Complex dynamics of 1.3.5-trimethylbenzene-2.4.6-D3 studied by proton spin–lattice NMR relaxation and second moment of NMR line

•A mechanism of narrowing the NMR line at zero Kelvin is proposed.•Two reductions of second moment below Ttun temperature are explained.•Single reduction of second moment above Ttun temperature is explained.•A mechanism of temperature independence of T1 at low temperatures is proposed.•Larmor frequency independence and high values of T1 are explained.

Molecular dynamics of a solid 1.3.5-trimethylbenzene-2.4.6-D3 in phase I is studied on the basis of the proton T1 (24.7 MHz and 15 MHz) relaxation time measurements and the proton second moment of NMR line, M2. The measurements of the T1 were performed for temperatures from 20 to 167 K, while those of the second moment M2 from 23 to 220 K. The phase I was accurately prepared. The obtained second moment, M2 values were correlated with those based on T1 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 τ3T and τ3H, referring to the tunneling and over the barrier jumps in a triple potential. Forτ3Hthe Arrhenius temperature dependence was assumed, while forτ3T – the Schrödinger one. The jumps over the barrier causes a minimum in T1 (24.7 MHz) at temperature about 35 K. The high temperatures slope of this minimum permits evaluation of the activation energy as EH=2.0 kJ/mol. The relaxation time T1 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 (τ3T≈τ03TeBEH at lowest temperatures). The tunneling jumps of methyl protons reduce M2 from the rigid lattice value 22.6 G2 to the value 5.7 G2 at zero Kelvin temperature. The second reduction to the value 1.41 G2 at 4.5–7 K is due to C3 jumps over the barrier. According to the Schrödinger equation the tunnelling jumps ceases above Ttun temperature where the thermal energy is equal to the activation energy. The Ttun equals 43.8 K (from T1 data fit, EH=2.0 kJ/mol) or 35 K (from M2 data fit, EH=1.47 kJ/mol). The second moment assumes again the value 5.7 G2 above Ttun temperature.The tunneling splitting, ωT, was estimated equal 2.47 GHz as best fit parameter from the T1 fit. The symmetrical T1 minimum indicates the same value of ωT for the all methyl groups. This frequency is in good agreement with the value of ωT (ℏωTℏωT=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 T1 relaxation time. The presented results are compared to those of Köksal et al.

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