J. Phys. Chem. 1988, 92, 147-151
147
corresponding thermal rate coefficients for the two principal reactions are too small to permit trajectory calculation at 300 K. Over the range 1500 K 6 T S 2500 K, they are found to be 1.38 X 1014 exp[-13600/RT] and 1.90 X 1013 exp[-11040/RT] cm'/(mol.s) for the formation of CH2CH2F and CH,=CHF, respectively. Virtually all of the reaction exothermicity is partitioned into the internal modes of CH2CH2For CH,=CHF. Very little energy appears in the form of relative translational motion of the products. H F is usually formed in the u = 0, 1, or 2 vibrational state. The calculated center-of-mass differential cross section for F atom scattering shows a strong backward component along with an isotropic component. Examination of individual trajectories shows that the first of these arises from a direct reaction mechanism while the second is the result of complex formation. Formation of CH,=CHF is shown to occur via a complex mechanism involving the formation of 1,2-difluoroethane as an intermediate. No evidence is found for mode-specific rate enhancement of the reaction leading to the formation of CH,=CHF. However, there is some evidence for its presence in the reaction forming the fluoroethyl radical. In this case, excitation of the C-H stretching modes seems to be more efficient in promoting the reaction than a similar excitation of the either the C=C stretch or the CH, bending or rocking modes. The magnitude of the effect, however, is small and could be the result of statistical or sampling error. The dynamics of the gas-phase reaction of C,H4 F2 are found to be very different from those observed by Frei et al.] in their study of this reaction under matrix isolation conditions.
increased from 953 to 4209 cm-'. Such a difference is not unexpected, however, since in the gas-phase calculations the relative translational energy is 1.046 eV in contrast to its near zero value in the matrix experiments.' Consequently, the percentage increase in total available energy upon vibrational excitation is much greater in the matrix than in the gas-phase reaction. Mode specificity was observed by Frei et a1.l in their matrix studies of the C2H4 F, reaction. However, it too is different than that found in the present calculations. In the matrix, excitation of the u2 v12 combination band at 3076 cm-] was found to yield a quantum efficiency greater than that for excitation of ug at 3105 cm-'. In the gas phase, this behavior is reversed with ug being more effective than the combination excitation. Since even the products of the gas-phase reaction are different than those observed under matrix isolation conditions, it is not surprising that the detailed dynamics of the two processes are likewise completely different.
+
+
IV. Summary A quasi-classical trajectory study of the bimolecular reaction dynamics for the reaction of Fz with ethylene has been carried out on a previously described potential energy surfaces on which all important reaction channels are open. The surface yields equilibrium geometries, reaction exothermicities, and fundamental vibrational frequencies in fair-to-good accord with measured values. The major reaction products of the gas-phase collision of F2 with C2H4are found to be CH,CH2F and fluorine atoms. The secondary products are H F and CH,=CHF. 1,2-Difluoroethane is never found as a final product although it is observed as an intermediate in the reaction leading to the formation of CHI= CHF. The calculated reaction cross sections are all less than 5 A2 even when the translational energy is more than 1 eV in excess of the reaction threshold. The small cross sections are primarily the result of the demanding steric requirements for these reactions. The
+
Acknowledgment. All calculations in this paper were carried out on a VAX 11/780 and a microVAX I1 purchased, in part, with funds provided by grants from the Department of Defense University Instrumentation Program, AFOSR-85-0115, and the Air Force Office of Scientific Research, AFOSR-86-0043. Registry No. C2H4,74-85-1; F,, 7782-41-4; CH2=CHF, 75-02-5; CHZCHZF, 28761-00-4; FCH2CH*F, 624-72-6; H, 1333-74-0.
