The HPh’ is not a stable species in DMSO and a disproportionation reaction is probable.
2 HPh’ -% HzPh
+ Ph
(12)
The concentration of HPh’ should be small and can be disregarded, especially in the early portion of the reaction.
-d‘HzPhl = ki[HnPh][‘OH] - kz[HPh’I2 dt = klK112&lzPh][Hz02]112 - k2[HPh’l2
Further experimentation is required to verify the postulated mechanisms.
(13)
RECEIVED for review October 6, 1971. Accepted December 14, 1971. This work was supported by the National Science Foundation under Grant No. GP-16114. We are grateful to the Public Health Service for an Environmental Sciences Traineeship for R. Y. K., PHS Grant No. 5 TO1 ES 00084-03.
Comparative Study of a Wide Variety of Polarographic Techniques with Multifunctional Instrumentation A. M. Bond Department of Inorganic Chemistry, Unioersity of Melbourne, Parkuille, 3052, Victoria, Australia
D. R. Canterford Department of Physical Chemistry, University of Melbourne, ParkoilLe, 3052, Victoria, Australia Recent advances in electronics have enabled the possibility of building extremely versatile multifunctional polarographic instrumentation. Such instrumentation provides opportunity for realistic experimental evaluation and comparison of a large number of polarographic techniques. Using the PAR Model 170 Electrochemistry System, a comparative study of the determination of copper in 1M NaN03 by conventional and rapid dc; Tast dc; derivative Tast dc; conventional and rapid ac (both phase-sensitive and nonphase-sensitive); Tast ac; pulse; derivative pulse; differential pulse and inverse or anodic stripping dc, ac, and pulse polarography has been undertaken. The results are reported critically, with emphasis on limits of detection and suitability for routine analysis. The development of the highly promising technique of rapid phasesensitive ac polarography is reported. The electrode parameters for the copper(l1) reduction are obtained from ac measurements.
THEPAST TWO DECADES have seen the development of a considerable number of new polarographic (voltammetric) techniques (see References 1-8 for example) to supplement the conventional form of dc polarography, which has been in existence for almost 50 years. Pulse polarography, phase(1) B. Breyer and H. H. Bauer, “Chemical Analysis, Vol. XIII,
Alternating Current Polarography and Tensammetry,” Interscience, New YorkiLondon, 1963. (2) H. Schmidt and M. von Stackelberg, “Modern Polarographic Methods,” Academic Press, New York-London, 1963. (3) D. E. Smith, in “Electroanalytical Chemistry,” A. J. Bard, Ed., Marcel Dekker, New York, N.Y., 1966, Vol. 1, Chap. 1. (4) J. J. Lingane, “Electroanalytical Chemistry,” second ed., Interscience, New York, N.Y., 1958. (5) L. Meites, “Polarographic Techniques,” second ed., Interscience, New York, N.Y., 1965. (6) G. Charlot. Ed., “Modern Electroanalytical Methods, Proceedings of the International Symposium on Modern Electrochemical Methods of Analysis. Paris, 1957,” Elsevier, Amsterdam, 1958. (7) J. K. Taylor, E. J. Maienthal, and G. Marinenko, in “Trace Analysis, Electrochemical Methods,” G. H. Morrison, Ed., Interscience, New York, N.Y., 1965. (8) G. P. Rao and S. K. Rangarajan, Trans. SOC.Adcan. Electrochern. Sci. Teclzrzoi., 4, 116 (1969).
sensitive ac polarography, second haromonic ac polarography, square wave polarography, derivative polarography, and differential polarography may be cited as examples in this respect. As well as being important in fundamental studies, such as detailed examination of electrode processes and their mechanisms, these new techniques have been widely used in trace analysis. Polarographic techniques for trace analysis (7, 8) have infiltrated almost every field in which analytical chemistry is used. The scope of these applications is illustrated by the following examples : pollution, with particular reference to water analysis (9, 10); pharmaceuticals (11); rocks and minerals, (12-14); pesticides (15); and petroleum products (16). The extraordinary variety of methodology possible in polarography, which has become available in such a short period of time, has created a problem. A new worker in the field, and indeed even the expert, is now confronted with an extremely difficult task in choosing which method to use for the trace determination of a particular species. This almost overwhelming choice of methodology, within the discipline of polarography, is in contrast to most other analytical disciplines, such as atomic absorption spectrometry, neutron activation, spectrophotometry, and X-ray spectrography. Each of the polarographic methods, in general, requires unique features of instrumentation and, at least in the past, each method has required the purchase of separate polarographic equipment. That is, if one wished to use (9) E. J. Maienthal and J. K. Taylor, A d m i . Chem. Ser., No. 73, 1968. (10) E. B. Buchanan, Jr., T. D. Schroeder, and B. Novosel, ANAL. CHEM.,42, 370 (1970). (11) R. Kalvoda, Cesk. Farm., 4, 501 (1955). (12) D. Cozzi, in “Progress in Polarography,” P. Zuman and 1. M. Kolthoff. Ed., Vol. 2 . Interscience, New York, N.Y., 1962, pp 703-711. (13) S. L. Tackett and P. T. Ong, Anal. Lett., 3, 169 (1970). (14) A. M. Bond, T. A. O’Donnell, A. B. Waugh, and R . J. W. McLaughlin, ANAL.CHEM., 42, 1168 (1970). (15) J. G. Koen, J. F. K, Huber, H. Poppe, and G. den Boef, J . Cliromatogr. Sci., 8, 192 (1970). (16) T. Ishii and S. Musha, Rer. Polarogr. (Japan), 16, 61 (1969). ANALYTICAL C H E M I S T R Y , VOL. 44, NO. 4, A P R I L 1972
721
02
0.1
0
-01
VOLT vs. Ag/AgCI
02
0 1
VOLT
VS.
