turing and pive full scale response at low nanomole and picomole concentrations. (iii) Ethanol can be used both as an esterification agent and as a stabilizing agent to prevent formation of extraneous peaks when HFBA is used in the presence of trace amounts of ethyl ether. (iv) The HFRA reagent mixture will react under the same condition with amines to produce derivatives that are highly electron capturing. The capacity of HFBA-py to catalyze esterification of carboxyl groups was further tested by substituting propanol, butanol, and fi-trichloroethanol for ethanol in the reagent mixture. Both GLC and mass spectral analysis revealed that the carboxyl groups of the acids were esterified with the substituted alcohol: however, only etharlol showed stabilizing properties to HFBA in the presence of ethyl ether. In another study in which we used /3-trichloroethanol and substituted borontrifluoride (BF?) for HFRA-py as a catalyst, we found that, as judged by peak she, HFRA-py catalyzed the formation of more ester than did BF?. When two alcoho!s, ethanol and butanol, were included in the reaction mixture along with lactic acid, two peaks were obtained. One peak corresponded in retention time on both polav and nonpolar columns to the HFBA-ethvl ester of lactic acid and the second peak to the HFBA-botvl ester of lactic acid. When the alcohol standard mixture ( 3 ) was cornbjwd with the acid standard mixture ( 3 ) and derivatized with HFBA-py-ethanol, the alcohols were esterified with HFBA and the acids with ethanol. There was no detectable interference between the dilute alcohol in the Sample and esterification of the carboxyl groups with ethanol. Thus, the data. indicate that the alcohol must be present in
sufficient concentration before it can compete for esterification of the carboxyl group in the presence of HFBA-py. However, there is enough ethanol present in ethyl ether that has been stabilized with ethanol to compete with larger amounts of other alcohols for esterification of the carboxyl group in the presence of HFBA-py. The procedure described above reproducibly produced derivatives that can be effectively used with EC-GLC to selectively detect minute quantities of hydroxy acids, alcohols, or amines in small amounts (2 ml) of synovial fluid (Figure 1, curves A and B ) . The chromatogram was obtained by analysis of 2 ml of synovial fluid taken from a patient with juvenile rheumatoid arthritis. The patient was receiving salicylate treatment and this acid was easily detected (Figure l, curve B ) . Identification of the compound was confirmed by GLC mass spectrometry as the HFBAethyl ester derivative of salicylic acid. Basic extractable HFBA reactive compounds were detected in the pH 10 extraction (Figure 1, curve A ) , but these have not been identified. The above procedure has been applied to the study of a limited number of synovial fluid samples taken from people with arthritis, and several EC-GLC profiles have been obtained that differ according to the form of arthritis involved
RECEIVEDfor review April 22, 1974. Accepted July 22, 1974. TJse of trade names is for identification only and does not constitute endorsement by the Public Health Service or by the U.S. Department of Health, Education, and Welfare.
Alternating Current Linear Sweep and Cyclic Voltammetry at a Dropping Mercury Electrode with Phase-Selective Fundamental and Second Harmonic Detection H. Blutstein and A. M. Bond Department of Inorganic Chemistry, University of Melbourne, Parkville, Victoria, 3052, Australia
The analytical application of phase-selective ac linear sweep voltammetry (fundamental and second harmonic) with scan rate synchronized to a dropping mercury electrode is considered. Commercially available instrumentation was adapted to provide the technique, and the theoretical response was obtained over a wide range of operating conditions for both the faradaic and charging current components. The techniques combine the advantages of fast scan rates (up to 200 mV/sec used in this work), extremely high reproducibility (better than 1 % at the 10-6Mlevel), and linear calibration curves over a wide concentration range. With the second harmonic method, flat base lines were obtained despite the growth of the mercury drop during the scan duration. and this would appear to be the preferred technique. At the high frequencies necessitated by the condition AEwt >> vf, slight non-ideality leads to sloping base lines in the fundamental mode. Comparison with the dc method shows considerable advantage of ac techniques with respect to resolution. Cyclic ac voltammograms can also be obtained at the dropping mercury electrode with the same instrumentation. 1934
Limitations associated with the analytical use of conventional dc polarography include the relatively poor sensitivity result,ing from the high contribution of the charging current at low concentrations, difficulties in measuring wave heights, which frequently show non-ideal exponential shape current-potential curves, and the length of time required to record a po1arogra.m. Many of the recent advances in polarographic methodology have been aimed a t minimizing these limitations and making polarography more competitive with other commonly used instrumental analytical techniques such as molecular spectroscopy, chromatography, and atomic absorption spectrometry. The use of phase-selective fundamental ac polarography (I ), second order ac techniques (1 ), pulse and current sampled dc polarography (2) successfully discriminates against the charging current. These methods frequently increase the sensitivity by two or more orders of magnitude over conventional dc polarography. (1) D. E. Smith in "Electroanalytical Chemistry," A. J. Bard, Ed., Marcel Dekker, New York, N.Y.. 1966, Vol. 1, Chap. 1. (2) H. Schmidt and M. yon Stackelberg, "Modern Polarographic Methods," Academic Press, New York, N.Y., 1963.
