Clarifying the Mechanism of Reverse Structuring during

Feb 14, 2012 - The convection of the electrolyte was studied in situ by astigmatism particle tracking velocimetry (APTV). It was revealed that during ...
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Clarifying the Mechanism of Reverse Structuring during Electrodeposition in Magnetic Gradient Fields Kristina Tschulik,*,†,‡ Christian Cierpka,§ Gerd Mutschke,∥ Annett Gebert,† Ludwig Schultz,† and Margitta Uhlemann† †

IFW Dresden, Post Office Box 270016, D-01171 Dresden, Germany Faculty of Sciences and ∥Institute for Fluid Dynamics, Dresden University of Technology, 01062 Dresden, Germany § Institute of Fluid Dynamics and Aerodynamics, Universität der Bundeswehr München, Werner-Heisenberg-Weg 39, 85577 Neubiberg, Germany ‡

S Supporting Information *

ABSTRACT: Deviating from the common expectation, magnetoelectrochemical structuring during deposition of diamagnetic ions was demonstrated, very recently. To achieve this, electrochemically inert paramagnetic ions have to be added to the electrolyte and the deposition has to be performed in a magnetic gradient field. A reverse structuring occurs, yielding thinner deposits near high gradient regions. In this paper we aim to clarify the mechanism of this reverse structuring. Potentiodynamic and potentiostatic investigations were performed, including measurements of the deposited mass with an electrochemical quartz crystal microbalance (EQCM). The convection of the electrolyte was studied in situ by astigmatism particle tracking velocimetry (APTV). It was revealed that during the reverse structuring a convection is induced in the electrolyte, which is directed away from the working electrode in regions of high magnetic gradients. Due to this additional convection, the overall deposition rate is increased, whereby it is locally reduced in regions of high magnetic gradients. The mechanism for reverse structuring is discussed in detail. Also, the influence of all relevant magnetic forces is addressed.

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deposits, which makes the method cost-efficient and flexible enough for possible industrial applications.5−7 Since the structuring effect was found to be based on the magnetic field gradient force (F∇B),7 it was assumed to be limited to electrodeposition of paramagnetic species. This assumption is based on the fact that F∇B is typically 2−3 orders of magnitude lower,8,9 when only diamagnetic species are involved in the electrochemical reaction, and thus, its influence should vanish.10,11 Indeed, for electrodeposition of Cu from paramagnetic Cu2+ ions, structured deposits were obtained, while no structuring occurred for electrodeposition of Bi from an electrolyte containing diamagnetic Bi3+ ions.4 During the deposition of Cu, an electrode-normal convection toward regions of maximum F∇B at the working electrode (WE) was observed in situ by astigmatism particle tracking velocimetry (APTV).12 On the contrary, for electrodeposition of Bi from diamagnetic Bi3+ ions, no such F∇B induced local convection was detected. Very recently, it was reported by two different groups that magnetoelectrochemical structuring also succeeds when none of the electrochemical active species is paramagnetic.5,13 The

ithin the last years, the demand for micrometer-scaled metallic structures and devices increased remarkably, as microelectronics and microelectromechanical systems (MEMS) became widespread. Such structures are also of great interest as microelectrodes for analytical applications, for example, in micro total analysis systems (μTAS).1 Consequently, reliable and inexpensive techniques capable for mass production of micrometer-scaled metallic structures have to be established. Electrodeposition is known to meet these requirements, but usually elaborate lithographic masking techniques are necessary to obtain deposits of specific shapes.2 However, it was found that structuring of electrodeposits is also possible by electrodeposition in heterogeneous magnetic fields.3−5 Moreover, it was demonstrated that free-standing Cu structures can be obtained by pulse-reverse plating in magnetic gradient fields.6 With this technique, the structure shape can be easily adjusted by the superimposed magnetic field gradient. The structure height is tunable via the deposition time and the number of pulse-reverse plating cycles.6 Sufficient magnetic gradients can be achieved by ferromagnetic building blocks of desired shape, size and configuration, magnetized by either an electromagnet or by a NdFeB permanent magnet.3,4 It was reported, that even the heterogeneous magnetic fields generated by small NdFeB permanent magnets are sufficient to cause a structuring of metal © 2012 American Chemical Society

