Complex methyl groups dynamics in [(CH_3)_4P]_3Sb_2Br_9 (PBA) from low to high temperatures by proton spin-lattice relaxation and narrowing of proton NMR spectrum

摘要

Molecular dynamics of a polycrystalline sample of [(CH_3)_4P]_3Sb_2Br_9 (PBA) has been studied on the basis of the T_1 (24.7 MHz) relaxation time measurement, the proton second moment of NMR and the earlier published T_1 (90 MHz) relaxation times. The study was performed in a wide range of temperatures (30-337 K). The tunnel splitting ω_r of the methyl groups was estimated as of low frequency (from kHz to few MHz). The proton spin pairs of the methyl group are known to perform a complex internal motion being a resultant of four components. Three of them involve mass transportation over and through the potential barrier and are characterized by the correlation times τ~3 and τ~T of the jumps over the barrier and tunnel jumps in the threefold potential of the methyl group and τ~(iso) the correlation time of isotropic rotation of the whole TMP cation. For τ~3 and τ~(iso) the Arrhenius temperature dependence was assumed, while for τ~T-the Schrodinger one. The fourth motion causes fluctuations of the tunnel splitting frequency, ω_r, and it is related to the lifetime of the methyl spin at the energy level. The correlation function for this fourth motion (τ~ω correlation time) has been proposed by Muller-Warmuth et al. [15]. In this paper a formula for the correlation function and spectral density of the complex motion made of the above-mentioned four components was derived and used in interpretation of the T_1 relaxation time. The second moment of proton NMR line at temperatures below 50 K is four times lower than its value for the rigid structure. The three components of the internal motion characterized by τ~T, τ~H, and τ~(iso) were proved to reduce the second moment of the NMR line. The tunnel jumps of the methyl group reduce M_2 at almost 0 K, the classical jumps over the barrier reduce M_2 in the vicinity of 50 K, while the isotropic motion near 150 K. Results of the study on the dynamics of CH_3 groups of TMP cation based on the second moment measurements were correlated with those based on T_1 time measurements.