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Anal. Chem. 1985, 57,2652-2855
Application of On-Line Fast Fourier Transform Faradaic Admittance Measurements to Deconvolution of Heterogeneous Charge Transfer Kinetic Effects in Anodic Stripping Voltammetry Ari U. Ivaska* Department of Analytical Chemistry, Abo Akademi, 20500 Turku 50, Finland
Donald E. Smith' Department of Chemistry, Northwestern University, Evanston, Illinois 60201
The concept of fast Fourler transform (FFT) faradalc admlltance frequency spectral measurement Is applled to anodic stripping voltammetry. With the ald of the klnetlc deconvolutlon method the observed peak admlttance values are corrected for changes In the heterogeneous charge transfer kinetics. The method was tested uslng Cd'+(lO-' M)/Cd(Hg) In 0.1 M HCI as the model system. I n the presence of a surface-actlve compound, the observed peak admlttance value was decreased due to the slower rate In the heterogeneous charge transfer reactlon. By use of the kinetic deconvolution method, the reverslble response could be calculated from the observed quasl-reverslble faradaic slgnal. The klnetlcally corrected slgnal was linear over the range 5 X 10" M to 1 X lo-' M wlth standard deviation 15-1%. Slmilar results were observed for Zn In acetate buffer. Adsorption of the metal Ions on the electrode surface was found In studylng Pb and Cu. The method was applled to determlnatlon of Zn In lake and lap water.
Both anodic and cathodic stripping methods have become widely used in determination of many compounds at low concentrationlevels. Both methods consist of a preelectrolysis step where the compound to be determined is deposited on the working electrode. When a hanging mercury drop is used as the working electrode (HMDE), the compound deposited either forms an amalgam and dissolves in mercury or forms an adsorbed layer on the surface. There are also cases where both processes occur simultaneously. In cathodic stripping the deposited material is adsorbed on the surface. Some metal ions can also be specifically adsorbed on the electrode surface by some selective compounds ( I ) . After the deposition step either anodic or cathodic scan is initiated and the material being dissolved in mercury or adsorbed on the surface is reoxidized or rereduced into the solution. Some organic compounds can also be determined by stripping methods. They are first accumulated by adsorption on the electrode surface and then stripped off (2). There are several techniques to monitor the stripping process. Dc and pulse voltammetry have so far been the most commonly used techniques. Ac voltammetry has also been used in a number of laboratories but it has not reached the same popularity. One of the reasons may be that ac polarographic instruments are not readily available. Most manufacturers have not included an ac mode in their instruments mainly because of lack of applications of this technique tu analytical problems. Some manufacturers Deceased.
provide their ac instrument with phase sensitive detection which allows direct monitoring of the faradaic component of the measured ac signal in aqueous solutions where the iR drop is small. Dependence of the ac signal on kinetic effects of the electrode reaction is the main disadvantage of the ac technique limiting its applications to analytical problems. If the heterogeneous charge transfer is fast, the signal only depends on the mass transfer of electroactive species to the electrode surface. In this case concentration of the electroactive species is the only chemical variable which determines the magnitude of the ac signal. In the case that the heterogeneous charge transfer is slow, the ac signal depends not only on diffusion of electroactive species to the electrode but also on the electrode reaction kinetics. A reaction which on the dc time scale still can be considered reversible may on the ac time scale be quasi-reversible. In such a case the ac peak becomes broader and decreases in height. Kinetics of the electrode reaction of the same redox couple may depend on several factors such as, e.g., condition of the electrode surface when solid electrodes are used, and the supporting electrolyte has its effects on the rate of the electrode reaction on mercury electrodes. Surface active compounds are known to have a large effect on the heterogeneous charge transfer rate and therefore affect the observed ac signal. These compounds are frequently present in "real" samples such as natural waters. Because their concentration varies from sample to sample, the ac signals also vary, although concentration of the electroactive species to be determined may remain constant. Equations which describe the magnitude of the ac signal of a quasi-reversible reaction include the rate constant k, of the heterogeneous charge transfer reaction and the charge transfer coefficient a as kinetic parameters. If these are determined and all the other parameters are known, the concentration of the electroactive species can be calculated from the observed signal, but this approach is complicated and definitely not practical. The aim of this work was to develop a method by which the kinetic fluctuations in the heterogeneous charge transfer reaction are considered and the kinetically effected ac signal corrected to the reversible signal. THEORY Let us consider a simple, single step electrode reaction ( 3 ) O+ne-R (R1) where 0 is the oxidized species initially present in the solution. The frequency domain response of the faradaic total admittance for this reaction may be written IA(wt)l = A,,J(t)G(w) (11 where A,,, is the admittance of the reversible reaction and can be expressed as
