Download Electrochemical Behavior of Lithium in Alkaline

1326
Journal of The Electrochemical Society, 146 (4) 1326-1335 (1999)
S0013-4651(98)05-082-4 CCC: $7.00 © The Electrochemical Society, Inc.
Electrochemical Behavior of Lithium in Alkaline Aqueous Electrolytes
II. Point Defect Model
Osvaldo Pensado-Rodríguez,a,* José R. Flores,a,* Mirna Urquidi-Macdonald,a,**,z and
Digby D. Macdonaldb,***
aDepartment
of Engineering Science and Mechanics, The Pennsylvania State University, University Park,
Pennsylvania 16802, USA
bSRI International, Pure and Applied Physical Sciences Division, Menlo Park, California 94025, USA
A theoretical model for lithium dissolution and passivation in alkaline electrolytes is presented. The production of anodic current
via lithium dissolution is understood in terms of a bilayer model for the passive film that incorporates anodic dissolution, bilayer
film formation, film dissolution, and hydrogen evolution. The total current density, anodic partial current density, and the cathodic (H2 evolution) partial current density depend strongly on the porosity of the LiOH outer layer that forms over a LiH barrier layer.
The porosity of the outer layer is postulated to depend on the applied voltage and on the electrolyte composition and concentration. The model, which is based on the previously developed point defect model for the formation and breakdown of passive films,
describes the behavior of the system over wide potential and electrolyte (aqueous KOH) composition ranges. Electrolyte additives,
such as sucrose, are included in the analysis. Analytical expressions for the total current density and hydrogen flux, as functions of
the voltage, are used to describe the experimental data obtained for different electrolyte (KOH) and additive (sucrose) concentrations. The results indicate that the additives decrease the porosity of the outer layer and hence have similar influences on both the
anodic and cathodic partial currents. The model is also extended to account for the transition from a lithium hydride barrier layer
to a lithium oxide barrier layer as the voltage is increased from 22.8 to 8 VSHE. This transition explains the increase in the current
at sufficiently positive potentials.
© 1999 The Electrochemical Society. S0013-4651(98)05-082-4. All rights reserved.
Manuscript submitted May 27, 1998; revised manuscript received December 15, 1998.
Experimental studies on lithium in concentrated lithium hydroxide aqueous solutions have confirmed the formation of a passive film
on the surface that controls the rate of the dissolution process.1,2 The
prevailing consensus is that the layer is an oxide-hydroxide film.
However, it has been shown in Part I of this series3 that, under opencircuit conditions, lithium hydride and lithium hydroxide are stable
phases, whereas lithium oxide cannot form even as a metastable
phase. Accordingly, the passive film formed under open-circuit conditions is of a bilayer lithium hydride/lithium hydroxide structure.
We analyze experimental data for lithium dissolution in terms of
a theoretical model postulating a lithium hydride-hydroxide bilayer
structure for the film. The model incorporates charge-transfer phenomena, hydrogen evolution, barrier-layer formation and dissolution,
and metal dissolution, and allows for a change in the porosity of the
outer layer as a function of the electrolyte composition and applied
voltage. The model succeeds in explaining a wide panorama of experimental data with minimal variation of the model parameters. Indeed,
the variation of only one parameter, related to the porosity of the
outer layer, is sufficient to account for all the observed trends in the
total current density and in the anodic and cathodic partial current
densities with respect to the independent experimental variables
(voltage and electrolyte and additive concentrations).
Theory
Thermodynamic calculations on the Li/H2O system indicate that
at the open-circuit potential (OCP) of the system (about
22.8 VSHE 1,4-6), the phase in contact with lithium is lithium hydride.3 The existence of a porous LiOH layer on the metal surface
can be inferred from the limited solubility of this compound in water
(and especially in the concentrated KOH solution used in this study),
and from the dissolution/precipitation mechanism that was postulated by Littauer and co-workers,1,2 who performed much of the early
work on the electrochemistry of the Li/H2O system. We postulated
that under open-circuit conditions a hydride barrier layer forms next
to the metal, whereas the outer layer consists of LiOH.
*** Electrochemical Society Student Member.
*** Electrochemical Society Active Member.
*** Electrochemical Society Fellow.
**z E-mail:[email protected]
Our model is based on the point defect model (PDM) for the
growth and breakdown of passive films,7-11 which is expanded to
take into account the formation of the lithium hydride (rather than a
defective oxide) barrier layer and the precipitation of a porous lithium hydroxide outer layer. Figure 1 shows the interfacial reactions
for vacancy generation and annihilation that are envisioned to occur
in the system, as well as the dissolution reaction (i.e., reaction 5 in
Fig. 1) responsible for the destruction of the barrier layer at the barrier layer/outer layer interface (BOI). The diagram is not scaled; the
thickness of the barrier layer is on the order of nanometers,7 whereas the outer layer may have a much greater thickness (up to a hundred microns).1
Reactions 1, 3, and 4 in Fig. 1 are lattice conservative, whereas
