Alternating Current Linear Sweep and Stripping Voltammetry with Phase-Selective Second Harmonic Detection H. Blutstein and A. M. Bond, Department of lnorganic Chemistry, University of Melbourne, Parkville, Victoria 3052, Australia
The techniques of second harmonic linear sweep and anodic stripping (inverse) voltammetry with phase-selective detection have been investigated. For reversible electrode processes the theory for second harmonic ac voltammetry is shown to be essentially the same as for- the polarographic technique at a dropping mercury electrode, and the techniques can therefore readily be used in a systematic fashion. Consequently, the wave shape and other aspects of the current-voltage curve provide the techniques with inherent advantages over linear sweep or even derivative linear sweep voltammetric techniques with respect to both resolution, charging current, and other considerations. A quantitative assessment of resolution is given, and the present work demonstrates that in both the linear sweep and stripping modes, phase-selective second harmonic ac voltammetry should provide one of the most sensitive electroanalytical techniques for determining species giving rise to reversible or close to reversible electrode processes. Application of the stripping method to the determination of trace metals in concentrated zinc sulfate solution and in river water is briefly described, along with a comparison with differential pulse anodic stripping voltammetry.
In many instances, solid electrodes (non-mercury stationary electrodes) ( I ) provide an excellent means for observing the voltammetric behavior of electroactive species not amenable to detection at a dropping mercury electrode (DME). One major problem arising from the use of mercury as an electrode material is its limited positive potential range. Another is the possibility that the mercury may participate in reactions subsequent to or preceding the charge-transfer step. The judicious choice of solid electrodes may in some cases overcome these problems while at the same time permitting the possibility of using extremely fast scan rates which exceed by several orders of magnitude scan rates possible at a DME. Thus, the use of linear sweep voltammetry at stationary electrodes can provide considerable time saving. In general, the analytical use of stationary electrode dc voltammetry is therefore made when the DME is unsuitable for the system, or else time saving is required. However, because of the depletion of depolarizer associated with a stationary electrode, a gradual decay occurs after a peak current is attained and the shape of the current-voltage curve is considerably different than that recorded a t a DME. This effect restricts the accurate determination of electroactive species occurring at more negative potentials than another reducible species, and the resolution of linear sweep voltammetry under such circumstances is rather poor ( 2 ) . Additionally, the charging current is rather high, particularly a t fast scan rates and in certain nonaqueous solvents. ( 1 ) R N Adams. "Electrochemistry at Solid Electrodes," Marcel Dekker Inc., New York, N Y , 1969 (2) K . J Martin and I. Shain, Anal. Chem., 30, 1808 (1958).
In a n attempt to overcome these problems for both voltammetric and anodic stripping analysis a t a hanging drop mercury electrode (HDME), the mathematical first, second, and third derivatives of the linear sweep technique have been employed (3-9). The first derivative wave shape gave an order of magnitude increase in sensitivity and improved resolution for multicomponent systems. (5, 7). However, with the second and third derivative, little or no further improvement was found (5, 7 ) . Underkofler and Shain (10) used phase-sensitive fundamental harmonic ac voltammetry a t a HDME as an alternative to dc methods. In stationary electrode voltammetry, the linear sweep ac wave shape is not, in fact, equivalent to the derivative of the linear sweep dc voltammogram, unlike the case in polarography; and under appropriate conditions, the ac linear sweep wave shape is, in fact, still described by the equation applicable at a dropping mercury electrode (DME) (11). This earlier work has since been recently extended by Moorhead and Davis (12). In the linear sweep mode, therefore, the use of second harmonic technique should offer even further advantages over the fundamental harmonic mode, since the charging current contribution is negligible, under most conditions, and the technique has proved to have considerable scope in polarography. The use of non-phase-selective second harmonic ac voltammetry has, in fact, already been used at stationary and rotating disk electrodes (13) to avoid detecting the large charging current usually associated with these types of electrodes. Fast sweep second harmonic techniques at a dropping mercury electrode have also recently been reported (14). However, a detailed study of the analytical capabilities of linear sweep second harmonic ac voltammetry has yet to be undertaken, and phase-selective detection has yet to be introduced into the technique. The purpose of this work is, therefore, to examine the theory of the second harmonic linear sweep technique and experimentally compare it with measurements obtained at a number of different types of stationary electrodes. This work then enables us to assess the likely potential for analytical work. Additionally phase-selective second harmonic anodic stripping analysis at a HDME is discussed along with two examples, and the particular advantages of phase-sensitive detection are examined. (3) M . T. Kelley. H . C. Jones, and D. J. Fisher. Anal. Chem., 31, 1475 (1959). (4) D. J. Fisher, W L. Belew. and M. T Kelley, In "Polarography 1964," Vol. 1, G. J. Hills, Ed., Wiley Interscience, New York. N.Y., 1966 (5) T. R. Mueller. Chem. Instrum., 1 , 113 (1968). (6) F. B. Stephens and J . E. Harrar, Chem. Instrum.. 1 , 169 (1968). (7) S. P. Perone and T. R. Mueller. Anal. Chem., 37, 2 (1965) (8) S .P. Perone and J. R . Eirk, Anal. Chem.. 37, 9 (1965) (9) S. P. Perone, J, E. Harrar. F B. Stephens, and R E. Anderson, Anal. Chem., 40, 899 (1968). (10) W. L. Underkofler and I . Shain, Anal. Chem., 37, 218 (1965) (11) D. E. Smith in "Electroanalytical Chemistry," Vol. 1, A. J. Bard, Ed., Marcel Dekker, New York, N Y . , 1966. (12) E. D. Moorhead and P. H Davls.Anal. Chem.. 45, 2178 (1973). (13) M . Stulikovaand F. Vydra, J. Electroanal. Chem.. 42, 127 (1973). (14) R . D. Jee, Fresenius' 2. Anal. Chem.. 264, 143 (1973).
