Journal of Thermodynamics

Volume 2012 (2012), Article ID 109132, 10 pages

doi:10.1155/2012/109132

Research Article

Conductometric Studies of Thermodynamics of Complexation of Co²⁺, Ni²⁺, Cu²⁺, and Zn²⁺ Cations with Aza-18-crown-6 in Binary Acetonitrile-Methanol Mixtures

Mehdi Taghdiri, Mahmood Payehghadr, Reza Behjatmanesh-Ardakani, and Homa Gha'ari

Department of Chemistry, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran

Received 2 August 2012; Revised 16 October 2012; Accepted 16 October 2012

Academic Editor: Perla B. Balbuena

Copyright © 2012 Mehdi Taghdiri et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

The complexation reactions between aza-18-crown-6 (A18C6) and Co²⁺, Ni²⁺, Cu²⁺, and Zn²⁺ ions were studied conductometrically in different acetonitrile-methanol mixtures at various temperatures. The formation constants of the resulting 1 : 1 complexes were calculated from the computer fitting of the molar conductance-mole ratio data at different temperatures. Selectivity of A18C6 for Co²⁺, Ni²⁺, Cu²⁺, and Zn²⁺ cations is sensitive to the solvent composition. At 20°C and in acetonitrile solvent, the stability of the resulting complexes varied in the order but the order was reversed byadding 20% methanol. The enthalpy and entropy changes of the complexation reactions were evaluated from the temperature dependence of formation constants. It was found that the stability of the resulting complexes decreased with increasing methanol in the solvent mixture. The TΔS° versus ΔH° plot of thermodynamic data obtained shows a fairly good linear correlation indicating the existence of enthalpy-entropy compensation in the complexation reactions. In addition, binding energies of Ni²⁺, Cu²⁺, and Zn²⁺ complexes with A18C6 were calculated at B3LYP/6-31G level of theory.

1. Introduction

Macrocyclic polyethers (crown ethers), first prepared in the 1960s [1], constitute an important class of host molecules that have found broad application to studies of molecular recognition and inclusion phenomena [2]. They are macrocycles capable of ion encapsulation due to their cage like structures. The metal ion is held in the crown ether cavity by electrostatic attraction between the charged cation and dipoles created by the nonbonding electrons of donor atoms [3, 4]. The selectivity and stability of crown ethers are also influenced by their structural flexibility, the number and type of donor atoms on the cavity of the crown, and the solvation energy of the metal ion. Thus, compounds of this type have been used extensively for selective complexation and transport of cations, anions, and neutral molecules [5]. Macrocyclic crown compounds have gained a great deal of attention due to their wide applications in chemistry [6] such as microanalysis, sensing and separation of metal ions [7], and extraction of biogenic amines [8].

Aza-crown ethers have especially been focused on as useful ligands because of their versatility and applicability [8–11]. It was of interest to us to study the interaction of the various cations with aza-crown ethers. Since the nature of these compounds, the size of cavity, and solvent may strongly influence the stoichiometry and complexation of transition metal complexes in solution [6], the complexation reactions between aza-18-crown-6 (A18C6) (Figure 1) with Co²⁺, Ni²⁺, Cu²⁺, and Zn²⁺ ions were studied by conductometric in acetonitrile (AN) and different acetonitrile-methanol (MeOH) mixtures at various temperatures. The formation constants of the resulting 1 : 1 complexes were calculated from the computer fitting of the molar conductance-mole ratio data at different temperatures. Little work has been reported on the study of the stability of transition and heavy metal ion complexes with A18C6, mainly in binary solvent mixtures [12–14]. Thus, studies of complexation reactions as a function of the solvent composition in binary solvent mixtures might be used to investigate the factors contributing to the changes in complexation stability and selectivity of the resulting complexes [11–13]. It should be noted that AN and MeOH have different Gutmann donor numbers, (DN) (i.e., for AN, DN = 14.1, and for MeOH, DN = 19.0) [15]. The Gutmann donor numbers are a measure of the electron-donating properties of a solvent. The donor number is defined as the negative enthalpy value for the 1 : 1 adduct formation between a given electron-pair donor solvent and the standard Lewis acid SbCl₅, in dilute solution in the non-coordinating solvent 1,2-dichloroethane, for which a DN of zero is assigned. DN reflects the ability of the solvent to solvate cations and other Lewis acids. DN values range from zero, for solvents like hexane or tetrachloromethane, to 61.0 for triethylamine. In general, it is observed that the smaller the values of DN, the more stable the cation-crown ether complex [6].

