J . Phys. Chem. 1991, 95, 9601-9604
9601
NMR Study of the Stoichiometry, Stability, and Exchange Kinetics of Alkaline Earth Complexes with 18-Crown-6 in Some Nonaqueous Solutions Mohammad Kazem Amini and Mojtaba Shamsipur* Department of Chemistry, Shiraz University, Shiraz 332169, Iran (Received: February 8, 1991; In Final Form: May 14, 1991)
Proton NMR was used to study alkaline earth complexes with 18-crown-6 in nitromethane, acetonitrile,and dimethylformamide solutions. In all three solvents used, the stabilities of the resulting 1:l compiexes vary in the order Ba2+> Sr2+> Ca2+> Mg2+. There is an inverse relationship between the donicity of the solvents as expressed by the Gutmann donor numbers and stability of the resulting complexes. The dissociative kinetics of the complexes were studied by proton NMR line-shape analysis. The exchange reaction rates and the activation parameters E,, AH', AS', and AG' for the exchange have been determined and found to be strongly solvent dependent. There is a correlation between the donor number of the solvents and the logarithm of the dissociation rates as well as the activation parameters for a given cation.
Introduction Since Pedersen's discovery of macrocyclic crown ethers,l an extensive amount of research work has been reported on the thermodynamics and kinetics of their complexes with a variety of cations in different solvent^.^^^ Kinetic studies of macrocyclic complexation reactions with metal ions not only result in important information on the rate and mechanism of complexation reactions but also lead to a better understanding of the high selectivity of these ligands toward different cations. Despite the valuable chemical information which could be obtained from such investigations, studies of the kinetics of crown ether complexation reactions with alkaline earth cations are rather sparse, as compared with the reported thermodynamic data.3 Eyring and co-worker~~*~ have studied the complexation kinetics of Ca2+,Sr2+,and Ba2+ ions with 15-crown-5 and 18-crown-6 in aqueous solutions by an ultrasonic absorption technique. A stopped-flow study of the kinetics of Sr2+ion complexation by 18-crown-6 in methanol at -15 OC has also been reported by Cox et It was of interest to us to study the thermodynamics and especially the kinetics of the complexation of macrocyclic ligands with alkali and alkaline earth cations in different nonaqueous solvents. We have previously studied the complexation kinetics of alkali ions with macrocyclic ligands in various nonaqueous solutions by multinuclear N M R techniques.'-" In this paper we discuss a study of thermodynamics and kinetics of Mg2+,Ca2+, Sr2+,and Ba2+ complexes with 18-crown-6 in nitromethane, acetonitrile, and dimethylformamide solutions. The stoichiometry and stability of the resulting complexes were determined from the measurement of IH chemical shift of the ligand at different cation/ligand mole ratios in various solutions. Proton N M R was also used to determine the kinetic parameters of the complexation reactions. (1) Pedenen, C. J. J . Am. Chem. Soc. 1967,89, 7017.
(2) Lamb, J. D.;Izatt, R. M.; Christensen, J. J.; Eatough, D. J. In Coordination Chemistry of Macrocyclic Compounds; Melson, G. A., Ed.; Plenum: New York, 1979; Chapter 1. (3) Izatt, R. M.;Bradshaw, J. S.;Nielsen, S.A.; Lamb, J. D.; Christensen, J. J.: Sen, D.Chem. Reo. 1985,85, 271. (4) Liesegang, G.W.;Farrow, M. M.; Vazquez, F. A.; Purdie, N.; Eyring, E. M. J . Am. Chem. Soc. 1977, 99, 3240. ( 5 ) Rodriguez. L. J.; Liesegang, G. W.; Farrow, M. M.; Purdie, N.; Eyring, E. M. J . Phys. Chem. 1978.82, 647. (6) Cox, B. G.;Firman, P.; Schneider, H . Inorg. Chim. Acta 1982,64, L263. (7) Strasser, 9. 0.; Shamsipur, M.; Popov, A. I. J. Phys. Chem. 1985,89, 4822. (8) Shamsipur, M.; Popov, A. 1. J . Phys. Chem. 1986, 90, 5997. (9) Szczygiel, P.; Shamsipur, M.; Hallenga, K.; Popov, A. 1. J . Phys. Chem. 1987, 91, 1252. (IO) Shamsipur, M.; Popov, A. I. J . Phys. Chem. 1987, 91,447. ( 1 1 ) Shamsipur, M.; Popov, A. 1. J . Phys. Chem. 1988, 92, 147.
