[Springer Series in Materials Science] Magneto-Science Volume 89 || Effects of Lorentz Force and Magnetohydrodynamic Effects

Effects of Lorentz Force and Magnetohydrodynamic Effects

Magnetic field effects (MFEs) based on Lorentz force clearly appear in electrochemical reactions and they have been investigated as magnetohydrodynamic (MHD) effects for electrolysis. But new aspects of MFEs have been appearing as a result of microscopic investigations under the influence of high magnetic fields. In this chapter, we describe the novel phenomena and mechanisms of magneto-electrochemical processing, metal deposition under magnetic fields, the magnetic induction of morphological chirality and metal shaping with alternating magnetic fields.

3.1 Magneto-electrochemical Processing

For magneto-electrochemical processing, it is important to utilize field forces induced by magnetic fields. Under magnetic fields, electrochemical systems receive various forces, which are mainly classified into three kinds, i.e., Lorentz force, heterogeneous and homogeneous magnetic forces. Lorentz force is induced by the interaction between electrolytic current and magnetic field; the force per unit volume is expressed by fi=IxB, where T is the current density, and B is the magnetic flux density. Heterogeneous magnetic force generated in a heterogeneous magnetic field is expressed by differentiating the magnetic energy stored in electrolyte solution per unit volume, i.e., fhe = (1 / 2)( j / jUo)V|5|\ where x is the magnetic susceptibility, /Uo the magnetic permeability and V the differential operator with regard to the position. Homogeneous magnetic force emerges in a homogeneous magnetic field, written as fho = (l/2)(|5f/AXo)V;f.

In electrochemical reactions, Lorentz force is generally predominant, so that the effects induced by Lorentz force, i.e., magnetohydrodynamic (MHD) and micro-MHD effects have been studied from the beginning.'^^ Effects in heterogeneous magnetic fields can be observed when MHD and micro-MHD effects are neglected.^^ Homogeneous magnetic force is the weakest among them, so few studies have been reported. ^ Therefore, in

112 3 Effects of Lorentz Force and MHD

this section, MHD and micro-MHD effects are first discussed, followed by examination of the effects on the heterogeneous force.

3.1.1 Application of Lorentz Force

A. MHD Electrode For the analysis of electrochemical reaction in a magnetic field, an electrode system called the MHD electrode is used. Fig. 3-1-1 is a schematic drawing of the MHD electrode, which is composed of a rectangular channel with two open ends. On the inner walls of the channel, a pair of electrodes each with the same area is placed face to face, i.e., one is the working electrode and the other is the counter electrode, and electrolytic current flows between them. The electrode potential of the working electrode is regulated by a reference electrode inserted from behind through a Luggin capillary. Magnetic field is applied vertically to the current, i.e., in parallel mode to the electrode, so that Lorentz force is generated along the channel, and as shown in Fig. 3-1-1, the solution inside the channel starts to move along the electrodes. Momentum balance of the induced fluid motion is expressed by the following Navier-Stokes equation,

^ + ( M . V ) M = - - V P + vV'w + - r x 5 (1)

dt p p where u is the velocity, P the pressure, p the density and v the kinematic viscosity. The solution flow is called the MHD flow, which is self-organized through an autocatalytic process between fluid motion and mass transfer. To see the process comprehensively, first, consider the electrolytic current flowing by the mass transfer of active species. Mass balance of active ionic species in the presence of a large amount of supporting

to potentiostat

Fig. 3-1-1 MHD electrode, a, working electrode; b, counter electrode; c, Luggin capillary; d, MHD flow; e, magnetic flux density; f, vessel. [Reproduced from K. Shinohara, R. Aogaki, Electrochemistry, 67, 127 (1999)]

3.1 Magneto-electrochemical Processing 113

electrolyte is expressed by

^^{aV)C = DV'C (2) dt

Current density at the electrode is, from Pick's first law, the y-component vertical to the electrode, which is given as

where Zm is the charge number, F the Faraday constant, D the diffusion constant and C the concentration of active species. Therefore, by the Lorentz force per unit volume iB, the solution, according to Eq. (1), starts to flow in the velocity u along the electrode, where B is the z-component of the magnetic flux density and u is the jc-component of the velocity. On the other hand, the flowing solution enhances the mass transfer, so that the concentration of the active species changes according to Eq. (2). The concentration gradient {dC/dy)^.^^ together with the velocity u also increases. As a result, the current density / in Eq. (3) again increases. All these processes are cycled until the steady state is achieved. In the case where the channel height and the velocity are large, the flow mode becomes inviscid, so that the average current density is given by ^

J^H\Q-C.f"B"' (4)

where

H* =0n5Xz^FDY'\vl DY'\''''p-''Y'H4^-^^^Y'\x^-x^)-''' (5)

where Cs and Cw are the bulk and surface concentrations, respectively. x\ and JC2 are the jc-coordinates of both ends of the electrode, y is the cell constant. Here it is noted that, except for the concentrations in the units of mol m~ , all the physical parameters in this section are expressed in SI units.

When the channel height and the velocity are small, the solution flows in viscous mode, and the average current density is ^

J^K\a-C.f"B"' (6)

where

K* =0,5QA{zr,Ff^Dh"\r]ir"^ (7)

where h is the channel height, 77 the viscosity and / the electrode length. As discussed above, MHD flow moves in quite a different mode from

the fluid motion driven by mechanical force. For example, in the rotating disk electrode, the solution velocity is one-sidedly determined by external mechanical force, whereas the velocity of MHD flow is controlled in close relation to electrode reactions.

In the vicinity of the electrode, MHD flows contain minute vortex


Structures called "micro-MHD flows," which are a kind of nonequilibrium fluctuation of MHD flows. Therefore, the micro-MHD flows can interact with other nonequilibrium fluctuations such as concentration fluctuation, so that electrode reactions receive specific effects called the micro-MHD effects from micro-MHD flows. The most important point is that although micro-MHD flows affect the mass transfer of active species, the mass transfer process is not always promoted, but sometimes suppressed. If the reaction contains some autocatalytic process of nonequilibrium fluctuations, such fluctuations are often suppressed by the micro-MHD flows, and the total reaction rate decreases.

B. Micro-MHD Effects a. Electrodeposition in parallel magnetic fields In electrodeposition, it is known that two kinds of nonequilibrium fluctuations play important roles, i.e., asymmetrical and symmetrical fluctuations yield two-dimensional (2D) and three-dimensional (3D) nuclei, respectively.^^^ As shown in Fig. 3-l-2(a), asymmetrical fluctuations arise in the electric double layer and fluctuate one-sidedly to a specific side of the electrostatic equilibrium where the reaction proceeds. ^ As a result of electrode reaction, a diffusion layer is formed, and symmetrical fluctuations occur simultaneously, so that, as shown in Fig. 3-l-2(b), the fluctuations change around their average values. After charging the electric double layer, with the developing diffusion layer, symmetrical fluctuations are promoted. Micro-MHD flows interact with symmetrical fluctuations, so that the 3D nucleation is markedly affected by a magnetic field.

