Surface and mass fractals in patchy particle aggregation

The fractal study plays an important role in predicting the properties of materials and the underlying growth mechanisms in self-aggregating systems such as colloids and proteins, since such systems form highly irregular, scale-invariant structures. In this work, we performed a simulation study of the aggregation of spherical patchy particles interacting via four irreversible patches arranged in a square geometry along with an isotropic potential whose interaction strength can be varied. Structural analysis shows that at low isotropic strengths, hexagonal lattices form, whereas at higher isotropic strengths, cubic structures are more prominent locally. The slopes obtained from the calculation of the structure factor revealed the presence of both mass and surface fractals. This was independently confirmed by calculating the mass fractal dimension from the cluster size distribution and the surface fractals from the surface roughness measurements of the cluster, revealing that both mass and surface fractals are possible in irreversible patchy particle systems.