Feasibility and applications of programmed speed control at rotating

Feasibility and Applications of Programmed Speed Control at Rotating Ring-Disk Electrodes Barry Miller, Maria I. Bellavance, and Stanley Bruckenstein] Bell Telephone Laboratories, Inc., Murray Hill, N .J. 07974

The electrochemical response of disk and ring-disk electrodes to fast angular velocity scanning or periodic modulation is described. The relative merits of speed programming as a linear, square, or exponential function of time with respect to rapid data acquisition at these electrodes have been investigated. At sufficiently high accelerations, lags in current response due to hydrodynamic relaxation effects can be detected. However, for appropriate scan programming rates or sinusoidal modulations of the speed and after allowing relaxation to occur after a step change of speed, the current response can be accurately described by steady state mathematics (Levich equation). The use of super-imposed modulations (sine, square wave) on a steady speed or on these scanning functions has led to several new electrochemical applications and experimental advantages. For example, currents due to convective-diffusion sensitive reactions may be separated from those not influenced by rotation speed such as many surface processes or supporting electrolyte reactions. The characteristics of an apparatus necessary to carry out these various speed control programs are given.

ELECTROCHEMICAL DATA at solid electrodes can best be obtained when the relevant experimental variables such as current, potential, and time scale are closely controlled. The unique feature of the rotating ring-disk electrode geometry lies in the independent control of mass transfer through angular velocity. The experimental advantages accruing from automatic control of current and potential are well-accepted. Programmed mass transfer is also highly beneficial and, in particular, permits the optimum control of the duration of ring-disk electrode experiments. However, information concerning deviations from nonsteady state hydrodynamic behavior is vital if one is to be able to justify using, under programmed velocity conditions, the mathematics developed for a rotating ring-disk electrode by assuming an effectively steady state hydrodynamic regime (Levich equation). In earlier work (1--3), neither the hydrodynamic deviations from an effective steady state that can occur at high angular acceleration rates, nor the time optimization of mass transfer programming was seriously considered. The scan rates were, in fact, chosen to avoid such problems. This paper describes an experimental study of these programming parameters employing a new apparatus. In particular, attention was paid in these studies to examining the time dependent response of the rotating ring-disk electrode system with regard to its effect on the measurement of quantities of interest, such as diffusion coefficients and concentrations of Permanent address, Department of Chemistry, State University of New York at Buffalo, Buffalo, N.Y. (1) S. C. Creason and R. F. Nelson, J . Electroanal. Chem., 21, 549 (1969). (2) Zbid.,27, 189 (1970). (3) B. Miller and S . Bruckenstein, J . Electrochem. SOC.,117, 1032 (1970).

electroactive species, and to the restrictions on controlling the latter for kinetic studies ( 3 , 4 ) . Optimum w8can. A linear dependence of angular velocity, w , on time is experimentally the simplest to achieve, but an w112 = kt characteristic has a demonstrable analytical utility (3),as is apparent from the Levich equation

i

=

0.62nFAw”20213y-1/6CCb- C’j

(1)

where the conventional symbology is used in Equation 1. The usefulness of an exponential function w = nek1is based on the theoretical treatment of Benton (5). He found that steady state flow at a disk that is impulsively started from rest to a speed w is approached after about 2 radians of rotation. Assuming that a similar relation holds generally after an impulsive speed change from a constant initial velocity, then the time it takes to make a change in speed is inversely proportional to since a constant angular distance must be traversed. This approximate analysis suggests that a control function obtained from dwiw = kdt, or w = Ae”, produces the most rapid program for scanning between two rotation speeds while maintaining hydrodynamic equilibrium. This conclusion is supported by the work of Creason and Nelson (2). They used an exponential speed program based on their experimental observation of closer adherence of limiting currents to constant speed Levich values during a fixed time of scan when an exponential, rather than a linear, w-function was used. w1l2-Modulation. The change in current, Ai, on going from w11/2 to w21/2(Aw1’2)is found directly from Equation 1, i.e., i may be expressed as )I(

Ai

=

0.62nF,4D2/31,-1/6fCb t - CslAw’/2 i

(2)

or in an equivalent form

As will be demonstrated experimentally, the quantity Ai can be determined using either square wave or sinusoidal modulation. If a sinusoidal variation of w 1 / 2 about a mean w ~ = ~ ( ~’ ~ 1~’ 2 w2”2)/2 is imposed, a sinusoidal i2)/2 is found. variation of i about an average current (il Appropriate filtering and signal processing allows the observation of the dc component, (il$i2)/2, and the peak-topeak values of Ai and In our experiments we use a 24 dbjoctave (Butterworth) bandpass filter to obtain the sinusoidal component. This filtering scheme very effectively distinguishes between convective-diffusion processes obeying Equations 2 and 3, and nonconvective-diffusion processes independent of w. Consider the situation in which w112 is modulated sinusoidally at a frequency J’about a fixed angular velocity W O , while scanning the potential of the electrode at a speed slow

+

+

(4) B. Miller, M. I. Bellavance, and S . Bruckenstein, ibid., 118, 1082(1971). ( 5 ) E. R. Benton,J. Fluid Mech., 24,781 (1966).

