J. Phys. Chem. 1986, 90, 5997-5999
5997
Lithium-7 NMR Study of the Kinetics of Li' Ion Complexation by C222 and C221 Cryptates in Acetonitrile, Propylene Carbonate, and Acetone Solutions Mojtaba Shamsipur' and Alexander I. Popov* Department of Chemistry, Michigan State University, East Lansing, Michigan 48824 (Received: April 21, 1986)
The kinetics of the complexation of the Li+ ion with ligands cryptand 222 and cryptand 221 (C222 and C221) were studied in acetonitrile, propylene carbonate, and acetone solutions by lithium-7 NMR line-shape analysis. The predominant mechanism of exchange between the solvated and the complexed Li+ ion sites for the C222-Li' system in all solvents is dissociative, while a bimolecular mechanism predominates for the C221-Li' system in acetonitrile and propylene carbonate solutions. The kinetic parameters for the exchange have been determined. For the dissociative exchange mechanism, there is a correlation between the solvating abilities of the solvents, as expressed by the Gutmann donor numbers, and the dissociation rates as well as the activation parameters of the reactions. In systems where a bimolecular exchange mechanism predominates, the free-energy barrier for the exchange processes appears to be independent of the nature of the solvent.
Introduction Kinetic studies of macrocyclic complexation reactions with alkali cations not only result in important information on the rates and mechanisms of complexation reactions but also lead to a better understanding of the high selectivity of these ligands toward different cations. This area of research, however, has received less attention than the ubiquitous thermodynamic studies. We have previously reported the use of line-shape analysis of the 7Li,2 23Na,339K,4and 133Cs5N M R resonance lines in studies of the kinetics of the complexation reactions of Li+, Na+, K+, and Cs+ cations with different crown ethers and cryptands in a number of different solvents. It has been found that the ligand structure, solvent properties, and the nature of the counterion have considerable effects on the reaction rates, activation parameters, and exchange mechanism of cations between the solvated and the complexed sites. Our previous kinetic studies by 7Li dynamic N M R have been largely limited to the Li+C211 compiex in nonaqueous solvents since the cavity size of C211 is consonant with the dimensions of the Li+ ion, and therefore, the stability of the Li'C211 complex is much higher than those of the Li+ complexes with larger cryptands, C221 and C222.6 It was of interest to us to compare the kinetics and the exchange mechanisms of lithium complexes with C221 and C222 with the data previously obtained with C211. Experimental Section The C222 and C221 cryptands were purchased from the Merck Co. and were used as received except for vacuum drying. Reagent grade lithium perchlorate (Alfa) was dried at 180 OC for several days. Acetonitrile (Baker, AN), propylene carbonate (Aldrich, PC), and acetone (Fisher, AC) were purified and dried by previously reported methods.' The water content of all solvents was found to be less than 100 ppm as determined by gas chromatography. Lithium-7 N M R measurements were carried out on a Bruker WH-180 spectrometer at a field of 42.27 kG and a frequency of 69.591 MHz. Line widths of the solvated and the complexed sites were measured by fitting a Lorentzian function to the spectra. (1) On leave from the Department of Chemistry, Razi University, Bakhtaran, Iran. (2) Cahen, Y.-M.; Dye, J. L.; Popov, A. I. J . Phys. Chey. 1975,79,1292. (3) (a) Strasser, B. 0.;Hallenga, K.; Popov, A. I. J. Am. Chem. Soc. 1985, 107, 789. (b) Strasser, B. 0.;Popov, A. I. J. Am. Chem. SOC.in press. c) Szczygiel, P.; Popov, A. I., submitted for publication in J . Am. Chem. SOC. (4) Schmidt, E.; Popov, A. I. J . Am. Chem. SOC.1983, 105, 1873. (5) (a) Mei, E.; Popov, A. I.; Dye, J. L. J . Am. Chem. Soc. 1977,99,6532. (b) Strasser, B. 0.;Shamsipur, M.; Popov, A. I. J . Phys. Chem. 1985, 89, 4822. (6) Lehn, J.-M.; Sauvage, J.-P. J . Am. Chem. SOC.1975, 97, 6760. (7) Cahen, Y.-M.; Handy, P. R.; Roach, E.; Popov, A. I. J . Phys. Chem. 1975, 79, 80.
