RECEIVED for review April 22, 1975. Accepted June 27, 1975. This work was performed under the auspices of the U.S. Energy Research and Development Administration. Presented at the 169th Meeting, ACS, Philadelphia, Pa., 1975. Reference to a company or product name does not
imply approval or recommendation of the product by the University of California or the U.S. Energy Research and Development Administration to the exclusion of others that may be suitable.
Use of Pulsed Direct Current Potential to Minimize Charging Current in Alternating Current Polarography A. M. Bond and R. J. O'Halloran Department of Inorganic Chemistry, University of Melbourne. Parkville, Victoria, 3052, Australia
The use of a pulsed dc potential rather than the usual linear ramp In ac polarography Is descrlbed. By measurlng the dlfference In alternatlng current In the presence and absence of the pulse, subtraction of the charging current from the readout can be achieved. An approxlmate theoretlcal treatment of the technique, called differential pulse ac polarography, is presented and experimentally verified. Conslderable advantages over normal ac polarography are exhlbNed. Partlcularly when coupled with phase selective detection, almost complete dlscriminetion against charging current ls possible, even at high frequencies and with concenM. A Convenient readout shape retrations well below sults, with the peak-to-peak current parameter being linearly dependent on concentration. Whlle considerably more theoretlcal and experlmental research Is required for a thorough evaluation of this technique, results demonstrate that the use of a pulsed dc potential ramp can make an important addltion to ac polarographic techniques. Comparison wlth dc differential pulse polarography Is also presented to show the complementary nature of the ac and dc methods.
Polarographic techniques have an inherent charging current contribution present as an integral part of the experiment. The charging current, which is independent of the concentration of electroactive species, constitutes part of the total current flowing through the cell. It thus needs to be subtracted so that the concentration-dependent faradaic current can be measured. At low concentrations of the electroactive species, the charging current contribution becomes larger than the faradaic current and accurate corrections are difficult or impossible. The concentration of electroactive species a t which the charging current equals the faradaic current establishes the limit of detection. Several methods for overcoming the charging current problem are currently available. In dc polarography, the use of pulse and differential pulse techniques (instead of a linear dc potential ramp) discriminates against charging current ( I ) . With ac polarography, a sinusoidal voltage is normally applied to a linear dc ramp. The resultant ac current contains a significant charging current due to the capacitive nature of the electrode. This charging current can be shown to be 90' out of phase with the input signal. Since the faradaic current is usually 145O out of phase, the use of a phase-selective detector to measure the in-phase component enables discrimination against the charging current (2, 3). At high frequencies, however (2-6), nonideal behavior and uncompensated resistance prevent complete rejec1906
tion of the charging current; and sloping base lines and other undesirable phenomena limit the detection level. In the present work, the use of a differential pulse dc ramp as an alternative to a linear dc ramp is shown to provide a substantial improvement in ac polarography. Figure 1 shows a schematic diagram of the technique. The measurement of the difference in alternating current with and without the application of the pulse effectively subtracts out the charging current from the readout via a readily implemented electronic approach and provides a curve of extremely convenient shape for use in analytical work (see Figure 2 for example). The peak-to-peak current (Ai,-,) is a linear function of concentration and, since this parameter can be measured from the top of the positive peak to the bottom of the negative one, no base-line estimation is necessary. EXPERIMENTAL All chemicals used were of reagent grade purity. Cadmium solutions were prepared in 1M K N 0 3 supporting electrolyte. Solutions were thermostated at 25.0 f 0.1 "C and degassed with argon for 10 minutes. Polarograms were recorded using a Princeton Applied Research Corp, Princeton, N.J., Model 174 Polarographic Analyzer. A PAR Model 129 two-phasehector lock-in amplifier was used to obtain phase selective and total current measurements. An external ac sinewave oscillator (Optimation Inc; Model RCD-10) provided both the input and reference signals. The polarographic analyzer and ac circuitry were interfaced with PAR accessory 174/50.The pulsed ramp and differential amplifier were those normally used in the differential pulse polarography mode of the 174 Polarographic Analyzer. To minimize instrumental artifacts of the kind recently reported (7), time constants in the sample-and-hold circuitry were decreased by a factor of 100 compared with those supplied by the manufacturer. All measurements were made with a three-electrode system with Ag/AgCl as the reference electrode and platinum as the auxiliary electrode.