ANALYTICAL CHEMISTRY, VOL. 46, NO. 13, NOVEMBER 1974
Derivative dc and pulse techniques (2) and harmonic and intermodular ac polarography (1) also give vastly improved forms of readout in which the wave height is easily measured from a peak. A number of approaches have been applied to reducing the polarographic analysis time. The use of very short mechanically controlled drop times in the polarographic experiment ( 3 ) enables the scan rate to be increased, thereby substantially decreasing the time scale. Another approach enabling the use of even faster scan rates is linear sweep voltammetry at stationary electrodes ( 4 ) .With dc voltammetry, an asymmetric wave shape (5, 6) is observed with this technique and the current does not return to zero a t potentials beyond the peak as in some other methods. Thus resolution is not entirely satisfactory. Furthermore, considerable charging current is present, particularly with increasing scan rates. Linear sweep ac methods (7, 8 ) can also be employed at stationary electrodes. The readout of these methods is essentially the same as in ac polarography (7, 8), and phase-selective detection can be used with considerable advantage to reduce charging current. This has been achieved with both fundamental ( 7 ) and second harmonic (8) ac techniques at a hanging drop mercury electrode (HDME) and other stationary electrodes. However the reproducibility of most voltammetric techniques is not as high as in polarography because of the difficulty in obtaining a constant electrode surface area. An early approach to obtaining a reproducible area of a mercury drop, in dc voltammetry, involved synchronizing the potential sweep to a dropping mercury electrode (DME) so that the complete dc voltammogram could be recorded in the lifetime of a single drop (9). Although the drop area is completely reproducible using this technique and very high precision can be attained, because this technique was only applied in the dc mode, other disadvantages remain. In addition to the analytically somewhat unattractive wave shape, charging current and sloping base lines caused by the growth of the mercury drop during the potential scan provide restrictions which can only be minimized by the experimentally difficult procedure of a differential technique using two synchronized dropping mercury electrodes. In this work, we now combine all the advantages of phase-selective fundamental and second harmonic ac modes to the linear sweep technique at a DME. In this manner, the electrode area can be easily reproduced and fast scan rates readily used, because charging current problems are minimized. Both phase-selective fundamental and second harmonic ac voltammetry are compared to each other and to the dc technique. The technique of cyclic ac voltammetry a t a DME is also briefly described. Previously, some experiments on ac linear sweep voltammetry a t a DME (10-13) have been reported. The only detailed investigation by Jee et al. (12, 1 3 ) was carried out on instrumentation which gave far from the expected theoretical response and the real assessment of the capabilities of (3) A. M. Bond, J. Nectrochem. SOC.,118, 1588 (1971) and references
cited therein. (4) R. N . Adams. "Electrochemistry at Solid Electrodes," Marcel Dekker, New York, N.Y., 1969. (5) R. S. Nicholson and I. S h a h Anal. Chem., 36, 706 (1964). (6) S.P. Perone and T. R . Mueller. Anal. Chern., 37, 2 (1965). (7) W. L. Underkofler and I. Shah. Anal. Chem., 37,218 (1965). (8)H. Blutstein and A. M. Bond, Anal. Chern., 46, 1531 (1974). (9) L. A . Matheson and N. Nichols, Trans. Arner. Electrochem. Soc., 73, 193 (1938). (10) C.I. Mooring, Polarogr. Ber., 6,63 (1958). (11) R. Neeb, Fresenius'. Z.Anal. Chern., 186, 53(1962). (12) B. Fleet, R. D. Jee. and C. J. Little, J. Nectroanal. Chern., 43, 349 (1973). (13) R. D. Jee. Fresenius' 2. Anal. Chem., 264, 143 (1973)
