1252
J . Phys. Chem. 1987, 91, 1252-1255
NMR Study of the Exchange Kinetics of the Sodium Ion with Some 18-Crowns in Tetrahydrofuran Solutions Patrice Szczygiel, Mojtaba Shamsipur, Klaas Hallenga, and Alexander I. Popov* Department of Chemistry, Michigan State University, East Lansing, Michigan 48824 (Received: July 1 7 , 1986; In Final Form: October 15, 1986)
Kinetic studies were carried out on the complexation of the sodium ion by several 18-membered macrocycles in tetrahydrofuran solutions by line-shape analysis of the sodium-23 magnetic resonance. At room temperature an exchange process of the cation was observed to be slow on the chemical shift time scale (at 47.6 MHz) for sodium tetraphenylborate-dicyclohexano- 18-crown-6 (cis-anti-cis and cis-syn-cis) systems. The exchange was fast with sodium salts of other counterions such as thiocyanate, iodide, perchlorate, and pentamethylcyclopentadienide. Fast exchange was also observed with all of the above salts for the sodium complexes of diaza- and dithia-18-crown-6. Analysis of the diaza-18-crown-6-NaSCN system at different temperatures showed two exchange mechanisms. Associative-dissociative mechanism dominates above ---20 OC while bimolecular exchange mechanism prevails below --35 'C. A similar study of the NaSCN-DC18C6 systems showed the existence of only one exchange mechanism whose nature could not be determined unambiguously. Activation parameters for the decomplexation step for the three complexes were calculated.
Introduction We have recently reported some dynamic N M R studies in several nonaqueous solvents and solvent mixtures in order to elucidate the kinetics of complexation reactions involving macrocyclic polyethers and Na', K', and Cs' cations.'-3 In particular, we were interested in the influence of the counterion and of the solvent properties on the exchange mechanisms and on the kinetic parameters of the complexation reaction involving crown ether 18C6. In this paper, we report the influence of the modification of the 18C6 skeleton on the exchange kinetics of the sodium ion with 18-membered macrocyclic rings in tetrahydrofuran solutions by 23NaN M R . The crown ethers we used in this investigation were dibenzo-, dicyclohexano- (two isomers), diaza-, and dithia-18crown-6. Several sodium salts were used: tetraphenylborate, thiocyanate, iodide, perchlorate, and pentamethylcyclopentadienide. The latter salt was included because we previously* observed slow room-temperature exchange of the Na+ ion between the complexed and free sites only with large organic counterions such as tetraphenylborate and tetraalkylaluminate. We wished to see whether such a "generalization" would hold for another, somewhat similar, anion. Experimental Part Reagents. Sodium tetraphenylborate (Aldrich, Gold Label), sodium iodide (Matheson Coleman and Bell), and sodium perchlorate (G. Frederick Smith) were of analytical reagent grade quality and were not further purified, except for drying under vacuum, at room temperature for at least 2 days. Sodium pentamethylcyclopentadienide (Alfa) was obtained as a 0.86 M solution in tetrahydrofuran and was diluted to the desired concentration. Sodium thiocyanate (Mallinckrodt) was recrystallized from acetonitrile and dried under vacuum at 60 O C for 2 days. The mixed dicyclohexano-18-crown-6 diastereoisomers (DC 18C6, Aldrich) were separated by the procedure of Izatt et aL4 Macrocyclic polyether 18-crown-6 (I, 18C68 Aldrich) was purified by a previously described procedure.' Dibenzo-18-crown-6 (DB18C6, Parish) was recrystallized from benzene; diaza-18crown-6 (11, DAl8C6, MCB) was recrystallized from n-heptane. After recrystallization, both ligands were dried under vacuum at (1) Schmidt, E.; Popov, A. I. J. Am. Chem. SOC.1983, 105, 1873. (2) Strasser, B. 0.;Hallenga, K.; Popov, A. I. J . Am. Chem. SOC.1985,
107, 7 8 9 . (3) Strasser, B. 0.;Shamsipur, M.; Popov, A. I. J. Phys. Chem. 1985, 89, 4822. (4) Izatt, R. M.; Haymore, B. L.; Bradshaw, J. S.;Christensen, J . J. Inorg. Chem. 1985. 14. 3132.
