Magnetic field effects in electrochemical reactions

Article abstract of DOI:10.1016/j.electacta.2003.04.009

The influence of an external magnetic field B on the electrochemical behaviour of the systems Cu²⁺/Cu, Ni²⁺/Ni, and [IrCl ₆]^2-/[IrCl₆]^3- has been studied. In the case of Cu depositions in an electrochemical cell with a large ratio of the electrode area and the cell volume the increase of the limiting current density with B can be explained with the interplay of natural convection and the Lorentz force acting on the resulting flow profile (magneto hydrodynamic or MHD effect). Ni depositions also show an MHD effect as well as a tendency to form more fine grained material in the presence of a magnetic field. The results on the homogeneous redox system [IrCl₆]^2-/[IrCl ₆]^3- at 50μm diameter micro electrodes are in qualitative agreement with recently proposed relationships to describe the influence of a B field on the limiting current density.

Full text of DOI:10.1016/j.electacta.2003.04.009

Electrochimica Acta 49 (2003) 147–152
Magnetic field effects in electrochemical reactions
A. Bund∗, S. Koehler, H.H. Kuehnlein, W. Plieth
Institute of Physical Chemistry and Electrochemistry, Dresden University of Technology, Mommsenstr. 13, D-01062 Dresden, Germany
Received 16 December 2002; accepted 9 April 2003
Abstract
The influence of an external magnetic field B on the electrochemical behaviour of the systems Cu2+/Cu, Ni2+/Ni, and [IrCl6]2−/[IrCl6]3−
has been studied. In the case of Cu depositions in an electrochemical cell with a large ratio of the electrode area and the cell volume the
increase of the limiting current density with B can be explained with the interplay of natural convection and the Lorentz force acting on the
resulting flow profile (magneto hydrodynamic or MHD effect). Ni depositions also show an MHD effect as well as a tendency to form more fine
grained material in the presence of a magnetic field. The results on the homogeneous redox system [IrCl6]2−/[IrCl6]3− at 50 ␮m diameter micro
electrodes are in qualitative agreement with recently proposed relationships to describe the influence of a B field on the limiting current density.
© 2003 Elsevier Ltd. All rights reserved.
Keywords: Lorentz force; MHD effect; Magnetoelectrolysis
1. Introduction
where iL and iL,0 are the limiting current densities in the
presence and the absence of a magnetic field, respectively.
The parameters m and p are empirical constants, with p in
the range from 0.25 to 1.64.
In a systematic investigation on the influence of
the individual parameters Leventis et al. arrived at the
semi-empirical Eq. (2) for the limiting current density iL
(A cm−2) [5,6].
If one looks through the literature about magnetic field ef-
fects in electrochemical reactions (“magnetoelectrolysis”),
the first effect one will probably encounter is the magneto
hydrodynamic (MHD) effect. Its origin is the Lorentz force
FL acting on moving charges (ions) in a perpendicular mag-
netic field of flux density B, FL = i × B, where i is the
current density. In most cases the MHD effect will lead
to an increase of the limiting current density because the
thickness of the Nernst layer is reduced by the magnetically
stimulated convection. At the first glance it may seem that
the law of the conservation of energy is violated, because
a static magnetic field cannot transfer the energy, needed to
stir the system. The action of B is to induce a force compo-
nent which is perpendicular to the velocity vector and the B
field. However, the absolute value of the momentum of the
ion remains constant.
iL = 4.31 × 102 × n3/2FA−1/4B1/3Dν−1/4c4/3
(2)
with ν kinematic viscosity (cm2 s−1), D diffusion−c3oefficient
(cm2 s−1), A area (cm2), c concentration (mol cm ) and the
numerical constant has units of cm mol−1/3 T−1/3 s−1/4
.
An interesting feature of Eq. (2) is the dependence of
the current density on the electrode area and the exponent
3/2 for n, the number of transferred electrons, which was
explained with a “feedback mechanism according to which a
higher n causes a higher magnetic current which causes more
vigorous hydrodynamic stirring” [6]. However, Eq. (2) can
only be true for a certain range of B (and for B > 0) because
at B = 0 iL would be zero what is definitely not the case.
