We conducted a study to explore how colloidal droplets, which are tiny drops of liquid containing suspended particles, dry and break under different conditions. The drying process is influenced by the initial concentration of particles in the droplet, denoted by Ï, which affects how the particles pack together and how fast the liquid evaporates. We found that there is a special way of drying that allows the droplet to go from Ï=100% (all particles) to Ï=0% (no particles) without forming any cracks in the dried film. This is useful for making smooth and uniform films of nanoparticles for various applications. The final stage of drying depends on how the particles are arranged in a fractal pattern, which means that the pattern looks similar at different scales. The fractal dimension D measures how complex the pattern is: D=3 means that the particles are packed tightly together, while D=2 means that they are spread randomly. We discovered that the fractal dimension decreases gradually as the droplet dries, and that this affects the likelihood of crack formation. We also found that this mechanism works for a wide range of particle sizes, except for very large ones that tend to crack more easily (Fig. 2b). Our results reveal that it is possible and robust to prevent cracks in colloidal films by controlling the drying process and the particle packing. This work also gives us a better understanding of how cracks form and grow, and we suggest that the fractal nature of the particle packing plays an important role in this process. Cracks can have both positive and negative effects on the properties and functions of colloidal films. For example, cracks can help transport fluids in some energy systems, but they can also reduce the strength and permeability of materials like rocks and concrete. We hope that our study can help design colloidal films with desired cracking behavior for different purposes.
To understand the drying process of colloidal droplets, we need to consider the complex interplay between fluid dynamics, particle interactions, and mechanical deformations. When a colloidal droplet is deposited on a solid substrate, it first spreads and wets the surface according to the balance of surface tensions at the three-phase contact line. The contact line can either be pinned or move depending on the wetting properties of the substrate and the droplet. The motion of the contact line affects the flow field inside the droplet, which in turn influences the distribution of particles and solutes. As the solvent evaporates, the droplet shrinks and the concentration of particles increases. This leads to the formation of a dense particle layer at the droplet surface, which acts as a viscoelastic shell that resists further evaporation and deformation. The shell can also develop internal stresses due to differential drying and capillary forces. If these stresses exceed a critical value, the shell can buckle or fracture, resulting in various patterns in the dried film .
The onset and morphology of buckling and fracture depend on several factors, such as the particle size and shape, the initial particle concentration, the evaporation rate, and the substrate properties. In general, smaller particles tend to form more uniform films with less cracks than larger particles, because they can pack more densely and resist more stress. Similarly, higher initial particle concentrations can also reduce cracking by forming stronger shells. However, if the concentration is too high, the shell can become brittle and prone to fracture. The evaporation rate affects the drying kinetics and the stress development in the shell. Faster evaporation can cause more cracks due to rapid stress build-up, while slower evaporation can allow more relaxation and healing of defects. The substrate properties, such as roughness, porosity, and elasticity, can also influence the cracking behavior by modulating the contact line motion and the adhesion between the droplet and the surface .
One of our main findings is that there is a way to prevent cracking in colloidal films by controlling the colloid-polymer interactions. We mixed a nonadsorbing polymer with the colloidal suspension, which induced a short-range attraction between the particles due to depletion forces. This attraction caused gelation of the particles at a certain concentration threshold, which enhanced their cohesion and fracture resistance. We observed that gelation-driven crack prevention was effective for a wide range of particle sizes and initial concentrations, as long as the gel point was reached before cracking occurred. We also found that gelation did not affect the fractal dimension of the particle packing, which remained around 2.5 for all cases. This suggests that gelation preserves the random-packing tendency of the colloids while increasing their mechanical strength. 29c81ba772