Spin‐lattice NMR relaxation and second moment of NMR line in solids containing CH₃ groups

Abstract

Complex proton dynamics in solids containing methyl groups are studied over a wide temperature range. Temperature dependences of the proton T 1 relaxation time and the second moment of NMR lines are analyzed. General rules describing the temperature dependencies have been formulated from an analysis of the data. The second moments, M 2 , are correlated with those based on T 1 measurements. The C 3 jumps over the barrier cause a minimum in T 1 below the liquid nitrogen temperature in the presence of tunnelling splitting, or a little above 77 K when tunnelling splitting equals zero. The slope of the high-temperature side of this minimum permits evaluation of the activation energy, which can be used to characterize the tunnelling correlation time. The T 1 is temperature independent in the lowest temperature range, indicating that the tunnelling correlation time assumes a constant value. The tunnelling splitting was estimated as the best fit parameter from the T 1 temperature dependence. The high tunnelling splitting is responsible for T 1 values which are high and independent from the Larmor frequency. The tunnelling jumps reduce the rigid lattice second moment at zero Kelvin. The second reduction is caused by over the barrier C 3 jumps of methyl protons. The tunnelling jumps cease above a temperature T tun . The occurrence of the minimum T 1 above liquid nitrogen temperature, as well as the reduction of the second moment M 2 are due to slowest motion of protons, which can be the isotropic motion of molecule. This minimum is well described by the Woessner method of calculating the correlation function of complex motion. V C 2015 Wiley Periodicals, Inc. Concepts Magn Reson Part A 44A: 214-225, 2015.

Heterogeneous Polymer Dynamics Explored Using Static 1H NMR Spectra

“…The impact of multiple dynamic processes on the M 2 temperature behavior has previously been discussed by several authors [ 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 ]. For two noncorrelated dynamic processes, the M 2 behavior is defined by Equation (A10).…”

“…In the presence of dynamics, the pair-wise moments are related to the spectral density describing the correlation function of the reorientation, where the line width ±δν defines the frequencies impacting the M 2 [ 41 , 42 , 45 , 60 ]: …”

“…The variations of the NMR line shape M 2 due to averaging from multiple, complex internal dynamics have been described by a variety of different groups [ 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 ] and have included combinations of methyl tunneling and jump dynamics, 2-site and 3-site motions, and 3-site jumps plus and molecular reorientation, as well as diffusion across lattice sites. The temperature variation of the second moment M 2 in the presence of two uncorrelated dynamics, leading to the dipolar averaging, is described by [ 41 ] with where is the second moment of the NMR spectral line shape in the rigid lattice, is the second moment of the average NMR line shape due to the first dynamic process (e.g., local molecular fluctuations of the β-relaxation process), is the second moment of the averaged line shape due to the second dynamical process ( e.g., polymer chain fluctuations of the α-relaxation glass transition temperature), and 〈 〉 is the NMR line shape averaged by both the first and second dynamic processes.…”