In the MHD electrode, for a magnetic field parallel to the electrode

O A

^ 0 —

(a)

Distance

Diffusion layer

Double layer

>

c^

(b)

fffi

• .

fWYVWWYYy

Distance

Diffusion layer

• Double layer

Fig. 3-1-2 Schematics of (a) asymmetrical and (b) symmetrical concentration fluctuations in electrodeposition. The figure takes negative values from the electrostatic equilibrium state in the case of deposition (a), and positive and negative values around the average value (b). [Reproduced from R. Aogaki, / Chem. Phys., 103, 8603 (1995)]


surface, numerous micro-vortexes appear along the MHD flow.^^ As shown in Fig. 3-1-1, in the MHD electrode, the solution flows along the channel by the Lorentz force induced in the magnetic field. The micro-MHD flows in this case take the forms of minute rollers traveling along the electrode surface. These numerous rollers, in a manner, crush the nonequilibrium fluctuations accompanied by nucleation, and level the deposit surface. In electrodeposition, active species of ions are transported through a diff'usion layer and an electric double layer onto the electrode surface.^^ After dehydrating, the active species receives electrons at the surface, being adsorbed on the surface as adatoms. Then the adatoms diffuse along the electrode surface according to the local difference of their chemical potential. Finally, after traveling to unstable sites, the adatoms are incorporated into the substrate as lattice atoms. Such incorporation also occurs during surface diffusion. A series of nucleation generates symmetrical concentration fluctuation in the diffusion layer. This type of fluctuation, as mentioned above, takes positive and negative values, and in this sense, has symmetry. In the limiting-diffusion case, symmetrical fluctuations interact with micro-MHD flows. The important point is that the nucleation itself is controlled by the symmetrical fluctuations. Therefore, if the growth of symmetrical fluctuations is suppressed, crystal growth is also suppressed. In contrast, in the absence of interaction, the growth of symmetrical fluctuation is promoted, so crystal growth is also promoted.

Furthermore, to quantify the leveling process of deposit by magnetic field, the spatial power spectrum was theoretically derived for the surface morphology of deposit in the MHD electrode.^^ The spectrum indicates the existence ratios of the crystal grains with the diameters corresponding to the reciprocals of the wave numbers. The intensity of the spectrum decreases with magnetic flux density; the wave number receiving suppression is in the range of 10 m~\ which means that crystal grains of the order of 1 ^m are the most markedly suppressed by the micro-MHD flows. b. Electrodeposition in vertical magnetic fields In a vertical magnetic field, since almost all current lines are parallel to the magnetic field, it has been thought that MHD effect can be neglected. However, actually, as shown in Fig. 3-1-3, the electrode vertical to a magnetic field called the "vertical MHD electrode," yields characteristic deposits with regular holes called "micro-mystery circles."'^^ This is because the same macro- and micro-MHD flows as those in corrosion and electroless plating are generated by asymmetrical and symmetrical fluctuations. Interaction between the two kinds of flows involving nonequilibrium fluctuations leads to the partial suppression of deposition, yielding the characteristic holes. For a micro-electrode in the absence of the micro-MHD effect, the current density is enhanced by a tornado-like


motion, which is expressed by the following equation^^:

7 = OA5\7t-'y(Zr.FD)' D

{vrir'RBAC' (8)

where y is the cell constant, rj the viscosity, R the electrode radius and AC the concentration difference between the bulk and the surface. By using this type of electrode in copper deposition from an acidic copper sulfate solution, a single mystery circle was observed/^ c. Metal corrosion Metal corrosion is also accompanied by nonequilibrium fluctuations, i.e., asymmetrical and symmetrical fluctuations, which are characteristic to metal corrosion. ' In metal corrosion under magnetic field, total corrosion rate is suppressed. ' ^ Fig. 3-1-4 shows copper plates dipped in nitric acid solution under a vertical magnetic field. In the absence of a magnetic field, the copper plate is attacked by nitric acid, and almost all the original shape

i^ j i f -

Fig. 3-1-3 SEM image of copper dendrites deposited in a vertical magnetic field of 7 T (micro-mystery circles). [CUSO4] = 500 mol m -. [H2SO4] = 1000 mol m \ Applied overpotential was -0.4 V and deposition time 10 min. Electrode diameter 1 mm. [Reproduced from R. Aogaki, Magnetohydrodynamics, 39, 460 (2003)]

Initial state OT 5T lOT

2.5 cm -*\

Fig. 3-1-4 Photos of copper plates after immersion in 3 mol dm" nitric acid for 20 min. Copper plate was 2.5 X 2.5 cm" in area and 0.1 mm thick. Temperature was kept at 11 ±1°C. [Reproduced from K. Shinohara, R. Aogaki, Electrochemistry, 67, 128 (1999)]


is lost, whereas in a high magnetic field, the plate retains its original shape. This is called magnetic protection of corrosion.

It is well known that metal corrosion proceeds by the coupling of anodic metal dissolution and cathodic reduction of acid or oxygen, which, from an electrochemical viewpoint, is regarded to be the formation of a local cell composed of two partial reactions. Corrosion proceeds in the numerous local cells formed on a metal surface. In each cell, a circular current flows between the anodic and cathodic sites, and some part of the current leaks into the solution. This leaking current induces a local Lorentz force, so that on the metal surface, numerous minute vortexes, i. e., micro-MHD flows, are formed, which appear in a magnetic field vertical to the metal surface. The micro-vortexes come from symmetrical fluctuations, whereas the macroscopic rotations can be attributed to asymmetrical fluctuations. The latter motion often generates much larger scale motion than the former.

Copper dissolution in nitric acid solution proceeds with the autocatalytic attack of nitrate ions against a copper surface. In the case of a sufficiently high concentration of nitric acid, copper dissolution is rate-determining, so that the micro-MHD flows interfere with nonequilibrium fluctuations and suppress corrosion itself. It is theoretically predicted that the corrosion rate decreases in proportion to the -2/3 power of magnetic flux density. When the concentration of nitric acid is sufficiently low, nitric acid reduction is rate-determining. Since nitric acid reduction is not autocatalytic, the micro-MHD flows cannot suppress the total reaction but act to enhance the corrosion rate. As expected in this discussion, the corrosion rate increases in proportion to the 1/2 power of magnetic flux density.

Zinc powder dissolution in sulfuric acid solution was also carried out under vertical magnetic field.'^^ Zinc powder was mixed with 0.5 mol dm'^ sulfuric acid + 1 mol dm~ sodium sulfate solution under magnetic fields of up to 10 T. As a result, after floating on the solution surface, each zinc particle independently started to circulate in a given diameter, i.e, several mm at 10 T. The velocity was proportional to the applied magnetic flux density. In this case, at the anodic site, zinc dissolved, whereas at the cathodic site, hydrogen gas evolved, so that local cells formed on the particles. It was concluded that the induced Lorentz force makes each particle circulate, d. Electroless plating The same situation as described above also exists for electroless plating. Both metal corrosion and electroless plating are complex reactions in which cathodic and anodic partial reactions proceed simultaneously. Electroless plating proceeds by a similar local cell mechanism, i.e., metal reduction and reagent oxidation occur at cathodic and anodic sites, respectively. In this case, due to leaking circular currents, micro-MHD


Fig. 3-1-5 SEM images of copper-electroless plating onto a platinum plate in a vertical magnetic field, (a) fi = 0 T; (b) B = 5 T. Solution A contained 2.5 wt7c copper sulfate pentahydrate -1-3.5 wt% sodium hydroxide +12.1 wt% Rochell salt, and solution B contained 10 wt% formaldehyde. Prior to the experiment, solution A and solution B were quickly mixed in a volume ratio of 5:1, maintaining a temperature of 40°C. The plating time was 20 min. The diameter of the circular Pt plate was 1 mm. [Reproduced from Y. Oshikiri et al., Jpn. J. Appl. Phys., 43, 3599 (2004)]

flows also play an important role. As a result, when the autocatalytic process of electroless plating is suppressed by the micro-MHD flows, decrease in crystal grain size is observed. In Fig. 3-1-5, the grain sizes in the vertical magnetic field of 5 T actually decrease in comparison with those in zero magnetic field. ^

Electroless plating onto metal powder under a vertical magnetic field yields the same type of motion as that in the dissolution of zinc powder under a vertical magnetic field. For silver-displacement plating onto copper particles, copper powder was mixed with silver nitate solution under vertical magnetic fields of up to 10 T.' ^ Immediately after injecting a silver nitrate solution into a vessel filled with copper powder, thus dispersing the powder in the solution, the particles started to circulate along the vessel under vertical magnetic field with sudden changes in direction. The velocity of the motion increased with the magnetic flux density although the deposition rate remained constant. In this case, the specific motion can also be attributed to induced Lorentz force.

