J. Phys. Chem. 1992,96, 2185-2189 coefficients. In the first-order case, the coefficient of the linear term is the number-weighted first moment. For the second-order case, this coefficient is the number-squared-weighted first moment.
Acknowledgment. We wish to thank Professor Eric Weitz for providing cogent comments on the manuscript and for discussion
2185
concerning his experimental measurements with Dr. H. Krueger on oxygen atom recombination rates in xenon matrices. Financial support for this research from the Air Force Office of Scientific Research under Grant AFOSR-89-0085 is gratefully acknowledged. B.W.S. is pleased to acknowledge support from a Lew Wentz Scholarship.
Metal Interchange of Crown Ether-Alkali Metal Cation Complexes in Solution. 'Li Nuclear Magnetic Resonance Study of the Exchange Kinetics of Lithium 15-Crown-5 and Lithium Monobenzo-I5-crown-5 in Nitromethane' Kathleen M. Brieret and Christian Detellier* Ottawa- Carleton Chemistry Institute, Ottawa University Campus, Ottawa, Ontario Kl N 6N5,Canada (Received: August 13, 1991)
The exchange kinetics of (Li:lS-crown-5)+ and (Li:benzo-l5-crown-5)+ in nitromethane were studied by 'Li NMR. The lithium cation exchanges between two sites in solution: solvated and 1:l complexed with the crown ether. The chemical exchange between these two lithium sites was determined to proceed via a metal interchange mechanism, IM, in both cases, characterized by the following activation parameters: AZf* = 21 f 1 and 32 f 1 kJ mol-', AS* = -54 f 3 and -36 f 1 J mol K-' for (Li:l5C5)+ and (Li:B15C5)+, respectively. This interchange mechanism was predominant in the temperature range 263.0-300.0 K. The main factors controlling the exchange rate are conformationalrearrangements of the ligand during the concerted partial decomplexation of a lithium cation and partial complexation of a second one.
Introduction Detailed mechanisms of unidentate ligand substitution reactions on metal cation complexes in solution have been studied quite extensively during the past decades.2 The vast majority of exchange processes occurring in the first coordination sphere of a metal cation in solution can be rationalized by types of mechanisms ranging from purely dissociative to purely associative, in which the presence of a definite intermediate of lower or higher coordination number can be demonstrated? If no such intermediates are present, a concerted interchange (with eventually dissociative or d a t i v e character) mechanism This mechanistic description of unidentate ligand/solvent substitution reactions can provide the basis for the rationalization of macrocyclic, multidentate, ligand complexation reaction^.^ Cox and Schneider3 have recently suggested a simple mechanistic model, in which the solvent molecules occupying the first coordination sphere of a metal cation are successively replaced, in a fully stepwise manner, by the donor atoms of the macrocyclic ligand. A large majority of the systems involving alkali metal cation-macrocycle complexes follows this model, as shown by NMR4 and ultrasonic absorption techniq~es.~ Other mechanisms can be operative. For example, in aqueous media, c00rdi~tedmultidentate ligands can retain enough basicity to be protonated, so that an acid-catalyzed dissociation mechanism becomes competitive.6 Similarly, removal of coordinated ligands from a metal cation-ligand complex can be accelerated by the attack of a second metal cation on a site of the coordinated ligand.&-' This process, which is reminiscent of an electrophilic substitution reaction, SE2,8has been shown to occur in a number of systems,& for anionic monodentateg or porphyrinic'O ligands. In the case of neutral ligands, to the best of our knowledge, the only systems for which a similar mechanism has been conclusively shown are complexes of crown ethers and alkali-metal cations in poorly coordinating solvents." The global process described by eq 1, in which two metallic cations (M) are associated ML
+ M*
[M--L--M*]'+
M'L
+M
(1)
Present address: Institute for Biological Sciences, National Research Council, Ottawa, Ontario K1A OR6, Canada.
