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Enhancing the sensitivity of potential step voltammetry using chemometric resolution Jiarun Tu, Wensheng Cai and Xueguang Shao* Enhancing the sensitivity of analytical methods by improving the signal quality is a universal goal in analytical chemistry. In analytical electrochemistry systems, the double layer charging current has been an obstacle to the accurate measurement of the faradaic current despite theoretical and experimental efforts. In this study, a method for sensitivity enhancement for potential step voltammetry is developed using chemometric resolution. Trilinear decomposition is used to extract the net faradaic current and double layer charging current directly from the data matrix of the decaying curves measured at different potentials. The feasibility of the method is proven using simulated data and further validated by two experimental datasets of diffusion and adsorption control reactions. Compared with the conventional approach that

Received 10th September 2013 Accepted 5th December 2013

records the current data at a later pulse time, the voltammogram of the extracted net faradaic current is an ideal sigmoid curve with a horizontal baseline, even for the samples of very low concentration. More

DOI: 10.1039/c3an01719b

importantly, the analytical sensitivity can be greatly improved when the net faradaic current is used for

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quantitative determination.

1

Introduction

Sensitivity is a key parameter for an analytical method, because it determines the analytical performance of the method in analyzing low concentration samples. In electroanalytical methods, many efforts have been made over the last several decades to enhance the sensitivity by improving the electrochemical signals.1–3 The double layer charging current, which is generated with the change of potential on the working electrode surface, causes interference with the accurate measurement of the faradaic current and restricts the detection limit.4–6 Since the analytical signal is usually generated by changing the potential in most electrochemical techniques, it is inevitable to include the charging current in the measured signal of an electroanalytical system. Therefore, elimination of the charging current has been an important goal in electrochemical analysis. There are two kinds of methods for reducing the inuence of the charging current on the faradaic current. One is implemented by experiment with the benet of real-time correction for the sampling current, such as circuitry design,7 background subtraction,8,9 microelectrode,10–12 differential pulse voltammetry and staircase voltammetry.13–15 Such methods, however, may not sufficiently reduce the effects of the charging current. For example, background subtraction can subtract the residual current of the blank solution from the total current by adopting Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), State Key Laboratory of Medicinal Chemical Biology, Research Center for Analytical Sciences, College of Chemistry, Nankai University, Tianjin 300071, People's Republic of China. E-mail: [email protected]; Fax: +86-22-23502458; Tel: +86-2223503430

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two duplicate cells, where it is assumed that the charging current is equal.8 In the actual situation, however, the experimental conditions in the two cells are hard to be completely consistent. The other way to reduce the effect of the charging current is mathematical post-processing techniques, which try to separate the charging current from the faradaic current by mathematical calculations based on the different responses of the two currents. These methods include curve-tting,16 Kalman lter,17 derivative techniques,18 Fourier transform,19,20 multivariate curve resolution alternating least squares (MCR-ALS),21 and iterative target transformation factor analysis (ITTFA),22 etc. With the advances of analytical instruments, high-dimensional data can be easily obtained in analytical chemistry. Therefore, chemometric methods for three- or higher-dimensional data analysis have been developed and are attracting lots of attention in many scientic elds.23–25 A series of algorithms for analyzing three-dimensional data arrays have been proposed to extract chemical information from the data. These algorithms include the generalized rank annihilation method (GRAM),26 the direct trilinear decomposition (DTLD),27 multivariate curve resolution alternating least squares (MCR-ALS),28 parallel factor analysis (PARAFAC),29 alternating trilinear decomposition (ATLD),30 alternating penalty trilinear decomposition (APTLD),31 and self-weighted alternating trilinear decomposition (SWATLD),32 etc. Among these algorithms, PARAFAC and ATLD have been widely applied in the resolution of three-dimensional data arrays. PARAFAC achieves decomposition of a data array in a unique manner, allowing relative concentrations and spectral proles of the individual components to be extracted directly.33,34 ATLD, however, is an

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improvement of the traditional PARAFAC algorithm without any constraints and is described as an alternative algorithm for the decomposition of data arrays.35,36 Furthermore, a MATLAB graphical interface toolbox of ATLD has been developed for treating high-dimensional data conveniently.37 In this paper, in order to extract the net faradaic current from the measured current in potential step voltammetry, an application of the three-dimensional algorithms was investigated with the aim of extracting the faradaic and charging currents from a data array constructed with the decaying curves at different potentials. Three datasets were studied including a simulated one and two experimental ones of a diffusion and an adsorption control reaction measured on a bare glassy carbon electrode. The method was proven to be very helpful for improving the sensitivity of the potential step voltammetry.