3.1.2 Application of Heterogeneous Magnetic Force

A. Magneto-convection In a concentrically heterogeneous magnetic field, paramagnetic materials receive concentric magnetic forces. Paramagnetic liquid placed between a pair of circular plates with a narrow gap moves concentrically outward. This phenomenon was applied to the measurement of magnetic susceptibility of a small amount of liquid.'^^ A vertical magnetic field generates magneto-convection together with the mass transfer of paramagnetic species in liquid phase. For example, it is known that dissolution of oxygen gas into water is promoted by magneto-


V B

Solution

/ / / Electrode

Fig. 3-1-6 Schematic figure of vertical magneto-convection cells occurring on an electrode surface. [Reproduced from A. Sugiyama et al., Electrochim. Acta, 49, 5116 (2004)]

convection/^^ Recently, oxygen dissolution into aqueous phase enhanced by magneto-convection has been theoretically and experimentally analyzed, and a simple mass transfer equation was formulated.'^^ In this case, it was assumed that at a gas-liquid interface, the vertically applied magnetic field concentrically takes on a parabolic distribution.'^^

The dissolution amount / through a circular interface is represented by

/ = 3.0D-^^^fl^Ml R'^C"'^tBli' (9) I jt/oT? )

where ao is the concentration coefficient of the magnetic susceptibility, )3 the parabolic-distribution coefficient of the magnetic flux density, BQ the magnetic flux density at the center of the circular interface, R the radial of the circular interface, AC the concentration difference between the interface and the bulk, and Af the dissolution time.

In a vertical magnetic field without any horizontal distribution, another type of magneto-convection is observed. In the dissolution process of copper-sulfate pentahydrate, due to dissolved paramagnetic cupric ions with paramagnetism, the heterogeneous magnetic force is generated, so that, as shown in Fig. 3-1-6, numerous minute convection cells appear in front of the dissolved crystal surface. This type of convection cell is quite different from the micro-MHD flows; the flow mode is nonvortex and somewhat similar to gravitational convection cells.'^^ The resulting magneto-convection promotes the mass-transfer rate of cupric ions, expressed by the following mass flux'^^

7nux=0.0969Df^^l 'lAC^ (10)

120 3 Effects ofLorentz Force and MHD

where «o is the concentration coefficient of the magnetic susceptibiUty, x^ the magnetic susceptibility at the surface concentration, and B and (d^/dz), = 0 are the magnetic flux density and its gradient at crystal surface ( = 0).

B. Spin Electrode In electrochemical reactions under a magnetic field, as discussed above, MHD and micro-MHD flows are predominant due to electrolytic current. Therefore, it is thought that magneto-convection can be observed only when the MHD and micro-MHD effects are neglected. If a micro-electrode of appropriate diameter is used, such a condition is easily achieved. The electrolytic current of magneto-convection was measured in a ferricyanide-ferrocyanide reaction with the current density expressed by ^

r = 0.0969z.FDf-L-rf |5l"" ' |Aq«^-^'^ ^ "aiy "" where x is the difference of the magnetic susceptibility between the product and the reactant. In this case, the change in magnetic susceptibility in the reaction can be measured in the form of electrolytic current. In electrochemical reactions, electron transfer accompanying reactions often changes the electron-spin state of reactants. For transition metal complexes, it is well known that the electron-spin number is proportional to the value of magnetic susceptibility. Therefore, from the measurement of electrolytic current, the change in electron-spin number in an electrode reaction can be determined. Recently, it has been ascertained that a special electrode with a sheath called a "spin electrode" is quite effective for measuring magneto-convection in electrode reactions. ^^

References

1. R. Aogaki, K. Fueki, T. Mukaibo, Denki Kagaku (Electrochemistry), 43, 504 (1975). 2. R. Aogaki, K. Fueki, T. Mukaibo, Denki Kagaku (Electrochemistry), 43, 509 (1975). 3. R. Aogaki, K. Fueki, J. Electrochem. Soc, 131, 1295 (1984). 4. A. Sugiyama, M. Hashiride, R. Morimoto, Y. Nagai, R. Aogaki, Elecrtochim. Acta,

49,5115(2004). 5. S. Kishioka, R. Aogaki, Chem. Lett, 2000, 659. 6. R. Aogaki, K. Fueki, T. Mukaibo, Denki Kagaku (Electrochemistry), 44, 89 (1976). 7. R. Aogaki, K. Kitazawa, Y. Kose, K. Fueki, Electrochim. Acta, 25, 965 (1980). 8. R. Aogaki, J, Chem. Phys., 103, 8602 (1995). 9. R. Aogaki, Proceedings of the Symposium on New Magneto-Science 2000, p. 27,

NRLM, JST, Omiya (2000). 10. R. Aogaki, Magnetohydrodynamics, 39, 453 (2003). 11. R. Aogaki, Modem Aspects of Electrochemistry No. 33 (R. E. White, J. O'M. Bockris,

B. E. Conway, eds.), p. 217, Kulwer/Plenum, New York (1999). 12. R. Aogaki, A. Tadano, K. Shinohara, Fluid Mechanics and Its Applications, Transfer

Phenomena in Magnetohydrodynamic and Electroconducting Flows Vol. 51 (A. Alemany, Ph. Marty, J. P. Tibault, eds.), p. 169, Kulwer, Dordrecht (1999).

3.2 Magnetic Field Effects in Silver Metal Deposition 121

13. K. Shinohara, R. Aogaki, Electrochemistry^ 67, 126 (1999). 14. M. Asanuma, R. Aogaki, Electrochemical Approach to Selected Corrosion and

Corrosion Control Studies (P. L. Bonora et al., eds.), p. 310, lOM Communications, London (2000).

15. R. Aogaki, Magnetohydrodynamics, 37, 1-2, 143 (2001). 16. S. Yonemochi, R. Aogaki, Chem. Lett., 2000, 388. 17. O. Devos, R. Aogaki, Anal. Chem., 72, 2835 (2000). 18. S. Kishioka, A. Yamada, R. Aogaki, Phys. Chem. Chem. Phys., 2, 4179 (2000). 19. A. Sugiyama, S. Morisaki, R. Aogaki, Jpn. J. Appl. Phys., 42, 5322 (2003). 20. A. Sugiyama, R. Aogaki, Proceedings of the Symposium on New Magneto-Science

2004, p. 58, NIMS, Tsukuba (2004). 21. Y. Ohshikiri, M. Sato, A. Yamada, R. Aogaki, Jpn. J. Appl Phys., 43, 3597 (2004).

3.2 Magnetic Field Effects in Silver Metal Deposition

The metal dendrite is generated through redox reactions at interfaces between metal surfaces and solutions. Since the reaction proceeds in the non-equilibrium state, the shape, pattern, distribution, growth rate and yield of the dendrites are affected by small perturbations such as magnetic force or Lorentz force.'^^ The dendrites obtained show various patterns depending on the growth conditions: whether the reaction system is three-dimensional or two-dimensional and whether the redox reaction contains paramagnetic species or only diamagnetic species.

