  Using computer simulations, we study the dynamic arrest in a schematic model
of colloid-polymer mixtures combining short-ranged attractions with long-ranged
repulsions. The arrested gel is a dilute rigid network of colloidal particles
bonded due to the strong attractions. Without repulsions, the gel forms at the
spinodal through arrested phase separation. In the ergodic suspension at
sufficiently high densities, colloidal clusters form temporary networks that
percolate space. Recently [Nat. Commun. 7, 11817 (2016)], it has been proposed
that the transition of these networks to directed percolation coincides with
the onset of the dynamic arrest, thus linking structure to dynamics. Here, we
evaluate for various screening lengths the underlying gas-liquid binodal and
the percolation transitions. We find that directed percolation shifts the
continuous percolation line to larger densities, but even beyond this line the
suspension remains ergodic. Only when approaching the spinodal does dynamic
arrest occur. Competing repulsions thus do not modify the qualitative scenario
for non-equilibrium gelation, although the structure of the emerging
percolating network shows some differences.
