Anal. Chem. 1995,67, 561-569
Interferometric Measurement of Depletion Layer Structure and Voltammetric Data in Concentrated Organic Redox Solutions QiangminLi and Henry S. White* Department of Chemistry, Henry Eyring Building, University of Utah, Salt Lake Cily, Utah 841 12
Phase-measurementinterferometric microscopy (PMIM) of the depletion layer surrounding 15-pm-radiusPt disk electrodes is described. PMIM images record spatial variations in the optical height (Ah)resulting h m refractive index gradients generated by an electrochemical reaction. Images obtained during the voltammetric reduction of 0.1- 1.5 M nitrobenzene in benzonilrile solutions containing 0.2 M tetra-n-butylammoniumh d u orophosphate are compared to predictions based on the Lorenlz-Lorenz formula and Saito’s analysis of transport to a disk-shaped electrode. Good agreement between theory and experimentis obtained at distances within f10 radii of the electrode; at larger distances, density-driven fluid convection reduces the refractive index (and concentration) gradients to negligible values. Optical voltammograms, i.e., plots of Ah vs electrode potential (E), are shown to faithfully mimic the true i-E response, allowing a purely optical measurement of the electrochemical response of a microdisk electrode. In recent reports, we have shown that it is possible to perform quantitative investigations of electrochemical phenomena in solutions containing unusually high concentrations (1-10 M) of an electroactive species. Examples of these studies include the electroreductions of 4-cyanobenzene’ and nitrobenzene2at 12.5 pm-radius platinum microdisks. Well-behaved, sigmoidal-shaped voltammograms are observed for the oneelectron reduction of these organic compounds, even in the absence of an inert diluting solvent. Extension of electroanalyticalmeasurements to the highconcentration regime allows electron-transfer reactions to be investigated under solution conditions that closely mimic those found in industrial technologies. This capability is particularly relevant in the scale-up of commercially promising electrosynthetic reactions. The ability to perform electrochemical investigations in concentrated solutions, without encountering insurmountableohmic potential losses, is a result of the convergent flux of supporting electrolyte counterions (typically present in our experiments at 0.1 M levels) to the microelectrode ~urface.~ A key issue in these investigations is whether or not the transport equations routinely employed in investigations of a dilute solution of redox species are applicable at high concentrations. In the case of a dilute redox species (e.g., 5 mM), the limiting current (id for a diffusion(1)Moms, R B.; Fischer, K F.; White, H. S. J. Phys. Chem. 1988,92,3506. (2) (a) Malmsten, R A; White, H. S.J. Electrochem. SOC.1986,133,1067. &I) Norton,J. D.; Anderson, S. A; White, H. S.J. Phys Chem. 1992,96,3. (3) Oldham, K B. J. Electroanal. Chem. 1988,250,1. 0003-2700/95/0367-0561$9.00/0 Q 1995 American Chemical Society
controlled process at a microdisk electrode is given by
ili, = 4nFDc*ro
where n is the number of electrons transferred per molecule, r, is the electrode radius, D is the diffusion constant of the reactant, F is Faraday’s constant, and c* is the bulk reactant concentration! Application of eq 1is questionable for the situation in which no solvent, or very little, is present in the solution. Under these conditions, the oxidation or reduction of the concentrated redoxactive component results in generation of molar quantities of a product, and it is reasonable to anticipate that the physical properties (e.g., viscosity) of the depletion layer region adjacent to the electrode surface may differ signiscantlyfrom those of the bulk solution. Direct evidence for such effects in voltammetric experiments’ has recently been obtained from electrochemical quartz crystal measurements of the potential-dependent solution density 6)and viscosity (7). In these experiments, changes in the oscillation frequency of the quartz crystal during oxidation or reduction of a soluble redox species reflect an increase or decrease in within the depletion layer and are readily detectable in solutions containing relatively low redox concentrations (20 mM) . Evidence for nonideal depletion layer properties is also apparent in the highly nonlinear dependence of ili, on the concentrationof redox-active species. For instance, for the reduction of nitrobenzene (NB e- NB-) in acetonitrile solutions containing 0.2 M tetra-n-butylammoniumperchlorate as supportingelectrolyte, the maximum limiting current occurs at a NB concentration of only -2 M.6 Further increases in the concentration result in a significant decrease in &, and in undiluted NB solutions (corresponding to a redox concentrationof 9.7 M), ili, is only -‘/3 of the value obtained at 2 M. Clearly, eq 1 does not accurately describe the dependence of current on the redox concentration in the highconcentration regime. Although the i-E response of microelectrodes reveals nonideal behavior in the highconcentration range, insight into the underlying causes can only be obtained through direct measurement of the properties of the solution near the electrode surface. Several analytical methods have recently been developed that allow in situ measurement of the redox concentration profiles within the depletion layer, as well as other pertinent physical properties.
+
-
(4) S i b , Y Rev. Polarogr. 1968,15,177.
