Relationship between Polyelectrolyte Bulk Complexation and Kinetics of Their Layer-by-Layer Assembly

Thermodynamic insights into polyelectrolyte complexation: A theoretical framework

In this study, we propose a theoretical framework to explore the interactions between flexible polymer chains, specifically polyelectrolytes (PEs). Our analysis reaffirms that the thermodynamic drive for complex coacervation is influenced by key factors such as the number of ions bound to the polymer backbone and the entropy associated with free ions. By calculating the free energy of the system while considering position-dependent mutual interactions and chain conformations, we gain valuable insights into the local dielectricity as PEs overlap. Our findings indicate that global thermodynamic behavior is significantly shaped by local factors such as dielectric constant, providing an explanation for the discrepancies observed between experimental and computational studies. In addition, we found that entropy gain is inversely proportional to the local dielectric constant, provided that the electrostatic temperature remains constant. This relationship underscores the importance of polymer-specific parameters when examining the thermodynamic behavior of charged polymer complexation.

Form Equals Function: Influence of Coacervate Architecture on Drug Delivery Applications

Complex coacervates, formed through electrostatic interactions between oppositely charged polymers, present a versatile platform for drug delivery, providing rapid assembly, selective encapsulation, and responsiveness to environmental stimuli. The architecture and properties of coacervates can be tuned by controlling structural and environmental design factors, which significantly impact the stability and delivery efficiency of the drugs. While environmental design factors such as salt, pH, and temperature play a crucial role in coacervate formation, structural design factors such as polymer concentration, polymer structure, mixing ratio, and chain length serve as the core framework that shapes coacervate architecture. These elements modulate the phase behavior and material properties of coacervates, allowing for a highly tunable system. In this review, we primarily analyze how these structural design factors contribute to the formation of diverse coacervate architecture, ranging from bulk coacervates to polyion complex micelles, vesicles, and cross-linked gels, though environmental design factors are considered. We then examine the effectiveness of these architectures in enhancing the delivery and efficacy of drugs across various administration routes, such as noninvasive (e.g., oral and transdermal) and invasive delivery. This review aims to provide foundational insights into the design of advanced drug delivery systems by examining how the origin and chemical structure of polymers influence coacervate architecture, which in turn defines their material properties. We then explore how the architecture can be tailored to optimize drug delivery for specific administration routes. This approach leverages the intrinsic properties derived from the coacervate architecture to enable targeted, controlled, and efficient drug release, ultimately enhancing therapeutic outcomes in precision medicine.

Solid-Liquid-Solution Phases in Poly(diallyldimethylammonium)/Poly(acrylic acid) Polyelectrolyte Complexes at Varying Temperatures

The coacervation and complexation of oppositely charged polyelectrolytes are dependent on numerous environmental and preparatory factors, but temperature is often overlooked. Temperature effects remain unclear because the temperature dependence of both the dielectric constant and polymer-solvent interaction parameter can yield lower and/or upper critical solution phase behaviors for PECs. Further, secondary interactions, such as hydrogen bonding, can affect the temperature response of a PEC. That is, mixtures of oppositely charged polyelectrolytes can exhibit phase separation upon lowering and/or increasing the mixture's temperature. Here, the phase behavior of poly(diallylmethylammonium)/poly(acrylic acid) (PDADMA/PAA) complexes under varying KBr ionic strengths, mixing ratios, and temperatures at a fixed pH (in which PAA hydrogen bonding can occur) is examined. At room temperature, the PDADMA/PAA PECs exhibit four different phase states: precipitate, coexisting precipitate and coacervate, solid-like gel, and coacervate. Variable-temperature optical microscopy reveals the upper critical solution temperature (UCST) at which each phase transitioned to a solution state. Interestingly, the UCST value is highly dependent on the original phase of the PEC, in which solid-like precipitates exhibit higher UCST values. Large-scale all-atom molecular dynamics (MD) simulations support that precipitates exhibit kinetic trapping, which may contribute to the higher UCST values observed in the experiment. Taken together, this study highlights the significance of temperature on the phase behavior of PECs, which may play a larger role in stimuli-responsive materials, membraneless organelles, and separations applications.

