Magnetic resonance imaging of a magnetic field-dependent chemical wave

Article abstract of DOI:10.1016/j.cplett.2004.08.079

The magnetic field dependence of the travelling wave formed during the reaction of (ethylenediaminetetraacetato)cobalt(II) (Co(II)EDTA^2-) and hydrogen peroxide was studied using magnetic resonance imaging (MRI). The reaction was investigated in a vertical tube, in which the wave was initiated from above. The wave propagated downwards, initially with a flat wavefront before forming a finger. Magnetic field effects were observed only once the finger had formed. The wave propagation was accelerated by a magnetic field with a negative gradient (i.e., when the field was stronger at the top of the tube than at the bottom) and slightly decelerated by positive field gradients.

Full text of DOI:10.1016/j.cplett.2004.08.079

Chemical Physics Letters 397 (2004) 67–72
www.elsevier.com/locate/cplett
Magnetic resonance imaging of a magnetic
field-dependent chemical wave
a
Robert Evans , Christiane R. Timmel , P.J. Hore , Melanie M. Britton
a
a
b,
*
a
Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Rd, Oxford, OX1 3QZ, UK
b
Department of Chemical Engineering, Magnetic Resonance Research Centre, University of Cambridge, New Museums Site,
Pembroke St., Cambridge, CB2 3RA, UK
Received 15 June 2004; in final form 12 August 2004
Available online 12 September 2004
Abstract
The magnetic field dependence of the travelling wave formed during the reaction of (ethylenediaminetetraacetato)cobalt(II)
(Co(II)EDTA2ꢀ) and hydrogen peroxide was studied using magnetic resonance imaging (MRI). The reaction was investigated in
a vertical tube, in which the wave was initiated from above. The wave propagated downwards, initially with a flat wavefront before
forming a finger. Magnetic field effects were observed only once the finger had formed. The wave propagation was accelerated by a
magnetic field with a negative gradient (i.e., when the field was stronger at the top of the tube than at the bottom) and slightly decel-
erated by positive field gradients.
ꢀ 2004 Elsevier B.V. All rights reserved.
1. Introduction
creased by the reaction then diffuses to neighbouring
regions and similarly catalyses the reaction there, thus
propagating the wave.
An interesting feature of this reaction is the con-
version of paramagnetic Co(II)EDTA2ꢀ ions to dia-
magnetic Co(III)EDTAꢀ ions and the subsequent
production of a concentration gradient and hence a
Exploring chemical wave reactions, which can model
wave or oscillatory behaviour in biological processes
such as chemotaxis or calcium waves, has been an area
of increasing interest in recent years [1]. One such reac-
tion is that of (ethylenediaminetetraacetato)cobalt(II)
(Co(II)EDTA2ꢀ) and hydrogen peroxide [2], at pH 4.
In this reaction the cobalt complex is oxidised to a
Co(III)EDTAꢀ complex (Eq. (1)).
´
magnetic susceptibility gradient. Work by Nagypal
and co-workers [2,3] showed that the propagating wave
produced in this reaction could be manipulated using
magnetic fields. Experiments were conducted by placing
a shallow layer of the Co(II)EDTA2ꢀ and hydrogen per-
oxide solution into a Petri dish. A drop of sodium
hydroxide solution was then added to the centre of the
Petri dish to initiate the autocatalytic reaction. In the
absence of a magnetic field, the resulting wave propa-
gated isotropically (Fig. 1a). In the presence of an inho-
mogeneous magnetic field, such as that produced by the
arrangement of bar magnets placed below the Petri dish
(Fig. 1c), the wave propagates in the shape of a cross
(Fig. 1b). A qualitative explanation for this effect
has been postulated [2] and is based on the different
2CoðIIÞEDTA2ꢀ þ H2O2 ! 2CoðIIIÞEDTAꢀ þ 2OHꢀ
ð1Þ
The reaction is catalysed by hydroxide ions and is
therefore autocatalytic. By introducing sodium hydrox-
ide into a localised region of the reaction mixture, it is
possible to produce a travelling wave [2]. The local con-
centration of hydroxide ions is autocatalytically in-
*
Corresponding author.
