Modeling of aluminium deposition from chloroaluminate ionic liquids

Article abstract of DOI:10.1149/1.3623781

A finite-element model of the electrodeposition of aluminium from chloroaluminate ionic liquids is introduced. The purpose of this model is to give an explanation for the reasonable current densities that can be achieved in chloroaluminate ionic liquids despite the fact that the electrochemically active Al 2 Cl 7 - complexes are transformed into inactive AlCl 4 - complexes during the electrodeposition of aluminium. The obtainable current density in the electrodeposition from chloroaluminate ionic liquids strongly depends on the chemical rate constants for establishing the equilibrium Al 2 Cl 7 - + Cl - 2 AlCl 4 -. A high current (up to 3000 A m^-2) was found for both high and low rate constants whereas a minimum current (200 A m^-2) was found for intermediate rate constants due to kinetics and thermodynamics. The model is compared to experiments conducted in the ionic liquid AlCl₃ - [C₂mim]Cl (60/40 mol) where [C₂mim]Cl is 1-ethyl-3-methylimidazolium chloride.

Full text of DOI:10.1149/1.3623781

D634
Journal of The Electrochemical Society, 158 (10) D634-D639 (2011)
0013-4651/2011/158(10)/D634/6/$28.00 The Electrochemical Society
C
V
Modeling of Aluminium Deposition from Chloroaluminate Ionic
Liquids
a,
a, ,z
*
*
b,**
Stijn Schaltin,a, Murugan Ganapathi, Koen Binnemans,
and Jan Fransaer **
aDepartment of Metallurgy and Materials Engineering and bDepartment of Chemistry, Katholieke Universiteit Leuven,
B-3001 Leuven, Belgium
A finite-element model of the electrodeposition of aluminium from chloroaluminate ionic liquids is introduced. The purpose of
this model is to give an explanation for the reasonable current densities that can be achieved in chloroaluminate ionic liquids de-
spite the fact that the electrochemically active Al2Clꢀ7 complexes are transformed into inactive AlClꢀ4 complexes during the elec-
trodeposition of aluminium. The obtainable current density in the electrodeposition from chloroaluminate ionic liquids strongly
depends on the chemical rate constants for establishing the equilibrium Al2Clꢀ7 þ Clꢀ ꢀ 2AlCl4ꢀ. A high current (up to 3000
A mꢀ2) was found for both high and low rate constants whereas a minimum current (200 A mꢀ2) was found for intermediate rate
constants due to kinetics and thermodynamics. The model is compared to experiments conducted in the ionic liquid AlCl3
[C2mim]Cl (60/40 mol%) where [C2mim]Cl is 1-ethyl-3-methylimidazolium chloride.
-
C
V
2011 The Electrochemical Society. [DOI: 10.1149/1.3623781] All rights reserved.
Manuscript submitted March 30, 2011; revised manuscript received July 15, 2011. Published August 12, 2011.
The electrodeposition of aluminium from ionic liquids was
reported for the first time by Hurley and Wier in 1951.1 Within the
field of the electrodeposition of metals from ionic liquids, the elec-
trodeposition of aluminium is by far the most investigated topic. A
possible application for electrodeposited aluminium is as surface
coatings for corrosion protection in marine environments, where
zinc coatings cannot be used due to chemical reactions with sea salt.
The electrodeposition of aluminium is often carried out from chlor-
oaluminates.2–22 These are binary mixtures of AlCl3 with quaternary
ammonium, imidazolium or pyridinium salts. In these solutions, the
mole fraction of AlCl3 should be higher than 0.5 (Lewis acidic solu-
tions) to get the electrochemically active Al2Clꢀ7 complex in the
melt. For a mole fraction smaller than 0.5 (Lewis basic melts), the
sole aluminium species is AlClꢀ4 which is not electrochemically
active within the electrochemical window of the organic cations.
The electrodeposition of aluminium alloys is also a widely investi-
gated topic.20–31
although macroscopically correct, might not be the real reaction hap-
pening at the electrode’s surface. In this paper we propose an exten-
sion of reaction 1 by taking into account the kinetics of reaction 3.
