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that the process of sealing the tube at high temperature produces an area of active glass which adsorbs, or exchanges with, either the water vapor or the hydrogen. This occurred despite the fact that the break-seal tube had been necked down to a narrow diameter and the area of hot glass was minimal. Similarly, the choice of zinc reagent also seems to be important. The grain size is critical: use of coarser shot often produced incomplete reaction, while finer material was more difficult to handle. Attempts to use the zinc in other physical forms, wire, dust, or turnings, give incomplete yields of hydrogen and isotopically fractionate the sample (7). At one stage of the development of the technique, the water was introduced to the reaction tube in a sealed glass capillary which was broken by expansion of the water on heating. However, an inexperienced operator could not always produce reproducible results; this arose from two causes. If too long a time were taken to seal the capillary with a gas torch, some of the water evaporated, leading to large isotopic fractionation. The other difficulty occurred if the capillary tube was nat completely full, Eiince the presence of even a small amount of
air may preferentially oxidize the zinc and result in isotopic fractionation from an incomplete reaction. ACKNOWLEDGMENT We are grateful to Dave Halliday of the Medical Research Council's Clinical Research Unit at Northwick Park, Harrow, for his help, advice, and provision of standard water samphs LITERATURE CITED (1) Bigelelsen, J.; Perlman, M. L.; Prosser, H. C. Anal. Chem. 1952, 2 4 , 1356. (2) Friedman, I.; Smith, R. L. Geochim. Cosmochim. Acta 1958, f 5 , 218. (3) Hagemann, R.; Lohez, P. Adv. Mass Spectrom. 1978, 7 4 , 504. (4) Hartley, P. E. Anal. Chem. 1980, 52, 2232. (5) Weast, R. C., Ed. "CRC Handbook of Chemistry and Physics", 62nd ed.; CRC Press: Boca Ratan, FL, 1981: p b-163. (6) Gonfiantinl, R. Nature (London) 1978, 2 7 1 , 534. (7) O'Neil, J. R., U.S.G.S., Menlo Park, CA, personal communication, 1960.
RECEIVED for review October 23, 1981. Accepted February 8, 1982. This paper is published with the approval of the Director of the Institute of Geological Sciences (Natural Environment Research Council).
CORRESPONDENCE Integration of Differential Pulse Voltammograms for Concentration Measurements Sir: Differential pulfie techniques have been shown to be one of the most sensitive electroanalytical methods (1,2) and because of this have been widely used since their inception by Barker (3, 4). The sensitivity of these methods arises because the potential wave form and data acquisition timing discriminateagainst charging current contributions. Although several variants now exitit, the most commonly used potential wave form consists of a ramp with superimposed pulses and the output is a differential current (Ai). The current is sampled at a time where the residual current has decayed significantly relative to the faradaic current. Quantitative analysis with differential pulse polarography or voltammetry 1i3 usually done by measuring the differential current at its maximum and comparing this to a calibration curve (5-7). However, in several reports it has been demonstrated that small perturbations in the resistance of the electrochemical cell, or in the degree of electrochemical or chemical reversibility, can greatly affect both the differential current amplitude and its location on the applied potential axis (5,6,8-10). All of these parameters are affected by the solution composition and therefore lead to a degree of uncertainty when samples are analyzed and compared to standards. To compensate for this shift on the potential axis, a commercial automated polarograph (Princeton Applied Research, Model 384) has incorporated a 100-mV potential window in its search routine to find the current maximum. An alternate but little used method for evaluating differential pulse curves is to measure the area under the curve. In fact, the derivative of the current-voltage curve for a one-electronreversible system fits the differential pulse curve very well for pulse amplitudes (AE) less than 25 mV (11),and thus the area of the curve under these conditions is proportional to concentration. We have considered the equations
