The process of aggregation of the oppositely charged polyions (positively
charged liposomes and negatively charged polyelectrolyte sodium polyacrylate)
was studied by means of Monte Carlo simulation [131]. The model accounted for
heterogeneous charge distribution at the particle surface, related with the correlated
polyion adsorption [46]. Formation of long-living clusters of polyelectrolytedecorated particles was demonstrated. Molecular dynamics simulations were
performed to study the polyampholyte–polyelectrolyte complexes in solutions
[124, 132]. It was demonstrated that polyampholyte chain binds to a polyelectrolyte
in a way optimizing electrostatic interactions between the ionic groups in both
polymeric chains. Formation of the micellar complex by anionic polyelectrolyte
and cationic surfactants (in monomeric and dimeric forms) was investigated by
molecular dynamics simulation [133]. Results have shown that the dimeric form
interacts more strongly with the polyanion and the size of the micellar complex
becomes larger with an increase in the surfactant concentration.
3.4 Effect of Dipolar Interactions
The effects of dipolar interactions on DLA processes were studied in details for 2D
and 3D off-lattice models [134–137]. The fractal dimensionality d f was a monotonically increasing function of the temperature (or decreasing function of dipolar
forces). For example, it varied continuously from about 1.78 for small dipolar
interactions to about 1.35 for large dipolar interactions (3D model) [134, 135].
Therefore, the structure of clusters formed at low temperatures or strong dipolar
forces was less branched and more open (d f ~ 1) than in free DLA with no
interactions. On increase in temperature or decrease in dipolar forces, the value
of d f reached the limit value of free DLA [136, 137]. The values d f ¼ 1.13 Æ 0.01
and d f ¼ 1.37 Æ 0.03 were obtained in the limit of zero temperature for 2D and 3D
systems, respectively. Transitions between an ordered, or quasi-ordered, and a
disordered phase were also observed for high values of the reduced temperature
[138]. The long range correlations between the dipoles were revealed in the lowtemperature ordered phase.
4 Kinetics of Aggregation
Kinetics of aggregation, coalescence, and annihilation or fragmentation are important in many physical, chemical and biological processes [21, 80, 139–141]. The
popular mean field Smoluchowski approach [73] gives good description of simple
aggregation systems. However, in the presence of restructuring, long range
interactions, and formation of clusters with fractal geometry, more complicated
approaches based on computer simulation methods are useful.
78
N.I. Lebovka
charged liposomes and negatively charged polyelectrolyte sodium polyacrylate)
was studied by means of Monte Carlo simulation [131]. The model accounted for
heterogeneous charge distribution at the particle surface, related with the correlated
polyion adsorption [46]. Formation of long-living clusters of polyelectrolytedecorated particles was demonstrated. Molecular dynamics simulations were
performed to study the polyampholyte–polyelectrolyte complexes in solutions
[124, 132]. It was demonstrated that polyampholyte chain binds to a polyelectrolyte
in a way optimizing electrostatic interactions between the ionic groups in both
polymeric chains. Formation of the micellar complex by anionic polyelectrolyte
and cationic surfactants (in monomeric and dimeric forms) was investigated by
molecular dynamics simulation [133]. Results have shown that the dimeric form
interacts more strongly with the polyanion and the size of the micellar complex
becomes larger with an increase in the surfactant concentration.
3.4 Effect of Dipolar Interactions
The effects of dipolar interactions on DLA processes were studied in details for 2D
and 3D off-lattice models [134–137]. The fractal dimensionality d f was a monotonically increasing function of the temperature (or decreasing function of dipolar
forces). For example, it varied continuously from about 1.78 for small dipolar
interactions to about 1.35 for large dipolar interactions (3D model) [134, 135].
Therefore, the structure of clusters formed at low temperatures or strong dipolar
forces was less branched and more open (d f ~ 1) than in free DLA with no
interactions. On increase in temperature or decrease in dipolar forces, the value
of d f reached the limit value of free DLA [136, 137]. The values d f ¼ 1.13 Æ 0.01
and d f ¼ 1.37 Æ 0.03 were obtained in the limit of zero temperature for 2D and 3D
systems, respectively. Transitions between an ordered, or quasi-ordered, and a
disordered phase were also observed for high values of the reduced temperature
[138]. The long range correlations between the dipoles were revealed in the lowtemperature ordered phase.
4 Kinetics of Aggregation
Kinetics of aggregation, coalescence, and annihilation or fragmentation are important in many physical, chemical and biological processes [21, 80, 139–141]. The
popular mean field Smoluchowski approach [73] gives good description of simple
aggregation systems. However, in the presence of restructuring, long range
interactions, and formation of clusters with fractal geometry, more complicated
approaches based on computer simulation methods are useful.
78
N.I. Lebovka