Clusters, DLCA

An algorithm for generation of random fraetal (RF) elnsters has been described in Section 3.1.1. The major eomputer limitations were imposed by the number of cluster partieles N, and their proximity in terms of separation distanee between gold eoies. Our ealeulations ineluded both DLCA and ballistie RF... 

A three-dimensional lattice model (section 3.1.1) was used to simulate aggregation kinetics, in which single particles and intermediate clusters move on Brownian or linear trajectories. Initially, = 50,000 particles are placed randomly in a cubic lattice of size L = 215x 215x 215. A combined cluster is formed whenever a particle or a cluster moves to a lattice point adjacent to another particle or intermediate cluster. This model produces DLCA clusters [77] with fractal dimension around 1.8 (Brownian trajectories) and 2 (linear trajectories). A sequence of two integers is used to describe the... 

Figure 18. (a) Extinction specto of a 30-nm gold sol (dashed line 1) and its DLCA aggregates formed after addition of NaCl salt at a final concenftation of 0.046 M. Aggregation time equals 0.5 (2), 12 (3), and 50 (4) min. (b) T EM picture of a topical DLCA gold cluster after 60 min of aggregation. 

To explain these findings, we nse a compnter diffiision-hmited clnster-cluster aggregation model, as described in Section 3.1.1. The optical properties of the aggregates are compnted by the conpled dipole method and by a rigorous GMM and T-matrix methods. The bulk optical constants of metals are modified by the size-limiting effect of nanoparticles [20]. It was shown that a modified version of DDA [58] allows one to explain the shape of the experimental spectra for DLCA aggregates and the dependence of the spectra on the particle size. 

Computer simulations have shown that the value of fractal dimension largely depends on whether the aggregation process is controlled by the diffusion rate of the clusters and single particles or by their chemical reactivity at the time of collision, the latter being mainly controlled by the DLVO forces. This observation, in agreement with experimental work on aerosols and colloids, has led to a new classification of aggregation processes the reaction-limited and diffusion-limited cluster aggregation (RLCA and DLCA respectively) processes. 

In the comparison of DLCA results with experimental data on colloidal aerogels, in which the primary particles are relatively large and monodisperse, excellent agreement was obtained in nearly aU respects. Basic and neutral aerogels were not fit as well, which was hypothesized due to polydispersity and the neglect of deformations and restructuring effects. Finally, different measures for the average size of the clusters within the gel network were... 

JuUien R, Hasmy A, Anglaret E (1997) Effect of cluster deformations in the DLCA modeling of the sol-gel process. J Sol-Gel Sci Tech 8 819-824. 

Diffusion Limited Cluster Aggregation (DLCA) Process whereby clusters of particles undergoing a random walk due to Brownian motion, aggregate together. This theory, proposed by Witten and Sander in 1981... 

DLCA Diffusion-limited cluster aggregation, similar to DLA, but incorporating aggregation... 

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 collision kernels Kjj depend on the particle trajectories and the particle interaction. For purely diffusing particles and clusters without any particle interaction (i.e. diffusion-limited cluster aggregation—DLCA), Smoluchowski (1916) derived ... 

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