Polyelectrolyte Blends and Nontrivial Behavior in Effective Flory-Huggins Parameters

Predicting polymer solubility from phase diagrams to compatibility: a perspective on challenges and opportunities

Polymer processing, purification, and self-assembly have significant roles in the design of polymeric materials. Understanding how polymers behave in solution (e.g., their solubility, chemical properties, etc.) can improve our control over material properties via their processing-structure-property relationships. For many decades the polymer science community has relied on thermodynamic and physics-based models to aid in this endeavor, but all rely on disparate data sets and use-case scenarios. Hence, there are still significant challenges to predict a priori the solubility of a polymer, whether it is for selecting sustainable solvents, obtaining thermodynamic parameters for phase separation, or navigating the coexistence curve. This perspective aims to discuss the different approaches of applying computational tools to predict polymer solubility, with a significant focus on machine learning techniques to capture the rapid progress in that space. We examine challenges and opportunities that remain for creating a comprehensive solubility toolset that can accelerate the design of a broad range of applications including films, membranes, and pharmaceuticals.

Investigating miscibility and lithium ion transport in blends of poly(ethylene oxide) with a polyanion containing precisely-spaced delocalized charges

Synthesis of a precision single ion conductor with a phenylsulfonyl (TFSI) lithium salt pendant at every 5th carbon is reported and miscibility, conductivity, and transference studies are performed upon blending with PEO at varying compositions.

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.

Salt-Induced Liquid-Liquid Phase Separation: Combined Experimental and Theoretical Investigation of Water-Acetonitrile-Salt Mixtures

Salt-induced liquid-liquid phase separation in liquid mixtures is a common phenomenon in nature and in various applications, such as in separation and extraction of chemicals. Here, we present results of a systematic investigation of the phase behaviors in water-acetonitrile-salt mixtures using a combination of experiment and theory. We obtain complete ternary phase diagrams for nine representative salts in water-acetonitrile mixtures by cloud point and component analysis. We construct a thermodynamic free energy model by accounting for the nonideal mixing of the liquids, ion hydration, electrostatic interactions, and Born energy. Our theory yields phase diagrams in good agreement with the experimental data. By comparing the contributions due to the electrostatic interaction, Born energy, and hydration, we find that hydration is the main driving force for the liquid-liquid separation and is a major contributor to the specific ion effects. Our theory highlights the important role of entropy in the hydration driving force. We discuss the implications of our findings in the context of salting-out assisted liquid-liquid extraction and make suggestions for selecting salt ions to optimize the separation performance.

100th Anniversary of Macromolecular Science Viewpoint: Block Copolymers with Tethered Acid Groups: Challenges and Opportunities

Scientific research on advanced polymer electrolytes has led to the emergence of all-solid-state energy storage/transfer systems. Early research began with acid-tethered polymers half a century ago, and research interest has gradually shifted to high-precision polymers with controllable acid functional groups and nanoscale morphologies. Consequently, various self-assembled acid-tethered block polymer morphologies have been produced. Their ion properties are profoundly affected by the multiscale intermolecular interactions in confinements. The creation of hierarchically organized ion/dipole arrangements inside the block copolymer nanostructures has been highlighted as a future method for developing advanced single-ion polymers with decoupled ion dynamics and polymer chain relaxation. Several emerging practical applications of the acid-tethered block copolymers have been explored to draw attention to the challenges and opportunities in developing state-of-the-art electrochemical systems.

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.

All-atom molecular dynamics simulations of weak polyionic brushes: influence of charge density on the properties of polyelectrolyte chains, brush-supported counterions, and water molecules

All atom molecular dynamics (MD) simulations of planar Na+-counterion-neutralized polyacrylic acid (PAA) brushes are performed for varying degrees of ionization (and thereby varying charge density) and varying grafting density. Variation in the PE charge density (or degree of ionization) and grafting density leads to massive changes of the properties of the PE molecules (quantified by the changes in the height and the mobility of the PE brushes) as well as the local arrangement and distribution of the brush-supported counterions and water molecules within the brushes. The effect on the counterions is manifested by the corresponding variation of the counterion mobility, counterion concentration, extent of counterion binding to the charged site of the PE brushes, water-in-salt-like structure formation, and counterion-water-oxygen radial distribution function within the PE brushes. On the other hand, the effect on water molecules is manifested by the corresponding variation of water-oxygen-water-oxygen RDF, local water density, water-water and water-PE functional group hydrogen bond networks, static dielectric constant of water molecules, orientational tetrahedral order parameter, and water mobility. Enforcing such varying degree of ionization of weak polyelectrolytes is possible by changing the pH of the surrounding medium. Thus, our results provide insights into the changes in microstructure (at the atomistic level) of weak polyionic brushes at varying pH. We anticipate that this knowledge will prove to be vital for the efficient design of several nano-scale systems employing PE brushes such as nanomechanical gates, current rectifiers, etc.