0022-3654/87/2091-1252$01.50/0
TABLE I: Sodium Resonances in Sodium Tetraphenylborate-Crown Ether-Tetrahvdrofuran Svstems at Room Temwrature" salt
ligand
(J-)/(Na+) mol ratio
concn, M 0.050 0.051
18C6 DC18C6 (cis-anti-cis)
0.49
0.051
DC18C6 (cis-syn-cis)
0.48
-7.2 -13.4
0.049 0.050 0.0053
DA18C6 DT18C6 DB18C6
0.50 0.56 0.53
-8.2 -6.8
0.59
6
-7.1 -7.2
-15.0
b
"The probe temperature varied from 23.0 to 24.5 'C for different systems. *Insolublecomplex. room temperature for several days. Dithia-18-crown-6 (111, DT18C6, Parish) was dried under vacuum for several days. Structures of I, 11, and 111 are shown in Figure 1. Purification of tetrahydrofuran was described in a previous publication.2 The water content of the purified solvent was determined by gas chromatography and was found to be less than IO ppm. All of the solutions were prepared in a glovebox under dry nitrogen atmosphere. Measurements. 23NaN M R measurements were carried out in a Bruker WH-180 spectrometer at 42.27 kG and a frequency of 47.61 MHz. The details of the chemical shift measurements and of the line-shape analysis are given in previous publication^.^^^
Results and Discussion Diaza-18-crown-6. Sodium-23 resonance was measured in tetrahydrofuran solutions which were approximately 0.05 M in the sodium salt of the above-listed anions and approximately 0.025 M in the ligand. Sample spectra are shown in Figure 2, and typical data (for the tetraphenylborate) are given in Table I. It should be noted that due to the low dielectric constant of the solvent, metal salts are extensively ion-paired and, therefore, the chemical shift of the free sodium cation depends on the concentration of the s ~ l u t i o n . In ~ the case of 18C6 and the two isomers of DC18C6 the tetraphenylborate solutions show two 23Na signals. No observations could be made on the dibenzo- 18-crown-6 species since the sodium complex of this ligand is insoluble in THF. Only one 23Nasignal was observed with the diaza- and the dithia-18-crown-6 complexes. Thus, in contrast to 18C6, with these two ligands even sodium tetraphenylborate shows fast exchange at room temper(5) Greenberg. M.s.;Bodner, R. L.: Popov, A. I. J . Phys. Chem. 1973, 7 7 . 2449.
0 1987 American Chemical Society
The Journal of Physical Chemistry, Vol. 91, No. 5, 1987
18-Crowns in Tetrahydrofuran Solutions
1253
m
I
Figure 1. Structures of 18C6 (I), DB18C6 (11), and DT15C6 (111).
