Dipolar nuclear spin relaxation in liquids and plane fluids undergoing chemical reactions

Abstract

We describe the correlated translational and rotational relative brownian motions of two reacting groups of atoms, alternatively bound and free, by the normalized solutions of a set of coupled diffusion equations. Under equilibrium conditions we calculate the spectral densities j(ω) characteristic of the fluctuations of the intermolecular dipolar coupling between spins of these diffusing groups of atoms. When ωτ ≪ 1, where τ is the translational correlation time, the form of the spectral density j 2(ω) in three-dimensional liquids is j 2(0) - α3ω1/2. The coefficient α3 is independent of the molecular local order, of the diffusional rotation speed of the spin-carrying groups of atoms and of their association and dissociation rates. In plane fluids, when ωτ ≪ 1, the spectral density j (0)(ω) may be written as -a 2 ln (ωτ) where the dependence of a 2 on the average relative distribution of the interacting spins varies with the rate of the chemical reactions. In both three- and two-dimensional fluids spectral densities show an ω-3/2 or ω-2 behaviour for ωτ ≫ 1 according to the magnitude of the association rate of the reacting groups of atoms. In liquid glycerol we analyse the low- and high-frequency limits of the experimental proton relaxation rate 1/T 1 and 1/T 1ρ measured by Harmon, Harmon and Burnett, and Lenk. We also discuss the proton spin-lattice relaxation times measured by Kleinberg and Silbernagel in layered intercalation compounds TiS2-NH3 and TaS2-NH3.