Relaxation dynamics at different time scales in electrostatic complexes: time-salt superposition

Efficient Synthesis of Stable Polyelectrolyte Complex Nanoparticles by Electrostatic Assembly Directed Polymerization

Polyelectrolyte complex nanoparticles with integrated advances of coacervate complexes and nanomaterials have attracted considerable attention as soft templates and functional nano-carriers. Herein, a facile and robust strategy, namely electrostatic assembly directed polymerization (EADP), for efficient and scalable preparation of stable coacervate nanoparticles is presented. With homo-polyelectrolyte PAA (polyacrylic acid) as template and out of charge stoichiometry, the cationic monomers are polymerized together with cross-linkers, which creates coacervate nanoparticles featuring high stability against salt through one-pot synthesis. The particle size can be tuned by varying the cross-linker amount and salt concentrations during the polymerization and the composition of nanoparticles, as well as the corresponding properties can be regulated by combining different charged blocks from both strong and weak ionic monomers. The strategy can tolerate both high monomer concentrations and increased volume of up to l L, which is favorable for scaled-up preparations. Moreover, the coacervate nanoparticles can be freeze-dried to produce a product in powder form, which can be redispersed without any effect on the particle size and size distribution. Finally, the obtained nanoparticles loaded with enzyme and Au nanoparticles exhibit enhanced catalytic performance, demonstrating a great potential for exploring various applications of coacervate particles as soft and functional nano-carriers.

Connecting the Stimuli-Responsive Rheology of Biopolymer Hydrogels to Underlying Hydrogen-Bonding Interactions

Many biopolymer hydrogels are environmentally responsive because they are held together by physical associations that depend on pH and temperature. Here, we investigate how the pH and temperature responses of the rheology of hyaluronan hydrogels are connected to the underlying molecular interactions. Hyaluronan is an essential structural biopolymer in the human body with many applications in biomedicine. Using two-dimensional infrared spectroscopy, we show that hyaluronan chains become connected by hydrogen bonds when the pH is changed from 7.0 to 2.5 and that the bond density at pH 2.5 is independent of temperature. Temperature-dependent rheology measurements show that because of this hydrogen bonding the stress relaxation at pH 2.5 is strongly slowed down in comparison to pH 7.0, consistent with the sticky reptation model of associative polymers. From the flow activation energy, we conclude that each polymer is cross-linked by multiple (5-15) hydrogen bonds to others, causing slow macroscopic stress relaxation, despite the short time scale of breaking and reformation of each individual hydrogen bond. Our findings can aid the design of stimuli-responsive hydrogels with tailored viscoelastic properties for biomedical applications.

Effect of polyampholyte net charge on complex coacervation between polyampholytes and inorganic polyoxometalate giant anions

The effect of net charge of zwitterionic polymers on the phase behavior and viscoelastic properties of hybrid polyampholyte-polyoxometalate (POM) complexes in salted aqueous solutions is investigated with polyampholyte copolymers consisting of both positively and negatively charged monomers. Zwitterionic polyampholytes of varied net charge, abbreviated as PA_xM_y, are synthesized by varying the feeding molar ratio of negatively charged 2-acrylamido-2-methyl-1-propanesulfonic acid (AMPS) to positively charged [3-(methacryloylamino)propyl]trimethylammonium chloride (MAPTAC) monomers in aqueous solution. The coacervate formation between PA_xM_y and inorganic anionic metatungstate POM ({W₁₂}) in LiCl added aqueous solutions can be enhanced by increasing the molar fraction of positively charged MAPTAC monomer and LiCl concentration. The salt-broadened coacervation, clearly distinct from the salt-suppressed one between oppositely charged polyelectrolytes, suggests the account of zwitterion-anion pairing for PA_xM_y-{W₁₂} coacervate formation due to stronger binding of multivalent {W₁₂} giant ions with PA_xM_y than simple ions. Importantly, as AMPS or MAPTAC monomer fraction in polyampholytes is varied by merely ±5% from the effective net neutral case, the viscoelasticity of PA_xM_y-{W₁₂} coacervates can be modified by 4-5 folds, suggesting a new tuning parameter to fine control the macroionic interactions and material properties of biomimetic complex coacervates.