0022-3654/91/2095-9601$02.50/0
Experimental Section Reagents. Macrocyclic polyether 18-crown-6 (1 8C6, Merck) was precipitated as its acetonitrile complex;I2 the crystals were isolated and kept under vacuum at room temperature for at least 24 h to drive off the acetonitrile. Magnesium perchlorate was prepared by dissolving the metal (Merck) in perchloric acid. Calcium, strontium, and barium perchlorates were prepared from their carbonate salts (all from Merck) and perchloric acid. The resulting perchlorate salts were recrystallized several times from deionized water and dried in a vacuum oven at about 150 OC for 48 h. The salts were further dried at 200-250 OC under a flow of dry nitrogen for 24 h. Nitromethane (NM, Fluka) was dried over BaO and distilled at reduced pressure. Acetonitrile (AN, Merck) and dimethylformamide (DMF, Merck) were dried over molecular sieves and distilled at reduced pressure. The middle fraction of the distilled solvents was used in the experiments. NMR Meawrements. Proton NMR measurements were carried out on a Bruker AW-80 spectrometer a t a field of 18.79 kG. Temperature of the probe was adjusted with a Bruker temperature control unit using liquid nitrogen at low temperatures and a heating element a t high temperatures. To reach the equilibrium temperature, each sample tube was left in the probe for a t least 20 min before measurements. In all experiments, T M S was used as an internal standard. Dpta Hading. The formation constants of the complexes were calculated by fitting the observed 'Hchemical shifts a t various M2+/ 18C6 mole ratios to a previously derived equation" which expresses the observed shifts as a function of the free and complexed ligand and the formation constant by using a nonlinear least-squares program KINFIT." Line widths were measured by fitting a Lorentian function to the spectra. A complete line-shape analysis was conducted to determine the kinetic parameters for the exchange of 18C6 between the free and complexed sites, using the modified Bloch equations.I5 Equations used were of similar format to those used by Cahen et a1.I6 The KINFITprogram was used to fit 50-100 points of the spectra to the N M R exchange equations to extract the mean interaction lifetime, T , for each system at several temperatures. Results and Discussion Stoichiometry and Stability. The variation of the proton resonance frequency of 18C6 was measured in different solvents, as (12) Gokel. G. W.; Cram, D. J.; Liotta, C. L.; Harris, H. P.; Cook, F. L. Org. Synth. 1977, 56, 30. (13) Roach, E. T.;Handy, P. R.; Popov, A. I. Inorg. Nucl. Chem. Lett. 1973, 9, 359. (14) Nicely, V. A.; Dye, J. L. J . Chem. Educ. 1971, 48, 443. (15) Pople, J. A.; Schneider, W. G.; Bernstein, H. J. High Resolution Nuclear Magneric Resonance; McGraw-Hill: New York, 1959; p 218. (16) Cahen, Y. M.; Dye, J. L.; P o w , A. I. J. Phys. Chem. 1975,79,1292.
0 1991 American Chemical Society
9602
The Journal of Physical Chemistry, Vol. 95, No. 23, I991
t
315
Amini and Shamsipur TABLE I: Formation Constants and Umiting 'H Chemical Shifts of Alkaline Earth-18C6 Complexes in Various Solvents at 30 OC
solvent NM
AN
DN"
Db
cation
2.7
35.9
Mg2+
14.1
38.0
a
Figure 1. Variation of the IH chemical shift as a function of Mzt/18C6 mole ratio for the alkaline earth complexes with 18C6 in various solvents. The error bars associated are smaller than the dimensions of the symbols used. a function of the cation to ligand mole ratio at 30 OC; the results are shown in Figure I . In the case of acetonitrile solutions of 18C6, two 'H resonances for the ligand were observed where Sr2+ ion was present at cation to ligand mole ratios of less than I , which emphasizes a slow exchange of the ligand between the free and complexed sites at room temperature. The 18C6 NMR signal in DMF solution, in the presence of Mg2+and CaZ+ions, and in AN solution, in the presence of Ca2+ion, did not show any significant chemical shift, indicating that the immediate environment of the ligand protons has not changed significantly upon the addition of the cation. However, it should be noted that, in some cases, the formation of a weak complex may not change the electrical environment sufficiently to cause a chemical shift. In all other cases studied, only one population-averaged signal was observed, indicating a fast exchange of the ligand between the two sites at room temperature. In general, the behavior of chemical shift as a function of the cation/ligand mole ratio can be approximately divided into two groups: 1. In the case of the Ca2+, Sr2+,and BaZ+complexes in N M and BaZ+complex in AN, the downfield chemical shift of the ligand protons varies linearly with the mole ratio until the mole ratio of 1 is reached: further addition of the cation does not change the resonance frequency. This behavior is indicative of the formation of a strong 1 :1 complex. 2. In other cases studied, an increase in the cation concentration gradually shifts the proton resonance downfield and the chemical shift does not reach a limiting value even at a mole ratio of about 3, indicating the formation of a weak complex. The formation constants and limiting chemical shifts of the 18C6 complex, obtained by computer fitting of the mole ratio data, are listed in Table 1. It should be noted that the method generally becomes unreliable for very stable complexes (Le., Kf> IO5). The successful use of proton" and carbon-13'*J9 chemical shifts vs cation/ligand mole ratio data in the determination of the stability constants of some alkali ion-crown ether complexes in different solvents has been reported previously. (17) Live, D.; Chan, S . 1. J . Am. Chem. Soc. 1976, 98, 3769. (18) Shamsipur. M.; Popov, A. I. J . Am. Chem. SOC.1979, 101. 4051. (19) Lin, J. D.; Popov, A. 1. J . Am. Chem. SOC.1981, 103, 3773.
