Benzene spin-lattice relaxation times

A sample of benzene was placed in the magnetic field of an NMR spectrometer and (using a small value of 2 ) the spectrum was scanned repeatedly at intervals of 8.0 sec. The following relative intensities were observed on successive scans 2, 11, 16, 19, 21, 22i, 23Ultimately, the intensity reached 25. Find the spin-lattice relaxation time for benzene. (The first scan was made 6 sec after the sample was placed in the spectrometer. Is it necessary to know this )... 

Table 3.16. Spin-Lattice Relaxation Times T1 of the 13C Atoms in Benzene Derivatives3.

Fig. 1. Typical, 3C spin-lattice relaxation times (T, in seconds) for organo-transition metal complexes. (1) Benzene-d, 38°C (18) (2) benzene-d, 38°C (19) (3) benzene-d6, 35°C (4) toluene-d8,0°C (5), (6), and (7) toluene-d8, 35°C. All measurements at 25.2 MHz.

P15.22 At, say, room temperature, the tumbling rate of benzene, the small molecule, in a mobile solvent, may be close to the Larmor frequency, and hence its spin-lattice relaxation time will be short. As the temperature increases, the tumbling rate may increase well beyond the Larmor frequency, resulting in an increased spin-lattice relaxation time. 

Carbon-13 NMR has been used to study anisotropic rotational motion in liquids, as have combinations of techniques. Gillen and Griffiths (1972) have obtained the two reorientational relaxation times for benzene (a symmetric top) by combining reorientation relaxation times obtained from Raman band shapes and deuterium spin-lattice NMR relaxation times. The most extensive series of measurements probing anisotropic molecular reorientations have been made by Pecora and co-workers (Alms et al., (1973a, b)), who combined Carbon-13 spin lattice relaxation times with those obtained from depolarized Rayleigh spectra. 

The Carbon-13 spin-lattice relaxation-time measurements are related to the reorientation time of a C—H bond axis. For mesitylene the C—H bond axis observed was that of the ring carbons (not the methyl carbon). For symmetric top molecules such as benzene and mesitylene the tnmr is related to both r and r by (Huntress, 1968)... 

Alms, et al. (1973,1974) have performed depolarized Rayleigh scattering and Carbon-13 spin-lattice relaxation-time measurements on solutions of benzene and mesitylene as a function of solvent viscosity. The solvents used were isopentane, cyclooctane,... 

Naphthalene, in contrast to benzene, did not show any NMR-spectra line-width narrowing up to its melting temperature of 353 K. The mean experimental second moment was 9.1 compared to 10.1 G, estimated for the rigid crystal. Measurement of spin-lattice relaxation times indicated, however, also a slow reorientational jump motion about an axis normal to the molecular axis An activation energy of 105 kJ/mol was derived. Molecular dynamics simulations suggest that this reorientation about the axis of greatest inertia occurs with a frequency of 100 MHz within 20 K of fusion (353.6 K) Still, no plastic crystal behavior as found in cyclohexane and related compounds (see Sect. 3.1.1) is indicated for benzene or naphthalane, even close to the melting temperature. 

Fig. 5.20 The temperature dependence of the correlation time Tc of the protons in a benzene crystal, C6H5. It was obtained from the proton spin-lattice relaxation time T-. The corresponding activation energy is AE = 160 meV. After [24].

FIGURE 5.23 Mean spin-lattice relaxation time ( H NMR experiments) as a function of temperature of neat polystyrene PS-tij and with addition of 13% of benzene. (Adapted from J. Mol. Liquid., 86, Vogel, M., Medick, R, and Rbssler, E., Slow molecular dynamics in binary organic glass formers, 103-108, 2000, Copyright 2000, with permission from Elsevier.)... 

Suggest a reason why the spin-lattice relaxation time of benzene (a small molecule) in a mobile, deuterated hydrocarbon solvent increases whereas that of an oligopeptide (a large molecule) decreases. 

Three papers have dealt with NMR relaxation of small organic molecules dissolved in organic solvents. Kathmann et al. reported and spin-lattice relaxation measurements for cyclic amines (pyridine, 2,6-lutidine, 2,2,6,6-tertamethyl piperidine) in toluene and dichloromethane solutions. The rotational correlation times were derived from NMR data and compared with MD simulations. Alemany discussed highly resolved spectra for long-chain n-alkanes with 12-22 carbons, dissolved in benzene or toluene. Besides the chemical shifts, also the Ti data were obtained and related to segmental motions. Ekinci and co-workers studied Ti data for the chiral iV-benzil-2-isobutyl aza-15-crown-5-ether derivative as a function of temperature. The rotational correlation times and their activation energy were derived. 

---