0 1985 American Chemical Soclety 0003-2700/85/0357-2652$01.50/0
ANALYTICAL CHEMISTRY, VOL. 57, NO. 13, NOVEMBER 1985 * 2653
n 2 p ACo*(wDo)’i z A,,” = 4RT cosh2 G/2)
(2)
All parameters have their usual electrochemical meaning. For details see ref 3 and 5. F ( t ) is a term which embodies the effects of heterogeneous charge transfer kinetics on the dc time scale, It is unity for planar systems which are reversible on the dc time scale. The mathematical expression for F ( t ) is rather complicated (3). If the system is quasi-reversible also in the dc sense, F ( t ) will be dependent on the charge transfer parameters k , and a. By use of the stripping technique and HMDE, F ( t ) is assumed to have a constant value in the systems studied in this work. G(w) embodies the effects of heterogeneous charge transfer kinetics on the ac time scale and can mathematically be expressed as
G(w) =
(+ 1
)”
2 (cot
(3)
$12
where $ is the phase angle. The experimental observables in the computerized instrument used in this work are Edo w , inphase component A’(wt), and the quadrature component A”(&) of the total cell admittance value IA(wt)l. In the Fourier transformed time domain signal A’(wt) and A”(wt) are the real and the imaginary parts respectively and therefore they can be obtained experimentally. This allows us to determine the cotangent of the phase angle, cot $, for every frequency at every dc potential giving us an additional, experimentally determined parameter for data processing cot d, = A’(wt)/A’’(wt) (4) cot $ is a concentration independent observable but it is dependent on k , and a. Any change in these parameters will affect cot $ and therefore the changes can immediately be detectTed.In reversible systems cot $ = 1and G(w) = 1. When the reaction becomes quasi-reversible, cot d, > 1and G(w)< 1assuming that electroactive species are not adsorbed on the electrode surface. With HMDE the total cell admittance, IA(w)l,is a time-independent variable. Because cot d, is continuously monitored, G(w) can readily be calculated by using eq 3 and therefore A,,, can be obtained
A,,, = IA(u)l/G(w) (5) This means that the reversible response can always be calculated from the observed magnitude of the “nonreversible” cell admittance if the inphase and quadrature components of the cell response are measured and cot $ is calculated. The kinetic correction, when performed in the frequency domain as suggested in eq 5, i s equivalent to deconvolution of the heterogeneous kinetic effects of the observed signal in time domain.
drochloric acid (J. T. Baker, Reagent Grade) for 24 h at room temperature followed again by thorough rinsing with Millipore water before repeating the acid wash with 1:lO hydrochloric acid (J. T. Baker, quality for trace metal analysis) for 48 h at room temperature. After being rinsed with Millipore water, the items were air-dried and kept under plastic cover to protect against contamination from airborne particles. During the daily work every possible care was taken to prevent contamination. Sampling. Two samples of Lake Michigan water were taken. One was from a point approximately 1mile east from the university campus. This sample was taken into a 250-mL polyethylene bottle, immediatelyacidified to pH 2 with nitric acid, and frozen within a few hours before being analyzed after a few weeks. The second sample was taken from the lagoon inside the campus area. This lagoon has only a restricted connection to the lake. Sample of the lagoon water was directly pipetted into the polarographic cell. A sample of tap water was also analyzed. It was taken directly from the tap and pipetted into the polarographic cell. Procedure, When calibration curves were constructed for experiments with acetate buffer as electrolyte, the standard solutions of the metal ions were prepared in the electrochemically purified 0.1 M acetate buffer. In the actual analysis of the water samples, 4.5 mL of the sample was pipetted into the polarographic cell and 0.5 mL of the purified 1.0 M acetate buffer was added. When 0.1 M HC1 was used as the electrolyte, 40.4 pL of concentrated HC1 was added with a calibrated micropipet (Gilson Pipemat) to 5.0 mL of purified water. This solution was always checked for any impurities by ASV before standard solutions of the metal ions were added. When lake water samples were analyzed, the same amount of concentrated HC1 was added to 5.0 mL of the sample. The ac measurements were performed with the computerized array processor enhanced Fourier transform faradaic admittance measurement (FT-FAM) device (4). Minimization of the effect of the double-layer charging current was done digitally in the computer using a frequency domain strategy. In every measurement eight time domain and five frequency domain averages were taken. The PAR 303 electrochemical stand was used. It has a saturated Ag/AgCl reference electrode against which electrode all potentials in this work are measured. The auxiliary electrode was a Pt wire. The stand was used in the hanging mercury drop electrode mode (HMDE) with large drop size. The electrode area was measured to be 2.65 mmz. Deposition was done for 2 min 40 s under stirring followed by a 20-s rest period before initializing the anodic scan with the rate of 5 mV/s. Argon (Matheson Gas Products) was used to degas the cell solution. It was purified enroute to the cell by a column filled with molecular sieves followed by an oxygen scavenger (Ridox)column and R gas bubbler solvent saturator system. All measurements were performed under a blanket of argon.
