Two-dimensional NMR Eigenmode Correlation Spectroscopy

NMR has evolved into a prime tool for the study of porous materials, to unravel the morphology features and the hierarchy of interactions with fluids confined in its pore space [01]. During a 1D NMR relaxation experiment, it is customary to express the temporal magnetization including surface relaxation effect in terms of a serial expansion of eigenmodes [02] [03] . These modes can be categorized into two groups according to their spatial dependence. The ground eigenmode (n=0) governs the NMR relaxation times and depends on the pore size a and the surface relaxivity ρ. However, higher eigenmodes (n>1) do not rely on ρ which in turn provides a direct access to the pore length a. Based on this formalism, a unique approach taking advantage of the high modes was developed to determine the pore length scale of porous system [04], and was proven feasible at ¹H resonance frequencies down to 2 MHz [05].

Recent developed 2D NMR techniques provide more detailed insight of heterogeneous material properties through correlation and exchange patterns as compared to their 1D counterparts [06] [07]. Relying on the philosophy of this framework, the aforementioned ground and high eigenmodes, which describe different aspects of the characteristics of porous materials, can be readily correlated in successive time domains of 2D NMR experiments. Consequently, it allows one to obtain the pore length scales correlated to the NMR relaxation times, and to estimate surface relaxivity values from 2D eigenmode correlation maps. Therefore, a proposed 2D method, coupling the first higher T₁ mode with the ground T₂ mode, will be presented here [05] . A reference experiment is required and carried out which is only sensitive to the ground T₁ mode. Subsequent processing extracts the contributions of the higher eigenmodes only, while a further processing using 2D Inverse Laplace transform [08] allows one to obtain the correlation of pore length scale with the transverse relaxation time T₂, as well as the surface relaxivity ρ₂ of porous media.

By using the developed 2D method, the obtained pore length scales enable one to characterize the heterogeneity of porous materials. Furthermore, with the calibration of surface relaxivities yielded from 2D distributions, it is then possible to obtain the pore geometry information even from simple 1D NMR T₂ measurements.