1996_Magnetic Field Effects in Electrochemistry_ Voltammetric Reduction of Acetophenone at Microdisk Electrodes

8/12/2019 1996_Magnetic Field Effects in Electrochemistry_ Voltammetric Reduction of Acetophenone at Microdisk Electrodes

1/10

Magnetic Field Effects in Electrochemistry. Voltammetric Reduction of Acetophenone at

Microdisk Electrodes

Steven R. Ragsdale, Jeonghee Lee, Xiaoping Gao, and Henry S. White*

Department of Chemistry, UniVersity of Utah, Salt Lake City, Utah 84112

ReceiVed: October 30, 1995; In Final Form: January 22, 1996X

The influence of an external magnetic field on the electrochemical reduction of acetophenone (AP) at Pt andAu microdisk electrodes (radii ) 0.1, 6.4, 12.5, and 25 m) is described. Voltammetric measurements inCH3CN/[n-Bu4N]PF6 solutions containing between 3 mM and 8 M AP demonstrate that the mass-transfer-limited reduction of AP at a microdisk electrode may be significantly enhanced or diminished by an externalmagnetic field, depending on the redox concentration, the electrode radius, and the angular orientation of themicrodisk relative to the field. A mechanism for the magnetic field effect is presented that considers theforce arising from the divergent radial flux of electrogenerated radical anion (AP-) through a uniform magneticfield. Viscous drag on the field-accelerated ions results in convective fluid flow that alters the rate at whichelectroactive AP is transported to the surface. Both lateral and cyclotron fluid motion can be establishedwithin a microscopic volume element (30 nL) near the electrode surface depending on the orientation ofthe magnetic field with respect to the microdisk. The earths gravitational field is demonstrated to enhanceor diminish the magnetic field-induced convective flow, depending on the relative directions of the magnetic

and buoyancy forces at the electrode surface.

Introduction

A recent preliminary report from this laboratory demonstratedthe ability to control and alter the faradaic current at an 10-m-radius Pt microdisk electrode using an externally appliedmagnetic field.1 Specifically, the mass-transport-limited ratefor the reduction of a neutral and diamagnetic species, nitroben-zene, was found to be strongly affected by a magnetic field forflux densities between 0.05 and 1 T. In addition, in ourpreliminary account, we demonstrated that the faradaic currentat the microelectrode could be either enhanced (up to 100%)

or diminished, depending on the direction of the magnetic fieldwith respect to the microdisk surface.

Although the ability to alter currents in electrochemical cellsusing magnetic fields was first demonstrated over a century ago,2

and has been investigated extensively during the past severaldecades,3-9 all previous measurements of this phenomenon haveemployed conventional macroscopic electrodes. The recentdevelopment of electrochemical techniques employing electrodeswith dimensions ranging from nanometers to micrometers hasconsiderably extended the range of materials, as well as spatialand time domains, that may be explored in electrochemistry.10-12

We envision that these microelectrode techniques may openroutes for using the dependence of faradaic currents on magneticfield strength and orientation in fundamental investigations of

chemical kinetics and transport phenomena, as well as in thedevelopment of novel analytical methods. For instance, in thecurrent report, cyclotron-like ion motion occurring in a micro-scopic solution volume near the electrode surface is shown toresult from the interaction of a uniform magnetic field with theradial-divergent fluxes of electrogenerated ions at disk-shapedmicroelectrodes. The ability to control transport processes atthe microscopic level may find application in solution-phasefocusing and trapping of electrochemically-generated ions andmolecules.

It is generally accepted that the primary effect of a magneticfield on electrochemical reactions is to alter the rate of transport

of ions in the cell. (Only a few reports of magnetic field effectson the interfacial rate of electron transfer have been reported,and these effects appear negligibly small.)13-18 In addition tothe entropic and viscous forces which control diffusion of anelectroactive species, electric (E) and magnetic (B) fields willgenerate a force on solution ions, imparting a net drift to theseions in a direction that depends on the field vectors, as well asthe charge and velocity of the ions. Classical electromagneticsgives this force in terms of the Lorentz equation

whereq is the charge on the ion andv is the velocity at whichthe ion is moving through solution. By definition, the quantityqvin eq 1 is finite in an electrochemical cell whenever a faradaicreaction is occurring. Thus, it may be anticipated that anexternally imposed magnetic field, if sufficiently large, willdirectly affect the fluxes of reactants and/or products inelectrochemical experiments.

Although eq 1 describes the interaction of the magnetic fieldwith the ionic constituents of the solution, it does not providea description of how the observed electrochemical currents maybe altered by a magnetic field. While most investigations ofmagnetic field effects have employed charged electroactivespecies as probe molecules (e.g., Cu2+, Fe(CN)64-), it has been

demonstrated in several instances, including our preliminaryreport, that the rate of transport of an electricallyneutralspeciesmay also be significantly enhanced by a magnetic externalfield.1,4c,19,20 Since the Lorentzian force acting on a neutralspecies is zero, the field-induced enhancement of the flux of aneutral molecule must occur by an indirect mechanism(s). Theconsensus on this issue among active researchers is that theobserved flux and current enhancements are associated withconvective solution flow induced by the magnetic external field.This approach is described by classical magnetohydrodynamic(MHD) theory. At a molecular level, the solution flow describedby MHD theory results from momentum transfer from field-accelerated ions to neighboring ions and solvent molecules.Consequently, MHD theory describes the overall process inX Abstract published in AdVance ACS Abstracts, March 15, 1996.

F ) q(E + v B) (1)

5913J. Phys. Chem. 1996, 100, 5913-5922

0022-3654/96/20100-5913$12.00/0 1996 American Chemical Society


2/10

terms of a magnetic body force acting on a solution element,through which a distributed and continuous current, i, passes,rather than in terms of the direct interaction of the field ondiscrete current-carrying ions. In principle, the velocity ofconvective flow and, thus, the convective-diffusion transportof electroactive ions and neutral molecules may then becomputed by solving the equation of motion (Navier-Stokesequation) encompassing the magnetic body force. In practice,MHD theory has primarily been employed to guide and interpretempirical correlations between current, field strength, and

solution composition. An alternative approach to describingthe magnetic field effect in electrochemistry, more recentlydeveloped by Olivier and colleagues, is a statistical mechanicaltreatment of the motion of individual ions which takes intoaccount their diffusional properties in the presence of a magneticfield.21 The development of this theory is motivated in part bythe failure of MHD to predict various magnetic field phenomenain dilute ionic solutions. However, to the best of our knowledge,this latter theoretical treatment has not yet been formulated interms of working equations that predict a magnetic fieldenhancement of faradaic currents.