(5) Lee, W.-W.; Ward, M. D.; White, H.S. Anal. Chem. 1993,65,3232. (6) Malmsten, R A; Smith, C. P.; White, H. S. J Electroanal. Chem. 1986, 215,223.
Analytical Chemistry, Vol. 67, No. 3, February 1, 1995 561
c
- ZDa
8
zo
Figure I. (Top) Schematic diagram of the depletion layer region surrounding an inlaid microdisk electrode. Vertical lines indicate the optical path of the laser employed in interferometric imaging. The optical reference plane is assumed to be located at a distance (2) sufficiently far from the electrode surface (a) that the concentration gradients of the electrochemical reactants and products are negligibly small. (Bottom) Cylindrical coordinate system.
McCreery and co-~orkers,~ and others! have developed spatially resolved absorption spectroscopy (SRAS) to probe concentration profiles within the depletion layer. Absorption measurements have high sensitivity and selectivity and are relatively rapid, but deviations from the required assumption of a linear dependence of absorption on concentration occur at high concentrations. Scanning electrochemical microscopy (SECM),gin which a small metal tip is placed within the depletion layer, has also been used by Engstrom and cc-workers and ourselves to measure concentration profiles surrounding microdisk electrodes'O and pores in biological membranes." However, at small separation between the tip and surface, the SECM tip blocks the transport of electroactive species, altering the profiles that are being measured. In this report, we describe the use of interferometric microscopy for measuring optical distances, Ah, across the depletion layer surrounding a microdisk electrode and demonstrate that spatial variations in the measured values of Ah can be used to determine the structure of the depletion layer. The schematic diagram in Figure 1 shows the essential features of our strategy. We consider a microdisk electrode that is shrouded in an insulating material and poised at a potential such that reduction or oxidation of a redox species occurs. For a small disk-shaped (7) (a) Deputy, A; Wu, H.-P.; McCreery, R L. J Phys. Chem. 1990,94,3620. (b) Wu, H.-P.; McCreery, R L. J Electrochem. SOC.1989,136, 1375. (8) (a) Fosdick, L. E.; Anderson, J. L. Anal. Chem. 1982, 54, 2560. (b)
Fukunaka, IC;Denpo, IC;Iwata. M.; Maruoka, K; Kondo, Y.]. Electrochem. SOC.1983,130, 2492. (9) Bard, A J.; Fan, F.-R F.; Pierce, D. T.; Unwin, P. J.; Wipf, D. 0.;Zhou, F. Science 1991,254, 68. (10) (a) Engstrom, R C.; Meaney, T.; Tople, R ; Wightman, R M. Anal. Chem. 1987,59, 2005. (b) Engstrom, R C.; Weber, M.; Wunder, D. J.; Burgess, R; Wmquist, S. Anal. Chem. 1986,58,844. (11) (a) Scott, E. R; White, H. S.; Phipps, J. B. Solid State Ionics 1992,53-56, 176. (b) Scott, E. R; White, H. S.; Phipps, J. B. Anal. Chem. 1993,65, 1537. (c) Scott, E. R; White, H. S.; Phipps, J. B. Pharm. Res. 1993,10, 1699.
562 Analytical Chemistry, Vol. 67, No. 3, February 1, 1995
electrode, the concentration of the electroactive reactant has an approximately inverse dependence on the distance from the electrode surface. Since, to a very good approximation, the refractive index, n, of a solution is determined by the concentrations of the various solution components and their molar refractivities (through the Lorentz-Lorenz formula12 ), a local change in the composition of the solution resulting from a faradaic reaction will induce a corresponding change in the local refractive index. The gradient in the refractive index, as a function of position within the depletion layer, will track the gradients of the concentrations of the redox species, being largest at the electrode surface and decreasing to zero in the bulk solution. Using standard interferometric techniques, optical distances can readily be resolved to within 1 nm and better. Indeed, interferometric techniques have been used for decades to measure variations in refractive index near large planar electrode^.'^ In order to measure the spatial dependence of Ah with high resolution, it is necessary to couple the interferometric technique with optical imaging microscopy. In several reports, we have described the use of phase-measurement interferometric microscopy (PMIM) for ex situ and in situ imaging of electrode surfaces. PMIM is a noncontacting microscopy that employs a dynamic phase-measurement technique to determine spatial variations in optical distances between the microscope objective and test sample (see Experimental Section). In context of the microelectrode geometry shown in Figure 1,the optical distance, measured normal to the electrode surface (2-direction) will be a function of the radial distance, r (measured from the center of the electrode), if the electrochemical reaction causes a change in the optical properties of the solution. For example, if the product of the electrochemical reaction has a larger molar refractivity than that of the reactant, the optical distance between 2, and 2, will be largest at the center of the electrode and decrease as a function of r. Ultrahigh vertical resolution (0.5 A) and a large field of view make PMIM an ideal technique for studying spatial variations in the solution refractive index. For a microdisk electrode, the instrumental capabilities of PMIM allow quantitative analysis of the depletion layer structure at distances of up to 50 radii away from the electrode (vide infra). We report PMIM images of the depletion layer, obtained during reduction of 0.01-1.5 M nitrobenzene and show that the results are in good agreement with theoretical predictions computed by employing the LorentzLorenz formula and Saito's equation for concentration profles near a microdisk ele~trode.~ Agreement between experiment and theory breaks down at distances greater that -10 radii from the electrode due to free fluid convection. In addition to analysis of the depletion layer structure, we demonstrate that the voltammetric response of a microelectrode can be obtained using interferometric microscopy, providing a purely noncontacting optical method of obtaining i-E data. EXPERIMENTAL SECTION Apparatus. AU measurements were made with a Zygo Maxim
3D laser model 5700 Interferometric Microscope (Middlefield, CT), hereafter referred to as a phasemeasurement interferometric microscope (PMIM). A detailed description of the microscope (12) Born, M, Wolf, E. Principles of Optics, 2nd ed.; Pergamm Press: NewYork, 1964. (13) Srinivasan, V. S. Adu. Electrochem. Electrochem. Eng, 1973 9,369.
