Effects of a High Magnetic Field on the Growth of 3-Dimensional Silver Dendrites

Article abstract of DOI:10.1246/bcsj.77.275

A liquid/solid redox reaction between silver ions and copper metal was investigated under a vertical and inhomogeneous high magnetic field (maximum field strength: 15 T). The 3-dimensional silver dendrites produced via the reaction were drastically affected by the magnetic field. Black and round dendrites were obtained in the magnetic field, whereas metallic silver crystals were grown under the gray dendrites with no field. The yields of the silver dendrite and the copper ion increased significantly in presence of the magnetic field. The results are interpreted in terms of the magnetic convection of the solution, which is induced by the magnetic force on the paramagnetic copper ions generated in the reaction as well as by the Lorentz force on the ions.

Full text of DOI:10.1246/bcsj.77.275

Ó 2004 The Chemical Society of Japan
Bull. Chem. Soc. Jpn., 77, 275–279 (2004)
275
Effects of a High Magnetic Field on the Growth
of 3-Dimensional Silver Dendrites
ꢀ
1
1
Akio Katsuki, Ichiro Uechi, and Yoshifumi Tanimoto
Department of Chemistry, Faculty of Education, Shinshu University, Nishi-Nagano, Nagano 380-8544
1
Institute for Molecular Science, Myodaiji, Okazaki 444-8585
Received June 9, 2003; E-mail: akatuki@gipnc.shinshu-u.ac.jp
A liquid/solid redox reaction between silver ions and copper metal was investigated under a vertical and inhomo-
geneous high magnetic field (maximum field strength: 15 T). The 3-dimensional silver dendrites produced via the reaction
were drastically affected by the magnetic field. Black and round dendrites were obtained in the magnetic field, whereas
metallic silver crystals were grown under the gray dendrites with no field. The yields of the silver dendrite and the copper
ion increased significantly in presence of the magnetic field. The results are interpreted in terms of the magnetic convec-
tion of the solution, which is induced by the magnetic force on the paramagnetic copper ions generated in the reaction as
well as by the Lorentz force on the ions.
The control of a chemical reaction path with a high magnetic
field has been an interesting hot topic in chemistry. This is part-
ly because a superconducting magnet, which generates a high
magnetic field, is now commercially available, and also be-
cause new phenomena, which can not be observed in a low
magnetic field, emerge in the high magnetic field. Research
on spin control of intermediates or radical pairs by a magnetic
celeration of the reaction rate as well as morphological
changes.
Experimental
A superconducting magnet (Japan Superconductor Technology,
JMTD-LH15T40) was used in our experiment. It has a room tem-
perature bore tube with a diameter of 40 mm. The distribution of
the magnetic field is given in Fig. 1. The maximum field (B) and
1
field has been widely carried out. The control of crystal orien-
–9
2
tation by the high magnetic field has been investigated.2
Moreover, our group has found that typical redox reactions
field (B) ꢁ gradient field (dB=dz) were 15 T and 1500 T /m, re-
spectively, where z is the distance from the center of the bore tube
along the tube. Silver nitrate (Nacalai Tesque GR grade) was used
as received. Distilled water was used as the solvent. A copper metal
wire (Nilaco, 6ꢀ, 99.99%) was polished just before the experiment.
The silver nitrate solution (0.05 mol/L) was filled in a cylindrical
vessel (30ꢀ ꢁ 52 mm, ca. 34 mL). The vessel was capped with a
rubber stopper on which a copper wire (10 mm length) was fixed.
show drastic changes under a high magnetic field.2,10–12
These
reports strongly suggest that a high magnetic field is a very use-
ful tool in controlling chemical and physical processes.
Mogi et al. reported various 2D-patterns of silver dendrites in
a vertical and homogeneous magnetic field. Significant changes
induced by the magnetic field were interpreted in terms of the
magnetohydrodynamic mechanism in which the Lorentz force
affects the motions of ions in the magnetic field.13 We have
studied the effects of a horizontal and inhomogeneous magnetic
Three vessels were placed at the positions in the bore tube, of
2
which B and BdB=dz were 5.6 T and ꢂ940 T /m for the top posi-
2
tion, 15.0 T and þ50 T /m for the middle position, and 9.8 T and
2
þ1070 T /m for the bottom position, as shown in Fig. 1, and one
field on the 2D-pattern and yield of silver dendrites and showed
In a verti-
was placed outside of the tube as a control (leak field ca. 0.5 mT).