In the present report, we present the first detailed descriptionof magnetic field effects on the steady-state voltammetricresponse at microelectrodes having radii between 0.1 and 25m. The 1-e- reduction of acetophenone (AP) in acetonitrile(CH3CN) has been used to explore the effect of an externallyapplied magnetic field on the microelectrode response as afunction of electrode radius, redox concentration, field strength,and field orientation. AP is a liquid at room temperature andis completely miscible with CH3CN. Thus, this particular redoxsystem, combined with the use of microelectrode techniques,allows magnetic field effects to be investigated over anunprecedented range of redox concentrations (3 mM to 8 MAP). This experimental capability is especially significant infundamental investigations of magnetic field effects, since ithas been reported that the largest effects of a magnetic fieldare observed in concentrated redox solutions.1,3b,4c,9 In addition,because of the small size of microelectrodes, mass transport byconvective solution flow near the electrode surface can begreatly diminished (or entirely eliminated). For instance,density-driven natural convective flow has been recentlydemonstrated to be negligibly small when the radius of themicrodisk is reduced below 5 m.22 This characteristicproperty of microelectrodes should also hold true for magneticfield-induced convective flow, thus offering an experimentalmeans of distinguishing between current enhancements resultingfrom MHD flow or the increased flux of discrete ions.

Experimental Section

A one-compartment, three-electrode cell containing a Ag/AgxO reference electrode, a Pt wire auxiliary electrode, and a

Au or Pt microelectrode was used throughout the study. Au(6.4-m nominal radius) and Pt (12.5- and 25-m radius)microdisk electrodes were constructed by sealing Au or Pt wirein a glass tube and grinding down one end of the tube to exposethe metal microdisk. Electrodes were polished with Al2O3downto 0.01-0.02m and then placed in an ultrasonic H2O bath for2 min to remove polishing debris. Smaller Pt electrodes(100 nm) were purchased from Nanomics, Inc., and used asreceived. The exposed tips of these electrodes are reported bythe manufacturer to have a cone-shaped geometry.

A GMW Associates Model 5403 electromagnet was used toapply a uniform magnetic field, B, across the electrochemicalcell (see Figure 1). The magnet poles (7.6-cm diameter) wereseparated by 2 cm. The magnetic field strength, B ) |B|,

was varied between 0 and 0.8 T by adjusting the current throughthe electromagnet. Field strength and uniformity were measuredusing a gauss meter (F. W. Bell, Model 4048). The electro-chemical cell was aligned within the electromagnet such thatthe Au or Pt microdisk electrode was positioned directly at thecenter of the poles. The magnetic field varied by less than 0.01T over a radial distance of 1 cm from the center of the poles;thus, a small error in positioning the cell has a negligible effecton the magnetic field applied across the surface of themicroelectrode. Because the electrode surface areas are very

small (


3/10

solely by the divergent radial flux of the radical anions, AP -,away from the surface.23 By convention, the direction of thecurrent vector,i, corresponds to the flow of positive charge and,thus, points in the opposite direction of the flux of the chargecarrying ions (AP-). In addition, because the outward flux ofAP- is radially symmetric about the center of the microdisk,the component of the flux parallel to the surface is zero at anydistance from the electrode. Based on these considerations, thenet current vector, i, for an electrochemical reduction at amicrodisk is directed inward toward the electrode and is

orthogonal to the surface. The angle is formally defined bythe relationshipFmag ) i(l B), wherelis the unit displacementvector that points in the direction of net positive current flow.Thus, is the angle between i and B, measured counterclock-wise from i (Figure 2a). For this geometry, ) 90.

The second electrode arrangement, shown in Figure 2b, wasused to investigate the dependence of the voltammetric currentson the angle betweeniandB. A 90bend in the glass tubingwas made such that the microdisk surface was orientedvertically. Rotation of the glass tubing allowed (defined asabove and shown in Figure 2b) to be varied in a continuousfashion between 0 and 360. was measured using ahomemade scale with an estimated error of(4.

Acetonitrile (J. T. Baker Inc., Photrex reagent) and ac-

etophenone (EM Science, 98+%) were used as received. Tetra-(n-butyl)ammonium hexafluorophosphate, [n-Bu4N]PF6, wasrecrystallized and dried under vacuum. Dilute AP solutions(e10 mM) in CH3CN/[n-Bu4N]PF6were purged with nitrogenprior to the electrochemical measurements.

Results and Discussion

In the following sections, the voltammetric limiting currentcorresponding to the reduction of AP at microdisk electrodesis shown to be strongly influenced by magnetic and gravitationalfields. Subsection Ipresents an overview of the voltammetricresponse at Au and Pt microdisk electrodes in CH3CN/[n-Bu4N]-PF6solutions containing AP, in the presence and absence of an

externally-applied magnetic field. A qualitative explainationof observed magnetic field effects is presented that is based oncurrent theory of mass-transport phenomena at microelectrodes.InSubsection II, experimental data are presented that establisha correlation between the magnetic field effect and the magni-tude of the voltammetric current measured in the absence of anapplied field. InSubsection III, the angular dependence of themagnetic field effect is described. Nonideal asymmetries inthe angular dependence are shown to arise from gravity-drivenconvective flow.

I. Voltammetric Reduction of AP in the Absence and

Presence of a Magnetic Field. The voltammetric response ofa 25-m-radius Pt disk electrode (scan rate: 20 mV/s) in anCH3CN/0.2 M [n-Bu4N]PF6 solution containing 2.0 M AP is

shown in Figure 3. The sigmoidal-shaped voltammetric wavein the absence of an applied magnetic field (B ) 0) results fromthe reversible 1-e- reduction of AP to the corresponding radicalanion,

The shape of the wave is consistent with the flux beingdominated by diffusion of neutral AP to the microdisk surface.Although a small hysteresis is observed between the forwardand reverse scans, the shape and magnitude of the waves areessentially independent of the scan rate, , for < 50 mV/s.Thus, the voltammograms shown in Figure 3 represent thediffusion-limited, steady-state response at the microelectrode.

