High magnetic field effect on the growth of 3-dimensional silver dendrites

Article abstract of DOI:10.1246/cl.2002.1186

A liquid/solid redox reaction between silver ion and copper metal was investigated under high magnetic field (maximum field strength: 15 T). 3-Dimensional silver dendrites produced via the reaction were affected drastically by the magnetic field. Dense and large quantity dendrites were obtained under the magnetic field. Magnetic force will determine the shape and quantity of the silver dendrites.

Full text of DOI:10.1246/cl.2002.1186

1186
Chemistry Letters 2002
High Magnetic Field Effect on the Growth of 3-Dimensional Silver Dendrites
Akio Katsuki,ꢀ Ichiro Uechi,y Masao Fujiwara,y and Yoshifumi Tanimotoy
Department of Chemistry, Faculty of Education, Shinshu University, 6-Ro, Nishi-Nagano, Nagano 380-8544
yInstitute for Molecular Science, Okazaki 444-8585
(Received August 16, 2002; CL-020700)
A liquid/solid redox reaction between silver ion and copper
was used. A copper wire (10 mm), fixed on a rubber stopper, was
immersed in a 0.05 mol/dm3 silver nitrate solution, full-filled in a
glass vessel (54 mm high, 30 mm diameter, volume: ca. 34 mL). The
vessels were placed at z to À95 mm (bottom; 9.3 T, 980 T2/m), z to
0 mm (middle; 15 T, À160 T2/m), and z to 95 mm (top; 5.6T,
À940 T2/m) in the bore tube, as shown in Figure 1. One vessel was
placed outside of the magnet (<0:005 T) as a control experiment.
Hereafter, these positions shall be called bottom, middle, top, and
outside, respectively. After 2 h reaction, the shapes of dendrites
were recorded by a digital camera. Yields of silver dendrites were
determined by gravimetry and those of copper ion were determined
by absorption spectrometry (Hitachi, U-3500), where molar
extinction coefficient of copper ion, Cu2þ, was assumed to be
11.92 cmÀ1 molÀ1 dm3 at 807 nm. All the experiments were carried
out at room temperature.
metal was investigated under high magnetic field (maximum field
strength: 15 T). 3-Dimensional silver dendrites produced via the
reaction were affected drastically by the magnetic field. Dense and
large quantity dendrites were obtained under the magnetic field.
Magnetic force will determine the shape and quantity of the silver
dendrites.
Control of chemical reaction by magnetic field has been one of
the interesting topics in chemistry.1 In this paper, we studied a
liquid/solid redox reaction, i.e. the reaction between silver ion and
copper metal, under vertical high magnetic field how magnetic
forces affect 3D-pattern and chemical yield of silver dendrites. It is
demonstrated that the magnetic field affects significantly topology
and chemical yield of silver dendrites. The results are interpreted in
terms of magnetic convection of the solution which is induced by
the magnetic force on paramagnetic copper ions generated in the
reaction.
The liquid/solid redox reaction investigated is given by the
following equation:
2Agþ þ Cu ! 2Ag # þCu2þ
ð1Þ
The reaction progresses by the ionization tendency, and silver metal
deposits around a copper wire as a dendrite.
A superconducting magnet (JMT, JMTD-LH15T40, ꢁ15 T, ꢀ
40 mm vertical bore tube) was used in our experiment. Figure 1
shows axialdistributions of magnetic field, z being thedistance from
the center of the bore tube along the axis. Silver nitrate (Nacalai
Tesque GR grade) was used as supplied. Copper wire (Nilaco,
99.99%, ꢀ 6mm) was polished just before its use. Distilled water
Figure 2 shows the photographs of the silver dendrite produced
under various magnetic fields. The magnetic field caused drastic
changes in the color and shape of silver dendrites. At zero field,
branches of metallic silver grew in dendrite with metallic color
under the gray and cylindrical dendrites (Figure 2(a)). In the
magnetic fields of 9.3 T and 980 T2/m, the shape of the dendrites
becomes slightly spherical, and the size of the metallic branches tree
became small (Figure 3(b)). In the magnetic fields of 15 T and
À160 T2/m and 5.6T and À940 T2/m, dendrites are black in color
and almost spherical in shape (Figure 2(c), (d)). Figure 3 shows
photomicrographs of dendrites in magnetic fields. All dendrites
took tree-like structure. The length of each branch is longer than at
least 1 mm at zero field (a). The length became remarkably smaller
under the magnetic field ((b), (c)).
Table 1 shows the relative yields of the silver dendrites and the
copper ion produced through the present redox reaction. The value
Figure 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.
Figure 2. The photographs of silver dendrites after 2 h reaction. (a) the outside
of the bore tube (control, <0:0005 T), (b) the bottom position (9.3 T, 980 T2/m),
(c) the middle position (15 T, À160 T2/m), (d) the top position (5.6T, À940 T2/
m).
Copyright Ó 2002 The Chemical Society of Japan