2 Experimental 2.1

Data simulation

To simulate the measured currents in normal pulse voltammetry, the decaying currents in each pulse are assumed to include the faradaic and charging currents, and the two currents are simulated by their theoretical formulae if ¼

nFADox 1=2 c*ox 1 p1=2 t1=2 1 þ P "

nF   P ¼ exp RT E  E1=2 ic ¼

(1)

#

  DE t exp RU s

(2)

(3)

where if and ic represent the faradaic and double layer charging current, respectively, and n is the number of electrons exchanged per molecule, F is the Faraday constant, A is the area of the electrode, Dox is the diffusion coefficient of the oxidized species, c*ox is the concentration of the oxidized species, t is the duration time from the beginning of the potential pulse, R is the ideal gas constant (8.314 J mol1 K1), T is Kelvin temperature (298.15 K), E is the potential on the working electrode, E1/2 is the half-wave potential, RU is the uncompensated cell resistance, DE is the potential step, s is the cell time constant, and P is a parameter related to the potential and can be calculated using eqn (2). To construct a three-dimensional data array, simulations of the decaying currents for a series of potential steps from 0.6 to 0.2 V with an increment of 0.02 V and a group of concentrations are used. Decaying currents of different pulses for one sample can construct a two-dimensional data matrix, in which the decaying current of a pulse at different times is recorded in a row. Packing the data matrices of different samples forms a three-dimensional data array. 2.2

Reagents, instrument and measurement

All chemical reagents were of analytical grade. Emodin, purchased from Aladdin (Shanghai, China), is a standard for

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high performance liquid chromatography. Copper sulfate, anhydrous sodium sulfate, orthophosphoric acid, acetic acid and orthoboric acid were purchased from Guangfu Chemical Co., Ltd. (Tianjin, China). Copper sulfate and emodin solutions were prepared with 0.1 M sodium sulfate and 0.04 M Britton– Robinson (B–R) buffer (pH ¼ 4.0), respectively. Doubly distilled water was used in preparation of the samples. A self-made electrochemical workstation was used, consisting of a data acquisition card (NI USB-6211, National Instruments Corporation, Texas, USA), a potentiostat circuit board (Lanlike Chemistry & Electron High Technology Co., Ltd., Tianjin, China) and a personal computer (Lenovo, Beijing, China). The electrodes were purchased from Lanlike Chemistry & Electron High Technology Co., Ltd. Before the experiments, the performance of the workstation was validated by a xed resistor and potassium ferricyanide standard solution. The programs were written in MATLAB (The MathWorks Inc., USA). The three-electrode system was made up of a 3 mm-diameter bare glassy carbon electrode (working electrode), a 212-type saturated calomel electrode (reference electrode) and a 2  5  0.1 mm 213-type platinum sheet electrode (auxiliary electrode) was used for all the measurements. All potentials were referred to the saturated calomel electrode (SCE). All experiments were carried out at room temperature. For copper sulfate solution, the potential ranges of 0.4 to 0.4 V were increased by 0.02 V. For emodin solution, the potential ranges of 0.1 to 0.9 V were increased by 0.02 V and stirring adsorption for 2 min before each measurement. A pulse width of 60 ms and an interval of 1.0 s between successive pulses were used. The sampling rate was 20 000 points per second. All solutions were carefully degassed with high-purity nitrogen for 5 min prior to the measurements in order to remove oxygen. A two-dimensional data matrix can be constructed by taking the decaying current in each pulse as a row, and the matrices of different samples form a three-dimensional data matrix. 2.3

Calculation

For a three-dimensional data array X of dimension I  J  K (for example, in this study, I, J, K represent the number of data points sampled in a pulse, the number of pulses, and the number of samples, respectively) the trilinear model can be depicted as: xijk ¼

N X

ain bjn ckn þ eijk i ¼ 1; .; I; j ¼ 1; .; J; k ¼ 1; .; K

n¼1

(4) where xijk is an element (i, j, k) of X, the value of which is the measured current at the ith time of the jth pulse for the kth sample; N denotes the number of factors, which means the number of components (faradaic and charging current) in the measured signal; ain, bjn and ckn are the weights for the nth factor, representing the relative decaying current curve, the relative current at each potential (voltammogram) and the relative concentration in each sample; and eijk is the residual of the element.