reactions 2 and 5 are nonconservative; these latter two reactions
result in barrier-layer formation and dissolution, respectively.7-11
Reaction 6 accounts for hydrogen evolution via water reduction. Figure 2 is a schematic representation of the potential profile, which
recognizes potential drops across the barrier and outer layers, as well
as across the metal/barrier layer and BOIs. No potential drop occurs
at the outer layer/solution interface, because conduction occurs within an aqueous phase on both sides of the interface. The potential profile across the LiH barrier layer has the opposite gradient to that for
Figure 1. Interfacial reactions leading to generation and annihilation of point
defects within the passive film on lithium.
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Journal of The Electrochemical Society, 146 (4) 1326-1335 (1999)
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S0013-4651(98)05-082-4 CCC: $7.00 © The Electrochemical Society, Inc.
We assume that the porosity is constant throughout the width of the
outer layer; hence, the porosity must be numerically equal to u.
Under steady-state conditions, the fluxes of all the species are
constant, and the rate of formation of the barrier layer must be equal
to the rate of barrier-layer dissolution. Accordingly
a VMBI
9Li k1 5 uk3
k2 5 a
BOI
V •H
k2 5 a
Figure 2. Postulated potential profile in the system.
an oxide barrier layer, because the hydride forms cathodically
whereas an oxide forms anodically.
In accordance with previous work,7–11 we assume that the potential drop at the BOI, fBOI, is given by
fBOI 5 aVbl 1 bpHBOI 1 f oBOI
[7]
The parameter a is a dimensionless constant (the “polarizability” of
the BOI, b and f 0BOI are constants with units of voltage, and pHBOI is
the local pH at the BOI). The electric field is defined as e 5 2=f,
where f is the electrostatic potential.
In agreement with previous studies, it is assumed that the electric
field in the barrier layer, e, is a constant because of Esaki (band-toband) tunneling of electrons and holes.12 Thus, electrons in the conduction band and holes in the valence band, produced by a transitory increase in the electric field, redistribute and thereby generate a
counterelectric field that opposes the applied field. Accordingly, the
electric field is “buffered” by e2-h • generation such that it is independent of the applied voltage and hence, the thickness of the barrier layer. Furthermore, it is assumed that to a first approximation, the
electric field strength within the barrier layer is independent of position. The evidence for a voltage-independent electric field in oxide
barrier layers has been summarized by Macdonald,7 but no similar
analysis has been reported for hydrides. We note, however, that the
electric field in any material cannot increase in an unconstrained
manner because of the ultimate limit of the dielectric strength.
From Fig. 2 the following relationship can be derived
fMBI 5 (1 2 a)Vbl 2 b pHBOI 2 f oBOI 2 eLbl
[8]
The subscript MBI designates the metal/barrier layer interface. The
rate constants for the elementary reactions, as functions of the potential drops at the MBI and BOI, are given by
k1 5 k 1o9ea1gfMBI
[9]
k2 5 k 2o9ea2gfMBI
[10]
k3 5 k 3o9ea3gfBOI
[11]
k4 5 k 4o9ea4gfBOI
[12]
ks 5 k so
[13]
k ho9e2ahgfBOI
[14]
kh 5
The symbol g is defined as g 5 F/RT, where F is Faraday’s constant,
R is the ideal gas constant, and T is the kelvin temperature. The constants aj are dimensionless transfer coefficients having values 0 <
aj < 1, while k oj 9 is the standard rate constant for the jth elementary
reaction.
We define the fraction of the barrier layer that is not covered by
the LiOH of the porous outer layer as u, where
u5
active area
total area
[15]
[16]
BOI
aW
uk4
[17]
ukso
[18]
BOI
W
The symbol aj stands for the activity of species j. The superscript on
the activity indicates the point at which it is computed. Equation 16
is the result of requiring the rate of generation of lithium vacancies
at the BOI to be the same as the rate of annihilation of lithium vacancies at the MBI. Equation 17 arises from the requirement that the
creation of hydrogen anionic vacancies at the MBI must equal the
rate of annihilation of the same vacancies at the BOI. Finally, Eq. 18
states that the rate of hydride formation at the MBI equals the rate of
hydride dissolution at the BOI. Equations 10 and 18 can be used to
relate the thickness of the barrier layer to the potential drop, Vbl, as
Lbl 5
 k o a BOIu 
(1 2 a)
b
1
Vbl 2 pH BOI 2
ln  s Wo 
e
e
a 2 ge  k2 
[19]
which predicts that the LiH barrier layer thickness decreases with increasing applied voltage, because in this case e is negative. This is in
contrast to oxide barrier layers (e.g., NiO on Ni), which are predicted (and found7-12) to grow thicker with increasing applied voltage
because of a positive
value of e. Note that the constant k 2o is defined
o
o9 2a2gf oBOI
as k 2 5 k 2 e
.
Equation 19 can be used to define a relationship between the
activity of water, the porosity of the outer layer, and the rate constant
for reaction 2, Fig. 1. Assuming that the transfer coefficients a1 and
a2 are equal (equivalent to assuming k1 5 k 1o9k2/k 2o9, see Eq. 9 and
10), then from Eq. 18 it follows that
k1 5
k1o kso aWBOIu
k2o
[20]
o
where k 1o is defined as k 1o 5 k o19e2a1gf BOI. Substitution of Eq. 20 into
Eq. 16 yields
aWBOI 5
k2o k3
k1o kso a MBI
V9
[21]
Li
From the elementary reactions involving electronic transfer (reactions 1, 2, 4, and 6 in Fig. 1), the total steady-state current density is
IT 5 F  a MBI
k 1 k2 2 2 a BOI
aWBOIuk4 2 aWBOIukh 
VH9
 VLi9 1

