Simulations of ionization equilibria in weak polyelectrolyte solutions and gels.

This article recapitulates the state of the art regarding simulations of ionization equilibria of weak polyelectrolyte solutions and gels. We start out by reviewing the essential thermodynamics of ionization and show how the weak polyelectrolyte ionization differs from the ionization of simple weak acids and bases. Next, we describe simulation methods for ionization reactions, focusing on two methods: the constant-pH ensemble and the reaction ensemble. After discussing the advantages and limitations of both methods, we review the existing simulation literature. We discuss coarse-grained simulations of weak polyelectrolytes with respect to ionization equilibria, conformational properties, and the effects of salt, both in good and poor solvent conditions. This is followed by a discussion of branched star-like weak polyelectrolytes and weak polyelectrolyte gels. At the end we touch upon the interactions of weak polyelectrolytes with other polymers, surfaces, nanoparticles and proteins. Although proteins are an important class of weak polyelectrolytes, we explicitly exclude simulations of protein ionization equilibria, unless they involve protein-polyelectrolyte interactions. Finally, we try to identify gaps and open problems in the existing simulation literature, and propose challenges for future development.

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.

3D Structures of Responsive Nanocompartmentalized Microgels.

Compartmentalization in soft matter is important for segregating and coordinating chemical reactions, sequestering (re)active components, and integrating multifunctionality. Advances depend crucially on quantitative 3D visualization in situ with high spatiotemporal resolution. Here, we show the direct visualization of different compartments within adaptive microgels using a combination of in situ electron and super-resolved fluorescence microscopy. We unravel new levels of structural details and address the challenge of reconstructing 3D information from 2D projections for nonuniform soft matter as opposed to monodisperse proteins. Moreover, we visualize the thermally induced shrinkage of responsive core-shell microgels live in water. This strategy opens doors for systematic in situ studies of soft matter systems and their application as smart materials.

Interface-enforced complexation between copolymer blocks.

Binary diblock copolymers and corresponding ternary miktoarm stars are studied at oil-water interfaces. All polymers contain oil-soluble poly(propylene oxide) PPO, water-soluble poly(dimethylaminoethyl methacrylate) PDMAEMA and/or poly(ethylene oxide) PEO. The features of their Langmuir compression isotherms are well related to the ones of the corresponding homopolymers. Within the Langmuir-trough, PEO-b-PPO acts as the most effective amphiphile compared to the other PPO-containing copolymers. In contrast, the compression isotherms show a complexation of PPO and PDMAEMA for PPO-b-PDMAEMA and the star, reducing their overall amphiphilicity. Such complex formation between the blocks of PPO-b-PDMAEMA is prevented in bulk water but facilitated at the interface. The weakly-interacting blocks of PPO-b-PDMAEMA form a complex due to their enhanced proximity in such confined environments. Scanning force microscopy and Monte Carlo simulations with varying confinement support our results, which are regarded as compliant with the mathematical random walk theorem by Pólya. Finally, the results are expected to be of relevance for e.g. emulsion formulation and macromolecular engineering.

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.

Optimal Displacement Parameters in Monte Carlo Simulations.

An adaptive algorithm optimizing single-particle translational displacement parameters in Metropolis Monte Carlo simulations is presented. The optimization is based on maximizing the mean square displacement of a trial move. It is shown that a large mean square displacement is strongly correlated with a high precision of average potential energy. The method is here demonstrated on model systems representing a Lennard-Jones fluid and a dilute polymer solution at poor solvent conditions. Our adaptive algorithm removes the need to provide values of displacement parameters in simulations, and it is easily extendable to optimize parameters of other types of trial moves.