the moving particles (diffusion limited aggregation, DLA; reaction limited aggregation, RLA; ballistic aggregation, BA; and Eden-like aggregation) [74].
In the DLA model, the individual particles or clusters stochastically diffuse via
Brownian trajectories towards one another and every collision between them results
in formation of a larger cluster [75]. The clusters formed display a fractal morphology that depends upon the space dimension in the DLA model. In the RLA model,
the probability of attachment is small and only a small fraction of collisions
between clusters leads to formation of larger clusters. Traditionally, DLA and
RLA are called rapid and slow aggregations, respectively.
A similar mechanism of aggregation is used in the BA model; however, here the
trajectories of moving particles are assumed to be linear [76–78]. In the Eden-like
aggregation model, new single particles attach to the cluster at its perimeter [79].
The type of diffusion motion strongly affects the cluster morphology, e.g.,
Brownian motion generates typical fractal DLA clusters, linear trajectories lead
to compact structures, and Levy-flight trajectories allow continuous changes of the
cluster morphology [80].
The above models are irreversible. Finally, it is expected that clusters grow and
merge until formation of a single connected cluster. However, the experimental
studies show that some systems can display the presence of reversible aggregation.
In a rapid aggregation process, the clusters with loose structure arise initially, and
after a certain time they can restructure to more compact clusters with higher fractal
dimensionality [81, 82]. The process of thermal restructuring of fractal polymer
clusters dispersed in water was experimentally observed using small-angle light
scattering [83].
In the absence of aggregation, restructuring resulted in an increase in the fractal
dimension. A simple model of the restructuring kinetics, based on coalescence
theory of liquid droplets, was developed [83]. Reversible-growth models were also
built. These models allow unbinding of particles and imply that later on, during the
restructuring, the ramified clusters become compact [84, 85]. The details of cluster
morphology strongly depend on the interparticle interaction, the presence of
restructuring, and external fields [86]. Impact of interactions on the intrastructure
of colloidal clusters was recently studied by Brownian dynamics simulations [17].
It was shown that an increase in density of suspension results in stronger intercluster
interactions that affect the intrastructure of clusters. However, perturbation of the
intrastructure of clusters was shown to be low in diluted suspension.
3.2 Similarly Charged Particles
For colloidal suspensions, the influence of the combination of short-range
attractions and long-range repulsions on clustering phenomena [87] is extremely
interesting. It is expected for charged particles that cluster accumulates net charge
and may reject association of additional particles at a certain critical size.
Aggregation of Charged Colloidal Particles
69
In the DLA model, the individual particles or clusters stochastically diffuse via
Brownian trajectories towards one another and every collision between them results
in formation of a larger cluster [75]. The clusters formed display a fractal morphology that depends upon the space dimension in the DLA model. In the RLA model,
the probability of attachment is small and only a small fraction of collisions
between clusters leads to formation of larger clusters. Traditionally, DLA and
RLA are called rapid and slow aggregations, respectively.
A similar mechanism of aggregation is used in the BA model; however, here the
trajectories of moving particles are assumed to be linear [76–78]. In the Eden-like
aggregation model, new single particles attach to the cluster at its perimeter [79].
The type of diffusion motion strongly affects the cluster morphology, e.g.,
Brownian motion generates typical fractal DLA clusters, linear trajectories lead
to compact structures, and Levy-flight trajectories allow continuous changes of the
cluster morphology [80].
The above models are irreversible. Finally, it is expected that clusters grow and
merge until formation of a single connected cluster. However, the experimental
studies show that some systems can display the presence of reversible aggregation.
In a rapid aggregation process, the clusters with loose structure arise initially, and
after a certain time they can restructure to more compact clusters with higher fractal
dimensionality [81, 82]. The process of thermal restructuring of fractal polymer
clusters dispersed in water was experimentally observed using small-angle light
scattering [83].
In the absence of aggregation, restructuring resulted in an increase in the fractal
dimension. A simple model of the restructuring kinetics, based on coalescence
theory of liquid droplets, was developed [83]. Reversible-growth models were also
built. These models allow unbinding of particles and imply that later on, during the
restructuring, the ramified clusters become compact [84, 85]. The details of cluster
morphology strongly depend on the interparticle interaction, the presence of
restructuring, and external fields [86]. Impact of interactions on the intrastructure
of colloidal clusters was recently studied by Brownian dynamics simulations [17].
It was shown that an increase in density of suspension results in stronger intercluster
interactions that affect the intrastructure of clusters. However, perturbation of the
intrastructure of clusters was shown to be low in diluted suspension.
3.2 Similarly Charged Particles
For colloidal suspensions, the influence of the combination of short-range
attractions and long-range repulsions on clustering phenomena [87] is extremely
interesting. It is expected for charged particles that cluster accumulates net charge
and may reject association of additional particles at a certain critical size.
Aggregation of Charged Colloidal Particles
69