26.6
36.7
61im Hz 316.5 f 0.9 309.7 f 0.1 306.9 f 0.1 305.3 f 0.1
Ca2+
>5
>6 >6
Mg2+ CaZt
2.77 f 0.04 3.36 f 0.04c 4.1 f O . l d >5
300.5 f 0.1 297.5 f 0.1
2.67 f 0.04 3.81 f 0.03
305.4 f 0.5 301.5 f 0.2
Bazt
DMF
Kf
Srzt Ba2+
SrZt
P
1%
3.08 f 0.08
SrZt BaZt
301.3 f 0.5
" Donor number, ref 24. Dielectric constant. Reference 33. dEstimatedfrom the integrated intensities of the 18C6 NMR signals at the free and complexed sites. As it is seen from Table I, in all solvents used, the stability of the complexes decreases in the order Ba2+> Sr2+> CaZ+> Mg2+. This order follows the trend expected on the basis of the consonance between the size of 18C6 and of the cation^.^ The ring size of 18C6 is 2.6-3.2 Azo(estimated from molecular models), which nicely matches the size of barium ion (ion diameter of 2.7 A).21 Other cations with smaller ionic sizes are too loose a fit for the ligand cavity, resulting in weaker complexes. However, it should be noted that the thermodynamic stability constant is not just a measure of the absolute strength of the complex, an understanding from the "ion-in-the hole" model,3 but is also a measure of the relative strength as compared to the ionic solvation. Thus, it is only for the weakly solvated large ions (such as Ba2+ ion) that the cation size can be considered primarily responsible for the complexing characteristics. In the case of smaller cations such as Mg2+ ion, the cation is so strongly solvated that considerably more energy must be expended in the desolvation step than for the larger cations. Contributions of the solventcomplex and even solvent-ligand interactions to the stability of the resulting complexes cannot be i g n ~ r e d . ~ ~ . ~ ~ From Table I, it is obvious that the solvent properties play a very fundamental role in the complexation reactions. In all cases, the stability of 18C6 complexes increases with decreasing solvating ability of the solvents, as expressed by the Gutmann donor number.24*2s Dimethylformamide is the solvent with the highest donicity and, therefore, competes most effectively with the ligand molecules for cations, which in turn results in the least stable complexes in the series. Exchange Kinetics. The exchange kinetics of complexation of 18C6 with alkaline earth cations were studied in nitromethane, acetonitrile, and dimethylformamide solutions at different temperatures. The solvents used have very similar dielectric constants, in the range 35.9-38.5, but their donor numbers are quite different (Table I). In all cases, a 0.01 M solution of 18C6 was prepared containing alkaline earth perchlorates with the cation to ligand mole ratio of about 0.5. The proton NMR spectra of the resulting solutions were obtained at several different temperatures. Sample spectra are shown in Figure 2. At the same time, and under the same conditions, the N M R spectra of the free and complexed ligands (i.e., 0.01 M solutions of 18C6 with metal ion to ligand mole ratios of 0 and >1) were obtained and the line widths were measured by fitting a Lorentzian function to the spectra. The mean lifetime of the ligand, 7 , at different temperatures for each system was obtained by fitting the spectra to the NMR exchange equations. A sample computer fit of the proton NMR spectrum (20) Pedersen, C . J . J . Am. Chem. SOC.1970, 92, 386. (21) Shannon, R. D. Acta Crystallogr. Sect. A 1976, 32, 751. (22) DeBoer, J. A. A.; Reinhoudt. D. N.; Harkema, S.; Van Hummel, G. J.; deJong, F. J. J . Am. Chem. Soc. 1982, 104, 4073. (23) Mosier-Boss, P. A.; Popov, A. 1. J . Am. Chem. Soc. 1985,107,6168. (24) Gutmann, V. The Donor-Acceptor Approach to Molecular Interaclions; Plenum: New York, 1978. (25) Marcus, Y.J. Solution Chem. 1984, 13, 599.