Study of the Complexation Kinetics of Cs' Ion with Dibenzo-30-crown-10 in Some Nonaqueous Solvents by '%s NMR Mojtaba Shamsipur' and Alexander I. Popov* Department of Chemistry, Michigan State University, East Lansing, Michigan 48824 (Received: May 12, 1987)
The exchange kinetics of the complexation of the cesium ion with dibenzo-30-crown-10 were studied in nitromethane, acetonitrile, propylene carbonate, and methanol solutions by cesium-133 NMR line-shape analysis. In the last three solvents, when the temperature is below -10 O C , the predominant mechanism for the exchange of the Cs' ion between the solvated and complexed sites is the bimolecular process. In nitromethane solutions, at all temperatures studied, and in propylene carbonate and methanol solutions at '10 O C , the exchange process proceeds by the dissociation pathway. The activation parameters E,, AH*, AS*, and AG' for the exchange have been determined. In systems where the exchange mechanism is bimolecular, the free energy barrier for the exchange process appears to be independent of the solvent.
Introduction Among the macrocyclic crown ethers synthesized by Pedersen,' ligands with large rings such as dibenzo-30-crown-10 are particularly interesting. These ligands are quite flexible, and the rings are large enough to twist around a metal ion of proper size and form three-dimensional, "wrap-around" complexes. Such struc(1) On leave from the Department of Chemistry, Razi University, Bakhtaran, Iran. (2) Pedersen, C. J. J . Am. Chem. Sac. 1967, 89, 7017.
0022-3654/88/2092-0147$01.50/0
tures have been reported for crystalline dibenzo-30-crown- 10 complexes with potassium3 and rubidium4 ions. Experimental evidence for the existence of a "wrap-around" structure for the complexes between this ligand and K+ and Cs' ions in various nonaqueous solvents has also been r e p ~ r t e d . ~ , ~ (3) Bush, M. A.; Truter, M. R. J . Chem. Sac., Perkin Trans. 2 1972, 2, 345. (4) Hasek, J.; Huml, K.; Hlavata, D. Acta Crystallogr., Sect. 8 1979,835, 330. (5) Live, D.; Chan, S. I. J . Am. Chem. SOC.1976, 98, 3769.
0 1988 American Chemical Society
148 The Journal of Physical Chemistry, Vol. 92, No. I , I988
Shamsipur and Popov
Despite valuable information about the solution behavior which could be obtained from kinetic studies of alkali-metal complexation reactions with dibenzo-30-crown- 10, this field has been largely neglected. In 1972 Chock' proposed the following mechanism for the complexation reactions between dibenzo-30-crown-10 and alkali-metal, ammonium, and thallium(1) cations in methanol solutions
in which a fast equilibrium between an open (L,) and a closed (L2) conformation of the ligand is followed by a rate-determining associative-dissociative complexation reaction. Very recently, Detellier and co-workers reporteds a potassium-39 N M R relaxation study of the Kf ion complexed by DB30C10. Extensive studies of the complexation of alkali-metal cations with other crown ethers (especially 18-crown-6 and its derivatives) have been recently reported by this group and On the basis of ultrasonic relaxation measurements, Eyring, Petrucci, and ~ o - w o r k e r s suggested ~ ~ - ~ ~ the predominance of the Eigen-Winkler mechanism for the complexation reactions in different solvents. The general Eigen-Winkler processr9can be written as
where M+ and L represent the free solvated cation and free ligand, respectively, and Mi- - -L, ML+, and (ML)' represent three different conformations of the 1:l complex. It was of interest to us to study the solution behavior and exchange kinetics of alkali-metal ions with large crown ethers in different solvents. We recently reported a kinetic study of the complexation of the Cs' ion with dibenzo-21-crown-7 and dibenzo-24-crown-8 in acetone and methanol solution^.^ In this paper we discuss a study of the exchange kinetics of the cesium ion complex with dibenzo-30-crown-10 in nitromethane, acetonitrile, propylene carbonate, and methanol solutions. Cesium- 133 NMR line-shape analysis was used to determine kinetic parameters of the complexation reaction.