[22]
Substitution of Eq. 17, 18, 20, and 21 into Eq. 22 yields

 k ok u
 o
k1o
IT 5 F  a MBI
2
1
k
2
k
 o 2o 3MBI
s
h

V9
o

 Li k2
 k1 ks a VLi9
[23]
The terms of kh and k3 are decreasing and increasing functions, respectively, of the applied voltage. Later in this paper we show that u
is also voltage-dependent, and the corresponding voltage function is
determined.
Because only the hydride dissolution reaction (reaction 5, Fig. 1)
and the water reduction reaction (reaction 6) evolve hydrogen, the
molecular hydrogen flux is
k ok u
1
NH 2 5  kso 1 kh  o 2o 3MBI

2  k1 ks a V9
[24]
Li
In deriving Eq. 24, Eq. 21 was used to define the water activity as a
function of the applied voltage. Equations 23 and 24 yield
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1328
Journal of The Electrochemical Society, 146 (4) 1326-1335 (1999)
S0013-4651(98)05-082-4 CCC: $7.00 © The Electrochemical Society, Inc.
FNH 2
IT 1 2 FNH 2
5
k2o
o MBI
k1 a V9 1 k2o
Li
1
kh
k2o
o
2 ks  k o a MBI 1 k o 
2
 1 VLi9
[25]
Equation 25 can be used to obtain kinetic information (i.e., standard
rate constants) from an analysis of experimental hydrogen evolution
rate and current density data. The right side of Eq. 25 is an exponential function of voltage through kh. For example, if Vbl < V 1 fR
(Fig. 2, V is the applied voltage) and assuming that the pH contribution to the potential drop at the BOI is not voltage-dependent, then
Eq. 25 becomes
FNH 2
IT 1 2 FNH 2
5 a 1 be2a h gaV
[26]
where
a5
k2o
k1o a MBI
1 k2o
V9
um solubility in the interior of the pore is exceeded, precipitation of
lithium hydroxide occurs, causing a decrease in pore radius and
hence, a decrease in porosity. As a result, the porosity, u, is also a
function of the applied voltage. The functional dependence is discussed next.
In the interior of the pore, the reaction Li1 1 OH2 5 LiOH(s)
may be assumed to be in equilibrium, as previously noted. The Gibbs
energy of the LiOH surface in a pore depends on the pore radius in
the form15
m LiOH 5 m oLiOH 1
[27]
m(Li1 1 OH2) 5 moLi1 1 m oOH2 1 RT ln(aLi1)2
o
k2o kho9e2a h g(bpH BOI 1fBOI )
k o9e2a h g(bpH BOI 1fBOI 1afR )
5a h
2 kso
1 k2o 
2 kso  k1o a MBI
9
V
Li


[28]
[29]
A common approach taken in handling problems of this type is to
define an effective diffusion coefficient as uDi, where Di is the diffusion coefficient of the species i of interest through the bulk of the
solution. Thus, the quantity uDi is an effective diffusion coefficient
through the porous material, assuming that the species does not penetrate the matrix. If the pore is not aligned normal to the surface, a
tortuosity factor must be included to account for the added path
length (see Ref. 14, for example). In this study, tortuosity effects are
included in the diffusion coefficient.
We assume that that concentration of lithium ions inside the
pores is not position-dependent. This postulate is based on the concept that because the pore diameter is small, the pore solution is in
chemical equilibrium with a phase (LiOH) whose composition is
invariant with distance through the precipitated outer layer. Therefore, lithium ions migrate (rather than diffuse) in the interior of the
pores in the outer layer, and we have
uk3 5
uD
1
Li
Fe ol
RT
c
1
Li
ro
mo 1 1 mo
OH
2
2 m oLiOH
RT
[34]
1 2 ln (t o ) 1 2a3gaV
Equation 31 has been substituted in the equilibrium expression for
the pore radius. Let P be defined as the number of pores per unit of
surface area. Therefore, the fraction of the outer layer that consists
of pores is
u 5 Ppr 2 5
Ppro2