A N A L Y T I C A L C H E M I S T R Y , VOL. 46, NO. 11, SEPTEMBER 1974
1531
A quantitative account of resolution is given, and it is shown that the second harmonic technique is considerably superior to derivative dc techniques. EXPERIMENTAL Chemicals. All chemicals were of reagent grade purity. Cadmium(II), bismuth(III), and lead(I1) solutions were prepared for their nitrate salts in either 1M or 5M hydrochloric acid. Acetone (0.1M EtbNC104) was used as the solvent for bis(cyc1opentadienyl)vanadium(IV) N,N-isopropyldithiocarbamato tetraphenyl borate, [Cp2V1\dpdtc]PhrB, taking precautions described in the literature (Is). All solutions were thermostated at 25 f 0.1 "C and deoxygenated with argon unless otherwise stated. Instrumentation and Electrodes. All voltammograms were recorded with PAR Electrochemistry System Model 170 (Princeton Applied Research Corp., Princeton, N.J.). The second harmonic response was obtained using circuitry based on the use of electronic multiplication of the ac reference signal as described previously (16). An alternating potential of 1, 5 , or 10 mV peak-topeak was used on frequencies between 10 and 1100 Hz. A three-electrode system was employed. The reference electrodes used were Ag/AgCl (5M NaC1) for aqueous work and Ag/ AgCl (0.1M LiCl, acetone) in acetone, with either platinum or tungsten as the auxiliary electrode. The working electrodes were a hanging drop mercury electrode (Metrohm BM5-03), platinum wire (0.03-mm diameter), glassy carbon (Tokai), and a wax impregnated graphite electrode (PAR).
THEORY F O R T H E REVERSIBLE ELECTRODE PROCESS AND ITS EXPERIMENTAL VERIFICATION At stationary electrodes under dc conditions and even for very fast electron-transfer steps, the electrode process does not exhibit a polarographic type response because depletion of the electroactive species in the vicinity of the electrode results in complications in the waveform obtained. This situation for a reversible electrode process can be described by solving the Boundary Value Problem for a stationary electrode, in which spherical diffusion has been ignored (7, 17).
where A is the electrode area, CO* is the bulk concentration of the depolarizer, Do is the diffusion coefficient of the electroactive species, and a is equal to nFu/RT, where u is the scan rate. Other symbols have their usual meaning. The function at) has been defined by Nicholson and Shain (17), and can be calculated by numerical methods (7, 17). The kth derivative linear sweep dc voltammogram is obtained by differentiating Equation 1
The time scale of any linear sweep dc voltammogram is controlled by the scan rate term, which must be kept well below the time scale of the electron transfer step if the above relationship for a reversible electrode process is to hold. The depletion or the at) term in the dc theory causes curves to be asymmetric and because of the nature of the asymmetry resolution is not as good as is the case with derivative dc polarography, for example. For an ac electrode process, the potential of the electrode is given by the expression
E
= E,,
- A E sin ut
(3) Edc is the dc ramp potential, w is the angular frequency of the ac wave and AE the amplitude of the alternating po( 1 5 ) A M Bond. A T Casey, and J . R Thackeray. Inorg. Chem.. 12, 887 (1973) ( 1 6 ) H.Blutstein, A M Bond, and A . Norris, Ana/. Chem., in press. (17) R S Nicholson and I . Shain. Ana/. Chem.. 36, 706 (1964).
1532
A N A L Y T I C A L C H E M I S T R Y , V O L . 46,
NO. 11,
tential. The dual dc and ac nature of the experiment is apparent. The time domain of the ac experiment can therefore be described in two parts-scan rate (dc) and frequency (ac). Under conditions where the frequency time scale is very much greater than the scan rate and the electrode process is diffusion controlled, the experiment should be independent of dc terms as in the case of ac polarography where the drop time terms approaches unity ( 1 1 ) .Since
and following mathematical procedures described by Underkofler and Shain (10) and Smith ( 2 1 ) , the general equation for the linear-sweep second harmonic ac experiment will therefore be the same as in ac polarography except for the inclusion of a scan rate term, F ( u t ) . Thus, Z(2ot) =
VI n 3 F 3 A C , * ( ~ D , ) 1 / 2 Asi&( E2 j/2)F(ct) 16R2T?coshJ(j/2)
sin(2wt - ( x / 4 ) )
(5) where j = (nF'/RT)(&, - &,zr) and Ellzr is the reversible half-wave potential ( L E 5 16/n mV peak-to-peak). The term F(ut) represents the dependence of the second harmonic alternating current ( I ( 2 w t ) ) on the scan rate. For reasons given above, when AEwt >> u t then F ( u t ) 1 and Equation 5 reduces to the equation for the second harmonic ac response a t a DME.
