Simulation of Aqueous Dissolution of Lithium Manganate ... - CMS

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Simulation of Aqueous Dissolution of Lithium Manganate Spinel from First Principles R. Benedek* and M. M. Thackeray Chemical Sciences and Engineering Division, Argonne National Laboratory, Argonne, Illinois 60439, United States

J. Low Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Illinois 60439, United States

Tomás ̌ Bučko Department of Physical and Theoretical Chemistry, Faculty of Natural Sciences, Comenius University, Mlynská Dolina, SK-84215 Bratislava, Slovakia, and Institute of Inorganic Chemistry, Slovak Academy of Sciences, Dubravska cesta 9, SK-84236 Bratislava, Slovakia, and Fakultät für Physik and Center for Computational Materials Science, University of Vienna, Sensengasse 8/12, Wien 1090 Austria ABSTRACT: Constrained density functional theory at the GGA+U level, within the Blue Moon ensemble, as implemented in the VASP code, is applied to simulate aqueous dissolution of lithium manganate spinel, a candidate cathode material for lithium ion batteries. Ions are dissolved from stoichiometric slabs of composition LiMn2O4, with orientations (001) and (110), embedded in a cell with 20 Å water channels between periodically repeated slabs. Analysis of the Blue Moon ensemble forces for dissolution of Li, Mn, and O ions from lithium manganate indicate that bond breaking occurs sequentially, ordered from weak to strong bonds, where bond breaking occurs when a bond length is stretched about 50% relative to its equilibrium value. Substrate ions are displaced to maintain bond lengths close to equilibrium for bonds other than that the one being broken. The predicted free energies required to break the chemical bonds with the LiMn2O4 substrate are Mn3+, 1.4; O2−, 1.0; Mn2+, 0.8; and Li+, 0.35, in eV; an existing experimental measurement (Lu, C. H.; Lin, S. W. J. Mater. Res. 2002, 17, 1476) had yielded an effective dissolution activation energy of 0.7 eV. A mechanism for the role of acid in promoting lithium manganate dissolution is discussed.

I. INTRODUCTION Lithium manganate spinel, LiMn2O4, belongs to one of the three most extensively studied families of cathode materials for lithium ion batteries,1 and is attractive for its safety, low cost, and high rate capability. It is plagued, however, by capacity fade, particularly at elevated operating temperatures (e.g., 50 °C), which is thought to be related in part to its solubility in acid2 that is an unintended byproduct of side reactions of the electrolyte with stray water in the cell.3 In 1981, Hunter observed a proton-promoted dissolution reaction4,5 for LiMn2O4

function of pH and composition, based on a combination of first principles calculations for solid phases and empirical data for aqueous ions. This analysis6 addressed only bulk energies, and the influence of local atomic structure at the aqueous interface was not considered. Thus, the calculated free energies represent the limit of small surface-to-volume ratios, for a reaction going to completion. Dissolution at the LiMn2O 4 surface, in acid, could be addressed, in principle, by an extension of reaction 1:

LiMn2O4 + (2/N )H+

2LiMn2O4 + 4H+ → 3MnO2 + Mn

2+

+

+ 2Li + 2H2O

→ LiMn2 − 1/ N O4 − 1/ N + (1/N )Mn 2 + (1)

+ (1/N )H2O

in which Li and Mn ions are leached from the spinel host by HCl at pH below about 2.5, and the binary manganate product phase is a spinel with an empty Li sublattice. In previous work,6 the free energy of reaction 1 was analyzed [with aqueous species treated in their standard states], as a © 2012 American Chemical Society

(2)

Received: September 12, 2011 Revised: January 4, 2012 Published: January 17, 2012 4050

dx.doi.org/10.1021/jp208793k | J. Phys. Chem. C 2012, 116, 4050−4059

The Journal of Physical Chemistry C

Article

work, we simulate the dissolution of each of the component ions of stoichiometric lithium manganate. Blue Moon Ensemble. Within the Blue Moon ensemble, free energy differences are expressed as thermodynamic integrals of the force,

represents the dissolution of a single MnO unit from the surface of LiMn2O4, and, similarly