Emerging trends in the dynamics of polyelectrolyte complexes

Polyelectrolyte complexes (PECs) are highly tunable materials that result from the phase separation that occurs upon mixing oppositely charged polymers. Over the years, they have gained interest due to their broad range of applications such as drug delivery systems, protective coatings, food packaging, and surface adhesives. In this review, we summarize the structure, phase transitions, chain dynamics, and rheological and thermal properties of PECs. Although most literature focuses upon the thermodynamics and application of PECs, this review highlights the fundamental role of salt and water on mechanical and thermal properties impacting the PEC's dynamics. A special focus is placed upon experimental results and techniques. Specifically, the review examines phase behaviour and salt partitioning in PECs, as well as different techniques used to measure diffusion coefficients, relaxation times, various superpositioning principles, glass transitions, and water microenvironments in PECs. This review concludes with future areas of opportunity in fundamental studies and best practices in reporting.

The benefit of poor mixing: kinetics of coacervation

Complex coacervation has become a prominent area of research in the fields of food science, personal care, drug stabilization, and more. However, little has been reported on the kinetics of assembly of coacervation itself. Here, we describe a simple, low-cost way of looking at the kinetics of coacervation by creating poorly mixed samples. In particular, we examine how polymer chain length, the patterning and symmetry of charges on the oppositely charged polyelectrolytes, and the presence of salt and a zwitterionic buffer affect the kinetics of complex coacervation. Our results suggest an interesting relationship between the time for equilibration and the order of addition of polymers with asymmetric patterns of charge. Furthermore, we demonstrated that increasing polymer chain length resulted in a non-monotonic trend in the sample equilibration times as a result of opposing factors such as excluded volume and diffusion. We also observed differences in the rate of sample equilibration based on the presence of a neutral, zwitterionic buffer, as well as the presence and identity of added salt, consistent with previous reports of salt-specific effects on the rheology of complex coacervates. While not a replacement for more advanced characterization strategies, this turbidity-based method could serve as a screening tool to identify interesting and unique phenomena for further study.

Crossover from Rouse to Reptation Dynamics in Salt-Free Polyelectrolyte Complex Coacervates

Considerable interest in the dynamics and rheology of polyelectrolyte complex coacervates has been motivated by their industrial application as viscosity modifiers. A central question is the extent to which classical Rouse and reptation models can be applied to systems where electrostatic interactions play a critical role on the thermodynamics. By relying on molecular simulations, we present a direct analysis of the crossover from Rouse to reptation dynamics in salt-free complex coacervates as a function of chain length. This crossover shifts to shorter chain lengths as electrostatic interactions become stronger, which corresponds to the formation of denser coacervates. To distinguish the roles of Coulomb interactions and density, we compare the dynamics of coacervates to those of neutral, semidilute solutions at the same density. Both systems exhibit a universal dynamical behavior in the connectivity-dominated (subdiffusion and normal diffusion) regimes, but the monomer relaxation time in coacervates is much longer and increases with increasing Bjerrum length. This is similar to the cage effect observed in glass-forming polymers, but the local dynamical slowdown is caused here by strong Coulomb attractions (ion pairing) between oppositely charged monomers. Our findings provide a microscopic framework for the quantitative understanding of coacervate dynamics and rheology.

Time-Ionic Strength Superposition: A Unified Description of Chain Relaxation Dynamics in Polyelectrolyte Complexes

Addition of salt speeds up chain relaxation dynamics in polyelectrolyte complexes (PECs), and time-salt superposition (TSS) approaches to describe the linear viscoelastic response of PECs are well-established. However, TSS is carried out at fixed initial polyelectrolyte concentrations, and varying the initial polyelectrolyte concentration results in distinct TSS master curves. In this contribution, we show that accounting for the small ions that accompany the oppositely charged polyelectrolyte chains (designated as accompanying counterions) enables assimilation of these distinct TSS master curves into a single universal master curve. This approach, that we christen as time-ionic strength superposition (TISS), enables a unified description of the PEC viscoelastic response in terms of the solution ionic strength, that accounts for both the accompanying counterions and the added ions, and underlines the dynamic similarities between PECs and semidilute polymer solutions. The sticky electrostatic associations among the oppositely charged chains, however, contribute additional relaxation modes in the PECs. We demonstrate that the time scales of these additional relaxation modes are described quantitatively by a modified sticky Rouse model that accounts for the influence of solution ionic strength on electrostatic screening and chain friction.

