important in polyelectrolyte solutions with strong coupling of electrostatic and
hydrodynamic interactions between the polymer chains [67, 68].
2.8 Interaction Between Colloidal Aggregates
Until recently, there was no clear conception about interaction between two
aggregates consisting of many individual particles. Practically all efforts were
devoted to studies of interactions between single particles with an idealized
shape, e.g., spheres, cylinders, and ellipsoids.
The general schema of calculation of the van der Waals interaction energy
between irregularly shaped molecular aggregates was developed in 1998 [69].
More recently, the calculations of van der Waals and double layer interactions
between colloidal aggregates were performed [70, 71]. The direct numerical
calculations of the van der Waals interaction between fractal aggregates of colloidal
particles (based on a pairwise summation of interaction energies between all
particles) have shown that they can be fairly well approximated by the energy of
interaction between the closest pair of primary particles [70]. However, it was noted
that the surface distance between two aggregates is governed by the morphology of
clusters and there may be an apparent impact on the van der Waals interaction.
Similar estimations were done for the double layer interactions between fractal or
hexagonal closed-packed aggregates with considerable overlapping of double layer
inside the aggregates and between two interacting aggregates [71]. It was shown
that for the relatively thin double layer (l D 0.2r for closed-packed aggregates
and l D r for aggregates with a small fractal dimension), the interaction of
aggregates is close to the interaction of the nearest pair of the primary particles.
However, in thick double layers (l D > r), the overlapping of the double layer
inside the aggregate was noticeable and formation of a spheroidal double layer
around the aggregate was observed.
3 Simulation of Cluster Morphology
A number of theoretical models and computer simulation approaches were developed for description of the cluster morphology [72], reaction kinetics, and time
dependence of the cluster-size distributions [73].
3.1 Main Types of Computer Models
The cluster morphology may depend on details of colloidal particle interactions,
mechanism of particle attachment to the cluster, and dimensionality of the problem.
The existing models for cluster morphology simulation account for the trajectory of
68
N.I. Lebovka
hydrodynamic interactions between the polymer chains [67, 68].
2.8 Interaction Between Colloidal Aggregates
Until recently, there was no clear conception about interaction between two
aggregates consisting of many individual particles. Practically all efforts were
devoted to studies of interactions between single particles with an idealized
shape, e.g., spheres, cylinders, and ellipsoids.
The general schema of calculation of the van der Waals interaction energy
between irregularly shaped molecular aggregates was developed in 1998 [69].
More recently, the calculations of van der Waals and double layer interactions
between colloidal aggregates were performed [70, 71]. The direct numerical
calculations of the van der Waals interaction between fractal aggregates of colloidal
particles (based on a pairwise summation of interaction energies between all
particles) have shown that they can be fairly well approximated by the energy of
interaction between the closest pair of primary particles [70]. However, it was noted
that the surface distance between two aggregates is governed by the morphology of
clusters and there may be an apparent impact on the van der Waals interaction.
Similar estimations were done for the double layer interactions between fractal or
hexagonal closed-packed aggregates with considerable overlapping of double layer
inside the aggregates and between two interacting aggregates [71]. It was shown
that for the relatively thin double layer (l D 0.2r for closed-packed aggregates
and l D r for aggregates with a small fractal dimension), the interaction of
aggregates is close to the interaction of the nearest pair of the primary particles.
However, in thick double layers (l D > r), the overlapping of the double layer
inside the aggregate was noticeable and formation of a spheroidal double layer
around the aggregate was observed.
3 Simulation of Cluster Morphology
A number of theoretical models and computer simulation approaches were developed for description of the cluster morphology [72], reaction kinetics, and time
dependence of the cluster-size distributions [73].
3.1 Main Types of Computer Models
The cluster morphology may depend on details of colloidal particle interactions,
mechanism of particle attachment to the cluster, and dimensionality of the problem.
The existing models for cluster morphology simulation account for the trajectory of
68
N.I. Lebovka