and bridged by a common acyclic or macrocyclic multidentate ligand (L) in the transition state, could, a priori, represent an efficient path of cation exchange, particularly in solvents characterized by a low donicity number (DN).'* This metal interchange mechanism on a macrocyclic ligand will be labeled IM by analogy with the ligand interchange mechanism, I.2f Kinetic and mechanistic studies involving lithium macrocyclic (1) 15-Crown-5 (15C5): 2,3,5,6,8,9,11,12-octahydro-1,4,7,10,13-pentaoxacyclopentadecene. Monobenzo- 15-crown-5 (B15C5): 2,3,5,6,8,9,11,12octahydro- 1,4,7,10,13-pentaoxabenzocyclopentadecene. (2) (a) Langford, C. H.; Gray, H. B. Ligand Substirution Processes; Benjamin: New York, 1965. (b) Basolo, F.; Pearson, R. G. Mechanisms of Inorganic Reactions, 2nd ed.; John Wiley and Sons: New York, 1967. (c) Wilkins, R. G. The Study of Kinetics and Mechanisms of Reactions of Transition Meral Complexes; Allyn and Bacon Inc.: Boston, 1974. (d) van Eldik, R. Inorganic High Pressure Chemistry Kineiics and Mechanisms; Elsevier: Amsterdam, 1986. (e) Swaddle, T. W. Adu. Inorg. Bioinorg. Mech. 1983,2,95-138. (f) Merbach, A. E. Pure Appl. Chem. 1987,59, 161-172. (3) Cox, B. G.; Schneider, H. Pure Appl. Chem. 1990,62, 2259-2268. (4) Detellier, C.; Graves, H. P.; Briere, K. M. Alkali Metal NMR Studies of Synthetic and Natural Ionophore Complexes. In Isoropes in the Physical and Biomedical Science; Isotopic Applications in NMR Studies; B u n d , E., Jones, J. R., Eds.; Elsevier Sci. Publ.: Amsterdam, 1991; Chapter 4, pp 159-2 1 1. (5) (a) Eyring, E. M.; Petrucci, S.;Xu,M.; Rodriguez, L.J.; Cobranchi, D. P.; Masiker, M.; Firman, P. Pure Appl. Chem. 1990,62,2237-2241. (b) Eigen, M.; Winkler, R. In The Neurosciences: Second Study Program; Schmitt, F. O., Ed.; Rockefeller University Press: New York, 1970; pp 685-696. (6) See,for example: (a) ref 2c, Chapter 4. (b) Cox, B. G.; Garcia-Rms, J.; Schneider, H. J . Am. Chem. SOC.1981,103, 1054-1059. (c) Chang, C. A.; Chang, P. H. L.; Manchanda, V. K.; Kasprzyk, S.P. Inorg. Chem. 1988, 27, 3786-3789. (7) Jones, M. M.; Clark, H. R. J . Znorg. Nucl. Chem. 1971,33,413-419. ( 8 ) Guthrie, R. D.; Jencks, W. P. Acc. Chem. Res. 1989, 22, 343-349. (9) Ja) Armor, J. N.; Haim, A. J. Am. Chem. Soc. 1971,93,867-873. (b) Banyai, I.; Glaser, J. J . Am. Chem. SOC.1989, 111, 3186-3194. (c) Buckingham, D. A.; Clark, C. R.; Webley, W. S.Inorg. Chem. 1991,30,466-474. (10) Khosropour, R.; Hambright, P. J. Chem. Soc., Chem. Commun. 1972, 13-14. (1 1) Delville, A.; Stover, H. D. H.; Detellier, C. J . Am. Chem. Soc. 1987, 109, 7293-7301. (12) (a) Gutmann, V.;Wychera, E. Inorg. Nucl. Chem. Letr. 1966, 2, 257-260. (b) Gutmann, V. The Donor-Acceptor Approach to Molecular Interactions; Plenum Press: New York, 1978.