Li1Mn2O4 + (2/N )H+ → Li1 − 2/ N Mn2O4 − 1/ N + (2/N )Li+ + (1/N )H2O

ΔA1 → 2 =

(3)

represents the dissolution of a single Li2O unit, where N is the number of formula units contained in the LiMn2O 4 solid. (These reactions can be rewritten to describe dissolution in neutral water with hydroxyl ions among the products instead of protons among the reactants.) Reactions 2 and 3, however, envision dissolution via MnO and Li2O complexes rather than by successive (likely correlated7) dissolution of individual cations and anions. Incidentally, reaction 3 would require Li ion migration to form an Li2O complex, since O ions have only a single Li neighbor in the spinel structure. Although reactions 2 and 3 are useful heuristic models, they may not represent the lowest energy processes. These reactions also only consider the role of protons, and don′t address the possibly significant role of the acid anion.8 In recent years, rare-event simulations, based for example on metadynamics,9 Blue Moon ensemble,10 umbrella sampling,11 etc., have been extensively developed. Few applications have been made to the aqueous dissolution of metal oxides and silicates, however, owing partially to the huge numerical effort required, if implemented with first principles techniques, and adequate cell sizes. Very recently, aqueous dissolution simulations have been presented for NaCl,7 based on metadynamics, and Barite,12 based on metadynamics and umbrella sampling. Blue Moon ensemble simulations of quartz dissolution13,14 had previously demonstrated feasibility of that technique, at least at relatively high temperatures. This paper presents an application of the Blue Moon ensemble to the atomic-scale processes involved in the aqueous dissolution of LiMn2O4 at room temperature. The capability to model lithium manganate (and other metal oxide) dissolution rates in acid15 would be valuable for the prediction of lithium ion battery corrosion. Before addressing the additional complexity of acid-promoted dissolution, however, it seemed desirable to gain experience with the application of constrained DFT simulations of dissolution in neutral water. For example, it would be valuable to gain insight into which ions or complexes are likely dissolution candidates, and the coordination environments that are precursors to dissolution. To determine the hierarchy of dissolution energies in neutral water would be a helpful step toward development of a model of acid-promoted dissolution. Our objective in this work, therefore, was to establish benchmarks for the dissolution of lithium manganate spinel at room temperature in neutral water, based on the Blue Moon ensemble.

ξ(2)

∫ξ(1)

⎛ ∂A ⎞ dξ⎜ ⎟ ⎝ ∂ξ ⎠ξ*

(4)

along the path of a chosen reaction coordinate, ξ. A detailed expression for the force, (∂A/∂ξ)ξ*, suitable for numerical evaluation, was derived by Carter et al.;10 see also refs 18 and 19. To proceed with this approach, an explicit form of the reaction coordinate must be selected. Reaction Coordinate. At least two possible generic reaction coordinates come into consideration, namely the coordination number (CN) of the dissolving species,20 and the perpendicular distance, z, of the solute ion from the substrate.21 The coordination number is an attractive choice to describe the breaking of chemical bonds with the substrate,13,20 despite some arbitrariness in the mathematical form of CN. The sequential, rather than concurrent, breaking of bonds demonstrated in our results, and in previous work,7,12,13 provides some justification for the use of CN as reaction coordinate. When the dissolving ion is sufficiently removed from the substrate that chemical bonding is negligible, electrostatic interactions with the substrate, modulated by the structure of nearby water, become dominant. z is a convenient reaction coordinate to analyze these residual electrostatic interactions. Numerical results for the residual electrostatic interactions are presented for Li dissolution. We argue, however, that the residual electrostatic interactions may only be marginally relevant to the dissolution process, and the focus of this article is therefore on the chemical-bond breaking of the solute with the substrate. Mathematical Representation of CN. In the VASP implementation, individual bond i contributes 18

CNi = (1 − xin)/(1 − xim)

(5)

to the total CN for a given ion, where the reduced bond length xi = ri/rb is normalized to an effective bond length, rb, and n,m = 9,14.22 The effective bond length, rb, is selected so that CN is approximately the number of bonds of the dissolving ion to substrate ions before dissolution. The summation over i is restricted to the termination layer and the first layer below the termination layer, only. The parameters (n,m) that determine the smearing are set so that CNi approaches zero for xi at the first radial distribution function minimum,20 i.e., between the first and second coordination shells. This value of x coincides roughly with typical cutoff radii of ionocovalent interatomic potentials.23 Within a certain range, simulated results are expected to be relatively insensitive to the exact values of n,m and rb, or the adopted functional form of CNi. Substrate Configuration: Spinel Slabs. The structure of bulk lithium manganate spinel is illustrated in Figure 1a. The spin configuration of Mn is treated as ferromagnetic.6 The calculated equilibrium lattice constant is 8.415 Å . Distortions from the ideal spinel structure result from disproportionation of Mn into trivalent and tetravalent ions. The atomic coordinates obtained in previous simulations of LiMn2O4 slabs24 were employed as input data for the present

II. METHOD Code. Software for metadynamics and Blue Moon ensemble simulations has recently been implemented into the VASP code16,17 by Tomás ̌ Bučko.18 The Blue Moon ensemble enables simulation of the dissolution path of a selected species or complex, and is convenient for our present purpose. In this 4051