E-mail address: mmb29@cam.ac.uk (M.M. Britton).
0009-2614/$ - see front matter ꢀ 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.cplett.2004.08.079

68
R. Evans et al. / Chemical Physics Letters 397 (2004) 67–72
down the magnetic field gradient whilst attractive forces
cause the Co(II)EDTA2ꢀ ions to move into regions of
high magnetic field further increasing the concentration
gradient. However, discussion of these effects has been
based solely on the interpretation of visually obtained
results, with no quantitative measurements and no dis-
cussion of the forces that drive this behaviour.
It is easily shown that the thermal energy of the co-
balt ions in an aqueous solution (kBT) is much larger
than the magnetic energy of the ions in the magnetic
fields applied and hence it should not be possible to
separate these ions using an inhomogeneous magnetic
field. Indeed, it was noted by Boga et al. [3] that
Co(II)EDTA2ꢀ and Co(III)EDTAꢀ ions cannot be sep-
arated from a homogeneous solution and it was therefore
concluded that inhomogeneity of both the solution and
the applied magnetic field is essential for the evolution of
the magnetic field effects such as those depicted in
Fig. 1b.
*
The magnetic force, F M, per unit volume acting on a
droplet of pure Co(III)EDTAꢀ solution immersed in a
pure Co(II)EDTA2ꢀ solution is given by
*
*
F M / ðvCoðIIIÞ ꢀ vCoðIIÞÞð*B ꢁ rÞ *B;
ð2Þ
*
where B is the magnetic flux density and vCo(II) and
vCo(III) are the magnetic susceptibilities of the pure
Co(II)EDTA2ꢀ and Co(III)EDTAꢀ solutions, respec-
tively. The autocatalytic oxidation reaction described
by equation 1, has a complex time and concentration
dependence. Consequently, the relative concentrations
of Co(II)EDTA2ꢀ and Co(III)EDTAꢀ ions vary signif-
icantly across the solution with sharp concentration gra-
dients at the reaction front. Susceptibility measurements
of Co(II)EDTA2ꢀ and Co(III)EDTAꢀ solutions at the
concentrations used in Fig.
1 (0.02 M) yielded
v
Co(II) = ꢀ0.741 · 10ꢀ10 m3 kgꢀ1 and vCo(III) = ꢀ0.925 ·
10ꢀ10 m3 kgꢀ1, respectively. Hence, both solutions are in
fact diamagnetic although the Co(II)EDTA2ꢀ solution
is less diamagnetic than the Co(III)EDTAꢀ solution
resulting in a force down the magnetic field gradient,
*
F M, for Co(III)EDTAꢀ containing solution in a
Co(II)EDTA2ꢀ solution and a force up the magnetic
field gradient for the reversed scenario.
Fig. 1. Photographs of the reaction of Co(II)EDTA2ꢀ with H2O2 in a
shallow layer in a Petri dish 26 min after mixing, in the absence (a) and
presence (b) of an applied magnetic field. Light (pale pink) regions are
areas of unreacted Co(II)EDTA2ꢀ and the dark (purple) regions are
areas of reacted Co(III)EDTAꢀ solution. The orientation of the
magnets used for image (b) is shown in (c). (For interpretation of
the references to color in this figure legend, the reader is referred to the
web version of this article.)
The conversion of paramagnetic to diamagnetic ions
is not only crucial for the magneto-sensitivity of the
wave but it also allows a more quantitative study of
the reaction using magnetic resonance imaging (MRI).
