The Use of Factorial Design and Simplex Optimization to Improve Analytical Performance of In Situ Film Electrodes

Abstract

This work presents a systematic approach to determining the significance of the individual factors affecting the analytical performance of in-situ film electrode (FE) for the determination of Zn(II), Cd(II), and Pb(II). Analytical parameters were considered simultaneously, where the lowest limit of quantification, the widest linear concentration range, and the highest sensitivity, accuracy, and precision of the method evidenced a better analytical method. Significance was evaluated by means of a fractional factorial (experimental) design using five factors, i.e., the mass concentrations of Bi(III), Sn(II), and Sb(III), to design the in situ FE, the accumulation potential, and the accumulation time. Next, a simplex optimization procedure was employed to determine the optimum conditions for these factors. Such optimization of the in situ FE showed significant improvement in analytical performance compared to the in situ FEs in the initial experiments and compared to pure in situ FEs (bismuth-film, tin-film, and antimony-film electrodes). Moreover, using the optimized in situ FE electrode, a possible interference effect was checked for different species and the applicability of the electrode was demonstrated for a real tap water sample.

Keywords: factorial design; optimization; simplex; trace heavy metals.

Figure 1

Linear concentration ranges for (a) Zn(II), (c) Cd(II), and (e) Pb(II), and the stripping peak potentials for (b) Zn(II), (d) Cd(II), and (f) Pb(II). The measurements were performed using 1.00Bi0.60Sn0.34Sb in 0.1 M acetate buffer using t_acc = 100 s and E_acc = −1.380 V. Figure (g) shows the increase in stripping peaks with increasing concentration of the analytes (simultaneously). The full symbols in a,c,e) characterize the linear concentration range, whereas the empty symbols characterize concentrations above and below the linear concentration range.

Figure 2

The linear concentration ranges determined for Zn(II), Cd(II), and Pb(II) using different in situ film electrodes (FEs) in (a) factorial design and (b) the simplex procedure.

Figure 3

The change in the shape of the Cd(II) stripping peak with an increase in Cd(II) concentration.

Figure 4

Sensitivity determined as the calibration curve’s slope for the determination of (a,d) Zn(II), (b,e) Cd(II), and (c,f) Pb(II); the slopes were determined in the (a–c) factorial design and (d–f) the simplex procedure. The error bars represent the standard deviation of the replicate measurements.

Figure 5

Comparison of voltammograms measured in 0.1 M acetate buffer without analytes using 1.00Bi0.60Sn0.34Sb, 1.94Bi, 1.94Sn, and 1.94Sb in situ FEs (E_acc = −1.380 V, t_acc = 100 s).

Figure 6

The change in the shape of the voltammograms with and without possible interferents present in solution; (a) Cu(II), (b) As(III), (c) Mg(II), (d) Fe(II), (e) Ca(II), (f) K(I), (g) SO₄²⁻, (h) Cl⁻, and (i) NO₃⁻ at a mass concentration ratio of 1:1, 1:10, and 1:100 relative to the analytes. The measurements were performed with 1.00Bi0.60Sn0.34Sb (E_acc = −1.380 V, t_acc = 100 s) in 0.1 M acetate buffer containing 135.7 µg/L of all three analytes simultaneously.

Figure 7

Multiple standard addition method for the analysis of (a) Cd(II) and (b) Pb(II) using 1.00Bi0.60Sn0.34Sb (E_acc = −1.380 V, t_acc = 100 s). Six replicate measurements are shown in Figures a,b. (c) One example of the obtained voltammograms is shown in Figure c. The 0.1 M buffer solution was prepared using a real tap water sample.