1999_Magnetic-Field Effects on Fractal Electrodeposits

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Magnetic-field effects on fractal electrodeposits

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1999 Europhys. Lett. 47 267

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EUROPHYSICS LETTERS 15 July 1999

Europhys. Lett., 47(2), pp. 267-272 (1999)

Magnetic-field effects on fractal electrodeposits

J. M. D. Coey1, G. Hinds1 and M. E. G. Lyons2

1 Physics Department, Trinity College - Dublin 2, Ireland2 Chemistry Department, Trinity College - Dublin 2, Ireland

(received 26 January 1999; accepted in final form 19 May 1999)

PACS. 81.15Pq Electrodeposition, electroplating.

Abstract. A uniform magnetic field unexpectedly alters the form of copper deposits grownin a flat electrochemical cell; the patterns change from radial to unidirectional when the cell ishorizontal and vice versa when the cell is vertical. The electrodeposits are characterised by theirchirality and fractal dimension. Complex impedance spectra show that the effective diffusioncoefficient of the copper ions is doubled in a field of 1 T. The results demonstrate that the fieldproduces a body force comparable to that of gravity. From dimensional analysis, it is inferredthat the field modifies convective flow on a scale of a few microns close to the cathode.

Well-documented effects of magnetic fields on chemical reactions are uncommon [1]. Inelectrochemistry it is known that fields in the 1 tesla range can influence the rate of depositionof metal in simple redox reactions [2-4], although no mechanism has yet been established.It has been suggested that the magnetic field somehow alters the ion concentration near theelectrode surface [5], or that convection currents are enhanced by the Lorentz force acting oncharged species in solution [6,7]. The surface morphology of the deposit is also influenced bythe field [7]. Electrodeposits formed around a central cathode in a flat cell have a characteristicfractal form [8] which is sensitive to the electrolyte concentration and applied voltage [9], andmay be influenced by magnetic field [10].

Here we investigate a familiar electrochemical reaction, the electrodeposition of copper, in

the presence of a magnetic field. We have discovered that the form and fractal dimensionof the electrodeposits depend on the magnitude and direction of the applied field, and theorientation of the cell. Furthermore, the processes of diffusion and electron transfer change byabout a factor of two in fields of 1 T. Chirality, and asymmetry of stringy deposits obtainedwhen the field is applied in the plane of the cell establish that the magnetic body forces arecomparable to those involved in convection. As no measurable direct influence of the Lorentzforce on the diffusion coefficient is anticipated, it is suggested that the field acts to increaseconvection in the diffusion layer.

The fractal electrodeposits were grown from solutions of 0.2 M CuSO4 in a flat cell witha central cathode and ring anode, at an applied voltage of 6 V. A permanent magnet fluxsource [11] was used to apply variable fields, B , of up to 1 T either parallel or perpendicular

c EDP Sciences


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268 EUROPHYSICS LETTERS

Fig. 1. Copper electrodeposits grown around a central cathode in a horizontal flat circular cell(diameter 22 mm, thickness 2 mm) a) in zero applied field, b) 0.4 T upwards, c) 0.8 T downwards,d) 1 T horizontally, and in the same cell oriented vertically, e) in zero field and f) in 1 T perpendicularto the plane of the cell.

to the plane of the cell, which could be mounted either horizontally or vertically. Images ofthe resulting fractal patterns were analysed using the box-counting method [12].

Some typical fractal electrodeposits are shown in fig. 1. With the cell horizontal dense radial

growth is observed in zero field (fig. 1a), but when the field is applied perpendicular to theplane of the cell a branching spiral pattern forms instead (fig. 1b). If the direction of the fieldis inverted, the chirality of the spiral is reversed (fig. 1c). Furthermore, when the magneticfield is applied parallel to the plane of the cell, a stringy deposit appears (fig. 1d). It wassurprising to notice that growth of the stringy deposit predominated in one specific directionperpendicular to the field. Repeated measurements showed that this direction is the one inwhich the gravitational force and the Lorentz force are acting in unison. With the cell vertical,a dense deposit grows upwards from the electrode (fig. 1e); it becomes stringy in a verticalfield, but turns into a branching spiral when the field is perpendicular to the plane (fig. 1f).Chirality with respect to the field direction is oppositeto that in fig. 1b). These results aresummarized in table I; the influence of magnetic field on chirality and fractal dimension, D f,


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j. m. d. coey et al.: magnetic-field effects on fractal electrodeposits 269

Fig. 2. a) Fractal dimension and b) chirality of electrodeposits grown with the cell horizontal as afunction of applied field. The fractal dimensionality is shown for the field vertical () and horizontal ().Chirality is defined as the inverse radius of curvature of the main branches of electrodeposits like thosein fig. 1b) and c).

is presented in fig. 2. There is a broad increase in fractal dimension in a perpendicular field,but a clear decrease, from 1.8 to 1.6, when the field is applied in-plane, corresponding to theincreasingly stringy nature of the deposit.