for differential pulse voltammetry at larger pulse amplitudes for electrodes which show time-independent currents (i.e., disk electrodes with radii less than 1pm). As will be shown, the area of the curves under these conditions is also proportional to concentration. The current for the reduction of a reversible system at microelectrodes which shows time-independent behavior for a potential pulse ( E ) [assuming equal diffusion coefficients (D)for the oxidized and reduced species] is given by
where id = arnFDC, n, F, R, and T have the usual electrnchemical meaning, C is the bulk concentration of the oxidant, r is the radius of the electrode, and a is a coefficient which depends on the geometry of the electrode [a = 4n,2n, or 4 for a sphere (12), hemisphere (13),or disk (14, 15), respectively]. The differential pulse current can be obtained biy taking the difference of the currents (Ai) at the potential of the ramp (E,) and at the potential of the pulse (E,) (11). The result is
Ai =
id
P
+
P - Pa2 a + Pa2 + P2a
I
where P = exp((nF/RT)[(E2+ E1)/2]]and a = exp((nF/ RT)[(E, - E1)/2]). Similar equations have been derived for reversible systems at a dropping mercury electrode ( I I ) , rotated disk electrode (16),and stationary electrode which exhibit time-dependent chronoamperometric currents (8). In these cases id is simply the limiting current defined by the
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Table I. Normalized Area and Peak Height Values for Experimental Differential Pulse Voltammograms a electrode type dropping mercury rotated disk
electroactive species b AQ AQ i- BA Fe( CN):- (pH 3) Fe( CN):- (pH 9) AA
micro (carbon fiber) (gold)
Fe( CN):- (pH 3)
stationary
Ferrocene ODIA Fe( CN)i- (pH 3) AA
RU( NH,):+~
.f (( AidE/AE)/i,) 1.08 (0.02) 1.00 (0.01) 0.96 (0.007) 0.77 (0.02) 0.83 (0.01) 1.01 (0.02) 1.04 1.01 1.05 (0.02) 0.78 (0.02) 0.40 (0.09)
Ai,/Ai,(calcd) 1.01 (0.01) C
0.57 (0.02) 0.27 (0.01) C
0.68 (0.10) 0.79 0.96 0.99 (0.01) 0.66 (0.02) C
a All values are averages for at least three determinations. Parenthetic numbers are standard deviations. &I All electroactive species at 1 mM except ferrocene (5.01 mM). Theory for peak height not available. A E = 25 mV only.
factors affecting mass transport to the electrode. Integration of eq 2 results in
which, when evaluated at the appropriate limits, leads to AE (AE = Ez - El).Thus, at electrodes which exhibit steady-state behavior, and for all other electrodes which show a potential dependence as given by eq 2, the integral of the differential pulse curve, divided by the pulse amplitude employed, gives a value which is predicted by id. A similar approach can also be taken for quasi-reversible systems a t electrodes under steady-state conditions. In this case, the potential-dependent pulse current is given by -id.
(4)
where k , = k , exp[-(an,F/RT)(E - Eo)]and kb = k , exp[(l - a)(n,F/RT)(E - Eo)]where a is the charge transfer coefficient and Eo is the standard potential for the electroactive couple (17). By evaluating this expression a t different potentials (equally spaced by hE), we have generated differential pulse curves for different values of k , and a. Numerical integration of all of these curves by Simpson’s rule again leads to the result that the area of the differential pulse current is i d AE. Extension of this theory to other types of mass transport conditions is complicated since the mathematics for solution of time-dependent equations is extremely cumbersome. As shown, the areas under differential pulse curves for both reversible and irreversible systems are equal for electrodes which exhibit steady-state behavior. Since this is such a useful method to correct for errors introduced by changes in reversibility, we have experimentally examined this concept with several different electrochemical conditions (vide