0022-3654/86/2090-5997$01 .50/0
A full lithium-7 N M R line-shape analysis of solutions with [cryptand]/[Li+] mole ratios of less than 1 was used in order to extract the mean lifetime, T, for the exchange processes. Details have been given in previous publication^.^-^
Results and Discussion In order to study kinetics of the complexation reactions between cryptands C222 and C221 and the lithium ion in acetonitrile, propylene carbonate, and acetone solutions, three solutions in each solvent were prepared for each system. The concentration of lithium perchlorate in each solution was kept constants at 0.04 M, and the concentration of ligand was varied between 0.01 and 0.03 M. The 7Li N M R spectra of the resulted solutions were obtained at several different temperatures. Sample spectra are shown in Figure 1. At the same time, and under the same conditions, the 'Li N M R spectra of the solvated and the complexed sites (Le., 0.04 M solutions of LiC104 with respective ligand-tometal ion mole ratios of 0.25, 0.51, and 0.77) were obtained, and the line widths were measured by fitting a Lorentzian function to the spectra. It is interesting to note that in contrast to the crown ether complexes of the Na+ ion, in which the resonance lines of complexed Na+ ion are considerably broader than that of the solvated ~ a t i o nin , ~the above complexes the broadening of the resonance lines of the Li+ ion in the solvated shell and in the cryptate form is approximately equal. These observations imply that the symmetry of the electrical field gradients in both sites is very similar. This observation is not particularly surprising since the small lithium ion can be located in the center of the cavity of the cryptand, as it has been shown recently for the crystalline C222B-Li+A1C14- complex* where it is nearly symmetrically bonded to the six oxygen atoms of the ligand. Line-shape analysis of the spectra was carried out by fitting 60-90 points of the spectra to the N M R exchange equations2using a nonlinear least-squares program KINFIT' in order to extract the mean lifetime, T, at different temperatures for each system. The program requires evaluation of at least four parameters: amplitude, base line, zero-order phase correction, and mean lifetime. The are two possible mechanisms for the exchange of the lithium ion between the solvated and the complexed sites as previously proposed by Shchori et al.,IO namely a bimolecular exchange mechanism (I) and a dissociative mechanism (11). The mean *Li+ + Li+cryptate Li+
ki
+ cryptand
*Li+cryptate
ki -+
+ Li+
Li+cryptate
(I) (11)
(8) Ward, D. L.; Rhinebarger, R. R.; Popov, A. I., unpublished results. (9) Nicely, V. A.; Dye, J. A. J. Chem. Educ. 1971, 48, 443. (IO) Shchori, E.; Jagur-Gordzinski, J.; Luz, Z.; Shporer, H. J. Am. Chem. SOC.1971, 93, 7133.
0 1986 American Chemical Society
5998 The Journal of Physical Chemistry, Vol. 90, No. 22, 1986
Shamsipur and Popov
TABLE I: Kinetic Parameters for the Complexation of the Li+ Ion by Cryptnods C222 and C221 in Different Solvents at 298 K Em AH* AS*,cal AG*, ligand solvent DN D kcal mol-' kcal mol-' mol-' K-' kcal mol-' Kb C222 AN 14.1 38.0 3.30 f 0.21 2.78 f 0.12 -37.42 f 0.45 13.93 f 0.01 420 f 14' PC 15.1 69.0 4.10 f 0.10 3.59 f 0.10 -34.10 f 0.41 13.75 f 0.02 507 f 31" AC 17.0 20.7 5.30 f 0.16 4.82 f 0.18 -28.98 f 0.68 13.46 f 0.02 794 f 42' MeOHb 25.7 32.7 >300' 14.1 38.0 7.52 f 0.17 6.86 f 0.15 -24.03 f 0.46 13.60 f 0.01 C221 AN 680 f 42' 6.25 f 0.16 -25.99 f 0.50 13.58 f 0.1 15.1 69.0 6.68 f 0.13 892 f 50' PC 5.7 -3 1 6.3 15 78.4' MeOHd 25.7 32.7 12.9 f 0.4 -14.9 f 0.4 33.1 12.3 13.5 f 0.4 17.9 f 0.1 1.23 0.24 PYC 15.5 f 0.6 -13.8 f 1.4 19.7 f 0.1 (2.36 f 0.5) X C211 Me2SOf 29.8 45.0 16.1 f 0.6 9
mechanism
*
I1 I1 I1
I1 I I I1
I1 I1
'in s-l. bReference 12. 'In M-' d. dReference 13. eReference 17 'Representative results from ref 17.
