From colloidal aggregation to spinodal decomposition in sticky emulsions

Aggregation mechanisms of emulsions at high initial volume fractions (φ0 > 0.01) is studied using light scattering. We use emulsion droplets which can be made unstable towards aggregation by a temperature quench. For deep quenches and 0.1 > φ0 > 0.01, the aggregation mechanism is identified as diffusion-limited cluster aggregation (DLCA). An ordering of the clusters, which is reflected by a peak in the scattering intensity, is shown to result from the intercluster separation, exhibiting different scaling than that observed at lower volume fractions. This manifests an increasing similarity to spinodal decomposition observed as φ0 is increased. For φ0 > 0.1 and shallow quenches, different mechanisms, closer to spinodal decomposition, are observed. These results allow the subtle boundaries between DLCA and spinodal decomposition to be explored. PACS. 61.43.Hv Fractals; macroscopic aggregates (including diffusion-limited aggregates) – 82.70.Gg Gels and sols – 64.70.Ja Liquid-liquid transitions Colloid aggregation is a coarsening process driven solely by kinetics; colloidal particles stick irreversibly to one another as they collide due to their diffusive motion. The resultant bonds can be sufficiently strong to prevent further rearrangement, leading to highly disordered and tenuous clusters, whose structure can be well-described as fractal [1]. If there is no repulsive barrier preventing clusters from sticking upon collision, the coarsening is driven solely by the diffusion-induced collisions between the growing clusters. This regime, called diffusion-limited cluster aggregation (DLCA), is amenable to detailed theoretical analysis, and has become an important base case on which we can build our understanding of other kinetic growth processes. The initial growth of the DLCA clusters is completely random; nevertheless, recent experiments with slightly more concentrated suspensions than previously studied, have shown that a surprising order can develop, manifested by a pronounced peak in the small angle scattering intensity as a function of wave vector, I(q), which reflects the development of a characteristic length scale in the suspension [2,3]. While first observed in three-dimensional DLCA, similar behavior has also been reported for twodimensional aggregation of particles on the surface of a fluid [4]. This surprising observation suggests that DLCA has much in common with a completely different coarsening process, spinodal decomposition, which is not driven exclusively by diffusion, but which instead reflects the evoa e-mail: [email protected] lution of phase separation as the system is quenched away from equilibrium [5]. In both processes there is a pronounced peak in I(q); in both processes this peak moves to smaller q as the system coarsens; in both processes, I(q) exhibits scaling behavior [2,6–9]. At long times, DLCA must produce a gel which spans the system, preventing further coarsening. By contrast, spinodal decomposition must ultimately result in the complete separation of the two phases; however, recent studies of spinodal decomposition in colloidal systems [10] have shown that a deep quench can result in the formation of a gel-like structure, kinetically arresting the phase separation, and further enhancing the apparent similarity between the two coarsening processes. Despite the intriguing similarities in the two coarsening processes, there are intrinsic differences between DLCA and spinodal decomposition. In spinodal decomposition, the characteristic length scale is initially set by the fastest growth of a dominant fluctuation; by contrast, in DLCA, this length scale must originate solely from the diffusive motion of the particles. Thus, a complete understanding of their link remains elusive, calling for further exploration of their similarities. In this work, we report the results of an experimental study of the inherent similarities between aggregation and spinodal decomposition. We focus on the behavior of colloid aggregation as the initial volume fraction of particles, φ0, is increased, and show that the similarity to spinodal decomposition becomes even more pronounced with increasing φ0. We use monodisperse emulsion droplets, 278 The European Physical Journal B which can be made unstable towards aggregation by a temperature quench; this allows us to explore the DLCA process for suspensions with initial volume fractions above φ0 = 0.01. Index matching the suspensions enables us to probe their behavior with light scattering, even at these high volume fractions. We report the observation of three different scenarios for the aggregation; these are controlled by the quench depth and the initial volume fraction. Each of these scenarios bears a striking similarity to spinodal decomposition; together, they provide further important insight into the nature of this similarity. In the first case, when 0.008 < φ0 < 0.1, a pronounced peak in I(q) is observed at a scattering wave vector, qm. This evolves with time as qm ∼ t−1/3; this is in marked contrast to the behavior at lower φ0, where qm ∼ t−1/df , with df the fractal dimension of the clusters. However, in both cases, all the light scattering data at later times can be scaled onto a single curve, with the scaling reflecting the fractal structure of the clusters. Thus, while the fractal dimension of the clusters controls all the scaling at low φ0, it is the dimension of space that controls the scaling of qm with t for higher φ0, identical to the behavior observed for spinodal decomposition. In the second case, when φ0 > 0.1, completely different behavior is observed, and the similarity with spinodal decomposition becomes even more pronounced; we find that qm remains constant in time, while I(qm) increases exponentially with t, similar to the behavior expected in the early stages of a spinodal decomposition within the linear Cahn-Hilliard theory [5,11]. However, full phase separation is arrested by gelation of the system. Finally, the third case highlights the merging of aggregation and spinodal decomposition. When the temperature quench is not as deep, and samples with a high φ0 are used, no gelation is observed; instead we observe a process akin to a full phase separation in that the resultant clusters are highly compact and can not span the system to form a gel. Nevertheless, marked phase separation still occurs, as there are no remaining free particles in equilibrium with the clusters. These experimental results elucidate the nature of DLCA at higher volume fractions and further cement the intriguing analogy between aggregation and spinodal decomposition. We use emulsions composed of monodisperse silicone oil droplets in water mixed with glycerol (30% by weight) to increase the index of refraction and eliminate multiple scattering, and with 2 mM sodium dodecyl sulfate to stabilize the droplets. The droplet radius is a = 0.19 μm, as determined with static light scattering. The suspension also contains 0.35 M NaCl which makes the droplets sticky as the temperature is lowered to the onset of the attractive interaction at 35 ◦C. Above 35 ◦C, there is no appreciable attractive interaction; between 34.7 ◦C and 35 ◦C, the attraction is weak, leading to an equilibrium between dilute and concentrated phases of droplets; below 34.7 ◦C the attraction is much greater than kBT [12], the thermal energy, and the droplets stick strongly to one another upon collision. This allows us to rapidly and controllably induce aggregation and then gelation of the emulsions. This is accomplished by holding the sample temperature Fig. 1. Intensity as a function of scattering wave vector for an emulsion with φ0 = 0.04 at a series of times. The inset shows that, except at the earliest times, the data can be scaled onto