The Journal of Physical Chemistry, Vol. 95, No. 23, 1991 9603
NMR Study of Alkaline Earth-18-Crown-6
2
I I
I
312
I
1
1
298
A,nt
280
1
1
Figure 2. ‘HN M R spectra at various temperatures for 0.01 M solution of 18C6 in AN with Ca2+/18C6 mole ratio of 0.5.
I
I
‘1:)
:
I
I
I
Figure 3. Computer fit of IH NMR spectrum obtained with a 0.01 M solution of 18C6 containing Ca2+ion in AN with a cation to ligand mole ratio of 0.5 at -3 OC: ( X ) experimental point; ( 0 )calculated point; (=) experimental and calculated points are the same within the resolution of
the plot. is shown in Figure 3. As was pointed out earlier, the ligand may exchange between the free and complexed sites via a dissociative pathway:16-2628
M2+ + 18C6
kr
M2+-18C6
(1)
The expression for T, in terms of the dissociative mechanism, is7 1 / T = kd([~8C61~01/[~8C61f~ee) (2) (26) Lehn. J. M.; Sauvage, J. P.;Dietrich, B. J . Am. Chem. Soc. 1970, 92. 29 16. (27) Shchori, E.; Jagur-Grodzinski, J.; Luz, Z.; Shporer, H. J . Am. Chem. Soc. 1971, 93,7133. (28) Ceraso, J. M.; Smith, P. B.; Landers, S.; Dye, J. L. J . Phys. Chem. 1977, 81, 760. ~1
~
I
3.1
3.3
-
I
I
I
3.5
3.7
3.9
wo/T Figure 4. Arrhenius plots of In kd vs 1 T for different complexation systems: (A) Mg2+-18C6-NM; (B) Ca2‘-18C6-NM; (C) Ba2*-18C6NM; (D) Mg2+-18C6-AN; (E) Ba2+-18C6-AN; (F) Sr2+-18C6-NM; (G) Ba2+-18C6-DMF; (H) Ca2+-18C6-AN; (1) Sr2+-18C6-AN.
264
I
I
1
2.9
where [ 18C6],o, and [18C6Ifr, represent the total concentration and concentration of uncomplexed 18C6, respectively. According to eq 2, a linear dependence of 1/ T upon 1/ [ 18C6]fre confirms the predominance of a dissociative mechanism in the exchange process. In a study of the rate of exchange in water for the cryptand C222 complexes by proton NMR, Lehn and co-workers have also concluded that when the ligand is in excess, the ratedetermining step is the dissociation of the cryptate.26 Since the reciprocal of T is proportional to the decomplexation rate, a plot of In (1 /T) (or In kd) vs inverse temperature gives an Arrhenius plot. Such plots for the different systems studied are shown in Figure 4. Activation energies for the release of 18C6 from the complex were determined from the slopes of such plots, and the activation parameters i W , A S ,and AG*were calculated by using Eyring transition-state theory.29 The results of these calculations are given in Table 11. From Table 11, it is immediately obvious that the decomplexation rates and the activation parameters of all complexes studied are strongly dependent on the nature of the solvent. Actually, there is a good correlation between the donicity of the solvents, DN,”325 and log kd and the activation parameters (Figure 5 ) . The same kind of correlation has been previously reported for the alkali metal complexes with crown ethers30 and cryptands.E*10*31 As can be seen, the activation energy for the release of 18C6 from its complexes increases with increasing donicity of the solvent. This observation, which is opposite from the overall energy change of the complexation, emphasizes the necessity of a substantial ionic solvation in the transition state.8J6 This is also confirmed by the negative AS* values which mainly arise from the higher ionic (29)Lin, S.H.;Li, K. P.; Eyring, H. In Physical Chemistry, An Advanced Treatise; Eyring, H., Henderson, D., Jost, W.,Eds.; Academic Press: New York, 1977;Vol. VII, p I . (30)Strasser, B. 0.; Popov, A. I. J . Am. Chem. Soc. 1985, 107, 7921. (31)COX,B. G.;Garcia-Rosas, J.; Schneider, H. J . Am. Chem. Soc. 1981, 103, 1054.