the techniques could not be ascertained. In this study, we have used instrumentation based mainly on commercially available apparatus to obtain linear sweep and cyclic phase-selective fundamental and second harmonic ac voltammetric response at a DME and we have compared these experimental results with theory. Excellent agreement is now obtained. The ac charging current contribution at a quasi-stationary electrode has also been examined in detail for the first time. EXPERIMENTAL Reagents. All chemicals used were of reagent grade purity with cadmium(II), thallium(I), bismuth(III), and lead(I1) added as their nitrate salts. All measurements were made a t 25.0 f 0.1 "C and oxygen was removed when necessary, by bubbling argon through the solution 15 minutes prior t o a measurement. Apparatus. All polarograms and voltammograms were recorded on a PAR electrochemistry system Model 170 (Princeton Applied Research Corp.). The readout was obtained on either an X-Y recorder or Tektronix 5103N Oscilloscope System. The PAR linear sweep module accessory Model 174/51 was used to synchronize the potential scan to a dropping mercury electrode (DME). The linear sweep accessory was interfaced to a 170 electrochemistry system in accordance with directions provided by the manufacturer for use in the dc mode. However, this approach introduces a phase-shift with the ac circuitry which needs to be corrected prior t o recording linear sweep voltammograms. The second harmonic response was obtained using multiplication of the ac reference signal as described elsewhere (14). The instrumentation for the ac cyclic voltammetric technique has been reported in another communication by one of us (15). A three-electrode system was used with Ag/AgCl (saturated NaC1) as the reference electrode and tungsten was used as the auxiliary electrode.
'
.
.
RESULTS AND DISCUSSION Theory a n d Its Experimental Verification f o r t h e * Linear Sweep Techniques. The instrumentation used in this work involves programming a pre-sweep delay ( t o ) after commencement of the mercury drop growth. The PO- . tential scan therefore begins at a period well after the commencement of the drop life. A t the end of the potential. ' ' sweep, the drop is dislodged by an impulse applied to the, * DME and another sequence begins (14). This is shown &a. grammatically in Figure 1. This differs from the usual ap-" proach which uses a gravity controlled DME in which a . sudden increase in impedence caused by a drop falling off' triggers another sequence (16). ' The above technique represents a special form of voltammetry at a DME, which can be readily applied in the.aE " * . mode. The equations for the ac response can be derived 6, ' the same arguments as used when a stationary electrode i s . involved, except that the electrode area term must be corrected to account for growth of the mercury drop during . the potential scan. F a r a d a i c Current. For a reversible reduction, A ae *B, where species A and B are soluble, the equation for both the fundamental and second harmonic alternating ' current can be derived by considering a sinusoidally alternating potential being superimposed on a constant dc potential ramp
'.
.
:. 0 .
I
-
0
+
E = Ed, - AE sinwt
(1)'
The dc potential (Edc) is a function of time.
AE is the amplitude and w the frequency of the alternating (14) H. Blutstein, A. M. Bond, and A. Norris, Anal. Chern., 46, 1754 (1974). A. M. Bond, J. E/ectroana/. Chem., 50, 285 (1974). (16) R. C.Propst and M. H. Goosey. Anal. Chern., 36,2383 (1964).
(15)
ANALYTICAL CHEMISTRY, VOL. 46, NO. 13, NOVEMBER 1974
1935
..
.
.
Initial Potenmi(E,)
!
Tim Figure 1. Diagrammatic representation of the sequence involved in the present method of linear sweep voltammetry
c
potential. The fundamental and second harmonic ac responses are obtained a t frequencies f and 2f, respectively. Figure 2 shows dc, fundamental, and secord harmonic ac voltammograms (quadrature and in-phase modes). The equation for the small amplitude linear sweep fundamental harmonic response for a reversible electrode process was derived by Underkofler and Shain (7) in which r! tffusion to a plane electrode has been assumed.