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As summarized in the Introduction, several methods like PARAFAC and ATLD can be used for decomposing a threedimensional data array X into the components of its factors. In this study, ATLD was used and two factors (faradaic and charging current), i.e., N ¼ 2, were used in the calculation. From the measured data X, two vectors can be obtained for a, b and c, respectively. Clearly, the two vectors in a are the relative decaying current curves of the faradaic and charging currents. One vector in b is the voltammogram of the analyte and the other one is the variation of the charging current with the potential. As for the two vectors in c, one represents the relative concentrations of analyte in each sample and the other one represents the relative charging current in the measurement of different samples. Once ain, bjn and ckn are obtained, the two components, i.e. the faradaic and charging currents, at each time of each pulse for a sample can be obtained by xijk,n ¼ ainbjnckn (i ¼ 1, ., I; j ¼ 1, ., J; k ¼ 1, ., K)

(5)

where n ¼ 1 or 2 for the faradaic and charging currents, respectively. The calculated faradaic current can be known as net faradaic current, from which the voltammogram should be more ideal and the quantitative determination should be more accurate.

3 Results and discussion 3.1

Simulated data

To investigate the performance of the method, ve samples with concentrations from 0.5  103 to 2.0  103 mol L1 were simulated to construct the three-dimensional decaying current matrix X. Since the signals of the two kinds of current exist in the matrix X, two factors or principal components were used in the calculation. The results obtained by trilinear decomposition for the simulated data are shown in Fig. 1. The subgures (a), (b) and (c) in the gure correspond to ain, bjn and ckn, respectively. Fig. 1(a) shows the variation of the two kinds of currents with time. It can be seen that the charging current decays very fast to zero while the faradaic current decays slowly to a stable value. It is clearly consistent with the theory that the charging current decays exponentially with time while the faradaic current decays in accordance with square root of time. Fig. 1(b) displays the relative weights of the two currents in each pulse of different potentials. The variation of the weights forms the voltammogram. Obviously, the voltammogram of the faradaic current is an ideal sigmoidal curve with a horizontal straight baseline and plateaus whereas the voltammogram of the charging current is a straight line. More importantly, Fig. 1(c) demonstrates the relative values of the two currents in the signals of different samples. It can be found that the values of the faradaic current are proportional to the concentrations, but the values of the charging current are independent of the concentrations. From such results of the simulated data it can be concluded that the net faradaic current can be separated from the total current to obtain an ideal voltammogram and a parameter of

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Fig. 1 Results obtained for simulated data by trilinear decomposition: (a) relative current; (b) relative weight; (c) relative faradaic and charging currents of different concentration samples.

concentration. Furthermore, variation of the charging current with the potential and concentration can be obtained for investigation of the analyzing system. For further validation of the results, the faradaic and charging currents in each pulse were calculated using eqn (5). Compared with the simulated currents, the deviations, which are represented by the root mean squared errors, were found to be almost zero. This indicates that the calculated currents are almost identical to the simulated ones, demonstrating the correctness of the calculated results in Fig. 1.

3.2

Experimental data and application

To validate the practicability of the proposed method, an experimental data of copper sulfate (CuSO4) solutions was used. The system is a typical diffusion-controlled process and, thus, it is easy to obtain the data that accords with the theory well. Samples of different concentrations ((0.2–3.0)  103 mol L1) in 0.1 mol L1 Na2SO4 were employed in the experiments. The decaying current measured in each pulse for a sample was arranged as a two-dimensional matrix, and the matrices of all the samples form a three-dimensional matrix X. To investigate the components in the experimental data, singular value decomposition (SVD) was performed for the two-dimensional matrix of each sample. The result shows that the two larger eigenvalues explain more than 99% of the variances. This

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indicates that two principal components are included in the data matrices, corresponding to the faradaic and charging currents, respectively. Therefore, the two components were used for further analysis. Fig. 2 shows the variation of each current with time (ain), the relative weights of the two currents (bjn) and the relative values for the parameter related to the concentration (ckn), respectively. Fig. 2(a) shows that the charging current decays very fast in the same way as the simulated case above; the faradaic current, however, increases rapidly to a maximum and then decays slowly with time. This result indicates that the charging current complies with the theory very well in the actual potential step experiment, while there is a delay for the faradaic current to reach the maximum from zero. The delay may be explained by realizing that the potential across the double layer is actually ‘scanning’ toward its nal value.5 Furthermore, it can be seen clearly from the gure that, in the earlier stage of the time, the charging current plays a predominant role in the total current, whereas the faradaic current becomes dominant gradually with time. This was the reason for recording the current at a later pulse time in the conventional normal pulse voltammetry. Clearly, although the charging current decays very fast, the value is not zero. Therefore, the method can only reduce the inuence of the charging current; it is difficult, however, to obtain a clean faradaic current. When weak current is

Fig. 2 Results obtained by trilinear decomposition for CuSO4 in 0.1 mol L1 Na2SO4 solution: (a) relative current; (b) relative weight; (c) relative faradaic and charging currents of different concentration samples.

