Malic acid, Chrome Azurol S, Gd(III) nitrate and other chemicals were commercial products (Aldrich, Prolabo,…) of the purest available and analytical grade, used as received.

A standard Helios UV-visible spectrum-eter controlled by Vision 32 software was used for spectrometric measurements, using quartz cells of optical path length. The absorption measurements have been performed at room temperature and at wavelength. Stock solutions of Gd(III) nitrate and Chrome Azurol S, prepared with concentrations of respectively and. In a typical experiment, a solution () of the colored sacrificial complex was prepared

using as a buffer of MESH (0.1 M) [2-(N-morpholino) sulphonic ethane acid]. The initial solution also contained a calculated amount of 1 M NaOH in order to obtain the desired pH value, experimental pH range (5.5 - 7.5). pH values are measured with a Microprocessor pH Meter HANNA 210 equipped with a combined glass electrode and calibrated with comercial buffers (pH 4.00 and 7.00). Then aliquots of an aqueous solution of the malic acid were added, using a Gilson micropipet of 0.200 mL. After each addition, the resulting solution was left at least 5 min in order to reach equilibrium (and thus a constant absorption value). Addition was repeated until a maximum volume of 2.00 mL of the organic acid solution was added. The change in the total volume was neglected. For fixed pH environments, the apparent formation constants was calculated using a laboratory made computer program. The absorption values for the undissociated and the totally dissociated, sacrificial complex, are used as determined in experiments using pure Chrome Azurol S, and an excess of Gadolinium(III) (performed at pH intervals of 0.20). Assuming various integers for the Gadolinium and organic acid stoichiometry, a formation constant is calculated for each added amount of ligand and corresponding absorption value. The results are rejected when a systematic variation of occurs with increasing added amount of ligand or when individual values of differed from the mean value by more than 2%.

Samples were prepared by weighing the appropriate amount of malic acid (ligand) and adding, mixing and finally adjusting the pH with concentrated HCl or NaOH and concentrations of analyzed samples are 10⁻³ M. Analyses were performed using an infrared spectrometer, Fourier transform (FT-IR), Perkin Elmer BX, equipped with a DTGS detector, a splitter and a cesium iodide window. In this configuration, the interval of analysis is that the middle infrared, 6000 cm⁻¹ to 250 cm⁻¹ and analysis are conducted on small samples, whose size is less than 1 mm³. Liquid samples are placed between two plates of very pure salt (KBr), these plates are transparent to infrared light and the spectra relative to free ligand (malate ion) and complexed, have been plotted for frequencies from 4400 cm⁻¹ to 400 cm⁻¹.

The complex is precepts quickly at room temperature, at a concentration of 10^{−2 M} and fixed pH value (5.86) (Higher than the acidity constant of malic acid). The precipitate was filtered and dried in drying oven and the complex formed is insoluble in water, methanol and ethanol. The Raman spectra of the ligand (Malic acid) and its new Gd(III) complex was performed using an Fourier transformation Raman spectrometer (FT-Raman) VERTEX 70 with a range of measurement (4000 - 50) cm⁻¹, laser source NdYag (1.064 µm), a nominal power of 500 MW, detecting Ge with high sensitivity and a resolution of 4 cm⁻¹ (64 scan). The spectra relative to free malic acid and Gd(III)-carboxylate complex, have been plotted for frequencies from 3600 cm⁻¹ to 200 cm⁻¹.

The complexation reaction of x gadolinium ions with y malate ions and z protons, is given by expression (I):

represents the ligand (malate ion).

The formation constant (or stability constant of the complex is defined as the equilibrium constant :

Additionally, a conditional equilibrium constant is defined in case of constant pH value (buffered solution):

represents the analytical concentration of the uncomplexed ligand, all experiments are performed for pH values higher than and of malic acid, therefore, we have. Using this equality, Equation 1 can be written as:

Thus               (4)

The complexation of the ligand can be studied using a spectrophotometric method. Since the reagent (malic acid) and its detected gadolinium complex do not possess a characteristic UV-visible absorption spectrum, a second ligand (called the sacrificial ligand) is introduced. This second ligand must absorb in the UV-visible spectrum and form a colored complex with ions. Based on ligand-ligand displacement, the photometric method is said to be in the indirect mode. The dissociation of this colored complex has to cause large variations in the UVvisible spectrum which allow the calculation of the concentration of the sacrificial complex. Using the formation constant of this colored complex, the concentration of the unknown complex can be obtained. Therefore, the sacrificial ligand must form a single colored complex of lower stability than the gadolinium complex under study. In this work, 3”-sulfo-2”,6”-dichloro-3,3’-dimeth-yl-4’-hydroxy-fuchsone-5,5’-dicarboxylic acid, often called Chrome Azurol S and noted, has been used as sacrificial ligand. Chrome Azurol S is a tetraprotic acid with pKa values of 2.25, 4.71 and 11.82 [13]. In the experimental pH range (5.5 - 7.5), the formation of, and has been neglected. It is an indicator which is generally used for the photometric proportioning of the metal ions in solution [14,15]. The interaction of the with gadolinium ions (), gives a coloured reagent (l_max = 545 nm) of average stability for values of pH ranging between 5.50 and 7.50. The buffer “MESH”. [2-(N-morpholino) sulphonic ethane acid] was adopted to fix pH in the study of the sacrificial complex and the detected gadolinium-malate complex. We chosed this buffer because it does not present any interaction with ions and so that we would be able to work in range of pH where the stability of the sacrificial complex is maximal.