Evaporation-Induced Polyelectrolyte Complexation: The Role of Base Volatility and Cosolvents

Film formation is a vital step for coating applications where a homogeneous, defect-free solid phase should be obtained, starting from a liquid casting formulation. Recently, an alternative waterborne-coating approach was proposed, based on the formation of a polyelectrolyte complex film. In this approach, an evaporating base induces a pH change during drying that initiates the complexation of oppositely charged polyelectrolytes, followed by further densification. In previous studies, ammonia was used as the evaporative base, leading to relatively fast evaporation and resulting in films showing significant brittleness, which tended to crack at low relative humidity or larger thicknesses. We hypothesize that slower complexation and/or evaporation can reduce the problematic stress build-up in the prepared polyelectrolyte complex coatings. For this reason, we studied the changes in the film formation process when there are different bases and cosolvents. We found that reducing the evaporation rate by changing ammonia to the slower evaporating dimethylamine or by adding DMSO as a cosolvent, led to less internal stress build-up during film formation, which could be beneficial for film application. Indeed, films prepared with ammonia showed cracking after 1 h, while films prepared with dimethylamine only showed cracking after one month. The fast evaporation of ammonia was also found to cause a temporary turbid phase, indicating phase separation, while for the slower evaporating bases, this did not occur. All prepared films remained sensitive to humidity, which poses the next challenge for these promising coatings.

Theoretical treatment of complex coacervate core micelles: structure and pH-induced disassembly

Complex coacervate core micelles (C3Ms) are supramolecular soft nanostructures formed by the assembly of a block copolymer and an oppositely charged homopolymer. The coacervation of the charged segments in both macromolecules drives the formation of the core of the C3M, while the neutral block of the copolymer forms the corona. This work introduces a molecular theory (MOLT) that predicts the internal structure and stimuli-responsive properties of C3Ms and explicitly considers the chemical architecture of the polyelectrolytes, their acid-based equilibria and electrostatic and non-electrostatic interactions. In order to accurately predict complex coacervation, the correlations between charged species are incorporated into MOLT as ion-pairing processes, which are modeled using a coupled chemical equilibrium formalism. Very good agreement was observed between the experimental results in the literature and MOLT predictions for the scaling relationships that relate the dimensions of the micelle (aggregation number and sizes of the micelle and the core) to the lengths of the different blocks. MOLT was used to study the disassembly of the micelles when the solution pH is driven away from the value that guarantees the charge stoichiometry of the core. This study reveals that very sharp disassembly transitions can be obtained by tuning the length or architecture of the copolymer component, thereby suggesting potential routes to design C3Ms capable of releasing their components at very precise pH values.

Driving forces of the complex formation between highly charged disordered proteins

Highly disordered complexes between oppositely charged intrinsically disordered proteins present a new paradigm of biomolecular interactions. Here, we investigate the driving forces of such interactions for the example of the highly positively charged linker histone H1 and its highly negatively charged chaperone, prothymosin α (ProTα). Temperature-dependent single-molecule Förster resonance energy transfer (FRET) experiments and isothermal titration calorimetry reveal ProTα-H1 binding to be enthalpically unfavorable, and salt-dependent affinity measurements suggest counterion release entropy to be an important thermodynamic driving force. Using single-molecule FRET, we also identify ternary complexes between ProTα and H1 in addition to the heterodimer at equilibrium and show how they contribute to the thermodynamics observed in ensemble experiments. Finally, we explain the observed thermodynamics quantitatively with a mean-field polyelectrolyte theory that treats counterion release explicitly. ProTα-H1 complex formation resembles the interactions between synthetic polyelectrolytes, and the underlying principles are likely to be of broad relevance for interactions between charged biomolecules in general.

