Phase-Selective lntermodular Alternating Current Polarography and Voltammetry H. Blutstein' and A. M. Bond' Department of Inorganic Chemistry, University of Melbourne, Parkville, 3052, Victoria, Australia
A. Norris Clanor Instruments, P.O. Box 75, Balywn, 3 103, Victoria, Australia
A versatile instrumental approach in Intermodular alternating current polarography has been developed whlch enables phase-selective measurement to be made at variable frequency dlfferences and amplltude. A phase-selective detector actlng as a balanced modulator is used to generate the requlred reference signal by multiplying the two sine waves frequencies. The sum frequency terms are filtered out from the response leaving the frequency difference or intermodular component as the reference signal. The development of the new instrumental approach has allowed the theoretical response for a range of intermodular polarographic and voltammetrlc techniques to be verified. A comparison with phase-selective second harmonic ac polarography using equivalent instrumentatlonshows that the background current is relatively large in the intermodular method. On this basis, and for instrumental reasons, it is therefore concluded that second harmonic techniques are superior to the related second-order intermodular methods.
The technique of intermodular polarography, in which two sine waves are simultaneously applied to an electrochemical cell and the response at the frequency difference is measured, has received scant attention in the literature (1-5). Although intermodular ac polarography was first reported ( 1 ) only a few years after the related nonlinear technique, second harmonic polarography (6),its development has stagnated while second harmonic ac techniques have been developed into a useful method in kinetic (7,8) and analytical (9-13) studies. In previous work, intermodular polarographic instrumentation has been based on the use of tuned amplifiers and measurement capabilities have been restricted to a single difference frequency with total rather than phase-selective current detection. As a result, the technique cannot at the present point of time be satisfactorily compared using the data available in the literature with modern instrumental approaches in second harmonic ac polarography in which variable frequency and phase-selective detection is widely available (11).This is unfortunate because the intermodular theory has been shown to have remarkable similarities to the second harmonic ( 4 ) and consequently the intermodular method should share many of the advantages 6f second harmonic ac polarography, if not additional features. Paynter (2), in a thesis, compared the two second-order polarographic techniques at an early stage of their development using essentially equivalent instrumentation based on tuned amplifiers and band filters in which nonphase-selective polarograms were obtained. He concluded that intermodular ac polarography shows considerable improvements in reducing the double layer charging current, particularly at high Present address, Environment Protection Authority, 240 Victoria Parade, East Melbourne, 3002, Victoria, Australia.
frequencies. As a result of this property, the intermodular ac technique was recommended for kinetic studies (2).However, other workers have preferred the second harmonic ac method for analytical work ( 3 ) .Whether either or both of these conclusions are still valid with modern instrumental approaches is arguable. A realistic comparison of phase-selective second harmonic and intermodular ac polarography using equivalent instrumentation is now presented in this paper along with a detailed description of a new instrumental procedure for intermodular polarography which allows for variable frequency difference and phase-selective detection. EXPERIMENTAL All chemicals used were of reagent grade purity. Metal ions were added as their nitrate salts. Solutions were thermostated a t 25 f 0.1 "C and degassed with high purity argon for 15 min prior to recording a polarogram. All polarograms and voltammograms were recorded on a PAR Electrochemistry System Model 170 (Princeton Applied Research Corp., Princeton, N.J.). The second harmonic response was obtained using the modification described previously (11).The details of the intermodular circuitry interfaced to the Model 170 Electrochemistry System are given in the Instrumentation section. The external oscillator used was a Wavetek Model 142 and the frequency difference was recorded on a Hewlett-Packard Model 5248'1, Electronic Counter. A Tektronix Model 5103 N cathode ray oscilloscope was used in all the setting up procedures required for interfacing of the intermodular circuitry. A three-electrode system was used to record all polarograms with Ag/AgCl (1 M NaC1) as the reference electrode, platinium as the auxiliary electrode, and the working electrode was either a dropping mercury electrode (DME) or a Metrohm Model E 410 hanging drop mercury electrode (HDME). For recording fast sweep voltammograms at a DME, the instrumentation developed in an earlier publication (12)was used.
