In this form, \(k_{0}\) takes a value of \(0.043\) when \(D_{f}\) is 2.
[ For comparison to other studies, an approximate relationship with
the \(D_{\max}\) and \(R_{g}\) is useful to investigate. \citet{Lattuada_2003} found that the ratio of the minimum radius of a sphere encompassing the aggregate, \(R_s\), to the gyration radius to be increasing with \(N\), and almost approaching to an asymptotic value of 1.6-1.7. Note that \(R_{s} = \frac{1}{2}D_{max\ } + r_m\)]. In order to calculate the scattering field by a fractal aggregate one can define a particle-particle correlation function, \(g\left(r\right)\) , which represents in average how many monomers are located at a distance, r, as seen by individual monomers. Then the static structure factor, \(S\left(q\right)\), can be calculated as the Fourier transform of \(g\left(r\right)\). \(S\left(q\right)\) is p
The structure of the aggregate is computed as the distances