Structure and Dynamics of Polyelectrolyte Complex Coacervates Studied by Scattering of Neutrons, X-rays, and Light

Small ion effects on self-coacervation phenomena in block polyampholytes

Self-coacervation is a phenomenon in which a solution of polyampholytes spontaneously phase separates into a dense liquid coacervate phase, rich in the polyampholyte, coexisting with a dilute supernatant phase. Such coacervation results in the formation of membraneless organelles in vivo and has further been applied industrially as synthetic encapsulants and coatings. It has been suggested that coacervation is primarily driven by the entropy gain from releasing counter-ions upon complexation. Using fully fluctuating field-theoretic simulations employing complex Langevin sampling and complementary molecular dynamics simulations, we have determined that the small ions contribute only weakly to the self-coacervation behavior of charge-symmetric block polyampholytes in solution. Salt partitioning between the supernatant and coacervate is also found to be negligible in the weak-binding regime at low electrostatic strengths. Asymmetries in charge distribution along the polyampholytes can cause net-charges that lead to "tadpole" configurations in dilute solution and the suppression of phase separation at low salt content. The field and particle-based simulation results are compared with analytical predictions from the random phase approximation (RPA) and postulated scaling relationships. The qualitative trends are mostly captured by the RPA, but the approximation fails at low concentration.

Structure and Rheology of Polyelectrolyte Complexes in the Presence of a Hydrogen-Bonded Co-Solvent

Intermolecular interactions as well as macromolecular conformation affect the rheological and microstructural properties of polyelectrolyte complexes (PECs) solutions. The properties of semi-dilute solutions of weakly charged PECs can be controlled by the degree of ionization and solvent composition. In this work, we examined the effect of ethanol as a co-solvent on PECs composed of poly(allylamine hydrochloride) (PAH) and poly(acrylic acid) (PAA) at low pH. The aqueous PECs solution was turbid, indicating formation of large aggregates, whereas PECs solution in water/ethanol (60:40 w/w) was transparent, implying no aggregation, and demonstrated higher relative viscosity than the aqueous solution, implying pronounced network formation. Imaging PECs solution by transmission electron microscopy (TEM) demonstrated aggregation, whereas the solution prepared with the mixed solvent revealed almost no phase contrast. Small-angle X-ray scattering (SAXS) of PECs in the aqueous solution indicated the presence of aggregates, while PECs in mixed solvent demonstrated a swelled macromolecular conformation with diminished aggregation. PECs with no ionic interactions in the mixed solvent assumes a homogenous network structure, which enables PECs solution processing by electrospinning.

Designing Electrostatic Interactions via Polyelectrolyte Monomer Sequence

Charged polymers are ubiquitous in biological systems because electrostatic interactions can drive complicated structure formation and respond to environmental parameters such as ionic strength and pH. In these systems, function emerges from sophisticated molecular design; for example, intrinsically disordered proteins leverage specific sequences of monomeric charges to control the formation and function of intracellular compartments known as membraneless organelles. The role of a charged monomer sequence in dictating the strength of electrostatic interactions remains poorly understood despite extensive evidence that sequence is a powerful tool biology uses to tune soft materials. In this article, we use a combination of theory, experiment, and simulation to establish the physical principles governing sequence-driven control of electrostatic interactions. We predict how arbitrary sequences of charge give rise to drastic changes in electrostatic interactions and correspondingly phase behavior. We generalize a transfer matrix formalism that describes a phase separation phenomenon known as "complex coacervation" and provide a theoretical framework to predict the phase behavior of charge sequences. This work thus provides insights into both how charge sequence is used in biology and how it could be used to engineer properties of synthetic polymer systems.