 m o 1 1 m o 2 2 m oLiOH
OH
1 2 ln (t o ) 1 2a3gaV 
 Li

RT


2
[35]
From Eq. 23 and 24, and the use of Eq. 35, the anodic partial current
density, Ia, is
Ia 5 IT 1 2 FNH 2 5
a MBI
k1o 1 k2o
V9
Li
a MBI
k1o
V9
Fk3u
Li
5
j1e a3gaV
(1 2 a)(j 2 1 2a3gaV )2
[36]
where
j1 5 FPpr o2 k 3o9e2ahg(bpHBOI1f BOI1af R)
o
[37]
and
[30]
The left side of Eq. 30 represents the flux of lithium ions at the BOI
and the right side is the migrational flux in the outer layer. The symbol eol represents the electric field across the outer layer. An important conclusion from Eq. 30 is the the concentration of lithium ions
is proportional to k3. Consequently, to a first approximation
a Li1 5 toea3gaV
r5
Li
We now explore the voltage dependence of the porosity of the
outer layer, u(V). Let us assume that N j9 is the effective flux
(mol/cm 2 s) of the jth species in the interior of a pore in the outer
layer and that Nj is the flux measured by averaging over an area that
includes both the active surface and the LiOH matrix. Then, N j9 and
Nj are related as13,14
Nj 5 uN j9
[33]
Consequently, by equating Eq. 32 and 33, as required for equilibrium, the radius of the pore is
and
b5
[32]
where ro is a reference length and moLiOH is the standard chemical
potential of LiOH in a planar surface (i.e., for r r `). By assuming
that the concentration of lithium ions is equal to the concentration of
hydroxide ions in the interior of the pore (as required by electroneutrality), the chemical potential of the system Li1 1 OH2 results in
Li
o
RTro
r
[31]
The activity of the lithium ion is defined as a Li1 5 gLi1cLi1/c Loi1,
c Loi1 is the standard-state concentration, gLi1 is the activity coefficient of Li1, and the constant to is defined in terms of the physical
constants of the outer layer. Even though the argument leading to
Eq. 31 is simple, the conclusions drawn are in excellent agreement
with experimental observations.
Equation 31 states that the concentration of lithium ions in the
porous outer layer increases with increasing voltage. When the lithi-
j2 5
mo 1 1 mo
2
2 m oLiOH
1 2 ln (t o )
[38]
RT
Later in this paper we explain why Ia ; IT 1 2FNH2 is the anodic partial current density. Equation 36 can be used to find the parameters
j1, j2, and a3ga from a curve-fitting procedure. Ideally, changes in
the characteristics of the electrolyte affect only the properties of the
outer layer. Substitution of Eq. 36 into Eq. 26 yields
Li
OH
FNH 2 5
( a 1 be2a h gaV ) j1e a3gaV
(1 2 a)(j 2 1 2a3gaV )2
[39]
From Eq. 36 and 39, the total current density is
IT 5
[
]
j1e a3gaV 1 2 2 ( a 1 be2a h gaV )
(1 2 a)(j 2 1 2a3gaV )
2
[40]
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The root of Eq. 40 (i.e., the voltage of which IT 5 0) is
VOCP 5 2
The coulombic efficiency of the system can be defined as the
fraction of the total current produced by lithium oxidation that
appears as electron flow in external circuit, i.e.
1
1 2 2a 
ln 
a h ga  2 b 
o


kso ( k1o aVMBI
9i 2 k2 )
1
L

52
ln 
o
1afR ) 
a h ga  k o k o9e2a h g(bpH BOI 1fBOI
2
h


h(V ) 5
[41]
[42]
At potentials above the OCP, the total current density, IT, is positive,
BOI
which requires that a MBI
VL
9 i k1 2 k2 > a W ukh > 0. Because by hypotheo o
sis k2 5 k 2ok1/k1o, it follows that k1(a MBI
VL
9 i 2 k 2 /k1 ) > 0, which implies
o
o
that a MBI
k
>
k
.
This
inequality
is
independent
of the applied voltVL
9i 1
2
o
age, and Eq. 41 is properly defined. The condition k1oa MBI
VL
9 i > k 2 means
that charge conduction in the interior of the hydride barrier layer
occurs principally via the transport of cation vacancies. The flux of
cation vacancies, V9Li, is responsible for lithium dissolution, as illustrated in Fig. 1. On the other hand, the flux of anion vacancies, V H• , is
associated with the growth of the LiH film into the metal. Reaction 5
in Fig. 1, which is responsible for LiH dissolution, has a negative
change in standard Gibbs free energy, equal to 2204.732 kJ/mol, and
is independent of the applied potential. Therefore, we expect a nonzero rate of film dissolution, which implies a nonzero flux of anion
vacancies under steady-state conditions, so that the proper balance
between barrier-layer dissolution and formation can be attained. In
summary, both cation and anion vacancies contribute to charge transport in the barrier layer, but the major charge carriers are the cation
vacancies V9Li.
A number of authors have postulated that cation vacancies are
indeed the principal conducting defects in bulk LiH.16-19 Other
authors, however, such as Pandey and Stoneham20 and Haque and
Islam,21 have suggested that anion and cation vacancies, and interstitial species, play important roles in charge conduction in hydride
crystals. In the LiH film formed on lithium under open-circuit conditions, we conclude that cation and anion vacancies are both charge
carriers but that the flux of cation vacancies exceeds that of anion
vacancies.
Substitution of Eq. 16 into the expression after the second equality term in Eq. 36 yields
 MBI
ko 
MBI
Ia ; IT 1 2 FNH 2 5  aVL9i 1 2o  k1 5 aVL9i k1 1 k2
k

