3412
J. Phys. Chem. C 2007, 111, 3412-3416
Magnetic Field Induced Modulation of Anodic Area: Rest Potential Analysis of Zn and Fe F. M. F. Rhen*,† and J. M. D. Coey‡ Tyndall National Institute, UniVersity College Cork, Cork, Ireland, and School of Physics and CRANN, Trinity College, Dublin 2, Ireland ReceiVed: August 21, 2006; In Final Form: January 3, 2007
We have studied the effect of magnetic field (B) and rotation speed (ω) of a rotating disk electrode on the corrosion current and rest potential (open circuit potential) of Zn and Fe nitrate and dichromate solutions acidified with nitric acid and sulfuric acid, respectively. We show that the anodic area of Zn and Fe can be modulated by a magnetic field or electrode rotation speed, and we introduce a semiempirical model based on the Koutecky-Levich and Butler-Volmer equations to reconstruct the relative anodic area as a function of these variables. The driving force responsible for the magnetic field induced micro-magnetohydrodynamic convection is the Lorentz force. The corrosion currents of Zn and Fe were found to increase with rotation speed and magnetic field. Rest potential shifts as large as 60 mV for Zn and 200 mV for Fe were observed in 1 M KNO3 acidified with HNO3 to pH 0.9. The rest potential is controlled by anodic current density, whereas the corrosion current density is controlled by cathodic reaction.
The observation of the magnetic field induced rest-potential shift of iron dates back to the 19th century.1 Much effort has been made to understand the origin of this phenomenon from the magnetic point of view. Waskaas and Kharkats2 favored a concentration gradient force, due to the fact that they only observed the effect in systems involving a ferromagnetic electrode in paramagnetic solution. However, this force is now known to be insignificant in solutions used in electrochemistry.3 Perov et al.4 also studied a similar system and attributed the phenomena to the existence of a domain structure in the surface of the ferromagnetic electrode. Dass et al.5 revisited the problem and, in line with earlier finding of Hinds et al.,6 explained the rest potential in terms of field gradient force. Recently,7 we clarified the circumstances in which the rest-potential shift can be observed, showing that there can be a shift for a nonmagnetic electrode (Zn) immersed in a non-paramagnetic solution (KNO3). Furthermore, we identified the Lorentz force as the main driving force responsible for the field-induced rest-potential shift. This was followed by a systematic study showing that the restpotential shift is associated with corrosion and that it is related to enhancement of the mass-transport-limited cathodic current by the Lorentz force,8 accounting for anodic shifts of the open circuit potential. Although the magnetic origin of the field-induced restpotential shift seems clear, a satisfactory mathematical description of the rest-potential dependence on the magnetic field has not been reported. Mixed potential theory qualitatively describes the magnetic field induced rest-potential shift via an enhancement of the mass-transport-limited cathodic reaction. General models using the mixed potential theory have been published by many authors9-13 Attempts to include the magnetic field have been made by Lu et al.14 and Rhen et al.7 Lu et al. used mixed potential theory to model the rest potential of iron in dichromate solution acidified with H2SO4 in a magnetic field of up to 0.4 T. Rhen et al.7 studied the rest-potential shift of Zn and showed * Corresponding author. E-mail:
[email protected]. † Tyndall National Institute. ‡ Trinity College.
