Reactions of Singly-Reduced Ethylene Carbonate in Lithium Battery

Feb 21, 2012 - Reactions of Singly-Reduced Ethylene Carbonate in Lithium Battery Electrolytes: ... Wasatch Molecular, Inc., Salt Lake City, Utah 84103...
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Reactions of Singly-Reduced Ethylene Carbonate in Lithium Battery Electrolytes: A Molecular Dynamics Simulation Study Using the ReaxFF Dmitry Bedrov* Department of Materials Science and Engineering, University of Utah, Salt Lake City, Utah 84112, United States

Grant D. Smith Wasatch Molecular, Inc., Salt Lake City, Utah 84103, United States

Adri C. T. van Duin Department of Nuclear and Mechanical Engineering, Pennsylvania State University, State College, Pennsylvania 16802, United States ABSTRACT: We have conducted quantum chemistry calculations and gas- and solution-phase reactive molecular dynamics simulation studies of reactions involving the ethylene carbonate (EC) radical anion EC− using the reactive force field ReaxFF. Our studies reveal that the substantial barrier for transition from the closed (cyclic) form, denoted c-EC−, of the radical anion to the linear (open) form, denoted o-EC−, results in a relatively long lifetime of the c-EC− allowing this compound to react with other singly reduced alkyl carbonates. Using ReaxFF, we systematically investigate the fate of both c-EC− and o-EC− in the gas phase and EC solution. In the gas phase and EC solutions with a relatively low concentration of Li+/x-EC− (where x = o or c), radical termination reactions between radical pairs to form either dilithium butylene dicarbonate (CH2CH2OCO2Li)2 (by reacting two Li+/o-EC−) or ester-carbonate compound (by reacting Li+/o-EC− with Li+/c-EC−) are observed. At higher concentrations of Li+/x-EC− in solution, we observe the formation of diradicals which subsequently lead to formation of longer alkyl carbonates oligomers through reaction with other radicals or, in some cases, formation of (CH2OCO2Li)2 through elimination of C2H4. We conclude that the local ionic concentration is important in determining the fate of x-EC− and that the reaction of c-EC− with o-EC− may compete with the formation of various alkyl carbonates from o-EC−/o-EC− reactions.

I. INTRODUCTION The properties of the solid−electrolyte interface (SEI) that forms at the anode surface as a result of reduction of the electrolyte solvent and lithium salt are key elements in determining the performance of lithium ion batteries.1 In current batteries, the electrolyte solvent is typically comprised of a mixture of linear and cyclic carbonates, with ethylene carbonate (EC) being a major component of most electrolytes. The solvent and lithium salt anion undergo one- and twoelectron reduction at the anode, typically Li-intercalated graphite. During the first cycle, the reaction products of electrolyte reduction form a thin SEI film, which in the ideal case protects the electrolyte from further reductive decomposition during subsequent cycles. However, the SEI can contribute significantly to the resistance for Li+ exchange between the electrolyte and the electrode. Given the importance of the SEI in lithium batteries, it is clear that improved understanding of the mechanisms of electrolyte © 2012 American Chemical Society

decomposition and the formation of the SEI would facilitate optimization of battery performance. There have been a number of experimental studies focusing on understanding the mechanisms of the SEI formation. A detailed discussion of most of these can be found in ref 1. Here we only briefly summarize findings from this extensive literature that are most relevant to this study. In general, the SEI is thought to consist of an inner and an outer layer. The inner layer is believed to be primarily comprised of doubly reduced compounds, such as Li2CO3, while the outer SEI layer is thought to be comprised largely of reaction products of singly reduced electrolyte species.2,3 One electron reduction of EC yields the radical anion shown in Figure 1a, labeled c-EC− to indicate the cyclic (closed) form of the radical. The reduced EC has a negative charge and can be expected to be associated with Received: October 27, 2011 Revised: February 19, 2012 Published: February 21, 2012 2978

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1e) forms from the reaction of Li+/o-EC− with Li+/c-EC−. In terms of energy and free energy, the following trend has been observed: (CH2CH2OCO2Li)2 < (CH2OCO2Li)2 + CH2 CH2 < ester-carbonate compound.4 Furthermore, this DFT study revealed that, while Li+/o-EC− is much lower in energy than Li+/c-EC− (by 29 kcal/mol), there is a substantial energy barrier for opening Li+/c-EC− to form Li+/o-EC−, of around 12 kcal/mol in both potential and free energy. For the elementary reaction A ↔ A*, where A* represents an activated complex, the Eyring rate equation is given as9 ⎡ ΔG* ⎤ k T k = b exp⎢ − ⎥ h ⎣ kbT ⎦

(1)