INSTRUMENTATION Phase-Selective Intermodular ac Circuitry. On application of two (external and internal) frequencies, the nonlinear admittance characteristics of the electrochemical cell give rise to signals at the sum and difference frequencies. Signals at the fundamental and harmonic frequencies, arising from the two input signals, will also be present. Intermodular ac polarography is defined as the detection of the signal at the difference frequency ( 1 ) . Detection of the intermodular component is made possible by producing a reference signal at the difference frequency and feeding it into a phase-selective detector. The detailed reference signal circuitry is shown in Figure 1. The reference circuitry is essentially a phase-selective detector which acts as a balanced modulator and multiplies the two frequencies together. For two sine waves frequencies w1 and w~ then 2 sin w l t sin wzt = cos(w1t - w z t ) - cos(w1t
+ wzt)
(1)
and assuming that the sum frequency terms can be filtered out, the required response is obtained. In practice, the internal sine wave is shaped into a square wave and the two signals are
ANALYTICAL CHEMISTRY, VOL. 48, NO. 13, NOVEMBER 1976
1975
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not phase-locked so Equation 1 is therefore only a useful simplification to describe the functional response. A low-pass filter removes all unwanted frequencies giving a reference signal containing only the difference frequency. The reference signal generated in the above manner is fed into the internal phase-selective detector of the polarograph used and the phase-selective intermodular ac response is obtained. This 1976
approach allows all the original options of the normal ac instrument to be used, including variable difference frequency, variable amplitude etc. The only restriction is that the difference frequency must be less than twice the lower frequency and half of the higher frequency due to the harmonic relationships. Interfacing the Intermodular Circuitry. Figure 2 gives
ANALYTICAL CHEMISTRY, VOL. 48, NO. 13, NOVEMBER 1976
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Figure 3. Comparison between second harmonic and intermodular polarography (A) Phase-selective intermodular ac polarogram. f , = 500 Hz, f2 = 693 Hz, A f
= 193 Hz. (B) Phase-selective second harmonic ac polarogram. f = 193 Hz. M in 1 M NaCI, A€ = 10 mV [Cd] = 1 X
a block diagram of the intermodular circuitry, including its location in the PAR Model 170 Electrochemistry System into which the unit was inserted (14). Further details of the interfacing procedure can be obtained by writing to the authors. The amplitudes of both sine waves must be the same. The external oscillator, whose amplitude can be continuously varied, is fitted with a potentiometer across the output, the slider of which is fed into the Summing Amplifier. With the oscillator inputs matched, a modulation envelope is obtained on an oscilloscope at the input of the Summing Amplifier.
RESULTS AND DISCUSSION Investigation of t h e Theory for Intermodular Polarography. In intermodular ac polarography, the potential of the electrode ( E )is given by E = E d c - AE(sin w l t
+ sin w 2 t )
(2)
where Edc is the dc ramp and AE is the amplitude of the sinusoidal waves of frequency 0 1 and 02 that are superimposed onto the dc ramp. The current is detected at the difference frequency (01 - wz). The mathematical arguments used by Smith (7) to obtain the second harmonic ac expression are equally applicable to describe the intermodular ac response. For the simplest case of a diffusion controlled reaction using a small amplitude (AI3 6 16/n mV peak-to-peak) signal, the expression obtained is ( 4 )
x sin
[(wl
- wz)t + 3 ~ 1 4 1
(3)
where A is the electrode area, Ci is the bulk concentration of the electroactive species and j = (nFIRT) ( E d c - E:,2) with being the reversible half-wave potential. Equation 3 neglects the effects of spherical diffusion which may be important, particularly for amalgam-forming systems, and assumes the two input frequencies are phase-locked which is not strictly true in the present work. Equation 3 is remarkably similar to the equation for second harmonic ac polarography (2). The major differences are that the frequency term is replaced by the frequency difference and
Volt wsAg/AgC\ Figure 4. Effect of frequency difference on intermodular polarograms for 1 X lop6 M Cd(li) in 1 M NaCi. Drop time = 10.0 s, A € = 10 m V , f , = 1000 Hz, f, = 1200 Hz and 1500 Hz, respectively
6
5
/
m;
0 15
I
I
601
Arnpli tude/ mV
AFrequency/Hz
Figure 5. Dependence of background current on amplitude and frequency difference in 1 M NaCl (i) Amplitude: Potential = -0.300 volt, f, = 575 Hz, f2 = 737 Hz, A f = 162 Hz. (ii) Frequency Difference: Potential = -0.300 volt, f, = 1000 Hz, f2 = variable, A € = 10 mV