may have been used, which would make comparison of the techniques even more difficult. Because of this difficulty, reviewers of polarography have been unable to give a meaningful assessment of the relative merits of the various techniques. Only vague, nonquantitative, comparisons have usually been possible in the practical sense (e.g., References 2, 7, 8) although detailed theoretical and experimental accounts of why a particular technique should be better than conventional dc polarography are frequently encountered. An exception to this is the earlier work of Ferrett et al. (17) mentioned above. Although the instruments used by these workers are now outdated, the results of their work provide one of the few detailed comparisons of polarographic techniques. Therefore, at present it is generally difficult, if not impossible, to decide from the literature which polarographic method should be used for the particular application in mind. With the advent and expanding use of solid state electronics, integrated circuits, operational amplifiers, lock-in amplifiers, etc., the possibility of building extremely versatile and multifunctional instrumentation now exists (18-21). Indeed, such instruments are now commercially available (19); for example, the PAR Model 170 Electrochemistry System (Princeton Applied Research Corporation, Princeton, N.J.) used in this work. This instrument allows a wide range of polarographic techniques to be performed using the same basic electronic components. Therefore, by keeping other variables, such as supporting electrolyte, electrodes, and electrode processes constant, it is possible to give a realistic experimental evaluation and comparison of a large number of polarographic techniques. In light of the new opportunity provided by such instrumentation, a comparative study was undertaken of the determination of copper in 1M N a N 0 3 by conventional dc; rapid dc; Tast dc; derivative Tast dc; conventional and rapid
t, -61 Ag/AgCI
Figure 1. Conventional dc polarograms of copper(I1) in 1M
NaNOs Damping; time constant of 1 sec (a). [Cu(II)] = 1 X lO-‘M (b). [Cu(II)] = 5 X 10-BM
pulse polarography, a pulse polarograph was needed, while for ac polarography, an ac polarograph was needed. For example, in 1956 when Ferrett et al. (17) undertook a comprehensive comparison of several polarographic techniques, separate instrumentation was used for each method. At present, if one wishes to determine a species by polarography, a perusal of the literature may suggest, on the grounds of sensitivity, that one technique is superior to another for this particular species. However, since the data reported in the literature is likely to have been obtained on instruments of completely different performance and reliability, this suggested order of sensitivity may be more a function of the particular instrument used, rather than a reflection of the true merits of the respective methods. Furthermore, other variables, such as different supporting electrolytes and electrodes
(18) J. B. Flato, “A New Polyfunctional Electrochemical Instrument,” Princeton Applied Research, Technical Note T-193; Amer. Lab., Feb. 1969, p 10. (19) G. W. Ewing, J . Chem. Educ., 46, A717 (1969). (20) R. Bezman and P. S . McKinney, ANAL. CHEM.,41, 1560
(1969).
(17) D. J. Ferrett, G. W. C. Milner, H. I. Shalgosky, and L. J. Slee, Analyst, 81, 506 (1956).
centration (a). Tast dc polarography (b). Conventional and rapid dc polarography
cn .-c
r .-E
(21) R. G. Clem and W. W. Goldsworthy, ibid., 43, 918 (1971).
(bl 4
3
2.
I1
722
ANALYTICAL CHEMISTRY, VOL. 44, NO. 4, APRIL 1972
/*’
ac (both phase-sensitive and nonphase-sensitive); Tast ac; pulse; derivative pulse; differential pulse; and inverse or anodic stripping dc, ac, and pulse polarography. The results are reported in the belief that they will be of interest and assistance to other workers in the field. EXPERIMENTAL
A stock solution of copper(I1) was prepared by dissolving copper metal (Koch-Light, 99.95 %) in reagent-grade concentrated nitric acid. Excess acid was boiled off and the solution was made up to volume with distilled water. All subsequent Cu(I1) solutions were prepared by taking appropriate aliquots from this stock solution. The supporting electrolyte used in all solutions was 1.OM reagent-grade sodium nitrate. The distilled water used to prepare all solutions was shown to contain no polarographically detectable copper. All measurements were made at 25.0 f 0.1 “C and solutions were deaerated with oxygen-free nitrogen. Polarograms were recorded with the PAR Model 170 Electrochemistry System. A three-electrode system was used for all work. Controlled drop times for Tast dc and ac, derivative Tast dc, and all pulse techniques were obtained with a PAR Model 172 Mechanical Drop Timer. Short controlled drop times for the rapid dc and ac techniques were obtained with a Metrohm Polarographie Stand E 354. For the inverse or anodic stripping polarography, a Metrohm hanging drop mercury electrode BM5-03 was used. With this technique, a three-minute electrolysis time was used, two minutes with stirring and the last minute without stirring to allow equilibrium conditions to be attained. All potentials reported in this work are relative to a silver/ silver chloride reference electrode (Ag I AgCl, 5M NaC1) connected to the polarographic test solution by a salt-bridge containing 1M sodium nitrate. Tungsten wire sealed in glass was used as the third or auxiliary electrode.
02
01
------
0
VOLT
02
vs
0 1
0
Ag/AgCI
Figure 3. Effect of capacitance-compensation on the shape of the dc polarogram of 5 x 10-6M copper(I1) in 1M NaNO 3 Damping; time constant of 1 sec (a). Without capacitance-compensation (b). With capacitance-compensation
RESULTS AND DISCUSSION
The choice of a suitable electrode process for use in this work required careful consideration. The choice of copper(11) in 1M N a N 0 3was made on the following bases: The determination of copper is of wide interest. The electrode process in 1M N a N 0 3is Cu(I1)
+ 2e e Cu(ama1gam)
In this medium there was no complication due to formation of an intermediate Cu(1) oxidation state. For anodic stripping polarography the product needs to be an amalgam. A “typical” electrode process was required. A system such as the often quoted Cd(I1) reduction was not thought desirable because this is an extremely fast process and was not considered representative of the type of electrode process most frequently encountered in routine analysis. It should be noted that in this work we are concerned only with the determination of a single depolarizer. Comparison of the various techniques is based on the criteria of sensitivity, reproducibility, and the time required to perform the analysis. Other criteria, such as resolution of overlapping waves or the determination of a species in the presence of preceding electrode processes, are not considered. Obviously, in such cases, the readout of derivative or ac techniques gives these methods inherent advantages over conventional dc-type current-voltage curves.
