Slippery diffusion-limited aggregation

Colloidal particles that interact through strong, short-range, secondary attractions in liquids form irreversible “slippery” bonds that are not shear-rigid. Through event-driven simulations of slippery attractive spheres, we show that space-filling fractal clusters still emerge from the process of “slippery” diffusion-limited aggregation (DLA). Although slippery and classic DLA clusters have the same fractal dimension, $d_{\mathrm{f}}=2.5$, their average coordination numbers are quite different: $⟨z_{\mathrm{S}}⟩=6$ whereas $⟨z_{\mathrm{C}}⟩=2$. Local tetrahedral attractive jamming of the particles leads to a structure factor, $S\left(q\right)$, that exhibits dense cluster peaks at higher wave numbers, $q$, and a fractal power-law rise toward lower $q$.

Figure 1

(Color online) Aggregates ($N=50000$ spheres) obtained by (a) CDLA: classic shear-rigid bonding, (b) EDLA: each newly added sphere jams into the nearest node formed by an equilateral triangular face, and (c) SDLA: each newly added sphere jams into a node formed by any triangular face. Insets show detailed views of cluster tips. Scale bars represent 40 sphere radii (at the cluster’s center). Colors encode the order of release of the particles, and $n$ refers to the release number.

Figure 2

(Color online) Mass, $m$, of the fraction of the cluster enclosed within an imaginary sphere of radius, $r$, which is centered on a starting seed particle: classic DLA (∎), equilateral DLA (dashed line), and slippery DLA (●). The axes are normalized by the mass, $m_0$, and the radius, $a$, of a single spherical particle, respectively. The solid lines are fits in the scaling region, yielding $d_f=2.5\pm 0.1$. Inset: classic and slippery DLA scale together when $r∕a$ for SDLA is multiplied by 1.5.

Figure 3

(Color online) Normalized probability distribution of local coordination number, $p_z\left(z\right)$, for CDLA $⟨z_{\mathrm{C}}⟩=2.0$ (∎); EDLA $⟨z_{\mathrm{E}}⟩=6.0$ (엯); and SDLA $⟨z_{\mathrm{S}}⟩=6.0$ (●). Inset: the distribution of dimensionless edge lengths, $p_l(l∕d)$, of triangular bases prior to adding a new sphere for SDLA. The isosceles base triangle (white spheres), has an edge length of 1.08, accounting for the peak (arrow).

Figure 4

(Color online) Structure factor, $S\left(qd\right)$, vs dimensionless wave number, $qd$, for aggregates formed by CDLA (dashed line) and SDLA (solid line). Nearest-neighbor peaks at high $qd$ are more pronounced for SDLA. Inset: comparison of $S\left(qd\right)$ calculated for SDLA (line) to neutron scattering measurements of slippery nanoemulsion droplets (points).