Complex impedance measurements were carried out with a view to elucidating the effectof the field on the electrodeposition process. The electrochemical behaviour of the redoxcouple Cu2+/Cu may be divided into two distinct regimes, an activation regime where therate of reaction is governed by the kinetics of the electron transfer at the electrode, anda mass transport regime where diffusion of ions towards the electrode is rate-limiting. Inpotentiodynamic polarisation plots (cyclic voltammetry) the electron transfer process is rate-limiting in the Tafel region close to the rest potential, whereas mass transport is dominant

Table I. Form of copper electrodeposits in zero field or1 T.

Cell B= 0 B= 1 T (vertical) B= 1 T (horizontal)

Horizontal dense branched stringy

radial chiral unidirectional

Vertical dense stringy branched

unidirectional unidirectional chiral


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Fig. 3. a) Cole-Cole plots of the complex impedance spectrum of a 0.2 M CuSO4 solution with ()

and without () a 1 T magnetic field. b) Plot ofZ vs. 1/2 showing the effect of the field on thediffusion coefficient (eq. (1)).

in the region of the limiting current plateau. Complex impedance measurements providequantitative information about both processes. A small ac voltage is applied at the electrodeand the magnitudes of the real (Z) and imaginary (Z) parts of the impedance are measuredas a function of frequency. At high frequencies the kinetics of the electron transfer are rate-determining and a characteristic semicircle is observed in the Cole-Cole plot ofZ against Z.At low frequencies the rate of diffusion becomes dominant and a straight line is observed. Herethe Warburg impedance ZW is given by [13]

ZW= kBTe1/2

z2e2NAA

2D1/2, (1)

where D is the diffusion coefficient, = zeV/kBT, A is the area of the electrode, z = 2 for

Cu2+

andV is the dc potential. Hence, the diffusion coefficient of the ionic species in solutionmay be calculated from the slope of the plot ofZW against1/2.

Reproducible complex impedance data for the Cu2+/Cu system obtained with a platinumworking electrode in 0.2 M CuSO4 appear in fig. 3. The Cole-Cole plot shows the semicirclecharacteristic of activation control and the straight line associated with the diffusional Warburgimpedance. The effect of the magnetic field is to shift the upper intercept of the semicirclewith the real axis. This corresponds to a decrease in the electrochemical rate constantkETin the 1 T field. An opposite effect appears on the diffusion coefficient obtained from theslope of the plot ofZW against

1/2 in the Warburg region. From eq. (1) we calculate thatD increases from 8 1010 m2s1 to 1.6 109 m2s1 in a field of 1 T. This is similar tothe increase that is achieved by gentle stirring with a rotating electrode. The zero-field value


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j. m. d. coey et al.: magnetic-field effects on fractal electrodeposits 271

is in good agreement with the literature [14]. Evidence for the two effects was also seen in

potentiodynamic polarisation plots under similar conditions [4]. The Warburg region in similarexperiments with a fractal electrode was ill-defined.

Mass transport is the rate-limiting factor for the electrodeposits of fig. 1. The increase ofdiffusion coefficient in the field is consistent with the change in form of the electrodeposit.As the rate of mass transport increases, it has been found that the fractal dimensionalityof zinc deposits increases and their form changes from diffusion-limited aggregation (DLA)to dendritic [15]. The branched spiral deposits we observe are characterized as intermediatebetween DLA and dendritic in form. The problem is to understand how a magnetic field canhave such an impressive effect on diffusion and therefore on the mobility of the copper ions insolution. The direct effect of the Lorentz force should be utterly negligible given the low ionvelocities ( 400 m/s) and short mean free paths ( 1 nm).