Qualitatively similar voltammetric responses are obtained usingeither 6.4-m-radius Au and 12.5-m-radius Pt microdiskelectrodes in CH3CN solutions containing AP at concentrationsranging from 3 mM to 8.0 M (note: 8.0 M AP corresponds tosolutions containing only AP and electrolyte; i.e., no solvent ispresent).

Values ofilimmeasured using the 25-m-radius Pt microdiskare plotted in Figure 4 as a function of the redox concentration,[AP]. In the absence of a magnetic field and at low redoxconcentrations (i.e., [AP] < 0.05 M),ilimis proportional to [AP],

as expected for a diffusion-controlled reaction occurring at amicrodisk (ilimvalues for [AP] < 0.05 M are not shown in Figure4). In this concentration regime, i limis given by24

where n is the number of electrons transferred per molecule()1 for eq 2), F is Faradays constant, D is the diffusioncoefficient for AP in the CH3CN/0.2 M [n-Bu4N]PF6solution,and r0 is the radius of the microdisk. From measurements ofilim in dilute AP solutions, D is determined to be 2 10-5

cm2/s. In dilute AP solutions containing an excess quantity ofsupporting electrolyte, molecular diffusion also determines therate at which electrogenerated AP- is transported away fromthe surface.

AP + e-hAP

-(2)

Figure 3. Voltammetric response of a 25-m-radius Pt disk electrodeas a function of the magnetic field strength ( ) 90, horizontal surfaceorientation). The CH3CN solution contained 2 M AP and 0.2 M[n-Bu4N]PF6. Scan rate ) 20 mV/s.

Figure 4. Dependence of the voltammetric limiting current on theconcentration of AP in the presence and absence of an applied magnetic

field ( ) 90, horizontal surface orientation). Data correspond to thesteady-state voltammetric response at a 25-m-radius Pt disk (e.g.,Figure 3) in CH3CN/0.2 M [n-Bu4N]PF6 solutions.

ilim ) 4nFDr0[AP] (3)

Magnetic Field Effects in Electrochemistry J. Phys. Chem., Vol. 100, No. 14, 1996 5915


4/10

For a disk-shaped electrode of micrometer or smaller dimen-sions, the flux of AP- away from the electrode can beapproximated as a one-dimensional radially-divergent flux,J(r)(mol/cm2s), which decreases in proportion to the inverse ofthe distance, r, from the electrode surface.

In eq 4,Jsurfis the flux of AP- at the surface, which is definedby the limiting current (Jsurf ) ilim/r02nF). This use of the

radial-flux approximation is equivalent to modeling the micro-disk as a microhemisphere.23 In analogous fashion, theconcentration profile of AP- can be written in terms of itssurface concentration.

When the concentration of redox species is equal to or greaterthan that of the electrolyte ions (i.e., [AP] g [n-Bu4N+] ) [PF6-])0.2 M), the outward radial flux of electrogenerated AP- iscontrolled by both diffusion and migration. The migrationalflux arises when the density of supporting electrolyte ions isinsufficient to counteract the electric field engendered by theflux of AP-. HoweVer, eVen under these conditions, the

Voltammetric limiting current is still anticipated to be limitedsolely by diffusional transport of the uncharged reactant, AP,

from the bulk of the solution to the electrode surface, eq 3. Inaddition, the concentration and flux of AP- decrease as r-1,eqs 4 and 5, regardless of the relative concentrations of redoxspecies and electrolyte concentrations.25

Voltammetric measurements indicate that the dependency ofilim on redox concentration deviates from the expected linearrelationship (eq 3) when [AP] > 0.05 M. Specifically, we findthat the experimentally measured currents are significantlysmaller than the values predicted by eq 3. In addition, ilimobtains a maximum value when the concentration of theelectroactive species is 2 M. At higher concentrations (>2M), the steady-state current decreases as the concentration of

AP increases, Figure 4. This unusual dependence of ilim onredox concentration has also been observed for the reductionof nitrobenzene26 and benzophenone27 in CH3CN solutions. Themaximum in theilim-[AP] plot is due to an increase in the bulksolution viscosity at higher redox concentrations, resulting in adecrease in the rate of diffusive transport of the electroactivemolecule. Stated differently, the diffusion coefficient employedin eq 3 must be treated as a concentration-dependent variablewhen [AP] > 0.05 M. A detailed analysis of this behavior hasbeen presented in a separate report.27

Application of the magnetic field at ) 90 (horizontalsurface orientation, see Figure 2a) results in an increase in thelimiting current for AP reduction. For instance, Figure 3 showsthat an 100% increase inilimoccurs at a 25-m radius Pt disk

in a 2 M AP solution upon increasing B from 0 to 0.6 T.Although a similar field-induced enhancement ofilimis obtainedusing 6.4-m Au and 12.5-m Pt microdisks, the magnitude ofthe effect is a strong function of both the electrode radius andthe redox concentration (vide infra). Figure 4 shows thedependence ofi limon [AP] for measurements with B ) 0.7 T.Similar to the results obtained in the absence of a field, ilimreaches a maximum value when [AP] 2 M. In addition,Figure 4 demonstrates that the magnetic field effect (i.e., theenhancement in the current) is very small at both low and highredox concentrations.

The external magnetic field in our experiments is many ordersof magnitude larger than the internal magnetic field inducedby the faradaic current. By applying Amperes law to this

problem (Bdl )0ilim), and using the largest measured valueofilim(30A), we compute a maximum internal field strengthof3 10-7 T. This field is a factor of105 smaller thanthe smallest (non-zero) external field used in our investigations(0.025 T). Thus, the internal field generated by faradaic currentswill be ignored throughout our discussion.