Model
The modeling of the electrodeposition of aluminium on a rotat-
ing disk electrode from chloroaluminate ionic liquids is based on a
one-dimensional model (Fig. 1).
Point A represents the working electrode and point B the bulk solu-
tion. It is assumed that bulk conditions are valid at a distance of 1 mm
from the working electrode. This assumption will be validated (vide
infra). The modeled solution is AlCl3 - [C2mim]Cl (60/40 mol %)
where [C2mim]Cl is 1-ethyl-3-methylimidazolium chloride. Bulk con-
centrations of both Al2Clꢀ7 and AlCl4ꢀ are equal to 1981 mol mꢀ3 34
.
The net deposition reaction 1 is not suitable as the starting equa-
tion for the model. It does not give information on the different steps
in the electrodeposition process and it does not consider the pres-
ence of free Clꢀ ions, i.e. ions that are not bound to Al3þ. Therefore
reaction 1 is rewritten in a similar way as Lai and Skyllas-Kazacos8
The net reaction in the deposition of aluminium from acidic
chloroaluminates is32
4Al2Clꢀ7 þ 3eꢀ ! Al þ 7AlClꢀ4
[1]
4Al2Clꢀ7 þ 3eꢀ ! Al þ 4AlCl4ꢀ þ 3AlClꢀ4
[4]
This reaction is the sum of
Three Al3þ ions are no longer considered to form a complex with
chlorides and are regarded as free ions
Al2Clꢀ7 þ 3eꢀ ! Al þ AlCl4 þ 3Clꢀ
3Clꢀ þ 3Al2Cl7ꢀ ! 6AlClꢀ4
in which Al2Clꢀ7 can be viewed as a molecule of AlCl3 solvated by
AlClꢀ4 .32 The sum of both reactions can be considered as an electro-
chemical-chemical mechanism (EC mechanism) where a product of
the electrochemical reaction, Clꢀ, reacts with the solvent to produce
a species that is electrochemically inactive.33 Since AlCl4ꢀ cannot be
reduced within the electrochemical window of [C2mim]Cl, only one
out of two aluminium ions of Al2Clꢀ7 is reduced. The liberated chlo-
ride ions react further according to reaction 3 and if this reaction goes
fast, both reactions can be written simultaneously as reaction 1. The
sum reaction indicates that only one out of eight aluminium ions is
reduced to metallic aluminium and that the other ions become unavail-
able for reduction since they are transformed into the electrochemi-
cally inactive AlClꢀ4 ion. However, reasonable current densities (500–
1000 A mꢀ2) can be achieved during the electrodeposition of alumin-
ium from chloroaluminate ionic liquids. This suggests that reaction 1,
[2]
[3]
4Al2Clꢀ7 þ 3eꢀ ! Al þ 4AlClꢀ4 þ 3Al3þ þ 12Clꢀ
[5]
These three free Al3þ ions can be reduced, and this requires nine
additional electrons to the left-hand side of the reaction
4Al2Clꢀ7 þ 12eꢀ ! 4Al þ 4AlClꢀ4 þ 12Clꢀ
[6]
Dividing both sides by 4 gives
Al2Clꢀ7 þ 3eꢀ ! Al þ AlClꢀ4 þ 3Clꢀ
[7]
which is again Eq. 2. Equations 4–6 clarify the origin of Eq. 2. If the
Al2Clꢀ7 ion is considered as a molecule of AlCl3 solvated by
AlClꢀ4 ,32 reaction 7 represents that one aluminium ion is reduced
and that the solvating AlClꢀ4 is liberated together with three chloride
ions, which acted as ligands for Al3þ. Reaction 7 can be used to
study the complex formation behavior as it contains the three rele-
vant species Clꢀ, Al2Cl7ꢀ and AlClꢀ4 . The equilibrium between these
anions is expressed by the following autosolvolysis reaction
kf
Al2Clꢀ7 þ Clꢀ ꢀ 2AlClꢀ4
[8]
kb
*
**
Electrochemical Society Student Member.