infra). Because the electrodes used in this study do not have timeindependent currents at 48.5 ms, the average sampling time employed here, several caveats must be recognized. Chief among these is the depletion of electroactive species at stationary electrodes of the size routinely used for electroanalysis (18)-an effect which causes a decrease in the current when the electroactive couple is not totally reversible. Depletion effects at dropping mercury electrodes (10) and static mercury electrodes (19) and the effects of drop growth (20) may also cause deviation. Nevertheless, in the majority of cases we have examined, the differential pulse area normalized by AE has
been shown to be given by id. Although this may seem to be a circular argument that indicates normal pulse techniques are preferable, in fact, we find detection limits are improved with the area method. EXPERIMENTAL SECTION Anthraquinone (AQ, Eastman) and 3,3’-dimethoxybenzidine (ODIA,Eastman) were recrystallized from ethanol and acetonitrile, respectively. Benzoic acid (BA), K,Fe(CN)6,ascorbic acid (AA) (all Mallinckrodt),and (ICN Pharmaceuticals)were used as received. Ferrocene (Fisher) was sublimed prior to use. Cd(N03)z.4Hz0(Mallinckrodt) was dried in a vacuum oven at 110 “C for 12 h. Tetra-n-butylammonium perchlorate (TBAP, G. F. Smith) and KCI (MCB) were used as supportingelectrolytes for AQ or ferrocene in acetonitrile (Burdick and Jackson) and K3Fe(CNs),Ru(NH3),C13,or Cd(N03)2in water, respectively. A pH 7.4 citrate/phosphate buffer was used for AA and 1.0 M HzS04 for ODIA. Solutions were deoxygenated with a stream of Nz.All electrochemical experiments were performed with a Model 174A polarographic analyzer (Princeton Applied Research). Except for the concentration studies, the instrument was modified for a faster time response (21). A 0.5-s drop time (time between pulses) was used in all experiments and scan rates of 5 or 10 mV s-l were employed. The rotated disk electrode (RDE) was a Teflon-sheathedcarbon paste electrode (A = 0.203 cm2)mounted on a PIR rotator (Pine Instrument Co., Grove City, PA) that was operated at 900 rpm. The construction of the stationary carbon paste electrode (A = 0.0191 cm2)and carbon-fiber microelectrodes (average A = 1.54 X lo-’ cm2)have been reported previously (21). For the ferrocene/acetonitrile studies, a gold “fiber”microelectrode ( A = 8.76 X lo-’ cmz)was fabricated by sandwiching a f i e gold wire between two microscope slides which were held together with an acetonitrile-imperviousepoxy. Contact was made with conducting silver epoxy. These electrodes were used under conditions of semiinfiiite linear diffusion (SILD). A Pt auxiliary electrode and sodium chloride saturated calomel reference electrode (SSCE) were employed. Integration of the differential pulse voltammograms was accomplished electronically with an operational amplifier. The d.c. offset of the PAR 174A was wed to eliminatethe signal arising from differential residual current at high sensitivities. Published diffusion coefficients were used for calculations of the electrochemical signal for Cd(I1) (22),ferrocene (23),and ferricyanide (24);the diffusion coefficients for the other compounds were determined locally by chronoamperometry. RESULTS AND DISCUSSION The normalized area under differential pulse curves has been evaluated at four different types of electrodes with several different classes of compounds (Table I). To minimize base line effects, the concentrations were in the millimolar range. The data are reported as the ratio of the normalized area to id which was calculated from the Cottrell equation for the stationary and RDE electrode [the RDE was operated in the time-dependent region for a 48.5-ms pulse (IS)]. A time-independent term was added for the microelectrode which accounts for >80% of the current at 48.5 ms. A value
ANALYTICAL CHEMISTRY, VOL. 54, NO. 6, MAY 1982
997
+ z W
LL
LL
3
0
VOLTS vs. SC E
Differential pulse voltammogram of 1.00 mM Fe(CN):- in 0.5 M KCI at a carbon pa& RDE. Scan rate = 10 mV s-'; pulse amplitude = 25 mV. Flgure 1.
