Monte Carlo simulations of polyion−macroion complexes. 2. Polyion length and charge density dependence

The complexation between a polyion and an oppositely charged spherical macroion in the framework of the primitive model has been studied by the use of Monte Carlo simulations. The polyion length, linear charge density, and bare persistence length are varied systematically, while the properties of the macroion are kept constant. The polyion charge to macroion charge ratio is varied between 1/4 and 4. The structure of the complex is investigated by direct visualization; polyion bead complexation probability; loop, tail, and train characteristics; degree of overcharging; and tail joint probability functions. The strongest complexes are observed for flexible chains, where the polyion is folded around the macroion. In the case of fully flexible chains, a transition from a collapsed state to a fluctuating two-tail state and eventually to a one-tail state are observed as the chain length is increased. As the stiffness is increased, several complex structures, such as multiloop, single-loop, and solenoid arrangements, and finally a structure involving only a single contact between the polyion and the macroion occur. In particular, for long and highly charged polyions, a transition from the one-tail state to a two-tail state appears as the chain stiffness is increased. A discussion with recent theories and other simulation studies is also provided

Diblock polyampholytes grafted onto spherical particles : effect of stiffness, charge density, and grafting density

The structure of spherical brushes formed by symmetric diblock polyampholytes end-grafted onto small spherical particles in aqueous solution is examined within the framework of the so-called primitive model using Monte Carlo simulations. The properties of the two blocks are identical except for the sign of their charges. Three different chain flexibilities corresponding to flexible, semiflexible, and stiff blocks are considered at various polyampholyte linear charge densities and grafting densities. The link between the two blocks is flexible at all conditions, and the grafted segments are laterally mobile. Radial and lateral spatial distribution functions of different types and single-chain properties are analyzed. The brush structure strongly depends on the chain flexibility. With flexible chains, a disordered polyelectrolyte complex is formed at the surface of the particle, the complex becoming more compact at increasing linear charge density. With stiff blocks, the inner blocks are radially oriented. At low linear charged density, the outer blocks are orientationally disordered, whereas at increasing electrostatic interaction the two blocks of a polyampholyte are parallel and close to each other, leading to an ordered structure referred to as a polyampholyte star. As the grafting density is increased, the brush thickness responds differently for flexible and nonflexible chains, depending on a different balance between electrostatic interactions and excluded volume effects

Diblock polyampholytes grafted onto spherical particles : Monte Carlo simulation and lattice mean-field theory

Spherical brushes composed of diblock polyampholytes (diblock copolymers with oppositely charged blocks) grafted onto solid spherical particles in aqueous solution are investigated by using the primitive model solved with Monte Carlo simulations and by lattice mean-field theory. Polyampholyte chains of two compositions are considered: a copolymer with a long and a short block, A100B10, and a copolymer with two blocks of equal length, A50B50. The B block is end-grafted onto the surface, and its charge is varied, whereas the charge of the A block is fixed. Single-chain properties, radial and lateral spatial distributions of different types, and structure factors are analyzed. The brush structure strongly depends on the charge of the B block. In the limit of an uncharged B block, the chains are stretched and form an extended polyelectrolyte brush. In the other limit with the charges of the blocks compensating each other, the chains arecollapsedandformapolyelectrolytecomplexsurroundingtheparticles.Atintermediatechargeconditions, a polyelectrolyte brush and a polyelectrolyte complex coexist and constitute two substructures of the spherical brush. The differences of the brush structures formed by the A100B10 and A50B50 polyampholytes are also analyzed. Finally, a comparison of the predictions of the two theoretical approaches is made