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Anal. Chem. 1984, 56,2410-2413
i, was lower than 2.0 mA, and this fact is shown in Table I and 11. Therefore, we found that the present method was useful for studying bromination with slow reaction rate, although the accuracy and precision are slightly lower than those of usual CPC (below O.l%), because the magnitude of the i, noise is larger than that of the residual current noise in usual CPC.
215-31 5. (3) Harrar, J. E. In “Electroanalytical Chemistry”; Bard, A. J., Ed.; Marcel Dekker: New York, 1975; Vol. 8, pp 1-167. (4) Uchiyama, S.;Nozakl, K.; Muto, 0. Bunseki Kageku 1077, 26, 219-223. ( 5 ) Uchiyama, S.;Nozakl, K.; Muto, G. J . Electroenal. Chem. 1078, 9 7 , 301-308. (6) O’Reilly, J. E. Anal. Chem. 1075, 9 1 , 1077-1081. (7) Uchlyama, S.;Nozaki, K.; Muto, G. J . Nectroanal. Chem. 1077, 79, 413-414.
LITERATURE CITED (1) Meltes, L. Pure Appl. Chem. 1068, IS, 35-79, (2) Bard, A. J.; Santhanam, K. S. V. In “Electroanalytical Chemlstry”; Bard, A. J., Ed.; Marcel Dekker: New York, 1970; Vol. 4, pp
RECEIVED for review December 13,1983. Accepted May 21, 1984.
Hydrodynamic Modulation Applications to Electroanalysis and Diffusion Coefficient Measurement with a Commercial Disk Rotator Joseph M. Rosamilia and Barry Miller* AT&T Bell Laboratories, Murray Hill, New Jersey 07974
The frequency response of sinusoidal hydrodynamlc modulation at a rotating disk electrode has been applied to the determlnation of the diffuslon coefflclent ( D ) of oxygen in an aqueous electrolyte. Prevlous theory establlshed that this response Is dependent only on the frequency of modulatlon/frequency of rotation ratio and on the Schmidt number, klnematic viscoSny/D. The method does not require knowing the number of electrons transferred or the concentration of eiectroactive species. The latter fact is particularly advantageous In the case of a gas In different media and temperatures. A commercial controller/rotator has been used in thls work and the expected accuracy for D achieved.
Sinusoidal hydrodynamic modulation (SHM) at the rotating disk electrode provides electroanalysis with a versatile methodology applicable to the general range of electrode materials (1-5). The primary emphasis of this form of hydrodynamic modulation experiment was extracting a response selective to the mass-transfer component of current while rejecting those for the charging, surface, and irreversible solvent contributions (5). Operational improvements in the original technique (1) have led to higher sensitivity, a new derivative readout, and shortened experimental time. These were accomplished through data analysis refinements, higher amplitudes and frequencies of modulation, and optimized sweep rate-signal filtering considerations (2-4). The theory of the disk current frequency response on which we will rely in this work was derived and experimentally confirmed (6) and has been further treated in several laboratories (7-10). We wish here to broaden SHM practice not only through additional application but also by employing exclusively a commercially available motor/controller for the rotation function instead of our own (I). Clearly, the ready commercial availability of adequate band width, programable disk rotators is a prerequisite to the general acceptance of this analytical technique. The present application stems from the earlier theoretical proposal (6) for determining the diffusion coefficient (D) of an electroactive species from the frequency dependence of modulation response without knowledge of the concentration (C) or the electrons transferred (n)in the electrode reaction. 0003-2700/84/0356-2410$01.50/0
This is also a property of the response to a step function in rotation speed (8)and certain other AC or transient methods (see ref 8). A particular case in which not requiring n or C can be of important advantage is determining D in a solution containing an electroactive gas, here 02.A variety of media, temperatures, partial pressures, and degrees of approach to vapor/liquid equilibration may be of interest in fuel cell, corrosion, or catalysis studies. Concentration of oxygen in the electrolyte may be very difficult or tedious to come by in order to determine D through the conventional limiting current (the Levich equation). Another accurate (D2I3dependent) method for D at the disk is one applying the limiting current-time relation during an exhaustive electrolysis normally requiring tens of minutes (11). This does not require knowing the oxygen concentration but is likely awkward to use in the dissolved gas case. Our approach here to determining Do, illustrates two aspects of the SHM experiment. First, the technique allows resolution of the oxygen waves (n = 2 or 4 electrons) even at low concentration in the presence of surface and solvent reactions. We have chosen to use a gold electrode in basic solution for which two successive 2-electron waves are clearly defined. Second, the data defining the frequency dependence of response can be obtained in a few tens of seconds, presently limited more by switch-flipping and dial-changing functions than theoretical time requirements. Thus, the measurement may be made not only on unknown but even on slowly changing gas concentrations. The other information required is the kinematic viscosity ( v ) of the electrolyte, a standard measurement not dependent on any electrochemical considerations. We summarize the basis of the method as follows. The frequency response of the modulated current can be expressed (6) as a table of normalized modulation responses, A , defined in the equation