Therefore, at room temperature, the estimated lifetime of Li+/ c-EC−, given as 1/k, is around 100 μs. Hence, reactions involving the high-energy but long-lived c-EC− form of the EC radical anion to form the ester-carbonate compound shown in Figure 1e should be considered as a possible contributor to the outer SEI in EC-based electrolytes. While the presence of (CH2OCO2Li)2 in the SEI formed from EC-based electrolytes is not disputed, there is also evidence for the presence of (CH2CH2OCO2Li)2 and the estercarbonate compound. Aurbach et al. proposed (CH2CH2OCO2Li)2 as a species in the SEI formed on lithium metal anodes.5 The combined TEM/FTIR study that claimed evidence for the presence of (CH2OCO2Li)2 also found evidence for an alkyl carbonate compound with O/C ratio = 1, which the investigators associated with (CH2CH2OCO2Li)2.8 We note that this O/C ratio is also consistent with the estercarbonate compound. In contrast, NMR analysis of surface compounds formed on graphite electrodes that was consistent with the presence of (CH2OCO2Li)2 also appears to rule out the possibility of compounds of the structures shown in Figure 1d,e.7 In general, however, studies (e.g., FTIR and XPS) that reveal the presence of alkyl carbonates in the SEI formed in EC-based electrolytes do not allow for the differentiation between (CH2OCO2Li)2 and (CH2CH2OCO2Li)2 and the ester-carbonate compound. It also seems to us that even the ethylene glycol observed in the hydrolysis study of EC reduction products6 could be produced from the estercarbonate compound as well as from (CH2OCO2Li)2. In this work we have utilized reactive molecular dynamics simulations to gain insight into reactions of singly reduced EC in both gas and condensed (solution) phases. While real electrolytes contain a mixture of compounds and likely undergo reactions involving both single and double reduction pathways, we believe a study of a simplified system comprised of Li+ cations and EC radical anions in EC solution will provide insight into the competitive radical combination pathways available to singly reduced EC. Specifically, we apply the reactive ReaxFF force field (see below) in the study of the fate of singly reduced EC. In these studies, reactions of Li+/o-EC−, Li+/c-EC−, or both are followed using reactive molecular dynamics in the gas phase and in a solution of (neutral) EC molecules. We carry out studies of the free energy barrier in the gas and condensed phase for predefined pathways of radical combination reactions believed to be important. Also, in the condensed phase (EC solution), we carry out simulations without any imposed reaction pathway, that is, the system evolves (reacts) according to the thermodynamics and kinetics of the various competitive reactions as represented by the ReaxFF model as a function of ion concentration. We believe

Figure 1. Main components in formation of SEI in the EC-based electrolytes: (a) closed EC radical/Li+; (b) open EC radical/Li+; (c) dilithium ethylenedicarbonate; (d) dilithium butylenedicarbonate; (e) ester containing compound; (f) precursor for formation of (e).

a Li+ cation, as shown in Figure 1, yielding the complex denoted as Li+/c-EC−. The reduction of EC has been shown in ab initio electronic structure (quantum chemistry, or QC) calculations to be greatly facilitated by the presence of the Li+ cation.4 The cyclic Li+/c-EC− radical is then thought to undergo a ring-opening reaction forming Li+/o-EC−, as shown in Figure 1b. It has been well established that the open (linear) form of the EC radical anion is significantly lower in energy than the closed form.4 It is generally held that the reactions of o-EC− are central to the formation of the outer part of the SEI,1 and it is these reactions that are topic of this paper. Dilithium ethylene dicarbonate (CH2OCO2Li)2 has been proposed as a major component of the anode SEI1 resulting from combination reactions of pairs of Li+/o-EC− radicals. FTIR and XPS studies of SEI films formed on lithium metal in EC-based electrolytes reveal the presence of alkyl carbonates,2,5 while FTIR shows the presence of alkyl carbonates in the SEI formed from EC/diethyl carbonate electrolytes on graphite.3 Hydrolysis of alkyl carbonate species formed from reduction of EC on noble metal electrodes leads to the formation of ethylene glycol, which has been taken as evidence for the formation of (CH2OCO2Li)2.6 NMR studies of the surface species formed on graphite in EC electrolytes resulted in spectra consistent with that of alkyl carbonates and, in particular, the spectrum of (CH2OCO2Li)2.7 A combined TEM/FTIR study of the SEI formed on graphite in a EC/ LiClO4 electrolyte revealed the formation of alkyl carbonates, one of whose chemical composition (O/C ratio = 1.5) is consistent with (CH2OCO2Li)2.8 In addition to experimental investigations, QC studies have provided important insight into single reduction reactions of EC. In a seminal study, density functional theory (DFT) calculations at B3PW91/6-311++G(d,p) level of theory were performed in order to investigate the energetics of radical termination reactions of EC−.4 The important suggested radical combination products are shown in Figure 1c,d. Both (CH 2 OCO 2 Li) 2 and dilithium butylene dicarbonate, (CH2CH2OCO2Li)2, are believed to form by the reaction of two Li+/o-EC−, while the ester-carbonate compound (Figure 2979

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this study is the first to utilize a reactive force in the study of products formed from single electron reduction of EC. Furthermore, as shown below, our simulations result in the formation of products which are experimentally observed, and raise the possibility of additional products, particularly at high ion concentrations.