there is a phase-shift of a12 between the two responses. In Figure 3, phase-selective intermodular and second harmonic ac polarograms are compared. Visual inspection demonstrates that there is virtually no difference between their respective waveshapes. Equation 3 can be tested by plotting the current response, which is conveniently represented by the peak-to-peak current (I,,), as defined in Figure 3, vs. the variables that appear in Equation 3. The expected linear responses for the reduction of cadmium(I1) were obtained for the plots I,, vs. hE2between l and 10 mV for f l = 500 Hz and f z = 693 Hz, I,, vs. ( f z - f 1 ) l l 2 between 25 and 300 Hz where f l was fixed at 500 Hz and f z was varied between 525 and 800 Hz, and I,, vs. concentration over the range 1 X lop3 to 1X M. The intermodular polarograms obtained for 1 X 10-6 M cadmium(I1) at high and low difference frequencies are shown in Figure 4. The presence of a significant background current observed in Figure 4 was examined in more detail. The dependence of background current (Ib) on the frequency difference and sinusoidal amplitude are shown in Figure 5. As can be seen from these plots, the background current has the characteristics of a second-order charging current and the cell admittance therefore exhibits some nonideality in the sense that the charging current component is nonzero. Similar experiments with second harmonic ac polarography show that for M cadmium(II),nonideality is not as significant and
ANALYTICAL CHEMISTRY, VOL. 48, NO. 13, NOVEMBER 1976
1977
Table I. Data for Peak-to-Peak Separation (AE,) and for Reversible One-, Two-, and Inflection Potentials (Ei) Three-Electron Systems Using Intermodular ac Polarography a EilVolt E I/z’/Volt Electrode vs. Ag/ AE,l vs. Ag/ Supporting process electrolyte mV AgCl AgCl Fe(C204):- + e 0.25 M 67 -0.182 -0.181 -eFe(C204)s4K2C204 (PH 1.5) Cd(I1) 2 e F= 5 M HCI 36 -0.705 -0.703 Cd (Hg) Bi(II1) 3 e + M HCI 23 -0.180 -0.182 Bi(Hg) a A E = 10 mV, f l = 500 Hz, f2 = 693 Hz, Af = 193Hz, drop time = 10.0 s.
+ +
the charging current is not as high. The lower background current found in second harmonic ac polarography makes it a superior analytical technique to intermodular ac polarography. When generating frequency difference terms, much higher frequencies than the second harmonic frequency are often encountered. For example, to obtain a comparable result to a second harmonic signal generated from a 100-Hz sine wave, the two intermodular frequencies may need to be much larger, say f l = 900 Hz and f2 = 700 and it may well be that it is the use of these higher frequencies in the intermodular method that leads to a less favorable faradaic to charging current response and to the larger background current. If the second harmonic signal is detected at 2fl (1800 Hz) or 2f2 (1400 Hz) rather than a t 200 Hz,then the second harmonic method exhibits a similar degree of nonideality to that found in the intermodular method, providing substantial support for this hypothesis. The surface area of the mercury electrode may be expressed in terms of the drop time ( t )and flow rate (m)
A = 0.00853 m2/3t2/3
(4)
Under controlled drop time conditions, plots of I,, vs. m2/3 and I,, vs. t2l3both yield straight lines confirming the direct area dependence of Equation 3. Under gravity controlled conditions, the wave height should be independent of the mercury column height for a strictly diffusion controlled electrode reaction. However for reduction reactions at a mercury electrode in which the product forms an amalgam, a time-dependent term has been observed in fundamental (15, 16) and second harmonic (17-19) ac polarography. This effect has been attributed to the mass-transfer asymmetry involved in the amalgam forming step. However, under the conditions employed, amalgam effects were not found to be severe. Relevent data obtained from one-, two-, and three-electron reduction waves are presented in Table I. In intermodular and second harmonic ac polarography, the potential difference between the cathodic and anodic peaks (AE,)can be used as a simple “two-point” analysis to determine, on a semiquantitative basis, the degree of reversibility of an electron-transfer reduction. For intermodular ac polarography, Paynter ( 2 ) calculated AE, to be 68.4/n mV; this is the same value as was calculated for second harmonic ac polarography. Within experimental limits, values obtained in Table I for the systems studied agree with theory. This parameter is suitable for most analytical applications to determine the reversibility of the electron transfer step. Fast Potential Scan Methods in Intermodular Polarography. The use of a DME operating at gravity controlled drop times (for example 2 to 10 s) requires slow scan rates ( 6 5 1978
I -360
-080
-100
Volt vs
-080
060
Ag/AgCL