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Water Channel and Slab Hydroxylation. Unit cells were built with a 20 Å channel between periodically repeated spinel slabs. The channel was filled with 48 and 32 water molecules for the (001) and (110) slabs, which correspond approximately to the density of liquid water. To initialize, water molecules were placed at essentially random, nonoverlapping locations within the channel, and the unit cell was then relaxed by running molecular dynamics at 300K. Some water molecules dissociate during the relaxation, and the resultant hydroxyl ions adsorb to surface Mn ions, while an equal number of protons bond to O ions, at the MnO-terminated slab surfaces. Figure 2

Figure 2. Energy relaxation and hydroxylation of Mn−O terminated (001) slab vs MD simulation time. Water molecules randomly located in the channel between slabs in initial configuration, before relaxation.

illustrates the energy relaxation for the Mn−O terminated (001) slab, and the number of adsorbed hydroxyl ions (or protons) vs simulation time. After relaxation for about 10 ps, the fluctuations in average energy from one 1 ps MD run to the next are small, and the number of adsorbed hydroxyls, n(OH−) = 4. Since top and bottom slab faces each contain an Mn2O4 island, the unit cell contains a total of four termination layer Mn ions, and each is bonded to a hydroxyl. Termination layers contain twice as many O as Mn ions, and therefore only half of the O ions are protonated at this point in the relaxation. Since termination-layer Mn ions coordinate to four substrate O ions, they are therefore 5-fold coordinated in the singly hydroxylated state. Such a configuration (Figure 1b) was employed as starting point for the Blue Moon ensemble simulations for the (001) oriented slabs. Similar relaxation runs were performed for the Mn−O terminated (110) slab. In this case, the surface Mn ion is coordinated to three substrate O ions; with two adsorbed hydroxyls, a total coordination of five occurs, as illustrated in Figure 1c. By continuing the relaxation of the (001) oriented cell for longer times than shown in Figure 2, additional hydroxylation and protonation may occur, to complete the octahedral environment of the termination-layer Mn ions. The influence of this additional hydroxylation on the dissolution free energy, however, is expected to be relatively small. Computational Parameters. To enhance numerical efficiency, soft oxygen pseudopotentials and the gammapoint-only version of VASP are employed. Tritiated water is simulated, to enable stretching the molecular dynamics time step to 1 fs. As in previous work,24 the PW91 exchangecorrelation functional, and effective on-site coulomb interaction Uef f = 4.84 are used in the GGA+U implementation.25 The relevant temperature range for lithium manganate dissolution in

Figure 1. (a) Crystal structure of lithium manganate spinel. Large, intermediate, and small spheres represent O, Mn, and Li. Disproportionation of Mn is responsible for distortions from ideal spinel structure. Dark blue and yellow spheres represent a pair of Mn ions in a (001) layer and coordinated O ions. x, y, and z axes refer to cubic crystallographic axes. (b) Mn ions in (001) termination layer, and coordinated O ions; light-blue spheres represent protons. (c) Same as panel b, for (110)-oriented slab. In this case, the Mn is coordinated to three O ions in the substrate (one in the termination layer and two in the first layer below the termination layer), and two adsorbed hydroxyl ions. The z axis is parallel to 110 direction. Graphics created with VESTA.34.

work. To maintain exact stoichiometry, and to minimize spurious dipole moments across the slab, slabs were constructed with half of the termination-layer sites unoccupied.24 For the Mn−O terminated (001) slab, the constructed termination layers consist of Mn2O4 islands in the shape of isosceles right triangles, with Mn at the midpoints of the short sides of the triangle, and O at the vertices and the midpoint of the long side. The yellow and blue spheres in Figure 1a illustrate such a cluster; cf. also Figure 2 in ref 24. Figure 1b shows the termination layer Mn ions and the O ions to which they coordinated, after relaxation in the presence of water (see below), where the red spheres belong to hydroxyl ions. The simulated termination layers of Mn−O terminated (110) slabs consist of MnO dimers and O monomers, an arrangement which was found to be lower in energy than alternative configurations; cf. Figure 3 in ref 24. Figure 1c illustrated the coordination of Mn at the termination layer, with two adsorbed hydroxyl ions. 4052