RESULTS AND DISCUSSION
Cadmium ions in 0.1 M HC1 were chosen as the model system for experimental study of the method of kinetic deconvolution in anodic stripping voltammetry as outlined in the theoretical section of this paper. Plating was done at potential -0.75 V. Both the observed and the kinetically corrected ac stripping voltammograms of 1 X M Cd2” in EXPERIMENTAL SECTION 0.1 M HC1 are shown in Figure la. The corrected voltamReagents. The reagents CdCI, (Baker and Adamson),ZnS04 (Baker and Adamson), Pb(N03)2(J. T. Baker), arid CU(C~O,)~ mogram was obtained from the uncorrected total cell admittance values by first calculating cot $, eq 4, and G(w), eq (Pfaltz & Bauer) and the surfactants 1-butanol (Baker and Ad3, a t every dc potential and then using eq 5. In this system amson) and Triton X-100 (Sigma Chemical Co.) were of reagent the reaction is nearly reversible and therefore both the corgrade and used without further purification. Hydrochloric,nitric, and acetic acids were of quality for trace metal analysis (J. T. rected and uncorrected peak admittance values are almost the Baker). The acetate buffers 0.1 M and 1.0 M, pH 4.6, were same. Surface active compounds are known to decrease the prepared from acetic acid and sodium acetate (Baker and Adheterogeneous charge transfer rate of cadmium ion reduction, amson, Reagent Grade) and were electrochemically purified by and therefore the observed peak admittance value is decreased bulk electrolysis at -1.25 V for 4 days. When tested by ASV no and the peak broadened (3). This is demonstrated in Figure traces of the metals could then be found in the buffers. Highl b which shows the voltammograms after the solution from purity water was obtained by passing departmental distilled water the experiment of Figure l a was made 4 x with respect through a Millipore Corp. Milli-Q water purification system. to Triton X-100. As can be seen the observed peak value of Glassware and Plastics. All the glassware and plastics used the total cell admittance has decreased approximately 30% in this work were first carefully washed with detergents to remove all grease from the surfaces. Then they were thoroughly rinsed from the value in Figure l a although the concentration of with Millipore water. The next step was washing with 1 : l O hycadmium ions was not changed. This is due to the decreased
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ANALYTICAL CHEMISTRY, VOL. 57, NO. 13, NOVEMBER 1985
'7 .-. 'q !nu 0
b c
4 50
s P
10
Q
U
zol
t
10
-0 '15
-0 50
-0 60
-0 55 Edc,
'
-0 65
-0 70
-0 75
Figure 1. Anodic stripping voltammograms of 1 X lo-' Cd2+ In (a)0.1 M HCI and (b) 0.1 M HCI 4- 4 X lo-'% Triton X-100, plating for 3 min at -0.75 V: asterisk, observed; open circle, corrected values.
