The Second Moments of the Line Shapes of Multiple Quantum NMR Coherences in One-Dimensional Systems
- PDF / 469,332 Bytes
- 7 Pages / 612 x 792 pts (letter) Page_size
- 0 Downloads / 175 Views
ORDER, AND PHASE TRANSITION IN CONDENSED SYSTEM
The Second Moments of the Line Shapes of Multiple Quantum NMR Coherences in One-Dimensional Systems G. A. Bochkina,*, S. G. Vasil’eva, I. D. Lazareva,b, and E. B. Fel’dmana aInstitute of Problems of Chemical Physics, Russian Academy of Sciences, pr. Akademika Semenova 1, Chernogolovka, Moscow oblast, 142432 Russia b Moscow State University, Faculty of Fundamental Physical–Chemical Engineering, Moscow, 119991 Russia *e-mail: [email protected]
Received April 26, 2018
Abstract—The second moments of the line shapes of the zeroth- and second-order multiple quantum NMR coherences determined by the dipole–dipole interactions of nuclear spins in crystals have been calculated. The second moments determined by the zz part of the dipole–dipole interaction have been derived both by a direct calculation and based on the exact solution (in terms of the zz model) for the decay of the multiple quantum coherence intensities on the evolution period of a multi-quantum NMR experiment. The decay of the multiple quantum NMR coherence intensities in a single crystal of calcium fluorapatite is well described by the Gaussian curves with the calculated second moments. DOI: 10.1134/S1063776118090133
1. INTRODUCTION Multiple quantum (MQ) NMR spectroscopy [1] is an efficient method for studying the spatial distribution of nuclear spins in solids [1–3]. MQ NMR has also turned out to be useful for investigating the growth of correlated clusters [4, 5] on the preparation period of an MQ NMR experiment [1] and the dependence of the decoherence time of strongly correlated clusters on their size in both three-dimensional [4] and onedimensional [6] cases. Such studies are possible, because MQ NMR allows one not only to create many-spin (many-qubit) correlated clusters, but also to investigate their relaxation on the evolution period of an MQ NMR experiment [7, 8]. The most important characteristic of MQ NMR dynamics is the dependence of the intensities of MQ coherences observed in an experiment on their orders (MQ NMR coherence profile). The second moment of this profile is efficiently used to study the growth of correlated spin clusters on the preparation period of MQ NMR experiments [9, 10]. The MQ coherences formed on the preparation period of an experiment are subjected to relaxation on the evolution period due to the secular (with respect to the direction of the external magnetic field) dipole– dipole interaction (DDI). The second moments of the line shapes of MQ coherences of various orders are useful for estimating the dipolar MQ coherence relaxation. One-dimensional chains of nuclear spins are the simplest systems for studying the dynamics and relaxation of MQ NMR coherences. The exact solution for
MQ NMR dynamics in a one-dimensional system shows that in an initial thermodynamic equilibrium state only the zeroth- and plus/minus second-order coherences arise during its evolution [11–13]. The relaxation of MQ coherences can be investigated using the second moments of their line shapes [7, 8]
Data Loading...