0022-365419212096-2185%03.00/0 0 1992 American Chemical Society
2186 The Journal of Physical Chemistry, Vol. 96, No. 5, 1992
Britxe and Detellier
-0
20
-C IS
' T;
-I
(Hz)
8 (IJP'T)
10 -I
5
-I
1.0
0.s
0
1.s
P Figure 1. 'Li NMR chemical shifts as a function of p = [C]T/[LiCIO& in nitromethane at 300.0 0.5 K. C = 15C5 (M) [LiC1O4JT= 10.0 mM; B15C5 ( 0 )[LiC1O4IT= 10.6 mM.
*
complexes are rather parse.^.'^ 'Li NMRI4-l7 and ultrasonic absorption techniques'* have been used to study the formation/dissociation kinetics of lithium cation complexes with crown ethers or cryptands. In this paper, we demonstrate by 7Li NMR the associative nature of the lithium cation interchange in lithium:l5-crown-5, (Li:l5C5)+, and 1ithium:monobenzo-15-crown-5, (Li:B15C5)+, in the solvent nitromethane (NM), as shown in eq 1. Experimental Section Anhydrous LiC104(Baker analyzed reagent) was vacuum dried at 353 K in the presence of phosphorus pentoxide for at least 24 h prior to use. Bl5C5 (Aldrich 98%) was recrystallized from hexanes and vacuum dried at 303 K in the presence of phosphorus pentoxide for at least 24 h. 15C5 (Aldrich 98%) was vacuum distilled and vacuum dried in the presence of phapphorus pentoxide at room temperature for 6-8 h. Nitromethane (Aldrich 96% Gold Label) was dried under reflux over calcium hydride for 3 h, distilled under nitrogen atmosphere, and stored under argon. The solution samples, contained in 10-mm NMR tubes, were flushed with argon and sealed with Parafilm. All spectra were recorded within 48 h of sample preparation. 7Li NMR spectra were obtained on a Varian XL-300 spectrometer at 116.57 MHz and were recorded unlocked. The chemical shifts were referenced to 0.1 M lithium chloride in 20% D 2 0 / H 2 0 (v/v) and corrected for the different bulk magnetic susceptibilities of nitromethane and water. The 90° pulses were ~~
~
(13) (a) Olsher, U.; Izatt, R. M.; Bradshaw, J. S.;Dalley, N. K. Chem. Reo. 1991,91, 137-164. (b) Bajaj, A. V.; Poonia, N. S. Coord. Chem. Rev. 1988,87, 55-213. (14) Cahen, Y. M.; Dye, J. L.; Popov, A. I. J . Phys. Chem. 1975, 79, 1292- 129 5. (15) Aalmo, K. M.; Krane, J. Acta Chem. Scand. 1982, A36, 219-225. (16) (a) Lincoln, S. F.; Abou-Hamdan, A. Inorg. Chem. 1990, 29, 3584-3589. (b) Abou-Hamdan, A.; Lincoln, S. F. Inorg. Chem. 1991, 30, 462-466. (17) Btitre, K.M.; Dettman, H.; Detellier, C. J. Mugn. Reson. 1991, 94, 600-604.
(18) Cobranchi, D. P.; Philip, G. R.; Johnson, D. E.; Barton, R. M.; Rose, D. J.; Eyring, E. M. J . Phys. Chem. 1989, 93, 1396-1398.
C
1.0
0.5
1.5
P Figure 2. 'Li NMR transverse (i = 2; 0 ) and longitudinal ( i = 1; W) relaxation rates as a function of the ratio p = [B15C5]T/[LiC10,]Tin nitromethane. T = 300.0 f 0.5 K; [LiCIO.,]T = 10.6 mM. The data points are experimental and the Ti'curve (based on eq 4) was calculated from the value of k2 ( k 2 = 1.88 X 10' M-I S-I) determined from eq 7.