Received: November 14, 2011 Accepted: February 14, 2012 Published: February 14, 2012 2328

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presence of electrochemically inert paramagnetic ions was found to be sufficient for this purpose. In both studies, different electrochemical systems were used and deposition was performed under mass-transport-limited conditions. The deposited structures were reversed with respect to the distribution of |B∇B|. Minima of film thickness resulted at maximum magnitude of B∇B at the WE surface. This structuring is inverse to that observed for deposition of paramagnetic ions reported previously.3,4,6,7 In the two articles on reverse structuring, the explanation for this rather unexpected observation differs significantly. Dunne et al.5 claim that locally inhibited convection of the water molecules, which are released at the WE when initially solvated ions are deposited as metal atoms, is responsible for this effect. Tschulik et al.6 suggested several possible mechanisms. One explanation was based on local blocking of the WE surface in regions of high magnitude of B∇B, for example, due to adduct formation, and resulting in cooperative effects between the electrochemically inert paramagnetic ions. Another approach proposed a F∇B-induced electrode-normal convection away from the electrode in regions of high |B∇B|. According to all three explanations, the deposition rate of the electroactive diamagnetic species would be higher in regions of low magnitude of B∇B at the WE than in regions of high | B∇B|. This correlates with the experimental findings. One important difference has to be pointed out. The first and second proposed mechanisms assume an inhibited convection or a partial blocking of the WE, respectively; that is, a reduction of the overall mass-flow toward the WE or a reduction of the electroactive electrode area. Thus, the overall current density and the deposition rate of the electroactive species will be reduced during the reverse structuring in magnetic gradient fields. In contrast, the third mechanism suggests an additional convection. Due to the law of continuity of flow in viscous media, the flow, which is directed away from the WE in regions of high |B∇B|, has to be balanced by a stream of electrolyte from the bulk toward regions of the WE where a lower |B∇B| is superimposed. In those regions an increased mass transport toward the WE results, and accordingly, a higher overall current density and a higher deposition rate will be observed in magnetic gradient fields. The understanding of the mechanism of this reversed structuring is essential for a possible application of the magnetoelectrochemical structuring technique, not only of those compounds that can be deposited from their paramagnetic ions but also for those that form only diamagnetic species. With this study we intend to contribute to clarification of the mechanism of reverse structuring during electrodeposition in magnetic gradient fields in the presence of inert paramagnetic species. Systematic potentiodynamic and potentiostatic investigations, including measurements of the deposited mass with an electrochemical quartz crystal microbalance (EQCM) and in situ studies of the electrolyte convection by astigmatism particle tracking velocimetry (APTV), will be presented. Experimental findings, relevant magnetic forces, and the mechanism for reverse structuring will be discussed in detail.

electrochemical setup, EQCM setup, and APTV setup are included in the Supporting Information. Au films served as working electrodes (WEs), Pt was used as counter electrode (CE), and a saturated mercury sulfate electrode (MSE, Hg/Hg2SO4,K2SO4,sat ̧ E = 0.65 V versus standard hydrogen electrode, SHE) was the reference electrode (RE). A magnetic field gradient template (∇B template) was magnetized and placed behind the WE to generate high magnetic field gradients (Figure 1). The ∇B template contained 21 Fe wires for standard and EQCM measurements. For APTV studies, a ∇B template containing 1 Fe wire was used, and indium tin oxide (ITO) glass served as the CE. Two different electrolytes were used: (I) 0.01 mol/L Bi(NO3)3 in 0.1 mol/L HNO3(aq) and (II) 0.01 mol/L Bi(NO3)3 + 0.09 mol/L Mn(NO3)2 in 0.1 mol/L HNO3(aq). Please see the Supporting Information for details regarding measurement parameters of the potentiodynamic and potentiostatic investigations, as well as ECQM and APTV measurements. Details regarding the working principle and data processing for APTV and EQCM investigations have been reported elsewhere.12−15 Deposit Characterization. Sample topographies were analyzed by optical microscopy and optical profilometry (MicroProf, FRT). The focused ion beam (FIB) technique was applied to prepare cross-sectional cuts of selected areas of the samples. These cross sections, as well as the deposit morphologies, were studied by scanning electron microscopy (SEM; LEO Gemini 1530, Zeiss). The chemical composition and crystal structure of the deposits were investigated by energy-dispersive X-ray analysis (EDX; coupled to the SEM) and X-ray diffraction (XRD; XPertPro Philips), respectively. Magnetostatic Simulations. Simulations of the magnetic flux density distribution for various values of Bex and the applied ∇B template were performed with the magnetostatic field solver Amperes 8.0 (Enginia Research Inc.). It was found that for Bex ≥ 400 mT the ∇B template is magnetically saturated. Distribution of the resulting flux density gradient at the WE surface in Bex = 500 mT was visualized and discussed in detail previously.4 Distribution of the magnetic gradients is essentially the same for lower Bex, yet maximum values are reduced by about a factor of 10 for Bex = 100 mT and a factor of 2 for Bex = 300 mT (contour plots of the magnitude of B∇B at the WE are included as Figure S3 in the Supporting Information).