The protons in the water molecules surrounding the
Co(II)EDTA2ꢀ and Co(III)EDTAꢀ ions show very dif-
ferent relaxation characteristics, with paramagnetic
Co(II)EDTA2ꢀ ions significantly reducing both longitu-
dinal, T1, and transverse, T2, relaxation times. This pro-
duces the image contrast necessary to observe the wave
using MRI, highlighting where Co(II)EDTA2ꢀ or
Co(III)EDTAꢀ ions predominate.
behaviour of the paramagnetic and diamagnetic cobalt
ions in a magnetic field where there is a concentration
gradient [3]. As the reaction progresses, diamagnetic
Co(III) EDTAꢀ ions are produced and these are pushed

R. Evans et al. / Chemical Physics Letters 397 (2004) 67–72
69
MRI was used to follow the formation and motion of
1 s
6 s
6 s
6 s
11 s
5s
5s
11 s
gradient
train
the travelling wave and to investigate the effect of well-
defined applied magnetic field gradients. As the reaction
needed to be fitted into the MRI probe the reaction was
performed in a narrow vertical tube.
imaging
sequence
gradient
train
gradient
train
n
51 s
Fig. 2. Schematic representing the timings between imaging sequences
and gradient trains, which are looped n times.
2. Experimental
expected, however it is not significant and its point
spread function is less than a pixel.
Sodium hydroxide, EDTA, cobalt chloride and
hydrogen peroxide (35% by volume), all of ACS grade,
were obtained from Aldrich and were used without fur-
ther purification. A 0.02 M Co(II)EDTA2ꢀ solution was
made by dissolving equimolar quantities of EDTA and
CoCl2 in de-ionised water and then adjusting the acidity
to pH 4. The reacting solution was made from 0.02 M
Co(II)EDTA2ꢀ and hydrogen peroxide solutions, in a
9:1 ratio. The concentration of sodium hydroxide solu-
tion used to initiate the travelling wave was 0.0284 M.
The reaction was initiated inside the spectrometer
magnet, ensuring that the reacting sample was not
moved through the enormous stray field associated with
the magnet, which would have affected the wave front. A
delivery device was constructed which layered a small
amount of the sodium hydroxide solution on top of
the Co(II)EDTA2ꢀ solution. This layer was less dense
than the Co(II)EDTA2ꢀ solution, thus preventing any
initial density fingering.
MRI [4] experiments were performed on a Bruker
DMX-300 spectrometer equipped with a 7.0 T super-
conducting magnet, operating at a proton resonance fre-
quency of 300 MHz. All MRI experiments were carried
out at a temperature of 24 0.2 ꢁC. The reaction was
imaged inside 5 mm NMR tubes, using a 25 mm radio-
frequency coil.
Relaxation times for the water were measured [5] for
Co(II)EDTA2ꢀ and Co(III)EDTAꢀ solutions using
CPMG (transverse relaxation, T2) and saturation recov-
ery (longitudinal relaxation, T1) experiments. At 0.02 M,
a solution containing paramagnetic Co(II)EDTA2ꢀ ions
The vertical images had a slice thickness of 1 mm and
were positioned in the centre of the tube. The vertical
and horizontal fields of view were 50 and 10 mm, respec-
tively, and were composed of a 256 · 64 pixel array. The
corresponding pixel size was 195 lm (horizontal) by 156
lm (vertical). The relaxation time of the Co(III)EDTAꢀ
solution was sufficiently long that an image could be ob-
tained from a single excitation. Just one signal acquisi-
tion was required, so the experiment time, for each
image, was 1 s.
To follow the effect of magnetic field gradients on the
travelling wave, trains of gradient pulses were applied
between image acquisitions. Gradient trains were gener-
ated by the imaging gradients of the spectrometer and
comprised pulses, which were switched on for 2 ms
and off for 1 ms, cycled 2000 times, with amplitude of
+0.2 or ꢀ0.2 T mꢀ1. This produced an average gradient
of 0.133 T mꢀ1 over a period of 6 s. A constant gradi-
ent was not applied, as this could have damaged the gra-
dient coils. A set of three trains was applied, at 5 s
intervals and at equidistant intervals between images
(Fig. 2). As a control, an experiment was also done in
the absence of these additional gradients. As the imag-
ing sequences apply gradients (typically 0.03–0.04
T mꢀ1 for a duration of 340 ms), all the experiments
using ꢀ0.2, 0 and +0.2 T mꢀ1 gradient trains were ac-
quired at the same time intervals of 51 s, thus allowing
comparison between experiments. The relatively long
time interval of 51 s was chosen to minimise the influ-
ence of the magnetic field gradients involved in the imag-
ing sequence. For negative gradients, the field decreases
from top to bottom of the sample/image and increases
for positive gradients. Heating of the sample due to
the imaging sequence and gradient pulses was negligible.