Our group investigates magnetic field effects on the growth of silver metal dendrites, which are observed in three-dimensional systems and in two-dimensional systems on a plane parallel to the magnetic field direction under vertical or horizontal and inhomogeneous magnetic fields. ' ^ We present some reaction systems and interesting results below.

3.2.1 A Three-dimensional Reaction System: Copper Metal-Silver Ion System^ ^

When a paramagnetic species contributes to a reaction system, how is the three-dimensional dendrite affected? This reaction is given by the following equation.

2Ag^ + Cu->2Ag>L+Cu'^ (1)

The reaction proceeds due to the ionization tendency, and without electrolysis. The copper ion is the only paramagnetic species in this reaction.

Figures 3-2-l(a)-(d) show the photographs of silver dendrites after two hours reaction under various vertical magnetic fields (three vessels are placed in the vertical bore tube, and one vessel is placed outside the bore tube. The positions are designated "top" (9.3 T, 980 T^ m ' ) , "middle" (15 T, -160 T' m-^), "bottom" (5.6 T, -940 T- m" ) as observed from the top of the vertical bore, and "outside" (< 0.005 T). The magnetic field


(a) (b) (c) (d)

•'4' Magnetic

field

1 11' d r f l H Ag U ^g. I ^ |V U__^ I

Cu-\Ag* t Copper wire Magnetic force

Fig. 3-2-1 Photographs of silver dendrites after 2 hours reaction, (a) outside the bore tube (control, < 0.0005 T), (b) bottom, 9.3 T and 980 T- m '. (c) middle, 15 T and -160 T' m ' , (d) top, 5.6 T and -940 T' m"'. The images (e), (f), (g) and (h) illustrate the possible mechanism of the magnetic field effect, (e) outside, almost all motions of ions are due to diffusion and the convection caused by gravity, (0 bottom, the convection due to magnetic force on copper ions occurs in a small area, (g) the convection caused by Lorentz force on positive ions is effective for the horizontal direction, but ineffective for the vertical direction and (h) when the downward magnetic force is applied to copper ions, the convection is caused mainly by the magnetic force.

clearly caused dramatic changes in the color and shape of the silver dendrites. The dendrite grown at zero field shows tree-like branches with metallic silver (Fig. 3-2-1(a)). In contrast, the shape and color of the dendrites changed remarkably under the magnetic field. The color changed from a metallic color to gray or black. The shape changed from tree-like dendrites to spherical ones (Figs. 3-2-1(b), (c) and (d)).

The micrography of the dendrites grown under each condition was observed. The dendrites grown "outside" the bore show metallic color and tree-like shape a few millimeters in length. In contrast, the dendrites generated under the magnetic field had a shape similar to those at zero field, although their size was about 10 times smaller than those grown at zero field. These findings indicate that the growth of the dendrites occurs very fast under a magnetic field. The dendrites are black or dark gray in color, since the incident light is reflected many times by the small-size dendrites.

The time evolution of the copper ions generated through the reaction (1) was investigated. It was found clearly that the reaction occurs remarkably fast due to the magnetic field. Detailed investigation showed that the time evolution of the copper ions is sensitive to both magnetic force and magnetic field intensity. The rise time and equilibrium concentration clearly corresponds to the magnetic condition. In order to estimate reaction rate constants semi-quantitatively, the time dependence


of the yields is fitted tentatively with a single exponential function (2), although this reaction is not a first-order reaction;

A(0 = A(-){l-exp(-^r)} (2)

where A(t) and A(oo) are the concentration of copper ion at time t and infinite time, respectively, and k is the rate constant. The results of the fitting parameters, the rate constants k and the concentration at infinite time A(oo) are described as follows; ''outside": 1.06 x 10" min" and 0.013 mol dm ^ "bottom": 1.97 x 10" min" and 0.019 mol dm-\ "middle": 5.33 X 10- min"' and 0.017 mol dm"', and "top": 3.38 x 10 ' min" and 0.021 mol dm"^ Although the rate at the middle position, at which the magnetic field is maximum but the magnetic gradient is nearly zero, shows the maximum value, the equilibrium value is the minimum among the various magnetic conditions. This indicates two mechanisms, that is, magnetic force (FM) and Lorentz force (FL), contribute to the reaction, as described by the following equations.

FM=K^^B{Z) (3)

dz K = ^ (30

and

F L = ^ V X ^ (4)

where e is the electric charge of an ion, v is its velocity, B is the magnetic field, //o the magnetic permeability, x ^^^ ^ ^re the molar magnetic susceptibility, which are related by Eq. (30, and dB(z)/dz is the magnetic field gradient at the position z apart from the center of the magnetic field along the bore. Molar magnetic susceptibility K'S of copper metal, copper ion, silver, and silver ion are -5.46 x 10" J T'- mol"', +1.57 x 10" J T ' mor\ -1.95 X 10^ J T" mor\ and 4.57 x 10^ J T - mol' , respectively. The copper ions promote working of the magnetic force FM effectively. In a vertical magnetic field, the magnetic force FM works along the vertical direction. Therefore, the convection due to the magnetic force FM occurs vertically. On the other hand, the concentration of all ionic species promotes working of the Lorentz force FL. The FL works on the plane which is vertical to both v and B. Therefore, the convection due to the Lorentz force FL occurs horizontally. The ratio of the magnetic force and Lorentz force consequently depends on the gradient of the magnetic field and the concentration of copper ion.

Based on the result of the time evolution, let us consider how the magnetic field affects the redox reaction. The concentration of silver ions in bulk is very high and that of copper ions is very low at an early reaction time of up to 20 min. Consequently the rise rate at the middle position is much larger than at the other positions. However, after 20 min, as the


concentration of copper ion increases, the magnetic force begins to contribute to the convection. The convection due to the magnetic force is effective for the reaction, and therefore, the equilibrium concentration becomes large.

Figures 3-2-l(e)-(h) give a rough illustration of the convection at each condition. The reaction proceeds from diffusion and gravity without the magnetic field, hence the convection does not occur effectively (Fig. 3-2-1(e)). The Lorentz forces work as long as ionic species exist in the vessel with the magnetic field. When the concentration of copper ions is not sufficient to generate the magnetic force, the horizontal convection due to the Lorentz force occurs as shown in Fig. 3-2-1(g). Because the Lorentz force increases in proportion to the magnetic field intensity, the middle position, where the magnetic field intensity is maximum, shows a quick rise. The concentration of copper ions increases with the progression of the reaction, becomes sufficient to generate magnetic force, which gives rise to the vertical convection shown in Figs. 3-2-1(f) and (h). The convection occurs vertically and over a large region of the vessel especially at the top position (Fig. 3-2-1(h)). For example, the magnetic force on the copper ion at the top position (5.6 T, -940 T^ m"') is estimated to be -1.48 x lO'* Nmol ^ This is large enough to cause convection in solution. Therefore, the reaction is promoted remarkably at a later reaction time.

Thus growth of three-dimensional dendrites is affected by both Lorentz force and magnetic force; the former is effective early in the reaction time while the latter is effective later in the reaction time. The time the two forces work in the reaction depends on the concentration of the paramagnetic species, that is, the copper ion, and the reaction rate and efficiency depend on the magnetic field intensity and magnetic gradient.