White et al. were the first to introduce microelectrodes
(sometimes also called ultra microelectrodes, UMEs [7]) in
the field of magnetoelectrolysis. Their theoretical description
yields an expression for the net force on the diffusion layer
and qualitatively agrees with their experimental results [8].
Despite the increasing efforts to describe quantitatively the
The design of the electrochemical experiment (cell di-
mensions, size and arrangement of electrodes, etc.) strongly
influences the resulting flow profiles [1]. There are empiri-
cal relations in the form of Eq. (1) [2–4].
iL = iL,0 + mBp
(1)
∗
Corresponding author. Tel.: +49-351-463-34351;
fax: +49-351-463-37164.
E-mail address: andreas.bund@chemie.tu-dresden.de (A. Bund).
0013-4686/$ – see front matter © 2003 Elsevier Ltd. All rights reserved.
doi:10.1016/j.electacta.2003.04.009

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A. Bund et al. / Electrochimica Acta 49 (2003) 147–152
influence of the B field on the limiting current density a
quantitative description of the MHD effect based on the
Navier–Stokes equation is still pending. This is due to the
complex mathematics of hydrodynamics.
Phylatex, Karl-Marx-Stadt). The magnetic flux density B
was measured with a Hall probe (Lake Shore, model 450).
Note, that in the following, the expressions parallel and
perpendicular refer to the orientation of the B field rel-
ative to the electric current lines in the electrochemical
cell.
All solutions were prepared from ultra pure water and
analytical grade chemicals. As the electromagnet pro-
duces a lot of heat careful control of the temperature was
crucial in all experiments. Therefore all electrochemical
cells were equipped with a thermostating jacket which
was fed from a water thermostate (25.0 0.1 ◦C, Neslab
RTE-110).
If the magnetic field is in parallel with the current lines,
FL = 0. Nevertheless, there are reports of an influence of
the B field on the current characteristics of the cell under
these conditions [9–12]. In the case of large magnetic fields
(up to 9.4 T) White et al. could show that the increase of iL
is due to local gradients of the B field causing paramagnetic
forces [13]. The origin of these gradients can be either gra-
dients of the external field itself or gradients of the magnetic
susceptibility in the solution. During an electrochemical re-
action the magnetic susceptibility χ of the Nernst layer can
become different from the bulk value, because it is depleted
from the electro-active species. The gradient of χ, which is
proportional to the concentration gradient, can induce con-
vection by pulling paramagnetic ions into the direction of
higher B or by pushing diamagnetic ions out of the B field
[9,14–16]. According to the authors of refs. [17,18] the para-
magnetic forces as well as the Lorentz forces should be
6–7 orders of magnitude smaller than the diffusional forces
arising from typical concentration gradients. Therefore, the
question arises how such small forces can influence iL to a
measurable extent.
The question whether the electron transfer kinetics are
influenced by a B field is still discussed controversively in
literature [2,19,20]. It seems that these effects are small in
moderate B fields and will be paralleled in most cases by
paramagnetic and Lorentz force effects. Therefore, well re-
producible electrochemical systems with high exchange cur-
rent densities are needed as model systems for systematic
investigations on the B field influence on electrode kinetics.
This paper summarises some results from the authors’ lab
contributing to the above mentioned questions. One aim was
to investigate the B field effect in cells with a large ratio of
the electrode area A and the cell volume V (A/V ratio). In
such cases the experimental findings cannot be explained by
extrapolating the results from mini- and microelectrodes be-
cause the magnetic forces will set the whole electrolyte into
motion. Furthermore, the question if there is a B field effect
on the structure of an electrodeposited ferromagnetic metal
should be studied. Finally, many investigations on hetero-
geneous redox couples are done on the ferri/ferro cyanide
system, which is known to reveal some problems with re-
versibility. Most non-aqueous systems, which are also of-
ten used as model systems for systematic investigations on
the B field influence are experimentally more demanding.
