Reaction-limited cluster aggregation

Figure 8. Transmission electron micrographs of typical clusters of gold, silica, and polystyrene colloids, prepared by both diffusion-limited and reaction-limited cluster aggregation and by computer simulation. There is a striking similarity in the structure of the clusters of different colloids in each regime.

Figure 3. Illustration of the pH dependence of the hydrolysis, condensation, and dissolution rates of silica. Condensation rates are judged by the reciprocal of gel times. RLCA denotes reaction-limited cluster aggregation. (Reproduced with permission from reference 30. Copyright 1988.)...

Acid catalysis typically leads to polymeric gels by reaction limited cluster aggregation due to formation of small clusters under rapid hydrolysis followed by slow condensation of these clusters into the gel network. 

Figure AA Dependence of the mean square radius of gyration on the aggregate mass for a collection of reaction-limited cluster aggregation mechanism (RLCA) aggregates. Here, the scaling relationship Rl is verified.

RLCA Reaction-limited cluster aggregation, an aggregation model similar to DLCA, except with a finite probability of forming a bond upon contact between objects RSCE Rapid supercritical extraction method where the sol-gel precursors themselves brought to a supercritical state inside a pressurized mould... 

The formation of a particulate network with fractal structure has been reported, which suggests a reaction-limited cluster aggregation (RLCA) mechanism [34]. RLCA requires moderate repulsions to exist between the partides (Le., an energy barrier has to be overcome to permit a cluster-forming collision between particles). Since in ILs the classical electrostatic repukion should be annihilated, the alternate cation-anion layers patterning at the surface of the particles, which is induced by solvation, is thought to provide an effective repulsive barrier. 

Herein, ds is the space dimension, i.e. 2, and df is the fractal dimension (Hausdorff dimension) of the 2D aggregated particle cluster. Typical values for Hausdorff dimensions are e.g. 1.44 for diffusion limited cluster aggregation (DLCA) and 1.55 for reaction limited cluster aggregation (RLCA) [22, 31], Assuming isolated 2D aggregates which were formed by interfacial particle-particle aggregation, an exponent of about —6 is estimated. Close to the two- dimensional sol-gel transition, the system should behave like a percolated network and the corresponding exponent is determined to —9.5 [31],... 

---