EXPERIMENTAL METHODS Electrochemical Setup, Electrochemical Quartz Crystal Microbalance, and Astigmatism Particle Tracking Velocimetry. All electrochemical experiments were performed at room temperature in a cylindrical Teflon cell (Figure 1). A detailed description and schematic illustrations of the standard

RESULTS AND DISCUSSION Electrochemical Results. Electrolyte I: 0.01 mol/L Bi3+. First, the influence of magnetic gradient fields on the electrochemical deposition of Bi from electrolyte I, which contains only diamagnetic ions, was investigated by cyclic voltammetry. Cyclic voltammograms (CVs) obtained with a

Figure 1. Schematic drawings of (a) the electrochemical cell and (b) the ∇B template containing 21 Fe wires.

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nonmagnetized ∇B template (Bex = 0 mT, black squares) and the magnetically saturated ∇B template (Bex = 500 mT, red triangles) are compared in Figure 2. In both cases the Bi

Figure 2. Cyclic voltammograms obtained for electrolyte I (containing only Bi3+ ions) without superimposed Bex (black squares) and with the fully magnetized ∇B template (Bex = 500 mT; red triangles). Sweep rate = 10 mV/s.

deposition peak is observed at EMSE = −490 mV and the stripping peak at EMSE = −387 mV. Neither a change of the onset of the cathodic peak (EMSE = −450 mV) nor of its maximum amplitude (i = −2.80 mA/cm2) or the peak area can be observed in a superimposed magnetic gradient field. Hence, no impact of a ∇B on the Bi deposition from an electrolyte containing only Bi3+ ions can be concluded from these potentiodynamic investigations. To ensure that the cathodic peak is due to electrodeposition, cyclovoltammetric measurements in the EQCM setup were performed (see Figure S2 in the Supporting Information). At the onset of the cathodic current peak (EMSE = −450 mV), also an increase of the deposited mass is detected. The deposited mass increases further (up to 17.9 μg/cm2), as long as a cathodic current is measured, verifying that a deposition takes place in this potential region. The dissolution of the deposited Bi layer is indicated by an anodic current and a corresponding decrease of the mass signal until all Bi is dissolved from the WE and the detected mass equals zero. XRD and EDX measurements revealed that the deposit was rhombohedral Bi. Experiments with and without applied magnetic gradient fields yield identical results. Subsequent potentiostatic deposition experiments (EMSE = −520 mV) were performed from electrolyte I in homogeneous external fields of strengths varying from 0 to 500 mT. The resulting transients are given in Figure 3 for experiments (a) without and (b) with applied ∇B template. No effect of a homogeneous magnetic field or a gradient magnetic field on the Bi deposition from electrolyte I can be concluded from these current transients. As the insets of both figures reveal, no significant effect on the limiting current densities (ilim) can be observed and their values differ by less than 5% for all deposition experiments. Besides the limiting current density, the deposited mass is a useful indicator for the influence of magnetic fields on the electrodeposition process. For potentiostatic Bi deposition from electrolyte I without superimposed magnetic field, the ratio of the measured deposited mass [mEQCM(B, t) = mEQCM(0 T, 450 s) = 102 μg/cm2] and the theoretical mass calculated from the consumed charge [mq(dep)(0 T, 450 s) = 104 μg/cm2] yields a current efficiency (η) of 98%:

Figure 3. Potentiostatic Bi deposition from electrolyte I (containing only Bi3+ ions) for various external magnetic fields Bex(solid black squares) 0 mT, (open blue squares) 100 mT, (solid green triangles) 300 mT, and (open red triangles) 500 mT(a) without and (b) with applied ∇B template. The insets reveal that external magnetic fields do not affect the limiting current density.