II. QUANTUM CHEMISTRY CALCULATIONS AND REAXFF PARAMETERIZATION Quantum Chemistry Calculations. As we discussed above, QC calculations have been utilized to study the stability of and potential pathways in the gas phase for formation of various compounds believed to be important in reactions of reduced EC. In this work, we conducted several additional QC calculations with the primary purpose of providing the database for ReaxFF parametrization as well as validation of the relative stability of radical recombination products predicted from ReaxFF simulations. Here, we provide a brief description of our QC calculations while the ability of ReaxFF to reproduce these data is discussed below. As mentioned above, the substantial barrier for opening the closed form of singly reduced EC radical can potentially make this compound important in the formation of the SEI. Hence, the transition from Li+/c-EC− to Li+/o-EC− must be accurately modeled by ReaxFF. Therefore, we have performed additional quantum chemistry calculations in order to investigate the barrier for the Li+/c-EC− → Li+/o-EC− transition. We employed the aug-cc-pvDZ basis set for EC, while lithium was represented with a previously derived basis set.10 All geometry optimizations and energies were determined at the MP2 level and at the DFT level using the M05-2X functional.11 At the MP2 level we found a potential energy barrier for Li+/cEC− → Li+/o-EC− transition of around 15 kcal/mol, while the barrier at the DFT level was found to be between 16 and 17 kcal/mol. These values are somewhat larger than obtained in previous DFT calculations at the B3PW91/6-311++G(d,p) level (see Conclusions for additional discussion).4 We also investigated breaking of C2H4 from Li+/o-EC− as this process is potentially important in formation of (CH2OCO2Li)2 from two singly reduced radicals. Figure 2 shows the energy for this reaction from DFT calculations as a function of C−O bond length employing the M05-2X functional with the same basis sets as described above. These results indicate that the barrier to break C2H4 from Li+/o-EC− is high, between 26 and 27 kcal/mol, similar to the energy of the Li+/CO3− radical complex and C2H2 at large separation. The Li+/CO3−/C2H2 complex energy can be stabilized by about 9 kcal/mol by C2H2−Li+ interactions as shown in Figure 2. ReaxFF Concepts. ReaxFF is a bond-order based potential, which also includes a polarizable charge calculation (EEM12). ReaxFF uses a substantially longer-range bond-order than the first generation of bond-order based reactive force fields.13−15 These bond orders are adjusted for local over-coordination, enabling a good reproduction of energies for both stable compounds as well as transition states. ReaxFF calculates nonbonded interactions, including van der Waals and Coulomb interactions, between all atom pairs, including atoms sharing a bond or an valence angle. This, in combination with the bond order concept, enables ReaxFF applications to both covalent and ionic materials. Since its first formulation for hydrocarbons,16 ReaxFF has been applied to a wide range of materials, including covalent,16,17 metallic18,19 and (partially) ionic materials.20−22 The Li/C/H/O parameters used in this

Figure 2. Energy profile for breaking C2H4 from o-EC−/Li+, as obtained from QC calculations and gas phase simulations using ReaxFF at 10 K.