of 5.69 was used for the coefficient at the carbon fiber micropipet electrode (21),and a value of 4.0, which was experimentally determined by very slow cyclic voltammetry, was used for the coefficient of the gold-fiber microelectrode. (The disparity in these coefficients arises from the different geometries of the insulating material surrounding the electrodes.) In experiments with the dropping mercury electrode the diffusion-limited normal pulse current was used for id. In all experiments, the peak current (Ai,) was also measured and is reported as the ratio to that expected for a reversible case [eq 2 maximized with the appropriate id]. The measurements are the average of those obtained at AE of 5,10,25,50, and 100 mV. For the reversible systems [AQ (25),ODIA (24), and ferrocene] evaluated at three different types of electrodes, the ratio of the area to the diffusion-limited current and the ratio of the Ai, to eq 2 are essentially unity. Unity ratios for the area to id are also obtained for the quasi-reversible systems studied [Fe(CN)63-at pH 3 and for Ru(NHJs3+] for all cases except at the stationary electrode. The ratio of the measured peak current to that predicted for a reversible system differs markedly from unity as expected. AQ in the presence of BA and AA are examples of chemically irreversible systems involving two electrons. For AQ with BA at a dropping mercury electrode, good agreement of the differential pulse current integral with id is (observed. The chemical reaction of AA (26) is totally irreversible, in contrast to that for AQ with BA (25) which may lead to the lower experimental value observed for this compound, especiallly under SILD conditions. Thus, in all cases examined, except irreversible systems measured with conventionally sized stationary electrodes, the normalized area is in good agreement with id. The utility of this method of analysis is dramatically illustrated in Figure l. As shown, the reduction of Fe(CN):at a carbon paste electrode is greatly affected by pH (27). (This is an interfacial effect since the degree of reversibility for this reduction is not affected a t Pt electrodes.) As seen in Table I, the integral of the differential pulse current with the RDE is diminished for this extremely irreversible system at pH 9.0 (the integral is 80% of that at pH 3.0), but this effect is much less pronounced than the diminution in peak amplitude (47% of that at pH 3.0). While the change of reversibility given in this example is extreme, the greater precision via the area method is readily apparent, even though these experiments were run at rotation rates where the RDE gives time-dependent differential pulse curves. The previous examples En this paper have been at relatively high concentrations to demonstrate the utility of the integral
- 04
- 06 VOLTS vs SCE
- 08
Flgure 2. Voltammograms of 1.42 pM Cd(NO,), 4H,O in 0.1 M KCI at a DME: (A) differential pulse polarography; (B) integral of the differential current; (C)normal pulse polarography. Dashed lines are the background currents. Scan rate = 5 mV s-', pulse amplitude = 25 mV, drop time = 0.5 s.
of the differential pulse current. Obviously, at lower concentrations, problems are encountered because of residual currents. However, the area method can be used for trace analysis. For the reduction of Cd2+at a dropping mercury electrode, we find a linear dependence of the differential pulse curve area over the concentration range 3.7 X M to 3.6 X lo4 M with a correlation coefficient of 0.998 (n = 5). For the oxidation of ODIA at a stationary carbon paste electrode the area of the differential pulse curve vs. the concentration is linear with a correlation coefficient of 0.995 from 5 X to 1 X loT4M (n = 6). In both of these examples, the normalized areas are also equal to the limiting current. The sensitivity of the integral method exceeds that for normal pulse voltammetry (Figure 2) because base line effects can be more easily offset with the integral method; however, the limits of detection are not as good as with peak height measurements. As shown, the area of the differential pulse curve is linear with concentration and reduces errors in quantitative measurements by minimizing the effects of changes in reversibility. In all the cases examined here, except under SILD conditions with irreversible systems at a conventionally sized electrode, the area, normalized by the pulse height, is the limiting current. This is important so that evaluation of the faradaic efficiency of new electrode materials characterized by differential pulse voltammetry can be evaluated (28). The area method is also advantageous since it can provide improved sensitivity over normal pulse techniques. We believe that the choice of area vs. peak height measurements in quantitative analysis depends on the particular sample-if matrix effects are a concern, the area method is advantageouswhile the peak height method is superior for samples with an unstable base line. Area, as compared to peak height measurements, has also been considered for quantitative analysis of chromatograms (29,30) with the conclusion that the method of choicle is based on the particular sample. Since simultaneous area and peak height measurements are simple, especially under automated control, both types of data should be obtained, with the final decision of the value to use left to the analyst based on visual evaluation of the individual differential pulse curves. LITERATURE CITED (1) Bond, A. M.; Grabaric, B. S.Anal. Chem. 1979, 57, 337-341 (2) Bond, A. M. Anal. Chem. 1980,52, 1318-1322.