ANALYTICAL CHEMISTRY, VOL. 44, NO. 12, OCTOBER 1972

1983

$15 0

0 -45 VOLTS 0

0

Figure 1. Motor speed programming circuitry

compared to the frequency of the Aw’/Z-modulation. The output of the bandpass filter yields Ai as a function of E, and is equivalent to the plot of i L‘S. E, where Ai and i are related through Equation 3. Specifically, the occurrence of a nonconvective-diffusion controlled electrode surface oxidation or reduction process, e.g., with a gold electrode in appropriate media, will not affect the filter output, and will allow the recovery of information equivalent to that present in the usual i-E curve. Similarly, the normal masking of processes of interest by the oxidation or reduction of the supporting electrolytes will not occur if these latter highly concentrated reactants give currents independent of rotation speed in the interfering potential ranges. The reduction of hydrogen ion in 1M strong acids at gold, or the anodic generation of oxygen in most solutions fall into this category. An example of these is reported in this paper. Ring-Disk Electrode. Additional considerations enter into the use of rapid angular velocity sweeps or periodic w1/2-modulation when ring electrode current measurements are taken coincident with disk electrode data at a ring-disk electrode. For example, suppose that a species is generated at the disk, and detected at the ring. Then if the angular velocity is changed in a time comparable to, or shorter than, the transit time for species from disk to ring (6), the ring current may overshoot the new equilibrium value rather than approaching it smoothly as is the case for the disk. This overshoot can occur if the effective diffusion layer thickness decrease produced by an w step increase is achieved before material generated on the disk at the lower speed reaches the ring. Other ring electrode behavior may occur, depending on the disk electrode control scheme. If the disk current is con(6) S. Bruckenstein and G. A. Feldman, J. Electrounul. Chem., 9, 395 (1965). 1984

trolled, then disk potentials normally shift during an w step in order to reflect the surface concentration changes. The disk electrode surface concentration change due to this perturbation will be mirrored at the ring and may be detected by measurement of the ring currents. Interpretation of such results can provide information on adsorption, film dissolution rates, and other phenomena at the disk electrode. In this paper, our purpose is to establish the existence of such effects, rather than examining them in detail. Hence, we shall restrict ourselves to studying the ring response in situations parallel to some of those studied at the disk. In order to make the required studies, it was necessary to design a versatile apparatus for imposing various kinds of angular velocity control on the rotating ring-disk electrode. In addition, it was necessary that the angular acceleration obtainable with this apparatus be sufficient to permit the observation of significant effects associated with nonsteady state hydrodynamic behavior in order to determine the hydrodynamic limitations inherent in various types of fast angular velocity programming. Only two previous contributions have been reported in this area. Creason and Nelson ( I , 2 ) computed the square root of a voltage produced by a tachometer generator and thus recorded w 1 i 2 cs. current. They also described an exponential speed control program. We reported (3) on the use of a operational amplifier circuit containing a squaring module to program a commercial electronically regulated motor speed controller. This device produced, rather than computed, the frequently desired w1’* dependence, and it was applied to two new techniques of hydrodynamic voltammetry in addition to automatically obtaining Levich plots of i US. w l i 2 . The apparatus described below is capable of varying angular velocity, 0, as a linear, square, or exponential function of time. Also a periodic function such as a sine or square wave, supplied from an external waveform source, may be


superimposed on any of the above mentioned w-time functions.

Speed Control Circuit. The design compares the voltage output, E=', of a tachometer generator that is mechanicr"coupled to a low inertia dc motor to a reference volta -E,. Any net difference between ET' and -EJ contr the output of a unipolar, high power operational amplifi driving the motor in such a way as to restore balance. 1' propriate analog circuitry produces the required time , pendence of E,, and therefore of the motor speed. Figure 1 is a schematic of the motor programming electronics. The voltage sources at the left marked Scan, Manual, or Step are selected by switch I to yield E,,. E,, can thus be varied linearly, adjusted uia the rotation of the: l&turn, 10 K, potentiometer, or stepped from 0 to 10 volts in 1-volt increments using the 10-position selector switch. also be combined with the output of an external fun( erator, E,, in the differential amplifier configuratic erational amplifier 2 to give E,. Choosing E, to he a iinrar ramp (Scan position of SWI) and Ew = 0, the positions Xsquare), aexponential), or ylinear) at switch I1 yield, as the output of amplifier 4, E,, an W - f motor speed control function proportional to fa, e', or f. The squaring function is produced by a Burr-Brown 9875 Squaring Module. The antilog function is obtained with a Philbrick-Nexus 4350 Logarithmic Operator, trimmed to a 5 volt/decade log response. Amplifier 4 is necessary to the suuarine function and also orovides a reauired sim - inversion idthe a h o g path. Introduction of a Deriodic E. simal will make E, a more complicated function of time as compared to the^ sole use of Scan, Manual, or Step modes. This provision is desirable since it is important in some applications that Er have a periodic component of constant frequency (4). Amplifier 7 sums E, with the output ET',and determines .: r +Amrnprl the motor speed. The tachometer resistor R,. .L.......CU"" that the motor speed is given by rpm = -loa E, (volt An analysis of the S scheme which provides wl'* = kt 1.a* already heen given (3). Application of this analysis to 1ihe L and E circuitry requires the substitution of the exponent:ial or linear voltage functions for E 2 , where E, corresponds _ tn . . . E# in Figure 3 of Ref. 3. With the appropriate compcment E2 values inserted, -E, is given by -, lOWJ6)-1, or E, ir1 the 10 S. E. and L switch Dositions.. resoectivelv. Each of these . pio&amming scheme; is calibrated so that H maximum motor speed of 10,000 rpm IS produced when E? = 10 00 volts. bor E, = 0, the S and L functions are both zero (motor stopped, E, = 0).but in the E settine- E-, will be -0.100 volt (motor s&d l k r p m ) . A recordinn of E, us. time for is mven in Fimue 2 for the L, E, and-S schemes, with 'E. ZO. -The Scan mode was used to generate E*, with dE,/dt = 0.10 volt/sec. The exponential scan mode has the lowest acceleration at the shorter times where a given angular rotation requires a correspondingly 1ong:r time period. The constant acceleration of the linear scan mode is surpassed only after 0.5 of the scan time (2500 rpm) in the S scan mode and only after 0.668 (2171 rpm) in the E scan mode. In all switch positions EJ < 0 to make E, > 0, since the motor power source, amplifier JQE, requires a positive input. JQE is a Kepco Model JQE 100-2.5HS amplifier, and it may be considered to be a high powered (250 watts) unipolar operational amplifier that is being operated open loop with the motor as load. Negative outputs at E,, which result when

