Anal. Chem. 1983, 55, 1281-1285
1281
Hydrodynamically Modulated Rotating Disk Electrode Analysis in Derivative Mode Barry Miller” and Joseph M. RosamElla Bell Laboratories, Murray Hill, New Jersey 07974
Sinusoidal modulation around the center speed of a rotating disk electrode (RDE) gives rlse to a current response, seiectlve for mass transport sensitive reactions. Such a hydrodynamically modulated RDE (HMRDE) has been shqiwn to have wide analytical application. I n order to Increase the resolution of currents near the electrode or solvent decomposition limits and to provide the advantages of a peak rather than a wave-plateau output, a derivative mode of HMRDE analysis has been developed through computer dlff erdntlaltlon of modulated current-potential plots. Theoretical treatment shows this form of differential analysls has advantages over those applying conventional current-potential methods for irreversible reactions because of the nature of the modulated current-potential characteristic. The linear responso of the derivative HMRDE current function peaks to concentration of eiectroactive species and to moduiatlon amplitude is shown experlmentaily for a variety of cases. These range from single components to multicomponent solutions and situatialns with high interference currents from surface and electrolyte processes at solid electrodes, concurrently demonstrating the improvements in resolution offered by this operating mode.
The hydrodynamically modulated rotating disk electrode (HMRDE) with sinusoidal programming of the speed has attractive properties for electroanalysis at submicromolar levels ( I , 2). The method selectively extracts the disk current response to the superimposed sinusoidal speed modulation. This procedure extends the high inherent sensitivity of convective-diffusion controlled RDE currents to electrode materials encompassing nearly ideal ones (mercury coated disks) through the variety of materials (Pt, Au, #andforms of carbon) that are subject to various surface-associated interfering currents limiting their full application. In these cases the discrimination of HMRDE response for mass transport dependent reactions has eliminated most of the curreint components classically hindering their use, when H2 or O2 generation in aqueous environment is reached or at low concentration levels of electroactive species where the surface/ electrolyte components dominate. In the standard mode of this technique ( I , 2 )the modulated response of a component is isolated and rectified (synchronously, if retention of phase information irs important), to yield a “wave” in the manner of classical current (i)-potential (E) voltammetry or polarography. As can be well-appreciated from the evolution of polarographic methods, peak current outputs are popularly preferred over classical wave i-E data, for readability and clearer separation of successive components along the potential abscissa. We anticipate numerical differentiation of modulation current (Ai) vs, E plots to provide this form of derivative peak output while at the same time offering possible advantages in increasing the selectivity of the method, both in cases of multiple eledaoactivecomponents and in the resolution of signals near the limits at which the total current passing from modulation rejected components overwhelms the measuring system. The most powerful ap0003-2700/83/0355-12~B1$01.50/0
plication of HMRDE techniques is to the discrimination of convective diffusion controlled processes in the presence of very much higher levels of surface or electrolyte reactions ( I , 2). We will show that the derivative method can further improve this selectivity since it does not require resolution in the limiting current (id region. Particularly when reactions occur at solvent/electrolyte limits as either cathodic or anodic currents, resolution becomes difficult because the total current simply may become 1to0high, overloading the current follower of the potentiostat or the common mode rejection of the band-pass filter at potentials suitable for modulated output. In this report computer acquisition of Ai-E data is combined with running average smoothing and the successive difference determination of the limiting derivative d2i/dw1/2dE in the practical numerical form of A(Ai)/AE vs. E plots. The analytical characteristics of these data are shown for chemical systems containing ane to three electroactive components. We will discuss first the