On the estimate of blanks in differential pulse voltammetric techniques: application to detection limits evaluation as recommended by IUPAC

Analytica Chimica Acta 403 (2000) 117–123

On the estimate of blanks in differential pulse voltammetric techniques: application to detection limits evaluation as recommended by IUPAC R. Blanc, A. González-Casado, A. Navalón, J.L. V´ılchez ∗ Department of Analytical Chemistry, University of Granada, E-18071 Granada, Spain Received 22 January 1999; received in revised form 2 July 1999; accepted 26 July 1999

Abstract A new method to obtain the signal associated with a blank in differential pulse voltammetry and stripping voltammetry techniques is applied. The signal assigned to the blank is obtained by direct integration of the background noise extrapolated values of the base-peak width at different concentrations in order to obtain the zero concentration. Detection limits more amenable to a statistical evaluation are thus implemented, as recommended by the International Union of Pure and Applied Chemistry (IUPAC). ©2000 Elsevier Science B.V. All rights reserved. Keywords: Differential pulse voltammetry (DPV); Anodic stripping voltammetry (ASV); Blank signal; Detection limit

1. Introduction Due to their inherent sensitivity and selectivity, electroanalytical techniques are being increasingly selected as the analytical methods of choice [1]. Voltammetric methods are widely applied in biomedical and pharmacological analysis [2,3,4,5] as well as in analysis of metals [6,7,8]. Differential pulse voltammetry (DPV) is considered a convenient method because of the wide range of linearity, excellent reproducibility, low experimental cost and the attainment of low detection limit. Stripping voltammetry (SV) comprises a variety of electrochemical approaches, having a step of preconcentration onto the electrode surface prior to the voltammetric measurement. The major advantage of SV compared with direct voltammetric measurement is the preconcentration factor. In trace analysis ∗ Corresponding author. Tel.: +34-9-58-243-326; fax: +34-9-58-243-328 E-mail address: [email protected] (J.L. V´ılchez)

of heavy metal ions, anodic stripping voltammetric (ASV) is the most popular stripping voltammetric technique [9,10]. The absence of uniform criteria by the scientific community prevents unique and unified estimation in voltammetric analysis. In order to estimate the detection limits some alternative methods have been used to overcome difficulties such as: 1. Taking as a DL the concentration giving a signal three times the standard error plus the y-intercept [11]. 2. The analyte concentration giving a signal equal to the blank signal plus two standard deviations of the blank [12]. 3. The concentration giving a signal equal to three times the standard deviation of the blank signal, calculated from the calibration slope [13]. 4. The concentration signal-to-noise ratio (S/N = 2 or 3) [14,15]. 5. Calculations on errors propagation [16].

0003-2670/00/$ – see front matter ©2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 3 - 2 6 7 0 ( 9 9 ) 0 0 5 6 9 - 3

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6. Estimation based on the calibration set with or without signal of the black [17]. 7. Use of the robust regression method where the detection limit is dealt as a hypothesis test in relation to the presence of analyte in an unknown sample by using the experimental information provided by the calibration set [18]. All of these methods are not exempt of objections and practical difficulties. For instance, estimates based on the widely utilised S/N [19] lack of a suitable statistical test to ensure the quality of the measured values. Thus, there is a lack of statistical information to compare from the statistical point of view on the detection limits obtained by this method. The use of the errors propagation method leads to overestimates of the detection limit, while the use of the independent term from the calibration line deprives the IUPAC definition [20] of statistical meaning. The estimates based on considerations extrapolated from the experimental domain have problems as well. Here, a method adjusted to the IUPAC recommendations (DL = ksb /b; k = 2 ó 3) [21,22] is proposed to evaluate the signal from the blank. The background noise is calculated from the baseline of the voltammogram. Some information on the blank signal is superimposed to the normal noise from the background, because when voltammograms of samples with lower concentrations are carried out, the width of the decreasing signals registered as an voltammogram tends toward a permanent value regardless of the decrease in concentration. The analytes chosen to carry out this study were, three inorganic elements (Zn, Cd, Pb) and an organic compound, (imidacloprid). We have selected zinc, cadmiun and lead as inorganic analytes because it have been widely studied and have good electroanalytical properties. The organic analyte selected was imidacloprid [1-(6-chloro-3-pyridylmethyl)-N-nitroimidazolidin-2-ylideneamine] because it has been recentely introduced as an insecticide by Bayer AG.