I
I
20
0
1
-35
I
I
IO
0
I
- 20
CHEMICAL SHIFT IPPM)
Figure 2. 23NaNMR spectra of sodium tetraphenylborate solutions with
crown ether in tetrahydrofuran solutions. (A) 0.051 M NaBPh, and 0.025 M DC18C6 (cis-anti-cis). (B) 0.049 M NaBPh, and 0.025 M DA18C6. Reference peak at 0 ppm. TABLE II: Sodium-23 Resonances of Sodium Salts-Crown Ethers-Tetrahvdrofuran Svstem at Room Temwrature"
NaI
concn, M 0.051 0.049 0.049 0.05 0.050
0.052 0.050 0.050 NaCI04 0.053 0.051 0.051 0.049 NaCp(CH3)5 0.050 0.050
0.050 0.050 0.050 0.050
ligand DC18C6 (cis-anti-cis) DC18C6 (cis-syn-cis) DA18C6 DT18C6 DC18C6 (cis-anti-cis) DC18C6 (cis-syn-cis) DA18C6 DT18C6 DC18C6 (cis-anti-cis) DC18C6 (cis-syn-cis) DA18C6 DT18C6 18C6 DC18C6 (cis-anti-cis) DClSC6 (cis-syn-cis) DA18C6 DT18C6 DB18C6
(L)/(Na+) mole ratio 0.49 0.51 0.50 0.52 0.50 0.48 0.50 0.52 0.47 0.49 0.49 0.52 0.51 0.52 0.50 0.50
0.51 0.49
32
3.4
3.6
3.8
4.0
4.2
4.4
lo3 / T ( K - ' ) Figure 3. Arrhenius plot of In (1/7) vs. (1/T) for the DA18C6-NaSCN
system in tetrahydrofuran solutions with (DA18C6)/(Na+) mole ratios of (0)0.72 and ( 0 ) 0.53.
~
salt NaSCN
I
6
-5.9 -5.9 -4.1 -2.4 +0.7 +0.2 +0.9 +6.8 -10.6 -10.4 -7.9 -7.7 -35 -35 -35 -24.6 -29.6 -28.5
"The probe temperature was between 23 and 24.5 "C for different systems. ature. Fast exchange was also observed with NaSCN, NaI, NaC104, NaAsF6, and N ~ C P ( C H in ~ )combination ~ with all of the above ligands (Table 11). The generalization about "large bulky organic anions" did not hold in the last case. As expected, the resonance lines were broader for the complexed Na+ ion than for the solvated cation due to a larger electrical field gradient at the sodium nucleus in the complex. In general, an increase of electron density around the N a + nucleus is characterized by a paramagnetic (downfield) shift as shown by the fact that the 23Nachemical shift in different solvents varies approximately linearly6 with the Gutmann donor number of the s01vent.~ In all cases studied here, the shift upon com@exation was diamagnetic. Especially large diamagnetic shifts are observed for sodium pentamethylcyclopentadienide, which is probably due to the effect of the ring currents. These results indicate a decrease of electron density around the Na+ ion when the solvating T H F molecules are largely or completely replaced by the crown ethers. This behavior is consistent with the relatively high solvating ability of THF as indicated by its Gutmann donor number of 20.7
The line shapes of the 23Na resonance were studied in two solutions containing DA18C6 and NaSCN at crown to salt mole ratios of 0.53 and 0.72. The concentration of the Na+ ion was 0.010 M. The measurements were made in the +41 to -49 OC temperature range. Analysis of the 23Naline shape, as a function of temperature, gave the corresponding values of T. The Arrhenius plot of In 1 / vs. ~ inverse absolute temperature is shown in Figure 3. It should be noted that 1 / is~ directly proportional to the decomplexation rate k-2,*andnormally such Arrhenius plots are straight lines with a slope of -Ea/R. Obviously, this is not the case with our system. The nonlinearity of the plot may be due to a mechanism whose activation energy varies with the temperature or to the existence of two mechanisms whose overall contributions vary with temperature. Considering the two possible mechanisms, the bimolecular exchange (I) and the associative-dissociative process (11), as postulated by Shchori et a1.* k
*Na+
+ NaL+ 5N a + + *NaL+
(1)
we can easily derive the relationship
Plots of l/[~(Na+),,,,] vs. 1/(Na+)freeat various temperatures are shown in Figure 4. It is immediately obvious that, depending on the temperature, two different exchange mechanisms coexist to different extents. The bimolecular mechanism dominates at low temperatures (below -35 "C) while the associative-dissociative mechanism prevails above -20 OC. It is interesting to note that recently Detellier and co-workers reported a 23Na NMR study of a system where the exchange mechanism depends on the concentration of sodium tetraphenylborate and dibenzo-24-crown-8 in nitromethane s o l ~ t i o n s . ~ M, The room-temperature exchange is slow when (Na') < and the associative-dissociative mechanism is dominant. At (8) Shchori, E.; Jagur-Grodzinski, J.; Luz, 2.;Shporer, M. J . Am. Chem.
