Glasslike Arrest in Spinodal Decomposition as a Route to Colloidal Gelation

Abstract

Colloid-polymer mixtures can undergo spinodal decomposition into colloid-rich and colloid-poor regions. Gelation results when interconnected colloid-rich regions solidify. We show that this occurs when these regions undergo a glass transition, leading to dynamic arrest of the spinodal decomposition. The characteristic length scale of the gel decreases with increasing quench depth, and the nonergodicity parameter exhibits a pronounced dependence on scattering vector. Mode coupling theory gives a good description of the dynamics, provided we use the full static structure as input. DOI: 10.1103/PhysRevLett.95.238302 PACS numbers: 82.70.Dd, 64.70.Pf, 82.70.Gg Colloid-polymer mixtures exhibit a rich phase behavior. Depletion of polymer between two colloidal particles induces an attractive interaction whose magnitude U is set by the polymer concentration in the free volume, c p . The range of this interparticle attraction is determined by the radius of the polymer R p and is expressed by R p =a, with a the particle radius. The phase behavior is controlled by both c p and , as well as the colloid volume fraction, . The particles can form equilibrium phases, including crystals, fluids, and gases [1,2]. Additionally, there are a wide variety of nonequilibrium states, characterized by the dynamic arrest of the colloidal particles [3][4][5][6]. In the absence of polymer, crowding drives the system into a repulsive glassy state at 0:58, where particles are caged by their nearest neighbors. This dynamic arrest is captured by mode coupling theory (MCT), a mean-field-like theory which uses the static structure factor, Sq, to predict the dynamics [7,8]. Upon addition of a small amount of polymer, arrest is no longer driven by crowding, but instead by weak attraction between particles; surprisingly, this attractive glass can also be described by MCT [4,9]. In both cases, the dominant length scale in the structure corresponds to the nearest-neighbor particle separation. By contrast, at lower and higher U, the system can gel, forming a space-spanning network characterized by an additional, larger length scale. For systems at very low and sufficiently high U, gelation is a consequence of kinetics; fractal clusters grow and ultimately form a gel by clustercluster aggregation [10,11]. The theory for kinetic aggregation naturally includes the larger length scale, which is the cluster size. By contrast, at higher and lower U, phase separation, such as spinodal decomposition, can drive large-scale structuring, influencing the pathways for gel formation [12 -14]. In this case, the mechanisms for arrest during gelation are still unclear. Gelation requires the formation of a solidified, space-spanning network. In spinodal decomposition this is driven by dynamic arrest within the connected colloid-rich region; this may result from percolation [15][16][17][18][19], pinning [20], or a glasslike transition [6,12,13,17,21,22]. An experimental investigation that distinguishes these possible mechanisms, and that determines the correct underly...

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