work are an update of the previously developed ReaxFF parameters for Li/C/H systems.23 Parameterization and Validation. While ReaxFF has been shown to be transferable for a number of systems, it has not been utilized to study reaction pathways of the carbonate radical anions as carried out in this study. Hence, additional validation and training of ReaxFF against QC results for relevant compounds and reaction pathways were necessary. First, we investigated the ability of the previously reported ReaxFF Li/C/H parameter sets23 to reproduce the energetics of the ring-opening reaction Li+/c-EC− → Li+/o-EC−. The barrier and the energy difference between Li+/c-EC− and Li+/oEC− differed significantly from QC predictions and the geometry of Li+/EC− radical complexes were quite different from those predicted by QC. Therefore, we have reparameterized ReaxFF to better reproduce the QC data. To this end, we added these Li/EC QC-data to the ReaxFF Li/C/H/O training set, added relevant data from the C/H/O ReaxFF training set17 and reparameterized all Li/Li, Li/C, Li/H and H/ C/O angular terms. In this reparameterization, we also constrained the Li+ to have a charge of +1.0e and the carbonate group of EC radical equal to −1.0e. This constrain was necessary to correctly describe configuration of CH2CH2/ Li+/CO3− cluster discussed below. Figure 3 shows the energy surface for the ring-opening reaction Li+/c-EC− → Li+/o-EC−, as predicted by reparameterized ReaxFF. ReaxFF yields a saddle point energy of 11 kcal/ mol and an energy for Li+/o-EC− of −26 kcal/mol relative to Li+/c-EC−. Also shown in Figure 3 are the geometries and energies of the saddle point and Li+/o-EC− predicted at the MP2 and DFT level as discussed above as well as the B3PW91/ 6-311++G(d,p) level from the previously published study.4 A more recent study of the influence of basis set and electron correlation treatment on the Li+/c-EC− → Li+/o-EC− barrier yielded an estimated barrier of 15.6 kcal/mol at the highest level employed, CCST(T)/aug-cc-pVQZ.24 This same study yields a barrier of 17.2 kcal/mol at the MP2/aug-cc-pVDZ level, equivalent to our study, which yields a barrier of around 15 kcal/mol. Figure 3 reveals significant distortion of the r2 bond at the saddle point determined at the MP2 level. This 2980

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Figure 3. Contour map for c-EC−/Li+ opening R1, R2 as obtained from ReaxFF simulations at 10 K. Also shown are the location and energy for the saddle points obtained from QC calculations.

Note on Limitations of ReaxFF. While the ability of ReaxFF to reproduce key reaction properties obtained from QC calculations is encouraging and provides us confidence to apply ReaxFF to study certain aspects of SEI formation in lithium ion batteries, it is necessary to realize that ReaxFF has limitations. The current version of ReaxFF has difficulties in capturing the absolute values of electron affinity and therefore would have trouble describing the energetics of reduction process. For example, the reduction potential of the EC molecule in the gas phase predicted by ReaxFF is about −2.6 eV (−61 kcal/mol), while QC predicts around +0.3 eV (+8 kcal/mol).4 This serious deficiency of ReaxFF currently prevents accurate modeling of reduction process. For example, if ReaxFF simulations of Li metal/electrolyte interface were to be conducted, such as those in ref 25, then the rate of electrolyte reduction would be unrealistically too fast. While we are currently working on enhancement of ReaxFF model to eliminate this deficiency, ReaxFF simulations still can be quite useful in investigation of mechanisms of SEI formation if limitations of the model are realized and taken into account. Specifically, we believe that reactions of already reduced compounds, such as studied here, can be captured by ReaxFF quite well. Therefore, our primary focus here will be on reactions of reduced radical anions, rather than the modeling of the reduction process itself.

distortion was discovered during an effort to construct an energy contour map by systematically varying r1 and r2. Simply performing a scan on r1 yields another, higher energy saddle point with little distortion of r2. We believe the difference between our result and that of Han and Sang at the MP2/augcc-pVDZ level is due to different saddle point geometries. If we take the difference in energy between MP2/aug-cc-pVDZ and CCST(T)/aug-cc-pVQZ levels obtained by Han and Sang and apply this to our saddle point geometry, we obtain an estimated energy of around 13.4 kcal/mol The ReaxFF value for the saddle point (11 kcal/mol) was purposely kept somewhat lower than this best-estimate value, in order to facilitate this reaction to occur on time scales accessible to ReaxFF simulations. Figure 2 also compares energies obtained from QC and ReaxFF for the split of CH2CH2 from Li+/o-EC−. In this reaction, the initial configuration of Li+/o-EC− is such that the Li+ and ethylene group are on opposite sides of the carbonate group. As the O−C bond begins to increase, the energy of this complex is increasing both in QC and ReaxFF simulations. In QC calculations, the energy increased by about 27 kcal/mol (relative to the minimum energy configuration) at an O−C separation of about 2.4 Å. This energy change is very similar to the energy difference between Li+/o-EC− in the optimal configuration and the energy for CH2CH2 + Li+/CO3− at infinite separations. However, as the O−C separation increases beyond 2.4 Å, the CH2CH2 + Li+/CO3− cluster can rearrange its geometry such that Li+ is located between CO3− and CH2CH2. The QC energy for this optimal geometry is 17 kcal/mol above the minimum energy configuration of Li+/oEC−. As can be seen from Figure 2, ReaxFF predictions along this path are in good agreement with QC calculations.