Electrochemical Society Active Member.
z E-mail: Jan.Fransaer@mtm.kuleuven.be
in which kf and kb are the rate constants for the forward and back-
ward reaction, respectively. This reaction is the AlCl3-[C2mim]Cl
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Journal of The Electrochemical Society, 158 (10) D634-D639 (2011)
D635
lar velocity u is calculated by use of the coefficients from Fransaer
et al.35
The boundary conditions at point B are the bulk concentrations:
2
AlClꢀ
½
ꢁ
4
½Al2Clꢀ7 ꢁbulk ¼½AlCl4ꢀꢁbulk ¼1981 mol mꢀ3 and ½Clꢀꢁbulk
¼
.
Al Clꢀ buꢂlkKeq
½
ꢁ
2
7
bulk
The boundary conditions for point A are the molar fluxes N for all
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
three species: NAl Cl ;NAlCl and NCl . Both NAlCl and NCl are de-
2
7
4
4
pendent on NAl Cl . This is because as AlCl4 and Clꢀ are formed
ꢀ
ꢀ
2
7
during the electrodeposition from aluminium (reaction 7). Since one
AlClꢀ4 ion and three Clꢀ ions are formed for every Al2Clꢀ7 ion that
is reduced, the following two equations hold
Figure 1. Schematic representation of the one-dimensional model: point A
represents the active area of a rotating disk electrode and point B the bulk
solution.
ꢀ
ꢀ
7
NAlCl ¼ ꢀNAl Cl
[12]
[13]
2
4
solvent system equivalent of the autoionization reaction of water
(with OHꢀ the basic species and H3Oþ the acidic species) but with
Clꢀ as the Lewis basic species and Al2Clꢀ7 as the Lewis acidic spe-
cies.32 Reaction 7 was also used by Lai and Skyllas-Kazacos,8 and
if reaction 8 goes fast, it would yield the net reaction 1. The equilib-
rium constant for reaction 8 is given by the expression
ꢀ
ꢀ
NCl ¼ ꢀ3NAl Cl
2
7
ꢀ
NAl Cl evaluated on the electrode surface, is based on a Butler-
Volmer relationship
2
7
ꢂ
ꢃ
ꢂ
ꢃ
ꢀ
ꢁ
bnF
RgT
anF
RgT
NAl Cl ¼ koox exp
g
ꢀ Al2Clꢀ7
kroed exp ꢀ
g
ꢀ
ꢁ
ꢀ
2
AlClꢀ4
2
7
surf
kf
ꢀ
ꢁ
Keq
¼
¼
[9]
Al2Clꢀ7 ½Clꢀꢁ
kb
[14]
In Eq. 14, koox and kroed are the heterogeneous rate constants for oxi-
dation and reduction, a and b are the charge transfer coefficients, n
Literature values for the equilibrium constant Keq in AlCl3
[C2mim]Cl solutions are given in Table I.
-
In our model, the time-dependent reaction-convection-diffusion
equation
oc
ot
2
¼ R ꢀ u ꢂ rc þ Dr c
[10]
is solved for the three species of interest: Clꢀ, Al2Cl7ꢀ and AlCl4ꢀ. In
this equation, c represents the concentration (mol mꢀ3), D the diffu-
sion coefficient (m2 sꢀ1), R the reaction rates for the species in the
bulk (mol mꢀ3 ꢀ1) and u the fluid velocity vector (m sꢀ1). The
s
time-dependent reaction-convection-diffusion equation gives the
time-gradient of the concentration as a function of diffusion D!2c,
convection u ꢂ !c and the bulk reaction rate R. It is assumed that
the reaction rate R is given by
ꢀ
ꢁ
ꢀ
ꢁ
2
R ¼ kb AlClꢀ4 ꢀkf Al2Clꢀ7 ½Clꢀꢁ
[11]
The bulk reaction rate of any ion under investigation is a measure
for the amount of that ion that is generated (or consumed) due to
reaction 8. Therefore following conditions hold for the generation of
Al2Clꢀ7 and Clꢀ: RAl Cl ¼ RCl ¼ R, because Al2Clꢀ7 and Clꢀ react
ꢀ
ꢀ
2
7
in a 1:1 ratio and for AlClꢀ4 , RAlCl ¼ ꢀ2R since two AlCl4ꢀ ions are
ꢀ
4
formed for every reaction between Al2Clꢀ7 and Clꢀ. The negative
ꢀ
sign in the expression for RAlCl indicates that the formation of
AlClꢀ4 proceeds in the opposite re4action as for Al2Clꢀ7 and Clꢀ. This
is obvious from reaction 8. The fluid velocity vector u, caused by
the rotation of a rotating disc electrode, consists of three compo-
nents: the normal velocity uz, the radial velocity ur and the angular
velocity uh (see Fig. 1). Since convectional mass transport u ꢂ !c
mostly take place in the normal direction, u is simplified to a scalar
function u which gives the fluid speed normal to a rotating disk elec-
trode as a function of the distance z towards the electrode. This sca-
Table I. Values for the equilibrium constant Keq at different
temperatures.
