Ion Distribution in Microphase-Separated Copolymers with Periodic Dielectric Permittivity

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.

Nanostructured Block Polymer Electrolytes: Tailoring Self-Assembly to Unlock the Potential in Lithium-Ion Batteries

ConspectusIon-containing solid block polymer (BP) electrolytes can self-assemble into microphase-separated domains to facilitate the independent optimization of ion conduction and mechanical stability; this assembly behavior has the potential to improve the functionality and safety of lithium-ion batteries over liquid electrolytes to meet future demands (e.g., large capacities and long lifetimes) in various applications. However, significant enhancements in the ionic conductivity and processability of BPs must be realized for BP-based electrolytes to become robust alternatives in commercial devices. Toward this end, the controlled modification of BP electrolytes' intra-domain (nanometer-scale) and multi-grain (micrometer-scale) structure is one viable approach; intra-domain ion transport and segmental compatibility (related to the effective Flory-Huggins parameter, χ_eff) can be increased by tuning the ion and monomer-segment distributions, and the morphology can be selected such that the multi-grain transport is less sensitive to grain size and orientation.To highlight the characteristics of intra-domain structure that promote efficient ion transport, this Account begins by describing the relationship between BP thermodynamics (namely, χ_eff and the statistical segment length, b, which is indicative of chain stiffness) and local ion concentration. These thermodynamic insights are vital because they inform the selection of synthesis and formulation variables, such as polymer and ion chemistry, polymer molecular weight and composition, and ion concentration, which boost electrolyte performance. In addition to its relationship with local ion transport, χ_eff is also an important factor with respect to electrolyte processability. For example, a reduced χ_eff can allow BP electrolytes to be processed at lower temperatures (i.e., lower energy input), with less solvent (i.e., reduced waste), and/or for shorter times (i.e., higher throughput) yet still form desired nanostructures. This Account also examines the impact of electrolyte preparation and processing on the ion transport across nanostructured grains because of grain size and orientation. As morphologies with a 3D-connected versus 2D-connected conducting phase show different sensitivities to conductivity losses that can occur because of the fabrication methods, it is necessary to account for electrolyte processing effects when probing ion transport.The intra-domain and micrometer-scale structure also can be tuned using either tapered BPs (macromolecules with modified monomer-segment composition profiles between two homogeneous blocks) or blends of BPs and homopolymers, independent of the BP molecular weight and composition, as detailed herein. The application of TBPs or BP/HP blends as ion-conducting materials leads to improved ion transport, reduced χ_eff, and greater availability of morphologies with 3D connectivity relative to traditional (non-tapered and unblended) BP electrolytes. This feature results from the fact that ion transport is related more closely to the monomer-segment distributions within a domain than the overall nanoscale morphology or average polymer/ion mobilities. Taken together, this Account describes how ion transport and processability are influenced by BP architecture and nanostructural features, and it provides avenues to tune nanoassemblies that can contribute to improved lithium-ion battery technologies to meet future demands.

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.

Modulating Microphase Separation of Lamellae-Forming Diblock Copolymers via Ionic Junctions

We present a molecular dynamics simulation study investigating the phase behavior of lamellae-forming diblock copolymers with a single ionic junction on the backbone. Our results show qualitative agreement with experimental findings regarding enhanced microphase separation with the introduction of an ionic junction at the conjunction point, while further revealing nonmonotonic changes in domain spacing and order-disorder transition as a function of the electrostatic interaction strength. This highlights the dominant roles of entropic and binding effects of counterions under weak and strong ionic correlations, respectively. The location of the ionic junction is found to effectively modulate the charge distribution and chain conformation in the ordered domains; its presence in the middle of a block promotes folding of the block, leading to a smaller domain size. These findings demonstrate the interplay of ionic coupling with steric hindrance and chain end effects, which enhances our understanding of the delicate control over the microphase domain features.

Single chain in mean field simulation of flexible and semiflexible polymers: comparison with discrete chain self-consistent field theory

Single chain in mean field (SCMF) simulation is a theoretical framework performing Monte Carlo moves of explicit polymer chains under quasi-instantaneously updated external fields which were originally imported from the self-consistent field theory (SCFT). Even though functional-based hybrid simulations are often used to compare the results of SCFT and MC simulation, the adoption of a finite number of coarse-grained segments makes direct comparison rather difficult. In this study, we perform SCMF simulation of block copolymers using various chain models and quantitatively compare it with discrete chain SCFT (DCSCFT) which finds the mean field solution of polymers with a finite number of segments. By comparing free energy and natural period of the symmetric block copolymer lamellar phase, we systematically show that DCSCFT serves as an intermediate step between SCMF simulation and SCFT. In addition, by adopting angle dependent bond potential, we perform SCMF simulation of semiflexible polymers using bead-spring and freely jointed chain models. As the chain stiffness increases, the lamellar phase tends to align perpendicular to the surfaces when confined between two neutral walls. We also investigate the effects of fluctuation and chain stiffness on the distribution of chain ends. The tendency of chain end segregation towards the surfaces turns out to increase as the chain stiffness increases for both homopolymer and block copolymer systems.

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.

