Structure and Dynamics of Hybrid Colloid-Polyelectrolyte Coacervates

We develop a scaling theory for the structure and dynamics of "hybrid" complex coacervates formed from linear polyelectrolytes (PEs) and oppositely charged spherical colloids, such as globular proteins, solid nanoparticles, or spherical micelles of ionic surfactants. At low concentrations, in stoichiometric solutions, PEs adsorb at the colloids to form electrically neutral finite-size complexes. These clusters attract each other through bridging between the adsorbed PE layers. Above a threshold concentration, macroscopic phase separation sets in. The coacervate internal structure is defined by (i) the adsorption strength and (ii) the ratio of the resulting shell thickness to the colloid radius, H/R. A scaling diagram of different coacervate regimes is constructed in terms of the colloid charge and its radius for Θ and athermal solvents. For high charges of the colloids, the shell is thick, H ≫ R, and most of the volume of the coacervate is occupied by PEs, which determine its osmotic and rheological properties. The average density of hybrid coacervates exceeds that of their PE-PE counterparts and increases with nanoparticle charge, Q. At the same time, their osmotic moduli remain equal, and the surface tension of hybrid coacervates is lower, which is a consequence of the shell's inhomogeneous density decreasing with the distance from the colloid surface. When charge correlations are weak, hybrid coacervates remain liquid and follow Rouse/reptation dynamics with a Q-dependent viscosity, η Rouse ∼ Q 4/5 and η rep ∼ Q 28/15 for a Θ solvent. For an athermal solvent, these exponents are equal to 0.89 and 2.68, respectively. The diffusion coefficients of colloids are predicted to be strongly decreasing functions of their radius and charge. Our results on how Q affects the threshold coacervation concentration and colloidal dynamics in condensed phases are consistent with experimental observations for in vitro and in vivo studies of coacervation between supercationic green fluorescent proteins (GFPs) and RNA.

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.

Driving force and pathway in polyelectrolyte complex coacervation

There is notable discrepancy between experiments and coarse-grained model studies regarding the thermodynamic driving force in polyelectrolyte complex coacervation: experiments find the free energy change to be dominated by entropy, while simulations using coarse-grained models with implicit solvent usually report a large, even dominant energetic contribution in systems with weak to intermediate electrostatic strength. Here, using coarse-grained, implicit-solvent molecular dynamics simulation combined with thermodynamic analysis, we study the potential of mean force (PMF) in the two key stages on the coacervation pathway for symmetric polyelectrolyte mixtures: polycation-polyanion complexation and polyion pair-pair condensation. We show that the temperature dependence in the dielectric constant of water gives rise to a substantial entropic contribution in the electrostatic interaction. By accounting for this electrostatic entropy, which is due to solvent reorganization, we find that under common conditions (monovalent ions, room temperature) for aqueous systems, both stages are strongly entropy-driven with negligible or even unfavorable energetic contributions, consistent with experimental results. Furthermore, for weak to intermediate electrostatic strengths, this electrostatic entropy, rather than the counterion-release entropy, is the primary entropy contribution. From the calculated PMF, we find that the supernatant phase consists predominantly of polyion pairs with vanishingly small concentration of bare polyelectrolytes, and we provide an estimate of the spinodal of the supernatant phase. Finally, we show that prior to contact, two neutral polyion pairs weakly attract each other by mutually induced polarization, providing the initial driving force for the fusion of the pairs.

Wetting behavior of polyelectrolyte complex coacervates on solid surfaces

The wetting behavior of complex coacervates underpins their use in many emerging applications of surface science, particularly wet adhesives and coatings. Many factors dictate if a coacervate phase will condense on a solid surface, including solution conditions, the nature of the polymer-substrate interaction, and the underlying supernatant-coacervate bulk phase behavior. In this work, we use a simple inhomogeneous mean-field theory to study the wetting behavior of complex coacervates on solid surfaces both off-coexistence (wetting transitions) and on-coexistence (contact angles). We focus on the effects of salt concentration, the polycation/polyanion surface affinity, and the applied electrostatic potential on the wettability. We find that the coacervate generally wets the surface via a first order wetting transition with second order transitions possible above a surface critical point. Applying an electrostatic potential to a solid surface always improves the surface wettability when the polycation/polyanion-substrate interaction is symmetric. For asymmetric surface affinity, the wettability has a nonmonotonic dependence with the applied potential. We use simple scaling and thermodynamic arguments to explain our results.