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battery applications is room temperature or a few tens of degrees above.26 Temperature. Although first-principles MD underestimates the diffusivity of liquid water,27,28 results can be corrected approximately by scaling the temperatures down 20% relative to the nominal simulation temperature.28 Although most of the present simulation were done at 300 K, the 20% rule implies that 375 K simulations would approximately correspond to real water at room temperature. A few simulations were performed at 375 K, to provide an estimate of the influence of temperature on chemical-bond-breaking energies. Simulated Blue Moon forces at the CN at which the restoring forces are maximum are found to be of order 20% lower at 375 K than at 300 K. f (ξ) Evaluation. Slow thermal equilibration at 300K makes the evaluation of f(ξ) for LiMn2O4 dissolution challenging. The conflicting requirements of numerical precision at a given ξ and a fine enough spacing between successive values of ξ must be balanced. Individual MD runs for 1 ps (half of which is nominally allocated to equilibration) were employed. The initial input for each successive run is obtained by displacing the solute by a few pm, which corresponds to a change in ξ = CN of a few times 10−2. Averages fav(ξ) are performed as described below, to obtain a smooth curve for the force integrand. The aggregate simulation production time for each dissolution system (about 150−200 ξ points times 0.5 ps) is of order 100 ps, comparable to that employed in previous DFT Blue Moon ensemble simulations.13

Figure 3. Coordinates zLi, zO1, and zO2, during Li ion dissolution from Li-terminated (001) LiMn2O4 surface. Plotted points represent coordinates at the final step of MD runs with fixed CN. Vertical lines represent the approximate boundaries between regions of CN with different hydration numbers.

III. DISSOLUTION SIMULATIONS Dissolution is sensitive to surface coordination. Typical coordination numbers for flat low index surfaces, such as LiMn2O4(001) are 4, 2, and 2 for Mn, Li, and O, respectively.24 We consider Li dissolution from a Li-terminated (001)oriented slab, and (either Mn or O) dissolution from a MnO-terminated (001)-oriented slab. These configurations represent the majority of the simulations presented below. Lower coordination numbers, however, occur in the presence of surface defects, such as steps, which are thought to dominate the dissolution process29 in most circumstances. As an example of lower coordination, we consider the (110) surface, which exhibits 3-fold coordinated Mn (which may also occur at steps). Li Dissolution. To simulate Li-ion dissolution, a Literminated (001) slab with a 20 Å water-filled channel is constructed as outlined above. No hydroxylation of the Li ions at the slab surface was observed. Distance of Li from Substrate and Li−O Bond Lengths. The evolution of z (Figure 3) and bond lengths r(Li−O) (Figure 4) with decreasing CN help elucidate the structure in f(CN). In addition to zLi, Figure 3 also displays z of the substrate O ions coordinated to the dissolving Li ion. Before dissolution, CN ≈ 2.1 (based on rb(Li) = 2.25 Å), and the termination layer containing Li is separated by about 1 Å from the adjacent MnO layer. Each set of points (zLi,zO1,zO2) for a given CN corresponds to the coordinates at the end of a 1 ps run; results for about 150 runs are plotted. In the undissolved state, the Li ion is coordinated to two water molecules. For CN below about 1.2, the hydration number increases to 3, and below about 0.45, it increases to 4, its value in bulk water.30 The sum of the coordination and hydration numbers for Li is approximately conserved during dissolution. As CN decreases from 2.1 to about 1.6, the Li ion moves essentially parallel to the surface, and only with further decrease

Figure 4. Bond lengths r1 = r(Li − O1), r2 = r(Li − O1), and their difference, r1 − r2, as a function of CN, during Li ion dissolution from Li-terminated (001) LiMn2O4 surface. At CN=1.5 (0.7) O1 (O2) bond is broken. Chemical bonding occurs for bond lengths within the range between r(min) and r(max).

in CN does it move appreciably in the perpendicular direction. Figure 4 shows the bond lengths of the dissolving Li as a function of CN. The Li ion bonding to one of the O ions (O2) is slightly stronger than to the other (O1). Breaking Chemical Bonds: Force vs CN. The forces, f = (∂A/∂ξ)ξ*, and integrated energies ΔA1→2 (cf. eq 4) are plotted in Figure 5. Averages are computed for sequences of nav successive points i + nav − 1

ξav (i) = 1/nav

∑

ξ(j)

j=i i + nav − 1

fav (i) = 1/nav

∑ j=i

f (ξ(j)) (6)

with nav = 6, to reveal the structure of f(ξ), which would otherwise be masked by scatter in the data. A possible drawback of eq 6 is that it may wash out or attenuate some features in the force curve, f(CN). It is encouraging, however, that the total bond-breaking energies listed in Table 1 appear to be in a physically plausible range (cf. Discussion). 4053



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Figure 5. Force f (left-hand scale) and integrated energy ΔA (righthand scale) vs CN, for Li dissolution from Li-terminated LiMn2O4 surface. Vertical lines indicate CN at which bonds to substrate O ions are broken. The region of positive f, for CN less than 0.7, is attributed to the transition from constrained to unconstrained hydration.