(
sin ut
+ -1)
(3)
- 0 4 - 0 5 -36 -07
where j = (nF/RT)(Ed,- E112r), E1/zr is the reversible half-wave potential, Co* is the concentration of the depoY-vi-er and P ( u t ) is basically a function of scan rate (for 1 can be "e Condition a E w t >> ut, the limit F' ( u t ) " q h n ) . The electrode surface area, At, a t time t after the 3 1 commences is given by
* .
- Eo 2'
--a> ut, and phase-selective detection is even more important under these conditions. The dependence on I , (at constant m ) on area, is altered by varying the pre-sweep delay. Figure 3a shows a linear plot for I , us. At/m2/3as predicted by Equations 4 and 5 .
)]
2/3
n2F2Co*(wD,)'/24E
sin(wt
I, = 4RT
E , is the peak potential and the condition SEwt >> ut has been assumed. Using a 1 X lo-* M cadmium(I1) solution in 1M hydrochloric acid and a Scan rate of 50 mVlsec, plots of I , us. 01/2 (100-900 Hz) and SE (1-10 mV peak to peak) gave linear responses. The in-phase and quadrature components were also recorded (Figure 2B) and the expected phase-angle relationships obtained. The quadrature component, as in polarography, contained considerable charging current contribution in the linear sweep technique. Consequently, phase-selective detection provides considerable improvement in discriminating against the charging current. Furthermore fast scan rates necessitate the use of higher frequencies than in polarography, to maintain the condi1936
C.
Figure 2. AC and dc linear sweep voltammograms at a DME of 7.5 X 10-5Mcadmium(ll)in 1Mhydrochloric acid
Irhere n is the flow rate of mercury. The theory can be tested by comparing the experimental refponse when frequency, amp1itude, phase tration, and electrode area are varied and plotted us. the rrivirnum value of I ( o t ) ,or I,, where,
+ (E,
A
-35
VOLTS
-
0.00853 m 2 / 3 [ to
s
-C
a)
(5
The dependence of m2/3(at constant to) was confirmed by varying the mercury column height. A linear calibration curve was obtained over the concentration range 10-3 to 10-6M cadmium(I1) in 1M hydrochloric acid as shown in Figure 4. From Table I, we can conclude that the peak potential (E,) and half-widths for linear sweep voltammetry and polarography are the same. Furthermore, the peak potential is independent of AE and w within the limit of experimental error. Thus the equivalence of the equation to those in ac polarography is completely verified for the reversible electrode process. Similar arguments ( 7 ) to those used to derive Equation 3 can be employed t o obtain the equation for the linear sweep second harmonic alternation current a t a DME (8).
ANALYTICAL CHEMISTRY, VOL. 46, NO. 13, NOVEMBER 1974
I
10-5
10-6
10 3’
10-0
Concentration
M
Figure 4. Plots of peak current vs. concentration of cadmium(l1) in 1MHCI. (A) DC moue peak current, b = 5 sec v = 100 mV/sec ( 0 )Fundamental harmonic ac mode In-phase component A € = 10 mV w = 400 Hz to = 5 sec v = 50 mV/sec (0)Second harmonlc dc mode Peak-to-peak current In-phase component A € = 10 mV o = 400 Hz to = 5 sec v = 50 mV/sec L
I (*
0’
I-
P
I(2wt) =
-
60.