log Keq
T (ꢃC)
Ref.
17
RT
40
40
50
60
30
34
7
17.1
16.3
16.1
15.5
Figure 2. Calculated current densities for different rotation speeds. Only the
first 10 s are shown. The numbers on the graph indicate different values for n
7
in kb ¼ 10n m3 molꢀ1 sꢀ1
.
7
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D636
Journal of The Electrochemical Society, 158 (10) D634-D639 (2011)
Figure 3. Calculated concentration profiles for Al2Clꢀ7 , AlCl4ꢀ and Clꢀ after 100 s at ꢀ0.75 V. (- -) kb ¼ 10ꢀ25 m3 molꢀ1 sꢀ1, (–) kb ¼ 10ꢀ8 m3 molꢀ1 sꢀ1, (ꢂꢂ)
kb ¼ 10ꢀ5 m3 molꢀ1 sꢀ1. The graphs are explained in the text. Please note that the scale on the horizontal axis is different for the two rotation speeds.
ꢀ
ꢁ
!
Al2Clꢀ7
Al2Clꢀ7
the number of exchanged electrons from reaction 7, F the Faraday
constant, Rg the gas constant, T the temperature and g the overpo-
tential. g is determined by the potential difference DE, applied by a
potentiostat between the working and reference electrode, but cor-
rected for the concentration overpotential gc:
RgT
nF
surf
bulk
ꢀ
ꢁ
, g ¼ DE ꢀ gc ¼ E ꢀ
ln
[15]
With these relationships the model can be solved. In reality, kf and
kb are constants but are in this model considered as variables since
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Journal of The Electrochemical Society, 158 (10) D634-D639 (2011)
D637
values for the current density. This observation holds for both rota-
tion speeds. The concentration profiles near the electrode after 100 s
are shown in Fig. 3. To keep the graphs simple, only the curves for
kb ¼ 10ꢀ25, 10ꢀ8 and 10ꢀ5 m3 molꢀ1 sꢀ1 were plotted. These figures
show that the assumption of bulk concentrations at z ¼ 1 mm is cor-
rect: even for the unstirred solution, the concentrations do not devi-
ate from the bulk concentrations for z > 0.4 mm.
The concentration profile for Al2Clꢀ7 does not depend on kb on
the scale of the figure and the curves for different kb values can
therefore not be separated. Only close to the electrode surface can
the curves be distinguished, what explains the different current den-
sities for varying kb values. This is because the resulting current
depends on the value of the slope of the concentration profile, eval-
uated at the electrode surface. For AlClꢀ4 , the curves for kb ¼ 10ꢀ8
and 10ꢀ5 m3 molꢀ1 sꢀ1 coincide, but the curve for kb ¼ 10ꢀ25 has
lower values in the diffusion layer. Also for Clꢀ do the curves for
kb ¼ 10ꢀ8 and 10ꢀ5 m3 molꢀ1 sꢀ1 coincide with each other and the
horizontal axis. The rotation speed does not alter the relative posi-
tion of the curves for different kb values. It only influences the thick-
ness of the diffusion layer.
An ion of Al2Clꢀ7 entering the diffusion layer has two possible
reaction paths: it can react electrochemically according to reaction 7
by reaching the electrode thereby contributing to the current. The
second possible outcome is that it reacts chemically according to
reaction 8, a reaction that can take place in the entire diffusion layer
and does not contribute to the current. The current is thus deter-
mined by the amount of Al2Clꢀ7 ions that can diffuse through the
diffusion layer without reacting according to reaction 8. Whether or
not an incoming Al2Clꢀ7 ion will transform into AlClꢀ4 depends on
two opposite effects: kinetics and thermodynamics. The kinetics
depend on kf and kb: the higher their values, the faster the forward
and backward reactions in Eq. 8 will take place. The influence of
thermodynamics is clarified in Fig. 4.