HElNE
BEAMSPLllTER
MlRAU MICROSCOPE REFERENCE SURFACE AND BEAMSPLIllER
PIEZOELECTRICTRANSDUCER
SUBSTRATE
Figure 2. Schematic diagram of phase-measurement interferometric microscope.
is presented elsewhere;14only a brief outline of the measurement theory is presented here. Light emitted by a l-mW He-Ne laser (1= 632.8 nm) passes through a Mirau interferometricobjective (Figure 2) and illuminates a -0.04cm2 region of the electrode surface and surrounding insulation. The bottom of the objective contains a partially reflecting film that acts as the reference surface and the beam splitter for the interferometric analysis. Reflected light from the electrode surface and the reference surface interfere, and the resulting set of spatially resolved intensities, are recorded on a 256 x 256 pixel charge injection device (CID) array camera. The digitized output from the CID camera is analyzed to produce a phase map @(xy),representing the relative differences in optical height between the reference and test surfaces at each x, y surface coordinate. The phase map is generated for a rectangular region of the sample surface, the size of which depends on the total system magnification. In these studies, lox and 40x Mirau microscope objectives are used, corresponding to total system magnifications of 160x and 640x, and phase map areas of 920 x 820 and 230 x 210 pm2, respectively. A dynamic phase-measurement technique is used to determine the vertical optical heights. The intensity of light, I, detected by the CID array camera for position (x, y) on the test surface is given by
I = I, + I, cos[4(x,y) + a(t)l
(2)
I1 represents the time-averaged sum of reflected intensities from the reference and electrode surface. The second term on the right-hand side represents a time-varying component of the interference intensity, where @(xy)is the initial phase difference between reflected wave fronts originating at the electrode and reference surfaces. To measure the optical heights across the (14) White, H.S.;Earl,
1130.
D.J.; Norton, J. D.;IG-agt, H.J. Anal. Chem. 1990,62,
surface, five 90" phase shifts are introduced between the reference and substrate using a piezoelectric transducer to move the reference surface at a constant rate toward the electrode surface. The intensity at each pixel of the camera is integrated over each interval during this movement and recorded after phase changes of a(t) = 90, 180, 270, 360, and 450". Integration of the interference intensity over these five intervals yields five values:
A(x,y) = I{
+ I,'[cos &,y)
B(x,y) = I{ = Z,l[cos 4(x,y)
- sin 4(x,y)]
(3)
+ sin 4(x,y)l
(4)
from which the spatially dependent phase @(xy)is calculated
The optical height at position x, y is computed directly from the phase measurement using the equation
where 1 is the wavelength of the illumination. Differences in the optical heights at any two points on the surface are designated as Ah (Le., Ah = h(x'fl - h(xy)). Electrochemical Cell and Apparatus. The electrochemical cell was constructed from a 6hn"mdiameter glass petri dish, (Figure 3A). To reduce noise in the optical images, the microelectrode substrate (vide infra) was mounted on a 2 cm x 4 cm Analytical Chemistry, Vol. 67, No. 3, February 1, 1995
563
A)
Reference electrode
Mirau objective Solution filled with glass beads
Electrical contact to the microelectrode was made by attaching a thin gold wire to an exposed edge of the metal layer on one side of the substrate. The microelectrode and the wire were covered by epoxy except for an area of -0.6 x 0.6 cm2 centered around the Pt microdisk. Chemicals. Nitrobenzene (NB; Aldrich, HPLC grade) was dried over activated 3-A molecular sieves. Benzonitrile (Aldrich, HPLC grade) was used as received. Tetra-n-butylammonium hexafhorophosphate VBA-PFG)was recrystallized twice from ethyl acetate, dried under vacuum at 80 “C, and stored in a desiccator. RESULTS AND DISCUSSION
6)
-
l,m
/-
Si3N4
Tio.3Wo.7 Si
Figure 3. Schematic diagrams of the (A) electrochemical cell and (B) inlaid Pt disk electrode.
