Optimal Displacement Parameters in Monte Carlo Simulations

Monte Carlo simulations of weak polyampholyte microgels: pH-dependence of conformation and ionization

We performed Metropolis Monte Carlo simulations to investigate the impact of varying acid and base dissociation constants on the pH-dependent ionization and conformation of weak polyampholyte microgels under salt-free conditions and under explicit consideration of the chemical ionization equilibria of the acidic and basic groups and their electrostatic interaction. Irrespective of their relative acid and base dissociation constant, all of the microgels undergo a pH-dependent charge reversal from positive to negative with a neutral charge at the isoelectric point. This charge reversal is accompanied by a U-shaped swelling transition of the microgels with a minimum of their size at the point of charge neutrality. The width of the U-shaped swelling transition, however, is found to depend on the chosen relative acid and base dissociation constants through which the extent of the favorable electrostatic intramolecular interaction of the ionized acidic and basic groups is altered. The pH-dependent swelling transition of the microgels is found to become broader, the stronger the intramolecular electrostatic interaction of the oppositely charged ionized species is. In addition, the intramolecular charge compensation of the acidic and basic groups of the microgels allows their counterions to abandon the microgel and the associated gain in translational entropy further amplifies the broadening of the pH-dependent swelling transition. The analysis of the radial ionization profiles of the acidic and basic groups of the differently composed microgels reveals a variety of radial ionization patterns with a dependence on the overall charge of the microgels.

Monte Carlo simulations of weak polyelectrolyte microgels: pH-dependence of conformation and ionization

In this study, we investigated the effect of pH on single weak acidic polyelectrolyte microgels under salt-free conditions with (i) varying microgel concentration, (ii) varying content of acidic groups and (iii) different crosslinking densities using Monte Carlo simulations under explicit consideration of the protonation/deprotonation reaction. We assessed both global properties, such as the degree of ionization, the degree of swelling and the counterion distribution, and local properties such as the radial network ionization profile and the ionization along the polymer chains as a function of pH. We found a pronounced suppression of the pH-dependent ionization of the microgels, as compared to the ideal titration behavior and a shift of the titration curve to a higher pH originating in the proximity of acidic groups in the microgel. In contrast to macroscopic gels, counterions can leave the microgel, resulting in an effective charge of the network, which hinders the ionization. A decreasing microgel concentration leads to an increased effective charge of the microgel and a more pronounced shift of the titration curve. The number of acidic groups showed only a weak effect on the ionization behavior of the microgels. For two different microgels with different crosslinking densities, similar scaling of the gel size was observed. A distinct transition from an uncharged and unswollen to a highly charged and expanded polymer network was observed for all investigated microgels. The degree of swelling mainly depends on the degree of ionization. An inhomogeneous distribution of the degree of ionization along the radial profile of the microgel was found.

Spacer Chains Prevent the Intramolecular Complexation in Miktoarm Star Polymers

The influence of spacer chains on the intramolecular complexation in star-shaped heteroarm (miktoarm) polymers is investigated. To overcome the mutual attraction of different polymeric components present in a miktoarm star with different homopolymeric arms, spacer chains of different length are attached to the core of the star at three different positions. In most of the investigated cases, this leads to diblock copolymer arms within the miktoarm star. Hereby, the inner spacer separates the outer blocks from their attractively interacting homopolymeric arms. The effect on the intramolecular complexation and the structure of the star polymer is obtained by Monte Carlo simulations of a simple bead-spring model. Then, long spacers can completely prevent the complexation. Both, local shielding by the spacer chains and the increased distance between the complex-forming polymers due to the spacer chains inhibit the complex formation. For a range of spacer positions and lengths, an equilibrium between a system forming a complex and a complex free system is found. The spacer chains can be used as a tool to tune the intramolecular complexation.

Balancing Segregation and Complexation in Amphiphilic Copolymers by Architecture and Confinement

Segregation is a well-known principle for micellization, as solvophobic components try to minimize interactions with other entities (such as solvent) by self-assembly. An opposite principle is based on complexation (or coacervation), leading to the coassembly/association of different components. Most cases in the literature rely on only one of these modes, though the classical micellization scheme (such as spherical micelles, wormlike micelles, and vesicles) can be enriched by a subtle balance of segregation and complexation. Because of their counteraction, micellar constructs with unprecedented structure and behavior could be obtained. In this feature, systems are highlighted, which are between both mechanisms, and we study concentration, architecture, and confinement effects. Systems with inter- and intramolecular interactions are presented, and the effects of polymer topology and monomer sequence on the resulting structures are discussed. It is shown that complexation can lead to altered micellization behavior as the complex of one hydrophobic and one hydrophilic component can have a very low surface tension toward the solvent. Then, the more soluble component is enriched at the surface of the complex and acts as a microsurfactant. Although segregation dominates for amphiphilic copolymers in solution, the effect of the complexation can be enhanced by branching (change of architecture). Another possibility to enhance the complexation is by confining copolymers in a (pseudo-) 2D environment (like the one available at liquid-liquid interfaces). These observations show how new structural features can be achieved by tuning the subtle balance between segregation and complexation/solubilization.