Therefore, the usability of the aqueous heterogeneous redox
system [IrCl6]2−/[IrCl6]3− should be explored.
The electrochemical experiments were performed with a
Jaissle IMP 88PC-R potentiostat, controlled by the ECMWin
Software (IPS Schrems, Germany). All potentials are re-
ferred to a saturated (KCl) calomel electrode (SCE, Meins-
berg Sensortechnik, Meinsberg, Germany).
Copper depositions were studied from 10 mM CuSO4,
0.1 M Na2SO4 at pH 2. A PMMA cuvette (10 mm ×
10 mm × 45 mm) was used as the electrochemical cell
containing two Cu sheets (width 9 mm, thickness 0.5 mm)
as working electrode (WE) and counter electrode (CE),
respectively. The CE and WE were placed parallel to
each other at two opposite walls. For the WE two ver-
tical dimensions were investigated: A1 = 12 mm and
A2 = 40 mm, the CE had the larger height A2 in all exper-
iments. Cu deposition was performed for 80 s at −150 mV.
After each deposition the WE was polarised at 80 mV for
60 s to start each experiment with a reproducible surface
morphology.
Nickel depositions and dissolutions were studied in
a cylindrical thermostated glass cell (diameter 28 mm).
The Watts type electrolyte contained 0.17 M NiCl2·6H2O,
0.77 M NiSO4·6H2O, 0.65 M H3BO3, 1 mg/ml surfactant
Ni719 (Atotech, Berlin, Germany) and was adjusted to
pH 4.2 by adding solid NaHCO3. The electrolyte was
purged for 8 min with Ar (99.998%) prior to each exper-
iment. The WE (1.5 mm diameter Pt mini-disc electrode
sealed in a glass tube) was polished with abrasive pa-
per (Struers, SiC, P#4000). After each experiment the
Ni film was dissolved in 20% HCl. The surface was
checked before and after each Ni deposition with an op-
tical microscope (Reichert, Austria). The CE (Pt foil, ca.
10 mm ×10 mm) was placed at the bottom of the cell. Thus,
the magnetic field was always perpendicular to the current
lines.
The effect of a perpendicular B field on a homogeneous
redox couple was studied on the system [IrCl6]2−/[IrCl6]3−
in the same cuvettes as the Cu experiments. The elec-
trolyte contained 0.1 M NaCl, 2 mM K2[IrCl6] (Aldrich).
Lab-made 50 ␮m diameter Pt microelectrodes sealed in
glass tubes were used [21]. The CE was a Pt sheet. Five
cycles between 300 and 1100 mV were recorded at a scan
rate of 10 mV/s. Sweeps started at 700 mV into the cathodic
direction.
2. Experimental
All experiments were performed in the homogeneous
field of a water-cooled electromagnet (VEB Polytechnik,

A. Bund et al. / Electrochimica Acta 49 (2003) 147–152
149
Table 1
Relative increase of the limiting current density of the Cu reduction for
different orientations of the B field (details see Figs. 2 and 3) and different
sizes (A2 > A1) of the working electrode (WE)
Orientation Relative current increase at Relative current increase at
1 T (%) (area of WE A1)
1 T (%) (area of WE A2)
Fig. 2a
Fig. 2c
Fig. 3a
Fig. 3d
30
26
49
31
37
23
75
18
3. Results and discussion
3.1. Copper depositions
The limiting current density of Cu deposition showed a
strong dependence on the orientation of the magnetic field.
As a measure for the influence of the magnetic field the rela-
tive increase of the limiting current density (iB −iB=0)/iB=0
(measured at the end of the reduction step, see Section 2) is
taken. We can expect a MHD effect for a perpendicular ori-
entation of the B field relative to the current lines. Thus, as
the cell is rotated in the B field in steps of 90◦, one would ex-
pect two arrangements with a strong influence of the B field
(perpendicular) and two orientations with a negligible effect
(parallel). Interestingly, we found a distinct B field effect in
every position. Furthermore, the magnitude of the effect was
different for each of the four positions (Table 1). Measure-
ments at intermediate magnetic flux densities showed an al-
most linear behaviour of the relative current increase on B
(shown in Fig. 1 for the parallel orientations). For a perpen-
dicular magnetic field the increase of the limiting current
density was strongest in the orientation outlined in Fig. 2a,
i.e. the B field pointing away from the observer. If the cell is
rotated by 180◦ (B now points towards to observer, Fig. 2c),
the effect is considerably smaller.
