New Aspects of 2D Correlation Relaxometry in NMR

Various aspects of the method of two-dimensional (2D) NMR relaxometry in terms of the isolation and identification of dynamic phases are considered. The dispersion dependences of the nuclear magnetic relaxation times on the correlation time $\tau_c$ and the second moment $\Delta\omega^2$ are analyzed. The correlation time $\tau_c$ is determined from the autocorrelation function of the Hamiltonian of the spin interaction with its environment and characterizes the intensity of the stochastic motion of molecules. The second moment $\Delta\omega^2$ is interpreted depending on the proposed mechanism of nuclear magnetic relaxation and contains information about the structure of the system under study. A new method for calculating the joint distribution of correlation times $\tau_c$ and second moments $\Delta\omega^2$ is given. To obtain a joint distribution of the correlation times $\tau_c$ and the second moments of ${P}_{2}(\tau_c, \Delta \omega^2)$, Tikhonov regularization method is used with the introduction of a priori information about the non-negativity and 0-smoothness of the solution, as well as the preferential mechanism of nuclear magnetic relaxation in the system under study. The field of application of the technique is the study of slow molecular motions that meet the condition of the ratio of the spin-lattice relaxation time $T_1$ to the spin-spin relaxation time $T_2$: $T_1 /{T}_2 > 1.125$. In contrast to the well-known methods for calculating 2D maps of the joint distribution ${P}_{2}(T_1 , T_2)$, the proposed method for constructing a 2D map of the joint distribution ${P}_{2}(\tau_c, \Delta \omega^2)$ does not depend on the main characteristic of the NMR relaxometer~--- the resonance frequency $\omega_0$, that allows us to compare data obtained by various devices. The technique was used to analyze the characteristics of sorbed water in clay rocks~--- argillite.