Fluctuations, structure, and size inside coacervates

Aqueous solutions of oppositely charged macromolecules exhibit the ubiquitous phenomenon of coacervation. This subject is of considerable current interest due to numerous biotechnological applications of coacervates and the general premise of biomolecular condensates. Towards a theoretical foundation of structural features of coacervates, we present a field-theoretic treatment of coacervates formed by uniformly charged flexible polycations and polyanions in an electrolyte solution. We delineate different regimes of polymer concentration fluctuations and structural features of coacervates based on the concentrations of polycation and polyanion, salt concentration, and experimentally observable length scales. We present closed-form formulas for correlation length of polymer concentration fluctuations, scattering structure factor, and radius of gyration of a labelled polyelectrolyte chain inside a concentrated coacervate. Using random phase approximation suitable for concentrated polymer systems, we show that the inter-monomer electrostatic interaction is screened by interpenetration of all charged polymer chains and that the screening length depends on the individual concentrations of the polycation and the polyanion, as well as the salt concentration. Our calculations show that the scattering intensity decreases monotonically with scattering wave vector at higher salt concentrations, while it exhibits a peak at intermediate scattering wave vector at lower salt concentrations. Furthermore, we predict that the dependence of the radius of gyration of a labelled chain on its degree of polymerization generally obeys the Gaussian chain statistics. However, the chain is modestly swollen, the extent of which depending on polyelectrolyte composition, salt concentration, and the electrostatic features of the polycation and polyanion such as the degree of ionization.

Phase Behavior and Electrochemical Properties of Highly Asymmetric Redox Coacervates

This work reports the phase behavior and electrochemical properties of liquid coacervates made of ferricyanide and poly(ethylenimine). In contrast to the typical polyanion/polycation pairs used in liquid coacervates, the ferricyanide/poly(ethylenimine) system is highly asymmetric because poly(ethylenimine) has approximately 170 charges per molecule, while ferricyanide has only 3. Two types of phase diagrams were measured and fitted with a theoretical model. In the first type of diagram, the stability of the coacervate was studied in the plane given by the concentration of poly(ethylenimine) versus the concentration of ferricyanide for a fixed concentration of added monovalent salt (NaCl). The second type of diagram involved the plane given by the concentration of poly(ethylenimine) vs the concentration of the added monovalent salt for a fixed poly(ethyleneimine)/ferricyanide ratio. Interestingly, these phase diagrams displayed qualitative similarities to those of symmetric polyanion/polycation systems, suggesting that coacervates formed by a polyelectrolyte and a small multivalent ion can be treated as a specific case of polyelectrolyte coacervate. The characterization of the electrochemical properties of the coacervate revealed that the addition of monovalent salt greatly enhances charge transport, presumably by breaking ion pairs between ferricyanide and poly(ethylenimine). This finding highlights the significant influence of added salt on the transport properties of coacervates. This study provides the first comprehensive characterization of the phase behavior and transport properties of asymmetric coacervates and places these results within the broader context of the better-known symmetric polyelectrolyte coacervates.

Polyelectrolyte-multivalent molecule complexes: physicochemical properties and applications

The complexation of polyelectrolytes with other oppositely charged structures gives rise to a great variety of functional materials with potential applications in a wide spectrum of technological fields. Depending on the assembly conditions, polyelectrolyte complexes can acquire different macroscopic configurations such as dense precipitates, nanosized colloids and liquid coacervates. In the past 50 years, much progress has been achieved to understand the principles behind the phase separation induced by the interaction of two oppositely charged polyelectrolytes in aqueous solutions, especially for symmetric systems (systems in which both polyions have similar molecular weight and concentration). However, in recent years, the complexation of polyelectrolytes with alternative building blocks such as small charged molecules (multivalent inorganic species, oligopeptides, and oligoamines, among others) has gained attention in different areas. In this review, we discuss the physicochemical characteristics of the complexes formed by polyelectrolytes and multivalent small molecules, putting a special emphasis on their similarities with the well-known polycation-polyanion complexes. In addition, we analyze the potential of these complexes to act as versatile functional platforms in various technological fields, such as biomedicine and advanced materials engineering.

