in all cases. The overpotential is set to 0.2 V, corresponding to a relatively low-rate deposition. If the exchange current density of substrate/Li+ is comparable to that of Li/Li+, the nucleated Li can be well connected, resulting in uniform Li deposition. In contrast, a unique observation is the formation of Li islands when the exchange current density of substrate/Li+ is much smaller than that of Li/Li+. Similar spheroidal Li islands were also observed in recent experiments, with Li deposition on Cu.24,52 Therefore, it demonstrates that enhancing the affinity of Li reaction on the substrate leads to uniform deposition, while poor Li−substrate interactions could favor the growth of Li islands and dendrites. Recently, lithium nucleation on various substrates has been studied, which unraveled a substrate-dependent growth phenomenon that enables selective deposition of Li metal.53 Electrolyte Transport Implications. The electrochemical reaction rate at the electrode−electrolyte interface is directly influenced by diffusional transport of Li+ ions in the electrolyte, outlining the need to decipher its role. Consequently, the effect of Li-ion transport on Li deposition is investigated as well. Here, the reaction overpotential is fixed to 0.25 V and Li surface self-diffusion barrier is set to 0.3 eV. The energy 26322


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Figure 3. (a−c) Effect of Li-ion transport in the electrolyte on the electrodeposition morphology, with the energy barriers of 0.3, 0.4, and 0.5 eV, respectively. Transition from film morphology to dendritic morphology is observed as the transport of diffusion barrier is increased. (d) Li-ion distribution along the vertical direction corresponding to the three morphologies. Distance is computed beginning from the substrate surface.

Figure 4. Effect of substrate roughness on dendritic Li growth, with a periodically protrusive substrate surface. (a) The local overpotential of 0.35 V and Li surface self-diffusion barrier of 0.2 eV lead to needlelike Li deposits. (b) The local overpotential of 0.35 V and Li surface self-diffusion barrier of 0.5 eV lead to fractal (treelike) Li deposits.

Nondimensional Analysis of Deposition Phase Map. The preceding analysis underlines the importance of three competing phenomena: electrochemical reaction rate, Li selfdiffusion, and ionic diffusion rates on the nature of deposition. While the relative influence of reaction rate and electrolyte transport limitations has been elucidated in the past through the means of the dimensionless Wagner number (Wa),61,62 analysis of Li self-diffusion needs to be incorporated to provide a holistic picture. In this regard, we define a nondimensional electrochemical Damkohler number (Da) as the ratio of electrochemical reaction rate to diffusion rate and classify the observed regimes as a function of this number. Da ≫ 1 implies that the electrochemical reaction occurs at a much faster pace compared to surface self-diffusion. This leads to the formation of dendritic structures since the deposited Li will not have enough time to diffuse on the substrate. For Da ∼ 1, formation of Li islands should be observed due the equivalence of the reaction and self-diffusion rates. Finally, for Da ≪ 1, Li self-

diffusion eclipses the reaction rate and uniform deposition is obtained. Figure 5a shows the aforementioned regimes of deposition morphology for Li as a function of the electrochemical reaction and surface diffusion rate. Different isovalues of the Damköhler number are represented by the contour colors. As mentioned earlier, transition from high to low Damkohler number results in the morphological variation from dendritic to film-type structure. Figure 5b contrasts the Wagner number criteria for deposition outlining the relative influence of charge-transfer resistance (faradic resistance) and electrolyte transport resistance on deposition morphology. Large Wagner numbers (high faradic resistance and low transport resistance) imply substrate conformal deposition while increased transport resistance can cause depletion of Li+ ions close to the substrate surface resulting in dendritic protrusions. It is evident that both these numbers are pertinent to quantification of the deposition regime and are correlated through the reaction rate/faradic resistance term. Accurate prediction of the deposition regime 26323