III. MOLECULAR DYNAMICS SIMULATIONS OF EC− REACTIONS USING REAXFF A. Simulation Methodology. Systems for condensedphase simulations consisted of total 100 EC-based species (EC, Li+/o-EC− and Li+/c-EC−). Table 1 reports the number of all species in each investigated system. For each system, all species 2981

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Table 1. Composition of Mixtures Simulated Using ReaxFF in Condensed Phase system system system system

1 2 3 4

EC

c-EC−

o-EC−

Li+

50 50 90 50

50 45 0 0

0 5 10 50

50 50 10 50

were initially placed on a low-density lattice. Short (30−40 ps) equilibration simulations were performed to shrink the system to a density similar to the bulk density of EC liquid at room temperature. These runs were conducted at 50 K to inhibit any reactions during equilibration. Another short equilibration simulation was used to heat up the system to 313 K by steadily rescaling velocities of all atoms. Subsequent to these initial preparation runs, simulations over 200 ps were conducted in the NPT ensemble to establish the correct density for each system at atmospheric pressure and 313 K. Finally, production runs over 500 ps were conducted in NVT simulations to study reaction mechanisms. All simulations employed a 0.2 fs time step. To facilitate kinetics of reactions, some systems were also simulated at 513 K using cell dimensions obtained for atmospheric pressure at 313 K. For gas-phase simulations, the desired species were set up in a relatively large simulation cell (>6 nm in linear dimension). Most of these simulations were conducted to study predefined reaction pathways using biasing potentials described below. These simulations were performed at 10 K to facilitate comparison/validation against QC calculations as well as at 313 K to allow comparison with equivalent simulations in EC solution phase using ReaxFF. To enforce a desired reaction pathway (both in condensedand gas-phase simulations) an additional biasing potential was introduced between two atoms participating in the bond breaking/forming reaction. This biasing potential had the following form: Ubias = f * exp( −(r − r0)2 )

Figure 4. Reaction pathways between EC-based radicals. Also given are the energy difference and the barrier for each reaction predicted by ReaxFF in the gas phase at 10 K.

(2)

where f is a force constant ( f = −500 kcal/mol) and r0 and r are the target and actual separations between the atoms participating in the reaction. These simulations were conducted over 100 ps, with r0 changing every time step (0.2 fs) by δr0 = 2 × 10−5 Å. The constraint force and energy from the biasing potential as a function of reaction coordinate (r) were recorded and were used to determine the potential of mean force (PMF), or free energy, as a function of the reaction coordinate. In section B we focus on gas-phase simulations using ReaxFF in which radical−radical reaction paths are predefined. In Figure 4 we show main reactions pathways investigated. In section C we consider the chemistry of the EC− radical anions in EC solution. B. Gas Phase Reactions. Reactions between Li+/o-EC−. The most obvious reaction is direct recombination of two Li+/ o-EC− radicals (Figure 4a) resulting in the formation of (CH2CH2OCO2Li)2. The QC study of Balbuena et al.4 predicted that this reaction is the most energetically favorable for the reaction of two Li+/o-EC−, but provided no estimate of the reaction barrier. Gas phase ReaxFF simulations at 10 K predict a very small barrier of about 3.5 kcal/mol (energy and free energy are almost the same at this T) as well as about 47 kcal/mol of energy drop between reactants and the product. While the reaction shown in Figure 4a is the most obvious, it is

not typically discussed as the primary reaction of EC involved with formation of the outer SEI formation. Instead, the reaction path shown in Figure 4b, where the radical carbon from one Li+/o-EC− attacks oxygen on another Li+/o-EC−, resulting in the formation of (CH2OCO2Li)2 + CH2CH2, has been proposed (see Introduction). The PMF obtained from ReaxFF gas phase simulations at 10 K shows that the energy (free energy) change is quite favorable for this reaction (−29 kcal/ mol), although it is not as favorable as for the formation of (CH2CH2OCO2Li)2. The latter is consistent with Balbuena predictions, 4 which found that the formation of (CH2CH2OCO2Li)2 is about 11 kcal/mol more favorable than the formation of (CH2OCO2Li)2 + CH2CH2. However, the energy barrier for this reaction is much higher than for formation of (CH2CH2OCO2Li)2, about 14−15 kcal/mol. For a barrier of this magnitude, eq 1 predicts the time scale of several ms (at 313 K) for this reaction to occur, which is about 9 orders of magnitude longer than the time scale for the reaction in Figure 4a to occur. Hence, gas-phase ReaxFF simulations indicate that the reaction in Figure 4b is unimportant compared to the reaction in Figure 4a. Note that the radical termination shown in Figure 4a and b involves a 2982