that the rest-potential shift and the corrosion current density have the same power-law dependence on magnetic field for small values of the applied field. The saturation of the rest potential of Fe with magnetic field is a common feature which can found in the experimental data of iron reported by many authors4-6,8,14 and has only been addressed by Lu et al.14 In their formulation the saturation of the rest potential is associated with the change from mixed (kinetic and diffusion) control to kinetic control. However, as we shall now show, rotating disk electrode experiments indicate that no change in control regime occurs for iron and the rest potential should not be expected to saturate. We explain the saturation in terms of a change in the effective anodic area with the corrosion current, and we propose a new model to reconstruct the relative changes of the anodic area which depends on the rotation speed of a rotating disk electrode, or on magnetic applied field, for Fe and Zn electrodes. Model Electrodes can be classified as single electrodes or polyelectrodes, depending on the number of reaction couples occurring at the electrode surface. If only a single reaction couple occurs, such as Fe2+/Fe3+, the electrode is called a simple electrode. Polyelectrodes are those where more than one reaction couple take place at the surface and may not respect the Nernst equation15 due to the irreversible character of the reaction. The hydrazine (N2H4)/Pt system is a typical example, cited by Kodera et al.12 The rest potential of polyelectrodes is known as the mixed potential, a concept which was introduced by Wagner and Traud.16 A corroding electrode is classified as a polyelectrode, and according to Power and Ritchie13 the anodic current is activation-controlled. According to the Koutecky-Levich equation, the current density (j) through a heterogeneous (electrode/electrolyte) interface can be described by the following relation:17
1/j ) 1/jL + 1/jk
10.1021/jp065393o CCC: $37.00 © 2007 American Chemical Society Published on Web 02/07/2007
(1)
Magnetic Field Induced Modulation of Anodic Area
J. Phys. Chem. C, Vol. 111, No. 8, 2007 3413
where jL is the limiting current density and jk is the kinetic current density described by the Butler-Volmer equation:18
jk ) j0{exp[-Rc(E0 - E)nF/RT] - exp[Ra(E - E0)nF/RT]} (2) Here, j0 is the exchange current density, E is the equilibrium potential, E0 is the rest potential, n is the number of charges transferred, F is the Faraday constant (96 320 C mol-1), R is the universal gas constant (8.315 J mol-1 K-1), T is the temperature in Kelvin, and Rc and Ra are the charge-transfer coefficients for the cathodic and anodic reactions, respectively. Rotating disk electrode experiments can be carried out to identify the rate-determining step involved in electrode reactions. For a mass-transport-limited reaction, the Levich equation for the cathodic limiting current density has the form17
jL ) γω1/2 ) 0.62nFC0D2/3ν-1/6ω1/2
(3)
where γ, C0, D, ν, and ω are the slope (A s m-2), bulk concentration (mol m-3), diffusion constant (m2 s-1), viscosity (m2 s-1), and rotation speed (rad s-1), respectively. The cathodic (ic) and anodic currents (ia) balance each other (ic ) ia) during open-circuit corrosion. The anodic current density, ja ) ia/Sa, where Sa is the anodic area, can be described by the Butler-Volmer equation, which at large overpotential reduces to
ja ) j0 exp[Ra(E - E0)nF/RT]
(4)
Therefore a relation between Sa and the rest-potential can be obtained:
Sa ) (ia/j0) exp[-Ra(E - E0)nF/RT],
where ic ) ia
(5)
It is convenient to write the anodic area dependence on magnetic field B, in Tesla, and rotation speed in the following form:
Sa ) (1/j0)ia(ω,B) exp[-Ra(nF/RT) ∆E(ω,B)]
(6)
where ∆E is the rest-potential shift. Therefore the relative changes in area can be written as