Modification of Polydiallyldimethylammonium Chloride with Sodium Polystyrenesulfonate Dramatically Changes the Resistance of Polymer-Based Coatings towards Wash-Off from Both Hydrophilic and Hydrophobic Surfaces

Polymer coatings based on polycations represent a perspective class of protective antimicrobial coatings. Polydiallyldimethylammonium chloride (PDADMAC) and its water-soluble complexes with sodium polystyrenesulfonate (PSS) were studied by means of dynamic light-scattering, laser microelectrophoresis and turbidimetry. It was shown that addition of six mol.% of polyanion to polycation results in formation of interpolyelectrolyte complex (IPEC) that was stable towards phase separation in water-salt media with a concentration of salts (NaCl, CaCl₂, Na₂SO₄, MgSO₄) up to 0.5 M. Most of the polyelectrolyte coatings are made by layer-by-layer deposition. The utilization of water-soluble IPEC for the direct deposition on the surface was studied. The coatings from the PDADMAC and the PSS/PDADMAC complex were formed on the surfaces of hydrophilic glass and hydrophobic polyvinylchloride. It was found that formation IPEC allows one to increase the stability of the coating towards wash-off with water in comparison to individual PDADMAC coating on both types of substrates. The visualization of the coatings was performed by atomic force microscopy and scanning electron microscopy.

Molecular Mass Dependence of Interfacial Tension in Complex Coacervation

The interfacial tension of coacervates, the liquidlike phase composed of oppositely charged polymers that coexists at equilibrium with a supernatant, forms the basis for multiple technologies. Here we present a comprehensive set of experiments and molecular dynamics simulations to probe the effect of molecular mass on interfacial tension γ, far from the critical point, and derive γ=γ_{∞}(1-h/N), where N is the degree of polymerization, γ_{∞} is the infinite molecular mass limit, and h is a constant that physically corresponds to the number of monomers of one chain within the coacervate correlation volume.

Spatiotemporal Formation and Growth Kinetics of Polyelectrolyte Complex Micelles with Millisecond Resolution

We have directly observed the in situ self-assembly kinetics of polyelectrolyte complex (PEC) micelles by synchrotron time-resolved small-angle X-ray scattering, equipped with a stopped-flow device that provides millisecond temporal resolution. A synthesized neutral-charged diblock polycation and homopolyanion that we have previously investigated as a model charge-matched, core-shell micelle system were selected for this work. The initial micellization of the oppositely charged polyelectrolytes was completed within the dead time of mixing of 100 ms, followed by micelle growth and equilibration up to several seconds. By combining the structural evolution of the radius of gyration (R_g) with complementary molecular dynamics simulations, we show how the self-assemblies evolve incrementally in size over time through a two-step kinetic process: first, oppositely charged polyelectrolyte chains pair to form nascent aggregates that immediately assemble into spherical micelles, and second, these PEC micelles grow into larger micellar entities. This work has determined one possible kinetic pathway for the initial formation of PEC micelles, which provides useful physical insights for increasing fundamental understanding self-assembly dynamics, driven by polyelectrolyte complexation that occurs on ultrafast time scales.