Amini and Shamsipur
9604 The Journal of Physical Chemistry, Vol. 95, No. 23, 1991 TABLE 11: Kinetic Parameters for tbe Complexation of Alkaline Earth Ions by 18C6 in Various Nonaqueous Solvents E,, AH', As*, AG',"
ki,b
NM AN
kcal mol-l 3.3 f 0.1 4.0 f 0.2
kcal mol-l 2.8 f 0.1 3.4 f 0.2
cal mol-l K-' -33.7 f 0.5 -32.3 f 0.7
kcal mol-' 12.84 f 0.05 13.02 f 0.01
kd, S-I (2.6 f 0.1) X IO3 (1.8 f 0.2) X IO'
NM AN
3.5 f 0.3 7.1 f 0.2
2.9 f 0.3 6.5 f 0.2
-33.5 f 0.9 -27.7 f 0.7
12.85 f 0.02 14.75 f 0.02
(2.4 f 0.2) (9.2 f 0.3)
Sr2+
NM AN
3.7 f 0.3 7.4 f 0.1
3.2 f 0.3 6.8 f 0.1
-35.4 f 0.9 -31.3 f 0.2
13.75 f 0.03 16.12 f 0.04
Bal+
NM AN DMF
2.5 f 0.1 7.8 f 0.2 11.4 f 0.4
2.0 f 0.3 7.2 f 0.2 10.8 f 0.4
-35.6 f 0.2 -20.0 f 0.7 -10.4 f 0.9
12.6 f 0.2 13.16 f 0.01 13.9 f 0.1
cation
solvent
Mg2+ Ca2+
.
X X
IO3
IO'
M-I
s-I
3.1
X
1.1
x 106
IO6
3.8 X IO8 2.1 x 105
(5.5 f 0.2) X IO2 (1.0 f 0.1) X IO'
>5.5 >1.0
(1.9 f 0.1) x 103 (1.1 f 0.1) X IO3 (3.8 f 0.2) X IO2
>2.0 x
X X
IO8 IO6 1010
>1.0 X 10' 2.1 x 106
"The standard deviation calculated by using the approximate equation 6(AG') = 16(AhH*) - T6(AS*)l, ref 34. bCalculated from kf = Kfkd.
13.0
1
//
J, I
0
,
1
,
I
10
I3
a0
26
DN
Figure 5. Plots of log kd, E,, AH', As', and AG*vs the Gutmann donor number for Ba2+-1 8C6 complex in NM, AN, and DMF.
solvation of the transition state in comparison to the initial comple~.~~ Of course, the influence of a change in the rigidity of the macrocyclic ligand, brought about by the partial release of the (32) Loyola, V. M.;Pizer, R.: Wilkins, R.G. J. Am. Chem. Soc. 1977,99, 7185. (33) Semnani, A.; Shamsipur, M. Unpublished results. (34) Binsch, G.;Kessler, H. Angew. Chem., I n f . Ed. Engl. 1980, 19,41 I .
cation from its 18C6 complex in the transition state, on the overall entropy change of the system cannot be neglected." It is interesting to note that, with the exception of Ba2+ ion, the kd values in a given solvent decrease with increasing ionic size, which nicely reflects the observed increase in the stability of the 18C6 complexes with ionic size. However, in the case of Ba2+-18C6 complex in a given solvent the corresponding kd value is even higher than that of the Ca2+complex, while it forms the most stable complex in the series. This is presumably because of the exceptionally high kf value for the complex formation between the weakly solvated Ba2+ ion and the flexible 18C6 molecule, which can compensate for the relatively high kd value and results in the high thermodynamic stability of the resulting complex. The high complex formation rates (Table 11) suggest that the required solvation energy of the cation is largely compensated by interaction with the ligand in the transition state; the energy required decreases with decreasing solvation of ions. On the other hand, the flexibility of the ligand molecule can provide suitable conditions for a more ready interaction with the incoming cation, leading to more effective compensation for the loss of solvation energy. This behavior once more emphasizes the increased ease of reorientation of the cationic solvation shell in the transition-state.
Acknowledgment. We gratefully acknowledge the support of this work by the Shiraz University Research Council. We also acknowledge use of the research facilities of the Department of Chemistry, Esfahan University, during the course of this study. Registry NO. 18C6, 17455-13-9; NM, 75-52-5; AN, 75-05-8; DMF, 68- 12-2; Mg( 18C6)l+, 691 82-43-0; Ca( 18C6)lt, 57587-68-5: Sr( 18C6)2+, 61059-99-2; Ba( I8C6)lt, 61060-00-2; Mg, 7439-95-4; Ca, 7440-70-2; Sr, 7440-24-6; Ba, 7440-39-3.
