Imagine a pile of lightweight, friction‑less plastic balls arranged in different shapes. Some look like a porous sponge, others like a tighter cluster. When you press on these piles, the balls squeeze together and at a certain point the material "jams." The pressure becomes visible and the pile behaves like a solid platform.
Scientists created three types certainly using three different growth methods. The first method, called reaction‑limited aggregation, produces dense, compact structures. The second, ballistic particle‑cluster aggregation, creates intermediate‑density aggregates. The third, diffusion‑limited aggregation, forms very porous aggregates.
By compressing each aggregate with a shrinking circular boundary, researchers measured pressure as a function of the volume fraction occupied by the balls. For dense and intermediate aggregates, pressure jumps from zero to a finite value at a precise critical packing fraction φJ. For the most porous aggregate, the transition is smoother.
The jamming threshold depends on the initial structure: φJ ≈ 0.765 for the dense case, ≈ 0.727 for the intermediate case, and ≈ 0.602 for the porous case. Above φJ, pressure follows P ≈ A (φ‑φJ)², meaning bulk modulus K grows linearly with excess packing. Rigid‑cluster analysis shows that the average coordination number in the largest rigid cluster also rises linearly with φ‑φJ, mirroring random spring networks.
These findings suggest that particle sponges compact like spring networks, a behavior that could guide the design of soft, resilient materials.