A key component in the analysis of the observed enhancementof the current, Figures 3 and 4, is the fact that the steady-statefluxes of supporting electrolyte ions are zero, regardless of therelative concentrations of the redox species or supporting

electrolyte.23 On the other hand, electroneutrality requires thatthe charge created within the depletion layer by electrogenerationof AP- be balanced by an increase and/or decrease in theconcentrations of the supporting electrolyte cation and anion,respectively. Either of these processes may be accomplishedby the rapid transient flux of electrolyte ions on the slowtimescale of the voltammetric experiment. In dilute APsolutions, the quantity of AP- generated within the depletionlayer is small in comparison to the concentration of supportingelectrolyte, and thus, the supporting electrolyte cation and anionconcentrations in the depletion layer remain relatively unchangedfrom their bulk solution values. However, as the concentrationof AP is increased, the generation of AP- results in a significantincrease in the concentration ofn-Bu4N+ near the surface. In

the limiting case in which the bulk concentration of supportingelectrolyte is much less than that of the redox species, it can bereadily shown that electroneutrality within the depletion layeris maintained by the inward transient migration of the supportingelectrolyte cation. Thus, the following equality holds withinthe depletion layer when [AP] >> [(n-Bu4N)PF6].28

We focus our discussion on this limiting case, since the largestmagnetic field effects are observed in relatively concentratedAP solutions, Figure 4.

Based on the above description, the depletion layer at themicrodisk can be characterized as containing AP, AP-,

n-Bu4N+, and solvent. Of these, only AP and AP- have non-zero steady-state fluxes, and only AP- is electrically charged.Thus, it follows from the Lorentz equation that the only specieswhose flux may be directly altered by the magnetic field is theelectrochemical product, AP-. However, since the observedvoltammetric current is limited by molecular transport ofreactant, AP, any mechanism of the observed magnetic fieldenhancement of the current requires a description of how theinteraction of the product ion AP- with the field affects thetransport of the neutral reactant AP. We will assume that thefluxes of the electrochemical reactant (AP) and product (AP-)are coupled by convective flow resulting from viscous andelectrostatic drag by the solvent and electrolyte cationn-Bu4N+,respectively, on AP- ions accelerated by the magnetic field.

Although the effect of convective flow on voltammetric currentsis significantly reduced when employing electrodes of microme-ter dimensions, we have recently shown that density-drivennatural convection22 and forced convection29 result in measurableincreases in the limiting current at microdisks. Both naturaland forced convection increase the rate at which electrochemicalreactants (neutral or ionic) are transported to the surface. Ingeneral, the convective flow pattern at the electrode and, thus,the limiting current will depend on the electrode geometry andthe direction of the force responsible for the convection (e.g.,buoyancy force). As shown later in subsection III, the abilityto control the orientation of the magnetic field relative to themicrodisk surface provides a directional control over both theflow pattern and voltammetric current.

J(r) ) Jsurf(r0/r) (4)

[AP-

] ) [AP-

]surf(r0/r) (5)

[AP-

] [n-Bu4N+

]

5916 J. Phys. Chem., Vol. 100, No. 14, 1996 Ragsdale et al.


5/10

II. Correlation between the Magnetic Field Enhancement

and the Voltammetric Current Measured in the Absence of

a Magnetic Field. The dependency ofi limon B for a 25-m-radius disk (horizontal orientation, ) 90, Figure 2a) is shownin Figure 5 as a plot ofiB - i0vs B, where iB ) ilimmeasuredin the presence of the magnetic field and i0 ) ilim measuredwith the field off. The quantity iB - i0 represents theenhancement in the voltammetric current due to the externalmagnetic field. The curves plotted in Figure 5 correspond tosix different CH3CN solutions containing AP at concentrationsbetween 0.1 and 8 M. We observe thatiB - i0always increases

as the field strength is increased when the electrode surface ispositioned horizontally, regardless of the redox concentrationor electrode radius. Close inspection of the data plotted inFigure 5 shows that iB - i0has a slight nonlinear dependenceon B. At small B,iB - i0 increases very slowly, and in someinstances, a threshold value of B is necessary for the currentenhancement. A rapid increase in iB - i0 is observed atintermediate values ofB. Finally, at the largest fields availablefor the investigations, we observe that iB - i0 increasesapproximately linearly with B.

Figure 6 shows the results from similar experiments in whichthe concentration of AP was held constant (1 M) and theelectrode radius was varied between 6.4 and 25 m. NonlineariB - i0vs B plots were obtained for each electrode, similar in

shape to that described above. In addition, these data demon-strate that the enhancement in current drops precipitously asthe electrode radius is decreased. For example,iB - i0measuredat B ) 0.8 T is 25 times smaller for the 6.4-m-radiuselectrode than for the 25-m-radius electrode. In similarexperiments, we were unable to detect a significant magneticfield enhancement of the limiting current using a 0.1-m-radiusPt microelectrode. We note that the dependence of theenhancement of the limiting current on the microdisk radiusclosely parallels that observed for current enhancements result-ing from natural convection. In the latter case, we haveobserved that density-driven convective flow has a negligiblysmall effect on the limiting current for microdisks having radiiless that 6m.22 The similar critical values of the microdisk

radius below which an enhancement is not observed is consistentwith our contention that the magnetic field enhancement resultsfrom convective flow.

The dependencies ofiB - i0on redox concentration (Figures4 and 5) and electrode radius (Figure 6) are complex and donot readily lend themselves to the interpretation of the magneticfield effect. However, a more interesting and apparently generalrelationship exists betweeniB - i0and the value of the limitingcurrent in the absence of the magnetic field, i0. For instance,Figure 7 shows a plot of iB - i0 vs i0 constucted using datarecorded at constant flux density (B ) 0.7 T) using 6.4-, 12.5-,and 25-m-radius electrodes in solutions containing 0.01 < [AP]


6/10

current enhancement on i0 can be rewritten as (iB - i0)/i0 )

0.0675i0, it follows that both Fmag and (iB - i0)/i0 areproportional toi0. Thus, (iB - i0)/i0must also be proportionalto Fmag. This latter relationship is used in the next section todetermine the dependence ofFmagon the angular orientation.

A caveat in the above reasoning is that the transport of AP-

away from the microdisk electrode is radially divergent. Thus,both i and Fmag are position-dependent quantities that varythroughout the depletion layer. Clearly, the direction andmagnitude of the local magnetic force acting on the ionscontained within a small solution volume element will dependon the flux of ions within that volume element. For instance,as shown below, because of the symmetrical radial flux of ionsaway from a microdisk, it is possible for the net magnetic forcesummed over all current carrying ions to be zero, although the

force on individual ions remains finite. This situation is notencountered using macroscopic planar electrodes, where thecurrent and ion fluxes may be assumed to be essentially uniformand independent of spatial position in a steady-state voltam-metric measurement. However, several interesting phenomenaarise due to the spatial dependency of the ion flux near amicrodisk electrode. As detailed in the following section, theseeffects are readily explored by examining the dependence ofiB- i0 on the orientation of the magnetic field relative to theelectrode surface.