Structure-Property Relationships of Oligonucleotide Polyelectrolyte Complex Micelles

Polyelectrolyte complex micelles (PCMs), nanoparticles formed by electrostatic self-assembly of charged polymers with charged-neutral hydrophilic block copolymers, offer a potential solution to the challenging problem of delivering therapeutic nucleic acids into cells and organisms. Promising results have been reported in vitro and in animal models but basic structure-property relationships are largely lacking, and some reports have suggested that double-stranded nucleic acids cannot form PCMs due to their high bending rigidity. This letter reports a study of PCMs formed by DNA oligonucleotides of varied length and hybridization state and poly(l)lysine-poly(ethylene glycol) block copolymers with varying block lengths. We employ a multimodal characterization strategy combining small-angle X-ray scattering (SAXS), multiangle light scattering (MALS), and cryo-electron microscopy (cryo-TEM) to simultaneously probe the morphology and internal structure of the micelles. Over a wide range of parameters, we find that nanoparticle shape is controlled primarily by the hybridization state of the oligonucleotides with single-stranded oligonucleotides forming spheroidal micelles and double-stranded oligonucleotides forming wormlike micelles. The length of the charged block controls the radius of the nanoparticle, while oligonucleotide length appears to have little impact on either size or shape. At smaller length scales, we observe parallel packing of DNA helices inside the double-stranded nanoparticles, consistent with results from condensed genomic DNA. We also describe salt- and thermal-annealing protocols for preparing PCMs with high repeatability and low polydispersity. Together, these results provide a capability to rationally design PCMs with desired sizes and shapes that should greatly assist development of this promising delivery technology.

Polyelectrolyte complex coacervation by electrostatic dipolar interactions

We address complex coacervation, the liquid-liquid phase separation of a solution of oppositely charged polyelectrolyte chains into a polyelectrolyte rich complex coacervate phase and a dilute aqueous phase, based on the general premise of spontaneous formation of polycation-polyanion complexes even in the homogeneous phase. The complexes are treated as flexible chains made of dipolar segments and uniformly charged segments. Using a mean field theory that accounts for the entropy of all dissociated ions in the system, electrostatic interactions among dipolar and charged segments of complexes and uncomplexed polyelectrolytes, and polymer-solvent hydrophobicity, we have computed coacervate phase diagrams in terms of polyelectrolyte composition, added salt concentration, and temperature. For moderately hydrophobic polyelectrolytes in water at room temperature, neither hydrophobicity nor electrostatics alone is strong enough to cause phase separation, but their combined effect results in phase separation, arising from the enhancement of effective hydrophobicity by dipolar attractions. The computed phase diagrams capture key experimental observations including the suppression of complex coacervation due to increases in salt concentration, temperature, and polycation-polyanion composition asymmetry, and its promotion by increasing the chain length, and the preferential partitioning of salt into the polyelectrolyte dilute phase. We also provide new predictions such as the emergence of loops of instability with two critical points.

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.

Role of Associative Charging in the Entropy-Energy Balance of Polyelectrolyte Complexes

Polyelectrolytes may be classified into two primary categories (strong and weak) depending on how their charge state responds to the local environment. Both of these find use in many applications, including drug delivery, gene therapy, layer-by-layer films, and fabrication of ion filtration membranes. The mechanism of polyelectrolyte complexation is, however, still not completely understood, though experimental investigations suggest that entropy gain due to release of counterions is the key driving force for strong polyelectrolyte complexation. Here we perform a comprehensive thermodynamic investigation through coarse-grained molecular simulations permitting us to calculate the free energy of complex formation. Importantly, our expanded-ensemble methods permit the explicit separation of energetic and entropic contributions to the free energy. Our investigations indicate that entropic contributions indeed dominate the free energy of complex formation for strong polyelectrolytes, but are less important than energetic contributions when weak electrostatic coupling or weak polyelectrolytes are present. Our results provide a new view of the free energy of polyelectrolyte complex formation driven by polymer association, which should also arise in systems with large charge spacings or bulky counterions, both of which act to weaken ion-polymer binding.