-
I(2wt) = 12~ ~ F ~ A C , * ( U D , )E2 " ~sinh(j/2) A sin(2wt - ( x / 4 ) ) (6) 16R2T2coshJ(J/2) Under such conditions, equations describing the shape of the linear sweep second harmonic voltammogram will be identical to those obtained in second harmonic ac polarography (11), and this provides considerable simplification of the experiment. For the remainder of this work, it will be assumed that the required condition AEwt >> ut is met. Thus depletion terms operative in the dc terms of linear sweep voltammetry are not present in the readout of the ac experiment. Furthermore, as charging current terms are unimportant, the linear sweep second harmonic technique should provide considerable advantages with respect to both sensitivity and resolution. Taking derivatives of dc linear sweep voltammetry while improving the resolution and providing a more convenient readout form does not eliminate depletion terms causing asymmetry or eliminate charging current contributions and therefore the second harmonic experiment is likely to be substantially superior to second derivative linear sweep voltammetry in many respects. The validity of Equation 6 can be determined for both linear sweep and stripping analysis by plotting the peakto-peak wave height (I,,) of the second harmonic alternating current as a function of scan rate, wave shape, electrode area, depolarizer concentration, applied frequency, peak-to-peak applied amplitude, and phase angle. Dependence of IpDon Scan Rate. A series of curves were obtained a t 400 Hz with varying scan rate for the reduction of the vanadium complex (8) [cp,V"(dpdtc)]+
+ e * cp,V"'(dpdtc)
(7)
in acetone a t a platinum electrode. Figure 1 shows that I,, is independent of scan rates up to a t least 100 mV per second. However, in stripping analysis where amalgam formation is involved, dependence on scan rate analogous to the fundamental mode (12) was found.
SEPTEMBER 1974
V&
15
A3IA9CI
Figure 1. Reduction of [Cp2V1v(dpdtc)]+ at a platinum electrode w = 400 at different scan rates [Cp2VdpdtcIf 2.8 X 10-3M. H z . A€ = 10 m V p-p. In-phase component.
Shape and Position of Wave. Equation 6 can be rearranged to a more convenient form from which the experimental shapes can readily be tested (18). Figure 2. Comparison of the experimental (-
exp 2 j - exp j 1 exp j ) j
- - -) and theoretisecond harmonic ac voltammograms at a H D M E for Cd(1l) + 2e t' Cd(amalgam). w = 225 Hz. A € = 10 mV p-p. v = 10 mV/sec
cal
+
where 4 is the second harmonic alternating current at E d c and 4, is the peak current (which has been taken for the purpose of this work to be the larger of the two peaks). Figure 2 shows that the experimentally obtained wave for the reduction of cadmium(I1) at a HDME corresponds very closely to the waveshape obtained from Equation 8. The mass-transfer asymmetry arising out of spherical diffusion, previously observed in metal ion-metal amalgam systems (16, 19-21) is not as marked under the conditions used, although at larger drop areas this phenomenon was apparent. Equivalent plots for the vanadium complex at mercury, platinum, glassy carbon, and graphite electrodes also showed good agreement with theory. The peak-to-peak separation (AE,) can also be used to define the reversibility of a second harmonic wave, for a reversible system. For n = 1, AE, = 68 f 2 mV, n = 2, AEkl = 34 f 5 mV and for n = 3, AE, = 23 f 5 mV.
(-)
L 05
IO
I5
2 0
25
AREA (rnrn') Figure 3. Dependence of I,, on the area of a H D M E for reduction of cadmium. [Cd] = 1 X 1 0 - 4 M . w = 400 Hz. A€ = 10 mV p-p v = 10 mV/sec
Table I. Examples of One-, Two-, and Three-Electron Reductions giving Peak-to-Peak Separations (LEp) a n d Inflection Potentials ( E l ) ,Volt us. Ag 'AgCl) E, Electrode process
Supporting electrolyte
+
0 . 1 M EtdNCIOda
[ C ~ ~ ~ V " ~ d p d t c ]cz e Cp2V"'dpdtc Cd'+
+ 2e :< Cd (amalgam) + 2e ;ePb (amalgam) + 3e Bi (amalgam)
Pb2+ Bi3'
FA
(acetone) 1 M HC1 5 M HCl 5 M HC1
AED (mV)
Polarographic technique
Voltammetric technique, Volt
70
-0,428
-0,430 f 0.002a
35
33
-0.597 -0,505
-0,507
28
-0.180
-0.178
0.598
Data obtained on HDME, glassy carbon, platinum and graphite electrodes.
Table I shows representative systems for one-, two- and three-electron reductions in which the AE, are within our definition of reversibility. It should be noted that for n = 2 and 3 the values of AE exceed 16/n mV peak-to-peak, so the results obtained are acceptible. Additionally, for the one-electron [CpzVlvdpdtc]+ reduction AEp is 70 2 mV at all electrodes as required. Table I shows a comparison in the inflection or crossover potentials ( E , ) obtained for phase-selective second harmonic ac polarographic and voltammetric waves obtained at a HDME. Provided the assumptions made in the last section are conformed to, then the results from the two techniques should be identical. As can be seen
*
(18) A . M Bond, J. Electroanai. Chem., 35, 343 (1972). (19) T G . McCord, E R . Brown, and D. E. Smith, Anal. Chem., 38, 1615 ( 1 9 6 6 ) . (20) J R . Dalmastro and D E. Smith, Anal. Chem., 39, 1050 (1967). ( 2 1 ) T G . McCord and D. E. Smith, Anal. Chem.. 42, 126 (1970).
