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 \(T_{2}^{CP}\) 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 \(T_{2}^{CP}\) and details of the aggregate. We find that in the motional averaging regime \(T_{2}^{CP}\) 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 \(T_{2}^{CP} \propto N^{-0.44}\) for aggregates with \(d=2.2\), a value typical of diffusion limited aggregation. We also find that in two-nanoparticle systems, \(T_{2}^{CP}\) 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.