3.2.2 Two-dimensional Reaction Systems ' ^

In the three-dimensional system mentioned above, both the magnetic force FM and the Lorentz force FL contribute to the growth of dendrites. For simplification we investigated a two-dimensional system instead of a three-dimensional one. Since almost all motion of ion species acts parallel to the magnetic field direction, the contribution of the Lorentz force will decrease relatively. We study the following two reaction systems.

2Ag^ + Cu->2Ag>l-fCu-" (1)

2 Ag^ + Zn -^ 2 Ag i + Zn" (5)

Reaction (1) has been mentioned above as a three-dimensional reaction system. Moreover, reaction (5) contains only diamagnetic species. We show dendrites produced through the reactions with a magnetic field, and compare reaction (1) with reaction (5) in vertical and inhomogeneous magnetic fields.


A. Copper Metal-Silver Ion System In this section, we present the results of experiments using the copper metal-silver ion reaction in vertical and inhomogeneous magnetic fields. This reaction system contains a paramagnetic species, that is, copper ion. The magnetic force on copper ion will be effective. How do the results differ from those of the three-dimensional system?

Figure 3-2-2 shows the silver dendrites which grow from the copper metal-silver ion system with or without the vertical and inhomogeneous magnetic field. The appearance of all dendrites showed metallic and bright color. However, the distribution of the dendrites changed remarkably depending on the magnetic field. The dendrites outside grew more on the upside than on the downside (Fig. 3-2-2(a)). The tendency became more remarkable at the bottom position (Fig. 3-2-2(b)). In contrast, a completely opposite distribution was observed at the top position (Fig. 3-2-2(d)).

According to the SEM images, the dendrites growing outside showed hexagonal crystal faces of micrometer size. In contrast, the dendrites growing at the middle position consisted of dendrites of varying micrometer size, and their crystal faces were not observed clearly. The results imply that there was not enough time for the growth of crystal faces under the magnetic field, and that the dendrites grown under a magnetic field grow much faster than those grown without a magnetic field.

The X-ray diffraction (XRD) patterns of the dendrites grown with and without a magnetic field were somewhat different from each other.

1 I % I

111 11 mmmwmttl^mm. I A t r

m ^

^tpim^m^m^*'-Magnetic

field

Fig. 3-2-2 Photographs of the silver dendrites produced by the copper metal (thickness: 0.3 mm)-silver ion system after 30 min reaction in the vertical bore, (a) outside the bore tube (control < 0.0005 T), (b) bottom position (9.8 T, +1070 T" m' ) , (c) middle position (15.0 T, +50 T-m') , (d) top position (5.6 T, -940 T" m') .


The values of the diffraction angle (2^) at the outside were the same as those of pure silver metal. However, the ratio of the intensities was different from that of a powder. In almost all cases, only one peak was observed, and this was assigned to the face (111). This indicates that the hexagonal faces appearing in the SEM image without a magnetic field are the (111) faces. On the other hand, the pattern observed at the middle was very similar to the powder pattern. Because fast convection caused by a magnetic force and a Lorentz force occurs in the solution, the anisotropic distribution of the crystal faces will be averaged.

It is clear that the dendrites grow slowly and anisotropically without a magnet field. The pattern of the dendrites is affected by some kinds of perturbation, that is, gravity and the vertical magnetic field. The upside of the dendrites outside becomes denser than the downside (Fig. 3-2-2(a)). Sawada et al. reported that the diffusion field near dendrites was sensitive to a gravitational force.^ ^ This indicates that the distribution of the silver dendrites deviates from equality due to gravity. In contrast, they grow quickly and isotropically with a magnetic field because of the convection caused by the magnetic force and/or Lorentz force. The magnetic forces on the copper ions are very effective as described above. It is well known that the non-equilibrium state is very sensitive to perturbation due to a magnetic field. As the copper ion-rich solution near the copper sheet moves out by magnetic force, a fresh silver ion-rich solution is supplied on the surface of the copper sheet. As a result the redox reaction is effectively promoted. The distribution of the dendrites depends on the direction of the magnetic force. Moreover, local Lorentz forces will work around the dendrites. As a result, pseudo microgravity and overgravity conditions are provided by the magnetic field.

B. Zinc Metal-Silver Ion System^^^ In this section, we present the results of experiments using the zinc metal-silver ion system in vertical and inhomogeneous magnetic field. This reaction system contains only diamagnetic species so the magnetic force is expected to be ineffective. How do the results differ from those of the copper metal-silver ion system? Will the magnetic field effectively affect the diamagnetic reaction system?

Figure 3-2-3 shows the silver dendrites, which are generated from the zinc metal (thickness: 0.4 mm)-silver ion system with and without the vertical magnetic field. (The magnetic field condition is the same as that of the copper metal-silver ion system described in section 3.2.2 A). The reaction system contains only diamagnetic species. Nevertheless, a dramatic magnetic effect was observed. At the outside the dendrites on the upside grew more than those on the downside (Fig. 3-2-3 (a)). This pattern is similar to that of the copper metal-silver ion system described above. By contrast, the dendrites in the magnetic field showed unbranched shapes and


(a) (b)

a-) (d)

Magnetic

field

Fig. 3-2-3 Photographs of the silver dendrites produced by the zinc metal-silver ion system after 30 min reaction in the vertical bore. The thickness of the zinc metal sheet is 0.4 mm. (a) outside the bore tube (control, < 0.0005 T), (b) bottom position (9.8 T, +1070 T' m"'), (c) middle position (15.0 T, -i-50 T' m' ) , (d) top position (5.6 T, -940 T' m ' ) .

were oriented about ± 30 degrees toward the magnetic field axis. The angles of the dendrites slightly depended on the magnetic field intensity (1.75-15 T) and magnetic field gradient (29-1500 T' m"'). Moreover, the concentration of the silver ions and the thickness of the zinc sheet barely affected the tilt angle.

It is well known that the shape and growth of dendrites are sensitive to the convection of reaction solutions. Thus, the volume of reaction solution is an important factor for the growth of dendrites. The thickness of the zinc sheet corresponds to the volume in our experiment. In the case in which the thickness was 0.025 mm, the dendrites clearly showed an orientation of about 30 degrees at both sides under the magnetic field. At the outside the dendrites grew equally on both sides. This indicates that gravity and convection are ineffective in this solution: the convection caused by the Lorentz force will be hardly effective in such a thin solution. However, a clear magnetic field effect is observed. These observations indicate that this phenomenon is due to the character of silver crystal itself.

The SEM images showed the remarkable difference of the silver dendrites' morphology. The dendrites of the outside showed hexagonal crystal faces of micrometer order. In contrast, those of the middle position showed dendrites of many micrometers, and their crystal faces were not observed clearly, indicating that dendrites grow in a magnetic field much faster than outside. In this case the Lorentz force is the main force working on the species in the solution because they are all diamagnetic species and magnetic force is ineffective.


Os

Magnetic

field

Fig. 3-2-4 Image sequence of the precession of silver dendrites produced in the zinc metal-silver ion system in a horizontal magnetic field (8 T). The magnetic field direction is perpendicular. All images were obtained at a rate of 30 frame s"'. The scale bar represents 0.5 mm.

According to the XRD patterns of the silver dendrites grown in and outside a magnetic field, both diffraction patterns unexpectedly showed close similarity. The pattern of diffraction angles (29) was the same as that of pure silver metal powder, but the ratio of the peak intensities was different from a powder pattern. Only a single peak was observed, and the peak was assigned to the face (111). Moreover, the dendrites grown under a magnetic field had almost the same face distribution, although many small dendrites looked scattered, indicating that the dendrites grow anisotropically regardless of the magnetic field.