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Figure 5. Deposition morphology phase map as a function of (a) Damkohler number and (b) Wagner number. High Damkohler number and low Wagner number lead to dendritic deposits. (c) Potential profile in liquid electrolyte and solid Li for uniform substrate. (d) Potential profile in liquid electrolyte and solid Li for rough substrate with protrusion at the middle of electrode−electrolyte interface. Here, ϕe is the potential in the electrolyte phase and ϕs is the potential in the solid phase.

requires detailed investigations into both quantities. Generating a combined deposition map based on the Damkohler and Wagner numbers incorporating cell geometric features and operating conditions is the logical way forward and will be the focus of future investigations. Further, a macrohomogeneous deposition model was developed to supplement the findings of the mesoscale model. Figure 5c,d illustrates the effect of uniform substrate versus rough substrate on the resulting potential profiles inside the electrolyte and Li metal. Charge and species transports inside the electrolyte are coupled with electrochemical reaction kinetics at the electrolyte−Li metal interface and subsequent electronic transport inside the solid Li (see Supporting Information). The presence of structural inhomogeneities (see Figure 5d) results in nonuniform potential profiles, resulting in varying reaction rates at the electrode−electrolyte interface with higher local current density near the protrusion (near the middle). This further justifies the findings from the mesoscale model (see Figure 4) where preferential deposit of Li was observed on the substrate ridges. For low operating current densities, substrate roughness effects diminish and both uniform and rough substrates show similar behavior (Figure S6, Supporting Information). Thus, at low current rates, preferential deposition is minimal.

in Li electrodeposition morphology. On the basis of the kinetics model, various Li morphologies are found and their mechanisms are also addressed, including Li film, needlelike Li, fractal Li, and Li island. For Li film, the porosity is strongly governed by Li surface self-diffusion kinetics. In addition, the deposition morphology is affected by Li-ion transport in the electrolyte, and it shows that fast ion diffusion contributes to homogeneous Li deposition. The results also demonstrate the importance of the substrate surface roughness: metallic Li preferentially deposits over the surface protrusion at high reaction rate, thereby helping to initialize Li dendrite. This work provides a fundamental mesoscale understanding of the mechanism of Li deposition morphologies. The conclusions reported here are applicable to electrodeposition systems, shedding light on the mechanisms of deposition morphologies for other metals. In the current work, SEI is not considered. Recently, Wood et al. have found that the nonuniform reactivity of the electrode surface could produce nonuniform Li deposition morphology.63 Therefore, a new model needs to be developed to study the interactions between Li electrodeposition and inhomogeneous SEI in future.

CONCLUSIONS In summary, we investigated the role of the local reaction rate, Li surface self-diffusion kinetics, and Li-ion transport property

Coarse-Grained Mesoscale Model. At the solid−electrolyte interface, the redox reaction is Li+ + e ↔ Li, and Li atoms are crystallized on the substrate. The faradic current density generated by the reactions is expressed by the Butler−Volmer equation

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ACS Applied Materials & Interfaces i i αF zy i βF zyyzz J = i0jjjjexpjjj ηzz − expjjj− ηzzzz) k RT {{ k k RT {

from Valøen and Reimers65 for LiPF6 in propylene carbonate/ ethylene carbonate/dimethyl carbonate. The initial electrolyte concentration is taken to be 1200 mol/m3, and the system is assumed to be at 25 °C. The equations are coupled through the electrochemical reaction occurring at the electrolyte−electrode interface, which is given by the Butler−Volmer correlation, as shown earlier in eq 1. A slight modification is made to the correlation used for exchange current density, which is reported to have dependence on concentration.66 The exchange current density formula is given by

