J. Phys. Chem. 1984,88, 2541-2547 lack of kinetic isotope effect seen by us is certainly consistent with the above mechanism. The explanation for the observation of measurable rates in the cases of reactions 2 and 3 is quite obvious from the above reaction mechanism. The cyclohexadienyl radical formed in the case of, say, reaction 2 is C6D6H. This radical can decompose by two channels:
k-&
C,jDsH -t D
(-2b)
It is expected, as argued earlier, that the cyclohexadienyl radical is thermalized. Therefore, it is quite likely that this thermalized adduct can scramble H atoms and therefore, statistically speaking, reaction -2b would be 6 times more prevalent than reaction -2a. Since only H atom disappearance is monitored and since any subsequent reactions of the product D atom with C6D6would lead only to D atoms, the rate coefficient measured would be very close to that for reaction 2. This indeed is the case as shown by the values of kz and k3at high temperatures, Le., T > 600 K. They are very close to the values obtained from linear extrapolation of the low-temperature Arrhenius plots. This explanation is completely consistent with the unit yield of H in reaction 3. A similar argument has been proposed by Benson and Shawlo to explain the isotope exchange seen by them in their experiments on the thermal decomposition of cyclohexadiene in the presence of benzene-d,. The value of k, is lower than that of k3 at T > 700 K. One possible explanation for this observation may lie in the fact that as the decomposition rate of the adduct gets very large, the adduct might not have sufficient time to thermalize. However, an extrapolation of our thermal decomposition data suggests that even at 900 K the adduct must undergo tens of collisions before decomposition. The second possible explanation is that process-2
2541
exhibits a large kinetic isotope effect; Le., k-za/k-zpis large. A check for such a process would involve measuring the rate coefficient for reaction 2 on very short time scales where reaction -2 would not regenerate H atoms. Such short time scale experiments are not feasible because of the lack of a suitable H atom laser photolytic source which would not react with D and be thermally stable at these high temperatures. The use of a short pulsed laser with a pulse width > 1 is provided by calorimetric determination of the overall complexation constant K2 just completed for NaSCN 18C6 in EtOH at the University of Utah; giving log K2 = 5.0 f 0.1. Since K2 = Kl(l + K 2 ) and K, 1it results that Kz >> 1. In the case of ethanolic Li' 18C6 two relaxation processes are clearly visible as shown above with the relaxation parameters collected in Table 11. Independence of the relaxation processes with concentration within experimental error and linearity of both p I and pLII with C (Figure 4B) ensure that we are observing in ethanol a process schematized by eq 111, with pIl now showing a greater dependence on C than on pp It is likely that the greater desolvation energy and ligand rearrangement involved in complexing Li+ with respect to Naf force the appearance of a two-step process in EtOH for the Li+ case when reacting with 18C6. In other words, in the case of Li+ the energy barrier for stripping the solvent from its first-coordination shell and for rearranging the crown ether around it is large enough that two steps are necessary. The first step is an encounter process with a partial
+
+
(9) H. Rushton, University of Utah, private communication.
/
ANaSCN R=1.0
(XVI) 0 0
0.1
0.2
0.3
~ ~ 1 (rnole/crnJ) 0 3
Figure 7. Eyring and Lamb plots and EtOH.
fi
-
0.4
0.5
vs. C for NaC104 + 18C6 in
desolvation and ligand rearrangement; the second step is the complete encapsulation of the small Li+ in the oversized 18C6 cavity, forcing the ligand to wrap around Li+. It may be also of interest to compare the results for the same cation and 18C6 in different solvents. As reported above, in ethanol, Na+ reacts with 18C6 in a single step. On the contrary, Naf reacts with 18C6 in D M F by a two-step process. This indicates the importance of the solvent in determining the number of steps in the complexation process. It may be that the desolvation step in D M F has a larger energy barrier showing itself as a separate relaxation process. Also, Lif reacts by a two-step process in ethanol but only by a one-step process in DMF. One may speculate that in the last solvent the last process involving the elimination of the coordinating solvent around Li' by 18C6 cannot occur to a significant extent. In trying to assign reasons for the different behavior of Na+ 18C6 in ethanol and DMF, one should notice that the permittivity of the solvents is not different enough to justify the observed behavior. Hence, it is not the permittivity but some other property such as the donor number of the solvent that is the driving factor in the above behavior. One should not forget however that the appearance of a relaxation process depends on the existence of a well-separated energy barrier and the existence of a sizable concentration of the species in equilibrium and of a sizable isoentropic volume change related to a given kinetic step. All these factors may be crucial to the appearance of two separate relaxation processes in some of the systems quoted above. We wish now to discuss as the final point the isomeric relaxation of 18C6 in ethanol. A single Debye relaxation at low temperature is noticed in ethanol similar to the situation in methan01.~Equations XI11 and XIV without the position K , >> 1 are valid, namely for
+
C1
e
J. Phys. Chem. 1984, 88, 2547-2551 C2
KO = ko/k4
(XVII)
2547
with parameters KO,AHo,and AH4* (AS4*has been calculated). Trial and error analysis3reveals that the system is compatible for K~ = 4 x 10-3
