The speciation of copper (II)/ethylenediamine/oxalate system by evolving factor analysis

Principal component analysis and evolving factor analysis were applied to the study of the speciation of Cu (II)/ethylenediamine/ oxalate. Two programs were designed, based on mathematical algorithms. Error functions were calculated for evaluating the number of species. Submatrix analysis plots were constructed to estimate the species present in the system. The method should prove useful in studies of complex systems in environmental samples.


Introduction
Information about the speciation of metals in natural water is important in studies of the toxicity of metals for aquatic organisms. The study of speciation also contributes to the understanding of trace metal transport in the water environment. Biological effects on aquatic organisms and geochemical behaviour both depend greatly on the species of the element so the study of speciation has been one of the most important areas of environmental and analytical chemistry in recent years.
Studies of multiple equilibria in solution have solved a number of problems in speciation. Traditional approaches use least squares methods based on a chemical model and on compliance with the law of mass action [1]. A variety of instrumental techniques have been used for the determination of the number, nature and stabilities of multiple equilibria systems. Spectrophotometry has considerable advantages over the other techniques because of its simplicity. Gampp et al. [2] proposed a model-free method derived from principal component analysis (PCA): evolving factor analysis (EFA). EFA is a powerful method for analysing multivariate data with an intrinsic order produced by many modern hyphenated instruments, such as speciation in multiple equilibria systems using spectrophotometric titration. Data can be listed, according to its pH, from low to high. The first columns may contain the data measured at low pH values and the last columns those obtained at high pH values. The method is based upon repetitive eigenvalue analysis ofa set ofdata matrices obtained during the evolutionary process. Eigenanalysis is performed on a complete series of matrices, which are constructed by successively adding spectra to the previous matrix during the evolutionary process. As new absorbing species evolve, the eigenvalues of the abstract factors increase by an order of magnitude. The logarithmic eigenvalues are plotted as a function of the progessing titration. Every submatrix is calculated by PCA in turn.

Instruments and apparatus
The Shimadzu UV-265 and UV-120 spectrophotometers were used for all experiments; a GW 286 EX/16 microcomputer with a maths coprocessor was used for the calculations; and a Mettler DL21 titrator was used for standardization of standard solutions.

Reagents
All reagents were of analytical reagent grade. Doubly distilled and de-ionized water were used. Standard solutions of copper(II) nitrate, ethylenediamine and potassium oxalate were prepared and standardized according to generally accepted procedures.

Spectrophotometric titration
Solutions which contain Cu(II) ion and one or two of the ligands were titrated with a base at a constant ionic strength (0"5M) and temperature (25C). After each addition of titrant and equilibration, the pH was measured. The absorbance of spectra of each solution was measured at a different pH, with a wavelength range ti'om 480 nm to 820 nm, in 20 nm intervals. An experimental data. matrix, D, was built up from these data.

"Computer programs and their algorithm
The steps of the algorithm were as follows: (1) Building the data matrix D (N, M). Matrix D contains the spectra at N wavelengths of the M mixtures obtained at the successive titration points of the spectrometric titration.
(2) Factor analysis of the experimental data matrix D. The variance-covariance matrix A(DTD) can be subjected to single value decomposition for calculation of the eigenvalues and eigenvectors. The number of species is estimated by several criteria based on the theory of error in factor analysis [3].

Results and discussion
Three different systems were used in this work" (1) Cu(II)/oxalate (ox).
(3) Cu(II)/ox/en. The initial conditions used in the spectrophotometric titrations are shown in table 1. High ratios of ligand to copper ion were used in order to avoid copper hydroxide precipitation at neutral pH.
Estimating the number of species by factor analysis Nine criteria were used to estimate the number of species. Table 2 shows the principal component analysis applied to the Cu(II)/ox/en. When six components were considered, the real error or residual standard deviation function, RE, had a value of 0"0011; the imbedded error function, IE, had a value of0"007; and the extracted error, XE, had a value of 0"0009. In general, the RE function with values larger than 0.001 is for the expected number of components, thus a range somewhat above this value is the boundary between wanted and unwanted information. Malinowski's empirical factor function, IND, reached a minimum betweeen 4 and 6; the function increased rapidly after N= 6. A maximum of the eigenvalue ratio function, ER, appeared at 6 [4]. In 1987, Malinowski proposed calculation of reduced eigenvalues, REV [5]; REV values are calculated according to the equation: REV 2j/(l-j + 1)(k-j + 1) where and k are the number of rows and columns in matrix A, assuming that is greater than k; REVj is the jth reduced eigenvalue; and j is the order number. The magnitude of REV decreased rapidly in the system until stabilizing at N 6. As recommended by Gemperline  Fraci 2i / 2 /j=l where 2 is the th eigenvalue, and the sum is over that eigenvalue and all the remaining eigenvalues. The appropriate number of components is one less than that giving the minimum Fraci value. In the system, the Frac had a minimum at N 7, after 7 the change in Frac was quite small, suggesting that 6 was the optimum component number. From these criteria, it was concluded that six absorbing species were present. SPGRAFA was also used to deduce the number of components for Cu(II)/en and Cu(II)/ox systems. For the Cu(II)/en system, the results indicated that no appreciable decreases in RE, IE and XE values were observed from the number of components N 3 to 14. A maximum of the ER function appeared at N= 3.

Conclusions
Evolving factor analysis (EFA) is a powerful method using spectrophotometric titration for the study of speciation of multiple equilibria systems. The method does not require any assumptions about the chemical model of the equilibrium system. Based on mathematical algorithm of EFA, a program called SPGREFA was designed to investigate the speciation of the Cu(II)/ox/en system. Submatrix analyses are used to estimate the number of species and to show where the species arise and where they disappear. Based on the algorithm of PCA and some newer error functions recommended by Malinowski