Polyelectrolyte Complexes as Desiccants: Thirsty Saloplastics

Desiccants or drying agents are used extensively to remove water from liquids and gases. Many organic reactions, from the laboratory to the industrial scale, are sensitive to even trace amounts of water. A new class of desiccants made from complexed polyelectrolytes, PECs, is described here, exploiting the affinity of charged polymer repeat units for water. The enthalpy of hydration of dry PECs was used for the first time as a quantitative measure of PEC water affinity. Several combinations of positive, Pol+, and negative, Pol-, polymers were used to prepare PECs. All of these displayed significant exothermic (favorable) enthalpies of hydration, measured at room temperature using solution calorimetry. A PEC made from poly(diallyldimethylammonium) and poly(styrene sulfonate) was extruded into convenient shapes. This PEC was used to dry three common solvents, acetonitrile, tetrahydrofuran, and toluene, representing a range of polarities. Added water was radiolabeled with tritium to provide accurate and sensitive detection of residual water after treatment. This PEC was almost as efficient as the comparison desiccants, molecular sieve 3A and calcium sulfate, after 3 days of static drying but could be regenerated at a lower temperature (120 °C) and shed far fewer dust particles.

Polyelectrolyte complexation of two oppositely charged symmetric polymers: A minimal theory

Interplay of Coulomb interaction energy, free ion entropy, and conformational elasticity is a fascinating aspect in polyelectrolytes (PEs). We develop a theory for complexation of two oppositely charged PEs, a process known to be the precursor to the formation of complex coacervates in PE solutions, to explore the underlying thermodynamics of complex formation, at low salts. The theory considers general degrees of solvent polarity and dielectricity within an implicit solvent model, incorporating a varying Coulomb strength. Explicit calculation of the free energy of complexation and its components indicates that the entropy of free counterions and salt ions and the Coulomb enthalpy of bound ion-pairs dictate the equilibrium of PE complexation. This helps decouple the self-consistent dependency of charge and size of the uncomplexed parts of the polyions, derive an analytical expression for charge, and evaluate the free energy components as functions of chain overlap. Complexation is observed to be driven by enthalpy gain at low Coulomb strengths, driven by entropy gain of released counterions but opposed by enthalpy loss due to reduction of ion-pairs at moderate Coulomb strengths, and progressively less favorable due to enthalpy loss at even higher Coulomb strengths. The total free energy of the system is found to decrease linearly with an overlap of chains. Thermodynamic predictions from our model are in good quantitative agreement with simulations in literature.

Polymer/Enzyme Composite Materials—Versatile Catalysts with Multiple Applications

A significant interest was granted lately to enzymes, which are versatile catalysts characterized by natural origin, with high specificity and selectivity for particular substrates. Additionally, some enzymes are involved in the production of high-valuable products, such as antibiotics, while others are known for their ability to transform emerging contaminates, such as dyes and pesticides, to simpler molecules with a lower environmental impact. Nevertheless, the use of enzymes in industrial applications is limited by their reduced stability in extreme conditions and by their difficult recovery and reusability. Rationally, enzyme immobilization on organic or inorganic matrices proved to be one of the most successful innovative approaches to increase the stability of enzymatic catalysts. By the immobilization of enzymes on support materials, composite biocatalysts are obtained that pose an improved stability, preserving the enzymatic activity and some of the support material’s properties. Of high interest are the polymer/enzyme composites, which are obtained by the chemical or physical attachment of enzymes on polymer matrices. This review highlights some of the latest findings in the field of polymer/enzyme composites, classified according to the morphology of the resulting materials, following their most important applications.