.55-
‘+
50-
,45 -
.40 .40‘
n3F3A,C,*(2wD,)*.’2AE2 sinh(‘/z)F”(ot) 16 R zT’ cos h3(j/z )
25
30
35 3.5
where F” ( u t ) 1 when AEwt >> u t . All other terms have been previously defined. Experimental plots of the peak-to-peak height (Ipp)of the in-phase component against d 2and AE2gave linear curves for the reduction of cadmium(I1) as predicted by Equation 6. The inflection potential which is defined as the potential where the current is zero, is independent of (L‘ and AE, within experimental error. Figure 2 C shows the in-phase and quadrature components of the second harmonic ac voltammograms. The responses obtained obviously have a 7r/2 phase difference. However, in contrast to the fundamental harmonic, there is no evidence of significant charging current in either component. That is, as in second harmonic ac polarography (14), the double layer charging current is extremeiy small. The use of phase-sensitive detection with the second harmonic technique, while not necessary for minimizing the charging current, does offer advantages in the nature of‘tht. waveshape (8, 14). The area term in the second harmonic equations (at constant m ) was varied by changing the pre-sweep delay, and Figure 36 shows the resultant linear plot for both the maximum (i+) and minimum (i-) peaks where for a totally reversible reaction
A, = 0.00853 m 2 l 3 X
(
RT
fl)
Figure 3. (a) Plot of peak height vs. pre-sweep delay (area) for 1 X [ t o + Ei/zr 7 - l n ( 2 + - EO nF 10-4M Cd(ll) in 1M HCI. v = 50 mV/sec. w = 400 Hz. A€ = 10 mV. In-phase component. (b) Plot of the positive (i+) and negative (i-) 2) branches of the second harmonic wave vs. pre-sweep delay for 1 X l r 4 MCd(ll) in 1M HCI. L’ = 50 mV/SeC. W = 400 H Z . A€ = 10 m v . The in-phase component was again used to verify In-phase component equation. ANALYTICAL CHEMISTRY, VOL. 46, NO. 13. NOVEMBER 1974
this
1937
Table I. Comparison of Parameters Obtained from ac Linear Sweep Voltammetry at a DME and ac Polarography for Various Electrode Processes Polarography"' Fundamental harmonic
0
Second harmonic
ED(")
Half -width (mV)
Ei(V)
AEp(mV)
Ep(Vl
Half-width (mV)
Ei(V)
AEP(mV)
-0.565 -0.700 -0.502 -0.176
90 47 47 33
-0.564 - 0.698 -0.501 -0.170
69 36 32 23
-0.564 -0.697 -0.503 -0.174
90 45 45 32
-0.562 -0.699 -0.501 -0.170
67 37 33 23
Elechode process
Tl(1) in 5M HC1 Cd(I1) in 5,V HC1 Pb(I1) in 5'11 HC1 'Bi(II1) in 5111 HC1
Fundamental harmonic
Second harmonic
AE = 10 mV, w = 400 Hz. * Scan rate = 50 mV/sec. Drop time = 2 sec
Table 11. Reproducibility of dc, Fundamental and Second Harmonic ac Voltammetry at a DME for the Electrode Process Cd(I1) + 2e= Cd(Hg)a Reproducibilityb of peak heights for dc and a c linear sweep techniques at a DbtE
Concenhation
1x 1x 1x 1x
10-~~1 10-4~ 10-5114 10-94
Direct current C
Fundamental harmonic alternating current C
Second harmonic alternating cun'entc
0.4% 0.5% 0.7% 1.2%
0.1% 0.1% 0.2% 0.3%
0.2% 0.3% 0.5% 0.7%
Pre-sweep delay = 5 sec. Scan rate = 200 mV/sec. Initial potential = -0.400 volt. For ac techniques, AE = 10 mV, w = 400 Hz, in-phase component. Calculated as a standard deviation. Taken over three scans.
A linear dependence of I,, on concentration was obtained when concentration of cadmium was varied over the range to 10-6M (Figure 4). If the parameters inflection potential (Ei)and peak-topeak separation (AE,) are used to characterize the wave, then from Table I it can be seen that in the second harmonic mode, the criteria for reversibility in linear sweep voltammetry a t a DME are the same as found in polarography. Double-Layer Capacitance Current. The faradaic current in ac linear sweep voltammetry under conditions where AEwt >> u t , essentially gives the same equations as those found in polarography (7, 8) ( E independent of u for theoretical purposes), and it has been assumed that the charging current for linear sweep ac voltammetry is the same as that found in ac polarography. This aspect can be examined in detail, as the present experimental technique is most convenient for quantitatively studying the charging current. If we assume that the electroactive species does not affect the double layer (which is not strictly true (17, 18) under all conditions) and the dc and ac components can be considered independently, the expression for the capacitance current can be derived as follows.