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measured, e.g., in the case of low-concentration samples, the inuence of the charging current can be still signicant enough. In Fig. 2(b), the voltammograms of the faradaic and charging currents are displayed. The voltammogram of the faradaic current is almost a perfect sigmoidal curve and that of the charging current is a straight line. The former gives the information of the property (the half wave potential) and the quantity (the height) of the analyte, and the latter provides the information such as the cell time constant of the electrode process. Fig. 2(c) shows the parameter related to the concentration in the samples. It is clear that the parameter for the charging current is independent of concentration, but the parameter for the faradaic current is proportional to the concentration. The relative charging current is approximately a xed value at 42.42  1.74, which can be further used for analyzing the properties of the solution. For the faradaic current, a straight line with an excellent correlation coefficient R (0.9995) can be obtained using a least squares tting of the parameter with the concentrations. The line can be used as a calibration curve for quantitative determination. Although the information in Fig. 2 is useful for qualitative and quantitative analysis, the values are obtained by mathematical computation, instead of the real signals measured in the experiments. Fortunately, the real signal in each pulse can be obtained using eqn (5). Fig. 3(a) shows the decaying curves of the net faradaic current, from which further analysis can be performed. The curve of solid squares in Fig. 3(b) was obtained by plotting the maximal currents in the decaying curves with the pulse potentials (voltammogram) of a high-concentration

Fig. 3 Comparison results of the two methods: (a) actual faradaic current of each pulse for 2.0  104 mol L1 CuSO4; (b) comparison of voltammograms for 3.0  103 mol L1 CuSO4; (c) comparison of voltammograms for 2.0  104 mol L1 CuSO4; (d) comparison of quantity results with peak height. Curves 1 (–-–) and 2 (–A–) indicate voltammograms obtained by the proposed method at the maximum faradaic current time and 20 ms pulse time respectively; curve 3 (–:–) indicates the voltammogram recorded at a 20 ms pulse time by the conventional method.

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(3.0  103 mol L1) sample. The curve of solid squares in Fig. 3(c) shows the voltammogram of a low-concentration (2.0  104 mol L1) sample. For comparison, the voltammograms of the two samples plotted with the current at 20 ms were shown as the curves of diamonds in Fig. 3(b) and 3(c), respectively, and the voltammograms measured using conventional pulse voltammetry were plotted as the curves of triangles. Clearly, in the case of the high-concentration sample in Fig. 3(b), all three curves are accepted, but the inuence of the charging current on the triangle curve can be clearly seen. In the case of the lowconcentration sample in Fig. 3(c), however, the two curves plotted with the net faradaic current are still ideal voltammograms, but the sigmoidal curve was not obtained for conventional pulse voltammetry. The latter is obviously caused by the inuence of the charging current. On the other hand, it can be seen from Fig. 3(b) that there is no signicant difference between the voltammogram of the net faradaic current at 20 ms and the curve recorded by conventional pulse voltammetry, but the height of the voltammogram of the net faradaic current is 5 times greater than that obtained using conventional pulse voltammetry. For further comparison, the calibration curves for the samples in the concentration range of (0.6–3.0)  103 mol L1 obtained from the voltammograms of the net faradaic current and conventional pulse voltammetry were plotted in Fig. 3(d). The linear equations calculated by least squares tting are y ¼ 0.3698x + 0.1353 (R ¼ 0.9998) and y ¼ 0.0683x + 0.0021 (R ¼ 0.9997), respectively. The results clearly indicate that the proposed method can effectively eliminate the inuence of charging current and, consequently, signicantly improve the sensitivity for quantitative analysis. To further validate the practicability of the proposed method, the analysis of emodin was investigated. The system is an adsorption control process, in which the product or reactant is strongly adsorbed on the electrode. Therefore, an independent adsorption peak may occur prior to or aer the normal peak produced by diffusion. The peak may lead to a distorted sigmoidal curve to make the analysis by conventional pulse voltammetry difficult. In the experiment, samples with different concentrations ((1.0–7.0)  107 mol L1) of emodin in 0.04 mol L1 B–R buffer solution were used, and the decaying current in each pulse at different potentials forms a threedimensional matrix X. Fig. 4 shows the results obtained by trilinear decomposition. The results in Fig. 4(a) are similar to those in Fig. 2(a), i.e., the faradaic current increases very fast to a maximum and then decays with time, while the charging current decays rapidly. In Fig. 4(b), the voltammogram of the charging current is a straight line like that in Fig. 2(b), but the voltammogram of the faradaic current is not an ideal sigmoidal curve. The distortion in the latter result is obviously caused by the adsorption control process, which will make quantitative analysis more difficult. The end potential was set to 0.9 V because a more negative potential exceeds the suitable potential of the glassy carbon electrode. Importantly, the results in Fig. 4(c) are also similar to those in Fig. 2(c), i.e., the relative faradaic current is linearly proportional to the concentrations with an excellent correlation coefficient R ¼ 0.9994 and the relative charging current is

