cationic polyelectrolytes have been intensively studied in many theoretical
[116–121] and experimental [122–124] works.
The phase diagram of asymmetric positively and negatively charged chains in an
oppositely charged polyelectrolyte was theoretically obtained [125]. It was shown
that cylindrical and lamellar cluster structures with nonzero net charge were formed
at high polymer concentration. Nonuniform distribution of charge along the
annealed polyelectrolyte chains was observed [116, 121]. The theoretical
predictions and Monte Carlo simulations show that charges accumulate at the
ends of chains. [116]. The cluster size distribution functions of the oppositely
charged macroions in solution were studied using the Monte Carlo simulations
[120]. It was demonstrated that increasing electrostatic coupling results in formation of larger clusters, and a single cluster comprising all the macroions forms at the
strongest coupling. The structure of symmetric polycation–polyanion mixtures
without salt in good solvents was studied using the Langevin sampling simulation
technique and field-theoretic simulation methods [119, 126]. The obtained results
allowed explanation of the phenomenon of complex coacervation, a type of phase
separation in which dense liquid precipitates coexist with supernatant solvent.
Brownian dynamics computer simulations have shown that variation in electrostatic interactions changed the size, shape, and local density distribution of the
complexes formed by terminally charged hyperbranched polymers and oppositely
charged neutralizing linear polyelectrolytes [127]. The ultrasoft core model of
interpenetrating polycations and polyanions was proposed for investigation of the
polyelectrolyte aggregation using different theoretical approaches and molecular
dynamic simulations [117]. The clustering and segregation of the oppositely
charged species was observed. At sufficiently low temperatures and densities, the
oppositely charged polyions tend to form weakly interacting neutral pairs. The
break-up of ion pairs was observed with increase in temperature. This was followed
by the percolation transition from low temperature dielectric (insulator) state to
high temperature ionic (conductor) state [117].
The Monte Carlo simulations were applied to study the complexation, phase
separation, and redissolution of polyelectrolyte–macroion solutions [128]. It was
shown that introduction of the oppositely charged polyelectrolytes into a stable
macroion solution with repelling macroions resulted in a decrease in the solution
stability. The system was unstable at macromolecular charge equivalence when a
large and loose cluster of macroions and polyelectrolytes was forming. Finally,
redissolution of macroions occurred in the excess of polyelectrolyte.
The complexation between a polyampholyte and a charged particle was studied
using Monte Carlo simulations [129, 130]. The increasing charge density and
particle size resulted in change of configuration of the polyampholyte chain
adsorbed on the particle surface. At large charge density and particle size, collapse
of the polyampholyte chain on the particle surface was observed [129]. The effects
of different model parameters (polyampholyte contour length, nanoparticle surface
charge, pH of solvent, ionic concentration, etc.) on possible polyampholyte
conformations at the nanoparticle surface were investigated [130].
Aggregation of Charged Colloidal Particles
77
[116–121] and experimental [122–124] works.
The phase diagram of asymmetric positively and negatively charged chains in an
oppositely charged polyelectrolyte was theoretically obtained [125]. It was shown
that cylindrical and lamellar cluster structures with nonzero net charge were formed
at high polymer concentration. Nonuniform distribution of charge along the
annealed polyelectrolyte chains was observed [116, 121]. The theoretical
predictions and Monte Carlo simulations show that charges accumulate at the
ends of chains. [116]. The cluster size distribution functions of the oppositely
charged macroions in solution were studied using the Monte Carlo simulations
[120]. It was demonstrated that increasing electrostatic coupling results in formation of larger clusters, and a single cluster comprising all the macroions forms at the
strongest coupling. The structure of symmetric polycation–polyanion mixtures
without salt in good solvents was studied using the Langevin sampling simulation
technique and field-theoretic simulation methods [119, 126]. The obtained results
allowed explanation of the phenomenon of complex coacervation, a type of phase
separation in which dense liquid precipitates coexist with supernatant solvent.
Brownian dynamics computer simulations have shown that variation in electrostatic interactions changed the size, shape, and local density distribution of the
complexes formed by terminally charged hyperbranched polymers and oppositely
charged neutralizing linear polyelectrolytes [127]. The ultrasoft core model of
interpenetrating polycations and polyanions was proposed for investigation of the
polyelectrolyte aggregation using different theoretical approaches and molecular
dynamic simulations [117]. The clustering and segregation of the oppositely
charged species was observed. At sufficiently low temperatures and densities, the
oppositely charged polyions tend to form weakly interacting neutral pairs. The
break-up of ion pairs was observed with increase in temperature. This was followed
by the percolation transition from low temperature dielectric (insulator) state to
high temperature ionic (conductor) state [117].
The Monte Carlo simulations were applied to study the complexation, phase
separation, and redissolution of polyelectrolyte–macroion solutions [128]. It was
shown that introduction of the oppositely charged polyelectrolytes into a stable
macroion solution with repelling macroions resulted in a decrease in the solution
stability. The system was unstable at macromolecular charge equivalence when a
large and loose cluster of macroions and polyelectrolytes was forming. Finally,
redissolution of macroions occurred in the excess of polyelectrolyte.
The complexation between a polyampholyte and a charged particle was studied
using Monte Carlo simulations [129, 130]. The increasing charge density and
particle size resulted in change of configuration of the polyampholyte chain
adsorbed on the particle surface. At large charge density and particle size, collapse
of the polyampholyte chain on the particle surface was observed [129]. The effects
of different model parameters (polyampholyte contour length, nanoparticle surface
charge, pH of solvent, ionic concentration, etc.) on possible polyampholyte
conformations at the nanoparticle surface were investigated [130].
Aggregation of Charged Colloidal Particles
77