Hereafter, we shall call these positions top, middle, bottom, and
outside, respectively. All reactions were carried out at room tem-
perature. After the reaction, the silver dendrite was carefully
scratched off the copper wire, washed using distilled water, and
dried out at room temperature. The yield of the silver dendrite
was measured by gravimetry. The concentration of copper ions
was determined from the absorption spectrum of tetraammine-
copper(II) complex (the molar extinction coefficient of the com-
plex was estimated as 55.6 at 613 nm) using a HITACHI U-2000
spectrophotometer.
that magnetic forces lead to remarkable effects.1
0,11
cal and inhomogeneous magnetic field, the natural convection
due to earth’s gravity would be significantly affected by the
magnetic force, which is parallel or anti-parallel to gravity
and, therefore, a reaction would be influenced.
In this paper, we studied a liquid/solid redox reaction, i.e.,
the reaction between silver ions and copper metal, under a ver-
tical and inhomogeneous high magnetic field in order to clarify
how vertical magnetic forces affect the growth, 3D-pattern, and
2
chemical yield of silver dendrites. It was demonstrated that the
vertical magnetic forces significantly affect the morphology
and chemical yield of silver dendrites. These magnetic field ef-
fects are interpreted in terms of the magnetic force and Lorentz
force. The magnetic force on paramagnetic copper ions gener-
ated via the reaction as well as the Lorentz force on the ions in
solution induced convection in the solution, resulting in the ac-
Results
The liquid/solid redox reaction investigated is given by the
following equation:
þ
2þ
2
Ag þ Cu ! 2Ag# þ Cu
ð1Þ
Published on the web February 10, 2004; DOI 10.1246/bcsj.77.275

2
76 Bull. Chem. Soc. Jpn., 77, No. 2 (2004)
Magnetic Field Effects on Silver Dendrites
1
1
50
00
Vertical bore
Top
50
5
10
15
Copper rod
0
Middle
Sample vessel
-50
-
-
100
150
Bottom
B / T
z
Fig. 1. The distribution of the vertical magnetic field BðzÞ. z is the distance from the center of the magnetic field (15 T) along the
magnetic axis. The gray parts show the area of the magnetic fields where the sample vessels were placed. These positions shall
be called top, middle, and bottom from the top. The right-hand vertical bore’s picture corresponds to the plot of distribution of
the magnetic field.
(a)
(b)
(c)
(d)
Fig. 2. The photographs of the silver dendrites after 2 h reaction. (a) the outside of the bore tube (the control < 0.0005 T), (b) the
2
2
2
bottom position (9.8 T, þ1070 T /m), (c) the middle position (15.0 T, þ50 T /m), (d) the top position (5.6 T, ꢂ940 T /m).
The reaction occurs via the ionization potential of copper and
silver metal deposits around the copper wire as a dendrite.
Figure 2 shows the photographs of the silver dendrites which
grew with and without the magnetic field. The shape and color
of the silver dendrites were remarkably affected by the magnet-
ic field. In the control experiment, metallic and bright crystals
with tree-like shape were observed under the gray and bulky
dendrite. The dendrites that grew under the magnetic field be-
came almost round in shape and dark gray or black in color.
The microphotographs shown in Fig. 3 indicate that dendrites
generated under the magnetic field have a shape similar to those
at zero field, though their size is about 10 times smaller than
that grown at zero field. The dendrites grown at the top also
contained many small black particles.
ion yields at the top position were larger than those at the bot-
tom position, though the magnetic field intensity at the bottom
position was about two times larger than that at the top position.
The time evolution of the copper ion yield at each position is
shown in Fig. 4. Every value in the magnetic field rose quickly
as compared with the value on the outside. For reaction times
under 20 minutes, the yield at the middle position increased
faster than those at the other positions. When the reaction time
exceeded 20 minutes, the yield at the top position was the larg-
est one, and the yield of the middle position was smaller than
that at the bottom position.