(9) where p m is the charge density on the electrode surface, At the surface area of the DME, and E is the applied potential given by Equation 1. From the differential capacitance, which is defined as, (17) D Britz and H H Bauer, J Necboanal Chem, 16, 13 (1968) (18) D E Smith, CRCCrft Rev Anal Cbem, 2, 247 (1971)
1938
dqm d t = -dqrn =-.dE d t dE Equation 9 can now be written as,
ca
i, = - q m dAA dt
+ AtCd2' + A,CdAEw C O S w t
(11)
Hence the dc and ac components of charging current can be expressed as
The area terms in Equations 12a and 12b mean that the charging current will show a time dependence giving rise to the undesirable sloping base line found in both the linear sweep dc and fundamental harmonic ac voltammetric methods a t a DME. Equation 12a is well known (19) and has been shown to be approximately correct under a range of conditions. Equation 12b can be easily tested in the fundamental harmonic mode by using phase-selective detection since the capacitance current of the double layer should have a phase angle of T/Z--i.e., quadrature components should consist of pure charging current (20, 21). This equation was tested on a 1M hydrochloric acid solution and the expected phase angle was found a t the potential -0.700 volt us. AgIAgC1. However, as stated previously, higher frequencies than used in polarography generally need to be employed. The magnitude of the charging current is therefore high and some non-ideality is observed, in that the in-phase compo(19) P. Delahay. "New Instrumental Methods in Electrochemistry," Interscience, New York/London, 1954, pp 130-131. (20) A . M. Bond, Anal. Chern., 44, 315 (1972). (21) T. F. Retajczyk and D. K . Roe, J. Nectroanal. Chem., 16, 21 (1968).
ANALYTICAL CHEMISTRY, VOL. 46, NO. 13, NOVEMBER 1974
Frequency
(HA
Flgure 5. Plots ot charging current vs. various parameters in 1M HCI.Fundamental harmonic mode. Potential = -0.700 volt. Quadrature component ( a ) vs. Amplitude. to = 5 sec. ( D ) vs. Frequency. hE = 10 rnV. to = 5 sec. (c) vs. Pre-sweep delay (Area). A € = 10 mV, o = 600 Hz
nent does contain a small but finite charging current contribution. Thus, a sloping base line is observed with the fundamental harmonic even when phase-selective detection is used to record the faradaic current component in the in-phase rneasuiement. The expected linear dependencies were also obtained for plots i , us. SE (Figure 5 a ) and i, us. A J r n ' / 3 at a potential of -0.700 volt us. Ag/AgCl (Figure 5 c ) where A t was varied by altering the pre-sweep delay. However the i, us. w plot shows a slight departure from linearity above 600 Hz. As might be expected, a t slower scan rates, the growth in the mercury drop causes considerable sloping of the base line, as shown in Figure 6. The second harmonic BC capacitance current should be riegligi ble under ideal conditions ( 2 2 ) .In 1M hydrochloric acid, AE, w , and the drop area were varied. No significant charging current was observed a t equivalent sensitivities to that used for the experiments in the fundamental mode. Sloping base lines are therefore less of a problem in the second harmonic niode as can be seen in appropriate voltammograms. However, a small nonlinear charging current contribution was observed in the second harmonic technique when measuring concentrations of cadmium in the 1 W M range. Analytical Aspects. The linear sweep ac voltammetric technique at a DME provides a powerful analytical tool because, while providing a means of decreasing the time scale of the analysis, i t combines the advantages of fundamental and second harmonic ac techniques. Linear concentration calibration curves were readily ob-
( 2 2 ) B. Breyer and H. H. Bauer in "Alternating Current Polarography," P. J Elving and I. M. Kolthoff, Ed., Interscience, New York/London, 1963.
