Determining the Regimes of Dielectric Mismatch and Ionic Correlation Effects in Ionomer Blends

Effect of the counterion size on microphase separation in charged-neutral diblock copolymers

In this work, the question of the influence of the counterion size on the self-assembly in melts of diblock copolymers with one charged block was studied using coarse-grained molecular dynamics simulations. It was assumed that the blocks were fully compatible, i.e., the Flory-Huggins parameter χ between them was equal to 0. Due to the presence of correlation attraction (electrostatic cohesion) between the charged species, the systems with all types of counterions underwent transitions to ordered states, forming various morphologies, including lamellae, perforated lamellae, and hexagonally packed cylinders. Phase diagrams were constructed by varying the chain composition f_c and locating the order-disorder transition positions in terms of the electrostatic strength parameter λ (dimensionless Bjerrum length). Despite having a rather large ion size mismatch, the systems with smaller counterions demonstrated an even better tendency to form microphase separated states than the systems with larger ones. It was found that the differences between the phase diagrams of the systems with different counterions can be roughly rationalized by using coordinates (volume fraction of the charged block φ_c-modified interaction parameter λ*). The latter parameter assumes that the electrostatic energy is simply inversely proportional to the characteristic distance between the ions of different signs. Such an approach appeared to be rather effective and allowed the diagrams obtained for different counterion sizes to almost coincide. The results of this work suggest that the counterion size can be used as a tool to control the system morphology as well as the effective incompatibility between the blocks.

Structures of cationic and anionic polyelectrolytes in aqueous solutions: the sign effect

In this study, we use molecular dynamics simulation to explore the structures of anionic and cationic polyelectrolytes in aqueous solutions. We first confirm the significantly stronger solvation effects of single anions compared to cations in water at the fixed ion radii, due to the reversal orientations of asymmetric dipolar H₂O molecules around the ions. Based on this, we demonstrate that the solvation discrepancy of cations/anions and electrostatic correlations of ionic species can synergistically cause the nontrivial structural difference between single anionic and cationic polyelectrolytes. The cationic polyelectrolyte shows an extended structure whereas the anionic polyelectrolyte exhibits a collapsed structure, and their structural differences decline with increasing the counterion size. Furthermore, we corroborate that multiple cationic polyelectrolytes or multiple anionic polyelectrolytes can exhibit largely differential molecular architectures in aqueous solutions. In the solvation dominant regime, the polyelectrolyte solutions exhibit uniform structures; whereas, in the electrostatic correlation dominant regime, the polyelectrolyte solutions exhibit heterogeneous structures, in which the likely charged chains microscopically aggregate through counterion condensations. Increasing the intrinsic chain rigidity causes polyelectrolyte extension and hence moderately weakens the inter-chain clustering. Our work highlights the various, unique structures and molecular architectures of polyelectrolytes in solutions caused by the multi-body correlations between polyelectrolytes, counterions and asymmetric dipolar solvent molecules, which provides insights into the fundamental understanding of ion-containing polymers.

The effect of explicit polarity on the conformational behavior of a single polyelectrolyte chain

In this work using dissipative particle dynamics simulations with explicit treatment of polar species we demonstrate that the molecular nature of dielectric media has a significant impact on swelling and collapse of a polyelectrolyte chain in a dilute solution. We show that the small-scale effects related to the presence of polar species lead to the intensification of the electrostatic interactions when the charges are close to each other and/or their density is high enough. As a result, the electrostatic strength , usually regarded as the main parameter governing the polyelectrolyte chain collapse, does not have a universal meaning: the value of λ at which the coil-to-globule transition occurs is found to be dependent on the specific fixed value of the solvent bulk permittivity ε while varying the monomer unit charge Q and vice versa. This effect is observed even when the backbone and the counterions have the same polarity as the solvent beads, i.e. no dielectric mismatch is present. The reason for such behavior is rationalized in terms of the "effective" dielectric permittivity ε^eff which depends on the volume fraction φ of charged units inside the polymer chain volume; using ε^eff instead of ε collapses all data onto one master curve describing the chain shrinking with λ. Furthermore, it is shown that a polar chain adopts less swollen conformations in the polyelectrolyte regime and collapses more easily compared to a non-polar chain.

A Perspective on the Design of Ion-Containing Polymers for Polymer Electrolyte Applications

Ion-containing polymers have numerous potential applications as energy storage and conversion devices, water purification membranes, and gas separation membranes, to name a few. Given the low dielectric constant of the media, ions and charges on polymers in a molten state interact strongly producing large effects on chain statistics, thermodynamics, and diffusion properties. Here, we discuss recent research accomplishments on the effects of ionic correlation and dielectric heterogeneity on the phase behavior of ion-containing polymers. Progress made in studying ion transport properties in these material systems is also highlighted. Charged block copolymers (BCPs), among all kinds of ion-containing polymers, have a particular advantage owing to their robust mechanical support and ion conducting paths provided by the segregation of the neutral and charged blocks. Coulombic interactions among the charges play a critical role in determining the phase segregation in charged BCPs and the domain size of charge-rich regions. We show that strongly charged BCPs display ordered phases as a result of electrostatic interactions alone. In addition, bulky charge-containing side groups attached to the charged block lead to the formation of morphologies that provide continuous channels and better dissociation for ion conduction purposes. Finally, a few avenues for designing ion-containing polymers for energy applications are discussed.

Dissipative particle dynamics for systems with polar species: Interactions in dielectric media

In this work, we develop a method for simulating polar species in the dissipative particle dynamics (DPD) method. The main idea behind the method is to treat each bead as a dumb-bell, i.e., two sub-beads kept at a fixed distance, instead of a point-like particle. The relation between the bead dipole moment and the bulk dielectric permittivity was obtained. The interaction force of single charges in polar liquid showed that the effective dielectric permittivity is somewhat smaller than that obtained for the bulk case at large separation between the charges. In order to understand the reasons behind the observed drop in the dielectric permittivity, we calculate the electric field of an isolated charge in a polar liquid; no permittivity drop is observed for this case. We can assume that the behavior observed for the force is due to the fact that the probing point is always associated with the charged bead, which is a force center, which essentially leads to a non-homogeneous density distribution around it on average; this is not the case when the field is measured. The interaction of a single charge with an interface between two liquids with different permittivities was studied after that; the model is found to correctly reproduce the "mirror image" effects. Finally, we show why it is necessary to treat the polar species in DPD explicitly by investigating the behavior of a charged colloidal particle at a liquid-liquid interface.