systematically verified by the 360' null method and, depending on experimental conditions, varied between 15 and 20 fis. Longitudinal relaxation rate measurements were obtained with the inversion-recovery method, in connection with a three-parameter nonlinear regression on at least nine experimental points. The temperature of the probe was measured with a thermocouple dipped in N M in a nonspinning 10-mm NMR tube. For a temperature range between 240 and 310 K, the temperature of the sample was estimated to be reliable at fO.5 K. The pseudo-fmt-order rate constants were obtained from a full lineshap analysis for a two-site excl~ange.'~The digitized spectra were transferred from the XL-300 spectrometer to an Amdahl mainframe system.*O Nonlinear regressions of the spectral data yielded the corresponding rate constants. ReSUltS Figure 1 shows the variation of the 'Li chemical shift of a lithium perchlorate solution in nitromethane (NM) as a function of the ratio p = [c]T/[Liclo4]T for C = 15C5 or B15C5. There is a fair agreement between the results obtained for 15C5 in NM ([LiC1O4IT= 10.0 mM at 300.0 K) with those reported by Smetana and Popov for the same system ([LiCl0,IT = 20 mM at 300 K) at 23.3 MHze21At p = 0, the observed chemical shift (-0.62 ppm) is characteristic of the lithium cation in its solvated state, (Li+),.2' Upon the addition of the crown ethers to the Li+ solution, an upfield shift is observed. The linearity of the plots in the region 0 < p < 1, shown in Figure 1, followed by a plateau for p > 1, indicates the formation of the 1:l complexes (Li:15C5)+ and (Li:B15C5)+, represented by the equilibrium shown in eq 2.
(Li+),
+ C,+ (Li:C),+
(2)
(19) Sandstrom, J. Dynamic N M R Spectroscopy; Academic Press: New York, 1982. (20) Chen, Z.; Dettman, H.; Detellier, C. Polyhedron 1989,8,2029-2033. (21) Smetana, A. J.; Popov, A. I. J . Solution Chem. 1980, 9, 183-196.
The Journal of Physical Chemistry, Vol. 96, No. 5, 1992 2187
Crown Ether-Alkali Metal Cation Complexes
I
2.2 a
3522 o!o
-$A
-11.0
-01.1
PPY -21.0
0
S
10
[Lil,
(mM)
Figure 4. ( k A t k,) as a function of [LiC10,lT in NM. p = [ 15C5],/[LiC1041T = 0.53 in all cases. The data points are experimental and the lines result from linear regressions on eq 7. (0)300.0 & 0.5 K; (W) 263.0 0.5 K.
variation parallels that of the 7Li chemical shift (Figure 1). Whereas the TI-' is not affected by the chemical exchange, the T2-' is. It can be shown that the exchange contribution to the transverse relaxation rate (T2,=-')is directly related to the lifetime of 7Li+ in the two sites A and B, T = ( k A kB)-', and to the difference between the chemical shifts of the two sites, vA and
+
b
r i I o!o
( 1 1 ,
, I I I
-01.1
I , , ,
-20
, I
T , , ,
yg:25,26
-11.1 PPW-PI.0
Figure 3. 'Li NMR spectra of solutions containing equal populations ( p = 0.50) of (Li'), and (Li:B15C5)+ in nitromethane. From top to bottom, the [LiCIO,]T and (k, t kB),determined from full line-shape analyses, vary as shown: (a) 263.0 0.5 K; (b) 300.0 0.5 K.
