Paramagnetic relaxation enhancement (PRE) as a tool for probing diffusion in environmentally relevant porous media

The transport diffusivity of the paramagnetic molecule 2,2,6,6-tetramethylpiperidine-1-oxyl (TEMPO) was measured by monitoring its influence on the NMR transverse relaxation time (T₂) on surrounding water protons - also known as paramagnetic relaxation enhancement (PRE). Due to the nature of the PRE effect, few paramagnetic molecules are able to simultaneously reduce the T₂ of many NMR active nuclei, which represents a significant gain in sensitivity. In an aqueous solution, the minimal detectable TEMPO concentration was around 70 ppm. The value of the diffusivity was estimated by fitting the relaxation data, collected as a function of time, with the appropriate solutions of the second Fick's law in respect to the corresponding sample geometry and dimensions. Considering the experimentally determined TEMPO relaxivity in water ("TEMPO-water relaxivity"; R(TEMPO) = (1.05 ± 0.12) × 10⁻³ ppm⁻¹ s⁻¹), the obtained diffusion coefficients (D) of TEMPO in homogeneous solution and in a water saturated sand column (D(bulk) = (6.7 ± 0.4) × 10⁻¹⁰ m² s⁻¹ and D(sand) = (1.4 ± 0.5) × 10⁻¹⁰ m² s⁻¹, respectively) are in good agreement with the expected values (literature values: D(bulk) = 6.6 × 10⁻¹⁰ m² s⁻¹, 1.3 × 10⁻¹⁰ m² s⁻¹ < D(sand) < 2.3 × 10⁻¹⁰ m² s⁻¹). This new approach enables one to determine the diffusivity of paramagnetic molecules in homogeneous (aqueous solution) and porous media with basic NMR equipment, at low concentrations and in a noninvasive manner.