Application of rank annihilation factor analysis to the spectrophotometric determination of the formation constant of complex of a new synthesized tripodal ligand with Co2+

Reza Golbedaghi; Farzad Khajavi

doi:10.1016/j.arabjc.2013.09.035

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Original article

10 (

2_suppl

); S2580-S2583

doi:

10.1016/j.arabjc.2013.09.035

Application of rank annihilation factor analysis to the spectrophotometric determination of the formation constant of complex of a new synthesized tripodal ligand with Co²⁺

Reza Golbedaghi^⁎, Farzad Khajavi

Chemistry Department, Payame Noor University, 19395-4697 Tehran, Iran

⁎Corresponding author. Tel.: +98 8118234911; fax: +98 852 4224279. golbedaghi82@gmail.com (Reza Golbedaghi)

Received: 2012-10-8, Accepted: 2013-9-22, Published: 2013-05-01

Disclaimer:
This article was originally published by Elsevier and was migrated to Scientific Scholar after the change of Publisher.

Peer review under responsibility of King Saud University.

Abstract

The complex formation between a new synthesized tripodal ligand (L_22py) and the cation Co²⁺ in water was studied spectrophotometrically using rank annihilation factor analysis (RAFA). According to molar ratio data the stoichiometry of complexation between the ligand and the cation Co²⁺ was 1:1. Formation constant of this complex was derived using RAFA on spectrophotometric data. In this process the contribution of ligand is removed from the absorbance data matrix when the complex stability constant acts as an optimizing object and simply combined with the pure spectrum of ligand, the rank of original data matrix can be reduced by one by annihilating the information of the ligand from the original data matrix. The effect of ethanol, dimethylformamide (DMF) and acetonitrile (AN) was investigated on the formation constant of the Co²⁺ complex. Complex formation constant in water was estimated as log K_f = 5.09 ± 0.02. In mixtures of solvents of water and DMF and water and AN, the formation constant of the complex was increased because of lowering donor number of the solvent and in mixture of water and ethanol, the complex formation constant was decreased because of lowering of dielectric constant of the solvent.

Keywords

RAFA

Tripodal ligand

Complex formation constant

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1 Introduction

Stability constants can be key parameters for the investigation of equilibria in solution. They are very important in many fields such as industrial chemistry (Tewari, 1995), environmental studies (Pandey et al., 2000), medicinal (Ibrahim et al., 2000) and analytical chemistry (Pakhomova et al., 2001). Therefore complexation reactions of metal ions with different ligands have been widely studied (Hulanicki et al., 1983; Zhou et al., 1996; Colston and Robinson, 1997 ). Several methods for the determination of stability constants, such as potentiometric titration (Garrett and Weber, 2006), conductometry (Doe et al., 1987) and spectrophotometric determination (Safavi and Fotouhi, 1998), have been reported. Among the methods used for the determination of stability constants, spectrophotometric methods have the advantage of sensitivity and are suitable for determination of stability constants in solution under different experimental conditions. Overlapping of spectra of different chemical species involved in the equilibria is an important problem, because it makes the determination of stability constants by classical methods difficult or even impossible, and can cause great uncertainties on the obtained results. Chemometric methods can also easily resolve the overlapped spectra (Safavi and Abdollahi, 2001; Booksh and Kowalski, 1994) where one can analyze whole spectra, thereby utilizing all spectral information. RAFA as a powerful chemometric method can easily remove the contribution of ligand or complex in the highly overlapped spectra of the ligand and complex and therefore give the useful information about the chemical system. In this work, RAFA was used to analyze the experimental data and to derive the formation constant of the complex.

2 Theory

The basis of the application of RAFA in the determination of the formation constants for 1:1 complexes was described in our previous work (Afkhami et al., 2009).

For a 1:1 metal ligand molar ratio complex the equations are as follows

(1)

M + L \to ML

(2)

K_{f} = \frac{[ML]}{[M] [L]}

(3)

C_{L} = [L] + [ML]

(4)

C_{M} = [M] + [ML]

where [L], [M] and [ML] are the equilibrium concentrations of ligand, metal ion and the complex, respectively.

K_{f}

is the stability constant of the complex,

C_{L}

is the total concentration of ligand, which remains constant, and

C_{M}

is the total concentration of metal ion, which is varied when employing the molar ratio method.