Recent progress in the science of complex coacervation

Complex coacervation is an associative, liquid-liquid phase separation that can occur in solutions of oppositely-charged macromolecular species, such as proteins, polymers, and colloids. This process results in a coacervate phase, which is a dense mix of the oppositely-charged components, and a supernatant phase, which is primarily devoid of these same species. First observed almost a century ago, coacervates have since found relevance in a wide range of applications; they are used in personal care and food products, cutting edge biotechnology, and as a motif for materials design and self-assembly. There has recently been a renaissance in our understanding of this important class of material phenomena, bringing the science of coacervation to the forefront of polymer and colloid science, biophysics, and industrial materials design. In this review, we describe the emergence of a number of these new research directions, specifically in the context of polymer-polymer complex coacervates, which are inspired by a number of key physical and chemical insights and driven by a diverse range of experimental, theoretical, and computational approaches.

Driving Force for the Complexation of Charged Polypeptides

The phase separation of oppositely charged polyelectrolytes in solution is of current interest. In this work, we study the driving force for polyelectrolyte complexation using molecular dynamics simulations. We calculate the potential of mean force between poly(lysine) and poly(glutamate) oligomers using three different force fields, an atomistic force field and two coarse-grained force fields. There is qualitative agreement between all force fields, i.e., the sign and magnitude of the free energy and the nature of the driving force are similar, which suggests that the molecular nature of water does not play a significant role. For fully charged peptides, we find that the driving force for association is entropic in all cases when small ions either neutralize the poly ions, or are in excess. The removal of all counterions switches the driving force, making complexation energetic. This suggests that the entropy of complexation is dominated by the counterions. When only 6 residues of a 11-mer are charged, however, the driving force is energetic in the abscence of excess salt. The simulations shed insight into the mechanism of complex coacervation and the importance of realistic models for the polyions.

Stabilizing Coacervate by Microfluidic Engulfment Induced by Controlled Interfacial Energy

Low interfacial energy, an intrinsic property of complex coacervate, enables the complex coacervate to easily encapsulate desired cargo substances, making it widely used in encapsulation applications. Despite this advantage, the low interfacial energy of the complex coacervate makes it unstable against mechanical mixing, and changes in pH and salt concentration. Hence, a chemical cross-linker is usually added to enhance the stability of the complex coacervate at the expense of sacrificing all intrinsic properties of the coacervate, including phase transition of the coacervate from liquid to solid. In this study, we observed an abrupt increase in the interfacial energy of the coacervate phase in mineral oil. By controlling the interfacial energy of the coacervate phase using a microfluidic device, we successfully created double engulfed PEG-diacrylate (PEGDA) coacervate microparticles, named DEPOT, in which the coacervate is engulfed in a cross-linked PEGDA shell. The engulfed coacervate remained as a liquid phase, retained its original low interfacial energy property to encapsulate the desired cargo substances, and infiltrated into the target site by a simple solvent exchange from oil to water.

A comprehensive review of the structures and properties of ionic polymeric materials

This review focuses on the mechanistic approach, the structure–property relationship and applications of ionic polymeric materials.