from Table I, E , for both the voltammetric and polarographic techniques are the same, within experimental error. Dependence of I,, on Electrode Area. Figure 3 shows the straightline graph obtained by plotting the area of a HDME against I,, for the reduction of Cd(I1) in 1M HC1. Dependence of I,, on Concentration. A linear calibration curve was obtained for the reduction of cadmium(I1) to 10-6M. at a HDME over at least the range Dependence of I , , on Frequency. A linear plot was obtained for Zpp US. u1 (10-1100 Hz) for both linear sweep and stripping second harmonic ac voltammetry, for the Cd(II)/Cd(Hg)electrode process in 1M HC1 at a HDME. Dependence of I,, on Amplitude. To test that I,, is proportional to AE2, a series of curves were obtained at constant frequencies 100, 225, 400, 625, and 900 Hz for peak-to-peak amplitudes between 1 and 10 mV. For both linear sweep and stripping analysis, the cadmium elec-
ANALYTICAL C H E M I S T R Y , VOL. 46, NO. 1 1 , S E P T E M B E R 1974
1533
/H
-01
-03
VOLT
-05
vs
Figure 4. Multicomponent system P b ( l l ) , and C d ( l l ) in 5M HCI
-07
-09
Ag/AgCI containing 1
X
10-4M Bi(lII),
( I ) dc voltammogram v = 100 mV/sec ( 1 1 ) phase-selective fundamental harmonic ac voltammogram w = 400 Hz. A € = 10 mV p-p In-phase component v = 100 mV/sec (111) phase-selective second harmonic ac voltammogram w = 400 Hz A € = 10 mV p-p In-phase component v = 100 mV/sec
trode process a t a HDME gave linear plots when Zpp was plotted against AEz. Phase-Angle Measurements. The phase-angle dependence predicted by Equation 6 is observed. From the above, it can be seen that, for both the linear sweep and inverse second harmonic techniques, Equation 6 provides an adequate expression for use in assessing the analytical usefulness of the techniques. For nonreversible electrode processes, the F ( u t ) term will not be unity, and the theory will be considerably more complex. However, as ac techniques are most suitable for reversible electrode processes, an analytical assessment based on reversible theory is adequate. Analytical Applications. Dc and fundamental harmonic ac linear sweep voltammetry have considerable charging current associated with them ( I , IO). Phase-selective detection in the fundamental mode reduces the charging current contribution significantly ( I O ) ; however, it still remains a problem, particularly in trace analysis where uncompensated resistance terms and non-ideality may give rise to sloping base lines (23, 22-24). The second harmonic technique, with or without the use of phase-selective detection, contains negligible charg(22) D E Smith and W H Reinmuth, Anal Chern 32, 1892 (1960) (23) D N Walker R N Adams and A L Juliard Anal Chern, 32, 1526 (1960) (24) F Vydra and M Stulikova J Electroanal Chem 40,99 (1972)
1534
ing current (25) and, therefore, the limit of detection is theoretically dependent on the signal to instrumental and capillary noise (where applicable with the DME) ratio (16). Capillary noise arising from the use of a DME in second harmonic ac polarography obviously is not a factor affecting the sensitivity a t a stationary electrode and, therefore, the limit of detection should be lower in second harmonic ac voltammetry than with the polarographic technique. In practice, the charging current is of course not zero, but restrictions arising from this source do not provide limitations with most currently available instrumentation. Thus, for reversible electrode processes the linear sweep second harmonic technique could be expected to be one of the most sensitive available. In the present work, linear calibration curves of I,, US. concentration over at least the range to 10-6M were obtained. However, 10-6M is by no means the limit of detection although the noise level associated with detection of the signal a t this level decreased the reproducibility somewhat. Optimization of experimental and instrumental parameters, therefore, give a limit of detection well below the 10-6M level, and linear calibration curves over more than three or four orders of magnitude should be obtainable for reversible electrode processes. Furthermore, this technique can be combined with rapid scan and short analysis time. The waveshape of the second harmonic ac voltammogram, when phase-selective detection is used, resembles the derivative of the fundamental harmonic waveshape (26). Thus, the current parameter used in establishing a concentration calibration curve can be measured as a peak-to-peak height and not relative to a base line as is the case with most other techniques. This possibility provides high inherent precision as no experimenter judgment of measurement relative to a base line is required. Detailed discussion of this aspect of the phase-selective readout is presented elsewhere (16) with respect to second harmonic polarographic methods. Figure 4 shows a comparison between dc, phase-selective fundamental, and phase-selective second harmonic ac voltammograms at a HDME for a solution containing 1 X 10-4M Bi(III), Pb(II), and Cd(I1) in 5MHCl as supporting electrolyte. With the linear sweep dc technique, the bismuth peak height can be determined by subtracting the current from the wave due to oxidation of mercury, and similarly the lead height must be separated from the tail of the bismuth wave by graphical or other procedures. The reduction of cadmium(II) occurs a t potential close to that for the reduction of H+ and is not well resolved in the dc experiment. Thus, the waves in the dc experiment are not easily measured accurately for peak heights and multi-element analysis is difficult. Derivative techniques provide some improvement, but not as great as with ac methods shown below. Considerable improvement is obtained in the fundamental harmonic mode where, in contrast to the dc technique, the current rapidly decays to zero either side of the peak. However, a small charging current contribution is present even with phase-selective detection at the relatively high frequencies used. Note that the cadmium wave is now well defined and well separated from the hydrogen reduction. The phase-selective second harmonic linear sweep voltammogram for this system, shown in Figure 4(iii) exhibits a flat base line a t zero current, and all three (25) 6 . Breyer and H. H. Bauer in "Alternating Current Polarography," P. J. Elving and I M. Kolthoff, Ed., Interscience, New YorkiLondon, 1963 (26) A M . Bond, J. Electroanal. Chem., 36,235 (1972)
ANALYTICAL CHEMISTRY, VOL. 46, NO. 11, SEPTEMBER 1974
