Spinodal-type dynamics in fractal aggregation of colloidal clusters

Abstract

The aggregation of dense colloidal solutions has been investigated by means of low-angle static light scattering. We show that the scattered pattern exhibits a finite-^-vector peak, whose intensity and position q m change with time. We find that the intensity distributions scale according to S(q/q m ,t) -q m (t) ~dF(q/q m )y in agreement with the scaling law for spinodal decomposition. While </ -3 for spinodal decomposition, here scaling requires that d =df, the fractal dimension of the clusters. PACS numbers: 64.75.+g, 05.40,+j, 64.60.Ht, 82.70.Dd The spinodal decomposition (SD) is a phase-separation process that has been investigated in a large number of quite dissimilar systems like small-molecule liquid mixtures [1-4], metallic alloys [5,6], polymer blends [7,8], inorganic glasses [9], and thermodynamically unstable colloidal systems [10]. The peculiar feature of SD is that the long-wavelength diffusion coefficient becomes negative so that fluctuations grow instead of decaying. The fastest-growing fluctuation occurs at a finite wave vector and this gives rise to the well-known ring in the pattern of scattered radiation. The intensity and radius of the ring change in time as the thermodynamically stable state is approached. In spite of the diversity of the physical systems, universal features in the dynamics are observed. It should also be pointed out that other phase-separating systems, although not exactly falling in the class of SD, exhibit the same behavior [11,12].Colloidal aggregation is another area where a substantial amount of work has been produced in recent years [13]. In this case also diffusion plays an essential role. Monomers diffuse to form fractal clusters, and the clusters themselves diffuse to coalesce into even larger clusters and so on.In this paper we will show that colloidal aggregation exhibits the same features of SD in spite of the fact that nothing anomalous occurs to the diffusion coefficient of the monomers and clusters. By using very-low-angle static light scattering and high monomer concentration, we present for the first time clear evidence of a ring in the scattered intensity pattern. We will show that during the later stages the dynamics is in agreement with the scaling predictions of Marro, Lebowitz, and Kalos [14], also put forward by Furukawa [15] and by Binder and Stauffer [16].The position of the scattered peak q m and the scaled structure factor S(q/q m ,t) are related by the equation S(qlq m .t)=q m (t)-d F{qlq m ),where F(q/q m ) is a time-independent scaling function. For ordinary spinodal decomposition, rf -3, while here we find that the relation holds if we take d=d/, where dj is the fractal dimension of the clusters. The surprising similarities between these results and those related to the spinodal decomposition are likely to suggest some underlying common mechanism in the dynamics of these irreversible processes. The measurements have been performed on a solution of polystyrene spheres 0.0190 jim in diameter in a water-heavy-water mixture. The mixture was adjuste...

The effect of shear on colloidal aggregation and gelation studied using small-angle light scattering

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