*
The equilibrium constant of the complex formation, log Kf,is too large (>4) to be determined by this technique.22 In the region p > 1, a plateau is reached where the chemical shift reflects the presence of complexed lithium only: -1.15 ppm for (Li:B 15C5)+ and -1.35 ppm for (Li:lSCS)+. This behavior has been observed for several other alkali metal-crown ether complexes as well, typically in solvents of low donicity such as N M and acetonitrile (AN)."5'53 In the region of lithium concentrations studied (1-1 1 mM), the 7Li chemical shifts of LiC104, (Li:15C5)+, and (LiB15C5)+ in N M displayed a maximum variation of less than 0.1 ppm, indicating a negligible amount of ion pairing.24 The transverse and longitudinal relaxation r a t e of (Li:B15C5)+ in NM are shown in Figure 2. They are characteristic of a system undergoing moderately rapid chemical exchange of lithium between two sites, A and B (eq 3).'1925326In eq 3, kA and kB are M+ A
& (M:C)+ kB
B
TZ,,;' = 4PAPBT2(vA- U B ) ' ( ~ A
(22) Live, D.; Chan, S.I. J . Am. Chem. Soc. 1976, 98, 3769-3778. (23) (a) Lin, J. D.; Popov, A. I. J . Am. Chem. Soc. 1981,103,3773-3777. (b) Shamsipur, M.; Rounaghi, G.; Popov, A. I. J . Solution Chem. 1980, 9, 701-714. (24) Staver, H. D. H.; Detellier, C. J . Phys. Chem. 1989,93,3174-3178. (25) Woessner. D. E. J . Chem. Phys. 1961, 35, 41-48. (26) (a) Staver, H. D. H.; Delville, A,; Detellier, C. J . Am. Chem. SOC. 1985,107,4167-4171. (b) Delville, A.; Stiwer, H. D. H.; Detellier, C. J . Am. Chem. SOC.1985, 107,4172-4175.
(4)
Equation 4 is valid2s when k A , kB > T2,A-', T~,B-', I(vA - vB)l and 4T2(vA- u B ) ~>> (T2,A-I - T2,B-1)2,conditions which are fulfilled in the present study. Figure 3 shows the 7Li NMR spectra of a series of solutions containing equal populations of lithium solvated in N M and lithium complexed to B15C5. A lithium concentration coalescence is observed near 2 mM at 300.0 K (Figure 3a) and 11 mM at 263.0 K (Figure 3b). As the concentration of lithium increases, so does the corresponding (kA+ kB). This is similar to what was previously observed for Na+-B15C5 by 23NaNMR.27 The sum of the two pseudo-first-order rate constants, ( k A+ kB), can be interpreted in a meaningful way only if the corresponding mechanism of exchange is known. Two limiting mechanistic hypotheses,28of a dissociative exchange, shown in eq 5 (which (M:C)+ M+*
(3)
the pseudo-first-order rate constants for the forward and reverse reactions, respectively. A represents the solvated lithium, and B the complexed lithium. The 'Li longitudinal relaxation rate
+ kg)-'
M+* (kA
& M+ + C kl
k +C& (M*:C)+ k-1
+ (M:C)+
+ kB) = k-l(l
M+
- p)-'
(53) (5b)
+ (M*:C)+
(6)
+ k2[Li+IT
(7)
consists in the steps of dissociation (5a) and recombination (5b), following the models based on the Eigen-Winkler reaction mechanism3,s) and of an associative exchange, shown in eq 6 (27) (a) Bribe, K. M.; Detellier, C. J . Phys. Chem. 1987, 91,6097-6099. (b) Brisre, K. M.; Detellier, C. New J . Chem. 1989, 13, 145-150. (28) (a) Shchori, E.; Jagur-Grodzinski, J.; Luz, Z.; Shporer, M. J . Am. Chem. Soc. 1971, 93, 7133-7138. (b) Shchori, E.; Jagur-Grodzinski, J.; Shporer, M. J . Am. Chem. SOC.1973,95, 3842-3847.
2188 The Journal of Physical Chemistry, Vol. 96, No. 5, 1992
Brigre and Detellier -1
-1
*
-1
e"
-1
-1
-21
5
0
I 3.3
IO
Figure 5. ( k A + kB) as a function of [LiCI041T in N M . p = [ B ~ ~ C ~ ] T / [ L ~ C=~0.51 O & in all cases. The data points are experimental and the lines result from linear regressions on eq 7. ( 0 ) 300.0 f 0.5 K; (M) 263.0 f 0.5 K. TABLE I: Rate Constants, k2,and Activation Parameters for the Metal Interchange of ( M C ) + in Nitromethane
19 f 1 1.88 f 0.08 1.45 f 0.05 1.09 f 0.04 2.03 f 0.06
37.4 43.2 44.1 44.8 43.0
f 0.1 i 0.1 f 0.1 f 0.1 f 0.1
21 f 32 f 21 f 28 f nd
I 35
I
I 3.1
1 3.9
T-' [ xi0-3 K-' )
[ L i l T (mM)
(Li:15C5)+" (Li:B15C5)+" (Na:15C5)+b (Na:B15C5)+' (Na:B15C5)+@
I
1 1 1 3
-54 -36 -76 -57 nd
f3 f1 f2 f3
'Counteranion is C10; and T = 300.0 f 0.5 K. bReference 27b; counteranion is BPh, and T = 301.5 f 0.5 K. CReference27a; counteranion is BPh4- and T = 301.5 f 0.5 K.