I -

IO v

loolec

TIME OR EL

-linear .=".(L), _.square dependence of the motor speed (S), and exponential (E) taken at E> when functions,

~

.. . .. umen DY a linear sweep at E,.

time (sed

=

Horizontal axis at this rate has

10 E, (vole9)

Fixure 3. Promam E, (tor, trace) and tachometer derived ET'/* (bottom trice) us. time-

&"I

ET' > - RT - E, (motor going faster than proa-edspeed), RJ

yield a zero power supply output. The series diode DB(500

Eladrode cycled between 600 and 1005 rpm at 1.5 Hz. Vertical sensitivity 0.5 Vimajor division, horizontal sensitivily 100 mseejmajor a:..:-:*-

..

D ... ....""A."

"I:."

I."-

+ 1= ""A

*",.,.

%I*

,n.Jn"

readings) P N ) protects JQE from reverse voltage transients produced when the motor decelerates. Motor and Rotator. The motor used, a specially serieswound M-6 type of the Rae Motor Corporation, McHenry, Ill., was designed to have good acceleration characteristics and to have voltage and power requirements matching the Kepco supply. The previous side drive of the spindle holding the electrode (7)was replaced by an overhead motor mount coupled directly to the end of the electrode shaft (8) with PIC Design Corporation Precision Flexible Couplings. This change in drive is required for use of superimposed periodic inputs (E.),since the natural resonant frequency of the belt. drives tends to interfere with this mode of operation. Motor Braking. The deceleration characteristics of the motor control system are far poorer than the acceleration characteristics, since the feedback loop merely cuts offpower to the motor when the tachometer voltage is too high. This poor deceleration proves to be a serious limitation when nonsteady state hydrodynamic behavior becomes significant, ex.. for a steo or Deriodic change - in w . This DrOblem is (7) R. H.Sonner, R. E. Visco, and E. Miller, ANAL.C". 41, , 1498 (1969). (8) B. Miller, 1.Electrochem. SOC.,116,1117 (1969).

24

20

-

- 500

Figure 4. Left axis: Acceleration and deceleration of motor for 500 rpm L scheme steps, plotted us. average speed (center of step). Right axis: Rise time for motor to reach horizontally indicated speed from w = 0

Figure 5. Two square wave cycles at 5 Hz with Ei(upper trace, recorded twice) and E,'/* (two lower traces) Upper EFV2trace without brake, lower with 8 in.-oz braking. Vertical sensitivities and speed change identical to Figure 3. Horizontal sensitivity 20 mseclmajor division

largely alleviated by the combination of the parallel reversed diode, D,, (Figure 1) which provides a path for the inductive current produced on deceleration of the motor, and the friction of the three pairs of silver-graphite brushes on the electrode (7). A magnetic brake (Meltronics Corporation EHB 18-2), may be incorporated for modulation applications, and further improves deceleration by about a factor of 2 without significantly affecting acceleration. This brake should be inserted between the motor and the electrode shaft and its torque is varied up to 8 in.-oz drag by adjusting the current supplied to it. The frequency response of the motor system is improved over most of the speed range using this brake, at the expense of increasing the load on the motor and thus on the power supply. Except for Figure 5, given later in this paper showing the response improvement on using the brake, we report results without the brake. The large increase in power supply current and voltage output and subsequent motor heating dictate use of the brake only when special experimental needs exist. Control of is by W . A previous use of the S scanning mode (3) produced a controlled surface concentration at a rotating disk electrode. In that work, the linear voltage ramp, E,, (which controls motor speed) was used to generate a disk elec1986

trode current id, in a manner such that the ratio of ia/E, was constant while id varied. For an ideal motor control system E, 0: o1I2,hence in such a case, the ratio id/w1Iz would be constant. If -ETIIzis used for this purpose instead of the ramp voltage, E*, then possible errors in the constancy of the id/w'/a ratio due to the motor control system response lag are prevented. This approach was used when the modulating function of E, was applied for kinetic applications of isosurface concentration voltammetry' (4) and in the experiment reported in this paper on the differentiation of H P l data (4) usingsinusoidal w'~2modulation. Criteria and Tests of the Motor System Response. Depending on the scan or modulation mode being tested, certain comparisons between a reference voltage and a voltage related to the tachometer output were necessary. For example, in S scan mode experiments, it was convenient to produce a signal proportional to the o " ~ of the motor (I). This was done in Figure 1 by taking the square root of the output of voltage follower amplifier 5 with the Burr-Brown Model 9874 Squaring module. The input of amplifier 5 was the output of the tachometer generator (2.6 voltslk rpm) first scaled to 10.00 volts at 10,000 rpm by a divider and then filtered with an adjustable RC filter (R = 25 ka pot, C = 0.51 pf) to remove high frequency noise. In the S mode position, the imposed control signal, should be identical to the output of operational amplifier 6 provided the overall (labelled -d\/10E,"and also response of the system is ideal. In practice, this is not precisely the case, and a comparison of E, and E P was used as a criterion of overall system frequency response. A severe test of the motor speed control response is created by applying a periodic square wave and comparing it to the tachometer output voltage. Such a comparison of the magnitude of the imposed square wave, I&I, appearing at E, and the nominally equal tachometer response, is shown in Figure 3 with switch I1 in the S mode and switch 1in Manual. The motor's finite rise time from 600 to 1005 rpm and its longer slowing time back to 600 rpm can be determined from the -Ed12 trace. The overshoot of motor speed in either direction is minimal, and the same result is found for any size speed step between 0 and 10,000 rpm. In this, as well as other experiments where step w functions were used, the Wavetek 114 signal generator was manually triggered to provide both the step to operational amplifier 2 and a simultaneous sync pulse to a Tektronix 564 storage scope. The acceleration and deceleration characteristics of the

-a,

system are displayed in Figure 4.


