Scaling of transverse nuclear magnetic relaxation due to magnetic nanoparticle aggregation

Abstract

The aggregation of superparamagnetic iron oxide (SPIO) nanoparticles decreases the transverse nuclear magnetic resonance (NMR) relaxation time T[CP over 2] of adjacent water molecules measured by a Carr-Purcell-Meiboom-Gill (CPMG) pulse-echo sequence. This effect is commonly used to measure the concentrations of a variety of small molecules. We perform extensive Monte Carlo simulations of water diffusing around SPIO nanoparticle aggregates to determine the relationship between T[CP over 2] and details of the aggregate. We find that in the motional averaging regime T[CP over 2] scales as a power law with the number N of nanoparticles in an aggregate. The specific scaling is dependent on the fractal dimension d of the aggregates. We find T[CP over 2] ∝ Ν[superscript −0.44] for aggregates with d = 2.2, a value typical of diffusion limited aggregation. We also find that in two-nanoparticle systems, T[CP over 2] is strongly dependent on the orientation of the two nanoparticles relative to the external magnetic field, which implies that it may be possible to sense the orientation of a two-nanoparticle aggregate. To optimize the sensitivity of SPIO nanoparticle sensors, we propose that it is best to have aggregates with few nanoparticles, close together, measured with long pulse-echo times.