An Overview of Coacervates: The Special Disperse State of Amphiphilic and Polymeric Materials in Solution

Individual amphiphiles, polymers, and colloidal dispersions influenced by temperature, pH, and environmental conditions or interactions between their oppositely charged pairs in solvent medium often produce solvent-rich and solvent-poor phases in the system. The solvent-poor denser phase found either on the top or the bottom of the system is called coacervate. Coacervates have immense applications in various technological fields. This review comprises a concise introduction, focusing on the types of coacervates, and the influence of different factors in their formation, structures, and stability. In addition, their physicochemical properties, thermodynamics of formation, and uses and multifarious applications are also concisely presented and discussed.

How to Predict the Order of Phase Separation of Polyelectrolyte Complexes and Their Miscibility

The mixture of two oppositely charged polyelectrolyte solutions results in complexation that may lead to an associative phase separation, forming a highly concentrated phase in both polyelectrolytes in equilibrium with a dilute phase. In this work, we aim to investigate what controls the order of complexation when more polyelectrolytes of the same charge are present. For this, the effect of the addition of a third oppositely charged polyelectrolyte in a mixture of two polyelectrolytes with the same charge was studied. Our results show that, under certain conditions, the electrostatic complexation takes place selectively, where one polyanion (or polycation) phase separates first, followed by the other phase separation, with both complexes at their 1:1 charge stoichiometry. Infrared analyses of the phase-separated complexes confirmed that, in a mixture of polyanions, poly(styrenesulfonate) is complexed first, followed by poly(acrylate). For polycations, these analyses showed that poly(diallyldimethylammonium) is preferentially complexed over poly(allylamine). These results suggest that electrostatic complexation occurs following the sequence predicted as in an acid/base titration, where the acidic/basic strength of the involved polyions dictates which one is complexed first. In this respect, the order of complexation can be associated with the equivalence pH for each pair, which we propose can be used as a parameter to predict phase separation in polyelectrolyte mixtures. In addition, we have investigated the miscibility of these complex mixtures, confirming that multiphasic complexes are formed whenever the polyions display ionizable groups with different acid/basic strengths and that this can also be related to their equivalence pH.

Predicting the outcomes of interpolyelectrolyte neutralization at surfaces on the basis of complexation experiments and vice versa

This study was carried out with the aim of establishing how the outcomes of polyelectrolyte multilayer formation can be predicted on the basis of the results of complexation studies in solution and vice versa. For this purpose, the correlation between the processes of complex and multilayer formation involving three pairs of vinylic polyions in solutions of binary 1 : 1 sodium salts (NaX; X = F, Cl, Br, I, NO₃, ClO₄) was explored by means of dynamic and electrophoretic light scattering, potentiometry, microcalorimetry, spectrophotometry and quartz crystal microbalance. The gradual reactant mixing in solution at lower salt concentrations resulted in a Fuoss-Sadek sequence of events (primary complexes → secondary complexes → 1 : 1 flocculate), whereby the obtained nano-complexes could be successively overcharged. At high salt concentration and with excess polycation present, metastable nano-complexes and precipitates containing surplus of positively charged monomers were formed. The amount of extrinsically compensated charge was in accord with the polycation affinities toward counteranions, established by monitoring the electrolyte-induced aggregation of positively charged nano-complexes. Perfect analogy with respect to counteranion influence on the amount of adsorbed polycation was noticed for corresponding multilayers. Aside from providing a deeper understanding of interpolyelectrolyte neutralization, the gained insights can also be used to steer the polyelectrolyte multilayer composition and properties.

Molecular modeling of interfacial layer-by-layer assembly towards functionalized capsule materials