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the electrode during initial stages of SEI formation. ReaxFF simulations reveal that the Li+/c-EC− → Li+/o-EC− reaction in bulk EC has basically the same free energy barrier as in the gas phase (11−12 kcal/mol). In the system with a high concentration of Li+/c-EC−, the free energy barrier for different runs varied between 9 and 12 kcal/mol, indicating that a high concentration of Li+ and c-EC− ions in local environment can reduce the barrier for the ring-opening reaction. These simulations show that details of ion distribution in the local environment can influence reaction barriers and, hence, reaction mechanisms. This is consistent with our latest QC study of oxidation process of organic electrolytes where we found that the presence of a PF6− ion in the vicinity of PC has a significant influence on the PC oxidation process.26 Similarly, we have conducted simulations for radical recombination/propagation reactions shown in Figure 4a−f at 313 K. In bulk EC, the free energy difference between reactants and products and the reaction barriers were essentially unchanged compared to gas phase investigation. For some reactions, the barrier was found about 1.0 kcal/mol lower in the solution phase. More detailed investigation of influence of local environments on specific reaction paths relevant to SEI formation is currently underway using QC, QC-MD, and RMD methods. Unbiased Simulations. Finally, unbiased ReaxFF simulations of the radical solutions listed in Table 1 have been conducted at 313 and 513 K to study reaction mechanisms/ products in solution. First, we consider system 1 (Table 1), which has a large concentration of Li+/c-EC− complexes and no Li+/o-EC−. Simulations of this system at 313 K showed no reactions occurring on time scales of 500 ps. As we discussed above for biased simulations, the barrier for opening c-EC− in this environment is on the order of 9−12 kcal/mol, which means that the lifetime of closed EC radicals should be on the order of μs and therefore the probability of observing such a reaction on time scale of our simulations is extremely low. However, if the temperature is increased to 513 K the time scale for radical opening reaction moves into the ns scale and therefore there is a reasonable probability that during 500 ps simulation some c-EC− will undergo this reaction. Indeed, simulations of system 1 at 513 K reveal two Li+/c-EC− → Li+/ o-EC− reactions, with no other reactions occurring on the time scale of the simulation. While reactions between Li+/c-EC− are not expected due to very high reaction barriers obtained in the gas phase simulations, we expect that open radicals would eventually either recombine with other o-EC− (Figure 4a) or potentially could react with c-EC−/Li+ (Figure 4f). Taking into account that the barrier for the former reaction is only 3.5 kcal/mol compared to 12 kcal/mol for the latter, the first reaction should be favored kinetically. However, in systems where the concentration of Li+/c-EC− is much larger than Li+/o-EC− the second reaction would be favored. In order to investigate these competitive reaction mechanisms in more detail, we simulated system 2 in which five Li+/o-EC− were randomly distributed in the system. Simulations of system 2 at 313 K showed only two reactions over a 500 ps trajectory. Both of these reactions were of the type in Figure 4f. Simulations at 513 K as expected showed much more reactivity. At this temperature, we observed some of Li+/c-EC− going through ring-opening reaction therefore increasing the overall concentration of Li+/o-EC− in the system. We also observed radical termination reaction between two Li+/o-EC− with formation of

triplet (two single radicals) reactant state and a singlet product state. We were unable to determine the barrier from DFT calculations for these reactions by looking for crossing (in energy) of the triplet and singlet reaction pathways along the reaction coordinate indicated by the arrow in Figure 4a and 4b. We also point out that within the ReaxFF framework the triplet and single states are not differentiated and the barrier for a given reaction is determined by force field parameters. Other possible reactions between two Li+/o-EC− shown in Figure 4c,d have been also investigated. Both of these reactions do not result in radical termination and produce intermediate diradicals that undergo further reactions. ReaxFF predicts that in a gas phase these two reactions have moderate barriers as shown in Figure 4. The diradical product shown in Figure 4c in principle can go through radical termination reaction by eliminating ethylene and forming (CH2OCO2Li)2. ReaxFF predicts that the barrier for such a reaction is 10 kcal/mol in the gas phase, which is much lower than the barrier for one-step formation of (CH2OCO2Li)2 (Figure 4b). Based on ReaxFF investigation of reaction pathways of Li+/oEC− radicals in the gas phase, the only product we would expect with reasonable probability is the formation of (CH2CH2OCO2Li)2. To confirm that this is not an artifact of the applied biasing potentials, we have also conducted unbiased simulations of two Li+/o-EC− radicals in the gas phase at 313 K. In these simulations, two Li+/o-EC− complexes were placed in a cubic simulation cell of size 30 Å and run without any biasing potentials until reaction occurred. Numerous simulations using different initial configurations were conducted. In all simulations, only (CH2CH2OCO2Li)2 was obtained. Reactions Involving Li+/c-EC−. The PMF in the gas phase was also determined for the reactions of Li+/c-EC − with Li+/cEC− and Li+/o-EC−, as shown in Figure 4e,f. The energy barrier for the reaction between two Li+/c-EC − (Figure 4e) at 10 K is large (24 kcal/mol). However, the gas-phase reaction path for Li+/o-EC − with Li+/c-EC (Figure 4f) has a barrier of around 12 kcal/mol, which while substantial is comparable to that for the ring-opening reaction. These results imply that the reaction of Li+/o-EC− with Li+/c-EC− can occur rapidly enough and that this reaction could be important in the formation of the outer SEI in EC-based electrolytes. We note that while QC4 and ReaxFF predict the ester (open) form of the combined species of o-EC− with c-EC− (Figure 1e) to be lower in energy than the closed form (Figure 1f), ReaxFF predicts the barrier for this reaction (Figure 1f → Figure 1e) to be large. In contrast, QC calculations reveal that this barrier is actually quite small. We are currently working on an improved parametrization of the ReaxFF that will address this discrepancy. C. Solution Phase Reactions. Predefined Reaction Pathways. First, as in the gas phase, we consider simulations where the reaction pathway between two species is predefined and the reaction is forced on the time scale of 100 ps through a biasing potential. This time scale is sufficiently long to allow the surrounding solvent to adjust to the changing reaction coordinate. These simulations allow us to investigate the influence of the solution environment on the free energy barrier for important reactions. We first investigated the Li+/c-EC− → Li+/o-EC− reaction. Specifically, we investigated the PMF for this reaction in the gas phase, bulk EC liquid, and a 50/50 mixture of EC and Li+/c-EC− complexes at 313 K. In the latter system, the presence of c-EC−/Li+ represents a high salt concentration environment that, in principle, can occur near 2983