This figure shows the ratios
2
½AlClꢀ4 ꢁ
½Al2Clꢀ7
½Clꢀꢁ
and
ꢁ, which are
½Al2Clꢀꢁ½Clꢀꢁ
based on the calculated concentrati7on profiles of Fig. 3. For
2
½AlClꢀ4 ꢁ
kb ¼ 10ꢀ25, 10ꢀ20 and 10ꢀ15 m3 molꢀ1
s
ꢀ1, the ratio
is
½Al2Clꢀ7 ꢁ½Clꢀꢁ
orders of magnitude smaller than the equilibrium value
2
½AlClꢀ4 ꢁ
¼ Keq ¼ 1017:1. For higher values of kb, the curves are
½Al2Clꢀ7 ꢁ½Clꢀꢁ
coincident with the vertical axis. This means that for kb ¼ 10ꢀ25 m3
molꢀ1 ꢀ1, there is a large thermodynamic tendency to convert
s
Al2Clꢀ7 into AlClꢀ4 . This tendency decreases for increasing values of
kb as can be noticed in Fig. 4a. With these data, the minimum in cur-
rent as a function of kb can now be explained. If kb ¼ 10ꢀ25 m3
Figure 4. Calculated concentration ratios after 100 s at ꢀ0.75 V for the
stirred solution. The numbers on the graph indicate different values for n in
2
½AlClꢀ4 ꢁ
molꢀ1
s
ꢀ1, the ratio
deviates considerably from the equi-
½Al2Clꢀ7 ꢁ½Clꢀꢁ
kb ¼ 10n m3 molꢀ1 sꢀ1
.
librium value, meaning that an Al2Clꢀ7 ion feels a large driving force
to be converted to AlClꢀ4 . Furthermore Fig. 4b shows that the ratio
½Al2Clꢀ7 ꢁ
is smaller than 1 near the electrode’s surface, meaning that
½Clꢀꢁ
their exact values are unknown, only their ratio is known via Eq. 9.
The model is therefore solved for several values of kb, the corre-
sponding value for kf is then kf ¼ kb ꢂ Keq. An estimate for the value
of kb is based on a comparison between the experimental and calcu-
lated limiting current densities jL (vide infra).
there is a sufficient amount of Clꢀ to react with Al2Cl7ꢀ. Despite
these observations a large current can flow because the speed of
reaction to convert Al2Clꢀ7 into AlCl4ꢀ is very slow and a Al2Clꢀ7
ion entering the diffusion layer can reach the electrode relatively
unhindered. For
a
large rate constant kb, the reaction
2
½AlClꢀ4 ꢁ
Al2Clꢀ7 þ Clꢀ ! 2AlClꢀ4 proceeds quickly but the ratio
½Al2Clꢀ7 ꢁ½Clꢀꢁ
Results and discussion
already equals the equilibrium value so an incoming Al2Clꢀ7 ion
can easily reach the electrode and contribute to the current. For
intermediate values of kb, the opposite influences of kinetics
The presented current density versus time curves and concentra-
tion profiles are valid for a potentiostatic polarization at ꢀ0.75 V for
a disk electrode at rest, and rotating at 100 rotations per minute
(rpm). The resulting calculated current density-time curves are pre-
sented in Fig. 2.
and thermodynamics lead to
current.
a minimum in the calculated
As expected, the current density is higher for the stirred solution
than for the unstirred one and reaches a steady-state value whereas a
continuous decline in current is visible for the unstirred solution.