Fast sweep intermodular ac voltammetry with potential scan synchronized to a DME for 1 X M Cd(ll) in 5 M HCI. (B) Reverse sweep (anodic stripping) intermodular ac voltammogram with potential scan synchronized to a DME Flgure 6. (A)
Pre-sweep delay = 1 s, scan time = 5 s,scan rate = 200 mV/s, f, = 500 Hz, f 2 = 6 9 3 H z , A f = 1 9 3 H z , A E = 10mV
mV/s) to be used if sufficient data points are to be obtained on the potential-current curve. The recording of the entire polarogram is therefore a fairly lengthy process. Various modifications have been devised to increase the dc potential scan rate in other polarographic techniques and some of these have been investigated with respect to the phase-selective intermodular ac technique. Rapid polarography, in which the drop is mechanically dislodged, has been successfully applied to dc (20), fundamental (21), and second (13) harmonic ac studies. From Equation 4, a reduction in drop time leads to a decrease in area which in turn will result in a net decrease in the current per unit concentration. However, the faradaic to charging current ratio is unaltered and the sensitivity is essentially unchanged provided noise is not a problem associated with lower currents. The scan rate can alternatively be increased without suffering a decrease in the current magnitude by applying the potential sweep to a stationary electrode, although theoretical complications arise if the condition U ( w l - w2) >> u , where u is the potential scan rate, is not satisfied. Scan rates up to 100 mV/s were used in this work a t a hanging mercury drop electrode and the voltammetric waveshape for a reversible system was the same as that found for intermodular ac polarography. Instead of using a stationary electrode, voltammograms can be recorded at a DME by synchronizing the commencement of the potential sweep to a pre-set time into the drop lifetime. This method has been successfully used in the dc (22),fundamental ac (23)and second harmonic ac (12)modes. Jee (5) has in fact reported nonphase-selective intermodular ac voltammetry at a DME. However the waveshapes shown suggest a nontheoretical response was produced in Jee’s work. With the present instrumentation and using phase-selective detection, the waveshape obtained (Figure 6) was that predicted by Equation 3 after allowing for changes in the drop area term caused by drop growth during the potential scan. Voltammograms reproducible to better than 1%at the M level were recorded in this fashion. Comparison of Intermodular and Second Harmonic ac Methods. Having established intermodular instrumentation essentially equivalent in electronic performance to that for the second harmonic method, it is now possible to fairly compare the two second-order techniques of polarography. The shape of the readout obtained from intermodular polarography is identical with the second harmonic. It therefore shares the same advantages as the second harmonic method (11) in that the accurate measurement of a peak-to-peak current magnitude can be used as the parameter proportional to concentration in analytical work. However, the presence
ANALYTICAL CHEMISTRY, VOL. 48, NO. 13, NOVEMBER 1976
of a significantly larger charging current in intermodular ac polarography favors the use of second harmonic ac polarography. The magnitude of the charging current is the main factor determining the sensitivity of a polarographic technique. The limit of detection of the intermodular is therefore expected to be higher than the second harmonic. In the present work, it was found that the second harmonic method is about an order of magnitude more sensitive. Careful tuning of phase angles to minimum background current may slightly modify this conclusion, but this would not be an analytically expedient procedure. The instrumentation for the intermodular developed in this work is also more complicated than the simple multiplier approach developed (I1) for phase-selective second harmonic ac polarography. The need for an additional oscillator and phase-selective detector make the intermodular technique less attractive from the cost point of view. Finally, second harmonic polarography may be used over a wide amplitude and frequency range without any adjustment of the circuitry. On the other hand, the intermodular method has a restrictive frequency range and any changes to either frequency or amplitude require balancing of the two oscillators for the new conditions. In conclusion, for most analytical or electrode-kinetic applications no advantage is seen in using phase-selective intermodular over second harmonic ac polarography, and the latter technique is strongly recommended.
LITERATURE CITED (1) R. Neeb, Naturwissenschaffen, 49, 447 (1962). (2) J. Paynter, Doctoral Thesis, Columbia University, New York, 1964. (3) W. H. Reinmuth, Anal. Chem., 36, 211R (1964). (4) T. G. McCord, E. R. Brown, and D. E. Smith, Anal. Chem., 38, 1615
(1966).
