Article
pubs.acs.org/JPCC
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
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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
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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.
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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).
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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.
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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
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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
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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.,
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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.
■
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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