02
0 1
0
Q I
VOLT vs. AgIAgCI
02
0 1
0
-61
VOLT vs. Ag/AgCI
Figure 4. Rapid dc polarograms of copper(I1) in 1M N a N 0 3 Damping; time constant of 1 sec [CU(ZZ)] = I x 10-4~ (b). [CU(lZ)] = 5 x 10-6M
(a).
DIRECT CURRENT POLAROGRAPHIC METHODS Conventional Direct Current Polarography. Conventional dc polarograms of Cu(I1) were examined using a dropping mercury electrode with natural drop frequency and applying a scan rate of potential of 2 mV per second. Figure la shows a typical dc polarogram at a copper concentration of 1 X 10-4M. The wave is well defined with a half-wave potential of 0.073 f 0.002 volt (US. AglAgC1). At 5 X 10-6MCu(II), the charging or capacitive current from the supporting electrolyte has virtually masked the faradaic current from the electrode process (see Figure lb). Half-wave potentials were found to be independent of Cu(I1) concentration. Plots of Ede us. log[i/(id - i)] were linear with slope 29 i 2 mV, indicating that the electrode process is reversible in the dc sense. Figure 2 shows the analytical calibration curve which consists of a plot of the limiting or diffusion current (id) us. conANALYTICAL CHEMISTRY, VOL. 44, NO. 4, APRIL 1972
723
Figure 7. Derivative Tast dc polarogram of copper(1I) in 1M NaNOa [Cu(II)] = 1 X lO-*M. Drop time = 0.5 S ~ C
02 0
0 2 0 1
0
2
d
0 1
0
-01
VOLT vs. Ag/AgCI
0
VOLT vs. Ag/AgCI
Figure 5. Comparison of controlled drop time dc polarography with Tast dc polarography
ratio of faradaic-to-charging current found with longer drop times. The faradaic current, if, is proportional to ct116,where c is the concentration of the depolarizer and t is the drop time. The charging current, i, is proportional to t-1'3 and is independent of c. Hence,
Solution is 1 X 10-4M copper (11) in 1M NaNOs (a). Dc polarography with controlled drop time of 2 sec (b). Tast dc polarography with controlled drop time of 2 sec
Figure 6. Tast dc polarogram of 2 X 10-6M copper(1I) in 1M NaN03 Drop time
= 5 sec
li.l
O.O+A
0.2
0.1
0
-0.1
where k is a constant for a particular potential. Thus, for normal drop times, of say 4 seconds,
(*) IC
=2kc con".
For rapid controlled drop times, of say 0.16 second, ($)rapid
= 0.4 kc
(3)
VOLT vs. Ag/bgCI
centration of Cu(I1). The plot is linear down to 6 X 10-6M. Between this level and the detection limit of 2 X 10-6M, the relatively high contribution of the charging current to the total current made accurate evaluation of id difficult. At low concentrations, the use of capacitance compensation gave a more convenient form of readout by reducing the slope of the background, but it did not improve the detection limit. Compare Figures 3a and 36. Even at the limit of detection, currents could be measured without any interference from instrumental noise. Rapid Direct Current Polarography. Rapid dc polarograms obtained with a controlled drop time of 0.16 second and a scan rate of potential of 20 mV per second are shown in Figure 4. As with the conventional dc polarogram (Figure la) the wave is well defined at 1 X 10-4M (Figure 4a). At or near the detection limit, the charging current again masks the faradaic current, as shown in Figure 46 (compare with Figure 16). Half-wave potentials of 0.069 f 0.002 volt (us. AglAgC1) were close to those obtained from conventional dc measurements, and were found to be independent of Cu(I1) concentration. Plots of E d c us. log[i/(id - i)] were linear with slope 29 =!z 2 mV, indicating that the electrode process is reversible. A plot of limiting current us. Cu(I1) concentration is linear down to 6 X lO-6M, as shown in Figure 2. Below this level, the relatively high charging current makes evaluation of id difficult. The detection limit of 3 X 10-eM was similar to that found for conventional dc polarography. The slightly lower detection limit for conventional dc compared with rapid dc probably results from the more favorable 724
ANALYTICAL CHEMISTRY, VOL. 44, NO. 4, APRIL 1972
Therefore, the ratio of faradaic-to-charging current is less favorable under rapid polarographic conditions, for a given concentration. This is particularly apparent at low Cu(I1) concentrations, where the charging current makes a significant contribution to the total current (compare Figures l a and 46). Tast (Current-Sampled)DC Polarography. Tast dc polarograms were recorded using controlled drop times of 0.5, 1, 2, and 5 seconds. The current was sampled near the end of the drop life for 5 msec. Since the faradaic current, if, is proportional to t116,while the charging or capacitive current, i,, is proportional to t - l l 3 , the maximum value of the ratio if/icis obtained by measuring the current near maturity of the drop. The complete current-voltage curve for 1 X 10-4M Cu(I1) is shown in Figure 5a. Figure 56 shows the corresponding current-sampled readout form. The detection limit for Tast dc, 1 X 10-6M, was only marginally better than for the conventional or rapid dc methods. However, using Tast dc, it is much easier to evaluate id at low concentrations accurately because of the discrimination against the charging current (2). Compare Figure 6 with Figures 16 and 46 which all refer to 5 X 10-6M Cu(I1). This discrimination was found to be more beneficial at longer drop times (Le., 2 or 5 seconds), particularly at low Cu(I1) concentrations. The calibration curve shown in Figure 2 is linear down to 2 X 10-6M, and any uncertainty in measuring id was encountered only in the 1 to 2 X 10-6M range. Therefore, for the determination of copper(I1) in the 10-'jM range, Tast dc is superior to either conventional or rapid dc methods, For 10-5M Cu(II), or greater, this advantage of the Tast dc is no longer significant and the time saved in
02
0 1
0
VOLT
62 61 vs. Ag/AgCI
0
-0.1
Figure 9. Effect of scan rate of potential on derivative pulse peak height
02
0.1
0
-01
VOLT vs. AglAgCI
61 0 -61 VOLT vs. AgIAgCI
02