Figure 6. Force vs zLi for Li ion dissolution from Li-terminated (001) LiMn2O4 surface. zLi = 0.9, at which −f(z) turns positive, corresponds approximately to CN = 0.7 (Figure 3), at which f(CN) turns positive. For z greater than ∼1.4 Å, f(z) exhibits capacitive behavior (the Li ion is attracted to the slab).

Figure 5 indicates that when CN has decreased to 1.5, the chemical bonding force resisting dissolution is at a local minimum. At that point, the bond to O1 has been broken, while that to O2 remains intact. Thus, the Li−O2 bond length (green triangles) is little changed from its undissolved value, whereas the Li−O2 bond length has been stretched to about 1.5 times its original value (cf. Figure 4). As CN diminishes further (cf. Figure 4), it is the O2 bond that is stretched. When CN has decreased to 0.7, both chemical bonds to the substrate have been broken. Transition to Bulk Hydrated State. Although essentially no chemical bonding with the substrate remains when CN = 0.7, the Li ion has not yet achieved its bulk hydration state. Figure 6 shows the force resisting dissolution −f(z) as a function of distance from the slab. We attribute the positive values of −f between z = 1 and 1.4 (which correspond roughly to the region of positive f(CN) in Figure 5 for CN below about 0.7) to the transition between a Li ion with n(H2O) = 3, constrained by its proximity to the substrate, to its fully hydrated state. Residual Electrostatic Interactions. When z = 1.5 Å, the Li ion has achieved a hydration number of four, as in bulk water;30 however, a considerable electrostatic force still resists further displacement away from the substrate (Figure 6). Although the cell is essentially monopole and dipole free before dissolution, the LiMn2O4 slab becomes charged after Li moves into the water channel, and f(z) remain nonzero for all z (it is plotted in Figure 6 only up to z = 3.5 Å), which reflects capacitive behavior. The surface charge density for the adopted slab geometry, e/a2, where a is the spinel lattice constant, is unrealistically

large, since simultaneous events at adjacent surface unit cells would be highly unlikely. Instead, contemporaneous cation and anion dissolution events, which are likely correlated,7 would vastly diminish the surface charge density, relative to e/a2, and the resultant electric fields. Furthermore, electric fields for slabs are of longer range than for wires or particles, which are more realistic electrode geometries. Chemical-Bond Breaking Energy. Results are presented here only for the free energy differences for chemical bond breaking between substrate and solute. To evaluate this energy, the lower limit ξ(1) in eq 4 (CNmax in Table 1) is taken to be CN in the undissolved state, and the upper limit, ξ(2) (CNmin in Table 1), represents CN at which the last bond length crosses over r(max) (cf. Figure 3). The chemical bond breaking energies, ΔAbb, calculated in this way, are not strictly activation energies, since CNmin does not correspond to a transition state, but it seems reasonable to regard these energies as approximate effective activation energies. O Dissolution. The oxygen ions at a MnO-terminated (001) slab surface may either be in a protonated OH− complex or in a bare O2− oxidation state (cf. Figures 1b and 2). The results below are for the latter case. Mn1 and Mn2 denote the ions coordinated to the dissolving O ion. With an assumed effective bond length of rb(O) = 2.2 Å, CN is about 1.8 in the undissolved state. In Figure 7 are plotted z for the dissolving O, and for Mn1, and Mn2. The O ion captures a proton near CN = 1.36. As the O ion is displaced from the substrate, Mn2 is also displaced so as to maintain the O−Mn2 bond length (r(min)) at close to its

Table 1. Energies ΔAbb (eV) Required to Break Bonds of Solutes with LiMn2O4 Substrate, Obtained by Integration [eq 4] between CNmax and CNmina orientation

termination layer

CN

CNmax

CNmin

dissolving ion

ΔAbb

(001) (001) (001) (001) (110)

Li MnO MnO MnO MnO

2 2 4 4 3

2.1 1.8 3.9 4.0 2.75

0.7 0.25 0.5 0.3 0.5

Li+ O2− Mn3+ (MnO)+ Mn2+

0.41 (0.35) 1.3 (1.0) 1.8 (1.4) 2.7 (2.1) 1.0 (0.8)

a

Oxidation states listed in the sixth column are prior to dissolution. Parenthetical energies obtained by applying scaling factors described in section III to correct approximately for the slushiness of DFT water. 4054



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Figure 7. Coordinates zO, zMn1, and zMn2, during O ion dissolution from MnO-terminated (001) LiMn2O4 surface. The initially O2− ion captures a proton near CN = 1.36. Mn2 is drawn away from the substrate to maintain its ideal bond length, while the bond to Mn1 is being broken, and subsequently relaxes back to the substrate. A proton from a dissociated water molecule is attracted to the hydroxyl ion and is captured to form a water molecule at CN = 0.5.