This current efficiency for potentiostatic deposition of Bi is sufficiently close to 100% to exclude a major side reaction at a deposition potential of EMSE = −520 mV, which was already assumed from the lack of additional signals in the CVs. Most interestingly, EQCM measurements yielded reliable and precise values for the deposited mass not only in homogeneous magnetic fields but even in magnetic gradient fields, that is, with the ∇B template stacked behind the quartz crystal. The deposited mass determined by EQCM (mEQCM) and the theoretically deposited mass calculated from the consumed charge [mq(dep)] were compared for depositions with the applied ∇B template in an external magnetic field of various strengths (Bex). The data are listed in the Supporting Information in Table S1 and show that, irrespective of the applied magnetic field gradient, the measured deposited mass is equal to the theoretically calculated value. Within the accuracy of the measurement, neither the limiting current density nor the deposited amount of Bi was found to be changed in the magnetic gradient field. The same result was obtained for Bi deposition in a homogeneous magnetic field (see Figure 3). Hence, the electrochemical deposition of Bi from electrolyte I was found to be unaffected by a superimposed magnetic gradient field. Electrolyte II: 0.01 mol/L Bi3+ + 0.09 mol/L Mn2+. Due to the very negative deposition potential of Mn2+ ions [EØ(Mn2+/ Mn) = −1.185 V vs SHE],16 no deposition of Mn is expected at the moderate potentials applied in this study. Furthermore, no anomalous codeposition of BiMn alloys is reported in the literature; that is, Mn2+ ions are considered an electrochemically inert ion in this study. This expectation was proven by cyclovoltammetric studies for electrolyte II. Without a superimposed magnetic field, the shape of the obtained CV (Figure 4, black squares) is equal to those obtained with electrolyte I; that is, no additional peaks are visible. Again, the CV obtained in a homogeneous magnetic field of 500 mT (not displayed here) is nearly identical to that without superimposed magnetic field. The onset (EMSE = −450

η = mEQCM /mq(dep)·100 2330

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Figure 4. Cyclic voltammograms obtained for electrolyte II (containing Bi3+ and Mn2+ ions): (black squares) without superimposed Bex and (red triangles) with the fully magnetized ∇B template (Bex = 500 mT). Sweep rate = 10 mV/s.

mV) and the maximum (EMSE = −490 mV) of the Bi deposition peak are observed at the same potentials for the electrolytes with and without addition of Mn2+ ions. Comparison of the consumed charge and the deposited mass did not reveal any indication for a reaction besides the Bi deposition. Also, EDX and XRD analyses of the obtained deposits identified only rhombohedral Bi. Hence, it can be concluded that Mn2+ ions are, as expected, not involved in any electrochemical reaction in the investigated potential region; that is, they are electrochemically inert. Although Mn2+ ions were proven to be electrochemically inert by the above analyses without a superimposed magnetic field (and in a homogeneous magnetic field), a significant change in the CV is observed in superimposed gradient fields (Figure 4, red triangles). The onset of the cathodic peak is not affected (EMSE = −450 mV) and the measured current density values are identical to those without superimposed magnetic field, as long as the potential did not reach the peak potential (EMSE = −490 mV). Yet when the potential is swept to more negative potentials, an increased current density is detected in the magnetic field gradient. Also, during the backward sweep ivalues in the ∇B significantly exceed those without magnetic field (see inset, Figure 4). The area of the cathodic peak is increased by about 6% in the ∇B and the anodic peak area is increased by the same amount; that is, the current efficiency is not altered by the ∇B. Again, no indication for an unexpected codeposition of Mn was found by EDX and XRD analyses of the films deposited from electrolyte II in ∇B. This cyclovoltammetric study strongly indicates that in the ∇B the mass transport toward the WE is enhanced, since only under mass-transport-controlled conditionsthat is, once the potential of the maximum of the cathodic peak has been passedwas a change in the CV observed. The fact that the onset of the deposition peak is not changed by the superimposed ∇B shows that the electrochemical reaction is not affected by such moderate magnetic fields. This is in good agreement with similar studies in homogeneous B.17 Current density transients for potentiostatic experiments conducted with electrolyte II in various gradient magnetic fields are shown in Figure 5a. Contrary to electrolyte I (Figure 2b), a clear increase of the limiting current density with increasing Bex is observed. For Bex = 500 mT, the current enhancement for ilim is about 15% with respect to deposition without applied magnetic field (Figure 5). While i is not affected by ∇B for short deposition times (t < 10 s), for intermediate deposition times even stronger increases of i are observed (e.g., 25% for t = 90 s). Accordingly, the enhancement of the deposited