THEORY In differential pulse dc polarography, large current magnitudes per unit concentration are obtained with minimal charging current contribution. A periodic potential pulse of fixed amplitude E, is applied to the normal dc voltage ramp just prior to the end of drop life. The dc current is measured immediately before pulse application and again towards the end of the pulse duration. The difference between these two values of current is electronically stored (using sample-and-hold circuitry) and presented to a suitable readout device. The majority of the charging current is effectively subtracted out, although a small concentration independent dc component remains (8). If a similar pulse is now applied to the voltage ramp used
ANALYTICAL CHEMISTRY, VOL. 47, NO. 12, OCTOBER 1975
Figure 1. Representation of potential-time curve In dlfferential pulse ac polarography
-
(- -) Normal dlfferentlal pulse ramp, (--) pulsed ac ramp. tp = pulse duratlon, t = drop time, .? and r'. are current sampllng times before and durlng
pulse, respectlvely. EP = pulse height. In the present work, tp = 0.5 sec, t. = t', = 17 msec, ED = 5, IO,25, 50, 100 mV
= 57 msec, t
in ac polarography (i.e., to a dc ramp with a small sinusoidal ac voltage superimposed), then the resultant voltagetime curve will be as shown (Figure 1).Using the PAR Model 174 Polarographic analyzer, the sample time is 17 milliseconds (Le,, t , = t', = 17 msec). The duration of the pulse (t,) is 57 milliseconds and a drop time ( t )of 0.5 second was used. So long as there are a sufficient number of ac cycles during the pulse (Le., t , >> llw)and the ac amplitude ( A E ) is less than the pulse height (Le., AE < E , ) , then the applied ac potential will not significantly interact with the pulse potential. Thus, to a first-order approximation, both can be regarded as separate perturbations on the normal dc ramp, and the ac part of the signal can still be considered as a sine waveform, For a reversible process at a potential E1 (that is in the absence of the pulse), the ac current Z ( w t ) is given by (2):
( +
I ( w t ) l .- klCAEAlwl/Z sin ut
3
1
-d5 -66 .67 -0'8 LOL' vs Ag/Agci
-04
Figure 2. Differential pulse ac polarograms at varlous pulse amplltudes for 1.0 X lO-'MCd(ll) In 1.OM potassium nitrate Amplitude of ac potential (A€) = 30 mV peak-to-peak, frequency = 957 Hz, drop time = 0.5 sec, scan rate = 10 mV/sec. (a) EP 5 25 mV, (b) EP = 50 mV, (c) EP= 100 mV
(4)
while at E2,
where q = charge density on the electrode surface, A1 and A2 = area of electrode before and after application of the pulse, and E2 = E1 E,. Thus
+
AiC- = ( A * - -
(6)
(1)
where kl = constant for a given potential E l , C = concentration of electroactive species, AE = amplitude of ac potential, and A = drop area. The application of the pulse effectively changes the potential to E2 where:
where k2 = constant appropriate for potential E2. Using similar current sampling as in differential pulse dc polarography, a differential pulse ac polarogram results by subtracting I(wt)l from I ( w t ) 2 and plotting the difference in alternating current, hl(wt),vs. dc potential. Thus
It thus follows that AI(wt)should be linearly dependent on C, AE,and w1l2.Even if the sine wave were distorted by the pulse, the new waveform could be written as a Fourier Series to give hl(wt) a C A E W ~ For / ~ . a sufficient number of differential points (:i.e.,for a scan rate sufficiently slow that the potential increment between drops does not exceed more than about 2 mV) and assuming E , and AE are both small with AE < E , and l l w