1 
[44]
Substituting Eq. 39 and 40 into Eq. 44 yields
h(V) 5 1 2 2(a 1 be2ahgaV)
This voltage is the OCP. Thus, the OCP is defined by the kinetic
processes at both the MBI and the BOI. In order for Eq. 41 to be
o
properly defined, the term k1oa VMBI
9Li must be greater than k 2 . This is
always true, as explained later.
An equivalent expression for the total current density, Eq. 22,
using the steady-state relationship, Eq. 18, is
BOI
IT 5 F(a VMBI
9Li k1 2 k2 2 a W ukh)
IT
IT 1 2 FNH 2
[45]
which predicts that the coulombic efficiency increases with increasing applied voltage, corresponding to a decreasing impact of hydrogen evolution on the net current.
In Eq. 40, the exponential term implies that the total current density is an increasing function of voltage at very positive potentials.
Likewise, Eq. 39 indicates that the rate of hydrogen evolution is an
increasing function of the voltage at high positive potentials. However, we have modeled water reduction as an irreversible process
(Fig. 1). Such an approach is appropriate, because the OCP in our
system is very negative (22.8 VSHE) compared with the equilibrium
voltage of the hydrogen electrode reaction (about 20.95 VSHE in 8 M
KOH). For more positive voltages that are close to or exceed the
hydrogen electrode reaction (HER) equilibrium potential, the
reverse of reaction 6 becomes important. Therefore, Eq. 39 is valid
for V << E He 2/H2O.
It is likely that the valid voltage domain for Eq. 40 is also restricted. However, for high positive potentials, the ejection of lithium ions
from the barrier layer into the outer layer via reaction 3 (Fig. 1) is
enhanced. This results in a major production of cation vacancies in
the barrier layer, thereby increasing charge conduction and causing
the total current density to increase. Interestingly, we have observed
this increase in the total current density at potentials above 4 VSHE, as
we discuss later in this paper.
Experimental
Potentiostatic polarization studies were performed using an
EG&G Princeton Applied Research model 363 potentiostat/galvanostat. The electrochemical cell employed in our studies was comprised
of a cylindrically shaped poly(tetrafluoroethylene) (PTFE)
holder/sample as the working electrode, a hydrogen gas collector, and
a nickel wire counter electrode contained within a PTFE vessel
described elsewhere22 and depicted in Fig. 3. Nickel was used as the
counter-electrode material because of its known resistance to dissolution in concentrated alkaline solutions. The lithium (99.9% Li) sam-
[43]
Recall that the hypothesis k2 5 k 2ok1/k1o. The term Fa MBI
k represents
V9
Li 1
the rate of production of electrons via reaction 1 (Fig. 1) and Fk2 is
the rate of production of electrons by reaction 2. Consequently, Ia ;
IT 1 2FNH2 is the total rate of anodic production of electrons in the
system (the anodic partial current density). By definition, the cathodic partial current density, Ic, equals IT 2 Ia; i.e., Ic ; IT 2 Ia 5
22FNH2. The reactions contributing to the cathodic partial current
density are reactions 4 and 6. The cathodic current density associated with reaction 4 is 22a(IT 1 2FNH2), and the cathodic current density due to reaction 6 is 22[FNH2(1 2 2a) 2 aIT]. Adding these two
contributions yields the partial cathodic current density equal to
22FNH2. Therefore, the rate of hydrogen evolution represents the
cathodic processes in the system, reactions 4 and 6. In other systems,
where the only cathodic reaction and source of hydrogen is water
reduction (reaction 6) and/or hydrogen ion reduction, the same result
is obtained. It is remarkable that in the present, more complex system, the same simple result arises.
Figure 3. Electrochemical cell, standard three-electrode setup. The buret is
used for collection of the hydrogen evolved from the metal surface.
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ple was cylindrical, with a diameter of 1.1 cm and a length of 1 cm.
The flat end exposed to the solution had an area of 0.95 cm2. The side
surfaces were coated with Microstop to avoid crevice corrosion.
The saturated calomel reference electrode (SCE) was contained
within a separate compartment and was connected to the test cell via
a Luggin probe. The tip of the Luggin probe was placed within 0.4 cm
of the lithium surface in order to minimize the IR potential drop. No
dependence of the electrochemical data on the placement of the tip of
the Luggin probe was found, no doubt reflecting the high conductivity of the electrolyte. The evolved hydrogen was collected using an
inverted funnel gas buret placed above the working electrode.22 In this
configuration, the counter electrode was slightly above and outside
the rim of the hydrogen collector to avoid the capture of gases evolved
from the cathode. The aqueous electrolytes were prepared from ACS
potassium hydroxide pellets (85% KOH and 15% H2O). The solutions were made up to yield KOH concentrations of 7-12 M. Sucrose
was added to some of the electrolytes, and the solutions were stirred
until complete dissolution was achieved.
Polarization curves were determined potentiostatically, with the
potential being maintained constant for enough time (typically
10 min) to allow the current to stabilize and for an accurate determination of the hydrogen flux to be made. The potential was then
stepped to the next value and the procedure was repeated. The total
current density and the hydrogen flux were measured in both the
ascending and descending potential directions.
Results and Discussion
We explored the electrochemistry of lithium in concentrated
KOH solutions (7-12 M) by determining the total current density, the
cathodic partial current density, and the anodic partial current density as functions of the applied voltage and electrolyte composition.
The choice of KOH as the base electrolyte was dictated by the fact
that it has a higher specific conductivity than LiOH, RbOH, NaOH,
and CsOH aqueous electrolytes at equivalent concentrations.23 Because the solubility of KOH is much greater than that of LiOH (16 M
vs. 5.2 M, 24 respectively), KOH governs the activity of Li1, thereby regulating the concentration at which LiOH precipitates to form
and maintain the outer layer of the passive film.3 Previous work1,2
