Local diffusion in paramagnetic solutions by NMR relaxometry at one frequency

The relative diffusion coefficient D of a paramagnetic species and a diamagnetic probe molecule bearing nuclear spins is obtained from their measured relaxation times T1 and T2 (or T1rho). This is achieved by introducing the longitudinal relaxivity, r1, a linear expression of 1/T1, and the mixed relaxivity, rmix, a linear expression of 1/T1 and 1/T2 (or 1/T1rho). Under weak assumptions, D is proportional to (rmix - r1) to the power -2/3 and to rmix to the power -1, with easy-to-determine proportionality factors. The method is noninvasive and easy to use on standard NMR spectrometers and imagers. It is validated through the study of various solutions of a Gd(III)-based contrast agent for magnetic resonance imaging.