Multicomponent analysis of stripping voltammograms by target transformation factor analysis

Target transformationfactor analysis was studied for simultaneous determination of four simulated stripping voltammograms. A Gaussian function was used to generate synthetic stripping voltammograms. Two programs, SPGRELEP and ELECTTFA, were designed to perform voltammogram simulation and target transformation factor analysis. The method made use of full information of voltammogram and matrix data processing. The ELECTTFA program was used to determine the number of components, to identify the components and to yield a quantitative analysis of unknowns. Experimental results showed the method to be successful.


Introduction
Abstract factor analysis of the experimental data matrix D The covariance matrix Z(DTD) can be subjected to singular value decomposition for calculation of the eigenvalues and eigenvectors, Z USlfr, where S is a diagonal matrix of the eigenvalues and U is the matrix of eigenvectors. The D matrix can be represented as the product of two matrices: D RC, where R(P, F) are the current profiles of the present species and C(F, S) their concentration matrix (where F is the number of components). It is easy to compute: C U w and R DU due to the orthonormality of U-1 and UT. The number of principal components is estimated by several criteria, which are based on the theory of error in factor analysis [7]. Not all of the eigenvectors produced convey useful information; some are due to noise. After deleting the insignificant eigenvectors R and C become R (P, a) and C (a, S), where a is the number of principal components.
Chemometric methods have been applied to improve results in the multicomponent analytical techniques in spectroscopy [1][2][3], but they have rarely been used in electrochemistry. Target transformation factor analysis (TTFA) is a technique that is especially valuable for achieving meaningful transformations of the abstract factors obtained by abstract factor analysis (AFA) [4].
TTFA can be used to yield both qualitative and quantitative information. It also can be used to decide whether or not a suspected substance is present in the mixture and to deduce the composition of each mixture. This method has been applied to spectroscopic, nuclear magnetic resonance, chromatography and kinetic analysis [5, 6-1; attention has been paid, however, to applying TTFA to voltammetry. Many voltammetric techniques are of a local character, using only the peak currents or a limited number of points around the peak, thus losing much of the information contained in the remaining parts of the voltammogram. This paper describes the improvement of multicomponent determinations using the full information of voltammogram and matrix data processing.

Theoretical background and program algorithms
Building the data matrix D (P, S) The original data matrix, D, contains the anodic current response at P voltage values of S mixtures; each voltammogram being a column and the data taken at the same voltage being a row.

Target transformation
The abstract matrices must be rotated into significant real matrices. This oblique rotation is accomplished by transforming matrix T. The matrix T can be determined by using the target vector R 2 from the equations T= (RfR1)-IRfR2 or T=SIRT1R, and then the concentrations and the anodic current profiles of sample component are given by C o T-1CI and R 0 R 1T, respectively. In traditional factor analysis, the current profiles of pure components are always used as the R2 matrix to calculate T. This may cause errors due to interaction between the components. To overcome these, an R matrix, calculated from the standard mixtures by classical least squares analysis R 2 D3f(C3Cf)-1, and a non-zero intercept added to each voltage value, are used as the target vector instead of the pure component standards. C3 is the concentration matrix of the standard mixtures, D.3 is the response matrix of the standard mixtures.

Target testing
The aim of target testing is to decide whether a proposed target can be accepted as a real factor. The criteria used for accepting/rejecting target vectors is based on the similarity between the target vector and the predicted target vector. Malinowski and Howery suggested using the SPOIL function to decide whether a proposed target is acceptable or not [4]. The SPOIL function is defined as the ratio of the real error in the target vector (RET) to the real error in the predicted vector (REP): SPOIl. RET/REP. The apparent error in the test vector (AET) is calculated using: a Ctr_ REP is defined as REP RE(i)II 11 with 1, 2 a. Where T,ll is the Euclidean norm of the vector; RET is then evaluated by RET= [(AET) -(REP)2] 1/. Malinowski and Howery divided the value of the SPOIL function into three regions: (1) an acceptable region (0"0-3"0); (2) a fair region (3"0-6"0); and (3) an unacceptable region (>6"0).
Voltammogram simulation A Gaussian peak shape is assumed for the voltammograms of the pure component with peak position M, peak height C, and widths W: Two programs, SPGRELEP and ELECTTFA, which are based on the algorithms were designed to perform voltammogram simulation and TTFA.
Experimental Inslrumenl A GW 286 EX/16 microcomputer with a maths coprocessor was used for the calculations Simulated vollammograms Simulated data were used to evaluate the potential of TTFA for stripping voltammograms. The peak potentials of copper, lead, cadmium and zinc had the values of --0"35, --0"53, --0"70 and 1"10 V (VS.SCE). The peak widths of the four components were 0"05 V. Gaussian distributed noise was added to the voltammograms to simulate experimental noise as 1 of the average signal value. The background was assumed to be normally distributed with zero mean; the peak height of the background was 0"05 ppm. Taking background as baselines, the simulated voltammograms of nine unknown 10 1.5 -1 0  samples and baselines were plotted as shown in figure 1. The voltammograms of the standard samples were simulated in the same way as the unknown samples. Figure  2 is a three-dimensional plot of the simulated standard data matrix D 3.
Three-level orthogonal array design of standard samples For any orthogonal array design, a matrix, which consists of columns and rows, with various numbers at the intersections of each column and row, must be constructed. Table displays an L9(34) natrix. This is a three-level orthogonal array matrix which is made up of four columns and nine rows. Each column represents a factor, which is an independent variable, and each row represents an experimental trial. The numbers at the intersections indicate the level settings that apply to   2"5928E + 0 5"3084E--2 8"5573E-3 3 l'0900E + 1-4003E--3"8898E--3 1"1434E--8"0848E--2 1"3771E +0 2"3764E-2 3"3004E--3 4 7"7310E+0 1"0195E--2 4"0781E-4 7"5991E-3 6"7969E-3 7"0926E+2 2"0452E-2 2"3966E-3    According to the algorithms, the target matrix R 2 was calculated from the standard samples by the least squares method. The SPOIL thnction was developed, based on the similarity between the target vector and the predicted target vector, to the validity and usefulness of a predicted target vector. In order to judge whether the predicted target vectors were a successful target, the SPOIL values were calculated and the results are given in table 3. The SPOIL values of Cu, Pb and Cd were below 3"0 and the value of Zn was a little over 3"0, indicating that all the predicted target vectors can be considered to be true targets.