Less evident is the relationship between the current and the rate con-
stant kb: the highest currents are calculated for kb ¼ 10ꢀ25 and
kb ¼ 10ꢀ5 m3 molꢀꢀ11sꢀ1 and a minimum in current can be found for
Determination of input data and comparison
with experimental data
To determine input data for the model, such as diffusion coeffi-
cients and the heterogenous rate constant for reduction, linear poten-
tial scans were measured. The experimental scans can also be
kb ¼ 10ꢀ8 m3 mol
s
ꢀ1. Other values for kb lead to intermediate
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D638
Journal of The Electrochemical Society, 158 (10) D634-D639 (2011)
compared with the results calculated by the model. These experi-
ments were conducted at different rotation speeds in a mixture of
AlCl3 - [C2mim]Cl (60–40 mol %) at 40ꢃC. Platinum was used as a
working electrode, while an aluminium rod served as counter elec-
trode, all potentials are referred to an aluminium pseudo-reference
electrode. The recorded scans are presented in Fig. 5a.
Table II. Experimental jL values for different rotation speeds.
Also given are the kb values for which the calculated limiting cur-
rent density corresponds to the experimental value.
Rotation
speed (rpm)
Left intersection at
kb ¼ (m3 molꢀ1 sꢀ1
Right intersection
kb ¼ (m3 molꢀ1 sꢀ1
jjLj(A/m2)
)
)
For a potential of ꢀ0.75 V, the limiting current was reached for
rotation speeds up to 400 rpm. The purpose was to find the diffusion
ꢀ
100
150
200
250
300
400
403
492
552
630
683
775
10ꢀ20
10ꢀ6.7
coefficient DAl Cl of Al2Clꢀ7 and the value for kred by using the
o
10ꢀ19
10ꢀ7
2
Koutecky-Levich7equation36
10ꢀ18
10ꢀ7.1
10ꢀ7.3
10ꢀ7.3
10ꢀ7.5
10ꢀ17.1
10ꢀ15.6
10ꢀ9.5
h
ꢄ
ꢅꢄ
ꢅ
ꢄ
ꢅiꢀ1
ꢆ
ꢄ
ꢅꢀ1
2=3
jꢀL 1 ¼ 0:62nF DAl Clꢀ mꢀ1=6 x1=2 cAl Cl
o
ꢀ
ꢀ
þ nFkredcAl Cl
2
2
2
7
7
7
[16]
temperature of 40ꢃC in the same ionic liquid ([C2mim]Cl) are given
in Ref. 9. The reported values for a platinum working electrode
range from 0.55 to 3.33 ꢄ 10ꢀ11 m2 sꢀ1. Although these literature
values are based on n ¼ 0.75 and reaction 1, the diffusion coefficient
found in our work lies in the reported range. kroed is determined from
the intercept with the vertical axis of the fit in Fig. 5b, leading to
ꢇ
If the inverse of the limiting current density jꢀL 1 is plotted as a
function of the square root of inverse rotation speed (xꢀ1/2) a linear
behavior should be observed. This is evident from Fig. 5b. The dot-
ted line is a fit through the experimental data points. From the slope
of this fit, the diffusion coefficient can be calculated with a resulting
kred ¼ 1:89 ꢂ 10ꢀ5 m sꢀ1. The measured values for DAl Cl and kred
o
o
ꢀ
value of DAl Cl ¼ 1:17 ꢂ 10ꢀ11m2sꢀ1. For the calculation of this dif-
2
7
ꢀ
2
7
were used in the calculations. The diffusion coefficient
fusion coefficient, n was taken as n ¼ 3 thereby reflecting reaction 7.
DCl ¼ 6:1 ꢂ 10ꢀ11 m2 sꢀ1 was taken from literature,37 while DAlCl
ꢀ
4
ꢀ
Literature values for the diffusion coefficient of Al2Clꢀ7 at the same
ꢀ
was assumed to equal DCl
.
An estimate for the actual value of kb was derived from a compar-
ison of the experimental limiting current densities jL (see Table II)
and the calculated ones.