Experimental Section Dibenzo-30-crown-10 (DB30C10, Parish) was recrystallized from acetone and vacuum-dried. Cesium thiocyanate (Pfaltz and Bauer, reagent quality) was dried under vacuum at 60 OC for 72 h. Nitromethane (NM, Aldrich), acetonitrile (AN, Baker), propylene carbonate (PC, Aldrich), and methanol (MeOH, Baker) were purified and dried by using previously reported methods.20 Water content of the solvents, determined by gas chromatography, ( 6 ) Shamsipur, M.; Popov, A. I. J . Am. Chem. SOC.1979, 101, 4051. (7) Chock, P. B. Proc. Natl. Acad. Sei. U.S.A. 1972, 69, 1939. (8) Stover, H. D. H.; Robillard, M.; Detellier, C. Polyhedron 1987,6, 577. (9) Strasser, B. 0.;Shamsipur, M.; Popov, A. I. J . Phys. Chem. 1985;89, 4822.
(10) Strasser, B. 0.;Hallenga, K.; Popov, A. 1. J . A m . Chem. Sot. 1985,
107, 189.
( 1 1 ) Szczygiel, P.; Shamsipur, M.; Hallenga, K.; Popov, A . I. J . Phys. Chem. 1987, 91, 1252. (12) Strasser, B. 0.; Popov, A. I. J . A m . Chem. SOC.1985, 107, 7921. (13) Mei, E.; Dye, J. L.; Popov, A. 1. J . Am. Chem. Soc. 1977, 99, 5308. (14) Schmidt, E.; Popov, A. I. J . Am. Chem. SOC.1983, 105, 1873. (15) Maynard, Y.;Irish. D. E.; Eyring, E. M.; Petrucci, S. J . Phys. Chem. 1984, 88, 729. (16) Chen, C.; Wallace. W.; Eyring. . - E. M.; Petrucci, S. J . Phvs. Chem. 1984, 88, 2541 (17) Wallace, W.; Chen, C.; Eyring, E. M.; Petrucci, S. J . Phys. Chem. 1985, 89, 1357. (18) Deville, A,; Stover, H. D. H.; Detellier, C . J . A m . Chem. Soc. 1985. 107, 4172. (19) Eigen, E.; Winkler, R. In The Neuroscience: Second Study Program; Schmitt, F. D., Ed.; Rockfeller University: New York, 1970. (20) Greenberg, M . S.; Popov, A. I. Spectrochim. Acta. Part A 1975, 31A, 647.
t40t 2o
>AN, 20
0
-20
-40
-60
Temperature ( " C ) Figure 1. Variation of the cesium-I33 chemical shift as a function of temperature for the solvated 0.02 M CsSCN ( 0 ) and complexed [DB30C10]/[Csf] mole ratio of about 1:1 (*) in various nonaqueous solutions.
was invariably less than 100 ppm. Cesium-133 NMR measurements were carried out on a Bruker WH-180 spectrometer operating at a field of 42.27 kG and a frequency of 23.62 MHz. Cesium-I33 chemical shifts are corrected for bulk magnetic susceptibility and are referenced to infinitely dilute aqueous cesium chloride solution. Line widths were measured by fitting a Lorentzian function to the spectra. A complete N M R line-shape analysis technique was used to determine the kinetic parameters for the exchange between the solvated and complexed cesium ion sites. Equations used were of similar format to those used by Cahen et aL2' Some modifications were made to include exponential line broadening and delay time effects on the spectra.I0 A nonlinear least-squares program KIN FIT^' was used to fit 60-80 points of the spectra to the N M R exchange equations in order to extract the mean interaction lifetime, T, for each system at several temperatures.