Figure 9. Force f (left-hand scale) and integrated energy ΔA (righthand scale) for O dissolution from MnO-terminated (001) LiMn2O4 surface (analogous to Figure 5 for Li dissolution). The peaks (minima in the force resisting dissolution) at CN = 1 and 0.25 correspond approximately to the coordination numbers at which r(O−Mn1) and r(O−Mn2) cross r(max) (cf. Figure 8).

ideal value, while the bond with Mn1 is being stretched (cf. Figure 8). After the O ion captures a proton, Mn2 relaxes back to the substrate.

whereas in the other case, Mn dissolves along with a coordinated O ion, as in reaction 2. Figures 10−12 present

Figure 8. Bond lengths during O ion dissolution from MnOterminated (001) LiMn2O4 surface. The bond with Mn1 breaks near CN = 1 and that with Mn2 near CN = 0.25. The dissolving OH−1 captures a proton from a dissociated water molecule, and transforms to a water molecule at CN = 0.5.

Figure 10. Coordinates zMn and zO1−4, vs CN, during Mn ion dissolution from MnO-terminated (001) LiMn2O4 surface. Initially, the O4 ion, to which the Mn is most strongly bonded, is drawn into the water channel, to maintain its equilibrium bond length. Subsequently, it relaxes back to the substrate (see the following figure).

When CN has decreased below about 1.1, the O−Mn1 bond length crosses r(max), so that the bond is broken, and stretching of the O−Mn2 bond length commences. Concurrently, a proton dissociated from a water molecule (red circles in Figure 8) is attracted to the hydroxyl complex, and bonds to form a water molecule as CN decreases to about 0.5. The O−Mn2 bond length crosses r(max) at about CN = 0.25. The force curve in Figure 9 is analogous to that for Li in Figure 5: both exhibit maxima and minima in the forces resisting dissolution as each of the two bonds of the dissolving ion is broken. Mn Dissolution. The two Mn ions at the surface of the MnO terminated (001)-oriented slab (cf. Figure 1) are each coordinated to four substrate O ions; however, slight differences in the atomic configuration (associated, e.g., with Jahn−Teller distortions) result in two different types of dissolution histories: in one case, only the Mn ion dissolves,

results for the dissolution of 4-fold coordinated Mn unaccompanied by dissolution of an O ion, where rb = 2.4 Å was employed. Dissolution of 4-Fold Coordinated Mn. Perpendicular coordinates z for Mn and its coordination partners, Oj (j = 1,4) are plotted in Figure 10. Oxygen ions O2, O3, and O4 lie in the (001) termination layer and O1 lies in the first Mn−O layer below this layer. As CN decreases below 3.4, the Mn−O1 bond is broken, and stretching of the Mn−O2 bond length begins (Figure 11). As CN decreases below 2.5, the O2 bond is broken, and the O3 bond is broken near CN = 1.3. The O4 ion is displaced into the water channel to maintain the Mn−O4 bond length while Mn−O1, Mn−O2, and Mn−O3 bonds are being broken. When only the Mn−O4 bond remains, a competition occurs between the bonds of O4 to the dissolving 4055