suggests that the porosity of the outer layer exerts an important influence over the kinetics of anodic dissolution of lithium in aqueous
Figure 4. (a) Total current density (IT), located mainly above the horizontal
axis, and cathodic partial current density (22FNH2), located always below the
horizontal axis, as functions of the applied voltage (vs. SHE). (b) Anodic partial current density (IT 1 2FNH2). (c) Efficiency (defined as Eq. 44) vs. VSHE.
The solid line is the average function. The electrolyte is KOH with concentrations as indicated in the figure.
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Journal of The Electrochemical Society, 146 (4) 1326-1335 (1999)
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solution, and we postulate that it may also affect the kinetics of
hydrogen evolution. We have also investigated the addition of a surface active agent (sucrose) into the electrolyte, in the expectation
that it modifies the porosity of the outer layer, and hence, influences
the rates of the lithium dissolution and HERs. Sucrose was chosen
as an example of an extensively hydroxylated organic compound,
which is characterized by a large molecule that might interact
strongly with LiOH in the outer layer.
Impact of electrolyte concentration and composition.—Figures 4
and 5 show the experimental results for the polarization of lithium in
aqueous KOH electrolytes (7-12 M) and in 8 M KOH plus sucrose
(0.29-0.87 M), respectively. The cathodic and anodic partial current
densities, included in Fig. 4 and 5, have been computed as 22FNH2
and IT 1 2FNH2. It is interesting to note that Fig. 4c and 5c, which
display coulombic efficiency vs. potential (defined in Eq. 44) are
similar, within the experimental error, for both systems. Furthermore, comparable results were found for other additives, such as
Ga2O2 (results not presented here).
In both systems (7-12 M KOH and 8 M KOH 1 0.29-0.87 M
sucrose), the anodic partial current density (Fig. 4b and 5b) is found
to decrease with increasing voltage for a given composition and to
decrease with increasing concentration (KOH or sucrose) at a given
voltage. The first trend is consistent with the prediction of the model
that the porosity of the outer layer, and hence the anodic partial current, decreases with increasing voltage. Likewise, a higher KOH concentration in the bulk promotes the precipitation of LiOH in the pores
and hence decreases the porosity and the anodic partial current. The
second trend noted demonstrates that sucrose achieves the same
effects but at much lower concentrations than for the base, KOH electrolyte. Examination of the data for the cathodic partial current density shows the same trends, except that for 22.5 VSHE < V < 1 VSHE the
experimental accuracy is insufficient to define the concentration
dependencies of the cathodic partial current. Regardless of the
details, we conclude that the anodic and cathodic currents are affected by the same process, that is, a decrease in porosity of the outer
layer with increasing voltage and concentration (KOH and sucrose).
Equation 25 states that the coulombic efficiency is described by
an increasing exponential function (note that V is negative) and constants that do not depend explicitly on the solute. The success of the
model in fitting the experimental data over a range of [KOH] and
Figure 5. Total current density (IT), located mainly above the horizontal axis,
and cathodic partial current density (22FNH2), located always below the horizontal axis, as functions of the applied voltage (vs. SHE). (b) Anodic partial
current density (IT 1 2FNH2). (c) Efficiency (defined as Eq. 44) vs. VSHE. The
solid line is the average function. The electrolyte is 8 M KOH plus sucrose,
with the sucrose concentration as indicated in the figure.
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[sucrose] is evidence for the viability of the model, as discussed
later. The overall average coulombic efficiency was used to obtain
the parameters contained in the exponential function, Eq. 25, using
a least-squares fitting procedure. The parameter values so obtained
are listed in Table I.
We reproduced the experimental trends by maintaining all the
parameters in Eq. 39 and 40 invariant, with the exception of j1,
which was allowed to change as a function of the electrolyte composition. The values of the remaining parameters are listed on the
first column of Table I. The parameter j1 is proportional to the pore
density of the outer layer, P (see Eq. 37). Therefore, a possible effect
of the additives is to change the pore density of the outer layer.
Changes in the structure of the outer layer, local pH, and in the kinetics of the reactions at the base of a pore (i.e., at the BOI) are also feasible. It is evident that any impact on hydrogen evolution is mirrored
by a similar impact on lithium dissolution. This finding alone strongly suggests that a common factor (e.g., the porosity of the outer
layer) controls the rates of the two partial reaction.
Figure 6 displays the variation of j1 with respect to the KOH concentration in Fig. 6a and sucrose concentration in 6b. The plots are
superimposable, within experimental uncertainty, demonstrating that
the effects of [KOH] and [sucrose] on the outer-layer porosity are
indistinguishable, except that sucrose is more effective than KOH in
producing the effect, as noted previously. Figure 7 compares the calculated cathodic partial current density (Eq. 39), 22FNH2, and the
calculated current density (Eq. 40), IT, to the experimental data. The
data in Fig. 7 are the same as those in Fig. 4 and 5. The lines in Fig. 7
are found to describe the experimental data very well.
In summary, the model argues that the hydride layer couples the
hydrogen evolution and lithium dissolution processes. Thus, any
change in the properties of the outer layer simultaneously affects the
rates of lithium dissolution and hydrogen evolution. When the concentration of lithium ions in an outer-layer pore exceeds the lithium
solubility, lithium precipitates as LiOH, thereby reducing the pore
radius. As the concentration of lithium ions in the pore interior is voltage-dependent, the porosity of the outer layer is also voltage-dependent. This causes the anodic and cathodic partial current densities,