(5)R. D. Jee, Fresenius’ 2.Anal. Chem., 264, 143 (1973). (6) H. H. Bauer and P. J. Elving, Anal. Chem., 30, 341 (1958). (7) D. E. Smith in “Electroanalytical Chemistry”, A. J. Bard, Ed., M. Dekker, New York, 1966, Chap. 1 and references clted therein. (8) D. E. Smith, Crit. Rev. Anal. Chem., 2, 247 (1971) and references cited therein. (9) A. L. Woodson and D. E. Smith, Anal. Chem., 42, 242 (1970). (IO) H. Blutstein and A. M. Bond, Anal. Chem., 46, 1531 (1974). (1 1) H. Blutstein, A. M. Bond, and A. Norris, Anal. Chem., 46, 1754 (1974). (12) H. Blutstein and A. M. Bond, Anal. Chem., 46, 1934 (1974). (13) H. Blutstein and A. M. Bond, J. Electroanal. Chem., 56, 177 (1974). (14) Instruction Manual for PAR Electrochemistry System, Model 170, Section 11, Detector and Signal Processing Board, p IX-3, Princeton Applied Research Corp., Princeton, N.J., 1972. (15) J. R. Delmastro and D. E. Smith, Anal. Chem., 38, 109 (1966). (16) J. R. Delmastro and D. E. Smith, J. Electroanal. Chem., a, 192 (1965). (17) T. G. McCord and D. E. Smith, Anal. Chem., 41, 131 (1969). (18) T. G. McCord and D. E. Smith, Anal. Cheni., 42, 126 (1970). (19) I. Ruzic and D. E. Smith, Anal. Chem., 47, 530 (1975). (20) A. M. Bond, J. Electrochem. Soc., 118, 1588 (1971) and references clted therein. (21) A. Zatka, J. Nectroanal. Chem., 27, 164 (1970). (22) L. A. Matheson and N. Nichols, Trans. Am. Electrochem. Soc., 73, 193 (1938). (23) C. I. Mooring, Polarogr. Ber., 6, 63 (1958).
RECEIVEDfor review April 5,1976. Accepted August 6,1976. The authors express their appreciation to the Australian Research Grants Committee for financial support.
Intermetallic Compound Formation between Copper and Zinc in Mercury and Its Effects on Anodic Stripping Voltammetry Mark S. Shuman* and George P. Woodward, Jr. Department of Environmental Sciences and Engineering, School of Public Health, University of North Carolina, Chapel Hill, N.C. 275 14
Several Cu-Zn intermetallic compounds form during anodic stripping voltammetry (ASV) analysis of solutions containing both copper and zinc. There are three soluble compounds with copper to zinc ratlos of 1:1, 1:2, and 1:3. In addition, an insoluble compound also forms at high amalgam concentrations and has a copper to zinc ratio of 1:3. The formation of these compounds decreases the ASV zinc current and increases the copper current since the soluble compounds are electroactive and are oxidized at a potential very close to copper stripping potential. This interferencein the determination of copper and zinc by ASV is most serious with thin film electrodes where the small mercury volume leads to very high amalgam concentrations. Stepwlse instability constants for CuZn, CuZnp and CuZn3, respectively,were found to be K, = 1.9 X K2 = 7.6 X K3 = 2.1. The solubility product for the insoluble compound, CuZn3(s), was estimated to be Ksp= 3.1 X 10-5.
The formation of intermetallic compounds can cause error in the analysis of metals by anodic stripping voltammetry. For example, Cu-Zn compounds can interfere in the determination of Cu or Zn in environmental samples where, of the trace metals readily analyzed by ASV, these two metals are in greatest abundance. The formation of Cu-Zn compounds can be written
aCu
+ b Zn = Cu, Znb
Russell et al. ( I ) studied these by dissolving copper and zinc in a Hg pool and reported formation of several compounds with varying stoichiometry, a and b. Kemula et al. (2) were the first to recognize that these compounds interfered with the ASV analysis of Cu and Zn. The observed effect was a decrease in sensitivity of ASV to Zn when Cu was present. More recently Stromberg and co-workers ( 3 ) studied the formation of Cu-Zn compounds by ASV. Their method was to measure the diminished Zn stripping current when Cu was varied from 0.1 to 2 times the concentration of Zn. They concluded that the stoichiometry was 1:l and by assuming a priori that the compound in mercury was insoluble, calculated a solubility product of 5 X lo+. Kozlovsky and Zebreva ( 4 ) in reviewing the literature, observed that the solubility product values obtained from potentiometric data ranged from 2.8 X 10-5 to 7.1 X Further work by Stromberg and co-workers (5)and by Mesyats et al. (6) in which the stripping current of both copper and zinc was followed as a function of pre-electrolysis time indicated that a 1:l Cu-Zn compound was formed and was sparingly soluble with a solubility product of 1 X lov6,although their data did not fit their theory based on limited solubility. Rudolph (7) has also studied the electrochemical formation of these compounds and assumed a priori a limited solubility.
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