  The dynamical arrest of attractive colloidal particles into
out-of-equilibrium structures, known as gelation, is central to biophysics,
materials science, nanotechnology, and food and cosmetic applications, but a
complete understanding is lacking. In particular, for intermediate particle
density and attraction, the structure formation process remains unclear. Here,
we show that the gelation of short-range attractive particles is governed by a
nonequilibrium percolation process. We combine experiments on critical Casimir
colloidal suspensions, numerical simulations, and analytical modeling with a
master kinetic equation to show that cluster sizes and correlation lengths
diverge with exponents 1.6 and 0.8, respectively, consistent with percolation
theory, while detailed balance in the particle attachment and detachment
processes is broken. Cluster masses exhibit power-law distributions with
exponents -3/2 and -5/2 before and after percolation, as predicted by solutions
to the master kinetic equation. These results revealing a nonequilibrium
continuous phase transition unify the structural arrest and yielding into
related frameworks.