rate of the heterogeneous charge transfer reaction. The kinetically corrected voltammogram is also shown in Figure lb, and as can be seen the two corrected voltammograms in Figure 1 have the same shape and peak admittance value demonstrating the validity of the proposed method. Kinetic correction of data can be done with one frequency only. But in that case it should be known that the reaction is quasi-reversible and that the reaction mechanism is R1 and it is not complicated by any other chemical or electrochemical reactions. This is not always the case and therefore it is recommended to check this assumption by looking at the cot @--CJ/~ plot at the peak potential. According to the theory of quasi-reversible reactions the plot should be linear and have a value of unity at zero frequency. If the reaction at the electrode is not only the heterogeneous charge transfer but is complicated by other reactions, the cot 4-w1l2 plot will not be linear and the kinetic correction as outlined above is not valid. In this work we have used the linear regression line through the individual cot 4-u1/z points to calculate G(w) at the frequency of interest, in this work 107.4 Hz. By this way we can do an additional smoothing of the experimental data. If the kinetic correction is done with one frequency only, the experimental errors at this particular frequency may affect the result too much. As can be seen in eq 2 the corrected admittance value A,,, is a linear function of w1/2. The goodness of the kinetic correction can always be checked by looking at the linearity of the Arev-u1/2plot. If the A,, values are then further divided by u1j2,a constant value for Arevlw1/2should be obtained at every frequency. This variable is independent on frequency but dependent on concentration and is called frequency normalized reversible admittance. In Figure 2a the Arev-w1/2 plot of the data from Figure l b is shown. As can be seen the kinetic correction gives a linear relationship between A , and u1I2.The frequency normalized presentation of the same data is shown in Figure 2b, i.e., Arev/w1/2vs. u1I2and as can be seen,
0
no
io
zo
30
50
40
fin
in
BO i
(J12
Flgure 2. (a) Reversible peak admittance value and (b) frequency normalized reversible peak admittance values as functlon of u1l2data in Figure lb: asterisk, observed; open circle, corrected values.
iL
7 O0 0
7 0
-lag
6 L0
c,
Flgure 3. Calibration graph of -log ( A rev/ul/P) as function of -log C for Cd in 0.1 M HCI and Zn In 0.1 M acetate buffer pH 4.6, values in absence (") and in presence (0)of surface actlve compound.
almost a constant value is obtained for the kinetically corrected data at all frequencies. Uncorrected total admittance values from the same experiment are also included in Figure 2 to demonstrate the power of the correction method. Frequency normalized, reversible admittance values of reduction of cadmium ions at different concentrations in 0.1 M HC1 are shown in Figure 3 both in presence and in absence of 4 X Triton X-100. As can be seen the corrected values in both cases are almost identical. The signal in 1 X M Cd2+was already so low that when surfactant was added to the solution the peak diminished so much that the background noise made the kinetic correction unreliable. Figure 3 further shows that the calibration graph is linear over 2 orders of magnitude and the regression coefficient was calculated to be 0.999. Concentrations higher than 1 X M were not studied because cadmium in those concentrations can be determined by normal polarographic methods without using ASV. Standard deviations are 15% and 1% at the lower
ANALYTICAL CHEMISTRY, VOL. 57, NO. 13, NOVEMBER 1985
Table I. Analysis of Water Samples for Zinc in 0.1 M Acetate Buffer, pH 4.6, Plating for 3 Min at -1.1 V sample
lake water lagoon water
tap water
zinc concen, M kinetic deconvolution standard addition 2 x 10-8 6X 3 x 10-7
1.5 X 6x not used
and the upper end of the calibration graph, respectively. A calibration graph where the kinetically corrected and frequency normalized admittance values are plotted as a function of the concentration of the electroactive species can then be used although the sample matrix may vary from sample to sample. This is true naturally under the assumption that all the other experimental parameters such as drop size, plating time, and stirring rate are kept constant and that no competing reactions take place. These criteria are normally always fulfilled when similar samples are assayed. The common way to minimize the effect of the varying matrix in different samples is to use the method of standard addition. To compare the method proposed in this work with the standard addition method, an artificial sample of 5 X M Cd2+in 0.1 M HC1 and 4 X lo"% Triton X-100 was made. When the kinetic deconvolution method was used, a value of 4 x IO* M could be read from the calibration plot. After three additions of a standard Cd2+ solution were made and the kinetically uncorrected peak admittance values were measured, the standard addition method gave a value of 3 X M. The kinetic deconvolution method was also tested in ASV of zinc in 0.1 M acetate buffer of pH 4.6. Plating potential was -1.1 V and the stripping peak appeared at -0.955 V. The surfactant used in this case was 0.1 M 1-butanol. The results obtained were very similar to those in the study of cadmium. The calibration plot of Arev/wl/z vs. concentration of zinc is also included in Figure 3. As can be seen the plot is