The size and affinity effect of counterions on self-assembly of charged block copolymers

The effect of counterions' size and affinity on the microphase separated morphologies of neutral-charged diblock copolymers is investigated systematically using a random phase approximation (RPA) and self-consistent field theory (SCFT). The phase diagrams as a function of χ_AB and f_A at different counterion sizes and different affinities to neutral blocks are constructed, respectively. Stability limits calculated using the RPA are in good agreement with the disorder-body-centered cubic phase boundaries from SCFT calculations. It was found that increasing the size of counterions causes the phase diagram to shift upward and leftward, which is attributed to electrostatic interactions and the intrinsic volume of counterions. The domain size of the ordered phase shows an unexpected tendency that it decreases with increasing counterions' size. The counterions' distributions in H and G phases demonstrate that it is electrostatic interaction, instead of packing frustration, that plays a leading role in such systems. For finite size counterions, with the increase in affinity between counterions and neutral blocks, the phase diagram shifts upward, indicating the improved compatibility between different blocks. Furthermore, the affinity effect between counterions and neutral blocks can be mapped into an effective Flory parameter χ_AB ^' = χ_AB + 0.27χ_BC.

Manipulation of Confined Polyelectrolyte Conformations through Dielectric Mismatch

We demonstrate that a highly charged polyelectrolyte confined in a spherical cavity undergoes reversible transformations between amorphous conformations and a four-fold symmetry morphology as a function of dielectric mismatch between the media inside and outside the cavity. Surface polarization due to dielectric mismatch exhibits an extra "confinement" effect, which is most pronounced within a certain range of the cavity radius and the electrostatic strength between the monomers and counterions and multivalent counterions. For cavities with a charged surface, surface polarization leads to an increased amount of counterions adsorbed in the outer side, further compressing the confined polyelectrolyte into a four-fold symmetry morphology. The equilibrium conformation of the chain is dependent upon several key factors including the relative permittivities of the media inside and outside the cavity, multivalent counterion concentration, cavity radius relative to the chain length, and interface charge density. Our findings offer insights into the effects of dielectric mismatch in packaging and delivery of polyelectrolytes across media with different relative permittivities. Moreover, the reversible transformation of the polyelectrolyte conformations in response to environmental permittivity allows for potential applications in biosensing and medical monitoring.

Field-Theoretic Study of Salt-Induced Order and Disorder in a Polarizable Diblock Copolymer

We study a salt-doped polarizable symmetric diblock copolymer using a recently developed field theory that self-consistently embeds dielectric response, ion solvation energies, and van der Waals (vdW) attractions via the incorporation of segment polarizabilities and fixed dipoles. This field theory is amenable to direct simulation via the complex Langevin sampling technique and, thus, requires no approximations beyond the phenomenology of the underlying molecular model. We measure the shift in the order-disorder transition (ODT) of a diblock copolymer with salt-loading in field-theoretic simulations and observe rich behavior in which solvation, dilution and charge screening effects compete to determine whether the ordered or disordered phase is stabilized. At low salt concentrations, the salt behaves as a selective solvent, localizing into the high-dielectric domains and stabilizing the ordered phase. At high salt concentrations, however, the salt localization vanishes due to charge screening effects, and the salt behaves as a nonselective solvent that screens vdW attractions and stabilizes the disordered phase.

Surface morphologies of spherical polyelectrolyte brushes induced by trivalent salt ions

The surface morphologies of spherical polyelectrolyte brushes in salt solutions with opposite trivalent ions are studied using molecular dynamics (MD) simulations. The impact of salt concentration, grafting density, and charge fraction on brush morphologies is investigated systematically. A variety of surface patterns are predicted and the phase diagrams are presented. Both lateral and radial microphase separated structures in the brushes are observed upon varying the salt concentration. With low grafting density the spherical brush is separated into several patches, the number of which decreases with the addition of salt. At high grafting density, the polymer brush changes its morphology from an extended micelle to a 'carpet + brush' to the collapsed state upon increasing the salt concentration. Especially, the 'carpet + brush' structure consists of a core formed by partially collapsed brush chains and a corona formed by other stretched chains. The inter-chain 'bridging' interactions mediated by trivalent ions and the curvature effect play important roles in determining the chain conformations and brush structures.

Transferable MARTINI Model of Poly(ethylene Oxide)

Motivated by the deficiencies of the previous MARTINI models of poly(ethylene oxide) (PEO), we present a new model featuring a high degree of transferability. The model is parametrized on (a) a set of 8 free energies of transfer of dimethoxyethane (PEO dimer) from water to solvents of varying polarity; (b) the radius of gyration in water at high dilution; and (c) matching angle and dihedral distributions from atomistic simulations. We demonstrate that our model behaves well in five different areas of application: (1) it produces accurate densities and phase behavior or small PEO oligomers and water mixtures; (2) it yields chain dimensions in good agreement with the experiment in three different solvents (water, diglyme, and benzene) over a broad range of molecular weights (∼1.2 kg/mol to 21 kg/mol); (3) it reproduces qualitatively the structural features of lipid bilayers containing PEGylated lipids in the brush and mushroom regime; (4) it is able to reproduce the phase behavior of several PEO-based nonionic surfactants in water; and (5) it can be combined with the existing MARTINI PS to model PS-PEO block copolymers. Overall, the new PEO model outperforms previous models and features a high degree of transferability.