glass plate, which was epoxied to the bottom of the petri dish. The cell was filled with 3-mm spherical glass beads, as previously described,14to reduce fluid convection and rippling of the air/ electrolyte interface. x-y translation of the cell was controlled with use of a micrometer stage (0.002-mm resolution, Newport, CA). The distance between the air/electrolyte interface and the electrode was -2 mm. The distance between the air/electrolyte interface and the microscope was -1 mm. Focusing of the microscope was accomplished by motorized vertical translation of the microscope head. Ag/AgCl and Pt electrodes were used as reference and counter electrodes, respectively. Electrochemical data were obtained using a Princeton Applied Research Corp. (PAR) Model 173 potentiostat and a PAR Model 175 universal programmer. Voltammograms were recorded on a Kipp and Zonen Model BD-90 x-y recorder. Preparationof Electrode. The microelectrode schematically shown in Figure 3B was prepared by standard microelectronic fabrication methods. A 400-A-thick layer of Tio.3Wo.7 was sputter deposited on a clean Si wafer (2 x Torr vacuum, room temperature). A 5000-A-thick layer of Pt and an additional 400 A of Tii.3Wo.7were deposited sequentially under the same conditions. m e function of the Tio.3W0.7layers is to increase the adherence of the Pt layer to the layers above and below it.) A -2000-A layer of Si3N4 was deposited on the upper Tio.3W0.7layer by plasma deposition in a stream of SiHd, NH3, and N2 (14,40, and 100 cm3(STP) min-I, respectively) at 350 mTorr pressure and 300 “C. A thin layer of positive photoresist was deposited over the entire substrate by spin coating. The wafer was then exposed to a W light source for 40 s through a photolithographic mask defining a 30-pm-diameterdisk. The wafer was etched by CFq plasma gas to remove the layer of Si3N4 in a disk-shaped region. The underlying Pt was exposed by selective etching of the Ti0.3w0.7 layer using hydrogen peroxide at 50 “C for 20 s. The photoresist layer was removed from the entire substrate using 712 D stripper at 90 “C for 5 min. 564 Analytical Chemistry, Vol. 67, No. 3, February 1, 1995
The results are presented in the following order. In section I, the Lorentz-Lorenz formula is used to derive a general expression that relates the refractive index n(r) at any position, r, in solution to the local concentrations of electroactive reactant and product. In section 11, Saito’s equation for the concentration profiles surrounding a microdisk electrode is used to obtain an explicit expression for n(r) in terms of redox concentrations. The results in sections I and I1 provide a framework to relate optical height measurements to current density, as is shown in section 111. Experimental results are presented in section IV. I. Variation of Refractive Index in the Depletion Layer. The general system considered is the redox reaction
where “ox” and “red” are soluble halves of a redox system. It is assumed that the solution initially contains only the oxidized half of the couple (“ox”) as well as a supporting electrolyte. For any solution comprised of a redox-active species, an electrolyte, and a solvent, the molar refractivity (A) of the solution is, to a good approximation,the sum of the contributionsdue to each species.I2 Thus, when no faradaic reaction is occurring ( i = 0),
where A, and are the molar refractivities and molar concentrations, respectively, of each of the component species. In eq 11, and hereafter, the contributions from the individual ions that comprise the supporting electrolyte are lumped together (i.e., CelecAelec = CtAt + cA-1. When a faradaic reaction occurs (i t 0), the molar refractivity will be a function of the vector position r, since Coxand Cred are functions of r.
For a dilute redox system, the concentrations of solvent and electrolyte can be considered to be constant everywhere in solution, allowing C,l,(r) and Celec(r)to be replaced by their bulk solution values, C*soh and C*elec,respectively. Assuming that molecular transport occurs by diffusion, and that the diffusion
coefficients of
“OX”
and “ r e d are equal, yieldsl5
Substituting eqs 11 and 13 into eq 12, and using the following definition.
gives the molar refractivity as a function of the concentration of the product, Cred(r),of the electrochemical reaction
In the PMIM experiments described below, optical distances reflect variations in the refractive index of the solution as a function of the radial distance measured from the center of the electrode. In order to relate the concentration profile directly to an optical distance, it is first necessary to relate the molar refractivities of the pure components, “OX” and “red” in eq 14, to their respective refractive indexes. This is done by use of the Lorentz-Lorenz formula12
where 5 is the molar volume of component j in its pure state. Equation 15 can be approximated, with good accuracy,16by the expression
In dilute solution, the total molar volume does not change appreciably within the depletion layer: thus, K=o/Kz0(r) 1. Furthermore, since the solvent is by the far the major constituent of the solution, VoJK&) = VOx/V8,hi, where Kolvis the molar volume of the pure solvent. Employing these approximations,eq 16 reduces to the following expression.