/"'
-
8.0
7.0 -
-
6.0
e
-
2 5.0
n
'Q &
+-
b 4.0
-
3.0
C 1.0 ppm
Figure 1. 'Li NMR spectra at various temperatures for 0.04 M solutions of LiCI04 with C222 in acetone. The ligand-to-metal ion mole ratios are (A) 0.25, (B) 0.51, and (C) 0.77.
lifetime of the Li+ ion in terms of mechanisms I and I1 is expressed as eq 1 where [Li+],,, and [Li+Ifreeare the total concentration of LiC104 and the concentration of the free Li+ ion, respectively.
According to (1) the contribution of any of these mechanisms, at any temperature, can be determined from the slope of the plot of l/TILi+:Iot vs. 1/[Li+Ifr,. The values of kl and k-* can also be determined by using the intercepts and the slopes of the resultant straight lines, respectively. Plots of l/r[Li+],, vs. the inverse of free lithium concentration at 25 "C are shown in Figure 2. It is interesting to note that while the C222-Li' complex shows the dissociative pathway in all three solvents, the predominant exchange mechanism for C22 l-Li+ complexes in acetonitrile and propylene carbonate solutions is bimolecular. It is well-known that the cavities of C222 and C 2 2 1 cryptands are too large for the ionic size of Li+ ion and also that the former ligand has a more flexible It also must be taken into consideration that in the bimolecular mechanism, the ligand should have a conformation such that the simultaneous arrival of a free cation and departure of the complexed cation can easily occur. According to the results obtained in this study, it is reasonable to conclude that the cryptand C221, because of its relative rigidity, can conformationally satisfy the conditions for the bimolecular mechanism better than the more flexible C222. In fact, because of its flexibility, cryptand C222 possibly has the opportunity to wrap itself around the small Li+ ion in such a way that the only possible pathway for the exchange of the cation between the (11) Lehn, J.-M. Strucr. Bonding (Berlin), 1973, 16, 1.
2.0-
-
1.0
. 0
E,-*
IO 20 30 40 50 60 70 80 90 100 110
Figure 2. Plots of [T[L~+],J' vs. l/[Li+]frccfor different systems at 25 "C: (A) C222-Lit-AC, (B) C222-Li+-PC, (C) C222-Li+-AN, (D) C221-Li+-PC, and (E) C221-LP-AN. Right-hand ordinate for plots D and E.
solvated and the complexed sites would be the dissociative mechanism. It is obvious that factors other than geometrical structure of the complex such as the concentration of the cation,12 the nature of the ~ o l v e n t ,and ~ ~ *the ~ counterion and the temp e r a t ~ r ecould ~ ~ also be more or less important and cannot be ignored in the arguments. Arrhenius activation energy plots, log k-2 (or log k , ) vs. 1/ T, are shown in Figure 3. Since in the case of both bimolecular and dissociative exchange mechanisms 1 / is~ proportional to kd, it is obvious that the activation energy plots could also be obtained by plotting log (1/7) vs. inverse temperature. The activation energies for the release of the Li+ ion from the complex can be determined from the slopes of such plots. The activation parameters AH*,AS*,and AG* have been calculated by using transition-state theory, and the results are listed in Table I. As it can be seen, there is a satisfactory agreement between the data obtained in this study and those reported by Cox et al. in methanol sol~tions.'~J~ It is interesting to note that in systems in which the dissociation mechanism predominates, the nature of the solvent has a great (12) Delville, A.; Stover, H. D. M.; Detellier, C. J. Am. Chem. SOC.1985, 107,4172. (13) Cox, B. G.; Schneider, H.; Stroka, J. J . Am. Chem. SOC.1978, 100, 4146. (14) Cox, B. G.;Schneider, I.; Schneider, H. Ber. Bunsenges. Phys. Chem. 1980, 84, 470.