gave relaxation times of 340 1 ms (T1) and of 33
1
ms (T2) and solution containing diamagnetic
a
Co(III)EDTAꢀ ions 622 4 ms (T1) and 398 3 ms
(T2). Images were obtained using the fast imaging, mul-
tiple spin-echo sequence RARE [6]. Here a single excita-
tion pulse is used to excite the spins in the sample and
multiple echoes are acquired, which were encoded for
position using magnetic field gradients. The signal was
reconstructed using two-dimensional Fourier analysis,
producing a two-dimensional image. By collecting mul-
tiple echoes, after the initial excitation, T2 relaxation
contrast is possible, where regions of longer T2 appear
brighter than regions of shorter T2. As the sampling
time for the experiment is comparable with the T2 relax-
ation time of the imaged solution a degree of blurring is
3. Results
3.1. Flat wave fronts
After initiation of the reaction with NaOH solution, a
flat interface for the wave formed. Fig. 3 shows typical
images of the wave. The figure depicts the wave front
just after the reaction was initiated (a), with two further
images at 102 s (b) and 204 s (c), in the absence of any

70
R. Evans et al. / Chemical Physics Letters 397 (2004) 67–72
velocity on the sign or indeed presence of the magnetic
field gradient was observed.
3.2. Fingering
By investigating the reaction in a vertical tube, rather
than a shallow layer, there is an increased risk of hydro-
dynamic effects, where density differences associated
with the reaction may cause convection. This type of
behaviour has been observed in a number of travelling
wave reactions [1,8,9] and also appears to be present
in this system after the initial period in which the flat
wave front is dominant. The flat wave front persists
for typically 10–20 min after initiation of the reaction,
then a perturbation of the interface occurs, which devel-
ops into a finger or tendril. Fig. 4 shows a typical set of
images after fingering occurred. This experiment was
performed without additional gradients; similar images
were obtained for fingers formed in experiments in
which positive or negative gradients were applied. The
origins of this fingering are uncertain. Experiments have
been done where the reaction is initiated from the bot-
tom: no tendrils were observed propagating upwards.
This suggests that fingering is a manifestation of density
differences, arising from compositional differences
(D qC) or temperature differences (DqT). As the reaction
mixture used in this Letter is exothermic (DH = ꢀ8.15
1.25 kJ lꢀ1) a decrease in density (DqT < 0) for the re-
acted Co(III)EDTAꢀ solution is expected. To calculate
DqC, the densities of typical unreacted and fully oxidised
Fig. 3. MRI images of
a travelling wave in the reaction of
Co(II)EDTA2ꢀ with H2O2. Image (a) was taken immediately after
the reaction was initiated, through the addition of NaOH solution.
Images (b) and (c) were taken 102 and 204 s, respectively, afterwards.
No magnetic field gradients were applied in between images. Signal
intensity is high (bright) where Co(III)EDTAꢀ ions predominate and
low (dark) where Co(II)EDTA2ꢀ predominate.
applied magnetic field gradients, except those required
for imaging. Similar images were found for experiments
when additional magnetic field gradients were applied,
as described in Section 2. The signal intensity at 50%
of its maximum value (corresponding to the fully re-
acted Co(III)EDTAꢀ solution), served as a parameter
to define the position of the wave front and facilitated
the determination of the wave velocity. Table 1 gives
the velocity of waves, for the three magnetic field gradi-
ent conditions (ꢀ0.2, 0, +0.2 T mꢀ1). The velocities of
the waves in each experiment were small and constant,
and approximately 8 · 10ꢀ6 m sꢀ1. There appears to
be only a coupling between reaction and diffusion at this
stage [7]. Also, no significant dependence of the wave
Table 1
Wave velocities, where the interface remains flat and is unaffected by
fingering
Gradient pulse strength (T mꢀ1
)
Wave velocity (10ꢀ6 m sꢀ1
)
Fig. 4. MRI images after the development of fingering, in the reaction
of Co(II)EDTA2ꢀ with H2O2. No magnetic field gradients were
applied in between the images. Image (a) was taken when the fingering
distortion became fairly large and images (b)–(d) were taken at 51, 102
and 153 s after image (a), respectively.