Influence of Sodium Salts on the Swelling and Rheology of Hydrophobically Cross-linked Hydrogels Determined by QCM-D

Hydrophobically modified copolymers provide a versatile platform of hydrogel materials for diverse applications, but the influence of salts on the swelling and material properties of this class of hydrogels has not been extensively studied. Here, we investigate model hydrogels with three different sodium salts with anions chosen from the classic Hofmeister series to determine how these counterions influence the swelling and mechanical properties of neutral hydrogels. The gel chosen was based on a statistical copolymer of dimethylacrylamide and 2-(N-ethylperfluorooctane sulfonamido) ethyl acrylate (FOSA). Our measurements utilize a quartz crystal microbalance with dissipation (QCM-D) to quantify both swelling and rheological properties of these gels. We find that a 1 mol/L solution of Na₂SO₄, corresponding to a kosmotropic anion, leads to nearly a 2.6-fold gel deswelling and correspondingly, the complex modulus increases by an order of magnitude under these solution conditions. In contrast, an initial increase in swelling and then a swelling maximum is observed for a 0.02 mol/L concentration in the case of a chaotropic anion, NaClO₄, but the changes in the degree of gel swelling in this system are not directly correlated with changes in the gel shear modulus. The addition of NaBr, an anion salt closer to the middle of the chaotropic to kosmotropic range, leads to hydrogel deswelling where the degree of deswelling and the shear modulus are both nearly independent of salt concentration. Overall, the observed trends are broadly consistent with more kosmotropic ions causing diminished solubility ("salting out") and strongly chaotropic ions causing improved solubility ("salting in"), a trend characteristic of the Hoffmeister series governing the solubility of many proteins and synthetic water-soluble polymers, but trends in the shear stiffness with gel swelling are clearly different from those normally observed in chemically cross-linked gels and are correspondingly difficult to interpret. The salt specificity of swelling and mechanical properties of nonionic hydrogels is important for any potential application in which a wide range of salt concentrations and types are encountered.

Langevin Dynamics Simulations of the Exchange of Complex Coacervate Core Micelles: The Role of Nonelectrostatic Attraction and Polyelectrolyte Length

Complex coacervate core micelles (C3Ms) are promising encapsulators for a wide variety of (bio)molecules. To protect and stabilize their cargo, it is essential to control their exchange dynamics. Yet, to date, little is known about the kinetic stability of C3Ms and the dynamic equilibrium of molecular building blocks with micellar species. Here we study the C3M exchange during the initial micellization by using Langevin dynamics simulations. In this way, we show that charge neutral heterocomplexes consisting of multiple building blocks are the primary mediator for exchange. In addition, we show that the kinetic stability of the C3Ms can be tuned not only by the electrostatic interaction but also by the nonelectrostatic attraction between the polyelectrolytes, the polyelectrolyte length ratio, and the overall polyelectrolyte length. These insights offer new rational design guides to aid the development of new C3M encapsulation strategies.

Versatile and High-Throughput Polyelectrolyte Complex Membranes via Phase Inversion

High-flux filtration membranes constructed through scalable and sustainable methods are desirable for energy-efficient separations. Often, these criteria are difficult to be reconciled with one another. Polymeric membranes can provide high flux but frequently involve organic solvents in processing steps. Solubility of many polymeric membranes in organic media also restricts their implementation in solvent filtration. In the present work, we report a simple and high-throughput aqueous processing approach for polyelectrolyte complex (PEC) membranes with controllable porosity and stability in various aqueous and organic environments. PECs are materials composed of oppositely charged polymer chains that can form solids in aqueous environments, yet which can be dissolved in very specific salt solutions capable of breaking the interpolymer ion pairs. By exploiting the salt-induced dissolution and subsequent reformation of the complex, nano- to microporous films are rapidly synthesized which resemble membranes obtained through conventional solvent-phase inversion techniques. PECs remain stable in organic solvents because of the low dielectric constant of the environment, which enhances electrostatic interactions, making them suitable for a wide range of water and solvent filtration applications. Here, we elucidate how the polymer-phase behavior can be manipulated to exercise morphological control, test membrane performance for water and solvent filtration, and quantify the mechanical stability of PECs in relevant conditions.