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shows a configuration after two Mn−O bonds have been broken; note that one of the O ions (O4 in Figures 10−12) has been displaced into the water channel to maintain its bond to the dissolving Mn ion. In Figure 13c, all bonds to the substrate have been broken, and the dissolving Mn ion has been displaced about 2.5 Å into the channel. The Mn-ion hydration number, however, is only four, whereas octahedral coordination of Mn2+ is expected in bulk water.32 In Figure 13d, the Mn ion is displaced further from the substrate, and the hydration number has increased to five. The snapshots in Figure 14 contrast the two scenarios outlined above, in one of which only a Mn ion dissolves (Figure 14a), and in the other a Mn ion along with a coordinated O ion (Figure 14b). In the former case, the oxygen ion most strongly bound to the dissolving Mn eventually relaxes back to the substrate (Figures.13c and 13d). In the latter case (Figure 14b), however, an O ion is removed from the substrate, and evolves into a water molecule, shown about 5 Å from the substrate in the Figure. Dissolution of 3-Fold Coordinated Mn. To investigate the effects of lower Mn coordination, simulations were performed of the dissolution of 3-fold coordinated Mn from an MnOterminated (110)-oriented slab (Figure 1c). The corresponding force and energy curves are plotted in Figure 15. The extrema appear a bit sharper and more cusp-like than those in Figures 5, 9, and 12. Figure 15, shows shallow metastable minima in the integrated energy (triangles, right-hand scale), since the forces resisting dissolution go through zero, unlike those in Figures 5 and 9. The bond-breaking energy for dissolution of the 3-fold coordinated Mn is considerably lower than for 4-fold coordinated Mn (cf. Table 1). Dependence of Forces on Simulation Temperature. Simulations were performed at T = 375 K to compare with those at T = 300 K.28 A few representative values of CN were addressed: CN = 1.69 for Li ion dissolution, CN = 1.37 for O ion dissolution, and CN = 2.02 for Mn ion dissolution. In each case, simulations were performed for about 5 ps at both T = 300 and 375 K, sufficient to give reasonably well converged results, if the ion coordination (hydration number) remains constant. We find that f(375 K)/f(300 K) = 0.85, 0.76, and 0.79 for Li, O, and Mn ion dissolution, respectively. These scaling factors were applied to give the numbers in parentheses in Table 1, which we expect to be more realistic estimates of the energies for chemical-bond-breaking at room temperature than the uncorrected values.

Figure 11. MnO bond lengths vs CN. Analogous to Figures 4 and 8.

Figure 12. Force f and integrated energy A for Mn dissolution from (001)-oriented slab. Analogous to Figures 5 and 9.

Mn and to a substrate Mn in the termination layer. As CN is decreased below about 1.5, the slightly stronger bond to the substrate Mn ion wins the competition, and the O4 ion relaxes back to the substrate. The f vs CN curve is plotted in Figure 12. In the other Mn-ion dissolution scenario, which is analogous to reaction 2, an Mn ion and an O partner are both dissolved; the O4 ion is bonded slight more strongly to the dissolving Mn than to the substrate Mn ion, and it is the bond of O4 to the substrate that is broken. The bond-breaking energy for this reaction is higher than for the one in which only the Mn ion dissolves (cf. Table 1). Although Mn ions at the surface of LiMn2O4 are trivalent,24 aqueous Mn prefers a divalent state. The process of charge transfer (between substrate and Mn) therefore comes into consideration. In the simulation, a transition to a divalent state occurs when CN is in the range 2.5−3, and its distance from the termination layer is about 1 Å. In a real system, the charge transfer would likely occur by tunneling,31 however, charge transfer occurs essentially adiabatically in the simulation. Figures 13 and 14 show snapshots of atomic configurations at different stages of Mn dissolution. Figures 13 are taken from the simulations whose results are presented in Figures 10−12. The dissolving Mn is blue and the coordinated O ions yellow; other O ions are red, protons blue, Li ions green and Mn ions purple. In Figure 13a, the dissolving Mn is masked in the figure by O ions; it is coordinated to three O ions in the termination layer and one in the layer below; see also Figure 1b. Figure 13b

IV. DISCUSSION Phenomenology. In most of the simulations presented here, bond breaking was found to be sequential, ordered from the weakest to the strongest. As dissolution proceeds, displacements of substrate ions enable the strongest bonds to remain intact, while the weakest one is stretched and eventually broken. The breaking of solute bonds with the substrate during dissolution is complemented by the increased hydration of the solute. Although both processes are reflected in the Blue Moon forces, the chemical bond breaking dominates the structure of the force curve, f(CN), within the range of CN in which chemical bonding occurs. As a given bond is broken, the force resisting dissolution typically increases to a maximum as the bond length is initially stretched, and subsequently decreases to a minimum as the bond is fully broken (cf. Figures 5 and 9 for Li and O dissolution). A force curve with somewhat similar characteristics 4056



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Figure 13. Snapshots of the dissolution of Mn from Mn−O terminated (001) slab. Dissolving Mn ion is dark blue, coordinated O ions yellow. See text for discussion.

