Thermodynamics of Salt-Doped Block Copolymers

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.

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.

Sub-3-Nanometer Domain Spacings of Ultrahigh-χ Multiblock Copolymers with Pendant Ionic Groups

We investigated the temperature-dependent phase behavior and interaction parameter of polyethylene-based multiblock copolymers with pendant ionic groups. These step-growth polymers contain short polyester blocks with a single Li⁺SO₃^- group strictly alternating with polyethylene blocks of x-carbons (PESxLi, x = 12, 18, 23). At room temperature, these polymers exhibit layered morphologies with semicrystalline polyethylene blocks. Upon heating above the melting point (∼130 °C), PES18Li shows two order-to-order transitions involving Ia3̅d gyroid and hexagonal morphologies. For PES12Li, an order-to-disorder transition accompanies the melting of the polyethylene blocks. Notably, a Flory-Huggins interaction parameter was determined from the disordered morphologies of PES12Li using mean-field theory: χ(T) = 77.4/T + 2.95 (T in Kelvin) and χ(25 °C) ≈ 3.21. This ultrahigh χ indicates that the polar ionic and nonpolar polyethylene segments are highly incompatible and affords well-ordered morphologies even when the combined length of the alternating blocks is just 18-29 backbone atoms. This combination of ultrahigh χ and short multiblocks produces sub-3-nm domain spacings that facilitate the control of block copolymer self-assembly for various fields of study, including nanopatterning.

Influence of Charge Fraction on the Phase Behavior of Symmetric Single-Ion Conducting Diblock Copolymers

A series of symmetric poly[(oligo(ethylene glycol) methyl ether methacrylate-co-oligo(ethylene glycol) propyl sodium sulfonate methacrylate)]-block-polystyrene (PsOEGMA-PS) diblock copolymers were synthesized as a model system to probe the effect of charge fraction on the phase behavior of charged-neutral single-ion conducting diblock copolymers. Small-angle X-ray scattering (SAXS) experiments showed that increasing the charge fraction does not alter the ordered phase morphology (lamellar) but increases the order-disorder transition temperature (T_ODT) significantly. Additionally, the effective Flory-Huggins interaction parameter (χ_eff) was found to increase linearly with the charge fraction, similar to the case of conventional salt-doped diblock copolymers. This indicates that the effect of counterion solvation, attributed to the significant mismatch between the dielectric constant of each block, provides the dominant effect in tuning the phase behavior of this charged diblock copolymer. We therefore infer that electrostatic cohesion (local charge ordering induced by Coulombic interactions), which is predicted to suppress microphase separation and lead to asymmetric phase diagrams, only plays a minor role in this model system.

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.

Formation of a C15 Laves Phase with a Giant Unit Cell in Salt-Doped A/B/AB Ternary Polymer Blends

Salt-doped A/B/AB ternary polymer blends, wherein an AB copolymer acts as a surfactant to stabilize otherwise incompatible A and B homopolymers, display a wide range of nanostructured morphologies with significant tunability. Among these structures, a bicontinuous microemulsion (BμE) has been a notable target. Here, we report the surprising appearance of a robust C15 Laves phase, at compositions near where the BμE has recently been reported, in lithium bis(trifluoromethane) sulfonimide (LiTFSI)-doped low-molar-mass poly(ethylene oxide) (PEO)/polystyrene (PS)/symmetric PS-b-PEO block copolymer blends. The materials were analyzed by a combination of small-angle X-ray scattering (SAXS), ¹H NMR spectroscopy, and impedance spectroscopy. The C15 phase emerges at a high total homopolymer volume fraction ϕ_H = 0.8 with a salt composition r = 0.06 (Li⁺/[EO]) and persists as a coexisting phase across a large area of the isothermal phase diagram with high PS homopolymer compositions. Notably, the structure exhibits a huge unit cell size, a = 121 nm, with an unusually high micelle core volume fraction (f_core = 0.41) and an unusually low fraction of amphiphile (20%). This unit cell dimension is at least 50% larger than any previously reported C15 phase in soft matter, despite the low molar masses used, unlocking the possibility of copolymer-based photonic crystals without compromising processability. The nanostructured phase evolution from lamellar to hexagonal to C15 along the EO60 isopleth (ϕ_{PEO,homo-LiTFSI}/ϕ_H = 0.6) is rationalized as a consequence of asymmetry in the homopolymer solubility limit for each block, which leads to exclusion of PS homopolymer from the PS-b-PEO brush prior to exclusion of the PEO homopolymer, driving increased interfacial curvature and favoring the emergence of the C15 Laves phase.

