NMR relaxation parameters of a Lennard-Jones fluid from molecular-dynamics simulations

Abstract

Ensembles of soft spheres or of Lennard-Jones atoms were studied by molecular dynamics at reduced temperatures from 0.8 to 3, and radial distribution functions, diffusion coefficients, and magnetic dipole-dipole correlation functions were measured as functions of system size. The expected relation between the values of the correlation functions at zero lag time and the integrals of the radial distribution was verified for each system. The measured correlation functions were compared with theoretical expressions derived by [Ayant et al., J. Phys. (Paris) 36, 991 (1975)] and by [Hwang and Freed, J. Chem. Phys. 63, 4017 (1975)]. It was shown that, in order to recover the long-time behavior characteristic of diffusion-controlled relaxation processes, the simulation must comprise at least 10 000 particles. By fitting the simulation results to the Hwang-Freed function, independent values of the diffusion coefficient were obtained, similar but not identical to those computed using the Green-Kubo formalism. The spectral densities of the dipole-dipole interaction were computed as Fourier transforms of the correlation functions. These quantities are less sensitive to model imperfections and reproduce quite well the values derived from theory. The dimensionless spin-lattice and spin-spin relaxation rates were derived from the spectral densities. It was shown that the spin-lattice (longitudinal) relaxation rate goes through a maximum as the temperature increases, while the spin-spin (transverse) rate decreases monotonously.