Sa,R(ω,B) ) [ia(ω,B)/ia(ω0,B0)] exp{-Ra(nF/RT)[∆E (ω,B) - ∆E(ω0,B0)]} (7) where ia(ω,B) and ∆E(ω,B) represent the dependence of the anodic current and rest potential on the rotation rate of a disk electrode (ω) and on the magnetic field (B), respectively, and the subscript “0” denotes an arbitrary initial state. The dependences ia(ω,B) and ∆E(ω,B) are not known a priori and need to be determined experimentally. Experimental Setup The rest potential and corrosion were studied in 1 M KNO3 solution (nitrate solution) acidified to pH 0.9 with HNO3 and 50 mM K2Cr2O7 (dichromate solution) acidified to pH 0.8 with H2SO4. Nitrogen flow was bubbled through the solutions for 30 min prior to each experiment and maintained above the solution during the experiments. Fe and Zn electrodes were cut out from 99% pure foils into 8.5 mm diameter and 3 × 6 mm pieces for rotating disk electrode and magnetic field experiments, respectively. The foils were polished using sand paper grade 800 for each corrosion experiment to produce a reproducible initial surface state. Weight loss experiments were carried out
for periods of 5-25 min to determine the corrosion current density, which was found to be time-independent. A homogeneous magnetic field was applied parallel to the electrode surface either using an 1.5 T electromagnet with 50 mm gap or a 5 T superconductor magnet with a 105 mm bore. Rotating disk electrode experiments were done using an EG&G model 616 system. An Ag/AgCl electrode was used as reference electrode, and the rest potential shift was measured using either an EG&G potentiostat model 263A or a C. H. Instruments potentiostat model CHI660B. Results and Discussion The chemical reactions associated with the corrosion of Fe in nitric acid solution and dichromate solution are
anodic reaction Fe f Fe2+ + 2 e-
(8)
2 NO3- + 2e- + 4H+ f 2NO2 + 2H2O
(9)
Cr2O72- + 14H+ + 6e- f 2Cr3+ + 7H2O
(10)
cathodic reaction
The dependence of the corrosion current for Zn and Fe on the hydrodynamic condition near the electrode, jcorr(ω), is shown in Figure 1. Zn corrosion was studied in 1 M KNO3 (pH ) 0.9) nitric acid solution, whereas Fe was studied in dichromate and nitric acid solution. The corrosion current density dependence on the rotation rate of Fe and Zn show a linear dependence on ω1/2. All curves can individually be fitted to a straight line. The linear dependence of jcorr on ω1/2 is a clear indication that the cathodic reactions 9 and 10 are mass-transport-limited. Values of slope are summarized in Table 1. The dependence of the rest potential on the rotation rate of the Zn and Fe disk electrodes are shown in Figure 2. A rest potential shift of 68 mV at 625 rpm (ω1/2 ) 25, Figure 2c) is expected to produce a 15-fold (see eq 4) enhancement in the corrosion current for Fe in dichromate solution, taking the nominal area of the electrode. This is evidently inconsistent with our experimental observation (Figure 1c), which shows an increase in the current density by a factor of only 3. Therefore, the effective anodic area of the electrode must differ from the nominal anodic area. The rest potential shift is correlated with the anodic and cathodic current densities, which increase with rotation and approach saturation for Zn and Fe (Figure 2a-c). The balance between cathodic and anodic currents (ic ) ia) is always maintained, so after the rest potential reaches saturation, any further increase in the corrosion current must be accompanied by an expansion of the active anodic area (Sa), ic ) ia ) ja,LSa, where ja,L is anodic current density for the saturated rest potential. Therefore, after the rest potential saturates, expansion of the anodic active area must be responsible for any further increase in corrosion current. Figure 3 illustrates the surface of Fe electrode at low (300 rpm) and high rotation (3000 rpm) rates. The anodic reaction, Fe f Fe2+ + 2 e-, favors the formation of grooves on the electrode, whereas regions where cathodic reactions 9 and 10 mostly happen will change little. Although the anodic and cathodic sites do not occupy a fixed position on the electrode surface, the grooves in the photograph (Figure 3a) represent regions that behave mostly as anodic sites, whereas the flat regions behave mostly as cathodic sites. The limiting anodic current density (ja,L) corresponds to maximum
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Figure 1. Corrosion dependence on the electrode rotating rate for (a) zinc, (b) iron electrodes in 1.0 M KNO3 (pH 0.9) solutions, and (c) iron in 1 M H2SO4 with 50 mM of potassium dichromate solution, all at 295 K. Current densities are based on the nominal area of the electrode.