The result of in situ measurement using a fiberscope is very interesting (Fig. 3-2-4). ^ At an early reaction time of about five minutes, some dendrites showed precessions during growth. The direction was determined by the Lorentz force on the silver ions. The precessions sometimes stopped then started again. By the time the dendrites grew to a certain size, the precessions occurred. Although the dendrites grow two-dimensionally parallel to the magnetic field, the micro-MHD mechanism will be effective in the reaction.^' The infinitesimal existence of a component moving perpendicular to the magnetic field produces a Lorentz force and causes precession in the dendrites. This indicates that fast convection is generated in the solution, and the MHD mechanism due to Lorentz forces is very effective. The results agree with the SEM picture which shows dendrites growing very quickly in the magnetic field. The fast convection is confirmed by an experiment using tracers. However, the phenomena are not related to the orientation of the dendrites. The precessions can take any angle, and the phenomenon cannot explain why the dendrites lean about 30 degrees toward the magnetic field.

Generally, the orientation of materials under magneUc fields is caused by their magnetic anisotropic character. The anisotropic characteristics arise from 1) the anisotropy of a component molecule, complex or cluster, 2) the anisotropy of a crystal (magnetocrystalline anisotropy)*°^ and 3) the anisotropic shape (shape magnetic anisotropy).^^' ' ^ Many observations have been reported on the above mechanisms. For example, the orientation of organic molecules originates in the first term, ^


that of zinc or bismuth-tin alloy crystal is responsible for the second term^ ^ and that of fibers is ascribed to the first and third termsJ^^ In our case, silver crystal is reported as a face-centered cubic lattice (fee) which is isotropic. Therefore, the shape magnetic anisotropy of the dendrites is a possible mechanism. Usually, when a magnetic field is applied to a material, a certain demagnetizing field emerges in the material. The direction of the demagnetizing field depends on the shape of the material.^^' " In our experiments, the growth and shape of the silver dendrites are anisotropic according to the SEM pictures and the XRD patterns. The demagnetizing field in the silver dendrites will determine the direction of the dendrites. It is well known that a non-equilibrium state such as found in the growth of dendrites is very sensitive to perturbation due to a magnetic field. Although anisotropic growth will contribute to the orientation, the reason why the dendrites lean toward a certain angle is not clear, and it is uncertain whether the shape magnetic anisotropy of sub-micro order size crystal is effective. This mechanism is possible, but further investigation is required.

3.2.3 Conclusion

A magnetic field remarkably affects the growth, behavior, shape, distribution and amount of silver dendrites, even if the system contains only diamagnetic species. For the reaction system with paramagnetic species, magnetic forces on the species mainly contribute to the reaction. By contrast, for the reaction system with only diamagnetic species, the effect of Lorentz forces appears. Even in a two-dimensional system, in which the main growth direction is parallel to the magnetic field, precessions of dendrites caused by Lorentz forces are observed. Moreover, the magnetic field determines the orientation of the dendrites. The phenomenon occurs as a result of the shape magnetic anisotropy of the dendrites.

The main magnetic field effects are caused by the magnetic force and the Lorentz force, and the ratio depends on the reaction conditions. The dendrites are good probes for the effect of the magnetic field, and magnetic fields are highly useful in controlling redox reactions at the interface between liquid/solid phases.

References

1. A. Katsuki, S. Watanabe, R. Tokunaga, Y. Tanimoto, Chem. Lett., 1996, 219. 2. Y. Tanimoto, A. Katsuki, H. Yano, S. Watanabe, J. Phys. Chem. A, 101, 7359 (1997). 3. A. Katsuki, I. Uechi, M. Fujiwara, Y. Tanimoto, Chem. Lett., 2002, 1186. 4. A. Katsuki, I. Uechi, Y. Tanimoto, Bull. Chem. Soc. Jpn., 77, 275 (2004). 5. A. Katsuki, I. Uechi, Y. Tanimoto, Bull. Chem. Soc. Jpn., 78, 1251 (2005). 6. A. Katsuki, Y. Tanimoto, Chem. Lett., 34, 726 (2005). 7. T. Sawada, K. Takemura, K. Shigematsu, S. Yoda, K. Kawasaki, J. Crystal Growth,

191,225(1998).


8. T. Sawada, K. Takemura, K. Shigematsu, S. Yoda, K. Kawasaki, Phys. Rev. E, 51, R3834(1995).

9. R. Aogaki, A. Sugiyama, Proceedings of the 6th Symposium on New Magneto-Science 2002 (Nov. 6-8, 2002 Tsukuba, Jpn.), 136 (2002).

10. S. Chikazumi, Kyoujiseitai no butsuri. Shokabo, Tokyo (1984) (in Japanese). 11. Jikikagaku (K. Kitazawa, S. Ozeki, Y. Tanimoto, M. Yamaguchi, eds.), IPC, Tokyo

(2002) (in Japanese). 12. A. Katsuki, R. Tokunaga, S. Watanabe, Y. Tanimoto, Chem. Lett., 1996, 607. 13. T. Sugiyama, M. Tahashi, K. Sassa, S. Asai, ISIJ International, 43, 855 (2003). 14. J. Torbet, J.-M. Freyssinet, G. Hudry-Clergeon, Nature, 289, 91 (1981).

3.3 3D Morphological Chirality Induction Using Magnetic Fields

One dream of scientists studying magneto-science is the preparation of chiral molecules using a magnetic field. Recently, a group in Grenoble reported molecular chirality induction using a high magnetic field, although efficiency was negligibly small.'^ Another type of chirality observed in nature is morphological chirality, which is equally interesting for scientists. The present author and his research group studied three-dimensional morphological chirality induction of membrane tubes prepared by a silicate garden reaction using a high magnetic field. "* By the application of a magnetic field, right- or left-handed helical membrane tubes can be selectively prepared as well as twisted tubes in a silicate garden reaction. All the results are interpreted in terms of a boundary-assisted magnetohydrodynamics (boundary-assisted MHD) mechanism where a boundary plays an important role in determining the direction of convection.

3.3.1 Membrane l\ibes Grown along the Inner Surface of a Vessel

The silicate garden reaction is one of the best known reactions often used for chemical demonstrations to students. ^ When a sodium silicate aqueous solution is poured on a metal salt crystal, a colloidal semipermeable membrane, composed of silica and metal hydroxide, is formed on the crystal surface. Water diffuses osmotically into the space between the membrane and the crystal surface, dissolving the crystal. As a result of the osmotic inflow of water, the membrane is ruptured and the solution rich with metal ions flows out. Then the ions in outflow react with silicate ions outside the membrane, forming hollow tubes. Because of the different densities of the aqueous solution outside and inside the tube, hollow tubes grow upward.

Semipermeable membrane tubes were grown in cylindrical glass vessels (typical inner diameter, 6-13 mm) in vertical magnetic fields. Fig. 3-3-1 shows membrane tubes prepared from the reaction of sodium silicate aqueous solution (relative density, 1.06) and magnesium chloride, zinc

3.3 3D Morphological Chirality Induction Using Magnetic Fields 131

k'l^

(a) (b)

Fig. 3-3-1 Magnetic field effects on membrane tubes grown near the inner surface of a vessel wall. Mg(II) tubes at (a) 0 T and (b) 9 T, Zn(II) tubes at (c) 0 T and (d) 15 T, and Cu(II) tubes at (e)OTand(f) 15 T.

sulfate and copper sulfate in magnetic fields. Hereafter membrane tube names are referred to by the metal ion used. For example, the membrane tube prepared using zinc sulfate is called the Zn(II) tube. At zero field the tubes grow upwards. In magnetic fields all the tubes or bundles of tubes grow helically along the inner surface of the vessel. The pitch of the heUxes differs depending on the salt used. This happens because growth rates are different. The direction of the helixes is exclusively right-handed. In the case of Zn(II) tubes, helixes with diameters of 6 to 25 mm are prepared. When the magnetic field direction was reversed to the opposite direction, left-handed helical tubes were obtained in the case of Zn(II) and Mg(II) membrane tubes.

