  We present a detailed study of the kinetic cluster growth process during
gelation of weakly attractive colloidal particles by means of experiments on
critical Casimir attractive colloidal systems, simulations and analytical
theory. In the experiments and simulations, we follow the mean coordination
number of the particles during the growth of clusters to identify an
attractive-strength independent cluster evolution as a function of mean
coordination number. We relate this cluster evolution to the kinetic attachment
and detachment rates of particles and particle clusters. We find that
single-particle detachment dominates in the relevant weak attractive-strength
regime, while association rates are almost independent of the cluster size.
Using the limit of single-particle dissociation and size-independent
association rates, we solve the master kinetic equation of cluster growth
analytically to predict power-law cluster mass distributions with exponents
$-3/2$ and $-5/2$ before and after gelation, respectively, which are consistent
with the experimental and simulation data. These results suggest that the
observed critical Casimir-induced gelation is a second-order nonequilibrium
phase transition (with broken detailed balance). Consistent with this scenario,
the size of the largest cluster is observed to diverge with power-law exponent
according to three-dimensional percolation upon approaching the critical mean
coordination number.