Scaling Theory of Complex Coacervate Core Micelles

We propose scaling theory of complex coacervate core micelles (C3Ms). Such micelles arise upon electrostatically driven coassembly of bis-hydrophilic ionic/nonionic diblock copolymers with oppositely charged ionic blocks or bis-hydrophilic diblock copolymers with oppositely charged macroions. Structural properties of the C3Ms are studied as a function of the copolymer composition, degree of ionization of the ionic blocks, and ionic strength of the solution. It is demonstrated that at sufficiently large length of the polyelectrolyte blocks the C3Ms may exhibit polymorphism; that is, morphological transitions from spherical to cylindrical micelles and further to lamellar structure or polymersomes may be triggered by increasing salt concentration. A diagram of states of micellar aggregates in the salt concentration/ionization degree coordinates is constructed, and scaling laws for experimentally measurable properties, e.g., micelle aggregation number and core and corona sizes, are found.

Structure and rheology of polyelectrolyte complex coacervates

Scattering investigations of the structure and chain conformations, and the rheological properties of polyelectrolyte complexes (PECs) comprising model polyelectrolytes are presented. The use of charged polypeptides - (poly)-lysine and (poly)-glutamic acid with identical backbones allowed for facile tuning of the system parameters, including chain length, side-chain functionality, and chirality. Systematic studies using small-angle X-ray scattering (SAXS) of liquid PEC coacervates revealed a physical description of these materials as strongly screened semidilute polyelectrolyte solutions comprising oppositely charged chains. At the same time, solid PECs were found to be composed of hydrogen-bonding driven stiff ladder-like structures. While the coacervates behaved akin to semidilute polyelectrolyte solutions upon addition of salt, the solids were largely unaffected by it. Rheology measurements of PEC coacervates revealed a terminal relaxation regime, with an unusual plateauing of the storage modulus at low oscillation frequencies. The plateau may be ascribed to a combination of instrumental limitations and the long-range electrostatic interactions contributing to weak energy storage modes. Excellent superposition of the dynamic moduli was achieved by a time-salt superposition. The shift factors, however, varied more strongly than previously reported with added salt concentration.

Relaxation Behavior by Time-Salt and Time-Temperature Superpositions of Polyelectrolyte Complexes from Coacervate to Precipitate

Complexation between anionic and cationic polyelectrolytes results in solid-like precipitates or liquid-like coacervate depending on the added salt in the aqueous medium. However, the boundary between these polymer-rich phases is quite broad and the associated changes in the polymer relaxation in the complexes across the transition regime are poorly understood. In this work, the relaxation dynamics of complexes across this transition is probed over a wide timescale by measuring viscoelastic spectra and zero-shear viscosities at varying temperatures and salt concentrations for two different salt types. We find that the complexes exhibit time-temperature superposition (TTS) at all salt concentrations, while the range of overlapped-frequencies for time-temperature-salt superposition (TTSS) strongly depends on the salt concentration (Cs) and gradually shifts to higher frequencies as Cs is decreased. The sticky-Rouse model describes the relaxation behavior at all Cs. However, collective relaxation of polyelectrolyte complexes gradually approaches a rubbery regime and eventually exhibits a gel-like response as Cs is decreased and limits the validity of TTSS.

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.

Small-Angle Scattering from Nanoscale Fat Fractals

Small-angle scattering (of neutrons, x-ray, or light; SAS) is considered to describe the structural characteristics of deterministic nanoscale fat fractals. We show that in the case of a polydisperse fractal system, with equal probability for any orientation, one obtains the fractal dimensions and scaling factors at each structural level. This is in agreement with general results deduced in the context of small-angle scattering analysis of a system of randomly oriented, non-interacting, nano-/micro-fractals. We apply our results to a two-dimensional fat Cantor-like fractal, calculating analytic expressions for the scattering intensities and structure factors. We explain how the structural properties can be computed from experimental data and show their correlation to the variation of the scaling factor with the iteration number. The model can be used to interpret recorded experimental SAS data in the framework of fat fractals and can reveal structural properties of materials characterized by a regular law of changing of the fractal dimensions. It can describe successions of power-law decays, with arbitrary decreasing values of the scattering exponents, and interleaved by regions of constant intensity.