Figure 5. Time dependency of (a) current density and (b) deposited charge for potentiostatic Bi deposition from electrolyte II (containing Bi3+ and Mn2+ ions) with applied ∇B template for various external magnetic fields Bex: (solid black squares) 0 mT, (open blue squares) 100 mT, (solid green triangles) 300 mT, and (open red triangles) 500 mT. (c) Corresponding enhancement of ilim, mEQCM, and qdep for electrolyte II as a function of Bex. EMSE = −520 mV.

mass and charge (Figure 4c) is more pronounced than that of ilim. In the ∇B generated by the ∇B template in Bex = 500 mT, the mass of Bi deposition is increased by 24% as compared to deposition without applied ∇B (Bex = 0 mT). While no significant differences in the current density and mass transients were observed when magnetic fields of up to 100 mT were superimposed during the measurement, the enhancement for Bex = 300 mT ranks between those for 100 and 500 mT (Figure 5c). This observation is expected, since the external magnetic field is used to magnetize the ∇B template, which results in the superposition of a high ∇B at the WE. Since the ∇B template is built from Fe wires, the maximum gradient is formed when Fe is magnetically saturated, that is, in an external field of about 400 mT. Although Fe is a soft magnetic material, its magnetization in an external field of 100 mT is far below the saturation value. The magnitude of B∇B amounts to about 10% of the value reached for Bex = 500 mT; that is, only rather small gradients are superimposed at the WE. In a field of Bex = 300 mT, the magnetization of the Fe wire is much closer to the saturation value. The magnitude of B∇B is about 50% of the value reached at Bex = 500 mT (see Figure S3 in the Supporting Information and refs 4 and 21). For magnetic fields exceeding this value, only a small increase of i and m is observed (not 2331

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would be expected, when no additional convection occurs. In the setup used, this area with high magnitude of B∇B amounts to about 1/3 of the total WE area; that is, a significant decrease of the electrochemically active area would result and the effect should be measurable. Contrary to this, the potentiostatic measurements in an applied ∇B reveal a significant increase of the limiting current density and of the deposited mass. It was proven experimentally that no side reactions occurred due to the addition of Mn2+ ions. Also, all deposition experiments were performed in the mass transport limited regime and diffusion is known not to be affected by moderate magnetic fields.17,18 Thus, convection has to be induced in electrolyte II during Bi deposition in magnetic gradient fields. Moreover, it can be concluded that this predicted convection is directed toward the WE in regions of low |B∇B|, transporting ion-rich bulk electrolyte to the WE and enhancing the mass transport in these regions. This yields locally thicker deposits in low |B∇B| regions. For reasons of continuity, also a fluid flow away from the WE must occur. Under mass transport limitation, this upward-flowing stream of electrolyte is almost completely depleted of Bi3+ ions and thus, not increasing mass transport to the WE. This is likely to happen in regions of high |B∇B|, where the lowest deposit thickness is observed. Velocity Measurements. To verify the assumption of an additional convection being responsible for the increased deposition rate in ∇B, in situ measurements of the electrolyte velocity were performed by APTV. In Figure 7 the radial profile of the averaged electrodenormal velocity is shown for electrolytes I and II. The center of