þ
After a 180-min reaction, about 86, 66, 75, and 44% of Ag
ion in the solution was deposited at the top, middle, bottom, and
þ
outside positions, respectively, and the total amount of Ag in
the solution was 0.0017 mol. The apparent saturation in copper
ion yield observed in magnetic fields is attributable to the
Table 1 shows the relative yield of the silver dendrites and
the relative concentration of the copper ion after a 2 hour reac-
tion at each position. Both values demonstrate a similar mag-
netic field dependence. The values in the magnetic field were
larger than those on the outside. Both the silver and copper
þ
decrease in the Ag ion concentration with time.
In order to analyze the results semi-quantitatively, the time
dependence of the yields was fitted tentatively with a single ex-

A. Katsuki et al.
Bull. Chem. Soc. Jpn., 77, No. 2 (2004)
277
(
a)
(b)
(c)
1
mm
Fig. 3. The microphotographs of the silver dendrites after 2 h reaction. (a) the outside of the bore tube (the control), (b) the bottom
2
2
position (9.3 T, 980 T /m), (c) the top position (5.6 T, ꢂ940 T /m). The values of the magnetic field strength and magnetic gradient
force in (b) and (c) show different values slightly because of the slight different positions.
Table 1. The Effects of the Magnetic Field on the Relative
Yields of Copper Ion and Silver Dendrites
Table 2. Kinetic Rate Parameters of the Copper Ion
Magnetic force
ꢂ1
Rate
ratio
Yð1Þ
B/T
ꢃ0
Magnetic forcea)
Ratiob)
/T m
2
a)
ꢂ3
/mol dm
a)
B/T
/
T2 m
ꢂ1
Ag
Cu
2þ
Outside
Bottom
Middle
Top
ꢃ0
1.00
1.85
5.01
3.18
0.013
0.019
0.017
0.021
9.8
þ1070
þ50
Outside
Bottom
Middle
Top
ꢃ0
ꢃ0
1.00
1.29
2.08
2.06
1.00
1.54
2.29
2.12
15.0
5.6
9.3
15.0
5.6
980
ꢂ160
ꢂ940
ꢂ940
a) The values are the ratio of the yield in the magnetic field and
that of the control.
a) The values of the magnetic field strength and magnetic gra-
dient force show different values slightly because of the slight
different positions. b) The values are the ratio of the yield in the
magnetic field and that of the control. These data contain the
error of about 10%.
Discussion
The magnetic field caused obvious changes in the shape and
color of the silver dendrites (Fig. 2). The yield of the silver den-
drites and the copper ion concentration show similar changes in
the magnetic field dependence (Table 1). This fact suggests the
copper ion is produced through the reaction (1) quantitatively,
with no side reactions in the system.14 Although the color of the
dendrites in the magnet is different from those on the outside,
pure silver metal dendrites are generated. The microphoto-
graphs (Fig. 3) show that many small-size dendrites appear in
the magnetic field. The dendrites grown in magnetic fields
are black or dark gray in color, as the incident light will be
reflected many times by the small-size dendrites.
0
0
0
.025
0
.02
.015
0
.01
.005
0
In a reaction occurring at the interface of heterogeneous
phases like the present one, the rate of a reaction is frequently
not controlled by the rate of the reaction at the interface, but by
the rate of the transportation of reactants and products to and
from the reaction zone. Although diffusion is usually an impor-
tant process for mass transportation, convection is sometimes a
much more important one from a practical point of view. When
the temperature of the solution is uniform, natural convection is
induced by the difference in the density of solutes, as the grav-
itational force on each solute is different.
0
20
40
60
80
100
120
140
160
180
200
Time / min
Fig. 4. The time evolution of the copper ion concentration:
(
(
(
) the outsides (the control < 0.0005 T); ( ) the bottom
2
2
9.8 T, þ1070 T /m); ( ) the middle (15.0 T, þ50 T /m);
2
) the top (5.6 T, ꢂ940 T /m); the solid lines, simula-
tions based on a single exponential function (Eq. 2).
ponential function (2), though this reaction was not the first-
order reaction;
In the present experimental conditions, silver ions in the bulk
solution are supplied to the reaction zone, i.e., the surfaces of
the copper wire and the dendrites, by convection as well as dif-
fusion. Since the atomic weights of Ag and Cu are 107.9 and
YðtÞ ¼ Yð1Þð1 ꢂ expðꢂktÞÞ
ð2Þ
2þ
where YðtÞ and Yð1Þ are the yields of Cu at time t and infin-
ite, respectively, and k is the rate constant. The fitting results
are described in Fig. 4 as solid lines, and the ratios of the rate
constants in the magnetic field, at zero field, and Yð1Þ are list-
ed in Table 2. It is clear that the reaction is accelerated by the
magnetic field.