L 4.70 -080 VOLTS
A
-090 -1.00 -110
vs
Ag/AgCI
Figure 6. Dependence of charging cuirent on scan rate In 1M HCI. Fundamental narmoiiic mode. Quadraiure component. LE = 10 mV. o = 600 Hz. b = 2 sec
tained for cadmium over at least three orders of magnitude, a5 shown in Figure 4. The reproducibility for these voltammograins is virtually the thickness of the recorder pen and better than 1%.Table I1 gives the reproducibility over the concentration range 1 X to 1 X lWbM for all the linear sweep techniques used in this work The reproducibility can be Lonipred with values generally quoted for polarography at natural drop times of between 1-2% (23), or for voltammetry a t other stationary electrodes of between 2-5%. Figure 7 shows a comparison between dc, phase-selective fundamental and second harmonic ac voltammograms a t a DME for a solution containing 1 X 10-4M Bi(III), Pb(I1) and Cd(1I) in 5M hydrochloric acid. (23) W. L. Belew, D.J. Fisher, H. C. Jones, and M. T. Kelly, Anal. Chern..41, 779 (1969).
ANALYTICAL CHEMISTRY, VOL. 46, NO. 13, NOVEMBER 1974
e
1939
A
B
\
I
r
I
- 0 4 - 0 5 -06-07 -38 00
-02
-06
-04
VOLTS
vs
-08
AjIAjCI
Figure 7. Multicomponent system containing 1 X 10-4M Bi(llP), Pb(ll),
and Cd(1l) in 5MHCI. ( A ) Second harmonic ac voltammogram. 6 = 1 sec. Y = 200 mV/sec. A € = 10 mV. w = 400 Hz. In-phase component. (81 Fundamental harmonic ac voltammogram. 6 = 1 sec. v = 200 mV/sec. A€ = 10 mV. w = 400 Hz. Inphase component. (C) DC voltammogram. to = 1 sec. v = 200 mV/sec
In the dc technique, the waves for the more negatively reduced lead and cadmium species are not easily evaluated because the currents from the preceding electrode processes must be subtracted for analytically usable peak heights t o be obtained. Similarly, the mercury oxidation causes difficulties in evaluating the bismuth peak height. With the fundamental harmonic technique, the readout form is more conducive to accurate interpretation because the current rapidly decays to zero on both the positive and negative sides of the wave. This facilitates the measure1940
VOLTS
-10
vs
Ac&zJZI
Figure 8. Cyclic voltammograms at a DME of 1 X 10-4M Cd(ll) in 1M HCI (a) Direct current mode. to = 1 sec. v = 100 mV/sec. ( b )Fundamental harmonic ac mode. t~ = 1 sec. v = 100 mV/sec. A € = 10 mV. o = 400 Hz. In-phase component. ( c ) second harmonic ac mode. to = 1 sec. v = 50 mV/sec. A€ = 10 mV. w = 400 Hz. In-phase component. f = forward scan. r = reverse scan
ment of the peak height and no difficulties are encountered even in the presence of preceding waves. However, because of the need to work a t high frequencies if high scan rates are used and the concomitant large value of the charging current, non-ideality leads to the presence of charging current in the in-phase component. The double layer capacitance current varies with area (time) and, therefore, a sloping base line is observed as seen in Figure 7B. Consequently, fundamental harmonic ac voltammetry at a DME when nonphase detection is used, suffers greatly from the presence of charging current and is not even as sensitive as the
ANALYTICAL CHEMISTRY, VOL. 46, NO. 13, NOVEMBER 1974
dc method. The use of phase-selective detection with these techniques is therefore strongly recommended. The second harmonic ac voltammogram obtained at a DME is shown in Figure 8c. The system exhibits a virtually flat base line compared with the dc or fundamental harmonic ac techniques because little or no charging current is present (22).The resolution is also excellent and this technique would therefore appear to be more attractive than with the fundamental harmonic or dc methods. It should be noted, of course, that the present wor!c has been applied to reversible electrode processes and analytically applications will generally be restricted to this class of electrode process. However, this means that discrimination against nonreversible electrode processes should be considerable and this technique should be highly specific. AC Cyclic Voltammetry at a DME. DC cyclic voltammetry consists of applying a triangular dc voltage to the electrochemical cell and reading out the resultant dc current as a function of the applied voltage. This technique enables both the forward and reverse steps of the redox reaction to be studied. This method has been extended to the ac format at stationary electrodes by superimposing an ac voltage onto the dc triangular ramp and either the fundamental (15, 24, 25) or second harmonic (15) ac response is recorded as a function of the applied dc potential. As would be expected, this gives considerable advantage in readout format because of both wave shape and discrimination against charging current. Obviously, the ac technique can now be applied to the DME. Figure 8a, 8b, and 8c show dc, fundamental, and second harmonic ac cyclic voltammograms a t a DME for the reduction Cd(1Ij 2e * Cd(Hg). For the dc case, the peak to-peak separation is 30 mV compared to the normal reversible peak-to-peak separation of 29 mV when both species are soluble in the solution. The difference between those values and other departures from ideality can be attributed to amalgam formation (26). Although no quantitative theory is presently available for ac cyclic voltammetry, Bond (15) has suggested that for a totally reversible system, the forward and reverse scans should be identical, assuming linear diffusion and equal diffusion coefficients of the reduced and oxidized species.
