Colloidal Gel & Percolation Network

Gelation as a spanning-cluster phase transition
Volume fraction φ 0.15
Attraction ε/kT 2.0
Range r_c 1.5
Adjust parameters and simulate
Colloidal gels form when attractive particles cluster into a space-spanning network — a percolation transition. Above the percolation threshold (volume fraction × bonding probability > p_c), a system-spanning cluster appears: the gel. Gel networks show fractal structure with dimension d_f ≈ 1.8–2.0. The transition is continuous: cluster size distribution n(s) ~ s^{-τ} at p_c (Fisher exponent τ ≈ 2.05 in 3D).