þ
2þ
63.55, and since the molar ratio of Ag to Cu is 2:1 in the
þ
redox reaction, the density of the solution containing Ag will
2
þ
be higher than that containing Cu . This fact indicates that a
solution rich in Cu moves upward at zero field due to gravity,
2þ

2
78 Bull. Chem. Soc. Jpn., 77, No. 2 (2004)
Magnetic Field Effects on Silver Dendrites
Copper wire
2+
2+
2+
2+
+
+
Cu
Cu
Cu
Cu
Ag
Ag
+
+
+
+
Ag
Ag
Ag
Ag
2+
2+
Cu
Cu
Magnetic force
Magnetic force
(a)
(b)
(c)
Fig. 5. The possible mechanism of the magnetic field effect. (a) the outside; the convection caused by gravity, (b) the top (or middle)
and (c) the bottom; the convection caused by the magnetic force mainly.
leading to the natural convection of the solution localized with-
in the upper part of the solution in the vessel, as schematically
shown in Fig. 5(a). This was confirmed visually by the fact that
only the upper part of the solution in the vessel turned light blue
after the reaction. The lower part did not react within the ob-
served time duration. This is why Yð1Þ at zero field is about
one half of that in magnetic fields (Table 2).
In the presence of a magnetic field, the Lorentz and magnetic
forces on solutes and the solvent also induce convection in the
solution. The Lorentz force (FL) and magnetic force (FM) are
given by the following equations,
reasonable to think that both the Lorentz force and magnetic
force contribute in our interpretation of the present magnetic
field effects.
The area of highest yield of Cu2 ion is in the order of mid-
þ
ꢃ
dle ¼ top > bottom up to 20 minutes after the reaction starts,
and then changes to top > bottom > middle (Fig. 4). On the
other hand, B and jBdB=dzj are in order of middle > bottom
ꢃ
> top and bottom ¼ top > middle, respectively. The magnetic
field dependence of the yield does not match well with the mag-
netic field strength nor the magnetic field gradient strength. The
observed effects can not be explained solely by the Lorentz
force nor the magnetic force. They are explained by the combi-
nation of both forces, as discussed below.
FL ¼ ev ꢁ B
ð3Þ
and
In the early reaction stages, where the concentration of the
copper ion is low, the force due to Eq. 3 would dominate in
the reaction system. Therefore, before a reaction time of 20 mi-
nutes, the copper ion concentration at the middle position (15 T,
1
dBðzÞ
FM ¼ ꢁ
BðzÞ
ð4Þ
ꢂ0 dz
2
ꢂ1
where e is the electric charge of an ion, v is its velocity, B is the
magnetic field, ꢁ is the molar magnetic susceptibility, and
dBðzÞ=dz is the magnetic field gradient at the position z apart
from the center of the magnetic field along the bore. Molar
magnetic susceptibilities of copper metal, copper ion, silver,
ꢂ160 T m ) grew faster (Fig. 4) and the simulated reaction
rate was larger (Table 2) than those at the other positions.
The motion of silver ions is accelerated by the Lorentz force.