Chemistry Letters 2002
1187
higher field, whereas diamagnetic ones are pushed out to the lower
field. In the reaction (1), copper ion is solely a paramagnetic
whereas others are diamagnetic. Molar magnetic susceptibilities of
copper metal, copper ion, silver, and silver ion are
À4ꢃ ꢃ 5:46 ꢃ 10À12 m3 molÀ1
,
,
þ4ꢃ ꢃ 1:28 ꢃ 10À9 m3 molÀ1
,
À4ꢃ ꢃ 2:05 ꢃ 10À11 m3 molÀ1
and
À4ꢃ ꢃ 2:4 ꢃ 10À11
m3 molÀ1, respectively. At the top and bottom positions the forces
on copper ion are estimated at À12:0 N/mol and þ12:5 N/mol,
respectively, whereas the forces on which silver ion are estimated at
þ0:23 N/mol and À0:24 N/mol, respectively. The magnetic force
on copper ions is strong enough to induce convection of solution,
since it is about 19 times larger than gravity. The solution rich with
copper ions undergoes convection as a whole in magnetic fields,
since copper ions collide with their surroundings, i.e., water, and
other solutes.
Figure 3. The photomicrographs of the silver dendrite. (a) the outside of
the bore tube (control), (b) the bottom position (9.3 T, 980 T2/m), (c) the top
position (5.6T, À940 T2/m).
Table 1. The effects of magnetic fields on the yields of copper ion and
silver dendrites
Magnetic force
/T2mÀ1
Ratioa
[Cu2þ
B/T
At the top and middle positions, the magnetic forces around a
copper wire are downward. They will make the solution rich with
copper ions, move out from the copper metal and dendrite surfaces
and, as a natural consequence, a fresh bulk solution is supplied to the
surfaces. All of the solution in the vessel undergoes magnetic
convection. So, the redox reaction will be accelerated about the
double at the present condition. On the other hand, at the bottom
position, the magnetic force near the copper wire is upward and,
therefore, thesolution rich withcopper ionswill be restricted around
the copper wire, in addition of the magnetic convection of solution.
In this case, the direction of convection is reversed and localized at
the upper part of the solution. This reduces the efficiency in supply
of a fresh bulk solution to the reaction zone. As the result, the redox
reaction there will not be enhanced very efficiently.
So far we discussed the effects of magnetic fields on the
chemical yield of reaction (1). Analogously we can explain the
dense structure of dendrite in magnetic fields. However, within the
framework of the above-mentioned consideration, the shape of
dendrite should be cylindrical in shape in magnetic fields, which is
slightly different from the experimental results. The shape of
dendrites depend strongly on the detailed pattern of convection of
solution which will be affected by shape and size of a vessel, and
copper wire, and concentration of silver ions (i.e., copper ions
generated), and shape and intensities of magnetic force. Further
analysis of the results will be given in the near future.
Ag
]
Outside
Bottom
Middle
Top
ꢄ0
ꢄ0
980
1.00
1.29
1.00
1.54
2.29
9.3
15.0
5.6
À160
À940
2.08
2.062.12
aThe values are the ratio of the yield in magnetic field and that of control.
These data contain the error of about 10%.
obtained at zero field was set to a standard. The yields of the silver
metal and the copper ion at zero field were 0.078 g and 0.010 mol/
dm3, respectively. The magnetic field caused significant accelera-
tion of the redox reaction. Yields of both silver dendrite and copper
ion exhibit analogous increase in magnetic fields. The yields at the
middle and top positions showed the maximum yield of ꢂ2. But, the
yield at the bottom position was smaller than that at the top position
by nearly a half, though the magnetic field strength was stronger
than that at the top position and the magnetic force in both the
positions were almost equal except the direction of the force. These
results show that the Lorentz force is minor contribution to the
phenomenon.
The almost similar behavior of the yield of the silver and copper
ion implied that the reaction occurs quantitatively under magnetic
fields. The color of the dendrites growing under the magnetic field
was black. This would result from the multiple reflection of incident
light by the small-size dendrites.
In a previous paper, we have studied the effects of high
horizontal magnetic field (8 T, ca. Æ400 T2/m) on the 2D-pattern
and the yield of silver dendrite generated by the redox reaction
(1).2;3 A dendrite shape changed drastically and its yield increased
by about 50% in the magnetic field. All the results have been
interpreted in terms of the magnetic force on copper ion generated,
which induced magnetic convection of solution, though there were
several mechanisms for interpretation of observed magnetic field
effects. This interpretation was further verified by the computer
simulation study.4 Therefore, the results shown in Figure 2 and 3
could be explained predominantly by the term of the magnetic force,
though the Lorentz force5 could be partly responsible for the results
shown in Figure 2.
Conclusively the magnetic field affected the shape, color,
density and yield of the silver dendrite remarkably. The results are
explained by the magnetic convection of solution which is induced
by the magnetic force on paramagnetic copper ions generated by the
reaction. These findings strongly suggest that a magnetic force is a
potential tool to control not only chemical yields but also topology
of dendrites and crystals.
Thanks are due to the Ministry of Education, Culture, Sports,
Science and Technology (Grant-in-Aid for Encouragement of
Young Scientists, 14740396, 2002) and Saneyoshi Scholarship
Foundation, for partial financial support.
This magnetic force on a compound, of which molar magnetic
susceptibility is ꢁ, is given by the following equation.
References
1
‘‘Dynamic Spin Chemistry,’’ ed. by S. Nagakura, H. Hayashi, and T. Azumi,
Kodansha, Tokyo (1998).
1 dBðzÞ
2
3
A. Katsuki, S. Watanabe, R. Tokunaga, and Y. Tanimoto, Chem. Lett., 1996, 219.
Y. Tanimoto, A. Katsuki, H. Yano, and S. Watanabe, J. Phys. Chem. A, 101, 7359
(1997).
F ¼ ꢁ
BðzÞ
ð2Þ
ꢂ0 dz
where BðzÞ is the magnetic field at the position z and ꢂ0 is magnetic
4
5
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, 3200 (1991).
permeability of vacuum. Paramagnetic ions are attracted to the