Nuclear Relaxation of H₂ and H₂@C₆₀ in Organic Solvents

Abstract

We report an investigation of the nuclear spin-lattice relaxation of H 2 and H 2 @C 60 1 as a function of solvent and temperature. These studies explore and compare the nature of the interactions of a guest H 2 molecule confined transiently within the walls of a solvent cavity and a guest H 2 molecule encapsulated within the walls of the C 60 cavity.The relaxation time (T 1 ) of H 2 has been extensively studied in the gas phase and in liquid hydrogen at low temperatures. 6 The values of T 1 are 10-20 times smaller for H 2 @C 60 than for H 2 even though the ratios of T 1 for H 2 and H 2 @C 60 are similar in all the solvents.The temperature dependences of T 1 for H 2 and H 2 @C 60 were investigated in detail for toluene-d 8 ( Figure 1) and for benzene-d 6 , 1,1,2,2-tetrachloroethane-d 2 , 1,2-dichlorobenzene-d 4 , and chloroformd 1 . Striking features of the data are the occurrence of a maximum for T 1 at ∼240 K for both the H 2 and H 2 @C 60 in toluene-d 8 and a ratio of T 1 values which is nearly independent of temperature. A maximum of the value of T 1 with temperature is also found in 1,1,2,2-tetrachloroethane-d 2 and chloroform-d 1 . For benzene-d 6 and 1,2-dichlorobenzene-d 4 in the available range of temperatures, only a decrease of T 1 with increasing temperature was observed.This kind of dependence of T 1 on temperature is uncommon, although a maximum of T 1 has previously been observed for small molecules such as H 2 O, 7 HCl, and HBr in solution, 8,9 and it is consistent with two relaxation mechanisms with different temperature dependences dominating in turn below and above 240 K for both H 2 and H 2 @C 60 . Since the value of T 1 for both H 2 and H 2 @C 60 does not significantly change in going from benzene-h 6 to benzened 6 (Table 1), the dominating interactions determining H 2 and H 2 @C 60 nuclear relaxation must be intramolecular. Furthermore, the intramolecular dipole-dipole interaction and spin-rotation interaction are known 2 to be responsible for the relaxation of gaseous H 2 and their magnitude has been measured for H 2 in molecular beams. 10 Therefore it is likely that the relaxation of H 2 in solution also depends on the competition between intramolecular dipole-dipole interaction and spin-rotation interaction.The contribution to 1/T 1 (in extreme narrowing conditions) from intramolecular dipolar and spin-rotation interaction may be estimated by eq 1 2 and eq 2, 11,12 respectively:where γ H is the magnetogyric ratio for the proton, r is the equilibrium internuclear distance of H 2 (0.74 Å), C is the spinrotation coupling constant (7.16 × 10 5 rad s -1 ), 10 I is the moment of inertia of H 2 (4.6 × 10 -48 kg m 2 ), and k B is the Boltzmann constant. The correlation times τ dip and τ sr are measures of the timedependent fluctuations in the orientation and angular velocity of H 2 , respectively. Both correlation times are expected to be functions of viscosity and temperature which depend on the details of the motion of H 2 molecules and the surrounding medium. 11 Qualitatively, the dipole-...

Comparative NMR Properties of H2and HD in Toluene-d8and in H2/HD@C60

“…The qualitative features of this analysis may be summarized as follows: (1) Both correlation times are an order of magnitude longer for HY in C 60 than in toluene-d 8 , consistent with our earlier analysis. 1 It is consistent with our earlier proposed model in which the rotation of HY is slowed by some degree of interaction with the slowly rotating C 60 cage. …”

“…Figure 1b shows the values of the relaxation rate, 1/T 1 , for H 2 and HD in toluene-d 8 and in C 60 over the temperature range 200-340 K. The values for H 2 in the H 2 /HD mixture in both environments are indistinguishable from those reported previously. 1 The values of T 1 determined for each of the three lines of HD were the same within experimental error, and only the average value is shown in the figure. The value of the relaxation rate for HD is consistently smaller than that for H 2 .…”

“…Although the proton T 1 of pure HD (or HD as an impurity in H 2 or D 2 ) gas, 13a,14 liquid, 13b,15 and solid 13c, 15,16 has been reported, we are not aware of a previous determination of T 1 for HD in organic media. The detection of both H 2 and HD peaks in the same sample and the resolution of the HD coupling constant, J HD , also makes it possible to measure J HD and the 1 H chemical shift difference between the two species in the two media over a range of temperatures as a probe of the changes of these parameters compared to experimental 17 and theoretical 18 determinations for H 2 and HD in the gas phase.…”

“…In a previous communication 1 we compared the proton spin-lattice relaxation time, T 1 , for H 2 in several organic solvents with that in H 2 @C 60 dissolved in the same solvents. The results were analyzed assuming the relaxation to be due primarily to the spin-rotation and dipole-dipole interactions at high and low temperatures, respectively.…”

“…An empirical fit of the temperature dependence of a similar set of measurements of T 1 for H 2 in various organic solvents 5 required four parameters, including two activation energies. Earlier measurements of T 1 for H 2 in D 2 O 6 yielded an estimate of the reorientation correlation time at each of several temperatures but employed the assumption of a fixed ratio of the correlation times for dipole-dipole and spin-rotation contributions to T 1 .…”