Figure 1: Structure of aza-18-crown-6.

2. Experimental

Reagent-grade nitrate salts of cobalt, nickel, copper, and zinc, dried acetonitrile (H₂O < 0.005%) and methanol (all from Merck) were of the highest purity available and used as received. A18C6 was purchased from Fluka. All the AN-MeOH mixtures used were prepared by weight.

Conductance measurements were carried out with a Metrohm 712 conductivity meter. A dip-type conductivity cell made of platinum black was used. The cell constant at the different temperatures used was determined by conductivity measurements of a 0.010 M solution of analytical-grade KCl (Merck) in triply distilled deionized water. The specific conductance of this solution at various temperatures has been reported in the literature [16]. In all measurements, the cell was thermostated at the desired temperature ±0.1°C using a Haake D1 thermostat-circulator water bath.

In a typical experiment, 10 mL of the desired metal ion (5.0 × 10-5 M) was placed in the titration cell, thermostated to the desired temperature and the conductance of solution was measured. Then, a known amount of a concentrated A18C6 solution (5.0 × 10-3 M) was added in a stepwise manner using a calibrated micropipette. The conductance of the solution was measured after each addition. The ligand solution was continually added until the desired ligand to cation mole ratio was achieved. The dilution of the salt solution during the titration is negligible because the total volume of added concentrated A18C6 solution is 300 μL. Therefore, the conductance changes during the titration due to the dilution are very negligible and are neglected.

NMR spectra in deuterated acetonitrile (CD₃CN) were recorded on a Bruker Avance 300 spectrometer, and all chemical shifts are reported in δ units downfield from Me₄Si. In a typical measurement, 0.5 mL of ligand solution (0.02 M) in CD₃CN was placed in the 5 mm BBO NMR tube and the spectrum was recorded. Then a known amount of a concentrated solution of zinc nitrate (0.2 M) in CD₃CN was added in a stepwise manner using a 10-μL Hamilton syringe and the spectrum of the solution was recorded after each addition. The zinc ion solution was continually added until the desired cation to ligand molar ratio was achieved.

The formation constants, , and the limiting molar conductances, , of the resulting 1 : 1 complexes between A18C6 and the cations used, in different AN-MeOH mixtures and at various temperatures, were calculated by fitting the observed molar conductance, , at varying [A18C6]/[M²⁺] mole ratios to a previously derived equation [6, 17, 18] which expresses the as a function of the free and complexed metal ions. A nonlinear least squares curve fitting using Microsoft Excel Solver (version 11.0) was applied for the evaluation of formation constant and limiting molar conductance of the resulting 1 : 1 complexes. The large formation constant values () can be determined by this method.

Chi-square statistic was used to evaluate the fitness of equation to the experimental data. The Chi-square test statistic is the sum of the squares of the differences between the experimental data and data obtained by calculating from equation. The equivalent mathematical statement is

where and are the molar conductance obtained by experimental data and calculating from the equation, respectively. If calculated data are similar to the experimental data, will be a small number; if they are different, will be a large number.

3. Results and Discussion

The conductometric method has been extensively used for obtaining the formation constants of complexes of crown ethers with metal cations [6]. In order to evaluate the influence of adding A18C6 on the molar conductance of Co²⁺, Ni²⁺, Cu²⁺, and Zn²⁺ ions in different AN-MeOH mixtures, the molar conductance at a constant salt concentration was monitored while increasing the crown ether concentration at various temperatures. Some of the resulting molar conductances versus A18C6/cation mole ratio plots are shown in Figures 2 and 3.

(a)

(b)

(c)

(d)

Figure 2: Molar conductance (S cm2 mol⁻¹) versus [A18C6]/[M²⁺] mole ratio plots in 100% AN at various temperatures. The M²⁺ cations are (a) Co²⁺, (b) Ni²⁺, (c) Cu²⁺ and (d) Zn²⁺.

(a)

(b)

(c)

(d)

Figure 3: Molar conductance (S cm2 mol⁻¹) versus [A18C6]/[M²⁺] mole ratio plots in AN-MeOH (80 : 20) mixture at various temperatures. The M²⁺ cations are (a) Co²⁺, (b) Ni²⁺, (c) Cu²⁺, and (d) Zn²⁺.