Bicontinuous Microemulsions in Partially Charged Ternary Polymer Blends

We describe the phase behavior of a partially charged ternary polymer blend model system, comprising a compositionally symmetric poly[(oligo(ethylene glycol) methyl ether methacrylate-co-oligo(ethylene glycol) propyl sodium sulfonate methacrylate)]-b-polystyrene (POEGMA23-PS) diblock polymer and the constituent POEGMA23 and PS homopolymers, along the volumetrically symmetric isopleth, where 23 denotes the percentage of charged monomers in the POEGMA chain. Small-angle neutron and X-ray scattering and dynamic mechanical spectroscopy measurements reveal morphological transitions from a layered superlattice to swollen lamellae to a bicontinuous microemulsion (BμE), followed by macroscopic phase separation, with increasing homopolymer content. The BμE channel occurs between 85 and 90% homopolymer addition, positioned approximately at the isotropic Lifshitz composition predicted by mean-field theory for neutral systems. The resulting BμE morphology exhibits a periodicity of 26 nm, yielding a mesoscopically structured but macroscopically disordered bicontinuous structure. That this structure can be achieved in a charged polymer system is surprising, given the huge asymmetries typically induced by adding charge to either diblock copolymers or binary polymer blends.

Superlattice by charged block copolymer self-assembly

Charged block copolymers are of great interest due to their unique self-assembly and physicochemical properties. Understanding of the phase behavior of charged block copolymers, however, is still at a primitive stage. Here we report the discovery of an intriguing superlattice morphology from compositionally symmetric charged block copolymers, poly[(oligo(ethylene glycol) methyl ether methacrylate-co-oligo(ethylene glycol) propyl sodium sulfonate methacrylate)]-b-polystyrene (POEGMA-PS), achieved by systematic variation of the molecular structure in general, and the charge content in particular. POEGMA-PS self-assembles into a superlattice lamellar morphology, a previously unknown class of diblock nanostructures, but strikingly similar to oxygen-deficient perovskite derivatives, when the fraction of charged groups in the POEGMA block is about 5-25%. The charge fraction and the tethering of the ionic groups both play critical roles in driving the superlattice formation. This study highlights the accessibility of superlattice morphologies by introducing charges in a controlled manner.

Interfacial properties of polymeric complex coacervates from simulation and theory

Polymeric complex coacervation occurs when two oppositely charged polyelectrolytes undergo an associative phase separation in aqueous salt solution, resulting in a polymer-dense coacervate phase and a polymer-dilute supernatant phase. This phase separation process represents a powerful way to tune polymer solutions using electrostatic attraction and is sensitive to environmental conditions such as salt concentration and valency. One area of particular research interest is using this to create nanoscale polymer assemblies, via (for example) block copolymers with coacervate-forming blocks. The key to understanding coacervate-driven assembly is the formation of the interface between the coacervate and supernatant phases and its corresponding thermodynamics. In this work, we use recent advances in coacervate simulation and theory to probe the nature of the coacervate-supernatant interface. First, we show that self-consistent field theory informed by either Monte-Carlo simulations or transfer matrix theories is capable of reproducing interfacial features present in large-scale molecular dynamics simulations. The quantitative agreement between all three methods gives us a way to efficiently explore interfacial thermodynamics. We show how salt affects the interface, and we find qualitative agreement with literature measurements of interfacial tension. We also explore the influence of neutral polymers, which we predict to drastically influence the phase behavior of coacervates. These neutral polymers can significantly alter the interfacial tension in coacervates; this has a profound effect on the design and understanding of coacervate-driven self-assembly, where the equilibrium structure is tied to interfacial properties.

50th Anniversary Perspective: A Perspective on Polyelectrolyte Solutions

From the beginning of life with the information-containing polymers until the present era of a plethora of water-based materials in health care industry and biotechnology, polyelectrolytes are ubiquitous with a broad range of structural and functional properties. The main attribute of polyelectrolyte solutions is that all molecules are strongly correlated both topologically and electrostatically in their neutralizing background of charged ions in highly polarizable solvent. These strong correlations and the necessary use of numerous variables in experiments on polyelectrolytes have presented immense challenges toward fundamental understanding of the various behaviors of charged polymeric systems. This Perspective presents the author's subjective summary of several conceptual advances and the remaining persistent challenges in the contexts of charge and size of polymers, structures in homogeneous solutions, thermodynamic instability and phase transitions, structural evolution with oppositely charged polymers, dynamics in polyelectrolyte solutions, kinetics of phase separation, mobility of charged macromolecules between compartments, and implications to biological systems.