(6) Erlich, R. H.; Popov, A. I. J. Am. Chem. SOC.1971, 93, 5620. (7) Gutmann, V.; Wychera, E. Inorg. Nucl. Chem. Lett. 1966, 2, 257.
SOC.1971, 93, 7133.
(9) Delville, A.; Stover, H. D. M.; Detellier, C. J . Am. Chem. SOC.1985, 107, 4172.
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The Journal of Physical Chemistry, Vol. 91, No. 5, 1987
Szczygiel et al.
TABLE 111: Activation Parameters and Rates for the Dissociation of NaSCN ComDlexes in THF'
crown DA18C6
T,b OC
25.0 0.0
DC18C6 (cis-antikcis) DC18C6 (cis-syn-cis)
-40.0 25.0 25.0
E,,
kcal mol-' 1.9 f 0.2 1.9 f 0.2 9.2 f 0.4 2.8 f 0.2 2.6 f 0.4
AH, * ,
kcal mo1-I 1.3 f 0.2 1.4 f 0.2 8.8 f 0.4 2.1 f 0.2 1.9 f 0.4
Md', eu -38.6 f 0.5 -38.5 f 0.6
2.5 f 0.9 -26.0 f 0.7 -23.4 f 1.3
kd,' M-l s-l
AGd',
kcal mol-' 12.85 f 0.03 11.89 f 0.02 8.07 f 0.01 9.82 f 0.01 8.82 f 0.01
mechanismd
(2.34 f 0.09) X 10' (1.74 f 0.05) X lo3 (9.8 f 0.4) X IO4 (4.0 f 0.2) X lo5 (2.2 f 0.2) X lo6
"Obtainedwith 0.010 M NaSCN solution; the errors represent one standard deviation. bf0.3 "C. 'Rate of decomplexation in I = bimolecular mechanism; I1 = associative-dissociative mechanism.
I1 I1 I
I I s-l
when mecha-
nism I1 applies.
T* + 6 . Z ° C
-
Ts-34.9'C
1
3.2
3.3
3.4
3.5
3.6
3.7
3.0
T=-45.6.C
I
Do
I
I
L
200
300
400
103/~ (K-')
Figure 5. Arrhenius plot of In ( 1 / ~ vs. ) (1/T) for the DC18C6 (cis-
anti-cis)-NaSCN system in tetrahydrofuran solutions. The (ligand)/ (Na') mole ratio is 0.50. T ('C)
Figure 4. Plot of [~(Na+),,~]-lvs. l/(Na+)f,stfor the DA18C6-NaSCN system in tetrahydrofuran solutions at different temperatures. Total sodium ion concentration is 0.01024 and 0.01011 M at mole ratios (DA18C6)/(Na+) of 0.53 and 0.72, respectively.
concentrations above 5 X M, however, the exchange is fast and the exchange mechanism becomes bimolecular. Shchori et a1.8 reported that the exchange kinetics in macrocyclic ligand-alkali-metal cation systems are significantly dependent on the ionic strength of the solutions, which is a good indication of the influence of ion pairing on the exchange rates. In our case the measurements were made at a fixed concentration of the sodium salt and, therefore, the ionic strength was constant. While it appears that the extent of ion pairing of sodium thiocyanate in tetrahydrofuran solutions is not known, it can be reasonably estimated to be very large. Electrical conductance studies on sodium tetraphenylborate solution in THF'O show that at rmm temperature Kipis approximately 104. Since the equivalent conductance of 0.10 M NaSCN in THF is 2 orders of magnitude smaller than that of 0.10 M NaBPh,,* it is obvious that Ki,, for N a S C N must be much larger than lo4 and, therefore, the ionic strength of the solution should be quite low, especially in view of the fact that the total concentration of the sodium salt used was no larger than 0.01 1 M. The free energy, enthalpy, and entropy of the decomplexation steps were calculated in the usual way by using Eyring's transition-state theory, and the results are shown in Table 111; the dissociation rates at various temperatures are shown in Table IV. Some of the previously obtained kinetic data are also shown for comparison. At this time it seems difficult to find a compelling reason for this peculiar mutation of exchange mechanism, especially since the solution chemistry of this system is not fully understood. The change may be due to the temperature dependence of complexation (10) Carvajal, C.; Tolle, K. J.; Smid, J.; Szwarc, M . J . Am. Chem. SOC. 1965, 87, 5548.