estimating the initial and final potential on the voltammogram baseline by an adequate choice of integration parameters. Moreover, there can be a significant random error, because the evaluations are carried out in a region where the uncertainly caused by the background noise interacts strongly with the measured values [23,24]. For width evaluation we by-pass this problem using a parameter free of background noise namely the half-width W0.5h of the peak height which allows one to estimate then the base width Wb . It can be assumed that the DPV peak shape is a Gaussian-type one [25]. Practically speaking, the asymmetry of real DPV peak has led to the use of the so-called exponentially modified gaussian curves (EMG) [26,27]. Since the use of the exclusively Gaussiam model led to important errors in the characterization of DPV peaks [28]. However, provided the asymmetry of the peak is not too high, errors for peak-height or variance are not important [29], and this hypothesis will then be used as the method of calculation. For a Gaussian model adjusted to describe a DPV peak (Eq. (1)): 1 2 2 h = √ e−1/2(E−EP ) /σ 2


(1)

where h is the peak height for a given potential E, EP is the peak potential and σ is the peak variance. Particularising Eq. (1) for peak parameters (see Fig. 1) the following value for the variance can be obtained (Eq. (2)): s 1 W0.5 h (2) σ = 2 2ln(1)/2
h0.5 where W0.5h is the half-width of the peak and h0.5 the half-height of the peak whose normalised value is 0.1995.Estimate of Wb for 99.73% of the peak-area is then (Eq. (3)) [30]:

2. Theory

Wb = 6σ = 2.5479W0.5h

2.1. Calculation of the width Wb of a differential pulse voltammetric (DPV) peak

2.2. Measurement of the signal coming from the DPV blank

The base width Wb of a DPV peak can be estimated in a straight-forward manner from a voltammogram by

The first step are the calculation of the width at the base Wb0 at ‘zero concentration’. Extrapolation of

(3)

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Fig. 1. Half-width of the peak (W0.5h ) vs. concentration for the zinc, cadmium, lead and for the imidacloprid by differential pulse voltammetry (DPV) and anodic stripping voltammetry (ASV).

the graphical representations of the W0.5h at different concentrations of analyte can give us a good-enough statistically significant idea of the width of the base for ‘zero concentration’ (estimate of the blank). The adequate values of Wb0 are then those given by Eq. (3). Then, the blank signal for each analyte can be determined by integration over the base-line of the voltammograms taking a width EP ± 0.5Wb0 , where EP is the peak potential of the analyte and Wb0 has been evaluated as explained above. Finally, we test the signal ‘measured’ from the DPV blank to check that the measured values are coherent with the rest of the signals obtained. To get a calibration it is necessary to obtain a ‘non-significant’ conclusion when the test of ‘lack of fit’ [31] is carried out. This test requires a calibration made obtaining several replicates at each level of concentration, but if this is not possible we can use a robust regression techniques [32].

3. Experimental

stand. A three-electrode system was composed of a static mercury dropping electrode (SMDE), Ag0 /AgCl reference electrode and a glassic carbon auxiliary electrode. PGSTAT10 potentiostat/galvanostat was interfaced with an ADL Pentium MMX 200 microcomputer supplied with general purpose electrochemical system (GPES) sofware (Eco Chemie B.V.) for data acquisition and its subsequent analysis. The voltammograms for zinc(II) by DPV were recorder using a potential scan of 10 mV/s, a drop time of 1 s and a pulse amplitude of 50 mV. For imidacloprid by DPV the potential scan was 5 mV/s, a drop time 4 s and pulse amplitude of 50 mV were selected. The voltammograms for zinc(II), cadmium(II) and lead(II) by ASV were recorder using the same experimental variables indicated above with an accumulation potential of –1.2 V and accumulation time of 90 s. All pH measurements were made with an Ingold combined glass-calomel saturated electrode using a previously calibrated Crison 501 digital pH-meter. statgraphics [33] and alamin [34] software packages were used for the regression analysis (linear model) and for statistical treatment of data.

3.1. Apparatus and software 3.2. Reagents Voltammetric experiments were performed using an Autolab (Eco Chemie B.V.) PGSTAT10 potentiostat/galvanostat in conjuntion with a Metrohm 663 VA

All the experiments were performed with analyticalreagent grade chemicals and pure solvents. Reverse