- 0 9 -08 -07 - 0 6
Volt vs. Ag/AgCi
I
Figure 5. Phase-selective second harmonic ac anodic stripping voltammogram of cadmium in 1M HCI. [Cd] = 1 X 1 0 - 6 M , w = 225 H z , A€ = 10 mV p-p. Electrolysis time, 1 minute. In-phase component. Y = 5 mV/sec electrode processes under study are completely resolved. The readout with this technique presents no difficulty of measurement. All linear sweep voltammograms recorded at the HDME were obtained in this work under conditions of 1minute stirring and 0.5-minute rest period. A reproducibility of 2% was obtained at the lOP4Mlevel. Removal of oxygen was not necessary for both fundamental and second harmonic ac voltammetric studies of the solution containing 1 x 10-4M Bi(III), Pb(II), and Cd(I1) in 5M HC1. Stripping Second Harmonic AC Voltammetry. Anodic stripping voltammetry using a HDME provides a most valuable technique for analyzing extremely dilute solutions of metals which form amalgams. In 1M HC1, cadmium(I1) was detected down to 10-8M using only a 1-minute pre-electrolysis time. Figure 5 shows a second harmonic stripping curve at the 10-6M level. The absolute limit of detection with this technique must be exceedingly low as much longer electrolysis time can obviously be used. This was not attempted in 1M HC1 as stringent purification of chemicals and glassware is necessary for trace analysis below this level. Reproducibility of 3% at the 10-6M level was obtained at a HDME for cadmium in 1M HCl. The resolution of second harmonic stripping curves is far superior to those obtained by dc techniques. As in normal linear sweep techniques, the readout form is superior to that obtained for the fundamental ac mode and with dc techniques. Thus, considerable scope for instrumental automation of this technique should be possible. This and other aspects of the work are currently under investigation. Practical Examples and Comparison with Differential Pulse Voltammetry. Trace Metals in Concentrated Zinc Sulfate Solution. These laboratories were approached to develop an on-stream analytical method for the determination of trace metals in approximately 1.5M zinc sulfate solution (pH = 1). An initial approach to this problem involved anodic stripping analysis at a HDME using a 1-minute electrolysis time. Both differential pulse and second harmonic ac techniques were compared. Figure 6 shows the second harmonic and differential pulse anodic stripping voltammograms of a solution made up to 1 X 10W6MTl(1) and Cd(I1) in 1.5M ZnS04.7HzO. Actual samples contain these two elements in the to lO-'Mrange. The pulse duration used in the differential pulse technique and other instrumental artifacts limited the scan rate to 10 mV/sec, with the present instrumentation. On
d
-07
-DC,
05 -04 -03 -02
VOLTS
-07
vs
-06 -05
-04 -03 -02
Ag/AgCl
Figure
6. Anodic stripping voltammograms at a H D M E of 1 X 10-6M C d ( l l ) and T I ( I ) in ca 1 5 M Z n S 0 4 . 7 H 2 0 One-minute
electrolysis time used ( a ) Second harmonic mode (L' = 400 H z A € = 10 mV p-p v = 100 mV/sec In-phase component ( b ) Differential pulse mode Amplitude = 25 mV Time between pulses = 0 5 sec Time sampled = 25 msec Y = 10 mV/sec
the other hand, scan rates used in the second harmonic mode were only limited by the condition AEwt >> ut; scan rates up to 100 mV/sec were acceptable for the range of amplitudes and frequencies used in this work. Therefore, the time required for the second harmonic experiment is shorter than that required for the differential pulse experiment. Another time consuming step normally encountered in polarographic analysis is the need to remove dissolved oxygen from solution. The irreversible reduction of oxygen is selectively discriminated against relative to reversible electrode reactions by the second harmonic ac technique. Therefore, provided the species arising out of the reduction of oxygen do not interfere with the other electroactive species, there is no need to remove oxygen. The second harmonic voltammogram obtained in Figure 6a could therefore be obtained in the presence of oxygen, since oxygen does not interfere with either the cadmium or thallium electrode processes under the conditions used. However, the differential pulse technique (Figure 66) does not discriminate against oxygen to the same extent as the second harmonic technique, and it was found necessary to remove oxygen from solution providing a further disadvantage. It can also be seen from Figure 6 that the resolution of the Tl(1) and Cd(I1) waves is better in the second harmonic mode than with the differential pulse technique where the waves overlap to some extent. Virtually no overlap was found in the second harmonic method at the concentration ratios of thallium and cadmium encountered (approximately 1:2 to 2 : l ) . The separation in E , (=El,z) in zinc sulfate is 126 mV and by using Table I11 (see resolution section) both can be determined simultaneously at the 1% level over the required concentration ratios encountered. Further comparisons between the two techniques are made elsewhere (27) and, despite the fact that in the above application the second harmonic method is preferred, this is not always the case. (27) A
M Bond Submitted for publication. Ana/ C h m Acta
A N A L Y T I C A L C H E M I S T R Y , VOL.
46, NO. 1 1 , SEPTEMBER 1974
1535
-~
~
Table 11. Minimum Separation of Half-Wave Potentials ((AE1;JmV)for 1% Overlap in Two-Component Systems for a Variety of Linear Sweep and Polarographic Techniques. n~ = ny = 1 D C voltarnmetrybsc
AC voltammetryd
AC polarography, mVd
Second process overlaps first, mV
First process overlaps second, mV
1780
...
...
...
148
837
154
154
154
188 143e
275
144e
144e
1441
DC polarography, mVa
Second process overlaps first, mV
First process overlaps second, mV
236
168
154 143e
Normal First derivative dc (or fundamental harmonic ac) Second derivative dc (or second harmonic ac)
a From reference 4. From reference 5. For further details this reference should be consulted. These calculations are based on spherical diffusion. from reference 29.See also references 28 and 26. e First peak used for analysis. f Second peak used for analysis.
~
~
Calculated
~
Table 111. Resolution in Second Harmonic ac Voltammetry Given as the Tolerable Concentration Ratio of a Species Giving Rise to a Neighboring Electrode Process ( n 2 ) ,Such That the Overlap with the Electrode Process under Consideration (nl) Is Less Than the Quoted Percentage Separation in E , , mV
10
20
30
40
50
60
1536
Concentration ratio tolerable to stated level nl
n?