I t
3.1
3.2
3.3
3.4
3.5
3.6
3.7
103 / T ( K - ' )
Figure 6. Arrhenius plot of In ( 1 / ~ vs. ) (1/T) for the DC18C6 (cissyn-cis)-NaSCN system in tetrahydrofuran solutions. The (ligand)/ (Na') mole ratio is 0.51.
constants, to a change of dielectric constant with temperature which would affect ion pair formation, to a temperature-dependent change in ligand conformation, and/or to a combination of some or all of the above factors. It should be noted that if we use the AG' values obtained for mechanism I1 (298 and 273 K) to obtain an estimate of its value at 233 K, we get 10.4 kcal mol-I. This value is significantly higher than the 8.5 kcal mol-' we obtain for mechanism I. Thus, it seems possible that the change in mechanism may be due to the fact that at low temperatures the system chooses a lower energy pathway for the decomplexation step. Dicyclohexano-18-crown-6.The temperature dependence of the relaxation time for the two dicyclohexano- 18-crown-6 (cisanti-cis and cis-syn-cis) complexes with the sodium ion was
J . Phys. Chem. 1987, 91, 1255-1259 TABLE I V Values of the Dissociation Rates and 1/rNL+ for a THF Solution Containing NaSCN a d DAlSC6 at a Ligand/Nat Mole Ratio of 0.53 and at Different Temperatures T.OC k-,. s-l L , M-' s-l 1/ 7 N d +, s-l 6.2 2010 f 90 2010 f 90 -7.7 1640f 60 1640 f 60 -21.0 1240 f 50 1240 f 50 -34.9 72500 f 3500 700 f 40 -45.6 29000 f 4000 280 f 40
obtained from the 23Na line-shape analyses. The temperature dependence for both isomers is shown in Figures 5 and 6. The linearity of the plots shows that only one mechanism is operating in the temperature range studied. In order to determine the exchange mechanism for the two systems, several solutions with ligand/Na+ mole ratio ranging from 0.2 to 0.8 were studied at different temperatures; however, for solutions with mole ratio values greater than 0.55 or smaller than 0.45 the calculated values of T were too scattered to be useful. Thus, our data do not allow an unambiguous determination of the exchange mechanism.
1255
The rates of decomplexation were calculated from the T values, and the free energy, enthalpy, and entropy of activation were calculated, as previously described, for the decomplexation step. The results are given in Table 111. It is interesting to note that the activation parameters for the two isomers are quite close to those previously obtained for 18C6 for the NaSCN-18C6 system where the exchange followed mechanism I. Thus, it seems probable that in these two cases mechanism I also dominates. The faster decomplexation rates obtained with DC18C6 are probably related to the more rigid structure of these ligands which results in the destabilization of the sodium complex as compared to that of 18C6.
Acknowledgment. We gratefully acknowledge the support of this study by a National Science Foundation research grant (CHE-85 15474). Registry No. 18C6, 17455-13-9;(cis-anti-cis)-DC18C6,15128-66-2; (cis-syn-cis)-DC18C6, 15128-65-1; DAl8C6, 23978-55-4; DTI8C6, 296-39-9; DB18C6, 14187-32-7; NatPh4B-, 143-66-8; NaSCN, 54072-7; NaI, 7681-82-5; NaC104, 7601-89-0; NaCp(CH,)5, 40585-51-1; Na', 17341-25-2; Na, 7440-23-5.