and the total current density, to decrease with increasing voltage.
The fundamental action of sucrose on the properties of the outer,
LiOH layer remains to be resolved. Because sucrose does not dissociate to produce OH2, a common-ion effect cannot be the cause of
the observed decrease in the porosity of the outer layer. Instead, we
suggest that the fundamental effect is one of adsorption of sucrose
onto the pore walls, resulting in a decrease in the chemical potential
of LiOH in the surface. This has the effect of decreasing the solubility of LiOH in the pores, thereby decreasing the pore diameter. The
stabilizing effect of sucrose presumably is due to hydrogen bonding
between the hydroxyl groups of sucrose with those of LiOH.
Impact of highly positive polarization on film structure.—We
have noted that Eq. 40 predicts an increasing current density as a
function of voltage for highly positive voltages. However, the derivation of this equation assumed that the interfacial reactions, including
the HER (reaction 6, Fig. 1) are irreversible. While this assumption
is clearly valid for the highly negative potential range discussed, at
least for hydrogen evolution it is unreasonable as the potential transitions the equilibrium potential for the HER.
If we approximate Vbl as V 1 fR, it can be shown (see Eq. 19) that
the barrier-layer thickness, Lbl, is a decreasing function of the applied
voltage. It is assumed that the electric field strength, e, is independent
of the potential, in accordance with the PDM.7-11 The Pourbaix diagrams in Part I3 indicate that phases of LiH and Li2O can coexist, provided that the applied voltage lies between lines 4 and 9 in Fig. 7 of
Part I.3 The barrier layer may be composed of Li2O under those con-
Table I. Parameters obtained by fitting Eq. 26, 39, and 40 to
experimental data. The basic parameters were computed directly from a least-squares fitting technique. The derived parameters were obtained from the basic parameters and Eq. 27, 28,
38, and 41.
Basic parameters
a
5.21 3 1022
Derived parameters
VOCP
22.87 V
k1o a MBI
9i
VL
b
aha
a3a
j2
5.65 3 1025
.6..8 3 1022
11.2 3 1022
3.86
k2o
o
kho9e2a hg(bpH BOI1fBOI1afR )
kso
t0
..18.27 V
2.2 3 1023
..44.05 V
Figure 6. Parameter j1 vs. concentration. (a) j1 vs. KOH concentration, (b)
j1 vs. sucrose concentration. The parameter j1 is chosen so that the experimental results are closely reproduced by Eq. 39 and 40.
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ditions not favorable to the presence of LiH. The existence of a
LiH/Li2O composite phase is likewise feasible. In the present model,
for potentials near OCP, we neglected the presence of the oxide, because thermodynamics precludes the formation of Li2O, even as a
metastable phase. However, at sufficiently positive potentials, as the
thickness of the hydride barrier layer is reduced to zero, the formation
of a stable Li2O barrier layer is thermodynamically viable. Accordingly, the passive film then comprises a defective oxide (Li2O) barrier
layer with an outer layer of precipitated LiOH. In this case, the thickness of the barrier layer is predicted to increase with increasing applied voltage, resulting in an increasing current if the barrier layer is a
cation vacancy conductor, or in a constant current if the dominant
crystallographic defects are oxygen vacancies or metal interstitials.7-11
For lithium oxide, cation vacancies are most likely to be the dominant
species whose motion through the barrier layer accounts for the increase in current with increasing voltage for high positive potentials
(above 4 VSHE). This increase in current density with increasing voltage was confirmed experimentally and is shown in Fig. 8.
Figure 8. Total current density vs. applied voltage (with respect to SHE). The
experiment was carried out potentiodynamically, and the electrolyte consisted of 8 M KOH. The figure shows forward and reverse scans. It is evident
that the total current density is an increasing function of the voltage for
potentials above 4 VSHE.
The electric field in the oxide-layer film differs markedly from
the hydride barrier-layer case. In the hydride case, the electric field
(e 5 2=f) is postulated to be negative, corresponding to the cathodic formation of LiH (i.e., Li 1 H2O 1 e2 r LiH 1 OH2), whereas
that in the oxide barrier layer (at highly positive voltages) is positive,
as indicated in Fig. 2 and 9. Diagnostic criteria have been derived
elsewhere for the determination of the main charge carrier in the barrier layer.25 The criteria affected by a change in sign of e are only
those related to the barrier-layer thickness. The potential dependence
of Lbl on voltage is the main property affected by a reversal in sign
in e. As mentioned previously, the barrier-layer thickness is a decreasing function of the applied voltage, for the LiH barrier-layer
case, and it is an increasing function for the Li2O barrier-layer case.
The hydride barrier-layer transitions to an oxide barrier layer
over a 2.4 V range (i.e., between lines 4 and 9, Fig. 1, Part I3). Over
this range, both Li2O and LiH can coexist and it is possible that the
Figure 7. Polarization behavior of lithium, as described in Fig. 3 and 4. The
curves were obtained by adjusting the parameter j1, so that both the total and
cathodic partial current densities were approximately reproduced by Eq. 39
and 40.
Figure 9. Envisioned potential profile of the Li/Li2O/LiOH system at highly
positive applied potentials. Under these conditions, the barrier layer is postulated to consist of a defective oxide film and the outer layer to comprise a
porous phase of precipitated LiOH.
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barrier layer consists of a composite structure. If the regions of both
phases are sufficiently small, the electrical properties of the barrier
layer change gradually with increasing voltage. Accordingly, a discontinuity in the current is unexpected, and none is observed in the
present work.
Figure 10 shows the electrochemical reactions that are envisaged
to occur at highly positive potentials, at which only an oxide barrier
layer forms as a metastable phase (at potentials more positive than
that of the equilibrium potentials for reaction 9, Fig. 1, Part I3). For
this system, the current density is given by
 