(equivalent of eq 1 described in the Introduction), will be considered. They can be tested by the relationship between ( k A kB) and the crown ether and salt concentrations, shown in eq 7.27b In eqs 5 and 6, M is the metal cation and C is a macrocyclic ligand such as a crown ether or a cryptand. In eq 7, p has its usual meaning, [Li+ITis the total concentration of lithium, and k-, and k2 are the rate constants involved in the two specific mechanisms. The plots of (kA+ kB) as a function of [Li+ITat a constant value of p are shown in Figures 4 and 5 for (Li:l5C5)+ and (Li:BlSC5)+, respectively. Both plots are linear and extrapolate to the origin, indicating that any contribution from the dissociative exchange for both (Li:l5C5)+ and (LkB15C5)+cannot be observed. Testing for the mechanism at two different temperatures also reveals that the associative mechanism of eq 6 remains favored at 300.0 and 263.0 K. The values for k2 at 300.0 K, obtained directly from the slopes of the plots in Figures 4 and 5 , are shown in Table I. The activation parameters for the associative exchange of (Li:15C5)+ and (Li:B15C5)+ in N M were determined from a temperature study; the resulting Eyring plots are shown in Figure 6 and the corresponding energies of activation are given in Table I. For comparison, Table I also includes results obtained by 23Na NMR for the sodium cation27with the same crown ethers and
+
Figure 6. In ( k z h / k e T )as a function of TI.For 15C5 (M), [LiC1041T = 5.0 mM and p = 0.53; for B15C5 ( O ) , [LiCI04]T= 10.6 mM and p = 0.53.
solvent at similar temperatures.
Discussion This study demonstrates the efficiency of an associative (bimolecular) exchange mechanism in the case of Li+-l5C5 systems in nitromethane. The electrostatic repulsion of the two charged species brought together should be counterbalanced by the stronger favorable interaction of Li+ with the crown ether oxygen atoms than with the nitromethane molecules. This is reflected in the low values of the activated enthalpies (20-30 kJ mol-') for the associative exchange in nitromethane. As a comparison, in the same solvent, the previously determined value of the enthalpy of activation for the dissociative mechanism, in the case of Na+DB18C6 system, was 37 kJ mol-'.l' Despite the values of the entropies of activation which are large and negative (in good agreement with an associative process), because of the low enthalpic contribution, the free energies of activation for the associative process (eqs 1 or 6) are low enough to make this mechanism more efficient than the dissociative exchange (eqs 5a,b). The first evidence for the efficiency of such an associative mechanism was reported by Schmidt and Popov for the system (K+AsF,:18C6) in 1,3-dioxolane studied by 39KNMR.29 Since then, evidence for this mechanism has been found for a few other systems including sodium complexes studied by 23Na NMR,11,26127s30.31 cesium complexes studied by 133CsNMR,32and the system (Li+C104-:C221) in acetonitrile and propylene carbonate studied by 'Li NMR.33 As a general rule, the dissociative process is favored in solvents of high donicity number, and it is only in solvents of low donicity (29) Schmidt, E.; Popov, A. I. J . Am. Chem. SOC.1983,105, 1873-1878. (30) Graves, H. P.; Detellier, C. J . Am. Chem. Soc. 1988,110,6019-6024. (31) (a) Strasser, B. 0.;Hallenga, K.;Popov, A. I. J . Am. Chem. Soc. 1985,107,789-792. (b) Strasser, B. 0.; Popov, A. I. J . Am. Chem.Soc. 1985, 107, 7921-7924. (c) Szczygiel, P.; Shamsipur, M.; Hallenga, K.; Popov, A. I. J . Phys. Chem. 1987, 91, 1252-1255. (32) Strasser, B. 0.;Shamsipur, M.; Popov, A. I. J . Phys. Chem. 1985, 89, 4822-4824. (b) Shamsipur, M.; Popov, A. I. J. Phys. Chem. 1987,91, 447-451. (c) Shamsipur, M.; Popov, A. I. J . Phys. Chem. 1988,92, 147-151. (33) Shamsipur, M.; Popov, A. I. J . Phys. Chem. 1986, 90, 5997-5999.
