The target of this work is to study conformational properties of starlike polyelectrolytes with pH-sensitive (annealed) dissociation in salt-free solutions. We confront hybrid Monte Carlo (HMC) simulations with computationally less expensive approximate numerical self-consistent field (SCF) calculations and with analytical theories. We demonstrate when the mean-field results are reliable and their advantage over MC in terms of efficiency can be exploited and when not. In the interior of the star, where inter-arm interactions dominate over intra-arm ones, the mean-field approximation works well and SCF agrees with the MC results. Intra-arm interactions dominate at star periphery, and their role is underestimated by the mean field. Here, conformations and dissociation resemble those of linear polyelectrolytes. Consequently, the dissociation profile along the chain contour is qualitatively different between MC and SCF. Comparison of the two methods and a distinction between intra-arm and inter-arm contributions to interactions enables us to understand the transition in behavior from linear to starlike chain topology.

The paper describes the general features and trends of the electrostatic assembly (EA) of block polyelectrolytes. We performed computer simulations of the associative behavior of aqueous mixtures of diblock copolymers containing one neutral water-soluble block and one either positively or negatively charged polyelectolyte (PE) block. While the neutral block is readily soluble in water, the hydrophilic vs hydrophobic nature of the neutral backbone of the PE block and the compatibility of the blocks vary in a broad range. We investigated the role of (i) electrostatics, (ii) solvophobicity of the PE block, (iii) compatibility of the polymer blocks, and also (iv) compatibility of small ions with the polymer blocks. We employed the dissipative particle dynamics (DPD) method and used the generally recognized formula (J. Chem. Phys. 1997, 107, 4423) for recalculating the Flory−Huggins interaction parameters in DPD parameters of soft coarse-grained repulsion forces. The Coulomb interactions are described by the rigorous expression derived for the exponentially smeared charge with a fairly low charge decay length λ = 0.2. A low λ value has been used to reproduce the behavior of small counterions as realistically as possible at the DPD level. We compared the self-assembling behavior of charged and neutral copolymers for all the systems. The conclusions of the study can be briefly outlined as follows: Even though long-range electrostatic interactions are a prerequisite for electrostatic self-assembly and the increase in entropy due to liberation of mobile counterions represents an important driving force in all cases, the solvent quality for the PE backbone and incompatibility of blocks play an important role and substantially modify the association process. Only dimers containing one positively and one negatively charged chain are formed in systems with readily soluble PE blocks. The formation of large core−shell associates assumes (in addition to the effect of electrostatics) significantly unfavorable interactions of PE segments with water and with segments of the water-soluble block. The presence of opposite charges on different chains promotes the formation of associates, i.e., both the fraction of associates and association number increase, but the latter increase is fairly small (taking into account the value that is attained in corresponding neutral system).

The paper describes the pH-dependent selfassembly of a diblock copolymer, poly(2-vinylpyridine)-blockpoly(ethylene oxide), P2VP−PEO in aqueous media using computer simulations. We employed the dissipative particle dynamics (DPD) method and found that the copolymer with electrically neutral (i.e., deprotonated) or very low-protonated P2VP blocks form multimolecular spherical core−shell micelles with insoluble P2VP cores in neutral and alkaline solutions, while protonization (ionization) of P2VP blocks exceeding 25% provokes the dissociation of micelles in single chains in acidic media. The finding that a clearly pronounced transition occurs in a restricted pH region slightly above pK A ap (where pK A ap is the apparent dissociation constant of the conjugated acid P2VPH + ) is in good agreement with the experimental data (Macromolecules 1996, 29, 6071−6073). This suggests that (i) the tested model is reasonable and the mutual relationship between the parameters used in the soft repulsive and electrostatic potentials was set appropriately and (ii) the DPD method is a suitable simulation technique for studying phenomena accompanied by pronounced changes in the global properties of complex polymer and polyelectrolyte systems. Although we studied the behavior of only one specific system, the simulation yields a generic pattern for the pH-dependent self-assembly of copolymers containing one neutral water-soluble block and one annealed (weak) polyelectrolyte block with fairly hydrophobic backbone.

Intramolecular structures in amphiphilic graft copolymers with hydrophilic side chains and hydrophobic backbone have been studied by molecular dynamics simulations. In accordance with earlier theoretical predictions Zhulina, E. Macromolecules 2005, 38, 2506-2514, we have found that balance of repulsive and attractive intramolecular interactions may result in the pearl-necklace-type conformations. The globular "pearls" are formed by collapsed segments of the main chain comprising multiple spacers; these pearls are stabilized against aggregation by repulsive interactions of the hydrophilic grafts. The size of the pearls is controlled by the intramolecular hydrophilic-hydrophobic balance, whereas the total number of pearls in the graft copolymer depends on the length of the main chain. For graft copolymer with relatively long spacers we have observed intramolecular conformational transition from pearl-necklace structure to unimolecular cylindrical micelle upon a decrease in the solvent quality for the main chain. The results of simulations, in particular behavior of polymers of finite chain length, are rationalized on the basis of revised and extended scaling theory.

Multimolecular micelles, formed by polystyrene-block-poly(methacrylic acid) in water, are studied by lattice Monte Carlo method. Electrostatic interactions are calculated in the mean-field approximation by solving the Poisson-Boltzmann equation. The model is parametrized according to available experimental data. The dependence of micellar size on pH and ionic strength is calculated and compared with experimental data. A special attention is devoted to the behavior in solutions with a low ionic strength.