Figure 8. Pulse polarograms of copper(I0 in l M N a N O a Drop time = 2 sec (a). [CU(II)I = 1 x 1 0 - 4 ~ (6). [Cu(II)] = 5 X 10-6M
using very short controlled drop times and fast scan rates with the rapid dc method recommended the latter technique for routine analysis. Derivative Tast DC Polarography. Derivative Tast dc polarograms were recorded using the same drop times and current sampling procedure as described above with the Tast dc technique. Figure 7 shows that the polarogram consists of a peak superimposed on a relatively constant background, which is a more convenient form of readout than the corresponding Tast dc polarogram (Figure 56). Any noise present in the Tast dc polarogram appears to be greatly magnified when the derivative is recorded, and this noise becomes a problem at low concentrations. Consequently, for Cu(I1) less than lO-SM, reproducibility is very poor and the derivative Tast dc method is not recommended for trace analysis, within the context of this work, where resolution of overlapping waves is not taken into account, as mentioned earlier. Another disadvantage of derivative Tast dc polarography is that for irreversible processes, for which the conventional dc wave becomes drawn out, the derivative peak will become very broad and may be difficult to distinguish from the background noise, particularly at low concentrations. PULSE POLAROGRAPHIC METHODS
Pulse Polarography. In pulse polarography, as with Tast dc polarography, discrimination against capacitive current is effected by sampling the current near the end of the drop life. However, in contrast to dc polarography, the potential is applied to the electrode only for a short time near the end of the drop life, each succeeding drop having a slightly higher pulse applied to it. This minimizes the total amount of capacitive current. Burge (22) has discussed the various forms of pulse polarography and their mode of operation with the instrumentation used in this work. Pulse polarograms were recorded with controlled drop times of 0.5, 1, 2, and 5 seconds and the current was sampled for 5 msec. Most voltage scans were commenced at 0.2 volt us. Ag~ AgCl. (22) D. E. Burge, J . Chem. Educ., 47, A81 (1970).
Solution is 1 X lO-'M Cu(II) in 1M NaNOa. Drop time = lsec (a.) Scan rate = 5 mV/sec (6). Scan rate = 10 mV/sec
Figure 8a shows a typical pulse polarogram, for 1 X 10-4M Cu(I1). The shape of the current-voltage curve is essentially the same as for Tast dc. Figure 86 shows that in considerably more dilute solutions, the wave is still well defined. A small amount of noise is evident but it was not sufficient to cause difficulties in measuring the limiting current. The limit of detection was 5 x lO-'M. No difficulty was found in obtaining a linear calibration curve down to 1 X lo-". As for Tast dc, the best results are obtained with longer drop times of 2 or 5 seconds and the results reported here refer to these times. Below 1 x 10-6M,the slope of the base line from the supporting electrolyte caused uncertainties in measurement of the limiting current. Attempts to decrease the slope of the base line, such as using different starting potentials, stringent degassing, and the use of a polarographic cell incorporating a Luggin capillary to minimize resistance, were of no avail. For the determination of copper(I1) below 10-5M, the pulse technique is superior to any of the dc methods. The only comparable dc method in this concentration range is Tast dc polarography, but the significantly lower limit of detection for pulse polarography recommends the latter technique. The time required for recording a Tast dc or pulse polarogram is similar, since both techniques give better results at longer drop times. For 10-5MCu(I1) or greater, pulse polarography does not appear to possess any advantage over the dc methods and rapid dc is preferred in this concentration range because of its much faster scan rates. Derivative Pulse Polarography. In derivative pulse polarography, the current measured for a given pulse is subtracted from that for the succeeding pulse and the resulting difference is recorded. As for derivative Tast polarography, the readout is in the much more convenient form of a peak. With the instrumentation used in this work, the height of the peak depends on the scan rate, as shown in Figure 9, and on the drop time. At low concentrations, noise becomes a problem, and although the signal is quite detectable, accurate measurement of the peak height is difficult (see Figure lo). Therefore, this technique is not recommended for accurate trace analysis, although for {qualitative identification of copper(II), it is satisfactory certainly down to 1 X 10-eM. Differential Pulse Polarography. In this technique a linearly increasing dc voltage is applied and a pulse of fixed height is superimposed on the voltage near the end of the drop life. The current is sampled just before and at the ANALYTICAL CHEMISTRY, VOL. 44, NO. 4, APRIL 1972
725
Figure 10. Derivative pulse polarogram of 5 x 10-6M copper(@ in 1 M N a N 0 3
Figure 12. Differential pulse polarogram of 5 X 10-6M copper(II) in 1 M NaN03
Drop time = 2 sec. Scan rate = 5 mV/sec
Drop time = 2 sec Pulse amplitude =25 mV 0.1
02
0
-01
VOLT vs. Ag/AgCI
the process is not particularly fast and is certainly not reversible on the ac time scale. This or some other feature of the copper(I1) electrode process may account for the limit of detection being somewhat higher than expected. With the PAR Model 170 System it was also observed that theoretical relationships in pulse polarography were more nearly obeyed at slower scan rates. However, instrumental distortion incurred did not invalidate linear concentration versus current relationships. ALTERNATING CURRENT POLAROGRAPHIC METHODS
1 ’ 02
0’1
0
-0.1
VOLT vs Ag/b&l
02
01
0
-01
VOLT vs AqlAgu
Figure 11. Differential pulse polarograms of copper(I1) in lMNaNO3 Drop time
= 2 (a).
