A primer for nuclear magnetic relaxation in liquids

Abstract

ABSTRACT:This article is a primer that is intended to serve as a concise source of information for researchers interested in learning relaxation aspects in NMR. Explicit expressions have been derived for the equation of motion of nuclear spins in the solution state. General expressions valid for all motional regimes, including anisotropy of spin interactions and molecular motions, are presented. Intricate details that impact the validity of various expressions have been elaborated and efforts have been made to maintain consistent notation. The suitable examples given here should help in the understanding of the concepts developed in the theory.

Cross‐correlated and conventional dipolar carbon‐13 relaxation in methylene groups in small, symmetric molecules

“…The simple form of the conventional relaxation parameters in the presence of proton decoupling may also remain valid for more complicated spin systems. [8], with a factor of 2 accounting for the presence of two protons. A spin system of interest in the present work is a methylene group.…”

“…Equation [2] is given in a simplified form, valid for the case when the time dependence of the magnetization is followed on resonance. According to standard theory (1,(7)(8)(9), a more general description of relaxation processes can be formulated in terms of relaxation matrices. The theory is based on a second-order perturbation treatment, where the relaxation processes are caused by stochastic modulation of certain terms in the Hamiltonian (time-dependent perturbations, H 1 (t)) describing the mutual interactions between spins or between spins and their environment.…”

“…The spectral density functions in Eqs. [8]- [10] are normalized according to the convention used in the book by Kowalewski and Mäler (1). We shall come back to the form of J IS,IS (o) later.…”

“…The relaxation rate is given by a sum of two expressions analogous to Eq. [8], corresponding to the two dipolar (AM and AX) interactions. In the simplest cases, the contributions of the two interactions are equal, and a methylene carbon T Àl 1 is given by Eq.…”

“…In the simplest cases, the contributions of the two interactions are equal, and a methylene carbon T Àl 1 is given by Eq. [8], with a factor of 2 accounting for the presence of two protons. In the same way, the transverse carbon relaxation is described by a sum of two terms analogous to Eq.…”