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Fig. 4 Results obtained by trilinear decomposition for emodin in 0.04 mol L1 B–R buffer solution: (a) relative current; (b) relative weight; (c) relative faradaic and charging currents of different concentration samples.

approximately a xed value of around 16.5. The results indicate that, even for the adsorption control system, quantitative analysis using normal pulse voltammetry can be easily achieved with the help of the proposed method. For further analysis of the calculation results, the decaying curves of the net faradaic current in each pulse, calculated using eqn (5), were shown in Fig. 5(a). With the maximum current and the current at 20 ms, respectively, the voltammograms were plotted as curve 1 (-) and curve 2 (A) in Fig. 5(b) for a highconcentration (7.0  103 mol L1) sample. Curve 3 (:) in Fig. 5(b) was obtained by conventional pulse voltammetry. Fig. 5(c) shows the results for a low-concentration (2.0  107 mol L1) sample. Obviously, except for the abnormal shape of the sigmoidal curves resulting from the adsorption effect, the results are very similar with thosein Fig. 3, i.e., in the case of the high-concentration sample, the inuence of the charging current is not so signicant, but in the case of the lowconcentration sample, the charging current is the dominant component in the voltammogram. For adsorption control systems, quantitative analysis is commonly carried out by adsorptive voltammetry or adsorptive stripping voltammetry, instead of conventional pulse voltammetry due to the abnormal shape of the sigmoidal curve. However, in theory, the net faradaic current in normal pulse voltammetry of an adsorption control system is linearly

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and sensitive quantitative analysis. Therefore, trilinear decomposition may provide a powerful chemometric tool in analytical electrochemistry and may be an alternative way to obtain more information from experimental data of electrochemical measurements for exploring new applications.

Acknowledgements This work was supported by National Natural Science Foundation of China (no. 21175074).

References

Fig. 5 Comparison results of the two methods: (a) actual faradaic current of each pulse for 1.0  107 mol L1 emodin; (b) comparison of voltammograms for 7.0  107 mol L1 emodin; (c) comparison of voltammograms for 1.0  107 mol L1 emodin; (d) comparison of quantity results with peak height. Curves 1 (–-–) and 2 (–A–) indicate voltammograms obtained by the proposed method at the maximum faradaic current time and 20 ms pulse time respectively; curve 3 (–:–) indicates the voltammogram recorded at 20 ms pulse time by the conventional method.

proportional to the concentration.38 The result in Fig. 4(c) also shows that there is a parameter that is linearly related to the concentration. Therefore, the peak height in the voltammogram of the net faradaic current could be used for quantitative analysis. Fig. 5(d) shows the calibration curves using the maximum currents of curves 1 and 3 in Fig. 5(b) for the samples in the concentration range of (2.0–7.0)  107 mol L1. The two straight lines obtained by least squares tting are y ¼ 52.557x + 1.202 (R ¼ 0.9991) and y ¼ 8.8859x  7.5069 (R ¼ 0.9974), respectively. Clearly, the sensitivity of the net faradaic current by the proposed method is around 6 times greater than the conventional one.

4 Conclusions A method to improve the performance of conventional pulse voltammetry was proposed. By extracting the net faradaic current with trilinear decomposition from the data measured in potential step experiments, quantitative analysis can be achieved for both diffusion and adsorption control systems, and the sensitivity can be signicantly enhanced. The method was investigated using a simulated and two experimental datasets of diffusion and adsorption control systems measured on a bare glassy carbon electrode. The results show that the net faradaic and charging currents can be obtained by trilinear decomposition, and a parameter related to the concentration can be obtained and directly used for quantitative analysis. Furthermore, the inuence of the charging current can be clearly eliminated in the voltammograms plotted with the net faradaic currents, and thus the voltammograms can be used for accurate

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Enhancing the sensitivity of potential step voltammetry using chemometric resolution.

Enhancing the sensitivity of analytical methods by improving the signal quality is a universal goal in analytical chemistry. In analytical electrochem...
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