Rheological characterization of liquid-to-solid transitions in bulk polyelectrolyte complexes

Polyelectrolyte complexation has long been known to result in both liquid and solid complexes. However, the exact nature of the liquid-to-solid transition remains an open question. We have used rheology to explain this phenomenon for the model system of poly(4-styrenesulfonic acid, sodium salt) (PSS) and poly(diallyldimethyl ammonium chloride) (PDADMAC) in the presence of potassium bromide (KBr). The use of a time-salt superposition allows for a detailed analysis of changes in the linear viscoelastic response for both liquid complex coacervates and solid polyelectrolyte complexes as a function of salt concentration, and facilitates unambiguous determination of the mechanism for this phase transition. Decreasing salt concentration, and the commensurate decrease in the water content of PSS/PDADMAC/KBr complexes is shown to lead to the formation of a physical gel due to the development of a network with trapped electrostatic crosslinks that percolates the sample at a critical salt concentration.

Highly stretchable hydrogels from complex coacervation of natural polyelectrolytes

The controlled complex coacervation of oppositely charged hyaluronic acid (M_w ≈ 800-1000 kg mol^-1) and chitosan (M_w ≈ 160 kg mol^-1, degree of acetylation = 15%) led to hydrogels with controllable properties in terms of elasticity and strength. In this work, we performed desalting by dialysis of high ionic strength solutions of mixed polyelectrolytes and showed that the control of the pH during the polyelectrolyte assembly greatly impacts the mechanical properties of the hydrogel. First, for pHs from 5.5 to 7.5, a slight coacervation was observed due to low chitosan protonation and poor polyelectrolyte associations. Then, for pHs from 3.0 to 5.5, coacervation and syneresis led to free-standing and easy to handle hydrogels. Finally, for pHs from 2.0 to 3.0 (close to the pK_a of the hyaluronic acid), we observed the unusual stretchability of these hydrogels that could arise from the pre-folding of hyaluronic acid chains while physical crosslinking was achieved by hyaluronic acid/chitosan polyelectrolyte complexation.

Molecular and structural basis of low interfacial energy of complex coacervates in water

Complex coacervate refers to a phase-separated fluid, typically of two oppositely charged polyelectrolytes in solution, representing a complex fluid system that has been shown to be of essential interest to biological systems, as well as for soft materials processing owing to the expectation of superior underwater coating or adhesion properties. The significance and interest in complex coacervate fluids critically rely on its low interfacial tension with respect to water that, in turn, facilitates the wetting of macromolecular or material surfaces under aqueous conditions, provided there is attractive interaction between the polyelectrolyte constituents and the surface. However, the molecular and structural bases of these properties remain unclear. Recent studies propose that the formation of water-filled and bifluidic sponge-like nanostructured network, driven by the tuning of electrostatic interactions between the polyelectrolyte constituents or their complexes may be a common feature of complex coacervate fluids that display low fluid viscosity and low interfacial tension, but more studies are needed to verify the generality of these observations. In this review, we summarize representative studies of interfacial tension and ultrastructures of complex coacervate fluids. We highlight that a consensus property of the complex coacervate fluid is the observation of high or even bulk-like water dynamics within the dense complex coacervate phase that is consistent with a low cohesive energy fluid. Our own studies on this subject are enabled by the application of magnetic resonance relaxometry methods relying on spin labels tethered to polyelectrolyte constituents or added as spin labeled probe molecules that partition into the dense versus the equilibrium coacervate phase, permitting the extraction of information on local polymer dynamics, polymer packing and local water dynamics. We conclude with a snapshot of our current perspective on the molecular and structural bases of the low interfacial tension of complex coacervate fluids.