Salt-Dependent Rheology and Surface Tension of Protein Condensates Using Optical Traps

An increasing number of proteins with intrinsically disordered domains have been shown to phase separate in buffer to form liquidlike phases. These protein condensates serve as simple models for the investigation of the more complex membraneless organelles in cells. To understand the function of such proteins in cells, the material properties of the condensates they form are important. However, these material properties are not well understood. Here, we develop a novel method based on optical traps to study the frequency-dependent rheology and the surface tension of P-granule protein PGL-3 condensates as a function of salt concentration. We find that PGL-3 droplets are predominantly viscous but also exhibit elastic properties. As the salt concentration is reduced, their elastic modulus, viscosity, and surface tension increase. Our findings show that salt concentration has a strong influence on the rheology and dynamics of protein condensates suggesting an important role of electrostatic interactions for their material properties.

Polyelectrolyte association and solvation

There has been significant interest in the tendency of highly charged particles having the same charge to form dynamic clusters in solution, but an accepted theoretical framework that can account for this ubiquitous phenomenon has been slow to develop. The theoretical difficulties are especially great for flexible polyelectrolytes due to the additional complex coupling between the polyelectrolyte chain configurations and the spatial distribution of the ionic species in solution. For highly charged polyelectrolytes, this leads to the formation of a diffuse "polarizable" cloud of counter-ions around these polymers, an effect having significant implications for the function of proteins and other natural occurring polyelectrolytes, as emphasized long ago by Kirkwood and co-workers. To investigate this phenomenon, we perform molecular dynamics simulations of a minimal model of polyelectrolyte solutions that includes an explicit solvent and counter-ions, where the relative affinity of the counter-ions and the polymer for the solvent is tunable through the variation of the relative strength of the dispersion interactions of the polymer and ions. In particular, we find that these dispersion interactions can greatly influence the nature of the association between the polyelectrolyte chains under salt-free conditions. We calculate static and dynamic correlation functions to quantify the equilibrium structure and dynamics of these complex liquids. Based on our coarse-grained model of polyelectrolyte solutions, we identify conditions in which three distinct types of polyelectrolyte association arise. We rationalize these types of polyelectrolyte association based on the impact of the selective solvent affinity on the charge distribution and polymer solvation in these solutions. Our findings demonstrate the essential role of the solvent in the description of the polyelectrolyte solutions, as well as providing a guideline for the development of a more predictive theory of the properties of the thermodynamic and transport properties of these complex fluids.

Crack Initiation in Viscoelastic Materials

In viscoelastic materials, individually short-lived bonds collectively result in a mechanical resistance which is long lived but finite as, ultimately, cracks appear. Here, we provide a microscopic mechanism by which a critical crack length emerges from the nonlinear local bond dynamics. Because of this emerging length scale, macroscopic viscoelastic materials fracture in a fundamentally different manner from microscopically small systems considered in previous models. We provide and numerically verify analytical equations for the dependence of the critical crack length on the bond kinetics and applied stress.

Synthesis and Assembly of Designer Styrenic Diblock Polyelectrolytes

Harnessing molecular design principles toward functional applications of ion-containing macromolecules relies on diversifying experimental data sets of well-understood materials. Here, we report a simple, tunable framework for preparing styrenic polyelectrolytes, using aqueous reversible addition-fragmentation chain transfer (RAFT) polymerization in a parallel synthesis approach. A series of diblock polycations and polyanions were RAFT chain-extended from poly(ethylene oxide) (PEO) using (vinylbenzyl)trimethylammonium chloride (PEO-b-PVBTMA) and sodium 4-styrenesulfonate (PEO-b-PSS), with varying neutral PEO block lengths, charged styrenic block lengths, and RAFT end-group identity. The materials characterization and kinetics study of chain growth exhibited control of the molar mass distribution for both systems. These block polyelectrolytes were also demonstrated to form polyelectrolyte complex (PEC) driven self-assemblies. We present two simple outcomes of micellization to show the importance of polymer selection from a broadened pool of polyelectrolyte candidates: (i) uniform PEC-core micelles comprising PEO-b-PVBTMA and poly(acrylic acid) and (ii) PEC nanoaggregates comprising PEO-b-PVBTMA and PEO-b-PSS. The materials characteristics of these charged assemblies were investigated with dynamic light scattering, small-angle X-ray scattering, and cryogenic-transmission electron microscopy imaging. This model synthetic platform offers a straightforward path to expand the design space of conventional polyelectrolytes into gram-scale block polymer structures, which can ultimately enable the development of more sophisticated ionic materials into technology.