Equation 17 is general for any electrode geometry. The quantity c*,,/cC~ is the mole fraction of the electroactive species in the bulk solution. The quantity Vox/Vwb= MWOgwb/MWm~,, is readily calculated (where MWj and ej are the molecular weight and density, respectively, of the pure electroactive species and the solvent). The refractive index of the bulk solution, ni=o, is measurable using a conventionalrefractometer. Thus, calculation of nit&) only requires knowledge of the dimensionless concentration profile (Cred(r)/C*ox) and the difference in the refractive indexes (or molar refractivities, eq 15) of the electrochemical reactant and product. 11. Evaluation of n(r) for a Disk-Shaped Electrode. At steady state, the dimensionless concentration profile for the product species generated at a disk-shaped electrode, Cred(r,z) / C*,,, is given by Saito:
Ai= r/;.(unj+ b) In similar fashion, equations relating the molar refractivities of the solutions (Ai&) and A+o) can be expressed in terms of the refractive indexes of the solution
where i(@ is the current at any potential E. The cylindrical coordinate system defining the position r, z is shown in Figure 1. Substitution of eq 18 into eq 17 yields the variation in refractive index around a disk electrode as a function of the current, i(@.
where is the total molar volume of the solution when no current is flowing and Kit&) is the total molar volume of the solution at position r when a electrochemical reaction is occurring. Substituting these definitions into eq 6, the position-dependent refractive index is given by (15) Bard, A J.; Faulkner, L.R Electrochemicul Methods; Wdey: New York, 1982. (16) The linearized form of the Lorentz-Lorenz formula, Ai = Kfuni b3, provides a good approximation of the relationship between Ai and ni, over relatively small ranges of these variables. In the experiments reported here, the refractive index varies between -1.5 (= nod and -2 (= nred). The error in Ai resulting from using the approximate Lorentz-Lorenz formula, with coefficients u = 0.442 and b =-0.371, is less than 2%over this range (% error is defined here as @ppPmx. x 100).
+
111. Imaging of Depletion Layer Using Rehdive Index Gradients. The optical distance, h(r), between the microdisk plane (z = 0) and a reference plane located far from the electrode surface at a distance z,, is defined as
Analytical Chemistry, Vol. 67, No. 3, February 1, 1995
565
Substituting eq19 into eq 20 yields
7 I
”
”
“
”
I
6 5
< 4
z
4
3
2 1
where
0
~
0
20 40
60 80 100 120 140 160 180
r/ro
and 7/ = r/rO3d = z/ro, and j3 = zJro. Note that, at a iixed electrode potential, a has a constant value. When no reaction is occurring (Le., i = 01,
Figure 4. Plot of ANa vs b, showing the dependence of the of the optical reference apparent optical height on the location (2) plane. 300,
,
,
,
,
,
,
,
,
,
250
h(i=O) = (2, - ZFJni=O
(23)
Therefore, the variation in optical height, Ah(r),that results from the electrochemical reaction is obtained by subtraction of eq 23 from eq 21, yielding
Ah(r) =
Equation 24 can be employed in several ways. First, the value of Ah measured at any radial position 7 is a function only of the dimensionless parameters a and j3. From eq 22, a can be readily calculated if the molar refractivities of “ox”and “red” are known. Typically these constants will not be known, or cannot be independently measured if the electrochemical reaction generates an unstable species. However, since the molar refractivities are independent of concentration, the difference (aox- n,d> can be taken as a constant, albeit unknown. Thus, regardless of whether (n, - are&is known, eqs 22 and 24 indicate that Ah is proportional to the normalized voltammetric current i ( E ) / i h and the mole fraction of electrochemical reactant, C*ox/C*z. This result suggests that values of Ah(7) obtained at a fixed radial position (e.g., r = 0) will have the same dependence on potential and redox concentration as the faradaic current. Optical voltammograms, i.e., plots of Ah@)vs E, thus should contain the same information as the true i-E curve. In a later section, we show that calibration of the optical system allows Ah@) to be converted to values of faradaic current, providing a means of obtaining electrochemical data by a purely optical means. For a fixed radial position, 7, the definite integral in eq 24 depends only on the upper limit on integration, j3, which is the dimensionlessvalue of the distance between the electrode surface and reference plane = z,/ro). Figure 4 shows a plot of the integral (also equal to Ah(r)/a) as a function of j3. As expected for a quasi-spherical geometry, Ah(r)/a does not converge to a constant value as B increases, since the concentration profiles slowly decay into solution with an approximately l/r dependence. The nonconverging behavior of Ah(r)/a presents dif6culties in 566 Analytical Chemistry, Vol. 67,No. 3, February 1, 1995
250
-
200
-
0 ‘
a = 50.0
j
-20
-10
,
I
0
,
,
IO
I
I
20
rho Figure 5. Plot of Ah as a function of (a, top) a at constant B , and (b, bottom) /3 at constant a.
