Nuclear magnetic resonance in a two-dimensional system

Abstract

The NMR theory for a two‐dimensional (2D) system of spins coupled by dipolar interaction and undergoing diffusive motion is presented. The correlation functions (c.f.) of the dipolar coefficients are split in two parts: a ’’slow’’ one and a ’’fast’’ one. The c.f. are also written in a form which allows easy prediction of the angular dependence of the relaxation rates. It is demonstrated that, owing to the diffusion process, the slow part decays at long times as t⁻¹ and the fast one as t⁻². Measurements of T₂, T₁, T_1ρ on the protons of nitric acid intercalated in graphite have been performed in the temperature range −153 °C,+18 °C. The prediction of the model was checked both in the solid phases (where ω₀τ_D≫1 with τ_D= diffusional correlation time) and in the ’’liquid’’ phase (above −20 °C). The measurements at room temperature prove, over several decades of frequency, the logarithmic divergence of the slow part‐spectral density for ω→0. Also in the solid phases, the 2D‐diffusive model interprets the measurements. Using the experimental results, we can illustrate the angular dependence of the relaxation rates that are predicted by the theory for planar systems in different dynamical situations. The information given by NMR on graphite nitrate are also discussed.