As it is seen, in all cases, there is a gradual increase in the molar conductance with an increase in the crown ether concentration. Figure 2 shows that, in the case of all M²⁺-A18C6 system in AN solvent, the addition of A18C6 to the M²⁺ ion solution causes a continuous increase in the molar conductance, which begins to level off at a mole ratio greater than one. Such a conductance behavior is indicative of the formation of fairly stable 1 : 1 complexes in AN.

The formation constants of all A18C6-M²⁺ complexes in different solvent mixtures at various temperatures, obtained by computer fitting of the molar conductance-mole ratio data and Chi-square values (χ ²), are listed in Table 1. The computer fits of the molar ratio data are shown as solid lines. The small numbers of Chi-square indicate that our assumption of 1 : 1 stoichiometry seems reasonable in the light of the fair agreement between the observed and calculated molar conductances.

Table 1: Formation constants for different M²⁺-A18C6 complexes in various AN-MeOH mixtures.

Cationa
wt% AN
Log

10°C

20°C

30°C

40°C

Co²⁺ (1.50)
100
5.66
0.76
5.50
1.11
5.27
1.48
5.19
1.69

80
3.87
1.60
3.89
1.95
3.79
1.87
3.90
2.41

60
2.82
0.10
2.90
0.15
2.98
0.25
2.91
1.35

40
2.83
0.11
2.87
0.14
2.83
0.15
2.86
0.25

Ni²⁺ (1.38)
100
5.47
0.54
5.49
0.60
5.28
0.63
5.05
0.72

80
3.73
1.09
3.91
1.81
3.95
2.14
4.00
2.72

60
2.90
0.12
2.94
0.18
3.06
0.69
3.14
0.44

40
2.96
0.17
2.99
0.21
3.01
0.23
3.06
0.30

Cu²⁺ (1.54)
100
7.44
0.09
7.77
0.07
7.48
0.09
7.63
0.07

80
3.39
0.71
3.47
0.94
3.53
1.16
3.63
1.73

60
3.11
0.31
3.14
0.37
3.17
0.45
3.20
0.77

40
3.08
0.30
3.06
0.29
3.03
0.27
3.02
0.28

Zn²⁺ (1.48)
100
15.27
0.64
14.60
0.29
14.33
0.07
14.07
0.01

80
3.25
1.43
3.31
1.72
3.44
2.99
3.46
3.17

60
2.96
0.75
3.04
0.79
3.13
1.31
3.18
1.66

40
1.44
1.82
1.93
0.008
2.44
0.12
2.82
0.75

aThe values in parenthesis are the ionic sizes in Å [19].

In order to have a better understanding of the thermodynamics of complexation reactions of Co²⁺, Ni²⁺, Cu²⁺, and Zn²⁺ ions with A18C6, it is useful to investigate the enthalpic and entropic contributions to these reactions. The ΔH° and ΔS° of the complexation reactions in different AN-MeOH mixtures were evaluated from the temperature dependence of the formation constants by applying a linear least-squares analysis according to the van’t Hoff equation. The van’t Hoff plots of versus are shown in Figure 4. The enthalpies and entropies of complexation were determined in the usual manner from the slopes and intercepts of the plots, respectively and the results are listed in Table 2.

Table 2: Thermodynamic parameters for different M²⁺-A18C6 complexes in various AN-MeOH mixtures.

Cation
wt% AN
(kJ mol⁻¹)
(J mol⁻¹ K⁻¹)
(kJ mol⁻¹)

Co²⁺
100

80a

60b

40c

Ni²⁺
100

80

60

40

Cu²⁺
100
—d
—d
—d

80

60

40

Zn²⁺
100e

80

60

40

aWithout considering Log  at 30°C.

bWithout considering Log  at 40°C.

cWithout considering Log  at 20°C.

dHigh uncertainty.

eWithout considering Log  at 10°C.

(a)

(b)

(c)

(d)

Figure 4: van’t Hoff plots for the 1 : 1 complexation of Co²⁺ (a), Ni²⁺ (b), Cu²⁺ (c), and Zn²⁺ (d) with A18C6 in different solvent mixtures.