III. Angular Dependence of the Magnetic Field Effect.

The effect of varying the orientation of the external magneticfield, relative to the electrode, on the magnetic force exertedon ions within the depletion layer is qualitatively depicted in

Chart 1. The top drawing in Chart 1 shows a situation in whichthe magnetic field is oriented parallel to the disk surface,corresponding to ) 90. To determine the direction of themagnetic force at any point in solution, we recall that electro-generated AP- is transported away from the microdisk surfacein a quasi-radial pattern and that the direction of positive currentopposes that of the anion flux (i.e., positive current is directedinward toward the surface for this reaction). The direction ofthe magnetic force within any volume element in the depletionlayer is then determined from eq 1. For B parallel to theelectrode surface, Fmagpoints from left to right for essentiallyall regions of the solution layer adjacent to the electrode. Thus,the magnetic force tends to accelerate essentially all productions from left to right across the electrode surface. (This

description is not exactly correct; upward- and downward-directed forces occur near the left- and right-hand edges of theelectrode, respectively, as shown in the schematic drawing.) Inaddition, because of the radial divergence of the flux of AP-,the current density at any point in solution is approximatelyinversely proportional to the distance from the electrode at thatpoint, eq 4. Thus,Fmagfor any solution element is also expectedto decay rapidly as one moves from the electrode surface intothe bulk solution. Consequently, the magnetic force acting onthe charge-carrying ions is localized to the depletion layer region

adjacent to the microdisk surface. Arbitrarily defining thedepletion layer thickness,, as being equal to the distance awayfrom the surface where the current density falls to 10% of itsvalue at the surface, we calculate 250 m for a 25-m-radius microdisk. Thus, assuming a hemispherical depletionlayer geometry, the magnetic field effect is localized to asolution element of30 nL.

In analogous fashion, when B is oriented perpendicular tothe electrode surface (bottom of Chart 1, corresponding to )180), AP- will again be accelerated in a direction parallel tothe surface. However, the magnitude and direction of the forcefor this orientation vary as a function of the distance from theelectrode and the position across the electrode surface. For

instance, from electrostatics, the current flowing into anequipotential surface (e.g., the microdisk surface) must bedirected orthogonal to the surface. Thus,B will be parallel tothe flux of AP- in the solution element immediately adjacentto the surface. Consequently, the magnetic force will vanishin this region. For the same reason, Fmagis zero for solutionelements situated directly on the flux line defined by the centeraxis of the electrode. In addition, and as previously discussed,the current density and magnetic force rapidly decay as onemoves toward the bulk of the solution. On the other hand,Fmagwill have a finite value for positions off of the center axis (i.e.,toward the edge of the electrode) and at intermediate distancesfrom the surface. However, because of the symmetrical radialdiffusion pattern established at a microdisk, the direction of the

force rotates as one moves in a circular direction at a fixeddistance from the centerline axis. Consequently, the magneticfield will induce a net rotational motion (about the center ofthe electrode) of electrogenerated AP- as this species diffusesradially away from the electrode surface. BecauseFmagis zeroat the center of the electrode, as well as directly on the electrodesurface and at distances far from the electrode, only the ionswithin a doughnut shaped solution volume directly above theelectrode will be accelerated by the magnetic field. Within thisdoughnut-shaped volume, the net effect of the field will inducea rotational or cyclotron-like convective flow. It is importantto note here that this motion is superimposed on the normaldiffusion/migration of product ions away from the electrode.Thus, although the magnetic field will induce a net rotational

motion of the fluid above the electrode surface, individual ionswill not remain indefinitely in a circular path. Instead, radialdiffusion and migration, coupled with the rotational convectiveflow, must result in electrogenerated AP- being transported(on average) along a helical path that spirals outward away fromthe electrode surface.

The above concepts were explored by measuring the volta-mmetric limiting current as a function of the angular orientationusing the electrode geometry depicted in Figure 2b. Rotationof the bent microdisk electrode allows the angleto be variedbetween 0 and 360(see Experimental Section). Parts a and bof Figure 8 show the dependence of voltammetric currents on for different field strengths and electrode radii, respectively.The data were plotted as (iB - i0)/i0 vs , where (iB - i0)/i0

CHART 1: Direction of Magnetic Force (Indicated byArrows) on Electrogenerated Ions at a MicrodiskElectrodea

a Top: magnetic field parallel to the electrode surface. Bottom:magnetic field perpendicular to surface. Lines originating on theelectrode surface represent the diffusion-migration paths of electro-chemically generated anions. By convention,positiVe current flows intothe surface for an electrochemical reduction.



7/10

represents the enhancement in current normalized to the currentin the absence of the field. As shown in the previous section,the quantity (iB - i0)/i0is linearly related to the magnetic forceacting on the depletion layer. This representation of the dataalso allows the dependence of the magnetic field effect on tobe more easily visualized on the same plot for different fieldstrengths and electrode radii. All data were recorded forsolutions containing either 2 M (Figure 8a) or 1 M (Figure 8b)AP.

The results shown in Figure 8 demonstrate that the magnetic-field-induced enhancement of the current is largest at either )90 or 270. Both of these angles correspond toB parallelto the electrode surface (see top drawing in Chart 1). The

occurrence of maxima in (iB - i0)/i0 at ) 90 and 270 isclearly independent of B or the electrode radius. At anglesintermediate of ) 90 and 270, the enhancement in the currentrapidly decays. In some data sets, negative values of (iB -i0)/i0are observed at angles near ) 0 and 180, correspondingtoB directed normal to the electrode surface (bottom drawingof Chart 1). A negative value of (iB - i0)/i0 indicates thatapplication of the magnetic field results in a decrease in thevoltammetric limiting current.

