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.