sec. Pulse amplitude = 100 mV
[cum)]= 1 x i o - 4 (6). [Cu(II)] = 5 x 10-6M
~
end of the pulse, and the readout is the difference between the two currents. Fixed height pulses of 5, 10, 25, 50, and 100 mV were used in this work and controlled drop times were used as before. Differential pulse polarograms for 1 X lO-*M and 5 X 10-6MCu(I1) are shown in Figures l l a and llb. By using large amplitude pulses, it is possible to record a much higher “current” per unit concentration with differential polarography than with the polarographic techniques discussed previously. This enables almost noise-free polarograms to be recorded even at very low concentrations. However, the extreme broadness of the differential pulse peak is obvious from these figures. By using pulses of smaller amplitude, it is possible to obtain better resolution, but this also decreases the height of the peak, or sensitivity, as seen by comparing Figure 12 with Figure l l b . With slow scan rates (1 mV/sec or less), a long drop time ( 5 sec) and pulses of large amplitude, 1 X 10-7M Cu(I1) could be detected. However, under these conditions, the peak was so broad that it was of little use for accurate trace analysis. At least for the determination of Cu(I1) in routine analysis, there seems to be little advantage in using differential pulse rather than the normal pulse method, unless one is particularly interested in utilizing the slightly lower limit of detection. Comment on Pulse Polarographic Methods. Perusal of the literature would suggest that the detection limit for copper(I1) should have been lower than 1 X lO-’M with these methods, on the basis that the electrode process is reversible. The electrode process is reversible in the dc sense; however, ac measurements to be discussed in the next section show that 726
ANALYTICAL CHEMISTRY, VOL. 44, NO. 4, APRIL 1972
In ac polarography, a small amplitude alternating potential is superimposed on the dc voltage and the resulting alternating current is measured. With this method, there are a large number of variables. For example, the amplitude and frequency of the applied ac voltage may be varied over wide ranges, the readout may be in phase-sensitive or nonphasesensitive form, and controlled or natural drop times may be employed. Alternating current polarography provides a convenient approach to describe fully the electrode process in terms of kinetic parameters. Thus using this technique, in addition to the analytical considerations discussed with the other techniques, the electrochemical parameters for the Cu(I1)
+ 2e Ft Cu(ama1gam)
electrode process will be evaluated. AC Polarography with Natural Drop Time. Polarograms were examined using a dropping mercury electrode with natural drop time and applying a scan rate of potential of 2 mV per second. PHASE-SENSITIVE. In ac polarography, the charging current is 90” out of phase with the applied ac voltage, provided there are no effects due to Ohmic iR drop, whereas the faradaic current is usually 45” or less out of phase, depending on the nature of the electrode process. In principle complete discrimination against the charging current should be possible, with only the faradaic current being recorded, if measurements are made either in phase with the applied ac voltage, or 180” out of phase. However, because of resistance effects, complete separation of the charging and faradaic currents is not possible and some charging current is always measured (3, 23). Polarograms were recorded with applied ac voltages of 0.1, 1, and 10 mV (peak to peak) and frequencies varying from 10 to 1000 Hz. An ac voltage of 10 mV at a frequency of 100 Hz provided optimum conditions for the determination of copper(I1) by ac polarography. Table I gives a comprehensive account of the limits of detection found with various combinations of applied (23) A. M. Bond, ,” ANAL.CHEM., 44,315 (1972).
Table I. Determination of Copper(I1) by Phase-Sensitive AC Polarography at Various Applied Voltages and Frequencies Frequency, Hz [CUI,M AE, mV 10 100 lo00
oaol 6 VOLT vsAglAgcl
62
oi
0
VOLT vs.Ag&2
Figure 13. Comparison of phase-sensitive and nonphase-sensitiveac polarography
Solution is 4 X 10-5M copper(I1) in 1M NaN03. Damping; time constant of 1 sec (a). Phase-sensitive (b). Nonphase-sensitive AE = 10 mV, w = 100 Hz.
t
61 6 VOLT vs. Ae/Ascl
Q2
61 0 VOLT vs. A g w l
02
Figure 14. Comparison of phase-sensitive and nonphase-sensitiveac polarography A E = 10 mV, w = 100 Hz. Solution is 3 X 10-6M copper(I1) in 1M NaN03. Damping; time constant of 1 sec (a).