AiL/Aw1I2= AiL/w1I2 (1) iL is the limiting current from the Levich equation iL = KLno1I2C (2) where the system constants including the factors D2/3v-1/6 are collected in KL.The rotation speed, w , is the center value in an experiment in which Aw is the speed modulation amplitude 0 1984 Amerlcan Chemical Society
ANALYTICAL CHEMISTRY, VOL. 56, NO. 13, NOVEMBER 1984
2411
Table I. A R Values
P
sc
0.05
0.25
0.50
1.00
400
1.000
0.6927
0.3836
600
1,000
0.3367
800
1,000
0.6465 0.6101
0.1545 0.1299 0.1145
0.3052
and AiL the corresponding current modulation amplitude (both peak-to-peak). Our apparatus (1)linearly controls the square root of the speed (w1l2 and Aw1I2). The factor A is a function only of p and Sc where p = f/w, f being the frequency of modulation. Sc is the Schmidt number defiied as v / D . A condensed listing of A values taken from ref 6 is given in Table I as AR values, meaning that these numbers are normalized to unity at p = 0.05 instead of p 0 for the purposes of these experiments. We do this in order that the D determination only depends upon ratios of measurements whereby most electronic calibration errors are effectively canceled. The value of p is set experimentally, v is otherwise measured, and the values of AiL at different f and fixed w1I2 and are obtained. Note that w1I2 can be scanned or adjusted instead off. The measured Ai/Aw1I2 ratios are then normalized to the value for p = 0.05. This set of numbers will fit an AR vs. Sc plot when the Sc is that of the given solution, thus determining D. A simpler, more rapid scheme is to plot Sc vs. a ratio of a fiied pair of A values, e.g., ApaO.S/Ap-O.OS. Then, from the ratio of AiL/Aw112 values for p = 0.5 and 0.05 under the above described conditions, the corresponding D is obtained from the Sc axis. Only two measurements are made rather than a set large enough to fit an AR vs. Sc curve.
+
EXPERIMENTAL SECTION All modulation experiments employed an AFMSR rotator (serial no. 2125, Pine Instrument Co., Grove City, PA). Square-wave speed modulation with a different, earlier model of this rotator was reported by Austin et al. (12). Sinusoidal speed modulation was programmed by applying the output of the sum and square circuit already described (1)to the external input jacks of the Pine controller. It is this scheme which allows w1/2 and to be separately and linearly controlled by a voltage, a considerable convenience because of the form of the Levich equation. However, an external sine wave signal and the internal speed setting of the Pine controller should be adequate for most purposes. A Pine Instrument model RDE3 potentiostat was used with a 0.01-wF capacitor for frequency compensation (maximum time constant, 0.5 ms). The output from the current follower of the potentiostat was passed through a 4-pole Butterworth band-pass filter (Rockland 1000 F) with the frequency set between 1/2 and 2f and signal gain as required by the experiment. This amplified output was precision-rectified (13)with a following stage providing a gain of ?r to restore peak-to-peak amplitude scaling. An adjustable RC filter for smoothing the rectifier ripple, as recently discussed (5), was applied prior to the Ai readout. The actual motor response could also be measured directly by taking the square root of the tachometer voltage output from the Pine controller after first filtering and rectifying it the same way as the Ai signal. A thennostated cell was used to control the temperature at 25.0 "C. Three electrode cell configurations with saturated calomel reference and graphite rod counter electrodes were employed. A Pine Instrument epoxy-sealed Au disk electrode (AFMD28E) with an area of 0.197 cm2was used for all experiments. Saturated O2 and air-saturated solutions in 1.0 M KOH were obtained hy dispersing either gas through a fritted glass bubbler for 1 h. Nitrogen gas and air were blended to obtain levels of O2much lower than those of air-saturated solutions. Ai vs. f/w ratio data were obtained potentiostatically in the limiting current regions of either oxygen wave. The f / w ratio was varied by changing f over 0.75-15 Hz and holding w at 900 rpm
-1.6
-1.2
-0.0
0.0
-04
+04
E D , V v s SCE
Figure 1. Average current ( i ) and modulated current (AI) vs. potential for 0, in 1.0 M KOH at a gold disk electrode. Saturating gas, dilute
0, in N,. Scan rate 3 0 mVIs, = 5.16 rpml", w112 = 3600 rpm (60 Hz), f = 15 Hz (p = 0.25). Note: Aili ratio is not scaled to
Aw"2/w1'2.
(15 Hz). This provides a range of p = f / w from 0.05-1.00. was kept at 3 rpm1/2,a convenient level. The frequency of the filter was adjusted accordingly to keep the band-pass setting always at l/zf-2f. RC filtering of the rectifier was adjusted as required by f to provide