A surprisingly large asymmetry in the angular dependenceis apparent in the results shown in Figure 8. Specifically, valuesof (iB - i0)/i0 decrease very rapidly at angles slightly off of90, producing a sharper maxima in (iB - i0)/i0at 90 than at270. This result is unexpected since the magnitude of the

magnetic force acting on the electrogenerated ions within thedepletion layer is expected to be identical for any two valuesof that differ by exactly 180. Of course, the direction ofFmagwill depend on, i.e., Fmagis directed upward for 0 < < 180 and downward for 180 < < 360. However, thevoltammetric current should be the same for these two orienta-tions since the magnetic force magnitude and resulting convec-tive flow pattern should be identical in both cases. Clearly,the apparent asymmetry in Figure 8 must arise from forces otherthanFmag.

Figure 9 demonstrates that the asymmetry in the angulardependence is also a strong function of the concentration ofthe redox species. For AP concentrations greater than5 M,(iB - i0)/i0is positive for 0 < < 180 and negative for 180

< < 360. At [AP] ) 5 M, positive values of (iB - i0)/i0areobserved at values of near 270; however, the maxima in (iB- i0)/i0are more sharply peak shaped at 270than at 90. Thisparticular feature is reversed at lower concentrations (e.g., [AP]) 1 M), where the enhancement in current is more broadlydistributed around ) 270 than at ) 90. At intermediateredox concentrations ([AP] ) 3.5 M), the plot of (iB - i0)/i0vs has a more symmetrical shape.

The concentration-dependent asymmetry in the angulardependence of (iB - i 0)/i0 can be qualitatively understood byconsidering the combined effects of the applied magnetic fieldand the earths gravitational field.30 In a recent report, we

demonstrated that natural convection occurs at microdiskelectrodes (6.4-25-m radius) when the electrochemical reac-tion yields a product species that changes the solution densitynear the electrode surface. For instance, natural convectionaccounts for 15% of the total steady-state limiting current ata 25-m-radius Pt disk for the oxidation of 0.5 M Fe(CN)64-

in aqueous solutions.22

The influence of natural convection, in the absence of amagnetic field, on the reduction of AP was demonstrated in thecurrent investigation using a microelectrode bent at 90 andinserted horizontally into the electrochemical cell, as depictedin Figure 10. Rotation of this electrode allows the angle between the gravitational field, g, and the electrode surfacenormal,n to be varied over 360. The convention used in our

Figure 8. Angular dependence of the magnetic field effect (i.e., (iB -i0)/i0vs ) as a function of (a) field strength and (b) electrode radius.Data in part a correspond to CAP ) 2 M and ro ) 12.5m. Data in partb correspond to [AP] ) 1 M and B ) 0.7 T.

Figure 9. Dependence of (iB - i0)/i0 on as a function of APconcentration. Data correspond to steady-state voltammetric limitingcurrents measured at a 25-m-radius Pt microdisk electrode in CH3-CN/0.2 M [n-Bu4N]PF6solutions,B ) 0.7 T. The solid horizontal lineis where (iB - i 0)/i0 ) 0.

Figure 10. Schematic drawing depicting the rotation of a microdiskelectrode in the earths gravitational field, g. The electrode is insertedhorizontally into the cell and rotated about the angle defined by theelectrode surface normal,n, andg; ) 0corresponds to the electrodefacing downward.



8/10

investigations is that ) 0when the disk is facing downward

(i.e., n and g in the same direction).Voltammetric currents at a 25-m-radius Pt disk were

recorded for 0 < < 360 in CH3CN/0.2 M [n-Bu4N]PF6solutions containing between 2 and 8 M AP. The results areshown in Figure 11 as plots of (ig - i0)/i0, where igrepresentsthe limiting current at an arbitrary angle and io' representsthe current at ) 0. A positive value of (ig - i0)/i0indicatesthat the current measured at the angle is greater than at )0; conversely, a negative value indicates that the current issmaller than at ) 0. By definition, and as indicated in Figure11, (ig - i0)/i0 is equal to zero at ) 0. A non-zero valueof (ig - i0)/i0 indicates that natural convection makes asignificant contribution to the flux of AP. Inspection of Figure11 reveals that natural convection accounts for up to 15% of

the total flux of the reactant for the reduction of AP at a 25-m-radius disk.

The data plotted in Figure 11 suggest that natural convectivetransport has a complex dependence on the redox concentrationas well as . For [AP] ) 5 and 8 M, maxima in the limitingcurrent occur when the electrode is oriented in the verticalposition (i.e., ) 90 and 270). The current is also larger at ) 180 (electrode directed upward) than at ) 0. Theobserved behavior is consistent with the hypothesis that thereduction of AP results in a solution near the electrode surfacethat is less dense than the bulk solution. When the electrode isoriented at 180, the less dense depletion layer will tend to rise,resulting in the convective flow of fresh solution inward alongthe surface of the glass sheath surrounding the microdisk, Chart

2. Convective flow will increase mass transport of AP to theelectrode, resulting in an increase in the limiting current.Conversely, at ) 0, the convective upward flow of the lessdense depletion layer will be inhibited by the solid electrodesurface, resulting in little, if any, increase in the mass-transportrate. Completely analogous behavior has been observed for theoxidation of Fe(CN)64-.22

At AP concentrations below 3.5 M, a different dependenceof limiting current on is observed. For instance, at [AP] )2 M, the current at ) 0 is greater than that at ) 180,indicating that the density of the depletion layer is greater thanthat of the bulk solution. Thus, when the electrode is orienteddownward ( ) 0), the depletion layer sinks under the influenceof the gravitational force, resulting in an increase in limiting

current. Conversely, at ) 180, the electrode surface inhibits

fluid convection.The above results suggest that there is an inversion of the

relative densities of the depletion layer and bulk solution asthe redox concentration increases. Specifically, the data areconsistent with Fbulk > Fsurfat high redox concentrations andFbulk< Fsurfat low redox concentrations (where Fbulkand Fsurfrepresent the bulk and near-surface fluid densities). The resultsindicate the existence of an intermediate AP concentration whereFbulk ) Fsurf. Indeed, Figure 11 shows that the limiting currentis essentially independent of in solutions containing 3.5 MAP. Thus, at this particular concentration, the gravitational forceacting on the depletion layer is essentially zero, and the naturalconvection component of the current is correspondingly verysmall. Chart 2 summarizes the relative magnitude and direction

of the buoyancy forces acting on the depletion layer at low,intermediate, and high AP concentrations.