Fig. 2. Schematic representation of the interplay of the natural convection
and the MHD effect (B field perpendicular to the current lines).
For a parallel B field of 1 T with the orientation outlined
in Fig. 3a the current increase was 75%. Rotating the cell by
180◦ resulted in a current increase of 18% (Table 1). This is
a somewhat unexpected behaviour, because at a first glance
one would not expect a Lorentz force (and thus no MHD
effect) for neither of these two configurations.
As Eq. (2) was deduced from experiments with minielec-
trodes it will not be applicable to the situation here. The
A/V ratio of the cell used here is in the range from 0.2 to
1 cm−1 (see Section 2) and thus relatively large compared
to experiments with mini- and microelectrodes, where A/V
is typically well below 10−3 cm−1. Preliminary experiments
using laser Doppler anemometry showed that the magnetic
0.8
0.6
0.4
0.2
0.0
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
B / T
Fig. 1. Relative current increase of the limiting current density of Cu
deposition (0.1 M Na2SO4, 10 mM CuSO4, pH 2) at −150 mV (SCE) in
a parallel B field. Lines are drawn just as a guideline for the eye. A1
and A2 refer to the size of the WE (A2 > A1, see text). (᭺) WE A2,
orientation as in Fig. 3a, (ᮀ) WE A1, orientation as in Fig. 3a, ( ) WE
A1, orientation as in Fig. 3d, (ꢀ) WE A2, orientation as in Fig. 3d.
Fig. 3. Schematic representation of the interplay of the natural convection
and the MHD effect (B field parallel to the current lines).

150
A. Bund et al. / Electrochimica Acta 49 (2003) 147–152
Table 2
field induced convection in the whole cell [22]. Therefore,
to understand the above results at least qualitatively one
must take into consideration the flow profile in whole cell
and especially the role of natural convection. Natural con-
vection occurs in unstirred solutions as a consequence of
density gradients (Figs. 2 and 3, ρbulk > ρN) which arise
because the solution in front of the electrode (Nernst layer,
density ρN) is depleted from the electro-active species. As
a consequence volume elements with a higher density are
pushed from the bulk and move upwards in front of the elec-
trode. The result is a convective flow in the Nernst layer
pointing upwards. In Figs. 2 and 3 this flow is indicated
with the force vectors FC(y). The magnitude of the force
increases in the upward direction (positive y-axis), as the
density of the volume elements decreases on their way up
(depletion of electro-active species). Thus, under the con-
dition of natural convection the current has a component
in the y-direction. A perpendicular B field will now induce
a Lorentz force with two components, FL and FC,L. The
component FL is due to the deposition current i pointing
towards the electrode. Its direction will be in the negative
(down, Fig. 2a) or positive (up, Fig. 2c) y-direction, depend-
ing on the orientation of B (right hand rule). Furthermore,
there will be a component FC,L coming from the Lorentz
force acting on the convectional flow. This component will
be directed towards (Fig. 2b) or away from (Fig. 2d) the
electrode.
The model outlined above can explain the results for a
perpendicular B field shown in Table 1. For the configuration
Fig. 2a FC,L has the same direction as the deposition current
and will thus lead to a enhanced transport of electro-active
species towards the electrode. For the configuration Fig. 2c
FC,L points away from the electrode and should reduce the
limiting current density. Increasing the vertical dimension of
the WE from A1 to A2 increases FC and the resulting effects
on iL. Thus iL increases by 7% in the configuration Fig. 2a
when going from A1 to A2 whereas iL decreases by 3% in
the configuration Fig. 2c (Table 1).
