We attempt a classification of different colloidal gels based on colloid-colloid interactions. We discriminate primarily between non-equilibrium and equilibrium routes to gelation, the former case being slaved to thermodynamic phase separation while the latter is individuated in the framework of competing interactions and of patchy colloids. Emphasis is put on recent numerical simulations of colloidal gelation and their connection to experiments. Finally we underline typical signatures of different gel types, to be looked in more details in experiments.

We report theoretical and numerical evaluations of the phase diagram for patchy colloidal particles of new generation. We show that the reduction of the number of bonded nearest neighbors offers the possibility of generating liquid states (i.e., states with temperature $T$ lower than the liquid-gas critical temperature) with a vanishing occupied packing fraction ($\varphi$), a case which can not be realized with spherically interacting particles. Theoretical results suggest that such reduction is accompanied by an increase of the region of stability of the liquid phase in the ($T\mathrm{\text{−}}\varphi$) plane, possibly favoring the establishment of homogeneous disordered materials at small $\varphi$, i.e., stable equilibrium gels.

We study a model in which particles interact with short-ranged attractive and long-ranged repulsive interactions, in an attempt to model the equilibrium cluster phase recently discovered in sterically stabilized colloidal systems in the presence of depletion interactions. At low packing fractions, particles form stable equilibrium clusters which act as building blocks of a cluster fluid. We study the possibility that cluster fluids generate a low-density disordered arrested phase, a gel, via a glass transition driven by the repulsive interaction. In this model the gel formation is formally described with the same physics of the glass formation.

By reviewing experimental and theoretical works, we discuss the phase diagram of Laponite suspensions, with the aim of clarifying several issues that have caused a long-time controversy on the system. We claim that, if aging and sample preparation are correctly taken into account, a unifying picture emerges from different experimental studies. Multiple non-ergodic states are identified, including a low concentration equilibrium gel and a high concentration Wigner glass in the absence of salt. These findings are critically discussed also with respect to recent evidence of phase separation at extremely low densities and to existing theoretical and numerical works.