3.2. Formation of the Colored Sacrificial Complex

A series of experiments was conducted to determine, the composition, the stability of the colored sacrificial complex () and its formation reaction. Indeed, in 50 cm⁻³ of the auxiliary ligand solution of a concentration and pH = 5.91, we introduced increasing quantities of a ions solution of initial concentration 10^{−2 M}. The evolution of UVvisible spectra for the formation of this sacrificial complex is represented by the diagram in following Figure 1.

The UV-visible spectra show clearly that the maximum absorbance of the sacrificial complex is located at. So, we have studied the formation of this sacrificial complex at this maximum wavelength, depending on the ratio

as shown in the Figure 2.

The curve in Figure 2 indicates that the value of the ratio q, relative to the complete formation of this sacrificial complex is the intersection of the linear (positive slope), with the final segment (slope = 0) of the curve, this value of q is close to 1.50. This indicates that the

formation of the sacrificial complex is according to the following balanced reaction:

represents the analytical concentration of ligand in all its forms, z the number of protons involved during the reaction, while is the coefficient of complex formation, calculated from the experimental values of absorbance by the relation , with and which respectively represent the initial absorbance (free ligand) and final (100% of the complex).

Therefore, the expression of the apparent constant on the formation reaction according to the balanced reaction (II) is given by the following equation :

is calculated using a computer program written from the balanced reaction (II), we obtained constant values of for the pair for all experimental points, with a value of at. Under the same conditions of temperature and concentrations, several experiments were performed for pH values between 5.50 and 7.50. The same calculation program was used and the results clearly indicate that only the detected sacrificial complex, is formed in solution. For all studied solutions at known values of pH, the apparent constants were calculated and the obtained results are summarized in the Table 1. These results show that the stability of the sacrificial complex depends on the acidity of the medium.

For all these solutions, the formation constant on the sacrificial complex is given by the relationship. Hence, (conditional constant for a given pH), we plot the curve depending on the medium pH (Figure 3), and the slope value is the equivalent number of

ions that react, with 1.5 equivalents of ions and 1 equivalent of ions (composition adopted to make simple calculations). The linear function shown in Figure 3, clearly verifies the accuracy of the studied relationship, and its slope, calculates the equivalent number of hydronium ions, involved in the formation reaction of the detected gadolinium complex, and hence determines it exact composition, whereas the intercept expresses the stability constant of this sacrificial complex, with at V.

Thus, the complexation of ions by ions in the pH range 5.50 to 7.50, led to the formation of the colored tri-nuclear complex, by following balanced reaction:

The formation constant of this complex is defined as:

The conditional equilibrium constant for a fixed value of pH is given by:

Table 1. Evolution of the sacrificial complex stability, depending on the acidity of the medium.

If the studied ligand (malate ions), is added to a colored solution of the sacrificial complex, this chrome azurol S () complex will dissociate. To calculate the complexed concentration of the ions, the absorption values of the totally complexed, and completely dissociated ions have to be determined. Then the following equations can be used:

When the conditional equilibrium constant of the sacrificial complex is known, the concentration of free gadolinium ion (), can be calculated using Equations (7)-(9).

Knowing and, the concentration of the gadolinium complex under study (balanced reaction I) can be determined using the gadolinium mass balance equation :

being the initial gadolinium concentration. In a similar way, the concentration of the free ligand is obtained by

It should be also noted that a perfect knowledge of the characteristics of the sacrificial colored complex is necessary. The determination of the composition and the stability of the sacrificial complex and the precision of the conditions of its formation are paramount stages to apply the indirect photometry technique. In each experiment, the ligand (malate ions), is added stepwise in order to measure the absorption at different values (at least 12) of the overall initial concentration of this studied ligand. The correct is looked for by varying x and y in order to obtain a constant value for all values of. If is determined at different pH values, the slope of the. pH plot reveals the number z of protons, necessary for the formation of the studied gadolinium complex by use of equation 4, since the value of is independent of pH. Now the stability and the total composition of the gadoliniummalate complex have been determined.

With an aim of determining the composition and the stability constant of the gadolinium-malate complex, we monitored the evolution of the absorbance during disappearance of the sacrificial complex by addition of increasing quantities of malate ions. For a given volume (50 ml) of a solution containing sacrificial complex 10^{−2 M}, we added increasing quantities of malate ions solution, with known concentration. The spectrophotometric study carried out with fixed wavelength, showed a reduction in the absorbance of the solution progressively with the addition of the malate ions (Figure 4). The dissociation of the sacrificial complex, relating to the reduction in the absorbance by the addition of malate ions solution, is done in favour of the formation of the colourless complex between and malate ion species.