This causes an increase in the frequency of the collisions be-
tween the silver ions and the copper metal surface. As a result,
the efficiency of the redox reaction is improved. Most of the re-
action duration, however, is driven predominantly by the mag-
netic force in Eq. 4, primarily because the copper ion concen-
tration at the middle position is lower than that at the bottom
ꢂ12
3
ꢂ1
and silver ion are ꢂ4ꢃ ꢁ 5:46 ꢁ 10
m mol , þ4ꢃ ꢁ
ꢂ9
3
ꢂ1
3
ꢂ11
3
ꢂ1
1
:28 ꢁ 10 m mol , ꢂ4ꢃ ꢁ 2:05 ꢁ 10
m mol , and
m mol , respectively. The FL works in
ꢂ11
ꢂ1
ꢂ4ꢃ ꢁ 2:4 ꢁ 10
the direction which is vertical to both v and B. The motion of
ions in the horizontal plane is accelerated by FL. On the other
hand, FM works along the direction of B, and attracts or repels
ions and molecules in the vertical direction. In a high magnetic
field, the FM on a paramagnetic ion becomes strong enough to
induce convection. At the top and bottom positions the forces
on the copper ions are estimated at ꢂ12:0 N/mol and þ13:7
N/mol, respectively, whereas those on the silver ions are esti-
mated at ꢂ0:23 N/mol and þ0:26 N/mol, respectively. The
magnetic force on the copper ions is strong enough to induce
convection in a solution, since it is about 19 times larger than
gravity. The estimation of the Lorentz force on thermally mov-
ing ions in solution is very difficult, though it is easy for ions
moving in a vacuum. Ions in a solution are solvated by water,
and their mass and size are unknown. Solute–solvent and
solute–solute interactions affect the velocity of ions. The veloc-
ity of ions moving in a solution is unclear, even though it is
2
ꢂ1
position (9.3 T, 980 T m ) at 180 min, and, secondly, the
yield of the silver dendrite at the top position (5.6 T, ꢂ940
2
ꢂ1
T m ) is larger than that at the bottom position, even though
the magnetic field strength at the bottom position is stronger
than that at the top position. The appearance of the copper
ion causes a major change in the magnetic field. Accordingly,
the Lorentz force does not significantly contribute to the ob-
served results. This is because the direction of convection
due to the magnetic force is vertical, which is suitable for re-
2
þ
moving Cu from the reaction zone and, as a result, for sup-
plying fresh solution from the lower part of the vessel to the re-
action zone, whereas the Lorentz force induces convection of
the solution only in the horizontal plane.
We can explain the dense structure of the dendrite in the
17
magnetic field roughly as follows: At the top (and the middle )
position (Fig. 5(b)), the magnetic forces on the copper ions
around the copper wire are downward. As the copper ion rich
solution around the copper wire moves out by the magnetic
plausible that the Lorentz force appreciably affects the motion
Therefore, it is
of ions in solution, as previously reported.1
3,15,16

A. Katsuki et al.
Bull. Chem. Soc. Jpn., 77, No. 2 (2004)
279
forces, a fresh bulk solution, which is rich in silver ions, is sup-
plied to the surface of the copper wire. All of the solution in the
vessel undergoes the magnetic convection. As a result, the re-
dox reaction (1) is promoted effectively, and the yield acceler-
ated about double that at the present condition. On the other
hand, at the bottom position (Fig. 5(c)), the copper ions around
the wire receive an upward magnetic force. This means that the
convection zone becomes small as compared with that at the
top position. Accordingly, the reaction is not accelerated much
by the magnetic force.
present experimental condition, whereas that of the Lorentz
force is horizontal. The magnetic force intensifies or diminishes
a gravity force in chemical reaction. These results suggest that
magnetic fields are highly useful in controlling redox reactions
at the interface between liquid/solid phases.
This research was partially supported by the Joint Studies
Program (2002) of the Institute for Molecular Science (IMS).
A.K. thanks the Ministry of Education, Culture, Sports, Science
and Technology, Grant-in-Aid for Encouragement of Young
Scientists, 14740396, 2002 and Saneyoshi Scholarship Founda-
tion for their financial support.
Now, we move on to the shape of the dendrites in the mag-
netic field. For the purpose of comparison, the effects of the
þ
concentration of Ag on the shape of the dendrites were exam-
ined at zero field. At low concentration, the metallic and bright
crystals grew like a tree under the gray and bulky dendrites.
With increasing concentration, the color of the dendrites
changed to black, and no metallic crystals were formed. This
means that the morphology of the dendrites is significantly af-
fected by the reaction rate. At low concentration, the reaction
rate is slow and the metallic crystals grow slowly after the ini-
tial deposition of gray dendrites. At high concentration, the rate
is so fast that small particles and dendrites deposit on the copper
wire. Therefore, the morphological change induced by the mag-
netic field is attributable to the acceleration of the reaction rate
caused by the magnetic field-induced convection. Black and
round dendrites grew in the magnetic field due to the accelera-
tion, whereas tree-like crystals were formed at zero field.