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.

Self-Assembly of Charge-Containing Copolymers at the Liquid-Liquid Interface

Quantitatively understanding the self-assembly of amphiphilic macromolecules at liquid-liquid interfaces is a fundamental scientific concern due to its relevance to a broad range of applications including bottom-up nanopatterning, protein encapsulation, oil recovery, drug delivery, and other technologies. Elucidating the mechanisms that drive assembly of amphiphilic macromolecules at liquid-liquid interfaces is challenging due to the combination of hydrophobic, hydrophilic, and Coulomb interactions, which require consideration of the dielectric mismatch, solvation effects, ionic correlations, and entropic factors. Here we investigate the self-assembly of a model block copolymer with various charge fractions at the chloroform-water interface. We analyze the adsorption and conformation of poly(styrene)-block-poly(2-vinylpyridine) (PS-b-P2VP) and of the homopolymer poly(2-vinylpyridine) (P2VP) with varying charge fraction, which is controlled via a quaternization reaction and distributed randomly along the backbone. Interfacial tension measurements show that the polymer adsorption increases only marginally at low charge fractions (<5%) but increases more significantly at higher charge fractions for the copolymer, while the corresponding randomly charged P2VP homopolymer analogues display much more sensitivity to the presence of charged groups. Molecular dynamics (MD) simulations of the experimental systems reveal that the diblock copolymer (PS-b-P2VP) interfacial activity could be mediated by the formation of a rich set of complex interfacial copolymer aggregates. Circular domains to elongated stripes are observed in the simulations at the water-chloroform interface as the charge fraction increases. These structures are shown to resemble the spherical and cylindrical helicoid structures observed in bulk chloroform as the charge fraction increases. The self-assembly of charge-containing copolymers is found to be driven by the association of the charged component in the hydrophilic block, with the hydrophobic segments extending away from the hydrophilic cores into the chloroform phase.

Ion Correlation Effects in Salt-Doped Block Copolymers

We apply classical density functional theory to study how salt changes the microphase morphology of diblock copolymers. Polymers are freely jointed and one monomer type favorably interacts with ions, to account for the selective solvation that arises from different dielectric constants of the microphases. By including correlations from liquid state theory of an unbound reference fluid, the theory can treat chain behavior, microphase separation, ion correlations, and preferential solvation, at the same coarse-grained level. We show good agreement with molecular dynamics simulations.

Hybrid particle–field molecular dynamics simulation for polyelectrolyte systems

An effective hybrid computer simulation method combining molecular dynamics and self-consistent field theory is developed by including electrostatic interactions.

Controlled ionic conductivity via tapered block polymer electrolytes

Tapered block polymer electrolytes have been developed and exhibited enhanced room temperature conductivity relative to poly(styrene-b-ethylene oxide) (P(S-EO)) and non-tapered poly(s-b-oligo-oxyethylene methacrylate) (P(S-OEM)) counterparts.

Synergistic effects of ion pairs on the dielectric properties of diblock copolymer melts

We study the solvation of ion pairs in diblock copolymer melts. Our theory accounts for the size of the ions, the permanent dipole moment and the molecular polarizability of the monomers, the Kuhn length, the compressibility of the liquid mixtures, and the degrees of polymerization. We demonstrate that the electrostatic field near an ion pair causes marked, synergistic effects on the volume fractions of the two blocks and hence the dielectric function. In particular, we illustrate the oscillatory behavior of the dielectric function near an ion pair and the disparity of the dielectric functions between like and unlike charges. These results depend significantly on the chain length and Kuhn length of the diblock copolymers on the nanometer scale.