By substitution of [M] and [ML] from Eqs. (3) and (4) into Eq. (2) and rearranging yields

(5)

K_{f} {[L]}^{2} + (K_{f} C_{M} - K_{f} C_{L}) [L] + [L] - C_{L} = 0

A two-way data matrix with rank 2 can be formed by measuring absorbance under different wavelengths at a series of metal to ligand molar ratios with constant analytical concentrations of the ligand. By removing the contribution of one component from the original absorption data matrix using RAFA, the rank of the residual matrix decreases by one. By substitution of different values of K_f in Eq. (5) for a given amount of C_M and C_L, different vectors of ligand concentration will be obtained. The correct concentration profile will be obtained by substitution of the correct K_f value. The molar absorptivity of the ligand can be obtained from the spectrum of the pure ligand. Therefore the correct absorption spectra for the ligand at different metal–ligand molar ratios are obtained by multiplying the concentration profile of the ligand by its molar absorptivity. By removing the ligand spectra from the original absorption data matrix, the rank of the residual matrix reduces by one.

Based on principal component analysis (PCA), the R.S.D. (Relative Standard Deviation) method is widely used to determine the number of principal components (Malinowski, 1991; Elbengali et al., 1999). The R.S.D. is a measure of the lack of fit of a principal component model to a data set. The R.S.D. is defined as:

(6)

R.S.D. (n) = {(\frac{\sum_{i = n + 1}^{c} g_{i}}{n (c - 1)})}^{1 / 2}

where

g_{i}

is the eigenvalue, n is the number of considered principal components and c is the number of samples. The R.S.D. was used as a formula to obtain the optimum stability constant. In an iterative procedure, different stability constants are put in Eq. (5) and different concentration profiles of ligand are obtained. The contribution of ligand is removed from the absorbance data matrix (with rank 2) for each obtained concentration profile of ligand, then according to R.S.D. equation (Eq. (6)) the sum of eigen values of the residual matrix is obtained from eigenvalue 2 to c (number of samples). If the rank of the residual matrix is reduced by one, the sum of eigen values from eigenvalue 2 to c will equal to noise level and minimum R.S.D. is obtained. So by scanning K_f values and estimating R.S.D. per each K_f, the optimum stability constant will be obtained when R.S.D. has its lowest value.

3 Experimental

3.1

3.1 Apparatus and materials

Absorption spectra were obtained with a Perkin-Elmer Lambda 45 UV–VIS spectrophotometer using 1 cm path length glass cells and the measurements were performed at (25 ± 0.1) °C. All experiments were performed with analytical reagent grade chemicals. The ligand was synthesized in the laboratory. Dimethylformamide (DMF), acetonitrile (AN), ethanol, and chloride salt of Co²⁺ were purchased from Merck (Darmstadt, Germany). All solutions were prepared fresh daily. All calculations were performed in MATLAB 6.5 (Math Works, Cochituate Place, MA) and Microsoft Excel 2003.

3.2

3.2 General procedure for synthesis of tripodal ligand (L_22py)

The asymmetrical tripodal ligand (Fig. 1) was prepared as its hydrochloride salt by us (Salehzadeh and Golbedaghi, 2007).

Structure of the tripodal tetradentate ligand investigated here.

3.3

3.3 Procedure

Stock solutions of ligand and metal ion salt were prepared as aqueous solutions. The analytical ligand concentration was kept constant and different concentrations of metal ions were added to the ligand solution. Then after 1 h the spectrum of solution was obtained between 200 and 600 nm with the 1 nm intervals. The analytical concentration of the ligand was considered as 1.04 × 10⁻⁴ (mol $\cdot$ L⁻¹) with different concentrations of metal in the range of 0.0–2.0 M ratio of metal to ligand. The concentrations of metal were considered as: (1) 0.0, (2) 1.04 × 10⁻⁵, (3) 1.98 × 10⁻⁵, (4) 2.91 × 10⁻⁵, (5) 3.95 × 10⁻⁵, (6) 5.93 × 10⁻⁵, (7) 9.98 × 10⁻⁵, (8) 1.2 × 10⁻⁴, (9) 1.6 × 10⁻⁴, (10) 2.0 × 10⁻⁴ (mol $\cdot$ L⁻¹).

The molar ratio method was used to determine the stoichiometry of the metal–ligand complex and the RAFA program was used to calculate the complex formation constant.

4 Results and discussion

4.1

4.1 Simulated data

Fig. 2 shows the created absorption spectra for a 1:1 metal–ligand complex formation system, at a fixed concentration of ligand and various concentrations of metal ion.