shown here), which can be attributed to the increasing effect of the Lorentz force with increasing Bex.7 The experiments in electrolyte II again prove that the EQCM technique works reliably in magnetic gradient fields. This is especially interesting since from this electrolyte structured layers are deposited and the EQCM technique is typically said to require very smooth and homogeneous layers. The deposits investigated here are inhomogeneous in terms of surface topography and thickness. Yet, as the deposits are not porous, no significant incorporation of electrolyte inside the layers occurs, which usually causes deterioration of reliability of the EQCM technique. Hence, no remarkable error is observed when the magnetic field dependencies of the deposited mass and consumed charge are compared (see Figure 5). In all experiments the difference between the theoretically deposited mass (calculated from the deposited charge with the assumption of 100% current efficiency) and the measured value (mEQCM) was below 5%. Characterization of Bi Deposits. As reported previously,13 all layers deposited from electrolyte I (containing only Bi3+ ions) were homogeneous, irrespective of the superimposed magnetic field. Also, from electrolyte II homogeneous layers were deposited, as long as no or homogeneous magnetic fields were superimposed during the deposition process. The optical image of a homogeneous Bi layer deposited from electrolyte II in a homogeneous magnetic field of 500 mT is depicted in Figure 6a.

Figure 6. Optical images of the Bi deposits obtained from electrolyte II in (a) homogeneous Bex = 500 mT and (b) magnetic gradient generated by the ∇B template in Bex = 500 mT. EMSE = −520 mV; qdep = 400 mC.

On the contrary, in a superimposed ∇B a reverse-structuringeffect was observed, which was reported recently.5,13 Reverse structuring denotes that in regions of high ∇B a lower film thickness is observed than in regions of low ∇B. This is already visible from Figure 6b, where the optical image of a Bi film deposited from electrolyte II in ∇B, generated by the ∇B template in Bex = 500 mT, is shown. In those regions, where an Fe wire of the template was located (high |B∇B|), the golden color of the Au WE is visible through the thin Bi layer. In regions of low ∇B a dense and twice as thick gray Bi layer was observed by SEM analyses of the deposit cross section. A detailed description of the layer topography and the layer morphology, as well as of its cross-section, is given in ref 13. Reverse Structuring in Magnetic Gradient Fields. From the observed lower film thickness of the Bi deposit obtained from electrolyte II (containing electrochemically inert paramagnetic Mn2+ ions) in regions of high |B∇B|, it seems likely that these distinct regions are partially blocked during the deposition process. This was proposed in both reports that described the reverse structuring, although different ideas of the blocking species were suggested.5,13 In the case of a partial blocking of the electrode area with high superimposed |B∇B|, a decrease of the limiting current density and the deposited mass

Figure 7. Radial profiles of the electrode-normal velocity v for electrolytes I (black squares) and II (red triangles), in comparison to the flow profile of an electrolyte containing paramagnetic Cu2+ ions (blue dots). r-values represent the distance from the center (r = 0) of the cylindrical cell and the Fe wire. The rim of the Fe wire is located at r = 0.5 mm.

the cell (r = 0 mm) corresponds to the position of the Fe wire (rim at r = 0.5 mm), and only data close to the WE (z = 0 ... 1.5 mm) were taken into account. Here, only the part of the cell near the Fe wire (r ≤ 1.5 mm =̂ 3 · radius of the wire) is plotted, since in this region near high magnitudes of B∇B a change in the convection is expected for the different electrolytes.19 Although the magnitude of the velocity is quite low, trends are clearly visible. To compare the measurements of this setup with previous studies, a Cu2+ ion-containing electrolyte was used as well.12 As already discussed in detail in ref 12, the electrode-normal convection for the Cu2+ electrolyte points toward the WE (positive v) in regions of high magnitude of B∇B, near the Fe wire position. For electrolyte I containing Bi3+ ions only, no specific trend can be 2332

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observed and the magnitude of v is almost zero. On the contrary, the profile for the electrolyte containing Mn2+ and Bi3+ ions shows that the electrode-normal flow points away from the WE (negative v) in regions of high |B∇B|, near the Fe wire position. This observation is in perfect agreement with the above-mentioned hypothesis of a convection directed away from the WE in regions of high |B∇B|, causing the reverse structuring. Since the permanent magnet used in the APTV measurement configuration does not provide strictly electrode-normal magnetic field lines, fluid rotation due to Lorentz force was observed during all experiments. The value and the direction of this flow occurred irrespective of the electrolyte, as expected.12 Magnetic Forces Causing the Reverse-StructuringEffect. The driving forces for the observed convection have to originate from the inhomogeneous magnetic field. This is obvious, since in homogeneous magnetic fields a structuring of the deposit or an effect on current density or mass was observed neither for electrolyte I, containing only Bi3+ ions, nor for that with addition of Mn2+ ions (electrolyte II). The two magnetic forces of importance in nonhomogeneous magnetic fields are the Lorentz force FL and the magnetic field gradient force F∇B.17 FL is not a function of the magnetic properties of the electrolyte or of the dissolved ions but depends only on the magnetic flux density (B) and the ion flux density (i) toward the WE:20