151

(for linear mode L,

and AU steps of 500 rpm) is plotted on the left hand ordinate us. the average of the two step speeds. The right hand ordinate represents the time required to go from w = 0 to the speed indicated on the abscissa on applying the square wave impulse. The motor acceleration falls markedly only at the higher speeds where the available impulse power from JQE is relatively less and motor torque decreases. The deceleration is essentially constant over the usable speed range. The influence of an additional 8 in.-oz drag provided by the magnetic brake is shown in Figure 5 . No measurable loss in acceleration is visible but the slowing time is halved. A larger brake (>8 in.-oz) could be applied to make the acceleration and deceleration symmetrical around any speed below their cross-over point at 8600 rpm in Figure 4. However, in most of our applications, including modulation studies, this system has yielded an adequate response without the magnetic brake, despite this asymmetry. For scan times under 10 seconds (100 to 10,000 rpm), the S and E functions (Figure 2) require high accelerations at the upper speeds. Our system cannot always achieve these, and, for example, in a 10-second scan time of E2 from 0 to 10 volts, ET” (the scaled tachometer output) agrees with the line for EJ in Figure 2 to -9.8 seconds (nearly 9800 rpm) and then can no longer keep up because of motor acceleration limits. The S and E scans take about 10.5 and 11 seconds, respectively, to reach 10,000 rpm in this case. At a programmed 2.5-second scan from 100 to 10,000 rpm, the curve in Figure 2 and the S scan agree to -8700 rpm, while the E scan agrees to -7800 rpm. The total times to 10,000 rpm are -3.5 and -4 seconds, for the S and E scans, respectively. The L scan conforms to the imposed scanning function until the acceleration limits in Figure 4 are reached, i.e., a linear motor scan rate of 8 rpm/sec could be followed to -8000 rpm and would take 1.25 seconds starting from 0 rpm. Criteria for Determination of Hydrodynamic Relaxation Effects. Comparison of the motor speed and the electrochemical responses to demonstrate hydrodynamic relaxation effects in the system were made either oscilloscopically or by using a fast analog divider (Burr-Brown 4030A/16) to measure the ratio of appropriate voltages. One simple example of the latter procedure, described below, involves the determination of the instantaneous values of the apparent Levich ratio, id/w1I2,of a disk electrode from separate id and w 1 / 2 analog voltages, using the analog divider, and comparing this ratio to its steady state value. In all such experiments, the divider output was corrected for the separately measured error of the Burr Brown 4030 A/16 divider. This error is inversely related to the magnitude of the divisor (maximum 2.5%, 1-volt divisor), and was estimated by dividing a scanned voltage by itself to observe the variation of the divider output as a function of the magnitude of the divisor. Alternatively, analog voltages related to the actual instantaneous motor speed were recorded along with the electrochemical signal of interest. Comparison of these two signals permitted hydrodynamic relaxation effects to be detected. Chemicals, Electrodes, and Other Electronics. Solutions were prepared from reagent grade chemicals, and the house distilled water was doubly distilled from quartz. A 2.17mM Fe(II1)-1M H2S04solution and a 0.4M NaBr4N HS04 solution at an all platinum ring-disk electrode, and a 2mM CuC12-0.5M KC1 solution at an amalgamated gold ring-disk electrode were used to obtain the results described below. The disk and inner and outer ring radii were 0.239, 0.260, and 0.322 cm (Pt) and 0.238,0.256, and 0.316 cm (amalgamated Au). Collection efficiencies [corrected for the split ring-disk (8) form of these electrodes] were 0.354 (Pt) and 0.352 (amalgamated Au). The electrode construction, cells, and potentiostat-galvanostat electronics have been previously described (3, 7,8). A Wavetek Model 114 signal generator was used to provide step and periodic functions, i.e., E,.

2%

F T

N

--? V

1

-

I

0.50

1.00

2.00

Figure 6 . Analog divider output for the ratio

plotted us.

u1/2

Limiting current id measured at 0.0 V us. SCE for reduction of 2.17mM Fe(1II) in 1M H2SOaon Pt disk electrode. Current follower sensitivity 20 V/mA. Er1/2used for u 1 / Z in divider and for horizontal axis. Four square mode scan rates indicated on traces in rpm1/2sec-1. Traces are arbitrarily vertically displaced but markers representing 2 % and 10% of i d / w ’ / ? at 10,000 rpm are shown. Arrows mark scan direction. All id/W’/’ values at 10,000 rpm agree within 0.5 of the constant speed average

A bandpass filter-amplifier (Rockland 1000F-01) capable of handling the low frequency motor speed modulations was used in certain experiments to extract the periodic part of the signal (e.g., in disk current) from its dc, or linearly scanned component. In another case, a low pass configuration of the filter was used to suppress the modulated part of the signal for recording. Unless otherwise specified, the S scan mode was employed in modulation experiments. Oscilloscopic measurements were made using a Tektronix 564 storage scope with a Type 3A3 dual trace differential amplifier. RESULTS AND DISCUSSION