Paramagnetically Enhanced Nuclear Relaxation in Lamellar Phases J.-P. Korb, M. Ahadi: Laboratoire de Physique de la Mati&-eCondensDe, Groupe de Recherche No. 38 du Centre National de la Recherche Scientifque Ecole Polytechnique, 91 128 Palaiseau, France
and H.M. McConnell* Stauffer Laboratory for Physical Chemistry, Stanford University, Stanford, California 94305 (Received: July 31, 1986)
A statistical method is applied to calculate the spectral densities and the spin-relaxationrates arising from dipolar interactions between paramagnetic spin-labels and nuclei diffusing laterally in separated parallel planes. The intermolecular potential responsible for the nonuniform radial molecular distribution, observed at short distance between the head groups of each layer, is considered in the dynamical calculationsby means of a Smoluchowski equation for the conditional probability usually encountered in spin-relaxation theory. The solution of this equation by finite difference techniques permits the calculation of the enhanced nuclear relaxation rates due to the lateral diffusion of the paramagnetic spin-labels in lamellar phases. The simultaneous consideration of intermolecular potential and appropriate core boundary conditions between the head groups significantly increases the spin-label-enhancedlongitudinal nuclear relaxation rate in comparison with previous treatments. This method appears to be directly applicable to recent NMR measurements of diffusion coefficients and conformational properties of molecular surfactants in lamellar phases.
1. Introduction It is well-known that magnetic resonance can be used to obtain valuable structural information on lamellar phases, but difficulties still remain in obtaining dynamical information on these systems. From a theoretical point of view, these difficulties come mainly from the spin-relaxation models always needed to interpret the data. Certain problems require that 2D theory be used. This arises, for instance, when nuclear relaxation rates of membrane molecules are enhanced by dipolar interactions with membranebound paramagnetic ~pin-labels.'-~ In this case a previously proposed 2D theoretical model has encountered paradoxical divergences of the main observables of relaxation which were eliminated by considering two independent relaxation processes with different time scale^.^ This has provided a correct ad hoc procedure to cut off the otherwise long-time decay of pairwise dipolar correlation functions responsible for these divergences. Permanent address: Laboratoire de Chimie Physique, 11 Rue Pierre et Marie Curie, 75005 Paris, France.
0022-3654/87/2091-12S5%01.50/0
Recently, we have proposed a mathematical and physical understanding of these seemingly paradoxical divergenceson the basis of an original 2D theory of an ensemble of spins, undergoing dipolar interactions, which diffuse on a finite but arbitrarily large planar s ~ r f a c e . ~ - ~ In this paper the analysis is extended by considering, in the dynamical calculations, the intermolecular potential responsible (1) Kornberg, R. D.; McConnell, H. M. Proc. Null. Acad. Sci. U.S.A. 1971, 68, 2564.
(2) Lee, A. G.; Birsdall, N. J. M.; Metcalfe, J. C. Methods in Membrane Biology; Korn, E. D., Ed.; Plenum: New York, 1974; Vol. 2. ( 3 ) Godici, P. E.; Landsberger, F. R. Biochemistry 1974, 13, 362. (4) Brblet, Ph.; McConnell, H. M. Proc. Narl. Acad. Sci. U.S.A. 1975, 72, 1451. (5) Korb, J.-P.; Torney, D. C.; McConnell, H. M. J . Chem. Phys. 1983, 78, 5782. (6) Korb, J.-P.; Winterhalter, M.; McConnell, H. M. J. Chem. Phys. 1984, 80, 1059. (7) Korb, J.-P. J . Chem. Phys. 1985, 82, 1061. (8) Tabony, J.; Korb, J.-P. Mol. Phys. 1985, 56, 1281.
0 1987 American Chemical Society