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(CH2CH2OCO2Li)2 (Figure 4a) and multiple reactions between Li+/o-EC− and Li+/c-EC (Figure 4f). The latter reaction was dominant despite the fact that the former reaction has a much lower barrier. One can argue that concentration of Li+/o-EC− in the system is still relatively low and hence o-EC− radicals just did not have enough time or opportunity to “find” each other in order to allow the reaction in Figure 4a to occur. However, we observed formation of diradical species (Figure 4c,d) that involve reaction of two Li+/o-EC−. As we discussed above the reaction barrier for these reactions in the gas phase is larger than for the reaction in Figure 4a. Nevertheless, we see several of these reactions indicating that low concentration of Li+/o-EC− is not the primary reason we do not see dominance of (CH2CH2OCO2Li)2. At the latter stages of system 2 simulations, we observed that, after some time subsequent to its formation, the diradical shown in Figure 4c underwent a self-termination reaction splitting off C2H4 and forming (CH2OCO2Li)2. As we showed in Figure 4, the barrier for this reaction in the gas phase is about 10 kcal/mol, and hence, we can expect to see this reaction occur on similar time scales as opening of Li+/c-EC−. We have not observed the reaction in Figure 4b, which would allow direct formation of (CH2OCO2Li)2 from two Li+/o-EC−. Finally, the formation and presence of diradicals in Figure 4c and d in the system potentially can lead to the formation of longer alkyl carbonates by reacting with other radicals until all radical sites are eliminated. However, we have not observed these longer compounds in system 2 during our simulation, but we anticipate that they could form at later stages (see the discussion of system 4 below). We also investigated systems in which we only have o-EC−. System 3 contains a relatively low concentration of Li+/o-EC− representing conditions where the concentration of Li+/c-EC− is expected to be low and hence they would have plenty of time to undergo ring-opening reaction before they encounter another radical (i.e., reactions such as Figure 4f are expected to be rare). In this system, simulations at both temperatures yielded only the formation of (CH2CH2OCO2Li)2 compounds, indicating that in an environment with low radical and ion concentration (CH2CH2OCO2Li)2 is expected to be the dominant product of radical recombination. In system 4, we have significantly increased the concentration of Li+/o-EC−. In this system, simulation even at 313 K resulted in large number of reactions. Surprisingly, we observed only a few radical termination reactions resulting in (CH2CH2OCO2Li)2. Most of the reactions resulted in the formation of diradicals (Figure 4c,d). These diradicals subsequently reacting with other radicals resulted in formation of longer alkyl carbonates oligomers, some of which are shown in Figure 5. These longer alkyl carbonates still have radical sites available, and therefore, one can expect them to grow as simulations proceed. In this system, we have not observed the formation of (CH2OCO2Li)2; however, we expect that, as in system 2, this compound can eventually form from diradicals.