Molecular Origin of the Glass Transition in Polyelectrolyte Assemblies

Water plays a central role in the assembly and the dynamics of charged systems such as proteins, enzymes, DNA, and surfactants. Yet it remains a challenge to resolve how water affects relaxation at a molecular level, particularly for assemblies of oppositely charged macromolecules. Here, the molecular origin of water's influence on the glass transition is quantified for several charged macromolecular systems. It is revealed that the glass transition temperature (Tg) is controlled by the number of water molecules surrounding an oppositely charged polyelectrolyte-polyelectrolyte intrinsic ion pair as 1/Tg ∼ ln(nH2O/nintrinsic ion pair). This relationship is found to be "general", as it holds for two completely different types of charged systems (pH- and salt-sensitive) and for both polyelectrolyte complexes and polyelectrolyte multilayers, which are made by different paths. This suggests that water facilitates the relaxation of charged assemblies by reducing attractions between oppositely charged intrinsic ion pairs. This finding impacts current interpretations of relaxation dynamics in charged assemblies and points to water's important contribution at the molecular level.

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.

Filament turnover tunes both force generation and dissipation to control long-range flows in a model actomyosin cortex

Actomyosin-based cortical flow is a fundamental engine for cellular morphogenesis. Cortical flows are generated by cross-linked networks of actin filaments and myosin motors, in which active stress produced by motor activity is opposed by passive resistance to network deformation. Continuous flow requires local remodeling through crosslink unbinding and and/or filament disassembly. But how local remodeling tunes stress production and dissipation, and how this in turn shapes long range flow, remains poorly understood. Here, we study a computational model for a cross-linked network with active motors based on minimal requirements for production and dissipation of contractile stress: Asymmetric filament compliance, spatial heterogeneity of motor activity, reversible cross-links and filament turnover. We characterize how the production and dissipation of network stress depend, individually, on cross-link dynamics and filament turnover, and how these dependencies combine to determine overall rates of cortical flow. Our analysis predicts that filament turnover is required to maintain active stress against external resistance and steady state flow in response to external stress. Steady state stress increases with filament lifetime up to a characteristic time τm, then decreases with lifetime above τm. Effective viscosity increases with filament lifetime up to a characteristic time τc, and then becomes independent of filament lifetime and sharply dependent on crosslink dynamics. These individual dependencies of active stress and effective viscosity define multiple regimes of steady state flow. In particular our model predicts that when filament lifetimes are shorter than both τc and τm, the dependencies of effective viscosity and steady state stress on filament turnover cancel one another, such that flow speed is insensitive to filament turnover, and shows a simple dependence on motor activity and crosslink dynamics. These results provide a framework for understanding how animal cells tune cortical flow through local control of network remodeling.

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.

Water and the Glass Transition Temperature in a Polyelectrolyte Complex

Hydrated polyelectrolyte complexes, H-PECs, have recently started attracting renewed interest as a class of highly solvated/plasticized blends. H-PECs are observed to undergo a transition in mechanical properties close to room temperature. Whether this is a true glass transition has been questioned recently: the material has an unusually low modulus in the "glassy" state and molecular dynamics simulations have suggested temperature-induced dehydration and water structure changes are responsible for the transition. Using in situ infrared spectroscopic methods on thin films of a widely studied H-PEC we find no definitive evidence for changes in the hydration state of functional groups, the water content, or water structure on passing through T_g for stoichiometric and nonstoichiometric H-PECs. These complexes represent a promising platform for fundamental studies of the glass transition, since the coupling between chains can be modified by "doping" the material with salt, which breaks ion pairing cross-links. The Fox equation was used to estimate T_gs for paired and unpaired oppositely charged repeat units.