FL = i × B

electrolytes I and II. Hence, homogeneous deposits would be expected for both electrolytes, which contradicts the experimental results. When the deposition process in multi-ion electrolytes is considered more carefully, it becomes obvious that also electrochemically inert species can exhibit a remarkable concentration gradient. Since electroneutrality has to be maintained and a zero-flux condition of the inert ions has to be fulfilled during the deposition of Bi, considerable gradients of the inert ions are established near the WE. Due to the deposition of Bi, the concentration of Bi3+ ions will be reduced in the vicinity of the WE [∇c(Bi3+) > 0], while the concentration of the inert (Mn2+) ions, will be increased close to the WE [∇c(Mn2+) < 0] during the deposition process.23 In previous studies of electrodeposition in magnetic gradient fields the electrochemically inert species were diamagnetic, that is, their contribution to ∇F∇B was negligible in comparison to the dominating contribution of the electrochemically active paramagnetic species. The contribution of the strongly paramagnetic Mn2+ ions [χmol(Mn2+) = 183 × 10−9 m3/mol]17 to the small value of the rotational part of F∇B for the deposition of diamagnetic Bi3+ ions cannot be neglected, considering that |χmol(Mn2+)| ≈ 366|[χmol(Bi3+)]|. Consequently, even rather small changes in ∇c(Mn2+) will result in a dominating effect of the electrochemically inert species, as the curl of the magnetic gradient force changes its sign.24 According to eq 3, due to the negative sign of ∇c(Mn2+), the induced convection is directed away from the WE in regions of high magnitude of B∇B. Hence, in regions of high |B∇B| the diffusion zone will be enlarged with respect to regions of low |B∇B|, which is in agreement with the observed structuring of the Bi deposit (Figure 6b). Due to the continuity of flow in viscous media, this results in a flow toward the electrode in regions of low |B∇B|. Thus, the increased mass transport toward the WE in regions of low |B∇B|, which was proposed on the basis of the potentiostatic deposition experiments, can be explained on the basis of the established theory of F∇Binduced convection of the electrolyte. The fact that a reversal of the structuring with respect to the previously reported deposition of Cu from electrolytes containing paramagnetic Cu2+ ions occurs4,6 can be attributed to reversal of the sign of the concentration gradient of the dominating paramagnetic species. In this sense, reverse structuring during deposition from almost every diamagnetic species should be possible by addition of an inert paramagnetic species.

(1)

Since for electrolytes I and II the concentration of the electrochemically active species (Bi3+ ions) and the superimposed magnetic gradients were identical, the induced FL is supposed to be nearly identical as well. Consequently, the remarkable differences in the deposition behavior in magnetic gradient fields cannot be attributed to this force. This has already been demonstrated by numerical simulations for electrode position of Cu in gradient magnetic fields.7 Therefore, the reverse structuring must be due to a F∇B induced convection. F∇B depends on the magnetic flux density B, its gradient ∇B, the molar magnetic susceptibility χmol,k, and the concentration ck of every species k in the electrolyte, according to χ F∇ B = sol (B ·∇) ·B with χsol = ∑ χmol, kck μ0 (2) k

7

Mutschke et al. pointed out that in closed cells, as used for this study, only the rotational part of F∇B can drive convection: ∇ × F∇ B =

1 (∑ χmol, k∇ck) ×(∇B 2) 2μ0 k

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CONCLUSIONS For the system Bi3+/ Mn2+, the mechanism of reverse structuring during electrodeposition in magnetic gradient fields was studied by various electrochemical methods. It was demonstrated that the deposited mass can be precisely determined by an EQCM even in gradient magnet fields. The observed increase of deposition rate in magnetic gradient fields was attributed to an additional convection in the electrolyte. In situ velocity measurements proved that this convection evolves in the presence of inert paramagnetic Mn2+ ions. For an electrolyte containing only diamagnetic Bi3+ ions, no electrolyte convection was detected and homogeneous layers were obtained. It was concluded that the reverse structuring should be attributable to convective effects. Thus, a revised mechanism