Self-assembly of PS-PNaSS-PS triblock copolymers from solution to the solid state

Morphological development of block copolymer assemblies from solution to the solid state is explored to yield nanostructured materials.

Development of the modern theory of polymeric complex coacervation

Oppositely charged polymers can undergo the process of complex coacervation, which refers to a liquid-liquid phase separation driven by electrostatic attraction. These materials have demonstrated considerable promise as the basis for complex, self-assembled materials. In this review, we provide a broad overview of the theoretical tools used to understand the physical properties of polymeric coacervates. In particular, we discuss historic theories (Voorn-Overbeek, Random Phase Approximation), and then describe recent developments in the field (Field Theoretic, Counterion Release, Molecular Simulation, and Polymer Reference Interaction Site Model methods). We provide context for these methods, and map out the patchwork of theoretical models that are used to describe a diverse array of coacervate systems. We use this review of the literature to clarify a number of important theoretical challenges remaining in our physical understanding of complex coacervation.

Electrostatic Correlations in Polyelectrolyte Solutions

The major attribute of polyelectrolyte solutions is that all chains are strongly correlated both electrostatically and topologically. Even in very dilute solutions such that the chains are not interpenetrating, the chains are still strongly correlated. These correlations are manifest in the measured scattering intensity when such solutions are subjected to light, X-ray, and neutron radiation. The behavior of scattering intensity from polyelectrolyte solutions is qualitatively different from that of solutions of uncharged polymers. Using the technique introduced by Sir Sam Edwards, and extending the earlier work by the author on the thermodynamics of polyelectrolyte solutions, extrapolation formulas are derived for the scattering intensity from polyelectrolyte solutions. The emergence of the polyelectrolyte peak and its concentration dependence are derived. The derived theory shows that there are five regimes. Published experimental data from many laboratories are also collected into a master figure and a comparison between the present theory and experiments is presented.

Recent Developments in Fully Fluctuating Field-Theoretic Simulations of Polymer Melts and Solutions

We review the latest developments in computational methods for direct simulation of fully fluctuating field theories of polymeric assemblies. In this context, we describe a newly developed theoretical and computational framework for accurately computing fluctuation-corrected phase diagrams of mesostructured polymer systems and report the first such complete phase diagram for a diblock copolymer melt. The method is based on complex Langevin sampling of a UV regularized field-theoretic model, with Helmholtz free energies computed using thermodynamic integration. UV regularization ensures that the free energies do not have an arbitrary reference; they can be compared between incommensurate phases, permitting for the first time the computation of order-order transitions with fluctuation corrections. We further demonstrate that computed free energies are accurate in the disordered phase by comparison to perturbation theory on the one-loop level. Importantly, we note that our method uses no uncontrolled approximations beyond the initial definition of a coarse-grained molecular model for the polymer melt or solution. The method can be applied straightforwardly to melts and solutions containing multiple species with diverse polymer architectures.

Poly(N-isopropylacrylamide)-Based Mixed Brushes: A Computer Simulation Study

Temperature-sensitive poly(N-isopropylacrylamide) (PNIPAM) polymer brushes of fixed molecular weight and grafting density are modeled in the framework of a coarse-grained model with soft, nonbonded interactions and an implicit solvent. This model has been developed to address experimentally relevant, large invariant degrees of polymerization, and nonbonded interactions are expressed via a third-order (virial) expansion of the equation of state. The choice of interaction parameters is intended to mimic the swelling behavior of PNIPAM in water as the temperature increases toward the lower critical solution temperature (T(LCST)). Results of molecular dynamics simulations for one component brushes are compared to experimental data. Mixed brushes incorporating small and large amounts of grafted poly(ethylene glycol) polymers are then considered. The effects of mixing polymer components on the response of the mixed brushes to temperature changes are monitored, and the results are compared to experimental data. In the end, two design principles for biomolecule triggering using temperature-sensitive mixed polymer brushes with functional and switchable end-groups are proposed and studied. This work is in favor of establishing qualitative rules for the design, optimization, and comprehension of binary polymer brushes for bioengineering purposes.