Encapsulated nanomaterials, such as polymer-coated nanoemulsions, have highly tunable properties leading to versatile applications. A current lack of understanding of the fundamentals governing the choice of "capsule" materials (polyelectrolyte + surfactant) and its ensuing performance effectively precludes their widespread use. Computational methods can start to redress this by discovering molecule-scale attributes that significantly control the design of capsule materials tuned to fit desired properties. We use molecular dynamics (MD) to carry out the layer-by-layer (LbL) assembly of six unique polyelectrolyte bilayer systems at a surfactant-mediated interface, modeling early-stage capsule synthesis. Monolayer thickness is related to layer density and polyelectrolyte/surfactant interaction energy through polyelectrolyte molecular weight and radius of gyration, respectively, yielding a simple relationship between absorption kinetics and layer structure. For the second monolayer, faster absorption kinetics are observed for pairings of polyelectrolytes with similarly sized functional groups. Surfactants with a more delocalized charge on the head-group catalyze the build-up of ions at the interface, resulting in faster absorption kinetics and greater confinement of the encapsulated material but leading to thicker, less uniform bilayers. These relationships between capsule building block molecules and nanomaterial capsule properties provide a foundation for property prediction and rational design of optimized multi-functional capsule materials.

Preparation of Poly(acrylate)/Poly(diallyldimethylammonium) Coacervates without Small Counterions and Their Phase Behavior upon Salt Addition towards Poly-Ions Segregation

In this work, we report the phase behavior of polyelectrolyte complex coacervates (PECs) of poly(acrylate) (PA-) and poly(diallyldimethylammonium) (PDADMA+) in the presence of inorganic salts. Titrations of the polyelectrolytes in their acidic and alkaline forms were performed to obtain the coacervates in the absence of their small counterions. This approach was previously applied to the preparation of polymer-surfactant complexes, and we demonstrate that it also succeeded in producing complexes free of small counterions with a low extent of Hofmann elimination. For phase behavior studies, two different molar masses of poly(acrylate) and two different salts were employed over a wide concentration range. It was possible to define the regions at which associative and segregative phase separation take place. The latter one was exploited in more details because the segregation phenomenon in mixtures of oppositely charged polyelectrolytes is scarcely reported. Phase composition analyses showed that there is a strong segregation for both PA- and PDADMA+, who are accompanied by their small counterions. These results demonstrate that the occurrence of poly-ion segregation in these mixtures depends on the anion involved: in this case, it was observed with NaCl, but not with Na2SO4.

Energetically Preferred Bilayered Coacervation of Oppositely Charged ZrHP Nanoplatelets

A platform is introduced for bilayered coacervation of oppositely charged nanoplatelets (NPLs) at the oil-water interface. To this end, we synthesized two types of zirconium hydrogen phosphate (ZrHP) NPLs, cationically charged NPLs (CNPLs), and anionically charged NPLs (ANPLs) by conducting surface-initiated atom transfer radical polymerization. Taking advantage of the platelet geometry and controlled wettability, we demonstrated that ANPLs and CNPLs coacervate themselves to form a bilayered NPL membrane at the interface, which was directly confirmed by confocal laser scanning microscopy. Via theoretical consideration using the hit-and-miss Monte Carlo method, we determined that electrostatic attraction-driven coacervation of ANPLs and CNPLs at the interface shows a minimum attachment energy of ∼ -10⁶ k_BT, which is comparable to the cases where NPLs charged with the same type of ions are attached. Finally, this unique and novel interfacial coacervation behavior allowed us to develop a pH-responsive smart Pickering emulsion system.

Overcharging of polyelectrolyte complexes: an entropic phenomenon

Overcharging in complex coacervation, in which a polyelectrolyte complex coacervate (PEC) initially containing equal moles of the cationic and anionic monomers absorbs a large excess of one type of polyelectrolyte species, is predicted using a recently developed thermodynamic model describing complexation through a combination of reversible ion binding on the chains and long-range electrostatic correlations. We show that overcharging is favored roughly equally by the translational entropy of released counterions and the binding entropy of polyelectrolytes in the polyelectrolyte complex, thus helping resolve competing explanations for overcharging in the literature. We find that the extent of overcharging is non-monotonic in the concentration of added salt and increases with both strength of ion-pairing between polyions and chain hydrophobicity. The predicted extent of overcharging of the PEC is directly compared with that of multilayers made of poly(diallyldimethylammonium), PDADMA, and poly(styrene-sulfonate), PSS, overcompensated by the polycation in two different salts: KBr and NaCl. Accounting for the specificity of salt ion interactions with the polyelectrolytes, we find good qualitative agreement between theory and experiment.