3.3.2 Membrane T\ibes Grown along the Outer Surface of a Glass Rod Placed in a Vessel

Since helical tubes grow only on the inner surface of the vessel, it was examined whether they could grow on the outer surface of a glass rod placed within a vessel. As expected, Zn(II) membrane tubes grew along the outer surface of a circular glass rod (20), a square plastic rod (2 mm x 2 mm) and a triangular plastic rod (2 mm x 2 mm x 2.8 mm) in a magnetic field but the direction of helixes are always left-handed, as shown in Fig. 3-3-2. ^ When a 300-//m lead of a lead pencil is used, a left-handed helical membrane tube grows on its outer surface. By simply putting a glass rod inside a vessel, left-handed helical tubes can be exclusively obtained on the outer surface of the rod. These observations indicate that membrane tubes grow very accurately following the shape of the surface.


(a) (b) (c)

Fig. 3-3-2 Magnetic field effects on Mg(II) membrane tubes grown on the outer surfaces of (a) a 2-mm cylindrical glass rod, (b) a 2-mm square plastic bar and (c) a 2-mm right-angled triangular plastic bar. [Reproduced from I. Uechi et al., J. Phys. Chem. B, 108. 2529 (2004)]

3.3.3 Tubes Grown Apart from a Vessel Wall

We examined the shape of tubes grown apart from a vessel wall. Fig. 3-3-3 shows Mg(II) and Zn(II) membrane tubes grown apart from the vessel wall. At zero field they grow almost straight upward. In a magnetic field, they grow in twisted form. The twist direction is exclusively left-handed, which is opposite to that of helical tubes grown on the inner surface of a vessel. A magnetic field also influences the morphology of membrane tubes grown apart from a wall.

/

\ - ^

(a) (b) (c)

Fig. 3-3-3 Membrane tubes grown apart from the vessel wall, (a) Zn(II) tube at 0 T, (b) Zn(II) tube at 12 T, (c) Mg(II) tube at 0 T, (d) Mg(II) tube at 15 T. Magnification factor is x 175.


3.3.4 T\ibes Grown in Horizontal Magnetic Fields

The effects of a horizontal magnetic field were also examined using ZnS04 as a crystal/^ When sodium silicate aqueous solution is poured into a horizontal glass tube (60), Zn(II) tubes mainly grow upward in the tube, then grow horizontally along the ceiling of the tube at zero field. In the presence of a horizontal magnetic field of 8 T, they grow circularly along the inner surface of the vessel, as shown in Fig. 3-3-4. The absence of helical growth is attributable to the absence of a driving force growing in the horizontal direction at zero field. Furthermore, a few tubes also grew in the horizontal direction at zero field. In this case, they grow in a twisted shape in the magnetic field. Therefore, the effects of a horizontal magnetic field are essentially similar to those of a vertical field.

Fig. 3-3-4 Zn(n) membrane tubes grown along the inner surface of a glass tube (60) placed in a horizontal magnetic field (8 T).

3.3.5 In situ Observation of the Motion of the Solution in a Magnetic Field

In situ observation of the motion of the solution in a magnetic field was carried out using MgCl2 as a salt by adding tracers such as polyethylene particles in the solution."^^ At zero field, no convection was observed regardless of magnesium salts. Only when the salt was added to the solution and a magnetic field applied was convection of the solution observed. Typically, the rate of convection was 0.3-2 mm s~ under the experimental conditions. The rate of convection is dependent on the amount of the salt and its direction is dependent on the location of the salt in the vessel. When salts are placed near the vessel wall, right-handed convection is induced. When the salt is placed at the center of the vessel, left-handed convection is induced. In this case, membrane tubes growing on the salt themselves act as a boundary surface which induces anisotropic motion of the outflow. From these in situ observations, it is concluded that


the direction of the helix is the same as that of the convection of the solution.

3.3.6 Mechanism of 3D Morphological Chirality Induction

The above observations can only be explained by the boundary-assisted magnetohydrodynamics (boundary-assisted MHD) mechanism in which a magnetic torque on moving ions results in the convection of the solution whose direction is partly controlled by the relative orientation of the solution and boundary, in addition to the magnetic field direction.

When it moves in a magnetic field, an ion receives the Lorentz force FL, given by the following equation:

FL=qvxB (1)

where q is the charge of the ion, v its velocity and B the magnetic field flux density. In MHD mechanism, the Lorentz force on moving ions in a solution in a magnetic field results in the convection of the solution because of collision in the solution. However, in a bulk solution, the average of the forces is zero, since they move randomly in all directions and the forces on ions compensate each other. In the boundary-assisted MHD mechanism, a boundary plays an important role in inducing anisotropic motion of ions. Although those in a bulk solution can move freely in all directions, ions near a boundary, i.e., a wall, cannot move freely because of the restriction posed by the boundary. Then the ions, moving in an outer radial direction, bounce on the wall to the inner radial direction and, therefore, the direction of motion becomes anisotropic. As a result, the motion of ions induced by the Lorentz force becomes anisotropic near the wall. This anisotropic force on ions induces one-way convection of the solution near a wall.

In the silicate garden reacUon a metal ion-rich solution in a tube flows out upward from hollow tubes by osmotic pressure and reacts with silicate ions in the bulk solution near the exit of the tube. Since the outflow is rich with negative ions such as sulfate ions, the Lorentz force can affect the negative ions in the outflow, leading to convection of the solution. Near the exit of the tube, concentration gradients of silicate ion and zinc ion are induced as the precipitation of insoluble membrane formation so these ions diffuse to the exit. Sodium ions diffuse to the outflow along its concentration gradient. A magnetic field also affects these motions of ions in solution. However, the speed of the outflow rich with negative ions is the fastest, compared with the diffusion rates of other ions, because the solution is continuously pumped out from the tube by osmotic pressure. Therefore, the effect of Lorentz force on the outflow rich with negative ions is the largest, leading to the circular convection of the outflow.

Figure 3-3-5 shows schematically the mechanism of helical growth of a membrane tube. When the tube grows separate from the vessel wall.


O : Membrane tube

^=^ : Outflow 4 : Lorentz force

\ \ ^ ^ : Convection

Fig. 3-3-5 Mechanism of chirality induction in silicate garden reactions using a magnetic field (top view). [Reproduced from W. Duan et al., / Phys. Chem. B., 109, 13449 (2005)]

the outflow from its open top receives clockwise Lorentz force, viewed from the top, and clockwise convection of the solution near the tube is induced. As a result, the tubes are twisted in the clockwise direction (left-handed direction), as schematically shown in (a). When the tube grows near the inner surface of a vessel, the direction of the outflow near the wall is restricted by the wall and the flow to the wall is reflected to the opposite direction. The direction of the outflow becomes anisotropic. As a result, counterclockwise circular convection is induced by the Lorentz force and the tube grows in the counterclockwise direction (right-handed direction) (b). When a tube grows near the outer surface of a glass rod, the relative orientation of the outflow and the wall becomes opposite and the left-handed helical tube grows (c).