J. Phys. Chem. 1992,96, 2189-2196
number, in which not only the dissociative process is disfavored, but also the cation is poorly solvated, favoring the eventual formation of 2:l M+:C stoichiometries, that the associative process can become competitive. Evidence for the formation of 2:l M+:L complexes in nitromethane, where M is an alkali metal cation and L is a multidentate ligand, can be found in the l i t e r a t ~ r e . ~Nitromethane, ~ characterized by a very low donicity number12 (DN = 2.7; DNbulk= 6.835) and a relatively high dielectric constant (e = 35.9), is a particularly well-adapted medium for the formation of such dicationic complexes. In the same line, the equilibrium constants for the formation of 1:1 (Kn)and 2: 1 (Kn)Na+:L complexes in pyridine, where L is a spiro-bis-crown ether (dicoronand), was determined by 23NaNMR.36 Kn was only an order of magnitude lower than Kfl. This remarkably small negative cooperativity for the occupation of two close cavities by sodium cations was considered as encouraging for the design of inclusion complexes comprising several encapsulated metallic cations.37 Dimetallic catenates3* or multimetallic double-stranded helicates, which
2189
assemble spontaneously displaying positive c o ~ p e r a t i v i t yare ,~~ other examples of supramolecular organizations of cationic species. Within experimental errors, the enthalpies of activation for the cationic exchange in (Li:15C5)+ and (Na:l5C5)+ are identical, as well as those of (Li:B15C5)+ and (Na:B15C5)+ (see Table I), showing that the size of the cation does not play a governing role in the mechanism. The fact that the enthalpies of activation of the B15C5 complexes are slightly higher than the 15C5 complexes reflects the increased rigidity of the benzo-substituted crown ether. The entropies of activation are all largely negative, in agreement with an associative type mechanism. In another we have observed that the nature of the solvent plays also a minor role in the control of the activation parameters observed for the associative exchange. All these facts are in agreement with a control of this mechanism by conformational rearrangements of the ligand. Finally, the understanding of such associative cationic exchange mechanisms in simple model systems like the one studied here, could shed light on the more complex mechanisms of ionic permeation in biological multi-ion channels.40
Acknowledgment. The Natural Science and Engineering Research Council of Canada (NSERCC) is gratefully acknowledged for financial support. Registry No. (Li:15C5)+, 74060-72-3; (Li:Bl5C5)+, 73503-76-1;
(34) (a) Schmidt, E.; Hourdakis, A.; Popov, A. I. Inorg. Chim. Acta 1981, 52,91-95. (b) Stover, H. D. H.; Robillard, M.; Detellier, C. Polyhedron 1987, 6,577-581. (c) Shamsipur, M.; Popov, A. I. J . Am. Chem. Soc. 1979,101, 4051-4055. (d) Stover, H. D. H.; Maurice, L. J.; Delville, A.; Detellier, C. Polyhedron 1985, 4, 1091-1094. (35) Marcus, Y. J . Solution Chem. 1984, 13, 599-624. (36) Bouquant, J.; Delville, A.; Grandjean, J.; Laszlo, P. J . Am. Chem. SOC.1982, 104,686-691. (37) Detellier, C.; Laszlo, P. Studies of ion-moleculeinteractions by NMR spectroscopy in Studies in Physical and Theoretical Chemistry, 37, Topics in Molecular Interactions;Orville-Thomas,W. J., Ratajczak, H., Rao, C. N. R., Eds.; Elsevier Science Publishers: New York, 1985; pp 291-336.