Phase-sensitive
(6). Nonphase-sensitive
voltage and frequency. For all combinations, linear plots of peak current ( I p - ) us. concentration of Cu(I1) were obtained. Although the use of higher frequencies gave higher faradaic currents per unit concentration, the residual charging current increased with frequency at a greater rate than the faradaic current. At lower frequencies, the signal-to-noise ratio becomes unfavorable. With lower values of the applied ac voltage, a lower current per unit concentration is recorded, and the signal-to-noise ratio again becomes unfavorable. The choice of applied ac voltage and frequency therefore reflects a compromise between obtaining the highest faradaic current per unit concentration with the most acceptable faradaic current-to-charging current and signal-to-noise ratios. A detailed account of these phenomena has been given in a recent review by one of us (23). Figure 13a shows a typical phase-sensitive ac polarogram at 4 X lO-SM Cu(I1). At 3 X 10-6M Cu(II), the wave is still well defined, although noise is evident at this level (see Figure 14a). With an applied ac voltage of 10 mV and a frequency of 100 Hz, copper(I1) could be determined accurately down to 1 X
x
QD QD QD QD QD QD 4 x 10-4 QD QD QD QD 0.1 QD QD 1 x 10-4 10 QD QD 1.o QD QD D 0.1 QD 6x 10 QD QD 1.o QD QD D D 0.1 4 x 10-5 10 QD QD 1 .o QD QD ND D 0.1 1 x 10-5 10 QD QD 1 .o QD QD ND ND ND 0.1 D 6x 10 QD QD D D 1 .o ND ND ND 0.1 ND D ND 4 x 10-6 10 QD D D ND 1 .o ND ND ND 0.1 ND ND D 1 x 10-6 10 ND ND ND 1 .o ND ND ND 0.1 a QD = quantitatively detectable with better than 2% reproducibility. * D = detectable, but with less than 2% reproducibility. c ND = not detectable. 6
10 1.o 0.1 10 1.o
QD" D* NDc QD D ND QD D ND QD ND ND QD ND ND D ND
Table 11. Variation of Half-Width of AC Wave with Frequency Applied ac voltage = 10 mV. [Cu(II)] = 1 X 10-3M Frequency, Hz Half-width, mV lo00 71 800 600 500 200 100 10
68 67 63 56 53 48
10+M. The limit of detection was about 5 X 10-7M. The ac , these conditions was 0.073 j~ peak potential, [ E d c l P e B k under 0.002 volt us. Ag/AgCl, which coincides with the dc half-wave pontential. [EdClpeak was independent of concentration. NONPHASE-SENSITIVE. Nonphase-sensitive ac polarograms for 4 X 10-5M and 3 X 10-6M Cu(I1) are shown in Figures 13b and 14b, respectively. Comparison with the corresponding phase-sensitive polarograms shows the value of phase-sensitive instrumentation. It can be seen that at 3 X 10+M Cu(II), the charging current completely masks the faradaic current unless the phase-sensitive technique is used. Phase-sensitive detection gave about a tenfold improvement in the limit of detection for copper(I1). Calculation of Electrode Parameters from AC Polarography. From the dc polarography, it has been established that for Cu(I1) reduction in 1M NaN03, the dc electrode process is reversible. However, ac measurements show that the electrode process is not reversible or diffusion controlled in the ac sense. Table I1 gives the variation of half-width of the ac wave with frequency, at constant applied ac voltage. At the lowest ANALYTICAL CHEMISTRY, VOL. 44, NO. 4, APRIL 1972
727
a = charge transfer coefficient ks = heterogeneous charge transfer rate constant EaC = dc component of potential Ellsr = reversible dc half-wave potential F(t) is a function which reduces to unity for reversible dc charge transfer. Other symbols are those conventionally used. For the high frequency limit,
601
i! 501
/
/
i
1
I
i /
Using this equation, with ([Edclpeak - El/;) equal to 0.010 volt, a value of a of 0.31 was obtained. From Equation 8, = 0.338 when Edo = [Edclpeak, for the high frequency limit. Substituting for a,p, and j in Equation 5 gives (10) ‘Oli I
10 20 [ F R E Q U E N C Y ~~
0
Assuming Do = DR,Equation 6 gives D = DO = D R . At the potential where Edo = [E&~L, (I-)z equals the limiting peak current at high frequency, ( Z p ~ ) ~ . Substituting the appropriate terms in Equation 4 gives
30 $ 2
Figure 15. Variation of ac peak current with square root of frequency
(Ip)z frequency used, the half-width approaches that expected for a reversible process (Le., 90/n mV), but as the frequency is increased, considerable deviation from this value occurs. Similarly, at low frequency, the ac peak potential, [Edclpeak, is virtually coincident with the dc half-wave potential, but with increasing frequency, a positive shift in [EdClpsakwas observed. Figure 15 is a plot of ac peak current (I,-) us. square root of frequency. The plot approaches linearity at low frequency. All these observations are consistent with the electrode process approaching ac reversibility at low frequencies. That is, the electrode process can best be described as quasi-reversible, with reversible dc charge transfer (3, 23). The theory for this class of electrode process has been reviewed by Smith (24, and will be used to calculate the electrode parameters for the copper(I1) reduction. The limiting amplitude of the ac current at high frequency is given by the relationship (’-)’
=
n2F2ACDo1/2AEXF(t) 4RT cosh2(j/2) ks Dl12
= - (&
where
D
=
+
D,@DR“
p = 1 - a
(4) (5)
(6)
(7) (8)
and the symbols used are as follows, n = number of electrons in the charge transfer step A = area of electrode at end of drop life C = concentration of depolarizer DO = diffusion coefficient of oxidized species DR == diffusion coefficient of reduced species (23) Ref. (3), pp 26-42. 728
ANALYTICAL CHEMISTRY, VOL. 44, NO. 4, APRIL 1972
=
2 .I 62n 2F2ACAEks 0.338 4RT cosh2
(1)
The following parameters were used to calculate ks from Equation 11, n = 2 T = 298 OK c = 1 . 0 x 1 0 - 3 ~ R = 8.314 J deg-l mole-’ AE = 1OmV F = 96500 C mole-’ A = 0.85 rna/3t2/3 (see ref. 25) (Z,w)z = 85 pA = 0.032 cm2 giving a value of k , of 3.4 X cm sec-1. The most comparable data in the literature are those of Randles and Somerton (26) who found a value of k , of 4.5 x cm sec-1 in 1 M KNO3 at 20 “C by impedance measurements. The rate constant found in the present work is consistent with reversible dc charge transfer. Rapid AC Polarography. The technique of rapid ac polarography, with short controlled drop times and fast scan rates of potential, has been discussed in a recent paper (27). In this article it was pointed out how little use this technique has had, and it was concluded that the technique could be given much wider usage than presently accorded. Furthermore, it appears that phase-sensitive detection has not been employed with rapid ac polarography to date. The possibility of using phase-sensitive instrumentation with the rapid ac technique was therefore investigated. A controlled drop time of 0.16 sec and a scan rate of POtential of 20 mV/sec were used to record the rapid ac polarograms. PHASE-SENSITIVE. A preliminary survey showed that the theoretical relationships found with phase-sensitive ac polarography with natural drop time could be extended to rapid phase-sensitive ac polarography. (25) J. Heyrovsky and J. Kuta, “Principles of Polarography,” Academic Press, New YorkiLondon, 1966, p 40. (26) J. E. B. Randles and K. W. Somerton, Trans. Faraday SOC., 48, 951 (1952). (27) A. M. Bond, J . Electrochein. SOC.,118, 1588 (19711,
n
J
I -01
0
VOLT VOLT y5. As/AscI
VDLT vs As/A9cI
Figure 16. Comparison of phasesensitive and nonphase-sensitive rapid ac polarography A E = 10 mV, w = 400 Hz. Drop time = 0.16 sec. Solution is 1 X
10-3M copper(I1)in 1M NaNOa (a).