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(3) Barker, 0.C. “Progress in Polarography”; Zuman, P., Koltoff, I. M., Eds.; Interscience: New York, 1962; Vol. 2, Chapter 19. 1 Schmldt, H.; von Stackelberg, M. “Modern Polarographic Methods“; Academlc Press: New York. 1963: Chanter 1. Rlfkin, S. C.; Evans, D. H. Anal. &em. 7976, 4 8 , 2174-2179. Dlllard, J. W.; O’Dea, J. J.; Osteryoung, R. A. Anal. Chem. 1979, 51, 115-119. Leon, L. E.; Sawyer, D. T. Anal. Chem. 1981, 53, 706-709. Keiler, H. E.; Osteryoung, R. A. Anal. Chem. 1971, 4 3 , 342-348. Dlllard, J. W.; Hanck, K. W. Anal. Chem. 1976, 4 6 , 218-222. Blrke, R. L. Anal. Chem. 1976, 50, 1489-1496. Parry, E. P.; Osteryoung, R. A. Anal. Chern. 1965, 3 7 , 1634-1637. MacGiliavry, D.; Rideal, E. K. R e d . Trav. Chem. Pays-Bas WS7, 56, 1013-1 02 1, Biondl. C.; Bellugi, L. J . Elecfroanal. Chem. 1970, 24, 263-270. Salto, Y. Rev. Polarogr. 1968, 15, 178-186. Aoki, K.; Osteryoung, J. J . Electroanal. Chem. 1961, 122, 19-35. Myers, D. J.; Osteryoung, R. A. Anal. Chem. 1974, 46, 2089-2092. Shain, I.; Martin, K. J.; Ross, J. W. J . Phys. Chem. 1961, 65, 259-26 1. Oldham, K. 6.; Parry, E. P. Anal. Chem. 1986, 38, 867-872. Anderson, J. E.; Bond, A. M. Anal. Chem. 1981, 53, 504-508. Christie, J. H.; Osteryoung, R. A. J . Nectroanal. Chem. 1974, 49, 301-311. Dayton, M. A.; Brown, J. C.; Stutts, K. J.; Wightman, R. M. Anal. Chem. 1980, 52, 946-950. Cummings, T. E.; Elvlng, P. J. Anal. Chem. 1976, 50, 480-488. Kuwana, T.; Bablttz, D. E.; Hoh, G. J . Am. Chem. SOC. 1960, 82, 5811-5817. Adams, R. N. “Electrochemistry at Solid Electrodes”; Marcel Dekker: New York, 1969; Chapter 5. Wightman, R. M.; Cockrell, J. R.; Murray, R. W.; Burnett, J. N.; Jones,
S . 6. J . Am. Chem. SOC. 1976, 98, 2562-2570. (26) Perone, S. P.; Kretlow, W. J. Anal. Chem. 1966, 38, 1760-1763. (27) Panzer, R. E.; Elving, P. J. J . Nectmchem. SOC. 1972, 179, 864-874. (28) Gonon, F. G.; Fombarlet, C. M.; Buda, M. J.; Pujol, J. F. Anal. Chem. 1981, 53, 1386-1389. (29) Snyder, L. R.; Kirkland, J. J. “Introduction to Modern Liquid Chromatography”, 2nd ed.; Wiley-Interscience: New York, 1979; Chapter 13. (30) Klplniak, W. J . Chromatogr. Scl. 1961, 19, 332-337.