Simulated absorption spectra of a 1:1 metal–ligand complex formation system at a fixed concentration of ligand and various concentrations of metal ions. log Kf = 4.74, λ max ( L ) = 450 nm, λ max ( ML ) = 480 nm.

Table 1 presents the eigenvalues, ratios of consecutive eigenvalues and R.S.D. of the simulated matrix. The synthetic data matrix was processed by the RAFA method and the relationship between the R.S.D. of the residual matrix and the stability constant (K_f) is shown in Fig. 3. A minimum is observed in the R.S.D. curve shown in Fig. 3 which indicates the optimum value of log K_f. The applied noise was $\pm 0.1 %$ absorbance units.

Table 1 The results of PCA on simulated data.

i	$g_{i}$	$g_{i} / g_{i} + 1$	R.S.D.
1	2530.4	9.94000	7.130
2	254.60	5.30416	0.013
3	0.00048	1.11000	0.009
4	0.00043	1.07500	0.006
5	0.00040	1.08000	0.003
6	0.00037

The relationship between R.S.D. and stability constant, Kf, 1:1 complexation system obtained log (Kf) = 4.74.

As seen in Table 1, the ratio of two consecutive eigenvalues is too large at the second eigenvalue, so there are two principle components (absorptive species) in the simulated matrix. This method was also used to determine the number of principle components in the experimental absorbance matrices.

4.2

4.2 Real data

Fig. 4 shows the experimental absorption spectra for the complex of Co²⁺ and the investigated ligand when the ligand concentration is constant and the metal concentration is varied. PCA results showed that there are two principal components in the absorbance data matrix. The relationship between R.S.D. and K_f for cobalt experimental data after processing RAFA on the absorption matrix is shown in Fig. 5.

Experimental absorption spectra for the Co2+ complex with ligand. The analytical concentration of ligand is 1.04 × 10−4 (mol · L−1) with different concentrations of metal in the range of 0.0–2.0 M ratio of metal to ligand. The concentration of metal is: (1) 0.0, (2) 1.04 × 10−5, (3) 1.98 × 10−5, (4) 2.91 × 10−5, (5) 3.95 × 10−5, (6) 5.93 × 10−5, (7) 9.98 × 10−5, (8) 1.2 × 10−4, (9) 1.6 × 10−4, (10) 2.0 × 10−4 (mol · L−1).

The relationship between R.S.D. and stability constant, Kf for the cobalt complex.

As seen in Fig. 5, the estimated complex formation constant after processing RAFA on absorbance data matrix of Co²⁺ was obtained as 1.24 × 10⁵ L mol⁻¹.

The effect of the type of solvent was investigated on the formation constant of Co²⁺ complex. 10 volume percent of solvent was considered as ethanol, DMF and AN, then the formation constant was obtained. Table 2 shows the results. In 10 volume percent of DMF and AN, the stability constant of the complex decreases. It is well known that the Gutmann donor number and dielectric constant of solvents (Gutmann, 1968) is an important measure in complexation reactions. It is obvious that the stability of complex increases significantly by decreasing the donor number of the solvents and since DMF and AN have lower donor number with respect to water the complex formation constant of the complex decreases in these solvents. Dielectric constant of a solvent is the ability of that solvent to separate ions with different charges. Dielectric constant of the mixture of solvents is lower than water and it causes the dissociation of ions which is more difficult and therefore the stability constant decreases. In 10 volume percent of ethanol, the formation constant of complex reduces because of lowering dielectric constant of mixture of solvents.

Table 2 The results of K_f for Co–Ligand complex in 10 volume percent of different solvents.

Solvent	Water	10% DMF	10% AN	10% ethanol
log K_f	5.09 ± 0.02	4.95 ± 0.02	4.96 ± 0.01	5.04 ± 0.01

L, Ligand.

5 Conclusions

RAFA is proposed as an efficient chemometric algorithm for the complete analysis of complex formation systems by the spectrophotometric molar ratio method. The RAFA is based on the principle that the rank of a two-way bilinear matrix of pure compounds is one. The proposed method makes it possible to obtain the stability constants, pure absorption spectra and species concentration profiles in several ligand–metal complex formation systems when there is severe spectral overlapping.

The method was tested with simulated data sets and reliability was obtained by reproducing the input formation constants and species concentration profiles. The method was also applied to experimental data in 1:1 metal–ligand complex formation. The investigated ligand forms 1:1 complexes with Co²⁺.

Acknowledgements

The authors are grateful to the Payame Noor University for financial support.

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