choosing a particular value of j3 to use in evaluating the integral in eq 24. In the analysis of experimental images, we have chosen j3 to have a value that is suf6ciently large such that the concentration of “OX” and “red” can be considered to essentially equal their bulk values. Thus, for j3 = 100, Cox= 0.99C*0x.4Although this procedure is somewhat arbitrary, it is important to note that j3 is not a function of the electrode potential or redox concentration. Thus, Ah remains proportional to i(E)/&,,, and the redox concentration, regardless of the chosen value of j3. As noted below, the arbitrary nature of the selection of j3 prevents an accurate evaluation of (nox- nre&from experimental images. Figure 5 shows theoretical plots of Ah as function of the radial coordinate r, for various combinations of a and j3. As anticipated from the preceding discussion, Ah@) is proportional to a for any value of r and weakly dependent on j3, if j3 is sufficiently large. A key point that Figure 5 demonstrates is that the optical distance decays very slowly with radial distance from the electrode surface. For instance, for p = 100 and a = 50 (typical of experimentally obtained values, vide infra), the optical distance at a radial distance
T
350.2 nm
308.1 nm _
_
_
~
226.6 ~ r m h
T
“I
21 3.5 nm
4 -4
-3
-2
-1
0
Voltage (volt) vs AglAgCl
Figure 6. Voltammetric response of 31-pm diameter Pt disk electrode and corresponding PMIM images (inverted along z-axis) in a benzonitrile solution containing 0.3 M NB and 0.2 M TBA-PF6. The images were recorded at the potentials marked (a-d) on the voltammogram. The large cathodic wave beginning at --2.2 V corresponds to the reduction of the solvent (benzonitrile).
25 radii (r/ro= 25) away from the electrode surface is -l/3 of the value directly above the electrode surface (r/ro= 1). The weak dependence of Ah on r is the result of the optical distance being measured as the integral over the slowly varying concentration profile (which varies as -rl).More importantly, for the range of /?and a shown in Figure 5, the variation in Ah at relatively large values of r (e.g., r > lor,) is well above the demonstrated resolution (-1 nm) of the instrument in liquid electrolytes. For instance, for /3 = 100 and a = 50, Ah changes by -50 nm between r/ro= 10 and r/ro = 25. Thus, PMIM images should be able to readily detect variations in Ah due to a finite concentration gradient at relatively large radial distances. This point will be returned to in the analysis of experimental images. IV. Experimental Results. Figure 6 shows backgroundsubtracted PMIM images of the 15pm-radius microelectrode as a function of the applied potential in a benzonitrile solution
Figure 7. Noninverted image of the inlaid Pt disk electrode at zero current in a benzonitrile solution containing 0.3 M NB and 0.2 M TBAPF6. The electrode appears to protrude from the surface due to the difference in the refractive indexes of the benzonitrile solution (-1 53) and the Si3N4 (1.97) insulating layer (see text and scaled drawing of electrode in Figure 3b.)
containing 0.3 M NB and 0.2 M TBA-PFG. The corresponding steady-state voltammogram is shown in the lower portion of the figure. Potentials at which the PMIM images were recorded are indicated on the voltammogram. All images in Figure 6 are inverted along the vertical axis (z-axis), such that valleys appear as hills and vice versa. The apparent maximum in each of the PMIM images is centered directly above the microelectrode and represents an increase in the optical distance near the electrode surface. This finding is in qualitative agreement with the expectation that the radical anion, NB-, is more polarizable than the parent species, NB, and, thus, has a larger molar refractivity. The general shape of the images is consistent with the theoretical predictions presented above. First, the peak in the PMIM image, i.e., Ah at r = 0, increases with increasing i(E)/ ibm, as predicted from eqs 22 and 24. Second, Ah decreases with increasing distance from the electrode. Third, the PMIM images are independent of the time interval between applying the electrode potential and acquiring the image (the shortest time interval being -30 s). The latter results suggest that the images correspond a true steady-statedistribution of redox species around the electrode surface. A noninverted background image of the microelectrode in the 0.3 M NB solution is shown in Figure 7. Background images were recorded at zero current, and the feature apparent in Figure 7 represents the topographical optical image of the Pt electrode recessed in the insulating Si3N4 overlayer (see Figure 3). The Pt disk appears to protrude 27 nm above the insulating layer in the interferometric image, indicating that the optical path length over the Pt disk is shorter than that through the Si3N4 layer (consistent with the refractive index of Si3N4 (1.97) being greater than that of the benzonitrile solution (-1.53)). Background images of the microelectrode, such as the one shown in Figure 7, were analyzed by a previously published procedure for converting optical distances measured in PMIM images of multilayer structures into the physical dimensions of the e1e~trode.l~A value of 241 f 1 nm was obtained for the combined thickness of the upper Tio,,Wo.7 layer and Si3N4 overlayer, in agreement with the nominal value (17) (a) Smith, C. P.; Fritz. D. C.; Tirrell. M. V.; White, H. S. Thin Solid Films 1991,298,369. 0)Smith, C. P.; Kennedy, H. L;Kragt. H. J.; White, H. S. Anal. Gem. 1990, 62,1135.
Analytical Chemistry, Vol. 67, No. 3, February 1, 1995
567
I
,
d
1
fi.
