Ivanov, K., A. Yurkovskaya, and H.-M. Vieth, High resolution NMR study of T1 magnetic relaxation dispersion. I. Theoretical considerations of relaxation of scalar coupled spins at arbitrary magnetic field. J. Chem. Phys., 2008. 129(23): p. 234513-12.
http://dx.doi.org/10.1063/1.3040272
A theoretical approach to the description of longitudinal T1 relaxation in scalar coupled systems of spin 1/2 nuclei at arbitrary magnetic field is developed, which is based on the Redfield theory. The consideration is addressed to field-cycling relaxometry experiments with high-resolution NMR detection, in which the field dependence of T1-relaxation times, the nuclear magnetic relaxation dispersion NMRD, can be studied for individual spins of the molecule. Our study reveals well-pronounced effects of spin-spin couplings on the NMRD curves. First, coupled spins having completely different high-field T1 times tend to relax at low field with a common relaxation time. Second, the NMRD curves exhibit sharp features at the fields corresponding to the positions of nuclear spin level anticrossings. Such effects of spin-spin couplings show up not only for individual spins but also for the T1-relaxation of the total spin magnetization of the molecule. The influence of spin-spin coupling is of importance as long as the coupling strength J is larger than the inverse T1-relaxation times of the spins. Around J·T1=1 there is also a coherent contribution to the relaxation kinetics resulting in an oscillatory component of the kinetic curves. Application of the theory to experimental examples will be described in subsequent publications.