Relaxation of Multiple-Quantum Coherences in Dipolar Coupled ¹H Spin Pairs in Gypsum

The evolution and relaxation of MQ NMR coherences on the preparation period were investigated experimentally on a single crystal of gypsum, CaSO₄·2H₂O. The theory describing the dynamics of MQ coherences on the preparation period of MQ experiment for a pair of spins was developed based on the Lindblad master equation. This theory predicts the appearance of MQ coherences of only zeroth and second orders, oscillatory exchange of their intensities and exponential decay with increasing of the preparation time. The proposed theory describes the experimental data well. It is shown that the frequency of oscillations depends on the orientation of the crystal in the external magnetic field and determined by the dipolar coupling between protons of the water molecules contained in the gypsum crystal. The relaxation time of MQ coherences of zeroth and second orders, T_r = 150 ± 15 μs, were independent of the crystal orientation, which suggest a common source of relaxation due to the dipole-dipole interactions with protons surrounding water molecule.