linear over 2 orders of magnitude. Regression coefficient of the line is 0.998. Standard deviations are the same as those in the study of Cd. When the solution of 1 X M Zn2+was made 0.1 M with respect to 1-butanol, magnitude of the inphase component of the cell admittance decreased but was still well above the background noise. The quadrature component increased over the inphase component indicating adsorption which makes it not possible to use the kinetic deconvolution method the way it is described in this work. No adsorption was found in 1 X M Zn2+in 0.1 M acetate buffer only. When the concentration of zinc was increased to 5 X M with 0.1 M 1-butanol still maintained in the solution, the inphase component increased above the quadrature component indicating that the signal from the adsorption process was negligible compared with the signal from the faradaic process. Both zinc and cadmium were also studied using a 10-min plating time. In both cases the signal increased so much that a detectable signal could be observed even in solutions of 1 X M. Voltammograms from solutfons of 1 X M of both metal ions and with 10 min plating time were so smooth and well developed even in the presence of the surfactant, that the kinetic deconvolution method could be used. ASV of lead in 0.1 M acetate buffer of pH 4.6 and in the concentration range of 1 X M to 1 X M was also studied. Plating potential was -0.6 V and the stripping peak appeared at -0.45 V. In this case adsorption was found even in a solution of 1 X M Pb2+with no surfactant present. First when the lead concentration was increased to 5 x lo-' M, signal from the adsorption process became negligible compared with the signal from the faradaic process. Ad-
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sorption made i t not possible to use the proposed kinetic deconvolution method in low concentrations of lead. The inphase component of the observed cell admittance value in solutions with no surfactant gave a linear calibration plot over the whole concentration range studied. ASV of copper was studied in the concentration range 5 X M to 1 X lo4 M both in 0.1 M HC1 and in 0.1 M "0,. In 0.1 M HC1 the plating potential was -0.3 V and the peak potential of the stripping voltammogram was -0.12 V. In 0.1 M "OB plating was done at -0.15 V and the stripping peak appeared at -0.025 V. In both electrolytes signal from the adsorption process was greater than the signal from the faradaic process even at a concentration of 1 X M which made it not possible to use the kinetic deconvolution method. Because lead and copper were not found in the water samples analyzed, no thorough study on the adsorption and the effeat of surfactants on the stripping voltammograms of these metals was undertaken. The observed adsorption of the metal ions on the electrode surface is obviously anion induced (6). In the study of Zn by ASV, the electrode has such a negative charge that no adsorption of anions, at least not to any noticeable degree, takes place on the electrode surface. The observed weak adsorption of zinc in 1 X M solution and in the presence of the surfactant is obviously of an other origin. Cadmium stripping peak appears at ca. -0.60 V where the electrode still has a negative charge preventing the chloride ions from adsorbing on the surface. But chloride ion is not an easily polarizable ligand and therefore it is less likely than iodide and bromide to cause anion-induced adsorption of cadmium ions. The latter ligands were used by Anson et al. (6) in studying the same phenomenon. The specific adsorption of anions increases with increasing positive charge of the electrode, and at -0.45 V where the stripping peak of lead appears, adsorption of cations was already found. When the positive charge of the electrode still increases, the anion-induced adsorption of the metal ions becomes more promident as it was found in the stripping voltammograms of copper. Two different samples of lake water were analyzed by ASV, using the kinetic deconvolution method. In 0.1 M acetate buffer only a peak for zinc was observed. When the electrolyte was changed to 0.1 M HCl, no peaks were found indicating that concentrationsof cadmium, lead, and copper were at least lower than 1 X M. Kinetic deconvolution method was applied to the zinc peak in 0.1 M acetate buffer. Zinc was also determined in the samples by the standard addition method. A sample of tap water was also analyzed for zinc. These results are given in Table I. As can be seen both standard addition and kinetic deconvolution methods give approximately the same result. Registry No. Zn, 7440-66-6;water, 7732-18-5.
LITERATURE CITED (1) Bramina, Kh. 2. Fresenius' 2. Anal. Chem. 1982, 372, 428-437. (2) Kalvoda, R. Anal. Chim. Acta 1982, 738,11-18 (3) Smith, D. E. Anal. Chem. 1976, 4 8 , 517A-526A (4) Schwall, R. J.; Bond, A. M.; Loyd, R. J.; Larsen, G. J.; Smith, D. E Anal. Chem. 1977, 4 9 , 1797-1805. (5) Schwall. R. J.; Bond, A. M.; Smith, D. E. Anal. Chem. 1977, 4 9 , 1805-1812. (6) Anson, F. C.; Barclay, D. J. Anal. Chem. 1968, 4 0 , 1791-1798.
RECEIVED for review February 14,1985. Accepted June 18, 1985. The authors thank National Science Foundation grants (CHE77-15462and CHE82-10831)for support of this work. Personal grants from the Orion Corporation Research Foundation (Finland) and Academy of Finland to A.U.I. also are acknowledged. Part of this work was presented at the Euroanalysis V Conference in August 1984 in Cracow, Poland.