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osmosis-type quality water was used throughout. Zinc(II) stock solution 1 × 10−3 M, cadmium(II) stock solution 1 × 10−3 M and lead stock solution 1 × 10−3 M were prepared by exact weighing of the zinc nitrate, cadmium nitrate and lead nitrate reagents (Panreac) and dissolution in deionised water. Working solutions were obtained by appropriate dilutions with deionised water. Imidacloprid stock solution, 1 × 10−3 M prepared by exact weighing of the reagent (Bayer AG) and dissolution in deionised water. The solution was stable for at least 2 weeks if stored in the dark at 4◦ C. Working solutions were obtained by appropriate dilutions with deionised water. The supporting electrolyte was KNO3 for zinc(II), cadmium(II) and lead(II) and Britton–Robinson buffer prepared in the usual way, i.e., by adding to a solution 0.04 M in orthophosphoric acid (Merck), 0.04 M in acetic acid (Merck) and 0.04 M in boric acid (Merck) with the appropriate amount of 0.2 M sodium hydroxide (Merck) solution for imidacloprid. 3.3. Procedures 3.3.1. Procedure for zinc(II) determination by DPV The determination of Zinc(II) by DPV is well documented [35]. To a 50 ml calibrated flask containing between 10−7 and 1.5 × 10−6 M of zinc(II), 5 ml of KNO3 1 M were added, and the mixture was diluted with deionised water to the mark. The solution obtained was transferred to the electrochemical cell, deaerated by passing a nitrogen stream through it for 3 min and the voltammogram was registered at 20.0 ± 0.5◦ C under an inert atmosphere in the cell. A blank solution was prepared and treated in a similar way. The calibration graph was constructed in the same way using zinc solutions of known concentrations. 3.3.2. Procedure for zinc(II) cadmium(II) and lead(II) determination by ASV The determination of Zinc(II) cadmium(II) and lead(II) by ASV is well documented [36]. To a 50 ml calibrated flask containing between 1.5 × 10−7 and 6 × 10−7 M of zinc(II), cadmium(II) and lead(II), 5 ml of KNO3 1 M were added, and the mixture was diluted with deionised water to the mark. The solu-

tion obtained was transferred to the electrochemical cell, deaerated by passing a nitrogen stream through it for 3 min and the voltammogram was registered at 20.0±0.5◦ C under an inert atmosphere in the cell. A blank solution was prepared and treated in a similar way. The calibration graph was constructed in the same way using zinc(II), cadmium(II) and lead(II) solutions of known concentrations. 3.3.3. Procedure for imicloprid determination by DPV As proposed by us in a previous paper [37]. To a 50 ml calibrated flask containing between 10−8 and 1.5 × 10−7 M of imidacloprid, 5 ml of Britton–Robinson buffer solution (pH = 8.0) were added, and the mixture was diluted with deionised water to the mark. The solution obtained was transferred to the electrochemical cell, deaerated by passing a nitrogen stream through it for 5 min and the voltammogram was registered at 20.0 ± 0.5o C under an inert atmosphere in the cell. A blank solution was prepared and treated in a similar way. The calibration graph was constructed in the same way using imidacloprid solutions of known concentrations.

4. Results and discussion Fig. 1 shows W0.5h versus concentration for the zinc(II), cadmium(II) and lead(II) and W0.5h versus concentration for the imidacloprid. Table 1 collects for all analytes the W0.5h values at ‘zero concentration’ as well as the integration limits used to get the ‘signal from the blank’. Table 1 W0.5h and Wb0 extrapolated to ‘zero concentration’ of analyte Technique

Analyte

W0.5h

Wb0

EP ± 0.5Wb0 (V)

DPV

Zinc (II) Imidacloprid

0.0504 0.0705

0.1284 0.1796

−1.000 ± 0.064 −1.035 ± 0.090

ASV

Zinc(II) Cadmium(II) Lead(II)

0.0504 0.0504 0.0504

0.1284 0.1284 0.1284

−1.000 ± 0.064 −0.65 ± 0.064 −0.40 ± 0.064

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Table 2 Analytical signal obtained for the different analytes DPV

ASV 10−10 A)

M

Zn(II) (ip

M

0

2.371 2.641 2.401

0

1 × 10−7

5.290 7.250 3.210

1 × 10−8

Imidacloprid (ip 4.495 4.312 4.630

Zn(II) (ip 10−8 A) Cd(II) (ip 10−8 A) Pb(II) (ip 10−8 A)

M

0.024 0.029 0.030

0.014 0.017 0.025

0.192 0.142 0.112

14.30 18.00 12.44

1.5 × 10−7 3.558 2.987 3.862

3.686 3.984 3.157

2.752 2.265 3.215

3 × 10−7

6.907 6.502 7.267

6.851 7.215 6.592

5.185 5.400 4.897

4.5 × 10−7 10.26 9.856 11.56

10.02 12.05 9.789

7.619 7.264 8.015

6 × 10−7

13.18 15.67 12.45

10.05 13.26 9.740

5 × 10−7

18.17 15.07 16.00

5 × 10−8

53.21 60.01 46.04

1 × 10−6

33.89 34.39 33.12

1 × 10−7

101.4 110.3 91.89

1.5 × 10−6 51.28 49.58 47.78

10−11 A)

0

1.5 × 10−7 149.7 158.0 134.4

13.61 12.07 15.00

Table 3 Analytical signal obtained for the different analytes from zero concentration (IUPAC method) DPV Zn(II) (ip 1.806 3.184 2.991 3.164 1.925 2.708 2.188 3.532 2.708