Kenneth J. S t u t t s Mark A. Dayton R. Mark Wightman* Department of Chemistry Indiana University Bloomington, Indiana 47405 RECEIVED for review April 20, 1981. Resubmitted November 9, 1981. Accepted February 11, 1982. This research was supported by the National Science Foundation (Grant No. BNS 81-00044). M.A.D. is a combined Medical-Ph.D. candidate, Indiana University. R.M.W. is the recipient of a Research Career Development Award from the National Institutes of Health (Grant No. KO4 NS 00356) and an Alfred P. Sloan Fellow.
Exchange of Comments on Evaluation of the Copper Anodic Stripping Voltammetry Complexometric Titration for Complexing Capacities and Conditional Stability Constants Sir: Tuschall and Brezonik carried out an anodic stripping voltammetry (ASV) titrimetric procedure with Cu and Co as titrants and several organic ligands as analytes (1). Their stated objective was to evaluate its use for estimating complex conditional stability constants (2). Careful consideration of their research design, particularly their choice of model systems, raises questions about the validity of their conclusions. Estimation of conditional stability constants from the titration is based on the ability of ASV to distinguish between uncomplexed metal and metal bound to complexes which dissociate slowly. Two conditions or criteria must be fulfilled (1) the metal complex which is formed during titration must dissociate slowly and (2) the complex must be reduced at a potential sufficiently separated from the reduction of the noncomplexed metal (2). Separate detection of uncomplexed and complexed metal depends on selecting a preelectrolysis potential in a region where only uncomplexed metal is reduced. Selection must be made for the conditions of the titration, which means that both metal forms must be present. Tuschall and Brezonik selected their preelectrolysis potential on the basis of a separate solution of uncomplexed metal. This is clearly inadequate. When Tuschall and Brezonik (1) find that Cu complexes of histidine, p-hydroxycinnamic acid, gallic acid, pyrogallol, and desferal are reduced a t their arbitrarily selected preelectrolysis potential of -0.3 V vs. SCE, it simply means that these complexes are unsuitable for evaluation of the method. On the other hand, Tuschall and Brezonik find that Cu complexes of bovine serum albumin and Cu and Cd complexes of EDTA are not reduced significantly at the selected preelectrolysis potentials, although, this information alone is insufficient for deciding whether these complexes are suitable for evaluating the procedure. No evidence is given that uncomplexed metal is reduced separately from complex reduction
in the presence of excess ligand. The polarographic literature (3) shows that CdEDTA is suitable for the evaluation and the estimate of its conditional constant by Tuschall and Brezonik (1)was in excellent agreement with literature values, These authors (1) assume that CuEDTA should behave similarly although they give no evidence to support this view. For example, the CuEDTA pseudopolarograms they present for an equimolar mixture of Cu and EDTA show one reduction, that of the complex. These pseudopolarogramswould reveal two waves if the complex and uncomplexed Cu reduction could be resolved. When their estimate of the CuEDTA conditional c o n s h t is much lower than literature values, the authors fault the procedure although it is likely that CuEDTA is inappropriate for their purpose. The polarographic literature of CuEDTA reveals that, under some conditions, CuEDTA is reduced reversibly or quasi-reversibily ( 4 ) and that its reduction is sensitive to buffer capacity ( 5 ) and to the presence of alkaline earth ions (6). Pecsok ( 4 ) estimated the formation constant from Ellz data obtained below pH 6 and found agreement with other methods. This would imply a mobile equilibrium (rapid dissociation and association), at least at low pH values. On the other hand, Wheelwright et al. (7) estimated stability constants of rare earth-EDTA complexes polarographicallyby measuring the Cu displaced upon addition of rare earth to solutions equimolar in Cu and EDTA. Their values agreed with potentiometric estimates and indicated that uncomplexed Cu was accurately measured polarographically in the presence of CuEDTA complexes. This agreement implies that CuEDTA dissociates very slowly. The pseudopolarogramsin Tuschall and Brezonik’s Figure 1 if analyzed by plotting E vs. log ( i / ( i d - i)) would show that CuEDTA reduction is nonreversible (8). In addition, the plot of their stripping currents at -0.3 V vs. SCE against CM/(CL
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