Disk Electrode Behavior. Above a 10-second total motor scan time from 0 to 10,000 rpm, motor speed deviations from the imposed program are negligible. We have discussed these scan time limitations of our motor system for the various imposed control functions in the Experimental, and, in this section, we test the effect of rapidly changing the motor speed on the conformity of rotating disk electrodes to the Levich equation. We have found, as reported below, that distinguishable divergence from Levich equation behavior cannot be detected at the higher speeds for scans as short as 1.25 seconds. CONTINUOUS SCAN~ ~ O D E SLevich . equation tests examining the constancy of i d / w 1 l 2in the S scan mode at different scan rates were made with platinum disk electrodes potentiostated on the limiting current for Fe(II1) reduction. The value of i d / w ” * from the Burr-Brown divider output was recorded us. the analog voltage proportional to ~ ~ This 1 ~ plot is shown in Figure 6. The data were smoothed to remove tachometer noise present at low speeds and were corrected for systematic errors in the Burr-Brown divider. All id/w1’2 cs. w1’2 scans were made in both increasing and decreasing speed directions with 10,000 rpm as the upper speed limit. Data below 400 rpm are not shown. The slowest scan took 160 seconds and the fastest -8 seconds. No difference in id/w’” is observable in forward and reverse scans at 0.5 rpml’z sec-’ (160 second scan time), while a 1 maximum difference between the two scan directions was


1987

.

are shown for the S , E, and L schemes in Figure 7. At the start of the scan, a minimum in id/w'i2 is observed. The position and shape of this minimum depend on the scanning mode, rate, and the starting speed. As might be expected from the earlier discussion about the slope of Figure 2, the linear scan program consistently gives the largest deviation. (Note that starting each program from the same speed also means the elapsed time to 10,000 rpm is somewhat different for each mode.) The fastest scan time (1.25 seconds) amplifies the deviations, while starting at lower speeds emphasizes the minimum. The exponential scanning function gives the best behavior over the whole speed scan range. The i d / w 1 I 2 data are easentinllv within the divider error at motor sneeds areater ~~, t han 400 rpm for the 10-second scan time. All scan modes yield the same id/w1I2data for motor speeds €Feater than -1200 rpm even at the fastest scanning times that c:an be recorded on our X-Yplotter. "z.1 ..._ ,rnn *nnnn .-,... x Lu-secona expuncnnai b u n ~ L V VLU IV,UUU ~ p u qLMLJ about 12 seconds for a 400-10,000 rpm traverse, and is found to be constant to within 1% over the entire speed range. It is of interest to nnte that, for all scanning methods and at aU scan rates measured including the nominal 1.25-secondtime, data taken above about 2500 rpm are free of errors arising from scanning the speed of the electrode. This result would bold even if the motor acceleration were improved at the high end of the scan range so that the motor speed followed the imposed scanning programs. This conclusion follows from the earlier observation that the present upper limit of satisfactory performance of the motor lies well above 2500 rpm. PERIODIC FUNCTIONS. Hydrodynamic Relaxation. It is of considerable si€nificance that amperometric experunents at the rotating disl< electrode may be performed at mui:h faster motor velocity scanning rates than previously thought possible. Devi;,tinnr frnm irlesll nvmrrll hphavinr of the system may arise from two sources-failure of the motor scanning system and failure to attain an effective steady state in the hydrodynamics. These deviations may be examined most directly by looking at the effect of a periodic step chance 'iz ~ on~ motor meed and the resulting convective. ~ ~ in . .w~ . diffusion current relaxation. Such data are shown in Fii position of 10 successive square wave velocity srcpa iiuiii 900 to 1225 rpm. The upper trace gives the instantaneous difference between the programmed speed, &, and -Edi', I..L :A,." 11.. "1 *^ D "+ I." in L"C UCIIUIIICLCL pa,aur.=rs, 'Yc-y S'IU"L L Y z 4 "L ALL" .US ~~~~~~

~

~

~

~

~~~

Figure I. Ratio id/w'/l us. "'Iobtained ?, as per Figure 6, for exponential, square, and linear programs at nominal full w ' / > scale sweeps of 1.25 (lower set) and 10.0 (upper set) seconds Scan started from 100 rpm (upper) and both 100 and 400 rpm (lower). oldinate calibrated in volts of analog output for iajo'/> ratio. All scans made from slow to fast speeds. Tracings are unsmoothed

.

I.

-

~

__-\

..". .."....---.-.-.-.. -_..-.___

Figure 8. Upper trace: ferential 3A3 input

E,-(--E,'/?) measured using dif-

Flat part of trace is at zero sol@; vwtical sensitivity 1.0 V/major division. Programmed E, values are 3.0 and 3.5 V (900 and 1225 rpm) Lower trace: Limiting current for F e O reduction, conditions of Figure 6 Scale sensitivity 6 pA/major division (id zero approximately 20 major divisions below trace) Horizontal scale 100 msec/major division. Each trace is the superposition of ten sweeps triggered from E, source, S mode found at twice that rate. At low motor speeds an appreciable gap between the id/w1J2data for the forward and reverse scans develops at higher scan rates, but as noted earlier, no gap is risible at high motor speeds. All i,/w'lz values agree within 0.5% of their average for the separately measured id/w'i* valuesat the 10,000rpmlimit. For this disk electrode, id values obtained under scanning conditions differ by 1% from constant speed values for a 100-second scan, and are not detectably different for longer scans over this speed range. Results obtained in similar experiments for programmed forward scans for nominal 1.25- and 10-second scan times 1988

~~~

~

~

~~

--..