The Journal of Physical Chemistry, Vol. 90, No. 22, 1986 5999
Lithium-7 NMR
40t
--
E
5.0.
1-
-40
s Y
-38
c) v)
n,
n
- 36
Y
4.0.
a
-34
8
- 32
O
E
2 -
-2
W
3.0
.
- 30 140
15.0
160
I70
DN Figure 5. Plots of AS* (A), AH*(B), and E, (C) vs. the Gutmann donor number for lithium ion complexes of C222 in AN, PC, and AC.
I 2.6
I
30
1
34
I
I50
14.0
3.8
I
16.0
42
4.6
I
It0
DN Figure 4. Plots of AG* (A) and log k2(0) vs. the Gutmann donor number for lithium ion complexes of C222 in AN, PC, and AC.
influence on the kinetic parameters. In fact, confirming our earlier results, there is a good correlation between the activation parameters and the logarithm of decomplexation rates and the solvating ability of the solvents as expressed by the Gutmann donor number15 (Figures 4 and 5). This kind of correlation has also been reported for the complexes of 18-crown-6 and its substituted crown ethers with sodium ion3bas well as alkali metal-cryptates'6
in different solvents. As can be seen from Table I, the activation energy for the release of the Li+ ion from its C222 cryptate increases with increasing donicity of the solvent. This observation, which is opposite to the overall energy change of the complexation, emphasizes the necessity of a substantial ionic solvation in the transition state. On the other Hand, In systems with the bimolecular exchange mechanism, the activation energy decreases slightly with increasing donor number of the solvent. In this case we can assume that the solvents with higher donor number and higher dielectric constant (e.g., propylene carbonate) can more easily reduce the charge-charge repulsion of Li+ ions in the transition state so that less activation energy is needed for the system. In the transition state of a bimolecular process, two positive ions must approach one another. Therefore, it is obvious that we can expect for this mechanism the free energy of activation, AC', to be somewhat independent of the solvent. We previously reported studies of the exchange kinetics of the Li+ ion complexation with cryptand C211 in some high donicity solvents, using 'Li N M R line-shape analysis.2 Since the lithium ion has just the right size to properly fit inside the cavity of C211, the resulting complexes are very stable, even in such highly solvating solvents as water and dimethyl s~lfoxide."~'~ Thus, it is not unexpected to observe a very low dissociation rate for the C21l-Li+ cryptate in comparison with that obtained in this study for C221-Li+ and C222-Li+ cryptates which are about 5-6 orders of magnitude larger in the latter cases. Because of the same reason, the free energy of activation for the release of Li+ ion from the C211 cavity (-20 kcal mol-') is much larger than those observed for C221 and C222 cryptates. The activation energy for the release of the Li+ ion from the cryptates decreases in the order C211 > C221 > C222. Acknowledgment. We gratefully acknowledge the support of this work by a National Science Foundation Grant CHE-85 15474. Registry No. C222, 23978-09-8; C221, 31364-42-8; Li+, 17341-24-1.
~~
(15) Gutmann, V. Coordination Chemistry in Nonaqueous Solvents; Springer Verlag: Vienna, 1968. (16) Cox, B. G.; Garcia-Rasas, J.; Schneider, H. J. Am. Chem. Soc. 1981, 103, 1054.
(17) Cahen, Y. M.; Dye, J. L.; Popov, A. I. J. Phys. Chem. 1975,79, 1289. (18) Cox, B. G.; Garcia-Rosas, J.; Schneider, H. J. Am. Chem. SOC.1981, 103, 1389.
