Dense Cluster Formation during Aggregation and Gelation of Attractive Slippery Nanoemulsion Droplets

Using time-resolved small angle neutron scattering, we have measured the wave-number-dependent structure factor $S(q)$ of monodisperse nanoemulsions that aggregate and gel after we suddenly turn on a strong, short-range, slippery attraction between the droplets. At high $q$, peaks in $S(q)$ appear as dense clusters of droplets form, and $S(q)$ increases strongly toward low $q$, as these dense clusters become locked into a rigid gel network, despite the fluidity of the films between the droplets. The long-time high-$q$ structure of nanoemulsion gels formed by slippery diffusion-limited cluster aggregation is universal in shape and remarkably independent of the droplet volume fraction, $\varphi$.

Figure 1

Scattered neutron intensity from aggregating nanoemulsions as a function of wave number, $I(q)$, for a series of times, $t=0$ (●), 239 (△), 482 (◃), 724 (□), 968 (○), and 2100 s (▽), following an abrupt quench from 50 °C to 45 °C. The oil droplets have an average radius $⟨a⟩=51\pm 8\mathrm{nm}$ and a volume fraction $\varphi =0.12$. Lines guide the eye. Inset: 2D scattering intensity patterns before the quench (left) and at the longest time (right). Arrows indicate the related $I(q)$.

Figure 2

Temporal evolution of the structure factor as a function of wave number, $S(q,t)$, of aggregates of attractive nanodroplets. Symbols are defined in Fig. 1.

Figure 3

Time-dependent behavior of the key features in the structure factor, $S(q)$: (a) magnitude of $S$ at the lowest $q$ measured, $S_L(t)$ (●); minimum value of $S$, $S_{\min }(t)$ (■); and (b) value of $S$ at the first cluster minimum at higher $q$, $S_{\mathrm{cm}}(t)$. Arrows mark the onset of saturation, and dashed lines indicate long-time values.

Figure 4

Long-time scattering intensity, $I(q,t\to \infty )$, for droplet volume fractions, $\varphi =0.05$ (●), 0.12 (■), 0.20 (◆), 0.27 (▴). The data at lower $\varphi$ have been rescaled onto a master curve with absolute intensity corresponding to $\varphi =0.27$. Cluster peaks are evident at high $q$ over a wide range of $\varphi$ (arrows). Inset: the universal structure factor as a function of dimensionless wave number, $S(qa)$.

Figure 5

Slippery aggregation of spheres and clusters after the sudden onset of a short-range, central-force, non-shear-rigid attraction: (a) monomers diffuse and aggregate to form a dimer (b). A dimer and a monomer aggregate to form a trimer (c). A trimer and a monomer (or two dimers) aggregate to form a tetramer (d). Tetramers (e) are the minimal clusters of larger scale aggregates that are stable against thermal fluctuations (i.e., shear-rigid) and form extended, nonspherical structures (f), even fractal aggregates. At sufficiently large concentrations, the aggregates can form extended networks and even attractively jammed gels (g).