Experimental Evidence for Self-Similar Structures in the Aggregation of Porphyrins in Aqueous Solutions

We have studied the aggregation of the porphyrin $t{-\mathrm{H}}_2{\mathrm{P}}_{\mathrm{agg}}$ in aqueous solution by light scattering. The intensity profile of the elastically scattered light, studied in the exchanged wave-vector range $0.2\le q\le 31.4\mu {\mathrm{m}}^{-1\mathrm{}}$, indicates that the aggregation produces large monodisperse clusters having a fractal structure, and is driven by diffusion-limited aggregation kinetics. Additional measurements performed at different $q$ values confirm such a picture giving a hydrodynamic radius $R_H$ consistent with the radius of gyration $R_g$ measured by elastic scattering. This is explained taking into account the $q^2$ dependence observed in the mean decay rate of the intensity-intensity correlation function and the effect on this latter dynamical quantity of anisotropies in the cluster structure.