TABLE 1: Slope of Corrosion Current Density Dependence on Rotation Speed for Zn and Fe Electrodes electrode
slope, A cm-2 rpm-1/2
solution
Zn Fe Fe
4.30 × 2.73 × 10-3 6.55 × 10-3
1 M KNO3, pH 0.9 1 M KNO3, pH 0.9 dichromate, pH 0.8
10-3
current density before passivation (jcrit),17 which is about 0.2 A cm-2 for stationary Fe electrodes in nitric acid solution at pH 1.8 The dependence of the corrosion current density on the magnetic field and the corrosion pattern in magnetic field are illustrated in Figure 4a,b, respectively. The enhancement of the corrosion current produced by the magnetic field and the corrosion pattern are similar to that produced by rotating the disk electrode. Both magnetic field and rotation act in a way to enhance the convection in the vicinity of the electrode and thereby enhance the corrosion current via forced convection. Equivalence between magnetic field and rotation can be obtained from comparison between the corrosion dependence on the magnetic field and rotation. The agitation produced by a rotation speed of 200 RPM produce a corrosion current density
Rhen and Coey
Figure 2. Rest-potential dependence on the rotation speed of rotating disk electrodes made of (a) zinc, (b) iron electrodes in 1.0 M KNO3 (pH 0.9) solutions, and (c) iron in 1 M H2SO4 with 50 mM of potassium dichromate solution, all at 295 K.
equivalent to that of a 1.5 T magnetic field applied to Fe electrode corroding in 1 M KNO3 at pH 0.9. The rest potential shift dependence of iron on the applied magnetic field, ∆E0(B), is shown in Figure 5. The behavior of ∆E0(B) is similar to that of ∆E0(ω). As the magnetic field increases, the rest-potential shift increases and reaches saturation. The rest-potential shift of zinc and iron in nitrate solution show a tendency to saturate with increasing rotation speed, as can be seen in Figure 2a,b, despite the fact that the corrosion current density increases monotonically with rotation rate, Figure 1a,b, respectively. The same behavior is observed for iron in dichromate solution (Figure 2c). The rest potential of iron reaches a limiting value, ∼200 mV for nitrate (Figure 2b) and ∼80 mV for dichromate solutions, despite the fact that the cathodic current density is mass-transport-limited. Lu et al.,14 in their formulation for the rest-potential Fe in dichromate solution, assume that the corrosion is in a mixed regime (1/j ) 1/jk + 1/jL), with both kinetic and mass-transport control. They attributed the saturation of the rest potential of Fe to a transition from mixed control to kinetic control regime. However, our experimental data indicate that there is no regime transition for the cathodic current density and it remains masstransport-controlled, jcorr ∼ jL (see Figure 1c), even after the
Magnetic Field Induced Modulation of Anodic Area
Figure 3. Photographs showing the pattern created by a flow of 1 M KNO3 (pH 0.9) on the surface of Fe disk electrodes rotating at (a) 300 and (b) 3000 rpm. The grooves represent the anodic sites. The electrode diameter is 8.5 mm.
rest potential has reached saturation. Therefore, the basis of these authors formulation is invalid and no saturation of the rest potential is expected in their model. So, how then can the rest potential of the Fe or Zn electrode be limited? The saturation of the rest potential is related to the fact that the anodic current density reaches a critical value, which corresponds to critical current of passivation in the vicinity of the anodic sites. After the limiting current is reached, the anodic area expands to balance the increasing cathodic current and the rest potential no longer varies with the rotation rate. The dependence of the anodic area on magnetic field can also be explained in a similar manner. The experimental data show that the anodic area cannot be taken as constant as is usually assumed.13,14 The relative anodic area dependence for Zn and Fe (eq 7) on the rotation speed are calculated from the corresponding ia(ω)/ia(ω0) ) jcorr(ω)/jcorr(ω0) (Figure 1a,b) and ∆E0(ω) (Figure 2a,b) data with Ra ) 0.5 and shown in Figure 6a,b, respectively. Intermediate values of jcorr(ω) were obtained by linear interpolation of adjacent data points. They are quite different for the two metals. The anodic area of zinc increases with the rotation, whereas for Fe it sharply decreases. At first sight, it seems counterintuitive that the anodic area can change or be reduced with increasing rotation rate since the roughness of the electrode is expected to increase with corrosion current and time and hence with increasing rotation speed (ω). This apparent discrepancy is resolved when we consider that at a given rotation rate the anodic sites are constantly changing their position in such a way that the weak points on the surface always corrode faster, resulting in the observed increase of roughness. Since the cathodic mass transfer controls the whole reaction process, the change in anodic area is indifferent to the increasing surface roughness. Therefore the average temporal anodic area is maintained constant while the
J. Phys. Chem. C, Vol. 111, No. 8, 2007 3415
Figure 4. (a) Corrosion current dependence on the applied magnetic field for Fe in 1 M KNO3 (pH 0.9) and (b) photography of the corrosion pattern of the electrode. The electrode is facing down, and magnetic field (µoH) is applied parallel to the electrode surface. The current density is based on the nominal electrode area.
