Thermal relaxation and coherence dynamics of spin 3/2. I. Static and fluctuating quadrupolar interactions in the multipole basis

Abstract

ABSTRACT:The relaxation dynamics of the spin 3/2 density operator in the presence of fluctuating and static quadrupolar interactions is reviewed. The nuclear magnetic resonance (NMR) line shapes are analyzed for any value of the static quadrupolar interaction, ranging from isotropic systems to systems exhibiting large splitting far exceeding the line widths. Pulse sequences optimized for the elimination of line broadening due to an inhomogeneous static quadrupolar interaction and for the detection of nuclei involved in slow molecular motion and/or in anisotropic, liquid crystalline environment are discussed. In Part II, the dynamics of spin 3/2 in the presence of a (pulsed) radio frequency (RF) field is reviewed.

NMR and conductivity studies of the mixed glass former effect in lithium borophosphate glasses

“…For I = 3/2, a slightly non-exponential relaxation is generally expected at low temperatures. The relaxation rate 1/T 1 for an isotropic motional process at sufficiently low temperatures and caused by a fluctuating quadrupolar interaction is customarily related to the spectral density J n (nω) = 2τ c /[1+(nωτ c ) 2 ] at multiples of the Larmor frequency, 43,44 1…”

Multi-Quanta Spin-Locking Nuclear Magnetic Resonance Relaxation Measurements: An Analysis of the Long-Time Dynamical Properties of Ions and Water Molecules Confined within Dense Clay Sediments

“…Finally, a complete basis set of coherences is required to translate Equation (A14) into a matrix form [18,64,[78][79][80].…”

“…To simplify the derivations of these matrices, we selected symmetric and antisymmetric combinations of the coherences [78][79][80]; see Equation (A17). By using these coherences, the three spin operators, I x , I y and I z , become proportional to T 11 (a), T 11 (s) and T 10 , respectively, simplifying the formulation of the Hamiltonians describing the irradiation pulse and the heteronuclear dipolar coupling (see Equations (A7)-(A9)).…”

“…For spin I = 3/2 nuclei, the whole set of coherences splits again into two independent sub-sets [79,80] Figure A3. The eigenvalues ±iλ p with p ∈ {0, · · · , 6} describing their time evolution under the influence of the static quadrupolar Hamiltonian and irradiation pulse [64,79,80] By contrast, the corresponding eigenvectors must be calculated numerically [83].…”

“…The eigenvalues ±iλ p with p ∈ {0, · · · , 6} describing their time evolution under the influence of the static quadrupolar Hamiltonian and irradiation pulse [64,79,80] By contrast, the corresponding eigenvectors must be calculated numerically [83]. For spin I = 7/2 nuclei, no analytical solutions are available, and the eigenvalues and eigenvectors describing the time evolution of the 63 coherences must be solved numerically [55].…”