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.

Forward Flux Sampling of Polymer Desorption Paths from a Solid Surface into Dilute Solution

We compute desorption rates for isolated polymers adsorbed to a solid wall with a rare event sampling technique called multilevel splitting, also known as forward flux sampling. We interpret computed rates with theories based on the conjecture that the product tdesDRg2 of the desorption time tdes and diffusivity D divided by squared radius of gyration Rg scales with exp(h/Rg) where h is the equilibrium ratio of adsorbed surface concentration of polymer Γ to bulk concentration of polymer c. As the polymer-wall interaction energy is increased, the slope of lntdesDRg2 vs. NVMFkBT nearly approaches unity, as expected for strongly-adsorbing chains, where N is the degree of polymerization and VMF is the height-averaged monomer-wall interaction energy for a strongly adsorbed chain. However, we also find that this scaling law is only accurate when adsorption strength per monomer exceeds a threshold value on the order of 0.3-0.5 kBT for a freely jointed chain without or with excluded volume effects. Below the critical value, we observe that tdesDRg2 becomes nearly constant with N, so that tdes∝Nα, with α≈2. This suggests a crossover from "strong" detachment-controlled to a "weak" diffusion-controlled desorption rate as VMF/kBT drops below some threshold. These results may partially explain experimental data, that in some cases show "strong" exponential dependence of desorption time on chain length, while in others a "weak" power-law dependence is found. However, in the "strong" adsorption case, our results suggest much longer desorption times than those measured, while the reverse is true in the weak adsorption limit. We discuss possible reasons for these discrepancies.

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.

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.

A transport model and constitutive equation for oppositely charged polyelectrolyte mixtures with application to layer-by-layer assembly

We develop a general framework for transport of polyions, solvent and salt, with intended application to Layer-by-Layer (LbL) assembly of polyelectrolyte monolayers (PEMs). The formulation for the first time includes electrostatics, chemical potential gradients, and mechanical stress gradients as driving forces for mass transport. The general model allows all species to be mobile throughout the process and avoids the assumptions of stepwise instantaneous equilibrium and/or immobilized structures typical of previous approaches, while reducing to these models in appropriate limits. A simple constitutive equation is derived for a mixture of oppositely charged polyelectrolytes that accounts for network strand dilution and cross-chain ion pairing by appending reactive terms to the Smoluchowski probability diffusion equation for network strand end-to-end vectors. The resulting general framework encompasses the Poisson equation describing the electrostatic potential distribution, an osmotic pressure balance, a stress constitutive equation, and a generalized flux law of polymer transport. The computational domain is split into a PEM phase and an external solution phase with an appropriate boundary condition derived for the interface between the two. The mobile species (water and small salt ions) are taken to be in a state of dynamic equilibrium with their distributions enslaved to the perturbations in the two polyion compositions. The proposed model captures the swelling response of PEM films to external solutions. For the first time, we studied the effects of the temporal evolution of electrostatic and stress distribution on the rate of chain loss and absorption during rinsing and dipping of an idealized and arbitrarily selected and rigid brush layer into external solutions. The temporal evolution provides a kinetic basis for the ability of LbL films to grow under conditions that thermodynamics alone suggests would cause them to be washed away and to account for partial desorption during washing. The proposed transport framework constitutes a solid basis for eventual quantitative modeling of LbL assembly and transport in polyion networks more generally.

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.

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.