1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3 1 1
1 2 3
1%
1 2 3 1 2 3
1.1 x 4.2 x 6.2 x 8.4 X 1.3 X 7.9 x 3.2 X 3.6 X 1.6 X
1 2 3 1 2 3 1 2 3
8.5 1.9 8.1 2.2 2.3 2.7 5.3 4.2
1 2 3 1 2 3 1 2 3
1.6 X 1.8 x 6.2 X 9.0 x 4.2 X 7.0 X 2.8 X 9.6 X 1.2 x
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2
2.2 x 3.9 x 2.0 x 1.1 x 8.6 X 2.2 x 3.3 x 1.9 x 3.9 x 3.0 X 8.3 X 6.4 X 1.4 X 1.8 x 7.1 X 4.1 X 4.0 X 1.2 x 4.2 X 1.8 x
5%
10-2 10-3 10-3
lo-* lo-* 10-3 10-l
lo-? 1 . 3 X lo-* X
x
10-2
X lo-* x 10-2 X X 10-l x 10-2 X
lo-* 10-2 10-2
lo-* 10-l
lo-* 10-1 10-2
10-2 10-1 10-1
lo-* 10-1 10-1 10-1 10-1
lo-* 10-1 10-l 10-1 10-l 10-l
10-1 100
10-l
5.6 X 2.2 x 3.2 X 4.4 x 6.6 X 4.1 X 1.6 X 1.9 x 8.4 X 6.6 X 4.4 x 1.0 x 4.2 X 1.1 x 1.2 x 1.4 X 2.8 X 2.2 x 8.4 9.4 3.2 4.7 2.2 3.7 1.5 5.0 6.5
Separation in E,, mV
10-2 10-2 10-1
lo-* lo-* lo0 10-1
lo-*
70
10-1
10-l 10-1 10-1
lo0
80
X
x
10-2
X 10-l
x 10-1 x 10-1 x 10-1 X lo0 X 10-l X 10-l
1.1 x 2.0 x 1.0 x 5.7 x 4.5 x 1.2 x 1.7 x 1.0 x 2.0 x 1.5 X 4.3 x 3.3 x 7.3 x 9.5 x 3.7 x 2.1 x 2.1 x 6.5 X 2.2 x 9.4 x
90
100 10-1 10-1 100 100
10-l 10-1 100 10-1 10-1 100 100 100
loo
n.
1%
1 2 2 2 3 3
3 1 2 3 1 2 3
2.1 x 1.9 x 3.9 x 2.3 X 5.4 x 8.6 X 4.0 X 5.9 x 3.9 x 6.6 X 2.6 X 8.5 X 7.4 x 7.4 x 1.8 x 1.3 X
3 1
1 1 1 2 2 2
3 3 3 1 1 1 2 2 2 3 3 3
10-1 10-1
100 100
nl
1 1 2 2 2 3 3 3
10-2
10-l 10-1
Concentration ratio tolerable to stated level
100
110
10-1 10-1
A N A L Y T I C A L C H E M I S T R Y , V O L . 46, N O . 1 1 , SEPTEMBER 1 9 7 4
1 1 1 2 2 2 3 3 3 1 1 1 2
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
1 2 3 1
2 3 1 2 3 1 2 3 1 2 3 1
8.6 X 8.6 X 2.1 x 3.7 x 1.8 X 2.4 X 1.0 x 4.0 X 4.1 X 1.2 x 1.9 x 6.8 X 5.3 x 4.0 X 1.5 X 1.5 X 8.7 X 1.3 x 1.8x 4.1 X 2.2 x 7.7 x 8.7 X 2.4 X 2.1 x 1.9 x 4.3 x 2.7 X 8.9 x 7.1 x 1.1 x
5%
loo
1.1 x 9.9 x 2.0 x 1.2 x 2.8 X 4.5 x 2.1 x
10-2 10-1 100 10-l 10-l 100 10-1 100 10-l
3.1 2.1 3.5 1.4 4.4 3.8 3.8 9.6 6.7
100 10-1 10-1
lo0
10-1 10-l
10-1 10' 10-1
10"
lo1
100
loo 10'
10-1 10"
lo1
lo-'
loo lo0 lo0 100 102
10-1 10" 102 10-1 10"
lo? 100
10' 102
10-1
100 102
100
101 10-1 100 101
lo0
100 101
x 10-l x 100 x 10' X
x
lo0
100 X 10'
X X X
lo0 loo lo1
4.5 x 4.5 x 1.1 x 1.9 x 9.6 X 1.2 x 5.3 x 2.1 x 2.2 x
10-1 100 102 100 10" 102 10" 101 102
6.5 X 9.7 x 3.5 x 2.8 X 2.1 x 4.0 X 7.6 X 4.5 x 6.9 X 9.5 x 2.1 x 1.1 x 4 0 x 4.5 x 1.3 x 1.1 x 9.9 x 2.2 x P.4 x 4.6 X 3.7 x 5.8 X
10-l 10" 102
loo 10'
lo2 10" 101
lo2 10-1 101 103 10" 10' 103 101 101 103 100
10' 103
lo0
Table I11 (continued) Separation in E,, mV
120
130
140
150
160
Concentration ratio tolerable to stated level nl
nl
1%
5%
2 2 3 3 3
2 3 1 2 3
1 . 9 x 10' 7 . 9 x 102 3 . 1 X lo0 4 . 1 X 10' 1 . 4 x 103
9 . 9 x 10' 4.1 x 103 1 . 6 X 10' 2 . 2 x 102 7 . 1 x 103
1 1 1 2 2 2 3 3 3
1 2 3 1 2 3 1 2 3
3.9 x 1.9 x 2.3 X 1.6 X 4.1 X 2.5 x 4.5 x 9.0 x 4.4 x
2 . 0 x 100 1 . 0 x 102 1 . 2 x 104 8 . 5 X 100 2 . 1 x 102 1 . 3 x 104 2 . 3 X 101 4 . 7 x 102 2 . 3 x 104
10-1 10'
lo2 100 10' 103
100
10' 103
1 2 3 1 2 3 1 2 3
5 . 8 X lo-' 4 . 2 X 10' 7 . 3 x 103 2 . 4 X lo0 9 . 0 x 10' 8.1x 103 6 . 5 X loo 1 . 9 x 102 1 . 4 X lo4
3.0 X 2.2 x 3.8 x 1.2 x 4.7 x 4.2 x 3.4 x 1.0x 7.4 x
1 1 1 2 2 2 3 3 3
1 2 3 1 2 3 1 2 3
8 . 5 X 10-1 9 . 1 x 10' 2 . 4 x 104 3 . 5 X'100 2 . 0 x 102 2 . 6 x 104 9 . 6 X loo 4 . 3 x 102 4 . 6 x 104
4.4 x 100 4 . 8 X lo2 1 . 2 x 105 1 . 8 X 10' 1.0x 103 1 . 4 x 105 5 . 0 X 10' 2 . 2 x 103 2 . 4 x 105