In the case of complexation of macrocyclic ligands, there are many factors which can make significant contributions to the stability of their metal ion complexes: the cation size, the ionic solvation of the charged species involved, conformations of the free and complexed crown ethers, the electronic structure of metal ion and the binding strengths of solvent-ion and crown-ion. Moreover, the changes of the enthalpy and entropy influence the stability constant. Many factors contribute to changes in enthalpy and entropy of complexation reactions. It seems that solvent properties such as donor number, relative permittivity (dielectric constant) and their dipole moments influence upon the enthalpy and entropy.

The data given in Table 1 clearly illustrate the fundamental role of the solvent properties in the M²⁺-A18C6 complexation reactions studied. The stability of the resulting complexes decreases strongly with increasing weight percent of MeOH in the solvent mixture (Figure 5). It is well known that the solvating ability of the solvent, as expressed by the Gutmann donor number [15], plays an important role in different complexation reactions [4, 16, 18, 20, 21]. There is actually an inverse relationship between the stabilities of the complexes and the solvating abilities of the solvents. Methanol has a higher donicity (DN = 19.0) than acetonitrile (DN = 14.1) and, therefore, shows more competition with the crown ether for mentioned ions; thus, it is not unexpected to observe that addition of methanol to acetonitrile will decrease the stability of the complexes. In addition, selectivity for certain cations over others may be altered according to the nature of solvent. The order of stability of complexes in pure AN at 20°C is Zn2+ > Cu2+ > Co²⁺~Ni²⁺. It is interesting to note that the order of the stability of the complexes formed between A18C6 and these metal cations in AN-MeOH (wt% MeOH = 20) binary mixtures is reversed. This reversal of stabilities indicates the selectivity of macrocyclic ligands is sensitive to the solvent composition and may change in certain composition of the mixed solvent systems. A reversal in stabilities has been observed for -A18C6 ( = Ag⁺, Hg²⁺ and Pb²⁺) in DMSO-H₂O binary mixture [13]. The selectivity of complexation not only depends on the ratio of the cation diameter and the diameter of the crown ether cavity, but also on the solvent composition. The change of solvent composition influences upon the changes in complexation enthalpies and entropies and hence the selectivity of the crown ethers towards cations. It seems that solvent properties such as donor number, dielectric constant and the isosolvation point (the point at which both solvents participate equally in the inner salvation shell of the cation [22]) contribute to the changes of enthalpy and entropy as a function of solvent composition.

(a)

(b)

(c)

(d)

Figure 5: Variation of the stability constants of various A18C6-M²⁺ systems with the composition of the AN-MeOH binary mixture at different temperatures. The M²⁺ cations are (a) Co²⁺, (b) Ni²⁺, (c) Cu²⁺, and (d) Zn²⁺.

Table 2 shows that, as expected, for M²⁺-A18C6 systems studied, the thermodynamic data vary significantly with the solvent properties. However, the observed increase (or decrease, depending on the nature of the metal ion) in ΔH° value upon addition of MeOH to the solvent mixture will be compensated by an increase (or decrease) in the corresponding ΔS° value. The existence of such a compensating effect (Figure 6) between ΔH° and ΔS° values, which has been frequently reported for a variety of metal-ligand systems [23–25], would cause the overall change in the ΔG° value of the complex to be smaller than might be expected from the change in either ΔH° or ΔS° independently. There is an entropy-driven stabilization for Co²⁺, Ni²⁺, Cu²⁺, and Zn²⁺ complexation in AN-MeOH mixtures. These cations have small ionic sizes (Table 1) and are strongly solvated by MeOH. Therefore, complete or partial desolvation of cations and ligand are important steps of complexation process and seems to be mainly responsible for increasing of entropy.

Figure 6: Plot of TΔS° (kJ mol⁻¹) versus ΔH° (kJ mol⁻¹) for 1 : 1 complexation of Co²⁺, Ni²⁺, Cu²⁺, and Zn²⁺ ions with A18C6 in different AN-MeOH binary mixtures ().