Figure 6 shows the calculated jL values as a function of kb for dif-
ferent rotation speeds. Because the jL versus kb curves have a mini-
mum, each line has two kb values for which the calculated current
density corresponds to the experimental value. These points are indi-
cated by þ and ꢄ for the intersections at low and high kb values
respectively and they are summarized in Table II. At the left side of
the minimum, the estimated kb value varies between 10ꢀ20 and 10ꢀ9.5
m3 molꢀ1 sꢀ1, on the right side of the minimum kb estimates are com-
prised between 10ꢀ7.5 and 10ꢀ6.7 m3 molꢀ1 ꢀ1, which is a much
s
smaller range. As in the ideal case, kb should be independent of the
rotation speed, these results indicate that the real kb value lies between
10ꢀ7.5 and 10ꢀ6.7 m3 molꢀ1 ꢀ1, which is within a factor of 6.3. A
s
possible explanation for the fact that a range is observed instead of a
fixed value might be that the kinetics of reaction 8 is not described by
reaction 11 but by a more general expression of the form
Figure 6. Calculated limiting current density jL as a function of kb for differ-
ent rotation rates. The þ and ꢄ signs indicate the intersection with the experi-
mental jL values (Fig. 5a).
Figure 5. Linear potential scans for different rotation speeds at 20 mV sꢀ1
and Koutecky-Levich plot of AlCl3 - [C2mim]Cl (60–40 mol %) at 40ꢃC.
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Journal of The Electrochemical Society, 158 (10) D634-D639 (2011)
D639
ꢀ
ꢁ ꢀ
ꢁ
ꢀ
ꢁ ꢀ
ꢁ
a
b
d
e
koox heterogeneous rate constant for oxidation, 1.89ꢂ10ꢀ5 mol sꢀ1 mꢀ2
c
f
R ¼ kb AlClꢀ4 Al2Cl7ꢀ ½Clꢀꢁ ꢀkf AlCl4ꢀ Al2Clꢀ7 ½Clꢀꢁ
kroed heterogeneous rate constant for reduction, 1.89ꢂ10ꢀ5 m sꢀ1
[17]
n
N
r
number of exchanged electrons from reaction 7, 3
molar flux, mol mꢀ2 sꢀ1
In Table I it is shown that values of Keq can vary, even if the temper-
ature is kept constant. Therefore, the limiting current density jL was
calculated as a function of kb (as in Fig. 6) but for different Keq val-
ues, ranging from 1015 untill 1019. These calculations showed that
the jL versus kb curves shift to the left hand side for increasing
values of Keq. Furthermore, the estimated kb values, based on these
alternative Keq values showed a larger range than the values deter-
radial coordinate, m
bulk reaction rate, mol mꢀ3 sꢀ1
R
Rg gas constant, 8.31 J molꢀ1 K
t
T
u
u
time, s
temperature, 313 K
fluid velocity vector, m sꢀ1
scalar fluid velocity, m sꢀ1
axial coordinate, m
mined using Keq ¼ 1017.1
.
z
a
b
g
charge transfer coefficient for reduction, 0.5
charge transfer coefficient for oxidation, 0.5
E ꢀ gc, V
Conclusion
gc concentration overpotential, V
We presented a finite element model of the electrodeposition of
aluminium from chloroaluminate ionic liquids. It is shown that the
calculated current densities strongly depend on the rate constants kb
and kf of the autosolvolysis reaction. This is caused by the effect of
these constants on the kinetics and thermodynamics of the autosol-
volysis which change in opposite directions for variations in kb.
These opposing effects lead to a minimum in the calculated current
density for intermediate kb values. A comparison of the calculated
data and the experimental limiting current densities indicates that
h
m
x
angular coordinate, rad
kinematic viscosity, 8.34 ꢄ 10ꢀ6 m2 sꢀ1
60
ꢆ
ꢇ
2prpm
rotation speed
¼
, rad sꢀ1
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Acknowledgments
This research was funded by a Ph.D grant of the Institute for the
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the IWT-Flanders (SBO-project IWT 80031 “MAPIL”) and the sup-
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List of symbols
[. . .] concentration of species. . ., mol mꢀ3
[. . .]surf surface concentration of species. . ., mol mꢀ3
c
concentration, mol mꢀ3
diffusion coefficient, m2 sꢀ1
D
DE applied potential difference, V
F
Faraday constant, 96485 C molꢀ1
jL limiting current density, A mꢀ2
kb, kf backward and forward reaction rate constants, m3 molꢀ1 sꢀ1
Keq equilibrium constant for reaction 8, 1017.1 (Ref. 34)
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