In the case of silicate garden reactions a magnetic field affects the ions in the outflow. The Lorentz force-induced convection is also observed in the diffusion-controlled redox reaction of silver ion and zinc metal, forming silver dendrite.^^ Thus, the boundary-assisted MHD mechanism could be operative generally in liquid/solid reactions where ions in solution move to the solid surface in a magnetic field. In other words, a magnetic field may be a useful tool for preparing materials with chiral morphology.

References

4.

5.

G. L. J. A. Rikken, E. Raupach, Nature, 405, 932 (2000). I. Uechi, A. Katsuki, L. Dunin-Barkovskiy, Y. Tanimoto, J. Phys. Chem. B, 108, 2527 (2004). W. Duan, S. Kitamura, I. Uechi, A. Katsuki, Y. Tanimoto, J. Phys. Chem. B, 109, 13445 (2005). I. Uechi, A. Katsuki, Y. Tanimoto, Joint Symposium on Magneto-Science 2004 Yokohama, Dec. 2004, Abstr. No. 3AP20 (2004). B. Z. Chakhashiri, Chemical Demonstrations, Vol. 3, University of Wisconsin Press, Madison (1983). A. Katsuki, Y. Tanimoto, Chem. Lett., 34, 726 (2005).


3.4 Shaping of Molten Metal Using an Alternating Magnetic Field

The shaping of a molten metal is a well-known function of the alternating magnetic field. In this section the application of this function to a continuous casting process in the steel industry is described. The continuous casting of steel was first introduced successfully by adopting mold oscillation by Junghhans of Junghhans Schomdorf (Germany) and Rossi of Allegheny Ludlum Waterviliet (USA) in 1949.' Since then it has strongly been believed that mold oscillation, which makes a mold flux penetrate into a channel between metal and mold, is indispensable in the continuous casting of steel.

In this section a new method for the continuous casting of steel without employing mold oscillation is proposed. In this method mold oscillation is replaced by electromagnetic force. The possibility was first examined through a model experiment using molten gallium and tin to visualize the penetration behavior of the mold flux in the channel. Molten tin was continuously cast in a copper mold with slits under an intermittent alternating magnetic field instead of mold oscillation. Furthermore, the continuous casting of steel without mold oscillation was successfully demonstrated in a pilot scale experiment by pioneers at POSCO and RIST (Research Institute of Science & Technology) in South Korea. ^ The results obtained in the model and pilot experiments are promising, and the continuous casting of steel without mold oscillation will soon be realized on a commercial basis.

3.4.1 Concept of Soft Contacting Solidiflcation

In order to improve the surface quality of aluminum in continuous casting, the basic concept by which an alternating magnetic field with commercial frequency is applied from the outside of a mold was first proposed by Vives and Ricou. ^ The concept has been further developed and termed soft contacting solidification (SCS) ^ for the application of their process to steel casts. In this process segmented mold is used and a higher frequency alternating magnetic field than for the commercial frequency is applied. A brief explanation of the concept of SCS is as follows. As shown in Fig. 3-4-1, when an electric current is applied to a coil, a magnetic field is generated around the coil and induces an electric current in a segmented mold with slits, which generates another magnetic field in a molten metal, as if the magnetic field generated around the coil penetrates into the molten metal through the segmented mold. The magnetic field induces electric currents in the molten metal thus generating an electromagnetic force (Lorentz force) in the molten metal by the action of the magnetic field and the induced electric current. The segmented mold is used is to concentrate the magnetic field around the molten metal. The

3.4 Shaping of Molten Metal Using Alternating Magnetic Field 137

Nozzle Mold

Conventional

continuous casting

Soft contact

EMC

Fig. 3-4-1 The concept of EMC using the slit mold. [Reproduced with permission from J. Park et al.. Proceedings of the International Symposium on Heating by Electromagnetic Sources (2004)]

electromagnetic force enlarges the channel of the mold flux between the metal and the mold, increases the flow rate of the mold flux and at the same time reduces the contact pressure in the mold flux between a solidified shell and the mold. Furthermore, Joule heat generated by the induced current retards solidification of the flux existing in the channel and accelerates the heat transfer between the solidifying shell and the mold.

3.4.2 Soft Contacting Solidification without Mold Oscillation (SCSMO)'^

The concept of SCS was first realized in an international project supported by the former Ministry of Trade and Industry of Japan^^ and also independently by POSCO. ^ In this section, the work done by Park et al. at RIST and POSCO in which a high frequency alternating magnetic field was employed on the continuous casting of steel without mold oscillation is introduced.

The amount of mold powder consumed in the SCS operation is shown in Fig. 3-4-2 for various casting conditions in comparison with a conventional method. The mold powder consumption in the SCS operation without mold oscillation was no less than that in conventional casting.

Figure 3-4-3 shows typical billet surface aspects for various coil currents. In the case in which the coil current is 0 A, i.e., conventional casting, billets had oscillation marks (OSMs) of normal depth in the range of 0.45 ± 0.15 mm. When the coil current is 500 A, the OSM are


^ 1 . 5 "

1.0-

8 0.5-

o

c

EMC with Conventional EMC without

mold oscillation casting mold oscillation

Fig. 3-4-2 Mold powder consumption versus casting conditions. [Reproduced with permission from J. Park et al.. Proceedings of the International Symposium on Heating by Electromagnetic Sources (2004)]

1? .1

(a)OA (b)500A

(d) 1200 A (c) 1000 A

Fig. 3-4-3 Typical surface appearance of billets. [Reproduced with permission from J. Park et al., Proceedings of the International Symposium on Heating by Electromagnetic Sources (2004)]

suppressed to a depth of 0.20 ± 0.05 mm, except for the corner region. When the coil current is 1000 A, the OSM appears everywhere with a depth of 0.10 ± 0.04 mm. When the coil current increases to 1200 A, the OSMs appear again like wave marks with depth of 0.18 ± 0.05 mm.

Generally speaking, we believed that mold oscillation was

3.4 Shaping of Molten Metal Using Alternating Magnetic Field 139

Fig. 3-4-4 Appearance of billet strands under coil current of 1000 A, no mold oscillation and casting speed of 1.5 m min'. [Reproduced with permission from J. Park et al.. Proceedings of the International Symposium on Heating by Electromagnetic Sources (2004)]

indispensable in the continuous casting of steel. However, the SCS operation increases consumption of the mold flux as shown in Fig. 3-4-2, suggesting that continuous casting of steel without mold oscillation may be possible. The photograph shown in Fig. 3-4-4 is the surface aspect of the billet cast without mold oscillation conducted under a coil current of 1000 A. The surface quality was greatly improved to a roughness of within 0.1 mm, and better than that of the billets cast with mold oscillation shown in Fig. 3-4-3. This suggests that continuous casting of steel without mold oscillation may be possible using the SCS operation even on a commercial scale.

References

1. The History of Continuous Casting of Steel in Japan (N. Sano, ed.), ISIJ, p. 17(1996).

2. J. Park, H. Jeong, G. Kim, H. Kim, Proceedings of the International Symposium on

Heating by Electromagnetic Sources, Padua, Italy, June 2004, p. 123.

3. Ch. Vives, R. Ricou, Metals. Trans. B., 16, 337 (1985).

4. I. Sumi, K. Sassa, S. Asai, Tetsu-to Hagane, 78, 447 (1992) (in Japanese).

5. K. Ayata, K. Miyazawa, N. Bessho, T. Toh, Proceedings of the 4th European

Continuous Casting Conference, 7, p. 15, lOM Communications, Birmingham (2002).

Documents

[Springer Series in Materials Science] Magneto-Science Volume 89 || Effects of Lorentz Force and Magnetohydrodynamic Effects