Results and Discussion Figure 1 shows the temperature dependence of the cesium-I33 chemical shift for the solvated (0.02 M CsSCN) and the complexed cesium ion in nitromethane, acetonitrile, propylene carbonate, and methanol solutions. It is interesting to note that while the chemical shifts of the solvated cesium ion in different solvents are quite scattered through a range of about 90 ppm, the chemical shifts of the complexed cation fall in a much more narrow range of about 20 ppm or less. These observations indicate that when the cesium ion is in the cavity of the ligand, it is largely isolated from the solution and thus confirms the existence of a "wraparound'' structure of the complex in solution^.^^^ Due to the symmetry of the electrical field gradient at the complexed cesium nucleus (which results from the "wrap-around" structure of the complex), the resonance lines of the solvated and the complexed cesium ions are both narrow and of approximately the same width (2-10 Hz). As it can be seen in Figure 1, the cesium-133 resonance of the cesium ion in all solvents shows a linear paramagnetic shift with decreasing temperature. Since the dielectric constants of solvents increase with decreasing temperature, ion pair formation decreases as the temperature of the solution is lowered.23 Therefore, at lower temperatures, there is an increase in the solvent-cation interaction which leads to a paramagnetic shift of the cesium ion The chemical shift of the complexed cesium ion also (21) Cahen, Y. M.; Dye, J. L.; Popov, A. I. J . Phys. Chem. 1975, 79, 1292. (22) Nicely, V. A.; Dye, J. L. J . Chem. Educ. 1971, 48, 443. (23) (a) Wurflinger, A. Ber. Bunsen-Ges. Phys. Chem. 1980,84, 653. (b) Simeral, L.; Amey, R. L. J . Phys. Chem. 1970, 74, 1443. (c) Davidson, D. W. Can. J . Chem. 1957, 35, 458. (24) Kauffmann, E.; Dye, J. L.; Lehn, J. M.; Popov, A . I . J . Am. Chem. SOC.1980, 102, 2274.
Complexation of Cs+ with Dibenzo-30-crown-10
The Journal of Physical Chemistry, Vol. 92, No. 1. 1988 149
"C
TABLE I: Mean Lifetimes as a Function of Temperature for CsSCN.DB30C10 in Nitromethane and Propylene Carbonate Solutions
solvent nitromethane
[DB30C10]/ [CsSCN] mole ratio 0.25 0.50 0.75 0.25 0.50 0.75 0.25 0.50 0.75 0.25 0.50 0.75 0.25 0.50 0.75 0.25
T, f 1 "C -3 5 -28 -20 -12 -5 10
0.50
propylene carbonate
0.75 0.26 0.51 0.85 0.26 0.51 0.85 0.26 0.51 0.88 0.26 0.51 0.85 0.26 0.5 1 0.85 0.26 0.51 0.85 0.26 0.51 0.85
-58 -50 -40 -30 -20 -10 +10
lo%, s 6.53 f 0.33 5.59 f 0.51 2.46 0.17 6.4 f 0.15 3.81 f 0.21 1.80 f 0.13 4.06 f 0.30 2.44 f 0.13 1.43 f 0.20 4.30 0.29 2.46 f 0.31 1.16 f 0.11 2.76 f 0.13 1.94 f 0.12 0.95 f 0.14 2.07 f 0.15 1.42 f 0.06 0.69 f 0.06 525 f 11 501 f 12 492 f 10 168 & 5 189 f 5 179 f 8 11.6 f 2.7 72.6 f 2.3 70.4 & 2.8 26.9 f 0.6 26.4 f 1.4 26.0 f 1.1 9.32 f 0.51 9.58 f 0.43 8.88 f 0.65 3.69 f 0.30 3.29 f 0.33 2.84 f 0.54 4.76 f 0.46 3.27 f 0.19 0.53 f 0.17
*
*
shifts in the paramagnetic direction with decreasing temperature, but the dependence is no longer linear. In acetonitrile, propylene carbonate, and methanol solutions, chemical shifts, at lower temperatures, converge toward a value which is independent of the solvent. Similar behavior was observed previously for the cesium complex with cryptand C222,i3,24and it indicates a more tightly bound complex where the ligand essentially insulates the cation from a direct contact with solvent molecules. Consequently, solvent influence on the 133Cschemical shift is eliminated. Cesium- 133 NMR spectra were obtained at several temperatures in the above-mentioned solvents. In each solvent three solutions of cesium thiocyanate were prepared which contained the same concentration of the salt but different concentrations of the ligand. The ligand-to-metal mole ratio was always smaller than one, and thus each solution contained free and complexed Cs' ion. From the above measurement values of mean lifetime, T , were obtained as a function of temperature; some typical examples are shown in Table I. As we have pointed out in previous publication^,^^'^ it has been proposed by Shchori et aLZSthat the exchange of the cesium ion between the free and the complexed site may occur by two possible mechanisms, a bimolecular exchange mechanism (I) and a associative-dissociative pathway (11):
-
*CS+ + Cs+*DB30ClO CS'
+ DB30C10
kl
kl
*Cs+.DB30C10
+ CS+
Cs+*DB30C10
(I) (11)
(25) Shchori, E.: Jagur-Grodzinski, J.; Luz, Shporer, M. J . Am. Chem. SOC.1971, 93, 7133.