1 1 1 2 2 2
1 2 3 1 2 3 1 2 3
1.3x 2.0 x 7.6 x 5.2 X 4.3 x 8.4 X 1.4 X 9.2 X 1.5 x
1
1.8X 100
6.5 X 1 . 0x 3.9 x 2.7 X 2.2 x 4.4 x 7.3 x 4.8 x 7.6 x 9.6 X
3 3 3 1
102
104 100 102
lo4 10'
lo2 105
102 104
101 102
170
180
104 10' 103 104
190
100
103 105 10' 103 105 10' 103
105 100
Trace Metals in Riuer Water. The second harmonic stripping technique is also ideally suited for the determination of zinc, copper, cadmium, and lead in fresh and salt river water. Work in these laboratories (28) on the upper (fresh water) and lower reaches (salt water) of the Yarra River (Victoria, Australia) shows that the range 5 X to 10-8M can be determined with a 15-minute electrolysis time. These results show that the second harmonic method can be used a t the really trace level in practical situations. Quantitative Calculation of Resolution. Equation 8 has been shown to be valid for both linear sweep and stripping second harmonic voltammograms. Access to an analytical solution allows resolution to be quantitatively computed readily (29).One format for comparing the resolution is to define the separation in half-wave potentials for (28) A M Bond Unpublishedresults (29) A M Bond and R C Boston, Rev A n a / Chem , in press
Separation in Ei,mV
lo0
1 1 1 2 2 2 3 3 3
100
Concentration ratio tolerable to stated level
200
nl
n2
1%
1 1 2 2 2 3 3 3
2 3 1. 2 3 1 2 3
4 . 3 x 102 2 . 4 x 105 7 . 6 X loo 9 . 3 x 102 2 . 7 x 105 2 . 1 x 10' 2 . 0 x 103 4 . 7 x 105
2.3 x 1.3 X 4.0 X 4.8 x 1.4 X 1.1x 1.1 x 2.5 X
1 1 1 2 2 2 3 3 3
1 2 3 1 2 3 1 2 3
2.7 X 9.4 x 7.8 x 1.1 x 2.0 x 8.7 x 3.1 X 4.4 x 1.5 X
1 1 1 2 2 2 3
1 2 3 1 2 3 1 2
3
4.0 2.1 2.5 1.7 4.4 2.8 4.5 9.6 4.9
1.4 X 4.9 x 4.1 X 5.9 x 1.1)< 4.5 x 1.6 X 2.3 X 7.9 x 2.1 x 1.1 x 1.3 x 8.6 X 2.3 x 1.5 X 2.3 X 5.0 X 2.5 X
1 2 3 1 2 3 1 2 3
5.9 4.5 8.1 X 2.5 X 9.6 x 9.0 x 6.6 X 2.1 x 1.6 X
1 2 3 1 2 3 1
8.7 9.8 2.6 3.6 2.1 2.9 9.8 4.6 5.0
3 3 1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3
3
Y
3
X
x
5%
100 102 105 10' 103 105
lo1 103
lo6 lo0 103
X 106
X 10' x 103 X lo6
x x x x x
101 103 106
100 103
lo6 10' 103
106 lo1 104 10'
X 100
x x
103
107 X 10' x 104 X loi X 10' X 104 X 107
3.1 X 2.3 x 4.2 x 1.3 x 5.0 X 4.7 x 3.5 x 1.1 x 8.2 X
103
lo6 10' 103
lo6 102 104
loG 10' 103
lo6 101
10,' 106 10' 101 106 10' 104 10'
lo1
104
10'
lo2 lo4 lo6 10' 104 107 102
lo4 107 102 106
loi
4 . 5 x 10' 5 . 1 x 104 1 . 3 X lo* 1 . 9 x 102
1.1 x 105
1.5 5.1 2.4 2.6
X 108 X lo2 X 105 X lo8
1% overlap in two-component systems ( 5 ) . Table I1 gives values for dc and ac polarography, dc linear sweep voltammetry ("normal," first and second derivative) and ac voltammetry (fundamental and second harmonic modes). From Table 111, it can be clearly seen that in the situation where a species is to be determined in the presence of another more positively reduced species, resolution in the ac voltammetric techniques is far superior to the dc linear sweep techniques. This basically arises from the depletion asymmetry at)) encountered in the dc techniques a t potentials more negative than El 2. An alternative and analytically more useful tabulation of resolution data is given in Table 111. This table gives the concentration of a neighboring species tolerable for a given separation in E1,2 for electrode processes with various n values, such that the peak height is unaffected a t the 1%(linear-sweep) and 5% (linear sweep stripping) levels (29).