relationship of the conventional Ai output a t limiting current, thus sensitive only to mass transport, to the derivative response which is a function of Ai vs. E wave shape and, thereby, kinetics. This is a characteristic difference encountered in applying derivative methods generally, but with special features here because of the nature of the Ai-E relations (3). That is, Ai-E curves already reflect the kinetics governing the i-E characteristics. When the electrode process is not reversible the Ai-E trace has an inherent asymmetry (3) with respect to the i-E function which will affect the relative derivative plots. There is, of course, no loss of sensitivity for irreversibility when only Ai limiting current ( A ~ L values ) are applied ( I , 2 ) , but a d2i/ do1l2dE derivative method will be sensitive to wave shape differently than conventional di/dE procedures ( 4 ) . Theoretical Background. The relationships between i, Ai, iL, AiL, and E hLave been given (3) for the mixed mass transfer-charge trainsfer case for a redox reaction
Ox + ne = Red
(1) For present purposes we will consider only the limiting cases of reversible and totally irreversible charge transfer. In these instances, at sufficiently low frequencies of modulation, f, we have from ref 3 .-Ai - i - -(reversible) AiL iL and
(i) 2
ai AiL =
(totally irreversible)
(3)
The corresponding current-potential curves are, for t,he reversible case
E = E l / 2f n F In E = E l / 2 f RT 2 In
0 1983 American Chemical Soclety
(;
- 1)
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1282
ANALYTICAL CHEMISTRY, VOL. 55, NO. 8,JULY 1983
and, for the irreversible case
E = Ellz f a n F In E = ElI2f aRT n F In
[
(F
- 1)
'* I 0
w \ 73
'4
v
( q 2 - 1 ]
(7)
08
6 w
where a is the transfer coefficient. Thus, from (4) and (5), it can be seen that reversible case normalized Ai-E and i-E potential plots superimpose whereas from (6) and (7) it is clear that the corresponding curves for an irreversible system differ as a consequence of (3). We are interested in the relative response of the pairs of peak-shaped differential plots of di/@ or d2i/dw1/2dEvs. E for the respective reversible and irreversible cases. That for di/dE is well-known (4) and has theoretical peak values of (nFIR7') (iL/4) and (anF/RT)(i~/4)for the reversible and irreversible cases. For differentiation of a reversible Ai-E plot, the parallel treatment for peak height yields (nF/ R7')(Ai~/4),identical in the normalized limit (multiplication by wo1/z/Au1/2)to the (nF/RT)(iL/4) result. For the totally irreversible case we rewrite (7) as
06
-
v
04
0.2 -120
-80
0 E, m V
-40
40
80
120
Flgure 1. Normalized current plots of / / i L ,A//AiL,d//dE, and dA/ld€ vs. E for a reversible reaction with n = 1 and an irreversible reaction with an = 1. Numerical computation is at 0.5 mV A€ intervals. E, V vs SCE
-04
-02
00
02
04
0.6
40
120
The desired function d2i/dw1/2dEis approximated by dAi -2AiL exp e
-- d~
(I
+ exp
180
-
-803
(9)
Differentiating (9), setting it equal to zero, and solving the equation give the potential, Epkmd, at the maximum of (9) as that for which E, V vs SCE
exp c = 1/2
(10)
(as opposed to unity for the symmetrical reversible case). This locates Epkmd at Ellzf 0.0178/an (+ ox, -red), between Ell2 and E112.mod= Ell2 f 0.02265/an, the latter from ref 3. Substitution of (10) into (9) yields pk
8 anF 27 RT
which has a higher numerical coefficient than the reversible case by (8/27)/(1/4) = 32/27 = 1.185. These relations are summarized and c o n f i i e d in the computer-derived numerical differentiations of the i-Ai-E relations shown in Figure 1. The asymmetry of (7), qualitatively originating in the kinetics "lag" a t the foot of the irreversible Ai-E plot and the "catch-up" a t the mass transfer controlled limit, yields a relative enhancement in the derivative response with respect to methods based on the shape of the i-E characteristic itself. The Ai-E relations for mixed mass-electron transfer control (3) are intermediate between the reversible and irreversible limits and this will be reflected in the derivative mode as well.
EXPERIMENTAL SECTION All procedures and equipment are as previously described ( I , 2) except for obtaining the derivative output dAi/dE. The Ai-E points at sufficiently close A E values are obtained from the data acquisition procedure (2)based on a Hewlett-Packard Model 85F computer. Digital simulations as employed in Figure 1gave the step widths in millivolts (=lo) for which