(b).
Phase-sensitive Nonphase-sensitive (b)
(0)
n
I I
JL
i
02
vo LT
VS.
61 0 AgfAgCI
Figure 17. Comparison of controlled drop time ac polarography with Tast ac polarography A E = 10 mV, w = 100 Hz. Phasesensitive detection. Solution is 1 X 10-4Mcopper(II) in 1M NaN03 (a). ac polarography with controlled drop time of 1 sec (b). Tast ac polarography with controlled drop time of 1 sec
A rapid phase-sensitive polarogram for 1 X lO+M Cu(II), recorded at an applied ac voltage of 10 mV and frequency of 400 Hz,is shown in Figure 16a. The considerable discrimination against charging current may be seen by comparing this polarogram with the corresponding nonphase-sensitive polarogram shown in Figure 16b. The detection limit with this technique was similar to that for phase-sensitive ac with natural drop time, with 1 X 10-6M Cu(I1) readily being detected. With Tast dc and pulse polarography, very short drop times and rapid scan rates of potential are not practical because the relative amount of discrimination against the charging current decreases as the drop time decreases. However, with ac polarography it appears that phase-sensitive detection enables almost complete discrimination against the charging current regardless of the drop time. With the use of rapid scan rates and the corresponding short analysis times possible, the technique of rapid phasesensitive ac polarography appears to have great potential. A detailed investigation of its analytical applications is being carried out, the results of which will be reported in a later communication. NON-PHASE-SENSITIVE. The limit of detection for rapid nonphase-sensitive ac polarography at 400 Hz is about 4 X 10-6M
a
02
vz &/A@
Figure 18. Inverse dc polarogram of 2 x 10-nM copper(I1) in 1M NaNOa
Cu(II), since the charging current almost completely masks the faradaic current at this level. By comparison, the corresponding phase-sensitive wave at this level and at this frequency is still very well defined. Phase-sensitive detection is obviously considerably superior to nonphase-sensitive detection with rapid ac polarography. For this reason and because the latter technique has been investigated in detail recently (27), no further work was undertaken on reduction of copper(I1) by rapid nonphase-sensitive ac polarography. Tast (Current-Sampled) AC Polarography. Tast ac polarograms were recorded with controlled drop times of 0.5, 1, 2, and 5 seconds. The current was sampled near the end of the drop life for 5 msec. Figure 17 shows a comparison of a controlled drop time polarogram, with and without current sampling. Current sampling, with either phase-sensitive or nonphase-sensitive detection, appears to have limited practical application in ac polarography, because it provides no discrimination against the charging current. Its only function is to provide what might be considered a more convenient form of readout. This is in contrast to dc polarography where current sampling discriminates against the charging current and gives considerable improvement in the precision of measurement of i d at low concentrations. INVERSE (ANODIC STRIPPING) POLAROGRAPHIC METHODS
With inverse or anodic stripping polarographic (voltammetric) methods, a sufficiently negative potential is applied to the hanging mercury drop electrode (HMDE) to reduce the copper(I1) to copper(0). By controlled electrolysis at this potential, the Cu(0) can be concentrated into the HMDE by forming an amalgam. The copper amalgam can then be stripped of its copper by changing the potential of the HMDE in a positive direction, and the peak height of a currentvoltage curve obtained in this manner is proportional to the concentration of copper. In this work, hanging mercury drops 0.76 mm in diameter and with a surface area of 1.80 c 0.05 mmz were used. The Cu(I1) solutions were electrolyzed in the presence of 1MNaNO3at a potential of -0.1 V us. Ag AgCl for 3 minutes. The copper amalgam was then stripped by scanning the dc potential by dc, ac, or pulse methods in the positive direction. With the dc and ac methods, scan rates of potential between 20 and 100 mV per sec were used. With pulse techniques much slower scan rates had to be used. Figures 18 and 19 show the inverse dc and ac scans, respectively, for 2 X 10-6MCU(II). The inverse dc wave was found to be reversible with the inverse dc El/?being approxiANALYTICAL CHEMISTRY, VOL. 44, NO. 4, APRIL 1972
729
,u i/
vi
0
QI
VOLT
02
vs. AglAgCI
‘ 1
Figure 19. Inverse ac polarogram of 2 X 10-EMcopper(1I) in 1M NaN08
T - 0i:
0
-01
VOLT
0 4
--
-
0.2
VOLT
Ag/AgU 0.1
02
vs. Ag/Ag€I
mately 28/n mV more anodic than the polarographic dc Ell2, as theoretically predicted (28). The inverse ac peak potential was found to be extremely close to the polarographic dc Ell2,and the shape of the wave was similar to that obtained with the dropping mercury electrode. At a frequency of 100 Hz, the half-width of the inverse ac peak was 50 mV, which is in excellent agreement with the value obtained with the dropping mercury electrode (see Table 11). These results are in agreement with theory (29). (28) R. S. Nicholson and I. Shain, ANAL.CHEM.,36, 706 (1964). (29) W. L. Underkofler and I. Shain, ibid.,37, 218 (1965).