 o o

k1o 0
0
o a o gfBOI  k2 0 k3 0u
IT 5 F kso 0  a MBI
e a3gfBOI
9i o 0 1 1 1 kO e
VL
k2
 
 k1o 0 kso 0 a MBI

9i
VL
[46]
In this expression, k j0 symbolizes the rate constant associated with
reaction number j in Fig. 10, and k oj 0 represents the standard rate
constant (cf. Eq. 9-14). the double prime symbol (0) has been used
to differentiate the present symbols from the kinetic parameters of
the hydride/hydroxide model. The standard rate constant for oxygen
evolution is denoted k oO. Note that in Eq. 46, there are two exponential terms, both of which depend on the potential drop at the BOI.
Because the potential drop, fBOI, is an increasing function of applied
potential (see Eq. 8), it follows that IT is an increasing function of the
potential. Even when there is no oxygen evolution, which can be
described by setting k Oo 5 0, Eq. 46 still predicts an increasing current density as a function of the voltage at sufficiently positive voltages, as observed experimentally.
Finally, the theory presented is quite general and is applicable to
any metal for which the barrier layer of the passive film is a hydride
at sufficiently negative potentials and transitions into an oxide at sufficiently positive potentials. These metals presumably include the
reactive metals (Li, Be, Mg, ....) as well as the classical “hydride formers,” such as Zr, Ti, Ta, Y, .... Our present work leads us to believe
that hydride barrier layers may be more prevalent than has been recognized in the past.
Conclusions
A comprehensive theoretical model based on the PDM has been
developed to describe the electrochemistry of lithium in highly alkaline environments. The model accounts for all the experimental data
for lithium dissolution in concentrated alkaline solutions. Furthermore, the model predicts the observed polarization behavior at highly positive applied potentials. The model proposes the transition of
the barrier (or inner) layer from lithium hydride to lithium oxide on
increasing the potential from the OCP (22.8 VSHE) to positive potentials (above 8 VSHE).
The film formed on the lithium surface, in contact with an alkaline electrolyte under open-circuit conditions, have been modeled as
consisting of two layers with different chemical and physical properties. The inner layer has been postulated to be a compact film of
Figure 10. Electrochemical reactions that are envisaged to occur in the interface region at highly positive voltages.
lithium hydride, which is covered by a porous outer layer of lithium
hydroxide.
The hydrogen evolution rate depends on the water activity at the
BOI, which is regulated by the porosity of the outer layer. The
hydride film, in the steady state, couples the total current density to
the rate of hydrogen evolution such that as the anodic partial current
density decreases, so does the hydrogen evolution rate. Both increasing the KOH concentration and increasing the sucrose concentration
decrease the porosity of the outer layer, with the effect of sucrose
being greater for equivalent changes in concentration. The effect of
[KOH] is attributed to the common-ion (OH2) effect on the solubility of LiOH, whereas it is postulated that sucrose decreases the
LiOH solubility by lowering the chemical potential of lithium
hydroxide on the pore surface.
We have shown that the voltage of zero current density (OCP) is
governed by the kinetics of the processes that occur in the MBI and
the BOI. Furthermore, at highly negative potentials, additives are
found to affect the anodic and cathodic partial processes equally well.
Therefore, the OCP is approximately constant, i.e., it is nearly independent of the electrolyte composition and additive concentration.
Finally, the model predicts that the LiH barrier-layer thickness is
a decreasing function of the applied voltage. However, the model
suggests that at highly positive potentials, the identity of the barrier
layer changes from lithium hydride to lithium oxide, whose thickness increases with increasing potential. Under these conditions, the
total current density is predicted to increase with increasing potential, as verified experimentally in this research.
Acknowledgments
The authors gratefully acknowledge the financial support of the
Government of the United States. O.P.-R. and J.R.F. also wish to
express their gratitude for the partial support granted by CONACyT,
Mexico.
The Pennsylvania State University assisted in meeting the publication
costs of this article.
List of Symbols
a
see Eq. 27, dimensionless constant
aj
activity of j species, dimensionless
b
see Eq. 28, dimensionless constant
F
Faraday’s constant, F 5 96485 C/equiv
Ia
anodic partial current density, A/m2
Ic
cathodic partial current density, A/m2
IT
total current density, A/m2
kj
rate constant of reaction j, mol cm22 s21
o
kj 9
standard rate constant of reaction j (see Eq. 9-14), mol m22 s21
o
k oj 5 k oj 9e2ajgf BOI
(mol cm22 s21)
Lbl
barrier layer thickness, m
NH2
hydrogen evolution flux, mol m22 s21
P
number of pores per unit of outer-layer surface area, m22
r
outer-layer pore radius, m
ro
reference radius, m
R
ideal gas constant, R 5 8.314 J mol21 K21
T
temperature, T 5 298 K
V
applied potential, V
Vbl
potential drop (see Fig. 2), V
VOCP open-circuit potential, V
Greek
a
polarizability of the barrier layer/outer layer interface (see Eq. 7),
dimensionless
aj
transfer coefficient of reaction j, dimensionless
b
proportionality constant (see Eq. 7), V
g 5 F/RT V21
e
electric filed in the barrier layer, V m21
eol
electric field in the outer layer, V m21
u
outer-layer porosity, dimensionless
m
chemical potential, J mol21
j1
see Eq. 37, A m22
j2
see Eq. 38, dimensionless constant
to
see Eq. 31, dimensionless constant
f
potential difference, V
fR
reference potential, V
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Subscripts
BOI quantity defined at the barrier layer/outer layer interface
LiOH lithium hydroxide
Li1 lithium cation
MBI quantity defined at the metal/barrier layer interface
OH2 hydroxide anion
VH•
hydrogen anion vacancy
V9Li
lithium cation vacancy
W
water
1, 2, 3, 4, s, h quantity mainly referred to reactions 1-6, in Fig. 1. Only in
Eq. 46 these subscripts refer to reactions 1-5 in Fig. 10 (the
subscript h is substituted by O).
Superscripts
BOI quantity defined at the barrier layer/outer layer interface
MBI quantity defined at the metal/barrier layer interface
o
reference constant
9
prime symbol, associated with kinetic parameters in Fig. 1
0
double prime symbol, associated with kinetic parameters in Fig. 10
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