Relative increase of the limiting current density and the amounts of fine
and coarse grained material during Ni depositions as a function of the
applied magnetic field
B (T)
Current
increase (%)
Relative amount of
fine grained material
(%)
Relative amount of
coarse grained
material (%)
0
0.5
1
–
10
21
64
73
77
36
27
23
4. Nickel depositions and strippings
For all Ni experiments the following sequence of poten-
tiostatic steps was used: 30 s at E1 = −550 mV, 70 s at E2 =
−1300 mV, 80 s at E3 = 200 mV, 150 s at E4 = 1000 mV.
At E1 only oxygen reduction occurs. At E2 the limiting cur-
rent density for the Ni deposition was reached after 70 s. The
stripping potentials E3 and E4 were chosen according to a
paper of Dahms and Schumacher [23]. They found that dis-
solution of dendrites and fine grained material occurs at E3
whereas at E4 the coarse grained material dissolves. Thus,
the two step stripping procedure should allow to quantify the
amounts of coarse and fine grained material, respectively.
Under the influence of a perpendicular magnetic field the ca-
thodic limiting current density increased (see Table 2). This
can be explained with a MHD effect, as discussed above,
and is in agreement with literature [24]. As the nickel depo-
sition current is accompanied by a hydrogen reduction cur-
rent we will not discuss the current increase quantitatively.
The focus of the Ni experiments is on structural effects.
In the presence of a B field the first stripping peak de-
creased, whereas the second increased (Fig. 4). Integration
of the stripping peaks revealed a reduction of the mean
grain size with increasing B field (Table 2). It was reported
by several authors, that the surface roughness of Ni de-
posits decreases if an external B field is applied during
In the case of a parallel B field (Fig. 3) the interaction
of natural convection and the Lorentz force leads to a ro-
tational flow in front of the electrode [8,13]. Reversing
the direction of the B field changes the sense of rotation
(Fig. 3c and f) and one would expect the same current
increase for both configurations. It has been proposed
that the current increase in parallel configurations comes
from the a gradient of the magnetic susceptibility (see
Section 1). The magnetic susceptibility χ of the Nernst layer
will be lower than in the bulk because it is depleted from the
paramagnetic ion Cu2+. This gradient of χ leads to para-
magnetic forces and can explain the influence of parallel B
fields in general. However, it cannot explain the difference
between the configuration Fig. 3a and c, because the χ gra-
dient effects are proportional to B2 and thus independent
on the direction of B [9]. Thus, the detailed mechanism of
the current increase in the parallel B field remains an open
question.
20
16
12
8
4
0
-4
-8
-12
0
50
100
150
200
250
time / s
Fig. 4. Current transients for the deposition and the stripping of Ni films
at a Pt mini electrode in a Watts electrolyte (details see text). (– –) B = 0
T, (—) B = 1.0 T.

A. Bund et al. / Electrochimica Acta 49 (2003) 147–152
151
electrodeposition [25–27]. However, care must be taken
0.04
0.02
when comparing our results with these results, because there
must be no direct relation between surface morphology and
grain size. Nevertheless, our results show that there is a
clear dependence of the structure of the electrodeposited
nickel and the external B field. A first tentative explanation
can be based on the theory of electrodeposition, which
states that the crystal size of many metals decreases as the
deposition rate increases [28]. Thus, the B field effect on
the morphology of electrodeposits would be induced indi-
rectly by paramagnetic and Lorentz forces. A similar result
has been found in the case of nickel deposits from a Watts
bath containing 2-butyne-1,4-diol as an organic inhibitor
[3].
