Fig. 3.

(a) Normalized transverse decay rate ${\tilde{T}}_2^{-1}$ vs. number N of nanoparticles in an aggregate. Each point is a simulation of a randomly assembled aggregate conformation. The line is a power law fit with an exponent of α = 0.444 ± 0.002. Spread about the fit is due to the dependence of ${\tilde{T}}_2^{-1}$ on the geometry of the aggregate. Error bars denote statistical error in each simulation. (b) Scaling exponent α vs. the ratio τ_D/τ_CP of the diffusion time τ_D to pulse-echo time τ_CP calculated by comparing aggregates with N = 1 and N = 25 at different values of τ_CP. The horizontal grey line denotes the average α = 0.444 ± 0.006 for τ_D/τ_CP < 10⁻³. The data point indicated as an ‘x’ represents the value of the fit in Fig. 3(a). The decrease in α as τ_D/τ_CP increases is due to the aggregate transitioning from the motional (MA) regime to the echo limited (EL) regime.