ASV 10−10

A)

Imidacloprid (ip 4.445 4.312 4.630 4.656 4.576 4.570 4.524 4.458 4.513

10−11

A)

Zn (II) (ip 10−10 A)

Cd (II) (ip 10−10 A)

Pb (II) (ip 10−10 A)

2.504 3.793 3.212 1.324 1.353 2.959 2.824 3.084 2.653

1.952 1.289 2.797 2.578 1.681 2.675 1.927 1.308 2.317

10.50 14.21 23.24 16.17 12.27 11.86 9.213 9.602 15.44

Equally spaced standard dilutions of zinc(II), cadmium(II), lead(II) and imidacloprid were used for calibration. Three experimental replicates were carried out. To the data thus obtained were added the signals from the ‘voltammetric blank’ of three different voltammograms obtained as described above from ‘zero concentration solutions’ of the analyte (see Table 2). Additionally nine voltammograms from zero concentration were carried out. The data obtained were employed for IUPAC method (see Table 3). The statistical parameters for each calibration are indicated in Table 4. Values of the standard deviation

at ‘zero concentration’ have been calculated from the calibration data using the adequate equation derived from linear regression [27]. We calculated the DL by applying different methods. Table 5 indicates different values of the detection limit obtained for each method. Fig. 2a show the measurement of the signal coming from the DPV blank by our proposed method and Fig. 2b show the most common method for determining the detection limit in voltametric method. The height obtained by integration of the blank as estimated in this work is applied to the IUPAC and calibration set methods.

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Table 4 Statistical parameters of calibrations shown in Table 2a DPV

ASV

Zn(II) syx a sa b sb PLOF sc0

Imidacloprid

Zn(II)

Cd(II)

1.434 × 10−10

6.650 × 10−11

7.254 × 10−9

8.569 × 10−9

5.503 × 10−11 3.162 × 10−3 6.568 × 10−5 40.41 1.918 × 10−8

2.553 × 10−11 9.524 × 10−3 3.047 × 10−4 99.26 1.512 × 10−10

3.244 × 10−9 0.2277 0.0088 93.53 3.432 × 10−10

3.832 × 10−9 0.2300 0.0104 96.25 2.605 × 10−10

1.891 × 10−10

5.155 × 10−11

7.060 × 10−10

7.859 × 10−10

Pb(II) 8.506 × 10−9 1.550 × 10−10 3.804 × 10−9 0.1775 0.0103 77.50 3.671 × 10−9

a s , regression standard deviation; a, intercept (A); s , standard deviation of the intercept; b, slope (A l mol−1 ); s , standard deviation yx a b of the slope; PLOF , Lack-of-fit test (p-value) (%); sc0 ; standard deviation from ‘zero concentration’.

Table 5 Detection limits (M) calculated from different models Model

IUPAC Approximated Calibration set S/N

DPV

ASV

Zn(II)

Imidacloprid

Zn(II)

Cd(II)

Pb(II)

5.76 × 10−8

4.54 × 10−10

1.03 × 10−9

7.81 × 10−10

1.10 × 10−8 1.51 × 10−7 1.09 × 10−7 1.77 × 10−8

1.41 × 10−7 1.34 × 10−7 1.80 × 10−7

2.28 × 10−8 1.45 × 10−8 8.72 × 10−9

Fig. 2. Measurement of the signal coming from the DPV blank by our proposed method (A) and signal–noise method (B).

We calculated the recommended IUPAC detection limit for instrumental methods, taking three times the standard deviation of the signal assigned to the zero concentration as the signal threshold to hint any presence of analyte. The calibration set method includes the blank signal obtained, as we proposed previously, as analytical signal corresponding to zero concentration in the calibration set. This implies homocedasticity in the variances and one gets values describing more adequately the

1.04 × 10−7 0.70 × 10−7 3.27 × 10−10

1.22 × 10−7 0.81 × 10−7 8.14 × 10−10

variability of the blank. In this case the detection limit value obtained is higher than this one corresponding to IUPAC method as it is shown in Table 5. This result can be explained considering the associated variability at each concentration level. The DL value obtained by the signal to noise ratio for instrumental methods with transitory signal is the highest DL found and the most commonly applied although it does not have any statistical criteria for its justification [17]. Finally an approximated method to calculate detection limit similar to this one called ‘calibration set’ but without signal for zero concentration has been applied. The obtained results by approximated and calibration set methods were similar. Acknowledgements This study is part of a project PB96-1404 financially supported by the DGCYT (Spain). References [1] G.W. Ewing, Analytical Instrumentation Handbook, Marcel Dekker, New York, 1997, Chap. 19, p. 20.

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