0
0 1
Figure 20 shows the inverse dc scan for 5 X lO-*M Cu(I1). The close proximity of mercury oxidation partially obscures the copper(I1) wave and limits the detection of copper to about this concentration. With inverse ac analysis, using phase-sensitive detection, 1 X lO+MCu(II) could be detected. The close proximity of mercury oxidation prevents the inverse ac wave from returning to the base line as shown in Figure 19. This effect is, of course, much more pronounced at low concentrations, and again limits the detection of copper. The inverse pulse scan for 2 x 10-6M Cu(I1) is shown in Figure 21. The limit of detection with this technique was about 1 X lO-*MCu(II). Inverse differential pulse scans are shown in Figure 22. The significantly higher “current” per unit concentration obtainable with this technique compared with the other inverse
-01
0.2
02
VOLT vs. AgIAgCI
VOLT vs. AglAgCI
Figure 22. Inverse differential pulse polarograms of copper(I1) in 1M NaN03 Pulse amplitude
= 50
(a). [Cu(II)] = 2 (b). [Cu(II)] = 5 730
vs
Figure 21. Inverse pulse polarogram of 2 X 10-6Mcopper(II) in 1MNaN03
-
Figure 20. Inverse dc polarogram of 5 X 1O-gM copper(I1) in 1 M N a N 0 3
-01
2,
ANALYTICAL CHEMISTRY, VOL. 44, NO. 4, APRIL 1972
x x
mV
10-6M 10-M
Method Conventional dc Rapid dc Tast dc
Table 111. Summary of Polarographic Data for Determination of Copper Concentration limit recommended for quantitative analysis, Limit of Comments M detection, M 2 x 10-0 3 x 10-6 1 x 10-6
1
.. x x x
5
x 10-7
Derivative Tast dc Pulse Derivative pulse Differential pulse Phase-sensitive ac with natural drop time Rapid phase-sensitive ac Tast ac
5 ~5
Sl
x
10-7
6 x 10-8 6 X 10-8 2 x 10-0
1
10-7
...
10-6
... ...
10-7
10-8
x
1 *1
x
10-6
x
10-0
...
techniques is readily apparent, [e.g., compare Figures 18 and 22a, which both refer to 2 x 10-6MCu(II)]. The extreme broadness of the inverse differential pulse peak evident with the larger pulse heights proves to be a considerable disadvantage for the determination of copper(II), as mercury oxidation tends to overlap the copper(I1) peak, as shown in Figure 22b. However, because of the higher “current” per unit concentration, this technique was found to be the most sensitive, with 5 x 10-9MCu(I1) being detectable. For routine analysis by the anodic stripping method, the ac technique is recommended as being the most convenient. The convenience arises from two points. One is the sharp peak form of the readout, but even more important is the possible use of rapid scan rates of the dc potential. By comparison, the inverse dc readout is not in as convenient a form, nor is the limit of detection as low. The inverse differential pulse technique although having a lower limit of detection, required much slower scan rates than the ac or dc techniques. In concluding this section, it should be noted that the limits of detection reported above are not considered by any means the absolute limits attainable with anodic stripping analysis. What has been attempted was a comparative study of the various techniques under identical conditions, and no endeavor was made to obtain the absolute limits by using a longer electrolysis time, purification of reagents, stringent removal of oxygen, etc. CONCLUSIONS Most of the polarographic techniques developed in the last 20 years or so have aimed at providing means of discriminating against the charging current. In the sense that they all succeed to a significant degree, they all provide improvement over conventional dc polarography. Furthermore, it is apparent that the state of the art for these techniques is now such that the sensitivities for an electrode process such as the reduction of copper(I1) are converging toward similar limitsthat is, the techniques which were aimed at discriminating against the charging current, investigated in this work, all provided detection limits in the 10-6-10-7M Cu(I1) range,
Considerable advantage gained by using short drop times. Considerable improvement over conventional dc for determination of Cu(I1) at low concentrations. Long drop times most favorable. Poor reproducibility at low concentrations. Not recommended for trace analysis. Superior to dc methods below 10-6M. Long drop times most favorable. As for derivative Tast dc. Most sensitive technique but waves broad under some conditions. Long drop times most favorable. AE = 10 mV and freq. N 100 Hz recommended. Far superior to nonphase-sensitive ac polarography. Measured with A E = 10 mV, freq. = 100 Hz. Far superior to nonphase-sensitive ac polarography. No discrimination against charging current provided by this form of readout in ac polarography.
with accurate quantitative analysis readily obtained to better than 5 for 10-gMCu(II) and above. With this in mind, considerations other than sensitivity should now tend to become most important. For routine trace analysis, the time taken for each analysis is also an important consideration, and the use of rapid polarographic techniques with short controlled drop times and fast scan rates of potential are strongly recommended. Of all the polarographic techniques used in this work which discriminate against the charging current, the only one which can use short drop times and still maintain the same degree of discrimination as with natural drop times, ;s rapid phase-sensitive ac polarography. Hence, for the routine determination of copper(I1) down to the 10-6M level by polarographic methods, rapid phasesensitive ac polarography, in our opinion, represents the most satisfactory technique. A summary of the results obtained with the polarographic techniques is given in Table 111, which includes detection limits and appropriate comments. For determination of copper(I1) below 1OU6Mby anodic stripping analysis, the ac technique again appears to be the most favorable. In arriving at these conclusions, we note that the pulse techniques are more sensitive than the ac techniques, but the difference does not appear sufficient to offset the considerable time saved with the rapid ac polarographic and ac anodic stripping techniques in routine analysis. Finally, it needs to be mentioned that although with an instrument such as the PAR Model 170 the same basic electronic components are used, this of course does not mean that the capabilities of each individual technique are served to the same degree. Therefore, while our comparisons are valid for this instrument, it may be that some other instrument could achieve a better sensitivity with one of the techniques that we have found to be less sensitive. RECEIVED for review October 12, 1971. Accepted December 14,1971.
ANALYTICAL CHEMISTRY, VOL. 44, NO. 4, APRIL 1972
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