The curve in Figure 4, clearly shows that the absorbance decreases and stabilizes. This stability indicates that all ions, initially present in the solution have reacted with added malate ions. Knowing the concentration of gadolinium ions and the quantity of ligand from the added volume of the malic acid solution, necessary to reach this stage of absorption, we could determine the molar ratio q , involved in the complexation reaction. The preceding experiment was carried out for different values of pH between 5.50 and 7.50, the way in which the absorption decreases, depends on the pH of the medium and on the formation constant of the detected complex (Gd-malate), as well as on the absorption values () and () of the free and totally complexed Chrome Azurol S (). Analyzing the experimental data with the computer program written from the balanced reaction (I), the results confirm the reproducibility of the molar ratio q and to determine the composition and apparent stability constant (Table 2). The data-processing treatment of the preceding experimental results, shows that this tri-nuclear detected complex

Table 2. The apparent stability of the tri-nuclear detected complex, depending on the acidity of the medium.

formed between the gadolinium ions and malate ions, resulting from the interaction of three ions equivalents with two equivalents of malate species, so a molar ratio.

Buffer, , ,

,

For all pH range we obtained, therefore, for the complexation reaction of ions with malate ions at this pH range, these results and the Equations (1)-(3) allow to write the following expressions:

The value of z can be positive, negative or null. The stability constant of this formed complex is defined by:

Conditional stability constant is defined in case of constant pH value (buffered solution):

For these experimental pH values higher than the and of malic acid, thus:

And

The evolution of at different pH values is represented on Figure 5, this evolution is linear and the slope of the straight line is equal to −2. The value () represents the number of protons involved in the formation reaction of this new tri-nuclear complex

(Gadolinium-Malate) species.

The IR spectroscopic studies can identify different groups of malic acid (ligand), which participate in chelation sites for the formation of the detected gadolinium complex. Three dilute solutions (10⁻¹ cm), respectively, the free malate ion, free malic acid (pH = 2.02) and detected gadolinium complex of malate ion (pH = 5.60), were prepared and their spectra recorded (Figure 6) and analyzed. Table 3 contains bibliographic data [17, 18], relative to vibrations intervals of various groups: OH, C=O, COO⁻ and C-C=O, and the intervals of vibration on the analyzed spectra (1, 2 and 3).

The experimental spectra obtained for the three analyzed samples, clearly indicate that the frequency for vibration of the groups: OH, C=O and COO⁻, have

Table 3. The vibration frequencies, for the studied spectra and bibliographic data.

seriously reduced 75%, 80% and 66% passing the free to complexed ligand (Figure 6). So, for each of the two malate ions involved in the formation of this detected tri-nuclear complex, the four oxygen atoms of the ionized carboxylic groups, participate in chelation sites, and the OH group in a position of the ionized group COO⁻.

FT-Raman spectra of free malic acid and its complex with Gadolinium ions, are shown in Figure 7. A detailed analysis of vibrations in Raman spectroscopy was performed on the basis of comparison of experimenttal vibrational spectra obtained of malic acid and its gadolinium complex. The Raman spectra obtained show that the OH vibrations 3350 ± 104 cm⁻¹ [12,19] and the free malic acid present two vibrations of C=O at 1677 cm⁻¹ and 1635 cm⁻¹ because the malic acid present two carbonyl functions aren’t the same environment [19,20], these vibrations of OH and C=O groups, were not detected in the complex spectra and the vibration of C-C=O group is reduced from free malic acid to its gadolinium complex. So, all oxygen atoms involved in the chelation sites of this new tri-nuclear complex.

The vibration spectra (weak broad) of the complex in 1600 cm⁻¹, indicate the existence of water molecules [21], the intense vibration observed in the complex near 1069 cm⁻¹ indicate the existence of the nitrate ions [12]. The new band vibrations related to Gd(III)-Oxygen carboxylate functions, are located at 600 and 547 cm⁻¹ with a weak bands [21,22], and the strong vibration of Gd(III)- oxygen nitrate appeared at 187 cm⁻¹ [23]. The different vibrations (stretching and deformation) of C-C (aliphatic chains) appeared in a long field (1400 - 400 cm⁻¹) with intense and medium intensities [21,20,24]. Bands in the 2590 ± 80 cm⁻¹ region were assigned to the vibrations of CH and CH₂ [25,26], these bands are moderate intensities in complex spectra These results clearly indicate that, this new tri-nuclear gadolinium complex contains two types of sites, a single central bidentate mono-nuclear site with participation of only OH groups in a position and two lateral tetradentate mono-nuclear sites, each consisting of four oxygen atoms of two ionized carboxylic functions, belonging to the two malate ions (⁻OOC-CHOH-COO⁻), involved in the formation of this new detected gadolinium organometallic complex. Indeed, all these results can offer for this trinuclear Gd-Malic acid, the structure presented in Figure 8.