I
[cs+lfree Figure 2. Plots of 1/r[Cst],,, vs for Cs+.DB30C10 complex at different temperatures in nitromethane.
"C
H
28 ---,
301
X
lot
-42
- 50 I
0
50
I
1
100
I50
200
Figure 3. Plots of l/r[Cst],,, vs 1/[CstIfr,, for Cs+.DB30C10 complexes at different temperatures in acetonitrile.
The general expression for the mean lifetime of the cesium ion, T , in terms of the above-mentioned mechanisms is 1 / = ~ kl[C~+],,,+ k-2(1) [CS'I free in which [Cs+],,, and [Cs+Ifr, refer to the total salt concentration and the concentration of the uncomplexed cesium ion, respectively. According to eq 1, at a given temperature a plot of {T[CS+],,,)-' vs 1/[Cs+Ifr, determines the contribution of the two mechanisms to the exchange process. Such plots are given in Figures 2-5. It is seen that in nitromethane solutions the dissociative exchange mechanism is dominant at all temperatures studied. On the other hand, in the other three solvents, the exchange is bimolecular below -10 "C. Above -10 "C, in propylene carbonate and methanol solutions, the exchange follows the dissociative pathway. In acetonitrile solution, at temperatures above -10 "C, the exchange is so fast that its mean lifetime cannot be determined [CS+1101
150 The Journal of Physical Chemistry, Vol. 92, No. I , 1988
Shamsipur and Popov
10 18
-
16
5
14 -
12-
(0
b
c
tl
I
X
I I
X
I
-12 F
I I
I
I
I
,
c
I
, I
I I
1‘
6-
’ -20
r ,‘
4-
I
J
2-
*-30 *-40 25 0 1
0‘
0
I
100
300
200
io3 -
400
I
cCs+lfree
Figure 4. Plots of 1/7[Cs+],,, vs l/[Cs+]fr, for Cs+-DB30C10 complexes at different temperatures in propylene carbonate. Right-hand ordinates for the system at 10 O C .
T Figure 6. Arrhenius activation plot of In kb vs 1 / T for Cst.DB30C10 complex in various nonaqueous solutions.
I
I
5
-
c
J
Figure 7. Proposed model for bimolecular exchange mechanism.
c
- +m
I I
I 3
I.
,R
II
I
I
DB21C7 > 18C6 > DB24C8. The cavities of ligands DB24C8 and 18C6 are not the right size for the Cs' ion, which fits well, however, into the DB21C7 ring; thus, the DB21C7.Cs' complex is somewhat more stable than D B ~ ~ C ~ . C S ' .Activation *~ entropy change goes to more positive values as the cavity size of crown ethers increases. This behavior probably reflects a more flexible structure for larger crown ethers in the transition state; AG* changes in the order 18C6 > DB21C7 > DB24C8 > DB30C10. It can be seen that the decomplexation reaction rate for the DB30ClO-Cs+ system in methanol reported by Chock' is about 2 orders of magnitude smaller than that obtained in this study. However, he assumed the existence of a dissociative-associative rate-determining step for the complexation reaction, while we find that in this system we have a bimolecular mechanism. Therefore, the units of the two rate constants are different.
Acknowledgment. We gratefully acknowledge the support of this work by National Science Foundation Research Grant CHE-8515474. Registry No. DB30C10, 17455-25-3; Cs', 18459-37-5. (26) Shamsipur, M.; Rounaghi, G.; Popov, A. I. J . Solurion Chem. 1980, 9, 701.