Figure 5. Snapshots of longer alkyl carbonates oligomers formed during the condensed phase ReaxFF simulations through radical propagation reactions.

leading to formation of o-EC− from c-EC− revealed by QC studies combined with the relatively low barrier for the formation of the ester-carbonate compound from the reaction of c-EC− with o-EC− implies that the presence of the estercarbonate compound as a component of the SEI in EC-based electrolytes should be given serious consideration. Using gasphase and solution-phase ReaxFF simulations, we believe that we have demonstrated that the (CH2CH2OCO2Li)2 compound can easily form through recombination of two o-EC− in the gas phase or at a low concentration of these radicals in EC solution. We note that our lower concentration solution has an ion concentration comparable to typical bulk electrolytes, albeit all in the form of Li+/EC− as opposed to the majority of ions coming from the lithium salt (e.g., LiPF6). However, at high concentrations of EC− radicals, this compound is not dominant despite having the most favorable free energy of formation and the lowest kinetic barrier (in the gas phase). Depending on the relative concentration of o-EC− and c-EC−, the most populous compounds are either the ester-carbonate compound formed by reaction between o-EC− and c-EC− or diradicals formed by reaction of two o-EC−. The latter can either undergo C2H4 elimination and form (CH2OCO2Li)2 (rare) or to continue to grow through further reactions with other radicals. The ion/ radical concentration in the higher concentration solutions is unphysically high. However, the purpose of this study was to investigate the possible influence of local radical/ion population on reaction mechanisms as the actual local environment in

IV. CONCLUSIONS A review of experimental and quantum chemical studies of compounds present or likely to be present in the outer SEI formed at the anode in EC-based electrolytes leads to the conclusion that these studies cannot be easily reconciled regarding the importance/presence of (CH2CH2OCO2Li)2, (CH2OCO2Li)2, and the ester-carbonate compound. The observed relatively large barrier for the ring-opening reaction 2984

dx.doi.org/10.1021/jp210345b | J. Phys. Chem. A 2012, 116, 2978−2985

The Journal of Physical Chemistry A

Article

(18) Mueller, J. E.; van Duin, A. C. T.; Goddard, W. A. J. Phys. Chem. C 2010, 114, 4939−4949. (19) LaBrosse, M. R.; Johnson, J. K.; van Duin, A. C. T. J. Phys. Chem. A 2010, 114, 5855−5861. (20) van Duin, A. C. T.; Merinov, B. V.; Jang, S. S.; Goddard, W. A. J. Phys. Chem. A 2008, 112, 3133−3140. (21) Raymand, D.; van Duin, A. C. T.; Baudin, M.; Hermansson, K. Surf. Sci. 2008, 602, 1020−1031. (22) Chenoweth, K.; van Duin, A. C. T.; Persson, P.; Cheng, M. J.; Oxgaard, J.; Goddard, W. A. J. Phys. Chem. C 2008, 112, 14645− 14654. (23) Han, S. S.; van Duin, A. C. T.; Goddard, W. A.; Lee, H. M. J. Phys. Chem. A 2005, 109, 4575−4582. (24) Han, Y.-K.; Lee, S. U. Theor. Chem. Acc. 2004, 112, 106−112. (25) Kim, S.-P.; Duin, A. C. T. v.; Shenoy, V. B. J. Power Sources 2011, 196, 8590−8597. (26) Xing., L.; Borodin, O.; Smith, G. D.; Li, W. J. Phys. Chem. A 2011, 115, 13896−13905. (27) Leung, K.; Qi, Y.; Zavadil, K. R.; Jung, Y. S.; Dillon, A. C.; Cavanagh, A. S.; Lee, S.-H.; George, S. M. J. Am. Chem. Soc. 2011, 133, 14741−14754.

which these reactions occur is unknown. Changing concentration influences the relative propensity of the reactions shown in Figure 4. Because all of these reactions are bimolecular, they would be expected to scale in the same fashion with increasing radical concentration (at the same fraction of open and closed radicals). Hence, the dramatic effect of radical concentration on reaction mechanisms appears to be due to increasing ion concentration. We would also like to point out that the importance of c-EC− in radical recombination necessitates a reasonable concentration of this species. While the lifetime of cEC− is estimated to be 100 μs or even longer, whether the concentration of this species will build up sufficiently to contributed to reduction products will depend upon the rate of electron injection into the electrolyte. Estimates of this rate during formation of single electron compounds on model electrodes27 seem to indicate that formation of significant concentrations of c-EC− is unlikely. Finally, the mechanism shown in Figure 4b for formation of (CH2OCO2Li)2, often suggested as the most important compound of the outer SEI, was not observed in any of our simulations.

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge financial support by the Department of Energy through DE-AC02-05CH11231 grant on PO No 6838611 to University of Utah. A.C.T.v.D. also acknowledges the support of the Fluid Interface Reactions, Structures and Transport (FIRST) Center, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences.

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dx.doi.org/10.1021/jp210345b | J. Phys. Chem. A 2012, 116, 2978−2985