J . Phys. Chem. 1992,96, 3833-3840
into the inertial limit of a completely free rotor model?* Figure 7 contains the plot of the NMR T, (22.49 MHz) vs q / T data for both C2 and C4 (=C5) of MEI. The intercept values are 2.14 and 2.12 ps, and the s l o p are 327 and 396 ps.KcP1 for C2 and (C4 + C5)/2, respectively. The intercepts yield values of 3.07 and 3.04 ps for (I,,,/kT)’/*from the free rotor model. These can be compared with 1.82 and 0.85 ps for Sn14 and PbC14 obtained by extrapolating (I,,,/kT)”*valuesa to infinite temperature. The slope of the plots in Figure 7 and eq 1 1 were used ( T =~ V/k) to calculate the unrealistic values of 1.03 and 1.09 A for the radius of the spherical tumbling moiety that contains the observed 13C nuclei. The results for this molecular ion may be compared with those obtained by other workers on molecules of similar size. In particular, studies of triphenylethylene in nonviscous solvents4’ and supercooled liquid cyclic carbonates49produced small values for the hydrodynamic radius, a. In both of these cases, the molecules were of a size (>5 A) similar to the ME1 cation, and yet the calculated value was less than 2.0 A.
4 12
0’ 0.00
I 0.03
0.06
0.08
0.1 1
0.14
Viscosity/T (cP/K)
Figure 7. rC (NMR) vs v / T for (C4
+ C5)/2 (X) and C2 (A).
pointed out. In fact, derivation of (1 1) is valid for large particles in a continuous medium, but not for diffusing particles.& Furthermore, there is no reason why a reorientation correlation time which depends on rotational motion should be a function of q, a translational property.46 The relationship between T, determined by NMR and temperature in the viscosity dependent region is given bf8 7, = 7 0 + ( v r c d / T ) (12) The intercept, T ~is, often equated with the free rotation times,“’ Tfr = ((2r/9)(IdkT)llZ); however, this represents an extrapolation out of the hydrodynamic region, through the kinetic region, and
(47)
3833
Waylishen, R. E.; Pettitt, B. A.; Danchura, W. Can. J . Chem. 1977,
55. 3602.
’(48) -&ere, R. T.; Kidd, R. G. In Annual Reports on NMR Spectroscopy; Webb, G. A., Ed.; Academic Press: New York, 1982; Vol. 13, p 319.
Conclusions Previous studie@ have shown that strong interactions exist between C1- and the three ring hydrogens of MEI+ in basic melts (mole fraction of AlCl,
