Recent Developments in Aggregation Kinetics
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time. The data show that the reaction kinetics change as one gradually moves from one mode of reaction to the other, and a change in the fractal dimension of the aggregates is also observed. The results are strongly suggestive of a continuous transition between RLCA and DLCA, although the question is left partially unanswered by the dilute solution studies. We then describe data obtained in dense solutions. Here, new and unexpected features appear. If the reaction is close to DLCA conditions, the scattering pattern exhibits a peak at a finite wave vector, much like in the process of spinodal decomposition (SD), and the aggregation is characterized by universal scaling laws similar to those valid for the final ripening stage of SD. Eventually the aggregation stops when the aggregates occupy all the sample volume, thereby creating a soft and tenuous gel. The peak feature, however, tends to disappear as the reaction proceeds according to the RLCA mode. We present a tentative explanation of the presence of the peak and of the conditions for its disappearance. Also, we point out that the data from dense solutions provide further evidence about the nature of the intermediate regimes. The picture that emerges is that these regimes are a crossover between the two universal modes, and RLCA ultimately reverts to DLCA. DLCA and RLCA: Dilute Solutions The idea that colloidal aggregation kinetics should follow either one of the universal routes or, more generally, a crossover track leading to DLCA, is an appealing one. For convenience, we summarize here the most relevant features of both DLCA and RLCA. Colloidal monomers can form a stable solution provided there is enough repulsion to prevent them
from coming too close and hence generating a stable bond via short-range attractive forces. In the DLVO scheme, the repulsion is coulombic and the attractive forces are van der Waals. Added salt can screen the surface charges so that diffusing monomers are not hindered from contacting each other and forming bonds. These are the conditions for DLCA. On the other hand, if the salt concentration is so low that an energy barrier of a few kT is present, monomers often fail to form a bond on close encounter and the reaction is RLCA. The two types of interactions lead to completely different scenarios. Since DLCA monomers (or already formed clusters) are easily grabbed by other partners as they move about, there is hardly any chance for deep interpenetration, and clusters tend to grow on the tips. The DLCA clusters are, therefore, rather tenuous, and their fractal dimension di is low (df » I.8).449 On the other hand, since many encounters are necessary for a bond under RLCA, readjustment of limbs is possible and the clusters are more dense, and the fractal dimension dt is higher (df » 2.1).6'9 These morphological results stem mostly from a great mass of simulation work. Other substantial differences between DLCA and RLCA relate to the average mass evolution. Simulations or scaling arguments applied to the Smoluchowsky Equation15 predict
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