The results with the cell vertical establish that convection of the solvent near the cathode

is important for mass transport. The Lorentz force associated with a current density j A/m2produces a magnetohydrodynamic body force of magnitude jB per unit volume. Directevidence that the body force is significant is the unidirectional nature of the stringy depositswheneverB is applied in-plane, and particularly the fact that these strings tend to grow inthe sense where the gravitational force and the Lorentz force add (fig. 1d). Further evidenceis the change from unidirectional to branched when the cell is vertical and the field is appliedperpendicular to the cell (fig. 1e and f ). The relevant quantity here is the dimensionless ratio

Rg = jB

g . (2)

This number will be 1 when the Lorentz and gravitational forces are equal in magnitude. Inour case,j

2

104 A/m2 at the beginning of the experiment and

1000 kg/m3 soRg

1

when B = 0.5 T.The sense of the chirality induced in the branched electrodeposits when the cell is horizontal

and field vertical is that expected from the Lorentz force (fig. 1b and c), showing that it plays arole here too, when the gravitational and Lorentz forces are perpendicular. The dimensionlessratio

RB = qB

6r (3)

of the transverse to the longitudinal forces acting on the moving ions turns out to be of order108 ifr is taken as the radius of the Cu2+ hydration sphere ( 1 nm), q= 2e and is theviscosity of the solution ( 103 Ns/m2). To yield observable chirality, RB should be of order0.1 which means that whenB = 1 T and q= (4/3)r3, where is the positive charge densityin solution, r should be a few m. This we interpret as the size of an eddy or of a convectioncell. Recent observations by Devos et al. of bubble tracks on nickel electrodes support theidea that the field influences convective flow [7].

In conclusion, by growing fractal electrodeposits in different orientations with and withoutan applied magnetic field, we have demonstrated unequivocally that the magnetic field hasan influence comparable to that of gravity. From impedance spectroscopy we show that thefield increases the effective diffusion coefficient D, thereby promoting mass transport duringelectrodeposition. The phenomenon is related to convection on a scale of a few microns in thediffusion layer near the cathode. The field may modify streamline convection on a very smallscale, but it is unlikely to create turbulence [16], since Reynolds number is of order 1.


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***

We are grateful toSiddharta Senand R. Skomskifor helpful discussions. The work waspartly supported by Enterprise Ireland.

REFERENCES

[1] Atkins P. W. and Lambert T., Ann. Rep. Prog. Chem. A, 72(1975) 67.

[2] Kelly E., J. Electrochem. Soc., 124(1977) 987.

[3] Chopart J. P., Dougdale J., Fricoteaux P. and Olivier A., Electrochim. Acta, 36(1991) 459.

[4] Hinds G., Coey J. M. D. and Lyons M. E. G., J. Appl. Phys., 83(1998) 6447.

[5] Noninski V., Electrochim. Acta, 42(1997) 251.

[6] Ragsdale S., Lee J. and White H., Anal. Chem., 69(1997) 2070.

[7] Devos O., Olivier A., Chopart J. P., Aaboudi O.and Maurin G.,J. Electrochem. Soc., 145(1998) 401; Devos O., Aaboudi O., Chopart J. P., Merienne E., Olivier A. and AmblardJ., J. Electrochem. Soc., 145(1998) 4135.

[8] Ben-Jacob E., Contemp. Phys., 34(1993) 247; Ben-Jacob E., Contemp. Phys., 38 (1997) 205.

[9] Sawada Y., Dougherty A. and Gollub J. P., Phys. Rev. Lett., 56(1986) 1260.

[10] Mogi I. and Kamiko M., J. Cryst. Growth, 166(1996) 276.

[11] Manufactured by Magnetic Solutions Ltd, Unit 13, IDA Centre, Pearse Street, Dublin 2, Ireland.

[12] Crilly A. J., Earnshaw R. A. and Jones H., Fractals and Chaos (Springer-Verlag, NewYork) 1991.

[13] Sluyters-Rehbach M. and Sluyters J. H., Electroanal. Chem., 4 (1970) 1.

[14] Atkins P. W., Physical Chemistry(Oxford University Press, Oxford) 1994.

[15] Grier D., Ben-Jacob E., Clarke R. and Sander L. M., Phys. Rev. Lett., 56(1986) 1264.

[16] Landahl M. T., Turbulence and Random Processes in Fluid Mechanics(Cambridge University

Press) 1992.

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1999_Magnetic-Field Effects on Fractal Electrodeposits