I..

the motor scanning system. In this experiment note that & = E,-E, is constant and E, is a square wave. On acceleration (left edge, initial zero level not visible) or deceleration (middle), the instantaneous difference of & and -Ep'iz is equal to the value of E,. The zero level is reestablished much more quickly on speed increase than decrease, as expected from the results already shown in Figures 3 and 4. The corresponding changes in the convective diffusion controlled disk current, lower trace, clearly take more time than can be accounted for on the basis of the speed lag shown in the upper trace. This additional delay is caused by the hydrodynamic relaxation process. For perturbations around higher average speeds, the relative delays displayed by the two traces of Figure 8 become more similar, and any relaxation effects of the disk current less prominent. The theoretical and experimental examination of these diffusion layer thickness changes is discussed


4 seck 1

TIME

-

J

Figure 9. Limiting current and tachometer response to 0.170 V, 0.5-Hzsine wave at Ez superimposed on constant 4.0 V Solution and potential of Figure 6. Separately determined square

mode responses resynchronized using simultaneously recorded Wavetek square wave output. Both outputs filtered with 0.25-1.00 I-Iz bandpass (24 db/octaverolloff) and amplified 1OX. Scales are in cell current and w 1 l 2units. 0.170 V g 1.7 rpm1/2,peak-to-peak speed change is 1537-1673 rpm

in detail elsewhere (9). It is our purpose to show that, although hydrodynamic relaxation processes in electrochemical systems can be produced, information about the magnitude of these relaxation effects makes it possible to avoid serious errors. This information makes it possible to decide which, of the many possible experimental methods for angular velocity modulation, may be interpreted using the results of steady state mathematics (4). When square wave modulation is superimposed about a constant motor speed, the Aid/Aw1/2 ratio (or some other desired electrochemical parameter from the cell) can be measured during the parts of the cycle where id (or the other quantity) has reached its steady state value. Obviously, the maximum usable frequency for square wave modulation is reached when the id at the higher and lower speeds no longer reaches steady state id value before the motor speed changes. Sinusoidal Modulation. Even though the approach of the electrochemical response of a disk electrode to steady state is more readily seen using a superimposed square wave modulation, for purposes of signal filtering, processing, and averaging, it is often better to use sinusoidal modulation. Such an example is given in Figure 9 for a 2.7mM Fe(lI1) solution in 1 M H2SO4 using a platinum disk electrode. The potential of the disk was set on the limiting current region, and a 0.5-Hz sinusoidal w112-modulation superimposed on the speed of rotation, using the S mode, thus producing a speed range from 1537-1673 rpm. The resulting response of the limiting Fe(II1) reduction current and motor speed E T 1 / ?were , individually processed in a 24 db/octave (Butterworth) bandpass filter with cut-offs set at 0.5 and 2X the center frequency, amplified, and recorded with an X-Y plotter. As seen in Figure 9 there is essentially no noise visible in the tracings even though the modulated current signal represents only a small percentage, -4 %, of the average total convective-diffusion current. The narrow bandpass and sharp rolloff of the filter effectively eliminate the usual noise spectrum without any further averaging. The experimental value of the ratio Aid/Awl/*(from the peak-to-peak averages of the displayed traces) is 4.13 pA-rpm-li2 and compares favorably to the Levich ratio obtained with the same cell and solution from the slope of id us. u 1 / 2 plots, 4.15 (9) S. Bruckenstein, M. I. Bellavance, and B. Miller, unpublished data. 1970.

L

I

I

0

20

40

I

1

w"',

80

60 rpm"2

0

Figure 10. Sinusoidal modulation conditions similar to Figure 9 but 0.3 Hz (0.15-0.60 Hz bandpass) superimposed on speed scan of 1 rpm1/2 sec-1 From 400 to >7000 rpm Aid/Aw'/? is constant with average value of 4.11 PA-rpm Solution and potential of Figure 6

Y I -0.8

I -0.4

I

I

I

I

I

0

0.4

0.8

1.2

1.6

Ed, V vs SCE

Figure 11. Traces A and AmOd-Controlledpotential cathodic scans at 5 mV/sec from oxygen to hydrogen evolution in 1 M H2S04at a gold disk rotating at a center speed of 1600 rpm with a superimposed 2.0-Hz sinusoidal modulation of 2 rpm'/?. Trace A is total current follower output, trace Amadis modulated current output processed through bandpass filter of 1.00 and 4.00 Hz and 24 db/octave rolloff with 1OOX gain. Traces B and Bmod-conditi0ns identical to above except 2mM C u s o 4 added to solution. Current sensitivities 200 MA per marker A and B, 10 PA per marker A m o d and Bmod

pA-rpm-1/2. Relatively little distortion in the sine wave output of the filter is ordinarily apparent in such experiments, with two exceptions. Distortion occurs first, at low speeds where hydrodynamic relaxation effects are important and second, at high speeds when the motor response falls off. In Figure 10 the results are given of an experiment in which a 0.3-Hz sinusoidal modulation was superimposed on a w112 scan (S mode) for the solution used in the previous experiment. The speed ranged from 400 to >7000 rpm, and = 1.7 rpmll?. The E T 1 / ?and id response from the bandpass filter are recorded us. the average wl/z (from the output of sweep amplifier 1). These tracings were separately


1989

UPPER

,

LOWER

I

-i100*0

1 .-

I

I

I

I

I

20

40

60

80

100

w " ~ rpm , "2

Figure 12. A w ' / ~= 3.0 rpm'/2 0.5 Hz square wave superimposed on a 1 rpm'l2sec-I w 1 l 2 scan. Solution and potential of Figure 6. Simultaneously recorded (upper trace) total id and (lower trace) id output low pass filtered (24 db/octave below 0.25 Hz) us. Lower trace slope 4.08 pA-rpm-'/2. Slope of either upper or lower envelope of total id trace 4.13 PArpm-1/2. Average Aid/AW'/' = 12.513.0 or 4.17 PA-rpm - 'I2(modulated component)

SI

-OS -OE

s

-

\ TIME

-

Figure 13. Effect of w ' / Z scan on i, at constant id of 500 PA anodic in 0.4M NaBr-4M H2S04;E, 0.0 V OS. SCE. Horizontal axis, time. Four experiments shown:

Upper trace S 1: i, during 1 rpml/z-sec-l (100 second) S scan where the concurrent w is recorded in the lower S 1-S 10 trace Upper trace S 10: as S 1 except 10-second rate Upper trace E 10: as S 10 except E scan with concurrent w in lower E 10 trace Upper trace L 10: as S 10 except L scan with concurrent w in lower L 10 trace Steady speed value of i, indicated by marker at right of each trace

recorded and the phase relation between id and tachometer signal, given correctly in Figure 9, is determined in Figure 10 by the time at which the scan was started. Hence the apparent phase difference shown is an artifact resulting from the lack of synchronization in the starting times of the recordings. This experiment clearly displays the w l / z range over which the slope of the id-w1l2plot is constant as shown by constant peak-topeak Aid for fixed It also illustrates where hydro1990

dynamic equilibrium and motor response considerations become important. The large, slowly changing dc component of the limiting current present in this sinusoidal o-modulation experiment is effectively rejected by the high pass section of the filter. This filtering scheme might also, for example, be employed to analyze precisely changes in slope of id us. w l i z plots caused by electrochemical or chemical kinetic processes. A more sophisticated application of this mode of operation is discussed elsewhere and involves the direct determination of overpotential-current slope by isosurface concentration voltammetry (4). Separation of Convective-Diflusion Processes from wIndependent Processes. The bandpass filtering scheme can also be used very effectively in separating sinusoidally modulated convective-diffusion controlled faradaic processes from certain nonconvective-diffusion controlled faradaic processes, and from charging currents. An example of this sort of application is shown in Figure 11 for the reduction of 2mM Cu(I1) in 1 M H2S04. Trace A is the i-E curve obtained in pure 1M H2S04at a gold disk electrode while scanning from oxygen to hydrogen evolution. During the voltage scan, the electrode rotation speed was simultaneously being sinusoidally modulated at 2.0 Hz at = 2 rpm*/zaround a center rotation speed of 40 rpm1/2. The modulated output of the disk current, amplified and filtered, is shown in trace A m o d . Trace B is the ordinary i-E curve obtained in a 2mM Cu(I1) solution in 1.OM HzS04, while trace B m o d is the Aw1'2-modulation response in this solution. The i and Ai scale sensitivities were chosen so that a convective-diffusion controlled wave would give a peak-topeak modulated signal of height equal to that of the steady state dc chart response (curves A and B ) at the central ol/z. There is no discernible response in trace A m o d to oxygen or hydrogen generation. (A modulation response is found for hydrogen generation at a platinum disk in the same solution. The much higher hydrogen exchange current results in the back reaction being sensitive to convective-diffusion transport at these current levels.) There is also none for oxide film reduction (-0.9 volt us. SCE) at this sensitivity. The i-E trace (B)when 2mM Cu(I1) is present can be compared to the modulated output @ m o d ) . Aw1/2-modulation produces a current, i i Ai/2, which shows as a thickening of i in trace B, and as a sine wave in trace &od. The modulated output (sine wave) reaches a constant limiting value which remains unchanged even well into hydrogen evolution. The peak-to-peak height (trace envelope) shown in B m o d is the true height of the Cu(I1) c u limiting current at the Au disk. The dc value of the limiting current is poorly defined in trace B because of the concomitant electrolyte reduction. is The superposition of square wave modulation on shown in Figure 12 for an i d - 0 1 / 2 scan experiment with a 2.17mM Fe(II1) solution in 1M HzSOa. The upper trace is the directly measured i signal, while the lower trace is the output of the low pass filter adjusted to remove the modulated part of id. In this experiment, the unfiltered and filtered i were simultaneously recorded. These traces show that the square wave modulation technique does not interfere with the normal Levich scan, since both plots have the same average slope and this slope agrees with the constant condition value. The square wave envelope, Aid/Ao'i2, of the upper trace also gives the same slope, 4.li &-rpmliZ. The accuracy of this measurement was limited principally by the chart reading error.


-

ZERO B

Figure 14. Response to square wave A w ' / ~of 10 rpm 'I2(12252025 rpm) at 1 Hz for 2.17mM Fe(II1) in 1 M H 2 S 0 4 . Ed = 0.00 V, E, = 1.0 V, both DS. SCE Upper trace: id at 30 fiA/major division (increasing down) Middle trace: ir at 5 pA/major division (increasing up) Lower trace: ET1/?at 2 V/major division, increasing up. (ET'/z recorded separately but with identical triggering to current traces) All scale zeros arbitrarily offset Horizontal axis 100 mseclmajor division

The shapes of the superimposed square waves in the upper trace of Figure 11 reflect all the factors discussed in conjunction with the individual oscilloscope pictures : rounding of the wave at lower speeds due to hydrodynamic effects, well-defined square wave response at intermediate and higher speeds, and mechanical rise time limitations at the highest speeds. Ring-Disk Electrode Behavior. A series of o-scanning experiments analogous to some of those carried out at a single disk electrode were performed at the ring of a ring-disk electrode. A qualitative description of the types of phenomena to be expected is presented in the Introduction, and the experimental results reported below bear these predictions out. CONTINUOUS SCAN MODES. Figure 13 gives results of ring electrode experiments carried out using motor scanning conditions analogous to the disk electrode experiments of Figures 6 and 7. The abscissa in Figure 13 is time, and the speed and scan direction for the various i,-t plots can be read from the corresponding w-t plots in the figure. However, in this experiment Br- was oxidized to Brz using a constant current at the disk electrode, thus generating a constant flux of Br2. The ring electrode potential was set to reduce Br2 to Br-. If complications from hydrodynamic relaxation did not occur, the ring electrode current would be constant and independent of speed and direction of the angular velocity scan. As seen in Figure 13, only at low speeds and high o scan rates do any significant deviations of the ring current from its hydrodynamic steady state value become apparent. These deviations are emphasized by the scan direction reversals. A scan in the S mode at 1 rprn1i2-sec-l and scans in all three modes for the nominal 100-second scan period (10 rprn1i2-sec-' rate in S) are given in Figure 13 in order to make it possible to compare the ring results with selected disk data in Figures 6 and 7. The slower scan shows a minor effect on i, at slow speeds and no distinguishable deviation from constancy at the reversal of speed program at 10,000rpm. The effect on ring current is only slightly more pronounced