NM, 75-52-5. (38) Dietrich-Buchecker,C. 0.;Hemmert, C.; Khgmiss, A.-K.; Sauvage, J.-P. J . Am. Chem. Soc. 1990, 112, 8002-8008. (39) Lehn, J.-M.; Rigault, A.; Siegel, J.; Harrowfield, J.; Chewier, B.; Moras, D. Proc. Natl. Acad. Sei. U.S.A. 1987, 84, 2565-2569. (40) Hill, J. A., Jr.; Coronado, R.; Straws, H. C. Biophys. J . 1989, 55, 35-46.
Factors Affecting Nonradlative Decay: Temperature Dependence of the Picosecond Fluorescence Lifetime of Pt2(pop)," Steven J. Milder*,' and Bruce S. Brunschwig* Department of Chemistry, Brookhaven National Laboratory, Upton, New York I I973 (Received: August 30, 1991)
The lifetime of the picosecond fluorescence of Pt2(pop),4- (pop = pP20SH2)has been observed to increase with decreasing temperature (e.g., from 40 ps at 290 K to 740 ps at 80 K in H20:glycerol(1:2)). The longer lifetimes at the lower temperatures are attributed to a decrease in the rate of the nonradiative decay of the short-lived emissive state, IA2,,, to the long-lived emissive state, 3A2u,of the complex. The variation of the lifetime of the ]A2, state with temperature has been fit to two-channel expressions that include both a temperature-independent term and a term that is derived from a single-mode quantum treatment of nonradiative decay in either its normal or high-temperature limit. The temperature dependence of the lifetime in each solvent yields sufficient information to define only three parameters, while the two-channel, single-mode quantum expression has five independent parameters. Thus, even when one of the five parameters is held constant, a range of values of the other four parameters gives reasonable fits to the data. When a two-channel expression with a single-mode quantum term in the high-temperature limit is used (kok = ko + (A/d/RT) exp(-E,/RT)), the three independent parameters can be well defined in each solvent. In nondeuterated solvents the decay of the lAlu state gives values of A that vary from 9.2 X 10l2 to 6.0 X lOI4 8,values of E, that vary from 890 to 1590 cm-I, values of ko that are almost independent of solvent ((1.5 0.2) X lo9 s-l), and low-temperaturelifetimes that vary from 620 to 850 ps. Upon solvent deuteration, the low-temperature lifetime of the lAzustate increases to 2170 ps. The temperature-dependentcomponent of the IAzudecay is attributed to a nonradiative pathway involving strong coupling between the fluorescent 1A2u('du*pa) state and a primarily ligand-field 3B2u(3du*d~-9) state; this pathway ultimately leads to population of the long-lived 3A2u(3du*po) state. The temperature-independent component of the ]Alu decay is dominated by a nonradiative pathway involving weak coupling between the 'Alu and 3A2ustates in which the high-energy modes of the solvent a r e important accepting modes.
*
Introduction The yield and lifetime of the luminescence of emissive transition-metal complexes are generally temperature dependent. The temperature dependence arises because most transition-metal (1) Send correspondence to this author at: Division of Natural Sciences, The Evergreen State College, Olympia, WA 98505.
0022-3654/92/2096-2189!§03.00/0
complexes possess electronically excited state@) only slightly higher in energy than the emissive state, and these states often provide a decay route@) to lower energy Or i%roundstates. AS a comequene, two te"rature regions are often observed when the effect of temperature on the decay rate of the emissive state is determined. In the higher temperature region the rate of decay often follows an Arrhenius type expression, while at low temperatures 0 1992 American Chemical Society