Figure 5. Rest-potential dependence on the applied magnetic field for Fe in 1 M KNO3 (pH 0.9). The magnetic field was applied vertically, parallel to the electrode surface.
spatial distribution of anodic sites changes with time. Weak regions of the surface experience large current density determining the rest-potential shift. For Fe however the anodic area diminishes, reaches a minimum, and then slightly expands with rotation speed (Figure 6b). The reduction of the anodic area at low rotation corresponds to weak sites on the electrode also experiencing large current densities, thereby accounting for a large rest-potential shift. After a limiting current density is reached, any additional increase in the cathodic current is followed by an increase in the anodic area. The behavior of the relative anodic area dependence of Fe on the magnetic field (Figure 7) is similar to the dependence on the rotation speed (Figure 6b). However, the relative anodic area does not reach such small values as those obtained using the rotating disk electrode. This may be related to the localized effect of the magnetic field, which is equivalent to a gentle
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Rhen and Coey field or by rotation of the electrode. Magnetic field and rotation induce forced convection, which increases the mass-transportlimited cathodic current and hence the overall corrosion current. The rest potential of Zn and Fe is associated with the anodic current density, and critical current density of passivation on the anodic sites determines the saturation of the rest potential. Magnetically induced convection is produced by Lorentz force acting on the ionic current flowing between anodic and cathodic sites on the electrode surface via the magneto-hydrodynamic effect (MHD).
Figure 6. Relative anodic area dependence on the rotation speed of an RDE electrode for (a) Zn and (b) Fe reconstructed from the restpotential shift and corrosion current according to eq 7. The inset in b shows the expansion of the anodic area of Fe at high rotation speeds.
Furthermore, the rest potential is correlated to the corrosion current. However an expression for the rest-potential shift dependence on the corrosion current cannot be established without prior knowledge of the anodic area dependence on the corrosion current. We introduce a model to reconstruct the relative anodic area dependence on the corrosion current, starting from the rest-potential and corrosion current dependencies on the rotation rate and applied magnetic field. The anodic area of Fe is initially found to decrease with magnetic field and rotation, whereas the Zn anodic area is found to increase with rotation. The behavior of the relative anodic area of Fe and Zn is linked to the anodic current and the anodic rest potential via an exponential function (eq 7). Therefore, if the rest potential varies faster than anodic current with rotation before saturation, which is the case for iron, the anodic area diminishes. In the case of Zn, the opposite happens and the relative anodic area increases.
Acknowledgment. This project was partially funded by PEIG Magnetics and Science Foundation Ireland (SFI).
References and Notes
Figure 7. Dependence of the relative anodic area of an iron electrode on the applied magnetic field. This curve was constructed using the corrosion current and rest-potential dependence on the magnetic field according to eq 7.
stirring in the vicinity of the electrode surface. A full description of the rest-potential dependence on the anodic corrosion current density (eq 4) requires prior knowledge of the anodic area dependence on the cathodic current. However, there is no analytical prediction of the anodic area dependence on cathodic current, and therefore a description of the dependence of the rest potential on the anodic current density requires experimental characterization, as we have shown. Conclusion The effective anodic area of Fe and Zn in acidified dichromate and nitrate solutions can be modulated by an applied magnetic
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