+
(24) A L Juliard, Nature, (London), 183, 1040 (1959) (25) A L Juliard. J Electronanal Chem , 1, 101 (1959) (26) F H Beyerlein and R S Nicholson, Anal Chem, 44, 1647 (1972)
This does not take into account influences of amalgam formation a:id spherical diffusion. Figures 8 b and 8c show the severe influence of amalgam formation in the ac cyclic experiment. In the fundamental harmonic ac mode, the peak separation of the forward and reverse scans is approximately 8 mV, with a scan rate of 50 mV/E;ec, and the waves are not equal to heights. (The “peak heights” referred to in this section have been corrected for drop area growth.) The second harmonic ac mode has a separation of inflection potentials of 7 mV, with a scan rate of 50 mVlsec, and the peak-to-peak heights of the forward and reverse scans are also not equal. At very much faster scan rates, the peak height of the reverse scan decreases in height and approaches the height of the forward scan. Also the separation of the forward and reverse scan peaks increases with increasing scan rate. This may indicate a departure from reversibility or may be due to amalgam formation t)r both. The considerable scan rate dependence observed seems to point to the amalgam formations as the major factor contributing to these observations. Obviously cyclic ac voltammetry should provide a powerful technique in investigating electrode processes, and work is in progress to obtain a quantitative theory (27). Presumably, the linear sweep theory in this work needs to be modified to take into account amalgam formation. In the present work, slight departures in wave shape from that theoretically predicted on the linear diffusion model result from amalgam formation in the forward linear sweep scan as is the case in ac polarography (14, 28-30). However for the reverse scan of the cyclic or stripping experiment, in particular, considerable scan rate dependence of peak heights, peak potential, or inflection potential, and wave shape is observed indicatinL considerable complexity arises from amalgam formation as indicated recently by Moorhead and Davis (31).
RECEIVEDfor review March 12, 1974. Accepted June 12, 1974. The authors thank the Australian Research Grants Committee for funds made available to support this research. (27) I. Ruzic, D. E. Smith, A. M. Bond, and R. J. O’Halloran, unpublished work. (28) T. G. McCord, E. R. Brown, and D. E. Smith, Anal. Chem., 38, 1615 (1966). (29) J. R. Delmastro and D. E. Smith, Anal. Chem., 39, 1050 (1967). (30) T. G. McCord and D. E. Smith. Anal. Chem., 42, 126 (1970). (31) E. D. Moorhead and P. H. Davis, Anal. Chem.. 45, 2178 (1973).
Steady State Current Analysis for Kinetic Studies Using Twin Packed Graphite Electrodes J. H. Strohl and J.
L. Hern
Department of Chemistry, West Virginia University, Morgantown, W. Va. 26506
A twin electrode flow cell has been developed which is applicable for kinetic studies of electrode coupled reactions having half-lives ranging from 1.3 seconds to several hundred seconds. Steady-state current analysis was employed to determine rate constants for two pseudo-1st-order systems. A new technique of allowing only a small portion of
the solution to be in the reactive form is used to determine rates which would ordinarily be too short lived to be studied by conventional steady-state systems. Reproducibility and convenience are also added improvements over other steady-state electrochemical systems.
ANALYTICAL CHEMISTRY, VOL. 46, NO. 13, NOVEMBER 1974
1941