Equilibration of Micelle-Polyelectrolyte Complexes: Mechanistic Differences between Static and Annealed Charge Distributions

The role of charge density and charge annealing in polyelectrolyte complexation was investigated through systematic comparison of two micelle-polyelectrolyte systems. First, poly(dimethylaminoethyl methacrylate)-block-poly(styrene) (PDMAEMA-b-PS) micelles were complexed with poly(styrenesulfonate) (PSS) at pH values above and below the pK_a of PDMAEMA to investigate the role of charge annealing in the complexation process. Second, complexes of poly(DMAEMA-stat-oligo(ethylene glycol) methyl ether methacrylate)-block-poly(styrene) (P(DMAEMA-stat-OEGMA)-b-PS) micelles with the same PSS at low pH were used to investigate how the complexation process differs when the charged sites are in fixed positions along the polymer chains. Characterization by turbidimetric titration, dynamic light scattering, and cryogenic transmission electron microscopy reveals that whether or not the charge distribution can rearrange during the complexation process significantly affects the structure and stability of the complexes. In complexes of PDMAEMA-b-PS micelles at elevated pH, in which the charge distributions can anneal, the charge sites redistribute along the corona chains upon complexation to favor more fully ion-paired configurations. This promotes rapid rearrangement to single-micelle species when the micelles are in excess but traps complexes formed with PSS in excess. In complexes with static charge distributions introduced by copolymerization of DMAEMA with neutral OEGMA monomers, on the other hand, the opposite is true: in this case, reducing the charge density promotes rearrangement to single-micelle complexes only when the polyanion is in excess. Molecular dynamics simulations show that disruption of the charge density in the corona brush reduces the barrier to rearrangement of individual ion pairs, suggesting that the inability of the brush to rearrange to form fully ion-paired complexes fundamentally alters the kinetics of complex formation and equilibration.

Characterization of Responsive Hydrogel Nanoparticles upon Polyelectrolyte Complexation

Characterization of responsive hydrogels and their interaction with other molecules have significantly expanded our understanding of the functional materials. We here report on the response of poly(N-isopropylacrylamide-co-acrylic acid) (pNIPAm-co-AAc) nanogels to the addition of the poly(allylamine hydrochloride) (PAH) in aqueous dispersions. We find that the hydrodynamic radius and stability of nanogels are dependent on the PAH/nanogel stoichiometry. If the nanogel solution is titrated with very small aliquots of PAH, the nanogels decrease in radius until the equivalence point, followed by aggregation at suprastoichiometric PAH additions. Conversely, when titrated with large aliquots, the nanogel charge switches rapidly from anionic to cationic, and no aggregation is observed. This behavior correlates well with electrophoretic mobility measurements, which shows the nanogel charge transitioning from negative to positive upon PAH addition. The volume phase transition temperature (VPTT) of the nanogels is also measured to discover the effect of polyelectrolyte complexation on the deswelling thermodynamics. These data show that charge neutralization upon PAH addition decreases the VPTT of the nanogel at pH 6.5. However, if an excess amount of PAH is added to the nanogel solution, the VPTT shifts back to higher temperatures due to the formation of a net positive charge in the nanogel network.

Growth Kinetics of Polyelectrolyte Complexes Formed from Oppositely-Charged Homopolymers Studied by Time-Resolved Ultra-Small-Angle X-ray Scattering

We have monitored the kinetic process of polyelectrolyte complex formation between sodium polyacrylate (SPA) and polyallylamine hydrochrolide (PAH) in aqueous NaCl solution by time-resolved ultra-small-angle X-ray scattering (TR-USAXS) combined with rapid mixing. SPA and PAH with different NaCl concentrations from 0 to 1 M were rapidly mixed in equimolar concentration of the monomer units using a stopped-flow apparatus with a dead time of about 2.5 ms. Within the dead time, percolated aggregate-like structures were observed suggesting that the initially formed small charge neutral aggregates further assembled to form higher order agglomerates. The early stage time evolution of the molar mass of the global structure in the presence of NaCl was found to be comparable to the Brownian-coagulation rate.

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.