(1)

where α and β are the charge-transfer coefficients, which obey α + β = 1, R is the gas constant, T is the operating temperature, F is the Faraday constant, η is the local overpotential driving the electrochemical reactions, and i0 is the exchange current density of the charge transfer. For a single lattice site in the model, the rate of the redox reactions is thus given as64

kr =

io = kF(ce)α

Ja2 Na F

(2)

where k is the deposition rate coefficient. The coupled equations need to be solved iteratively until steady-state conditions persist throughout the computational domain. The validation of the numerical study performed is obtained through monitoring of the Butler−Volmer current density values. For the uniform interface, applied current density should equal the Butler−Volmer current density at the interface to ensure charge conservation and is readily obtained from the simulation results. Similar computational analyses are performed for the rough interface with protrusion in the center of the domain of dimensions 5 μm × 5 μm. Here again, we ensure that the total current entering and leaving the electrolyte phase is the same (charge conservation). However, the presence of surface roughness ensures that current density will change at the surface features, although the net summation of current density at the interface will still equal the applied current density.

where a is the lattice constant and Na is Avogadro’s constant. For Li surface diffusion and Li-ion transport, their rates are estimated by Arrhenius formulation ij − E yz kd , ke = ν expjjj a zzz j k bT z k {

(3) 13 −1

where ν is the jumping frequency, approximately 10 −10 s , kb is the Boltzmann constant, and Ea is the energy barrier for Li diffusion on the metal surface or Li diffusion on the substrate or Li-ion transport in the electrolyte, i.e., the height of the barrier that needs to be overcome. The deposition is conducted under constant Li-ion concentration in the electrolyte. Here, Li-ion occupation ratio is defined as the ratio of the number of Li ions to the number of available Li-ion sites in the electrolyte, which is fixed to 5%. Therefore, new Li ions will be added to the electrolyte domain from the upper boundary in Figure S1, compensating for the consumption of Li ions at the reaction front. Periodic boundary condition is applied in the horizontal direction. The lattice is a 100 × 100 grid of 10 000 sites in the two-dimensional model. To be in line with the body-centered cubic Li, the lattice constants are 3.5 Å in the horizontal direction and 1.75 Å in the vertical direction. The operating process runs until 1800 Li atoms are deposited on the substrate. Li is assumed to be freely deposited on the substrate, without the growth resistance, such as the internal cell pressure and constraints from the separator. This assumption can be applied to the system with a low pressure during the initial Li nucleation and growth before the deposited Li contacts the separator. In a previous study, Wood et al. found that as Li dendrites impinge on the polymer separator, the highly pressurized internal volume can flatten the dendrite topography as a result of Li plastic deformation.2 All of the parameters used in the coarse-grained mesoscale model are listed in Table S1. Macrohomogeneous Model. Coupled species and charge transport inside the electrolyte and electronic transport are solved on the two-dimensional computational domain shown in Figure S4. The domain dimensions are 50 μm × 50 μm for each phase in the vertical and horizontal directions, respectively; thus, the overall dimension becomes 100 μm × 50 μm in the vertical and horizontal directions, respectively. The boundary conditions for the species and charge conservation equations are shown explicitly in Figure S4. Governing equations in the electrolyte and solid phase are given in eqs 4−6. 12

∇·(κ ∇ϕe) + ∇· (κD∇ϕe) = 0

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(5)

∇·(σ ∇ϕs) = 0

(6)

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsami.8b08796.

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Detailed description of the mesoscale model and effects of the substrate on Li deposition morphology, including Li diffusion kinetics on the substrate and the substrate roughness (PDF) Li-ion transport in the electrolyte on the electrodeposition morphology (AVI)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Partha P. Mukherjee: 0000-0001-7900-7261 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This study was funded in part by the Office of Energy Efficiency and Renewable Energy (EERE), U.S. Department of Energy, under Award DE-EE0007766.

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(4)

∂ce = ∇·(De∇ce) ∂t

(7)

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where κ is the ionic conductivity, κD is the diffusional conductivity, De is the ionic diffusivity in the electrolyte, σ is the electronic conductivity of Li metal, ϕe and ϕs are the potentials in electrolyte and solid phase, respectively, and ce is the concentration of Li+ ions in the electrolyte phase. Electrolyte property correlations (conductivity, diffusivity, transference number, thermodynamic factor) are taken 26325


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Mesoscale Complexations in Lithium Electrodeposition - American

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