A N A L Y T I C A L C H E M I S T R Y , V O L . 46, NO. 11. SEPTEMBER
1974
1537
CONCLUSIONS The present work demonstrates that linear sweep phase-selective second harmonic ac voltammetry should provide one of the most sensitive electroanalytical techniques for the determination of species exhibiting reversible or close to reversible electrode processes. For the reversible class of electrode process, the equations describing the voltammograms at stationary electrodes are essentially the same as those obtained under dropping mercury electrode (polarographic) conditions. Thus, the technique can readily be used in a systematic fashion like second har-
monic ac polarography. No restrictions, other than AEwt u t , are placed on the use of fast scan rates as charging current contributions are negligible and the resolution is somewhat better than derivative dc linear sweep techniques. The readout of the current-voltage curve and the nature of the experiment is most suitable for automation of the experiment and this aspect of the technique is currently under investigation.
>>
RECEIVED for review October 15, 1973. Accepted February 20, 1974.
Theoretical Treatment of the Selectivity and Detection Limit of Silver Compound Membrane Electrodes Werner E. Morf, Gunter Kahr, and Wilhelm Simon Laboratorium fur Organische Chemie der Eidgenossischen lechnischen Hochschule, Zurich, Switzerland
Based upon a universal integral equation for the steadystate EMF of an electrochemical cell containing any type of ion-selective membrane electrode, equations are derived that describe the selectivity behavior and the detection limits of different solid-state membrane electrodes. Using published values for solubility products and complex stability constants, the selectivities computed for silver compound electrodes that respond to anions, cations, as well as neutral complex forming species, are in perfect agreement with measured data. The detection limit is either dictated by the solubility of the membrane material or given by the activity of the silver defects in the membrane surface, whichever is larger. In consequence, anomalies in the response to I - and S'- ions with extremely high slopes have to be expected: this limits the useful activity range of the respective silver compound electrodes when using unbuffered sample solutions.
During recent years, solid-state membrane electrodes selective towards cations, anions, as well as other species forming complexes with membrane materials have been used for a variety of analytical applications (1-5). Here, a knowledge of different parameters, especially selectivities and detection limits, is of utmost importance. Corresponding theoretical treatments have been restricted to rather limited cases such as the anion selectivity of silver halide (6-11) and LaF3 (7, 8) membrane electrodes, and the detection limits of AgCl (8, 12) and LaF3 (12) solid(1) R . P. Buck, Anal. Chem., 44, 270R (1972). (2) J . Koryta. Anal. Chim. Acta, 61, 329 (1972). (3) G. J . Moody and J . D. R. Thomas, "Selective Ion Sensitive Electrodes,'' Merrow Publishing Co., Watford, Herts, England, 1971, (4) R. A. Durst, Ed., ''Ion-Selective Electrodes," National Bureau of Standards, Spec. Publ. 314, Washington, D.C., 1969. ( 5 ) E. Pungor, Pure Appl. Chem., 27, in press. (6) E. Pungor and K. Toth, Analyst ( L o n d o n ) , 95, 625 (1970); Hung. S o . Instrum., 18, 1 (1970). (7) J. W. Ross, Jr., in Ref. ( 4 ) . (8) R. P. Buck, Ana/. Chem., 40, 1432 (1968). (9) A. K . Covington, in Ref. ( 4 ) . (10) W. Jaenicke, Z. Elektrochem., 55, 648 (1951); W.Jaenicke and M . Haase. Z. Elektrochem., 63, 521 (1959). (11) G. P. Bound, B. Fleet, H. von Storp. and D. H. Evans, Ana/. Chem., 45, 788 (1973). (12) J. Havas. IUPAC International Symposium on Selective Ion-Sensitive Electrodes, April 9-12, 1973, Cardiff, England.
1538
state electrodes. The object of the work reported here is the presentation of generally applicable equations that describe the selectivities and detection limits of different solid-state membrane electrodes.
THEORY Based upon a set of clearly specified assumptions (131.9, a universal integral equation was derived (13) which describes the steady-state EMF of an electrochemical cell containing any type of ion-selective membrane electrode. In the application of this equation to homogeneous solidstate membranes, contributions to the EMF of the cell due to diffusion potentials within the membrane may be neglected (13)[see also (8)] and one obtains: EMF
=
E,,
RT +I 2 ,F
a,'a,(d)
n a m
where a,(O), a , ( d ) = activity of ion I*, on the membrane surface contacting the sample and reference solution, respectively: For homogeneous membranes: a,(O) = a,(d). a,', a," = activity in the boundary of solution contacting the membrane on the sample and reference side, respectively. These boundaries are in equilibrium with the membrane phase, which must not necessarily hold for the bulk of the sample (activity a,) and reference solution. For a given reference system, a," is constant throughout. Since membranes prepared from silver compounds Ag,X are of special analytical significance, they will be treated in detail here. Equation 1 therefore may be reduced to: EMF
=
E4g0
RT +T -lnaAg'
(2)
Using the solubility product L A , ~ , x :
LA,:, = a.Ag%' Equation 2 can be rewritten in the form:
(3)
(13) H.-R. Wuhrmann, W . E. Morf, and W. Simon, Helv. Chlm. Acta, 56, 1011 (1973). (14) W. E. Morf. D. Arnrnann, E. Pretsch. and W. Simon, Pure Appl. Chem., 36, 421 (1973). (15) G. Eisenman, in Ref. ( 4 ) .
A N A L Y T I C A L C H E M I S T R Y , VOL. 46, NO. 11, S E P T E M B E R 1974