(3)

Due to this, only species with nonvanishing concentration gradient ∇ck, have to be taken into consideration. For the presented deposition experiments it can be assumed that the concentration changes mainly along electrode-normal (z) direction, that is, ∇c(Bi3+) ≈ dc(Bi3+)/dz. The necessity of sufficient concentration gradients for magnetoelectrochemical structuring was also demonstrated experimentally for electrodeposition of Cu.21 On a first glance, it might be expected that the concentration gradient of Bi3+ ions [∇c(Bi3+)] is the only one that does not vanish in the presented experiments. Due to the low magnetic susceptibility of diamagnetic ions [χmol(Bi3+) = −0.5 × 10−9 m3/mol],22 ∇F∇B would be negligible in this case for 2333

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Analytical Chemistry

Article

(13) Tschulik, K.; Yang, X.; Mutschke, G.; Uhlemann, M.; Eckert, K.; Sueptitz, R.; Schultz, L.; Gebert, A. Electrochem. Commun. 2011, 13, 946−950. (14) Sauerbrey, G. Z. Phys. 1959, 155, 206−222. (15) Bund, A.; Schwitzgebel, G. Electrochim. Acta 2000, 45, 3703− 3710. (16) Lide, D. R. CRC Handbook of Chemistry and Physics, 84th ed.; CRC Press: Boca Raton, FL, 2003. (17) Coey, J. M. D.; Hinds, G. J. Alloys Compd. 2001, 326, 238−245. (18) Coey, J. M. D.; Aogaki, R.; Byrne, F.; Stamenov, P. Proc. Natl. Acad. Sci. U.S.A. 2009, 106, 8811−8817. (19) Due to the continuity of flow, this flow in the central region is balanced by an electrode-normal fluid flow in regions afar from the Fe wire (r ≥ 1.5 mm). This counterflow is less pronounced and differs only very slightly for the different electrolytes (see Figure S4 in Supporting Information). (20) Ragsdale, S. R.; Grant, K. M.; White, H. S. J. Am. Chem. Soc. 1998, 120, 13461−13468. (21) Tschulik, K.; Sueptitz, R.; Koza, J.; Uhlemann, M.; Mutschke, G.; Weier, T.; Gebert, A.; Schultz, L. Electrochim. Acta 2010, 56, 297− 304. (22) Prasad, M.; Kanekar, C. R.; Mulay, L. N. J. Chem. Phys. 1951, 19, 1440−1444. (23) Wagner, C J. Electrochem. Soc. 1949, 95, 161−174. (24) Mutschke, G.; Tschulik, K.; Weier, T.; Uhlemann, M.; Bund, A.; Alemany, A.; Fröhlich, J. Magnetohydrodynamics 2012.

of reverse structuring was presented and explained on the basis of magnetic field gradient force. The finding that magnetoelectrochemical structuring of metal deposits succeeds with paramagnetic and also with diamagnetic electroactive species extends the application of this cost-efficient structuring method to almost every electrochemical system. A challenging task of future studies will be to investigate whether submicrometer structures can be electrodeposited with the help of magnetic gradients fields, as well.

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ASSOCIATED CONTENT

S Supporting Information *

Additional text with details about electrochemical setup, EQCM, and APTV; four figures showing a cross-sectional drawing of the electrochemical cell utilized for APTV measurements, CV obtained with electrolyte I, distribution of the magnitude of B∇B at the WE, and radial profiles of the electrode-normal velocity v for electrolytes I and II; and one table showing enhancement of ilim, mEQCM, and mq(dep) in dependence of Bex for potentiostatic deposition of Bi from electrolyte I with applied ∇B template. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Tel. +493514659717; fax +493514659543; e-mail k.tschulik@ ifw-dresden.de. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The German National Academic Foundation and the German Research Foundation (Collaborative Research Center 609) are gratefully acknowledged for financial support of this work. We are grateful to Kerstin Eckert and Tom Weier for several fruitful discussions.

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REFERENCES

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dx.doi.org/10.1021/ac2029612 | Anal. Chem. 2012, 84, 2328−2334