Colloidal gels have unique mechanical and transport properties that stem from their bicontinuous nature, in which a colloidal network is intertwined with a viscous solvent, and have found numerous applications in foods, cosmetics, and construction materials and for medical applications, such as cartilage replacements. So far, our understanding of the process of colloidal gelation is limited to long-time dynamical effects, where gelation is viewed as a phase separation process interrupted by the glass transition. However, this purely out-of-equilibrium thermodynamic picture does not address the emergence of mechanical stability. With confocal microscopy experiments, we reveal that mechanical metastability is reached only after isotropic percolation of locally isostatic environments, establishing a direct link between the load-bearing ability of gels and the isostaticity condition. Our work suggests an operative description of gels based on mechanical equilibrium and isostaticity, providing the physical basis for the stability and rheology of these materials.

Viscoelastic phase separation of colloidal suspensions can be interrupted to form gels either by glass transition or by crystallization. With a new confocal microscopy protocol, we follow the entire kinetics of phase separation, from homogeneous phase to different arrested states. For the first time in experiments, our results unveil a novel crystallization pathway to sponge-like porous crystal structures. In the early stages, we show that nucleation requires a structural reorganization of the liquid phase, called stress-driven ageing. Once nucleation starts, we observe that crystallization follows three different routes: direct crystallization of the liquid phase, Bergeron process, and Ostwald ripening. Nucleation starts inside the reorganised network, but crystals grow past it by direct condensation of the gas phase on their surface, driving liquid evaporation, and producing a network structure different from the original phase separation pattern. We argue that similar crystal-gel states can be formed in monoatomic and molecular systems if the liquid phase is slow enough to induce viscoelastic phase separation, but fast enough to prevent immediate vitrification. This provides a novel pathway to form nano-porous crystals of metals and semiconductors without dealloying, which may be important for catalytic, optical, sensing, and filtration applications.Crystallization plays a fundamental role in many processes occurring in nature, such as ice formation in atmospheric clouds [1, 2], and in technological applications that are at the core of the chemical, pharmaceutical, and food industries. Many of the properties of crystals, like the shape, spatial arrangement, polymorph type, and size distribution of the crystallites, depend on the conditions at which the nucleation process took place. Controlling the early stages of crystallization is thus of fundamental importance in order to obtain in a reproducible manner crystals with the desired properties.Classical Nucleation Theory describes the formation of an ordered crystalline nucleus directly from the supersaturated solution. But crystallization can be preceded by the formation of dense liquid droplets as an intermediate step [3][4][5][6][7]. Understanding the process of crystal formation in mixed-phase systems (composed of gas, liquid, and solid phases) is thus of great importance for a variety of systems, from protein solutions to clouds.Colloidal suspensions offer a system where the crystallization process in a mixed-phase environment can be observed with single-particle resolution, and at the same timescales over which nucleation takes place. In colloids with short-range attractions the gas-liquid transition becomes metastable with respect to crystallization [8, 9], and can form gels [10][11][12][13][14]. This gel formation process can be regarded as viscoelastic phase separation [15] into a dense liquid phase with slow dynamics and a dilute gas phase with fast dynamics. This difference in the viscoelastic properties between the two phases allows the formation o...

Phase separation often leads to gelation in soft and biomatter. For colloidal suspensions, we have a consensus that gels form by the dynamical arrest of phase separation. In this gelation, percolation of the phase-separated structure occurs before the dynamical arrest, leading to the generation of mechanical stress in the gel network. Here, we find a previously unrecognized type of gelation in dilute colloidal suspensions, in which percolation occurs after the local dynamical arrest, i.e., the formation of mechanically stable, rigid clusters. Thus, topological percolation generates little mechanical stress, and the resulting gel is almost stress-free when formed. We also show that the selection of these two types of gelation (stressed and stress-free) is determined solely by the volume fraction as long as the interaction is short-ranged. This universal classification of gelation of particulate systems may have a substantial impact on material and biological science.