The asymmetry observed in the dependence of limitingcurrents on B, Figure 9, can be understood by assuming thatthe enhancement in current is proportional to the absolute valueof the total force acting on the depletion layer

whereFTcomprises both the magnetic and gravitational forces.

The absolute value ofFTis used in eq 6 since the enhancementin current that results from convection should be independentof the flow direction (e.g., (iB - i0)/i0 must be identicalregardless of whether FT points upwardly or downward).

In measuring (iB - i0)/i0 as a function of, Figure 9, thegravitational force, Fg, remains constant, since ) 90 for allvalues of. As a zero-order approximation, we assume thatFg is proportional to the measured enhancement in currentmeasured at ) 90 in the absence of a magnetic field, i.e.,

The magnetic force component of the total force can bewritten as

Figure 11. Dependence of normalized current enhancement, (ig - i0)/i0, as a function of the angle . Data correspond to the steady-statevoltammetric reduction of AP at a 25-m-radius Pt disk in CH3CNsolutions containing 0.2 M [n-Bu4N]PF6. i0 corresponds to thevoltammetric current measured at ) 0 (i.e., the surface normal ispointing in the same direction as g). The concentration of APcorresponding to each data set is indicated on the figure.

CHART 2: Qualitative Representation of BouyancyForces Acting on the Depletion Layer at a MicrodiskElectrode during the Steady-State Reduction of APa

a The lengths of the arrows indicate the relative magnitudes of theforce at different AP concentrations.

(iB - i0)/i0 |FT| (6)

FT ) Fmag + Fg (7)

Fg (ig - i0)/i0 (8)

Fmag ) Fmag( ) 90)sin (9)



9/10

where Fmag( ) 90) is the magnetic force at ) 90. ThequantityFmag( ) 90) cannot be directly measured because ofthe interfering effects of the gravitational field, which is alwayspresent. However, an estimate ofFmag( ) 90) can be obtainedby subtracting the component of the enhancement in currentdue to the gravitational force, (ig - i0)/i0, from the totalenhancement measured at ) 90, i.e., [(iB - i 0)/i0]90.

Thus, Fmag (eq 9) at any arbitrary angle is obtained bycombining eqs 9 and 10.

Assuming that the proportionality constants in eqs 8 and 11are nearly equal, the total force, FT, can be estimated fromexperimental data (Figures 9 and 11).

In Chart 3, we have used the above analysis to qualitativelydraw the directions and magnitudes of the vectors Fmagand Fgas a function of for solutions containing high (8.0 M),intermediate (5 M), and low (0.3 M) AP concentrations.Addition ofFmagand Fg(eq 7) yields the total force acting onthe depletion layer. The absolute value of the total force, |FT|) |Fmag + Fg|, which is the operative parameter in determiningthe observed enhancement of the current in the presence of bothgravitational and magnetic fields, eq 6, is shown in Chart 3.The solid horizontal line in the schematic represents zeroabsolute force; because gravity cannot be turned off duringthe measurement of the reference current, i0, the gravitationalforce, |Fg|, must be added to zero total force in order to comparethe relative angular dependencies of the |FT| and experimentalvalues of (iB - i0)/i0. Thus, the dashed horizontal lines in Chart3 show the baselines for |FT| after correcting for |Fg|.

For [AP] ) 8.0 M (part a of Chart 3), the absolute value ofFT(measured against the experimental reference frame (dashedline)) has a sinusoidal dependence on , with a maximum at90and minimum at 270. Based on the assumption that (iB -

i0)/i0is proportional to |FT|, maximum and minimum values of(iB - i0)/i0 are expected at ) 90 and 270, respectively, insolutions containing 8 M AP. This behavior is clearly observedin the experimental results shown in Figure 9. For [AP] )5M (part b of Chart 3), the absolute value of total force displaysmaxima at 90 and 270with the maximum at 90being slightlymore pronounced. For [AP]) 0.3 M (part c of Chart 3), themaxima are shown at 90 and 270, but the maximum at 270ismore pronounced. These patterns also closely approximate theexperimental results for [AP] ) 5 and 0.3 M shown in Figure9. Therefore, the asymmetry between the rise around 90 and270is well explained by the relative direction and magnitudeofFmagand Fg for all [AP].

The above analysis of FT was performed for solutionscontaining between 0.3 and 8 M AP, with the results shown inFigure 12. These computed curves should be directly comparedwith the experimental results shown in Figure 9. Although thisanalysis is highly approximate, it clearly captures essentiallyall of the qualitative concentration-dependent asymmetriesobserved in the dependence of (iB - i0)/i0on . These resultsalso provide a physical explanation of the field-induceddiminishment of the limiting current (i.e., negative values of(iB - i0)/i0). When Fmag and Fg are aligned parallel to eachother, but in opposite directions, the absolute value of the totalforce |FT| will be smaller than the magnitude of Fg in theabsence of the magnetic field (for example, at ) 270in the8.0 M AP solution). Thus, the magnetic force reduces convec-

tive mass transport of the electrochemical reactant to theelectrode surface.

Conclusion

We have demonstrated that an externally-applied magneticfield can significantly enhance or diminish the voltammetriclimiting current at microdisk electrodes having radii g 6 m.The magnetic field effect results from convective flow, engen-dered by viscous drag on the electrochemical product ions whichare accelerated by the magnetic force. An empirical correlation,iB - i0 i02, has been established between the magnitude ofthe current at a microdisk in the absence of the field and theenhancement of the current resulting from the externally-appliedmagnetic field. This correlation provides a basis for observa-

CHART 3: Qualitative Description of the Total Force,|FT|, Responsible for the Observed Enhancement orDiminishment of the Limiting Current as a Function ofAngle a

a

Part a corresponds to a high [AP], where the net bouyancy force,Fg, is directed upward and is larger than the magnetic force, Fmag. Partb corresponds to the intermediate [AP], where Fg is directed upwardand smaller than Fmag. Part c corresponds to low [AP], where Fg isdirected downward and is smaller than Fmag.

Fmag( ) 90) [(iB - i0)/i0]90 - (ig - i0)/i0 (10)

Fmag {[(iB - i0)/i0]90 - (ig - i0)/i0}sin (11)

Figure 12. Dependence of|FT| onas a function of AP concentrationcomputed from Fmag (eq 8) and Fg (eq 11) (see text). The dashedhorizontal line corresponds to |FT| ) |Fg|, measured relative to theexperimental reference frame.