Linear viscoelasticity of complex coacervates

Rheology is a powerful method for material characterization that can provide detailed information about the self-assembly, structure, and intermolecular interactions present in a material. Here, we review the use of linear viscoelastic measurements for the rheological characterization of complex coacervate-based materials. Complex coacervation is an electrostatically and entropically-driven associative liquid-liquid phase separation phenomenon that can result in the formation of bulk liquid phases, or the self-assembly of hierarchical, microphase separated materials. We discuss the need to link thermodynamic studies of coacervation phase behavior with characterization of material dynamics, and provide parallel examples of how parameters such as charge stoichiometry, ionic strength, and polymer chain length impact self-assembly and material dynamics. We conclude by highlighting key areas of need in the field, and specifically call for the development of a mechanistic understanding of how molecular-level interactions in complex coacervate-based materials affect both self-assembly and material dynamics.

Complex coacervation of supercharged proteins with polyelectrolytes

Complexation of proteins with polyelectrolytes or block copolymers can lead to phase separation to generate a coacervate phase or self-assembly of coacervate core micelles. However, many proteins do not coacervate at conditions near neutral pH and physiological ionic strength. Here, protein supercharging is used to systematically explore the effect of protein charge on the complex coacervation with polycations. Four model proteins were anionically supercharged to varying degrees as quantified by mass spectrometry. Proteins phase separated with strong polycations when the ratio of negatively charged residues to positively charged residues on the protein (α) was greater than 1.1-1.2. Efficient partitioning of the protein into the coacervate phase required larger α (1.5-2.0). The preferred charge ratio for coacervation was shifted away from charge symmetry for three of the four model proteins and indicated an excess of positive charge in the coacervate phase. The composition of protein and polymer in the coacervate phase was determined using fluorescently labeled components, revealing that several of the coacervates likely have both induced charging and a macromolecular charge imbalance. The model proteins were also encapsulated in complex coacervate core micelles and micelles formed when the protein charge ratio α was greater than 1.3-1.4. Small angle neutron scattering and transmission electron microscopy showed that the micelles were spherical. The stability of the coacervate phase in both the bulk and micelles improved to increased ionic strength as the net charge on the protein increased. The micelles were also stable to dehydration and elevated temperatures.

Chirality-selected phase behaviour in ionic polypeptide complexes

Polyelectrolyte complexes present new opportunities for self-assembled soft matter. Factors determining whether the phase of the complex is solid or liquid remain unclear. Ionic polypeptides enable examination of the effects of stereochemistry on complex formation. Here we demonstrate that chirality determines the state of polyelectrolyte complexes, formed from mixing dilute solutions of oppositely charged polypeptides, via a combination of electrostatic and hydrogen-bonding interactions. Fluid complexes occur when at least one of the polypeptides in the mixture is racemic, which disrupts backbone hydrogen-bonding networks. Pairs of purely chiral polypeptides, of any sense, form compact, fibrillar solids with a β-sheet structure. Analogous behaviour occurs in micelles formed from polypeptide block copolymers with polyethylene oxide, where assembly into aggregates with either solid or fluid cores, and eventually into ordered phases at high concentrations, is possible. Chirality is an exploitable tool for manipulating material properties in polyelectrolyte complexation.

Interfacial Tension of Polyelectrolyte Complex Coacervate Phases

We consider polyelectrolyte solutions which, under suitable conditions, phase separate into a liquid-like coacervate phase and a coexisting supernatant phase that exhibit an extremely low interfacial tension. Such interfacial tension provides the basis for most coacervate-based applications, but little is known about it, including its dependence on molecular weight, charge density, and salt concentration. By combining a Debye-Hückel treatment for electrostatic interactions with the Cahn-Hilliard theory, we derive explicit expressions for this interfacial tension. In the absence of added salts, we find that the interfacial tension scales as N^-3/2(η/η_c-1)^3/2 near the critical point of the demixing transition, and that it scales as η^1/2 far away from it, where N is the chain length and η measures the electrostatic interaction strength as a function of temperature, dielectric constant, and charge density of the polyelectrolytes. For the case with added salts, we find that the interfacial tension scales with the salt concentration ψ as N^-1/4(1-ψ/ψ_c)^3/2 near the critical salt concentration ψ_c. Our predictions are shown to be in quantitative agreement with experiments and provide a means to design new materials based on polyelectrolyte complexation.