A biocompatible betaine-functionalized polycation for coacervation

The aqueous nature of complex coacervates provides a biologically-relevant context for various therapeutic applications. In this sense, biological applications demand a corresponding level of biocompatibility from the polyelectrolytes that participate in complex coacervation. Continued development with naturally-occurring polyelectrolytes such as heparin and chitosan underscore such aims. Herein, we design a synthetic polycation, in which betaine is conjugated to a biodegradable polyester backbone. Betaine is a naturally-occurring methylated amino acid that is ubiquitously present in human plasma. Inspired by its vast range of benefits - including but not limited to anti-inflammation, anti-cancer, anti-bacterial, anti-oxidant, protein stabilization, and cardiovascular health - we aim to impart additional functionality to a polycation for eventual use in a complex coacervate with heparin. We report on its in vitro and in vivo biocompatibility, in vitro and in vivo effect on angiogenesis, in vitro effect on microbial growth, and ability to form complex coacervates with heparin.

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.

From polyelectrolyte complexes to polyelectrolyte multilayers: Electrostatic assembly, nanostructure, dynamics, and functional properties

Polyelectrolyte complexes (PECs) are three-dimensional macromolecular structures formed by association of oppositely charged polyelectrolytes in solution. Polyelectrolyte multilayers (PEMs) can be considered a special case of PECs prepared by layer-by-layer (LbL) assembly that involves sequential deposition of molecular-thick polyelectrolyte layers with nanoscale control over the size, shape, composition and internal organization. Although many functional PEMs with novel physical and chemical characteristics have been developed, the current practical applications of PEMs are limited to those that require only a few bilayers and are relatively easy to prepare. The viability of such engineered materials can be realized only after overcoming the scientific and engineering challenges of understanding the kinetics and transport phenomena involved in the multilayer growth and the factors governing their final structure, composition, and response to external stimuli. There is a great need to model PEMs and to connect PEM behavior with the characteristics of the PEC counterparts to allow for prediction of performance and better design of multilayered materials. This review focuses on the relationship between PEMs and PECs. The constitutive interactions, the thermodynamics and kinetics of polyelectrolyte complexation and PEM formation, PEC phase behavior, PEM growth, the internal structure and stability in PEMs and PECs, and their response to external stimuli are presented. Knowledge of such interactions and behavior can guide rapid fabrication of PEMs and can aid their applications as nanocomposites, coatings, nano-sized reactors, capsules, drug delivery systems, and in electrochemical and sensing devices. The challenges and opportunities in future research directions are also discussed.

Combined High Stretchability and Gas Barrier in Hydrogen-Bonded Multilayer Nanobrick Wall Thin Films

Hydrogen-bonded multilayer thin films are very stretchable, but their gas barrier properties are modest compared to more traditional ionically bonded assemblies. In an effort to improve the gas barrier of poly(ethylene oxide) (PEO)-poly(acrylic acid) (PAA) multilayer films without sacrificing stretchability, montmorillonite (MMT) clay platelets were combined with PAA and alternately deposited with PEO. A ten-bilayer PEO/PAA+MMT film (432 nm thick), deposited on a 1 mm PU substrate, resulted in a 54× reduction in oxygen transmission rate after exposure to a 20% strain. This system is the best combination of stretchability and gas barrier ever reported.

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.

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.

Early stage kinetics of polyelectrolyte complex coacervation monitored through stopped-flow light scattering

Polyelectrolyte complexes (PECs) between poly(acrylic acid) (PAA) and poly(diallyldimethylammonium chloride) (PDADMAC), a model system forming coacervate particles via electrostatic interaction at pH 10, were prepared by a stopped-flow (SF) fast mixing technique at different mixing charge ratios (z) and ionic strengths. Both PEC final morphologies prepared by either SF or manual one-shot mixing are similar at bench time. In situ light scattering combined with the SF technique pointed-out, however, the presence of three distinct early stage kinetic behaviors in the formation of PECs. The first stage observed at low z is ascribed to the relaxation/reorganization of soluble PECs. At higher z or in the presence of salt, a second stage is found corresponding to the aggregation and/or rearrangement of small soluble PECs into larger structures. Redistribution of excess charges among those PECs produces some neutral condensed coacervate droplets as well, coexisting with PECs in a wide range of mixing ratios. Finally, a last process featured with bell-shaped curves indicates the full coacervation that quickens while approaching charge neutrality and/or at higher ionic strength.