0.00
-0.02
-0.04
-0.06
0.0
0.2
0.4
0.6
0.8
1.0
(B/T)1/3
Fig. 6. Relative increase of the limiting current densities of the
[IrCl6]2−/[IrCl6]3− redox couple at a two similar 50 ␮m diameter micro
electrodes (0.1 M NaCl, 2 mM K2[IrCl6]). (ᮀ) Electrode 1, (᭺) electrode
2. A1 ≈ 1.4A2.
5. Homogeneous redox reactions
The system [Fe(CN)6]4−/[Fe(CN)6]3− is often used as
a model system to study the influence of B fields on ho-
mogeneous redox reactions. However, our experiments with
this system suffered from a poor reproducibility (results not
shown). The reason for this seems to be the formation of in-
soluble precipitates (prussian blue), leading to a poisoning
of the electrode [29]. The redox couple [IrCl6]2−/[IrCl6]3−
in aqueous solution is described as a reversible system with
a long term stability of several weeks [30].
UMEs were used because they show higher limiting cur-
rent densities than macroscopic electrodes and thus a larger
Tafel region. Furthermore, a steady-state is reached within
seconds and natural convection plays a minor role.
The cyclic voltammogram recorded at a UMEs with a di-
ameter of 50 ␮m showed the typical shape for a hemispher-
ical diffusion profile (Fig. 5, dashed line). In the presence
of a perpendicular magnetic field, both the cathodic and the
anodic limiting current density increased (Fig. 5, solid line)
which is a typical consequence of the MHD effect. As the
electrolyte contained only the oxidised species, [IrCl6]2− the
following discussion will focus on the reduction wave. The
power laws suggested by Eqs. (1) and (2) were tested by
plotting iL–iL,0 versus B1/3 for two similar UMEs (Fig. 6).
The absolute values of the limiting currents indicated that the
ratio of the areas of the two UMEs was ca. 1.4. The slopes of
the regression lines are (5.7 0.9)×10−5 A cm−2 T−1/3, and
(8 2)×10−5 A cm−2 T−1/3 for the somewhat smaller UME.
The larger slope for the smaller UME is in accordance with
Eq. (2) which implies higher values of iL with decreasing
area. Using A = 1.96×10−5 cm2, D = 6.6×10−6 cm2 s−1
,
ν = 0.01 cm2 s−1, and c = 2 × 10−6 mol cm−3 one ob-
tains a theoretical value of 3 ×10−4 A cm−2 T−1/3 (Eq. (2))
which is one order of magnitude larger than the experimen-
tal values. The reason for this deviation is not clear at the
moment. However, it must be borne in mind that Eq. (2)
was obtained by fitting experimental data from a variety of
electrochemical systems to an empirical power law. Further-
more, the area of the working electrode was in the range of
mm2 (millielectrodes) and as a consequence the diffusion
profiles were planar. The diffusion profiles of the UMEs
employed here will be mainly hemispherical (at least after
some seconds) [31]. As a consequence the diffusion limited
current will have components parallel to B field and the net
Lorentz force density should be smaller. Again it must be
stated that a profound theoretical treatment of the MHD ef-
fect must be based on a set of coupled differential equations,
Fick’s second law of diffusion and a modified form of the
Navier–Stokes equation taking into account magnetic field
effects [5].
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
From Tafel plots (not shown) the exchange current den-
sity of the [IrCl6]2−/[IrCl6]3− redox couple in 2 mM solu-
tion was estimated to 0.1 mA cm−2 which is ca. 15% of the
limiting current density. Therefore, if one uses small over-
potentials this system seems to be a promising candidate for
a systematic investigation of the influence of a B field on
the charge transfer kinetics.
200
400
600
800
1000
E vs SCE / mV
Fig. 5. Cyclic voltammogram (10 mV/s) of the [IrCl6]2−/[IrCl6]3− redox
couple at a 50 ␮m diameter micro electrode. 0.1 M NaCl, 2 mM K2[IrCl6],
(– –) B = 0 T, (—) B = 0.7 T.

152
A. Bund et al. / Electrochimica Acta 49 (2003) 147–152
Conway, et al. (Eds.), Kluwer Academic Publishers, New York, 1999,
6. Summary and conclusions
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on the resulting flow profiles. A strong influence of a paral-
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unclear. Future work will aim at the experimental determi-
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Acknowledgements
This work was financially supported by the “Deutsche
Forschungsgemeinschaft” within the “Sonderforschungs-
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der Chemischen Industrie” is gratefully acknowledged.
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