1

I

1

20 w"2,

I 40 rpm"*

I

60

Figure 15. Disk potential recorded during w''? scan (high to low) at 0.125 rpm%ec-' with superimposed 0.25 Hz-1 rpm'/? (peak-to-peak) sine wave modulation. Cathodic current 333 PA constant. HP-1 plot for amalgamated gold disk in 2 mM CuCI2-O.5 KCI Trace A: Ed cs. SCE including modulated output Trace B: Ed output from bandpass filter, 0.1-1.0 Hz, rolloff 24 db/octave,lOOX gain. Chart sensitivity 1 volt as marked

than on the disk current. It requires a somewhat slower scan in order to remain within 1% of the constant speed values over the whole 400-10,000 rpm range. Three different experiments involving the S, L, and E scan modes were performed, manually cycling the speed between approximately 400 and 10,000 rpm. These experimental results do not show as pronounced an advantage of the E over the S over the L mode for optimum ring current response over the full o range as was noted for the disk current. The point of initiation or reversal of scan has a marked effect on the deviation of i, from constancy, as found for disk current. The magnitude of &deviations also depends on the different elapsed times for the fixed o excursions (longest for L) and the complications introduced by the transit time situation. As a practical matter, ring electrode experiments are particularly sensitive to the presence of any reducible (or oxidizable) bulk impurity and to any accumulation of disk products (here BrI) in solution which naturally occurs during such an experiment. Convective-diffusive transport of Br2 or electroactive impurity from the bulk to the ring will produce an a l l 2 dependence in i, that will emphasize the natural direction shown by deviations from constancy of ir at faster scan rates over the wide w112 range (20-100 rpm"?) covered in Figure 12. Particular attention was paid to using fresh solutions (Br2free) for the data in this part of the study in order to minimize this phenomenon. PERIODICFUNCTIONS. The response of disk and ring electrode currents, with both electrodes potentiostated at limiting currents, and the response of the tachometer to square wave modulation in wliz are given in the oscilloscope traces of Figure 14. In this experiment Fe(II1) was reduced at a Pt disk and Fe(I1) oxidized at a Pt ring. During accelera-


1991

tion, the rise time of the motor and the transit time (6) for the “average speed” of the electrode are approximately equal (-40 msec) at this particular speed and wl/* step size. On deceleration the transit time is much less than the time the motor takes to reach 1225 rpm. At the instant of acceleration, both the ring and disk currents begin to increase simultaneously because of the shrinking of the hydrodynamic boundary layer. The effect of the increased amount of Fe(I1) reaching the ring electrode as a result of the increasing disk current begins to be important at somewhat longer times, on the order of the transit time. In combination, both of these processes lead to a negligible rise time difference in ring and disk currents as the boundary layer changes merge with those due to the transit time. [These results may be contrasted to constant speed detection of transit phenomena (6).] On deceleration, the transit time is also not apparent as the overall change is accomplished too slowly. An overshoot of the ring current above its new equilibrium value on increase in speed is seen if the “average speed” of 1600 rpm is reduced in the above experiment, because this makes the rise time of the motor shorter than the transit time for the ring-disk electrode. Thus, within the caveats illustrated by the results of Figures 1 3 and 14, the acquisition of ring-disk electrode data, as well as only disk electrode data, may be speeded up considerably by w scanning or periodic modulation procedures. The advantages accruing to analysis of disk data (filtering, signal averaging) should also be applicable to appropriate ring-disk electrode cases. METHODHP-1. As already shown in the case of Levich plots, modulation of speed can be used for differentiation of disk electrode data with respect to wllz, provided the w perturbation is small enough to yield an accurate estimate of the derivative. Earlier (3) we demonstrated the feasibility of a method of hydrodynamic potentiometry (HP-1 of the reference) which is a hydrodynamic analog of chronopotentiometry at stationary electrodes. In the HP-1 method, wllz is scanned while holding the disk current constant, and the disk potential is measured. Since w 1 i 2 is the controlled variable, the derivative plot measuring AEd/Aw112can be

1992

obtained by superimposing a small amplitude sinusoidal modulation on 0 1 1 2 and using the bandpass filter-amplifier to extract the periodic disk potential component. Such an experiment is shown in Figure 15, with both the modulated part of the potential and the total potential shown. The inflection points and slopes of the Ed-w112 relation are well correlated by the derivative signal. CONCLUSIONS

An apparatus has been described for scanning the speed of a rotating disk or ring-disk electrode as a linear, square, or exponential function of time with or without the superposition of a periodic function (sine, square wave). Hydrodynamic relaxation phenomena, rather than the motor system response, limit the maximum scan rate and frequency of applied periodic functions that can be used and interpreted by steady state theory (Levich equation). Even so, very rapid data acquisition is still possible using programmed speed control for a variety of rotating disk and ring-disk experiments. In addition, signal processing of modulated outputs from the electrochemical cell can lead to increased precision through noise reduction and data averaging (see also Reference 4). Applications of programmed motor speed control to convective-diffusion controlled amperometry and potentiometry are convenient and practical. The use of a periodic w1iZ modulation technique to separate currents which have a convective-diffusion related magnitude from those which do not, constitutes a particularly effective example of the methodology. These experimental examples given should be considered merely illustrative of a number of techniques to which one might advantageously apply controlled speed as a programmed electrochemical variable. RECEIVED for review February 14, 1972. Accepted May 3, 1972.


Feasibility and applications of programmed speed control at rotating

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