I
I
0
10
200nmI
b
-30 -20
-10
20
30
r/ro Figure 8. Experimental (points) and calculated (solid lines, eq 24) optical profiles of PMIM images recorded for the reduction of 0.3 M NB at different electrode potentials.The experimental data correspond to results presented in Figure 6. The calculated curves were plotted using best-fit values of a. The corresponding values of a and (noxnrd)are given in Table 1. The short horizontal lines along the vertical border indicates the baseline (Le., Ah = 0)for the theoretical curves.
(240 nm) expected from the fabrication procedure (see Experimental Section). The radius of the electrode was measured to be 15.5 pm. Background images were routinely recorded during experiments to avoid error in the subtraction procedure. As evidenced in Figure 6, no features of the electrode topography are apparent in PMIM images recorded during electroreduction of NB, indicating successful subtraction of the background image. In Figure 8, cross-sectionaloptical line profiles taken from the experimental images in Figure 3 (points) are plotted, along with the theoretical values (solid lines) computed by use of eq 24. As previously indicated, we have chosen a relatively large value of p (=loo) for analyzing the data, in order to reduce the dependence of the computed values of Ah on p. This strategy allows for a consistent means of comparing data obtained at different potentials or redox concentrations, but the rather arbitrary selection of ,B prevents an accurate determination of a. As is evident in Figure 8, the experimental optical profiles rapidly decay to background values, reaching Ah = 0 at distances of -10 radii from the electrode surface. This behavior is considerably different from theoretical curves (e.g., Figure 5), which, as discussed above, decay very slowly with increasing Y. Although the discrepancy in the general behavior of Ah appears quite large for Y > loro,the differences in the theoretical and experimental curves result from a small departure of the actual concentrations of “ox” and “red” from values predicted Saito’s equation. Values of a were obtained by fitting eq 24 to the experimental data over a radial distance equal to flOr, (corresponding to analysis of the nonzero Ah values over an -300pm lateral distance). Theoretical Ah vs r curves computed by use of the fitted values of a are shown in Figure 8. Reasonable agreement between theory and experiment is obtained for r < flOY,. 568 Analytical Chemistry, Vol. 67, No. 3, February 1, 7995
The departure from theory at distances larger than &loro (Figure 8), is most likely due to a small amount of free fluid convection that is driven by density gradients. It is important to realize, however, the agreement between the experiment and theory is quite good within 10 radii of the surface, suggesting that Saito’s analysis provides an adequate description of the concentration profiles around a microdisk electrode. As stated above, the discrepancy between the measured and computed values of Ah at large values of Y is indeed quite small. For instance, at Y = 20r0,the dimensionless concentration of the redox product (Cred(r,z))/Pox) calculated using eq 18 is -0.05; the optical profiles indicate that Crd(~,z))/C*ox at 20r0 is essentially equal to its bulk value of 0. As recently discussed in detail by Amatore et al.,18 a small difference in the redox concentrations from their true steady-state values (defined by eq 24) at large distances should have a negligible effect on the steady-state current. Thus, we believe that nonideal behavior revealed in Figure 8 has little consequence on the electrochemical (&E) behavior. In more highly concentrated solutions (C*NB> 3 M), microscopic convective eddies in close vicinity of the microelectrode are observed, in which the electrolyte solution is rapidly flowing in a regular pattern. Even under these extreme conditions, a true steady-state, sigmoidal-shaped,voltammetric curve is observed, with no discernible effect due to fluid convection. A complete analysis of this observation requires a detailed description of electrochemicallygenerated density gradients and is beyond the scope of our present report; however, the observation clearly suggests the possibility of natural convection playing a significant role at lower redox concentrations in determining the shape of the concentration profiles at large distances. This is in accord with earlier suggestions of Amatore et a1.I8 The difference in the refractive indexes of the electrochemical reactant and product, (nox - nred), was computed, using eq 22, from each value of a obtained from the fitting procedure described above. Values of i(E)/&, C*,,/C*z, and a for each curve shown in Figure 8 are presented in Table 1,along with the corresponding computed values of (n, - fired). Representative data from other experiments performed in solutions containing different concentrations of NB (0.05,0.1,0.3,and 0.7 M) are also included in Table 1. Values of (nox- nred) computed in this manner range from -0.43 to -0.47, independent of the redox concentration (C*NB) and faradaic current (i(E)). The negative value of (nOx- nreJ indicates that the molar refractivity of the NB radical anion is significantly larger than that of the parent species, although, as noted above, no significance should be attached to the absolute value of (n, - nred) due to the arbitrary selection of p. Surprisingly, (nox - tzred) is essentially independent of C*NB,including values obtained in solutions containing redox concentrations sufficiently large (>0.1 M) that the assumption of a diffusionlimited process is no longer valid. Qualitatively, in the concentration regime where C*NB> Pelect, migration of redox species and electrolyte ions will be ~ignificant,~~ invalidating the use of the Saito’s equation for a purely diffusion response. We are not presently able to derive an tractable expression for the mixed transport case and thus are unable to justify the results on a fundamental basis. However, the experimental results clearly (18)Amatore, C.; Fosset, B.; Maness, K M.; Wight”, R M. Anal. Chem. 1993, 65,2311. (19)Smith, C.P.; White, H.S.Anal. Chem. 1993,65,3343.