In a previous paper, we have studied the effects of a high
References
1
‘‘Dynamic Spin Chemistry,’’ ed by S. Nagakura, H.
Hayashi, and T. Azumi, Kodansha, Tokyo (1998).
A. Katsuki, I. Uechi, M. Fujiwara, and Y. Tanimoto, Chem.
Lett., 2002, 1186.
2
3 A. Katsuki, R. Tokunaga, S. Watanabe, and Y. Tanimoto,
Chem. Lett., 1996, 607.
4 M. Fujiwara, T. Chidiwa, R. Tokunaga, and Y. Tanimoto, J.
Phys. Chem. B, 102, 3417 (1998).
5 M. Fujiwara, R. Tokunaga, and Y. Tanimoto, J. Phys.
Chem. B, 102, 5996 (1998).
6 M. Fujiwara, M. Fukui, and Y. Tanimoto, J. Phys. Chem. B,
03, 2627 (1999).
1
7
Y. Tanimoto, R. Yamaguchi, Y. Kanazawa, and M.
Fujiwara, Bull. Chem. Soc. Jpn., 75, 1133 (2002).
J. Torbet, J.-M. Freyssinet, and G. Hudry-Clergeon, Nature,
89, 91 (1981).
M. Ataka, E. Katoh, and N. I. Wakayama, J. Cryst. Growth,
2
horizontal magnetic field (8 T, ca. 400 T /m) on the 2D-pattern
8
of silver dendrites generated by the redox reaction (1), where
the dendrites were deposited on chromatography paper.1
The dendrite shape changed remarkably, and the yield increas-
ed by about 50% in the magnetic field.11 In this experiment, the
magnetic field is perpendicular to gravity and, therefore, inter-
ference between the magnetic force and the gravitational force
is minimum. Furthermore, the Lorentz force does not contrib-
ute to the reaction, as the reaction was carried out in the two-
dimensional plane. These results were interpreted solely in
view of the magnetic force on the copper ion generated by
the redox reaction, which caused magnetic convection of the
2
0,11
9
173, 592 (1997).
10 A. Katsuki, S. Watanabe, R. Tokunaga, and Y. Tanimoto,
Chem. Lett., 1996, 219.
11 Y. Tanimoto, A. Katsuki, H. Yano, and S. Watanabe, J.
Phys. Chem. A, 101, 7359 (1997).
1
2
W. Duan, M. Fujiwara, and Y. Tanimoto, Bull. Chem. Soc.
Jpn., 73, 2461 (2000).
I. Mogi, S. Okubo, and Y. Nakagawa, J. Phys. Soc. Jpn., 60,
200 (1991).
The initial pH conditon of the solution was neutral. During
1
3
3
1
4
solution and accelerated the redox reaction. This interpretation
was further verified by the computer simulation study.12 In the
copper ions were produced by the redox reaction, precipitation
such as a copper hydroxide did not appear in our experimental con-
dition.
present experiment, since the reaction was carried out in 3-di-
mensional space, the influence of the Lorentz force in addition
to the magnetic force is also taken into consideration. The mor-
phology of dendrites at zero field would be affected partly by
the natural convection and would be further modified by the
magnetic force and the Lorentz force in the magnetic field.
1
1999).
5
K. Shinohara and R. Aogaki, Electrochemistry, 67, 126
(
1
6
A. Sugiyama, S. Morisaki, and R. Aogaki, Mater. Trans.,
JIM, 41, 1019 (2000).
The magnetic force at the middle position is much smaller
1
7
than that at the bottom position. Therefore, vertical convection
does not occur effectively at the middle position, though the direc-
tion of the convection of the copper ions is downward. In contrast,
at the bottom position, the vertical convection occurs, even though
the convection volume is small as shown in Fig. 5(c). As a result
the yield at the middle position becomes smaller than that at the
bottom position.
Conclusion
The magnetic field dramatically affects the growth behavior,
shape, and amount of the silver dendrites. The results are inter-
preted in terms of the magnetic and Lorentz forces, of which the
former contribution would be dominant compared to the latter.
This is because the direction of the magnetic force is vertical
which is suitable for convection of the whole solution at the