  The aggregation of superparamagnetic iron oxide (SPIO) nanoparticles
decreases the transverse nuclear magnetic resonance (NMR) relaxation time T2 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 T2 and details of the aggregate. We find that in the
motional averaging regime T2 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 T2 N^{-0.44} for aggregates with d=2.2,
a value typical of diffusion limited aggregation. We also find that in
two-nanoparticle systems, T2 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.
