Simulation of Aggregation Processes

The concentration of monomers plays a very important role in aggregation models. We discussed this earlier in Section 9.4.2, where we noted that percolation through a network becomes realized only when a limit concentration of connections is exceeded. 

Here we will analyze the behavior of cluster-cluster aggregation as a function of the momomer volume fractionWe will recognize features that relate to the behavior of percolation. A particular aim of the simulations is to analyze not only the aggregation but also the aging processes. Simulations on aging will be presented in Section 9.7.4. 

The results of off-lattice diffusion limited cluster-cluster aggregation (DLCA) simulations in two dimensions are presented in Fig. 9.26. Simulations are limited to two dimensions because it enables one to use large unit cells with many particles. Brownian trajectories are followed. Larger aggregates are generated as a result of bond formation between overlapping aggregates. One finds crossover from fractal to Euclidean behavior when a particular monomer concentration is exceeded. 

The lower limit of fractality Lo is assumed to be the monomer radius Rq. For distances L shorter than Lq, the density po of the initial primary scatterer is set to unity. The density p of the fractal region can be expressed in analogy to Eq. (9.4) as 

The upper length scale of fractality depends on (j)o and is smaller for high volume fractions. 

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In our studies, we consider several types of aggregated structures such as bispheres, linear chains, plane arrays on a plane rectangular lattice, compact and porous body-centered clusters embedded on the cubic lattice (bcc clusters, the porosity was simulated by random elimination of monomers), and random fractal aggregates (RF clusters). To generate RE clusters, a three-dimensional lattice model with Brownian or linear trajectories of both single particles and intermediate clusters was employed for computer simulations of aggregation process. At the initial time moment, = 50,000 particles are generated at... 

Self-similar behavior has also been observed in computer simulation of aggregation processes. Thus aggregates of colloidal particles in diffusion-limited aggregation processes have been found to display self-similar behavior (Meakin, 1983). 

Meakin P. Simulations of aggregation processes. Avnir D, ed. The Fractal Approach to Heterogeneous Chemistry. Chichester Wiley, 1990 131-160. 

Despite the restrictions of the molecular dynamics simulation technique, some important features of micellar structures have already been observed and reasonable results which coincide rather well with experimental data have been obtained. Nevertheless, in order to examine the dynamic of aggregation processes it is necessary to enlarge the simulation time drastically. A... 

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. 

Stoll, S. and Buffle, J. (1998). Computer simulation of flocculation processes the roles of chain conformation and chain/colloid concentration ratio in the aggregate stmctures. J. Colloid Interface Sci., 205,290-300. 

Wang, L. et al. (2005). CED simulation of aggregation and breakage processes in laminar Taylor-Couette flow. Journal of Colloid and Interface Science, Vol. 282, pp. 380-396. 

Photoinduced dynamics in extended molecular systems often fall into a short-time regime where inertial, coherent effects dominate and the many-particle dissipative dynamics has not yet set in. This generally precludes the use of standard system-bath approaches and necessitates an explicit dynamical treatment of the combined subsystem-plus-environment supermolecular system. The powerful QM/MM based simulation techniques that have been developed over recent years for the explicit simulation of photochemical processes in chromophore-solvent and chromophore-protein complexes, as well as extended systems like semiconducting polymers and various types of molecular aggregates have made great strides in this direction [19-21,54]. Even so, the need for complementary reduced-dimensional models and dynamical interpretations persists. In the present contribution, we have presented such a complementary perspective. 

Let us illustrate first how different (idealized) aggregation processes may result in different structures. There is extensive literature on diffusion-limited aggregation (DLA) (for a comprehensive review, see Meakin, 1988). Three methods of simulation are common (standard) diffusion-limited aggregation (DLA), reaction-limited aggregation (RLA), and linear trajectory aggregation (LTA). DLA structures are generated by placing a seed particle in the middle of a lattice. Other particles are placed in the lattice... 

A computer simulation carried out by C. Kuhn (2001) was able to confirm certain critical phases in the first steps of Kuhn s theory, such as the formation of aggregates (collector strand and hairpin strand). In this simulation, the process of the development of a simple genetic apparatus took place in three stages ... 

There are two other methods in which computers can be used to give information about defects in solids, often setting out from atomistic simulations or quantum mechanical foundations. Statistical methods, which can be applied to the generation of random walks, of relevance to diffusion of defects in solids or over surfaces, are well suited to a small computer. Similarly, the generation of patterns, such as the aggregation of atoms by diffusion, or superlattice arrays of defects, or defects formed by radiation damage, can be depicted visually, which leads to a better understanding of atomic processes. 

It is believed that, using this model and the methods of sequence design suitable for computer simulations, one can construct copolymers capable of forming nonaggregating heteropolymer globules, with the ultimate objective of learning how to manipulate the polymer chemistry and system conditions in order to preclude the aggregation processes. 

Figure 1. Computer simulation of the formation of clay tactoid by a process of aggregation of lCr particles. Ration length to thickness 9/1. In the three topmost diagrams each rectangle endorses a portion of the tactoid shown enlarged below, df is represented by the thickness of the line enclosing the sheets in contact. Adapted from ref. 6. N.B. With respect to the next section, the molar fraction xi consists of the water in the interlamellar space and in the closed spaces within the tactoid. The molar fraction xb is in a 10 A thick layer on the external contour of the tactoid.

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