ꢀ0.2
0
8.5 1.3
8.0 0.9
8.3 0.5
+0.2

R. Evans et al. / Chemical Physics Letters 397 (2004) 67–72
71
Table 2
Wave velocities, after the development of fingering
oxidation number of transition metal ions have been
used to image other wave-forming reactions using
MRI, the most-well known being the Belousov–Zhabo-
tinsky reaction [11] and the 1,4-cyclohexanedione-acid-
bromate reaction [12]. In addition to the measurement
of wave front behaviour, MRI can be used to measure
the hydrodynamic influences on the wave [13] and can
also provide a unique opportunity to investigate these
types of reactions in optically opaque systems, such
as packed beds.
Gradient pulse strength (T mꢀ1
)
Wave velocity (10ꢀ6 m sꢀ1
)
ꢀ0.2
0
173.2 17.7
135.1 3.3
125.8 3.6
+0.2
solutions were measured giving values of qCo(II)
1.077 0.001 g mlꢀ1 and
Co(III) = 1.0378
=
0.001
q
g mlꢀ1, respectively. This leads to a DqC, which like
DqT, is negative. However as a dicobalt species is formed
during this reaction [10], an increase in density is possi-
ble before the solution fully reacts and its density even-
tually falls. From observations of the wave propagating
upwards and downwards it seems likely that this possi-
ble contribution to the DqC, gives rise to the fingering.
The presence of the negative DqT will not prevent this,
but may lead to multicomponent or double-diffusive
convection [1].
The velocities of the waves were measured from the
MRI and again three sets of experiments were done, in
which gradient trains of 0, +0.2 and ꢀ0.2 T mꢀ1 were
applied. The development of these fingers was followed,
by taking consecutive images until the wave front prop-
agated out of the observable region of the imager. By
measuring the position of the leading edge of the finger,
in a similar way to measurement of the flat interface, its
displacement was measured. Table 2 shows velocities,
measured from typical experiments once the finger had
developed. Once the finger had formed, its velocity
was constant. As expected [1] these velocities are greater
for the displacing finger than for the flat interface. More
importantly there is a difference in behaviour depending
on the magnetic field gradient applied. The velocity of
the finger is significantly greater when a negative gradi-
ent is applied and a positive gradient slightly hinders the
progression of the wave.
This Letter presents the first quantitative measure-
ments of wave velocity and magnetic field effects for this
travelling wave reaction. The work by He et al. [2]
showed that the direction of wave propagation is con-
trolled by the properties of the applied magnetic field.
The experiments described here demonstrate clearly that
the velocity of the wave can be affected by the presence
and direction of a magnetic field gradient in conjunction
with a strong uniform magnetic field. We have shown
that the geometry of the interface is important: no mag-
netic effects were observed for a flat interface. It appears
that some sort of Ôsymmetry-breakingÕ [14] process is re-
quired, achieved here by the formation of chemical fin-
gers, before the wavefront becomes sensitive to the
applied magnetic field.
It seems plausible that similar magnetic convection
effects may be observable in other autocatalytic reac-
tions that show wave behaviour. A pre-requisite is that
the reactants and products, and possibly the reaction
intermediates, have significantly different magnetic sus-
ceptibilities and that large concentration gradients are
present.
Acknowledgements
M.M.B. thanks EPSRC for an Advanced Research
Fellowship. C.R.T. thanks the Royal Society for a Uni-
versity Research Fellowship. Thanks are given to K.B.
Henbest for helpful discussions.
An explanation for the acceleration of the wavefront
in a negative gradient most likely lies with an increase
in the transport of the autocatalytic hydroxide ions.
The finger, being more diamagnetic than the surrounding
solution, experiences a magnetic force directed down the
field gradient that would bring hydroxide ions to the
reacting front, thus propagating the wave more quickly.
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