2.8 Interaction Between Colloidal Aggregates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3 Simulation of Cluster Morphology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.1 Main Types of Computer Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.2 Similarly Charged Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.3 Oppositely Charged Particles . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . 76
3.4 Effect of Dipolar Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4 Kinetics of Aggregation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.1 Aggregation as a Second-Order Reaction . . . . . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . . .. . 79
4.2 Population Balance Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.3 Popular Kernels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.4 Classification of Kernels . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . 84
4.5 Dynamic Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
1 Introduction
Polymeric nanoparticles are colloidal particles consisting of macromolecular
compounds. Among these materials the polyelectrolyte complex (PEC) nanoparticles
are of particular interest. These particles with integrated drugs, proteins, vaccines, or
diagnostic agents can be used as carriers in different pharmaceutical and biomedical
applications [1]. The benefits of their use include controlled drug release and limited
toxicity. Moreover, water-soluble and biodegradable PEC nanoparticles may be used
as drug delivery systems in humans [2, 3].
PEC nanoparticles are prepared by mixing of two oppositely charged polyanions
and polycations. Formation of PEC nanoparticles is controlled by the structure of
the polycation/polyanion components, concentration, mixing order, mixing ratio,
ionic strength, pH, temperature, and other factors [4]. Key factors determining
successful applications of PEC nanoparticles are related to good reproducibility
of the formation process, monomodality, and the possibility of obtaining particles
with determined and graded sizes.
The process of PEC nanoparticle formation usually includes the initial diffusion
stage of mutual entanglement between polymers and formation of primary particles
and the further stage of their aggregation and rearrangement of the already formed
aggregates [2, 4]. The macroscopically homogeneous systems containing very
small primary PEC nanoparticles (approximately 5–20 nm) were developed using
special preparation techniques [5]. The process of aggregation of the primary PEC
nanoparticles may result in formation of larger nanoparticles. As a result, a turbid
colloidal, or two-phase system of supernatant liquid and precipitated PEC
nanoparticles is formed [6]. Using of consecutive centrifugation and separation
steps allows significant decrease in the polydispersity of the colloidal system,
elimination of the primary PEC nanoparticles, and, finally, prevailing of the secondary nanoparticles with radii of about 100–200 nm in dispersion [4]. The
secondary PEC nanoparticles have many particular advantages for applications in
58
N.I. Lebovka
3 Simulation of Cluster Morphology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.1 Main Types of Computer Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.2 Similarly Charged Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.3 Oppositely Charged Particles . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . 76
3.4 Effect of Dipolar Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4 Kinetics of Aggregation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.1 Aggregation as a Second-Order Reaction . . . . . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . . .. . 79
4.2 Population Balance Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.3 Popular Kernels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.4 Classification of Kernels . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . 84
4.5 Dynamic Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
1 Introduction
Polymeric nanoparticles are colloidal particles consisting of macromolecular
compounds. Among these materials the polyelectrolyte complex (PEC) nanoparticles
are of particular interest. These particles with integrated drugs, proteins, vaccines, or
diagnostic agents can be used as carriers in different pharmaceutical and biomedical
applications [1]. The benefits of their use include controlled drug release and limited
toxicity. Moreover, water-soluble and biodegradable PEC nanoparticles may be used
as drug delivery systems in humans [2, 3].
PEC nanoparticles are prepared by mixing of two oppositely charged polyanions
and polycations. Formation of PEC nanoparticles is controlled by the structure of
the polycation/polyanion components, concentration, mixing order, mixing ratio,
ionic strength, pH, temperature, and other factors [4]. Key factors determining
successful applications of PEC nanoparticles are related to good reproducibility
of the formation process, monomodality, and the possibility of obtaining particles
with determined and graded sizes.
The process of PEC nanoparticle formation usually includes the initial diffusion
stage of mutual entanglement between polymers and formation of primary particles
and the further stage of their aggregation and rearrangement of the already formed
aggregates [2, 4]. The macroscopically homogeneous systems containing very
small primary PEC nanoparticles (approximately 5–20 nm) were developed using
special preparation techniques [5]. The process of aggregation of the primary PEC
nanoparticles may result in formation of larger nanoparticles. As a result, a turbid
colloidal, or two-phase system of supernatant liquid and precipitated PEC
nanoparticles is formed [6]. Using of consecutive centrifugation and separation
steps allows significant decrease in the polydispersity of the colloidal system,
elimination of the primary PEC nanoparticles, and, finally, prevailing of the secondary nanoparticles with radii of about 100–200 nm in dispersion [4]. The
secondary PEC nanoparticles have many particular advantages for applications in
58
N.I. Lebovka