Gellation of rigid filament networks

We consider a model for gelation of rigid rods, in which rods that are initially placed at random undergo diffusion, and form cross-links when they collide. In the limit of point-like cross-links, the number N of croslinks per rod approaches N ~ 3.53. In a model with compliant cross-links of maximum length l_c, N(t) increases with time as N(t) ~ const. + cL^2 l_c ln(t), where c is concentration and L is rod length.