Mn ion followed by O ion), or by dissociation of water, followed by either protonation or hydroxylation of the substrate, to lower the electrostatic energy. Table 1 lists the bond-breaking energies, ΔAbb, obtained by integration of the force f from CNmax to CNmin in eq 4. For dissolution from (001) slabs, we find that the smallest ΔAbb occurs for Li dissolution and the largest for Mn dissolution. In view of the low predicted ΔAbb for Li dissolution, lithium may have a greater propensity for dissolution than the other components of LiMn2O4, perhaps accompanied by ion exchange with protons.33 Simulations of rocksalt dissolution7 predicted that anion dissolution precedes cation dissolution in that system. The results in Table 1 suggest that for LiMn2O4 dissolution at (001) surfaces, O ion dissolution would precede (4-fold coordinated) Mn ion dissolution. On the other hand, the opposite is true for (110) surfaces on which Mn is 3-fold coordinated. Simulations of the dissolution of Ba ions from BaSO412 have shown that the energy barrier to break the third bond with the substrate is greater than that for the first two. For Mn dissolution from LiMn2O4 (Figures 12 and 15), we also find that breaking a bond subsequent to the first one (the third bond for 4-fold coordinated Mn and the second bond for 3-fold coordinated Mn) costs the most energy. Dissolution Rates and Effective Activation Energies. The determination of bond-breaking energies (Table 1) is

was found in Blue Moon ensemble simulations of the high temperature and pressure aqueous dissolution of quartz.13 In the latter case, the force maximum has a wide plateau, in contrast to the more cusp-like structures seen in Figures 5 and 9; also, a shallow metastable energy minimum was found after the first bond is broken for quartz,13 but is not seen in Figures 5 and 9. For Li dissolution, Figure 5, a deep energy minimum occurs after the second bond is broken. We have suggested that this is associated with the transition of Li from a hydration number of 3, constrained by proximity to the substrate, to a hydration number of 4, with bulk behavior. In principle, a similar effect could occur for Mn dissolution as 6-fold coordination is approached, however, our simulations have not provided evidence for it. Shallow metastable energy minima are observed in Figure 15 after each bond is broken for 3-fold coordinated Mn. Chemical-Bond-Breaking Energies. In our discussions of the interactions that govern dissolution, we have focused on (i) chemical bond breaking with the substrate, (ii) transition to a fully hydrated solute, and (iii) residual electrostatic interactions. The first two of these are local properties, and are expected to be relatively insensitive to computational cell size and geometry. Residual electrostatic interactions, on the other hand, are highly sensitive to cell size and geometry. Their precise value for a single dissolving ion, however, may not be overly significant if the partial dissolution of one ion is followed promptly either by that of an oppositely charged species7 (e.g., 4057



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yield an effective activation energy. We have not attempted to calculate a dissolution rate for LiMn2O4 in the present work. The experimentally measured effective activation energy for LiMn2O4 of about 0.7 eV (in the presence of nonaqueous electrolyte)2 is slightly smaller than the predicted chemical bond breaking energy for divalent 3-fold coordinated Mn (Table 1). To make experimentally testable predictions of LiMn2O4 dissolution, acid4 must be included in the simulations. In an aqueous HF environment,3 an F ion may adsorb to a surface Mn ion, weaken its bonding to the substrate, and thereby lower the resultant bond-breaking energy. An analogous process that involves acidic protons may weaken oxygen bonding to the substrate. Such mechanisms are expected to be amenable to simulation.

V. CONCLUSIONS Blue Moon ensemble simulations provide a description of the aqueous dissolution of LiMn2O4 at room temperature. The results indicate that dissolution occurs by a sequence of bond breaking events, ordered from weak bonds to strong bonds. As a weak bond with a substrate ion is being broken, substrate ions more strongly bonded to the solute are displaced to maintain bond lengths close to the optimal value. Bonds are broken when the bond length has been stretched to about 1.5 times its equilibrium value. We intend to extend the simulations to treat acid promoted dissolution, a significant degradation mechanism in lithium-ion batteries.

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ACKNOWLEDGMENTS The submitted manuscript has been created by UChicago Argonne, LLC, Operator of Argonne National Laboratory (”Argonne”). Argonne, a U.S. Department of Energy Office of Science laboratory, is operated under Contract No. DEAC02-06CH11357. This work was supported at Argonne by the Office of FreedomCar and Vehicle Technologies (Batteries for Advanced Transportation Technologies (BATT) Program), U.S. Department of Energy. This research used resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02−05CH11231. A generous computer time allocation at the Fusion computer facility at Argonne National Laboratory is also gratefully acknowledged.

Figure 14. Snapshots of the dissolution of two different (slightly inequivalent) 4-fold coordinated Mn ions from Mn−O terminated (001) slab after two bonds have been broken, in each case. In event depicted in panel a (cf. Figure 13b), the O ion drawn into the channel subsequently relaxes back to substrate; in panel b, O ion bonds to the substrate are broken.

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Figure 15. Force f and integrated energy A for Mn dissolution from (110)-oriented slab. Analogous to Figures 5, 9, and 12.

a step toward the calculation of a dissolution rate. A full dissolution rate calculation requires identification of the metastable intermediate states on the path to bulk solvation.12 The temperature dependence of the predicted rate would then 4058



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