The stability constant between Zn²⁺ and A18C6 is much greater in AN than other studied cations. It also shows a slight decrease in the molar conductance after the mole ratio of one (Figure 2(d)). Therefore, the ¹H NMR spectra of a 0.02 M solution of A18C6 in deuterated AN in the presence of increasing concentration of zinc nitrate were recorded (Figure 7(a)). The resulting chemical shift versus metal ion to ligand mole ratio (shown in Figure 7(b)) revealed a distinct inflection point at a mole ratio of 1 : 2, indicating the formation of a ML₂ complex in solution. A sandwich type complex has been proposed for biphenyl containing A18C6 with Zn²⁺ from ¹HNMR, UV visible and fluorescence observations in AN [9]. The ML₂ complexes have been also proposed for 18C6-Cu²⁺ in methanol [26], A18C6-Pb²⁺ in H₂O, A18C6-Ag⁺ in DMSO-H₂O [13], and immobilized DB18C6-Zn²⁺ [27].

(a)

(b)

Figure 7: (a) The ¹HNMR spectra of A18C6 ligand in the presence of increasing concentration of Zn²⁺ ions in deuterated AN and (b) chemical shift versus [Zn²⁺]/[A18C6] plot.

An attempt was made to obtain more information from the quantum chemical calculations about the structures of both free and complex forms of A18C6. To do this, the initial structures of compounds were built with HyperChem 7.0 program [28]. All calculations were done with Gaussian 2003 suit of programs [29] on an Intel SMP computer with 8 processors and 8 GB of RAM. B3LYP/6-31G level of theory was used for all optimization and frequency calculations. All computations were done in the gas phase. Full geometry optimization was used with no symmetry or any constraints about bond lengths, bond angles, or bond torsions. Figure 8 shows the optimized geometries of both free and metal ion complexes of A18C6. Frequency analyses were done to test whether the optimized structures are stationary points or saddle points. In all outputs, number of imaginary frequency was equal to zero. This indicates that all structures are true optimized forms. Table 3 shows binding energies for A18C6-cation complexation for three metal cations of Ni²⁺, Cu²⁺, and Zn²⁺. Despite many attempts, we could not obtain binding energies for A18C6-Co²⁺. All binding energies are less than zero. It shows that all cations tend to form complex with A18C6 in the gas phase. It should be noted that these cations have relatively close ionic radii. The ML₂ structure for A18C6-Zn²⁺ (Figure 8(d)) indicates the strong interaction of Zn²⁺ with nitrogen atoms. The ¹HNMR study (Figure 7(a)) confirms this strong interaction. The ¹HNMR signal at δ = 2.17 ppm corresponding to N–H, disappears upon addition of Zn²⁺ to A18C6.

Table 3: Calculated electronic energies of different species and binding energies of complexes formed by interaction between A18C6 and Ni²⁺, Cu²⁺, and Zn²⁺. All calculations have been done with B3LYP/6-31G.

Compounds
Electronic energy (a.u.)
Binding energy (kcal/mol)a

A18C6
−903.07162832

Ni²⁺
−1507.14512292

Cu²⁺
−1639.396656

Zn²⁺
−1778.31513190

A18C6-Ni²⁺
−2410.87730681
−414.50

A18C6-Cu²⁺
−2543.10355707
−398.64

(A18C6)₂-Zn²⁺
−3585.13086395
−422.56

aBinding energy () is defined as = (complex)− E(Ligand)−E(Ion). 1 a.u. is equal to 627.5095 kcal/mol.

(a)

(b)

(c)

(d)

Figure 8: The optimized geometries of free A18C6 (a) and its complexes with Ni²⁺ (b), Cu²⁺ (c), and Zn²⁺(d).

4. Conclusions

From the conductometric results obtained on the thermodynamics of complexation of A18C6 with some transition metal ions in different AN-MeOH binary mixtures and quantum chemical calculations, the following can be concluded.

(1)The solvent illustrate the fundamental role in the M²⁺-A18C6 complexation reactions. In the case of all metal ions, the stability of the resulting complexes with A18C6 decreases and the order of stability vary with increasing MeOH in the solvent mixture. (2)Although the enthalpy and entropy changes are strongly solvent dependent, the observed increase (or decrease, depending on the nature of the metal ion) in ΔH° value upon addition of MeOH to AN will be compensated by an increase (or decrease) in the corresponding ΔS° value.(3)The quantum chemical calculations confirm the formation of stable A18C6-M²⁺ (M²⁺ = Ni²⁺ and Cu²⁺) and (A18C6)₂- Zn²⁺ complexes.

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