Complex dynamics of 1.3.5-trimethylbenzene-2.4.6-D3 studied by proton spin–lattice NMR relaxation and second moment of NMR line. (February 2015) - Hołderna-Natkaniec, K.; Latanowicz, L.; Medycki, W.; Świergiel, J.; Natkaniec, I.
Abstract: Molecular dynamics of a solid 1.3.5-trimethylbenzene-2.4.6-D3 in phase I is studied on the basis of the proton T 1 (24.7 MHz and 15 MHz) relaxation time measurements and the proton second moment of NMR line, M 2 . The measurements of the T 1 were performed for temperatures from 20 to 167 K, while those of the second moment M 2 from 23 to 220 K. The phase I was accurately prepared. The obtained second moment, M 2 values were correlated with those based on T 1 relaxation time measurements. The proton spin pairs of the methyl groups perform a complex motion being a resultant of two components characterized by the correlation times τ 3 T and τ 3 H, referring to the tunneling and over the barrier jumps in a triple potential. For τ 3 H the Arrhenius temperature dependence was assumed, while for τ 3 T – the Schrödinger one. The jumps over the barrier causes a minimum in T 1 (24.7 MHz) at temperature about 35 K. The high temperatures slope of this minimum permits evaluation of the activation energy as E H =2.0 kJ/mol. The relaxation time T 1 is temperature independent in the lowest temperature regime. This indicates that tunnelling correlation time assumes a constant value of about 1.3·10 -10 s according to the Schrödinger equation ( τ 3 T ≈ τ 03 T e B E H at lowest temperatures). The tunneling jumps of methyl protons reduce M 2 from the rigid lattice value 22.6 G 2 to the value 5.7 G 2 at zero Kelvin temperature. The second reduction to the value 1.41 G 2 at 4.5–7 K is due to C3 jumps over the barrier. According to the Schrödinger equation the tunnelling jumps ceases above T tun temperature where the thermal energy is equal to the activation energy. The T tun equals 43.8 K (from T 1 data fit, E H =2.0 kJ/mol) or 35 K (from M 2 data fit, E H =1.47 kJ/mol). The second moment assumes again the value 5.7 G 2 above T tun temperature. The tunneling splitting, ω T, was estimated equal 2.47 GHz as best fit parameter from the T 1 fit. The symmetrical T 1 minimum indicates the same value of ω T for the all methyl groups. This frequency is in good agreement with the value of ω T ( ℏ ω T =10.2 μeV, tunnel splitting energy) obtained from the neutron powder scattering method. This high tunneling splitting is responsible for the long and Larmor frequency independent of T 1 relaxation time. The presented results are compared to those of Köksal et al. Graphical abstract: Highlights: A mechanism of narrowing the NMR line at zero Kelvin is proposed. Two reductions of second moment below T tun temperature are explained. Single reduction of second moment above T tun temperature is explained. A mechanism of temperature independence of T 1 at low temperatures is proposed. Larmor frequency independence and high values of T 1 are explained.