10/10

tions of negligible magnetic field effects at very low and veryhigh redox concentrations (i.e., conditions where i0 is small).

The magnetic-field-induced diminishment of limiting currentsat specific angular orientations and redox concentrations hasbeen shown to result from partial cancellation of the gravitationalforce by the magnetic force. The ability to enhance or diminishconvective mass transport in microscopic domains using anexternal field may find application in analytical measurementsand in electrochemical synthesis of metal and semiconductingdeposits under highly controlled conditions.

Acknowledgment. This work was supported by the Officeof Naval Research (ASSERT).

References and Notes

(1) Lee, J.; Gao, X.; Hardy, L. D. A.; White, H. S. J. Electrochem.Soc. 1995, 142, L90.

(2) (a) Bagard, H. C. R. Acad. Sci. 1896, 122, 77. (b) Bagard, H. J.Phys. 1896, 5, 3, 499.

(3) (a) A review of the effects on imposed magnetic fields inelectrochemical processes is found in: Fahidy, T. Z.J. Applied Electrochem.1983, 13, 553. (b) Mohanta, S.; Fahidy, T. Z. Can. J. of Chem. Eng.1972,50, 248. (c) Mohanta, S.; Fahidy, T. Z. Electrochim. Acta1976,21, 25. (d)Quraishi, M. S.; Fahidy, T. Z. Electrochim. Acta1980,25, 591. (e) Gu, Z.H.; Fahidy, T. Z. J. Electrochem. Soc. 1987, 134, 2241. (f) Fahidy, T. Z.

Electrochim. Acta 1990, 35, 929.

(4) (a) Olivier, A.C. R. Acad. Sci.1970,271, 529. (b) Peyroz-Tronel,E.; Olivier, A. J. Chim. Phys. 1980,77, 427. (c) Olivier, A.; Chopart, J. P.;Douglade, J.; Gabrielli, C.J. Electroanal. Chem.1987,217, 443. (d) Olivier,A.; Chopart, J. P.; Douglade, J.; Gabrielli, C.; Tribollet, B. J. Electroanal.Chem.1987,227, 275. (e) Aaboubi, O.; Chopart, J. P.; Douglade, J.; Olivier,A.; Gabrielli, C.; Tribollet, B. J. Electrochem. Soc. 1990, 137, 1796.

(5) (a) Iwakura, C.; Edamoto, T.; Tamura, H. Denki Kagaku 1984,52, 596. (b) Iwakura, C.; Edamoto, T.; Tamura, H. Denki Kagaku 1984,52, 654. (c) Iwakura, C.; Kitayama, M.; Edamoto, T.; Tamura, H.

Electrochim. Acta 1985, 30, 747.(6) (a) Gak, E. Z.; Krylov, V. S.Elektrokhim. 1986,22, 829. (b) Gak,

E. Z.; Rokminson, E. K.; Bondarenko, N. F. Elektrokhim. 1975, 11, 529.

(c) Gak, E. Z. Elektrokhim. 1967, 3, 263.(7) Waskaas, M.J. Phys. Chem. 1993, 97, 6470.(8) Lielmezs, J.; Musbally, G. M. Electrochim. Acta 1972, 17, 1609.

(b) Lielmezs, J.; Aleman, H.Electrochim. Acta1976,21, 273. (c) Lielmezs,J.; Atwal, V.; Aleman, H. J. Electrochem. Soc. 1990, 137, 3809.

(9) Watanabe, T.; Tanimoto, Y.; Sakata, T.; Nakagaki, R.; Hiramatsu,M.; Nagakura, S. Chem. Soc. of Jpn. 1985, 58, 1251.

(10) Bond, A. M.; Fleischmann, M.; Robinson, J.J. Electroanal. Chem.1984, 180, 257.

(11) Howell, J. O.; Wightman, R. M. Anal. Chem. 1984, 56, 524.(12) Smith, C. P.; White, H. S. Anal. Chem. 1993, 65, 3343.(13) Kelly, E. J. J. Electrochem. Soc. 1977, 127, 987.

(14) Danilyuk, A. L.; Kurmashev, V. I.; Matyushkov, A. L.Thin SolidFilm 1990, 189, 247.

(15) Gu, Z. H.; Olivier, A.; Fahidy, T. Z. Electrochim. Acta 1990, 35,933.

(16) Chopart, J. P.; Douglade, J.; Fricoteaux, P.; Olivier, A. Electrochim.Acta 1991, 36, 459.

(17) Fricoteaux, P.; Olivier, A. J. Electrochem. Soc. 1992, 139, 1096.(18) Gu, Z. H.; Chen, J.; Fahidy, T. Z. Electrochim. Acta 1993, 38,

2631.(19) Mogi, I.; Kido, G.; Nakagawa, Y.Chem. Soc. Jpn. 1990,63, 1871.(20) Amarasinghe, S.; Leddy, J. J. Am. Chem. Soc. 1994,(21) Tronel-Peyroz, E.; Olivier, A.; Phys.-Chem. Hydrodynam. 1982,

3, 251.(22) Gao, X.; Lee, J.; White, H. S. Anal. Chem. 1995, 67, 1541.(23) Oldham, K. B. J. Electroanal. Chem. 1988, 250, 1.(24) Saito, Y.ReV. Polarogr. 1968, 15, 177.(25) Amatore, C.; Fosset, B.; Bartlet, J.; Deakin, M. R.; Wightman, M.

R. J. Electroanal. Chem. 1988, 256, 255.(26) Malmsten, R. A.; White, H. S. J. Electrochem. Soc. 1986, 133,

1067.(27) Okerlund, N.; Paulson, S.; White, H. S. Anal. Chem., in press.(28) Morris, R. B.; Fischer, K. F.; White, H. S. J. Phys. Chem. 1988,

92, 5306.(29) Gao, X.; White, H. S. Anal. Chem. 1995, 67, 4057.(30) Iwakura et al. (ref 5) also considered the combined influence of

graviational and magnetic fields on the voltammetric currents at macroscopicelectrodes.

JP9532024


Documents

1996_Magnetic Field Effects in Electrochemistry_ Voltammetric Reduction of Acetophenone at Microdisk Electrodes