1H spin–lattice relaxation enhancement caused by magnetic core–shell nanoparticles—Testing theoretical models

Abstract

Theoretical models of paramagnetic relaxation enhancement effects have been tested for 1H spin–lattice relaxation in water solutions of core–shell nanoparticles composed of NaDyF4 (core) and NaGdF4 (shell). The experimental data used for this testing have been collected in a broad frequency range, from 10 kHz to 400 MHz, vs temperature, for the core radius of the nanoparticles of 11 nm and the shell thicknesses of 0.55 and 1.3 nm. The models are based on a relatively simple description of the electron spin relaxation in terms of just two relaxation rates, depending on the amplitude of the Zero Field Splitting (ZFS) tensor (for Gd3+) and a correlation time and expressed in terms of Lorentzian spectral densities. This means that the description of the electron spin relaxation has been simplified, not considering either the influence of the ZFS coupling on the energy level structure of the electron spin or multiple relaxation rates associated with the high spin quantum number of Gd3+ (7/2). The time fluctuations of the dipole–dipole interactions causing the 1H relaxation processes have been attributed to the translational diffusion of water molecules. It has turned out that using this concept and introducing a phenomenological pre-factor to the model, one can accurately reproduce the 1H spin–lattice relaxation rates. Moreover, the pitfalls of superparamagnetic relaxation enhancement models applied to such systems have been discussed.