1400
Table I. Optical Parameters Obtained from PMIM Images
I
1200
0.0049
0.10
0.0097
0.30
0.029
0.70
0.068
-1.15 -1.30 -1.50 -1.60 -1.15 -1.20 -1.30 -1.40 -1.60 -1.30 -1.40 -1.60 -1.80 -2.00 -1.20 -1.30 -1.50 -1.70 -1.90 -2.10
0.54 0.94 0.99 1.00 0.52 0.72 0.89 0.94 1.00 0.13 0.46 0.90 0.97 1.00 0.08 0.27 0.79 0.96 0.99 1.00
12.5 22.0 22.2 22.9 24.3 32.3 41.6 42.8 42.4 17.2 63.9 129 138 134 25.2 85.1 250 296 306 310
-0.46 -0.47 -0.45 -0.46 -0.47 -0.46 -0.47 -0.46 -0.43 -0.45 -0.46 -0.46 -0.48 -0.45 -0.46 -0.46 -0.46 -0.45 -0.45 -0.45
Concentration of NB in benzonitrile solutions containing 0.2 M TBA-PF6. * Measured vs Ag/AgCl. Measured from best fit of M(r=O) vs E curves, using p = 100. Calculated using eq 22, with Vox/Vso~v = 1.008 and r, = 15.5 x cm.
show that (n, - nred is constant, suggesting that experimental values of Ah can be related directly to C*NBand/or i(E) in analytical measurements over a rather wide range of experimental conditions. This prediction is demonstrated in experiments described below. Figure 9 shows plots of Ah (r = 0) vs E recorded during voltammetric experiments at a sweep rate of 5 mV/s. Each data point in these “optical voltammograms” corresponds to the maximum value of Ah obtained from a PMIM image, recorded without interrupting the scan. As seen in these curves, the Ah(r = 0) vs E curves for C*NB= 0.0, 0.05, 0.3, and 0.7 M, closely resemble true voltammograms, including the appearance of the background processes. For comparison, the corresponding voltammogram (i-E) recorded during each experiment is also presented in Figure 9. Within error, the dependence of Ah and i on the electrode potential is identical. Thus, it is clearly possible to obtain the shape of the voltammetric curve from the optical measurement. This result is a purely empirical observation, independent of theoretical considerations presented above. The insets in Figure 9 show Ah(r = 0) and voltammetric limiting current as a function of the concentration of NB, C*NB. In each case, Ah(r = 0) was measured at a applied potential corresponding to a value on the limiting current plateau for the reduction of NB. A linear relationship between Ah(r = 0) and C*NBis observed for concentrations up to 1.5 M, in accord with eqs 22 and 24, and the finding (nox- n,d> is independent of C*NB. From the slope of the line through the data (-1000 nm/M), and using the resolution of the instrument (-1 nm for imaging though fluids), we estimate that the smallest concentration of NB that would give rise to a detectable peak in a PMIM image would be in the range of a few millimolar. This estimate is consistent with
I
I
I
1
I
l? i
’V,1 ‘0
i
W
2 0
r
I
?
- 41
[NBI,=M C * d C z potential! V i(O/ilim a: nm (n, - nredd 0.050
I
a
0.5 1 Conc. M I
1.5
1
1
I
I
I
I
I
I
I
I
I
I
I
I
I
I
8,
I~
1.5
4 ~
0.5
-0.5
-1.5
-2.5
E (volt) vs Ag/AgCl Figure 9. Comparison of Ah vs E (top) and i vs E (bottom) responses for a 31-pm-diameter Pt electrode in benzonitrile solutions containing (a) 0.00 (A), (b) 0.05 (O), (c) 0.3 (m), (d) and 0.7 M NB (0). All solutions contained 0.2 M TBA-PFe. Scan rate: 5 mV/s. The insets show Ah(r = 0 ) vs CNB and him vs CNB for NB reduction in benzonitrile solutions containing 0.2 M TBA-PF6.
our ability to record images for C*NB= 10 mM without signiiicant interference. CONCLUSION
PMIM images of the refractive index gradients near a microdisk electrode are in good accord with Saito’s equations for the concentration profiles of electrochemical products and reactants. At large distances from the electrode,free fluid convection appears to reduce the concentration gradient to negligible values. Optical heights measured in PMIM are proportional to redox concentration and faradaic current, suggesting a method for obtaining voltammetric data in situations where the current cannot be directly measured. For instance, the current associated with a region of localized corrosion, or an individual site of catalytic activity, could be measured independently and separated from the total current measured over a large surface. Such applications are currently being pursued in our laboratory. ACKNOWLEDGMENT
The authors gratefully acknowledgethe support of the National Science Foundation/Electric Power Research Institute Program. Received for review June 10, 1994. Accepted October 6, 1994.@ AC940597Z @Abstractpublished in Advance ACS Abstracts, November 15, 1994.
Analytical Chemistty, Vol. 67, No. 3, February 1, 1995
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