Ion Pairing and the Structure of Gel Coacervates

A scaling model for the structure of coacervates is presented for mixtures of oppositely-charged polyelectrolytes of both symmetric and asymmetric charge-densities for different degrees of electrostatic strength and levels of added salt. At low electrostatic strengths, weak coacervates, with the energy of electrostatic interactions between charges less than the thermal energy, k B T, are liquid. At higher electrostatic strengths, strong coacervates are gels with crosslinks formed by ion pairs of opposite charges bound to each other with energy higher than k B T. Charge-symmetric coacervates are formed for mixtures of oppositely-charged polyelectrolytes with equal and opposite charge-densities. While charge-symmetric weak coacervates form a semidilute polymer solution with a correlation length equal to the electrostatic blob size, charge-symmetric strong coacervates form reversible gels with a correlation length on the order of the distance between bound ion pairs. Charge-asymmetric coacervates are formed from mixtures of oppositely-charged polyelectrolytes with different charge-densities. While charge-asymmetric weak coacervates form double solutions with two correlation lengths and qualitatively different chain conformations of polycations and polyanions, charge-asymmetric strong coacervates form bottlebrush and star-like gels. Unlike liquid coacervates, for which an increase in the concentration of added salt screens electrostatic interactions, causing structural rearrangement and eventually leads to their dissolution, the salt does not affect the structure of strong coacervates until ion pairs dissociate and the gel disperses.

Unusual Structures of Interpolyelectrolyte Complexes: Vesicles and Perforated Vesicles

By means of computer simulation and analytical theory, we first demonstrated that the interpolyelectrolyte complexes in dilute solution can spontaneously form hollow spherical particles with thin continuous shells (vesicles) or with porous shells (perforated vesicles) if the polyions forming the complex differ in their affinity for the solvent. The solvent was considered good for the nonionic groups of one macroion and its quality was varied for the nonionic groups of the other macroion. It was found that if the electrostatic interactions are weak compared to the attraction induced by the hydrophobicity of the monomer units, the complex in poor solvent tends to form "dense core-loose shell" structures of different shapes. The strong electrostatic interactions favor the formation of the layered, the hollow, and the filled structured morphologies with the strongly segregated macroions. Vesicles with perforated walls were distinguished as the intermediate between the vesicular and the structured solid morphologies. The order parameter based on the spherical harmonics expansion was introduced to calculate the pore distribution in the perforated vesicles depending on the solvent quality. The conditions of the core-shell and hollow vesicular-like morphologies formation were determined theoretically via the calculations of their free energy. The results of the simulation and theoretical approaches are in good agreement.

Interpolyelectrolyte Complex Dissociation vs Polyelectrolyte Desorption from Oppositely Charged Surface upon Salt Addition

The structure of complexes formed by oppositely charged polyelectrolytes and adsorbed layers on charged surfaces is sensitive to low-molecular-weight salt. Furthermore, if the concentration exceeds some threshold value, the complexes and adsorbed chains can be "dissolved". This is due to the screening of the electrostatic interactions between charged units. In the current paper, we perform a comparative analysis of "dissolution" (dissociation) of complexes and layers upon addition of salt. For this, the conventional Brownian dynamics of computer simulations is used. We demonstrate that the complex based on linear chains dissociates at lower salt concentration than that required for desorption of equivalent chains from an oppositely charged surface. The physical reason is the difference in the symmetry of the electric field, which binds the chains into the complex (layer). In the salt-free regime, the intensity of the electric field (and attractive force) between two linear chains decays with the distance R between them, like for two spherical objects, ∼R^-2, if R is bigger than the characteristic size of the chain. On the contrary, the attractive force of the chain to the infinite surface does not depend on the distance to the surface (the electric field is constant). Therefore, if attractive forces in the condensed states of the two systems are equal, one needs to add more salt to screen the constant force than the decaying one. The computer simulation results on the adsorption of the chains were compared with the experimental data obtained for adsorption of cationic poly(4-vinylpyridine) on the surface of anionic liposomes. Good quantitative agreement was achieved.

Complex Coacervation in Asymmetric Solutions of Polycation and Polyanion

We study coacervation upon mixing two aqueous solutions of polyelectrolytes (PEs) with opposite charge, by considering asymmetric effects of PE composition and charge valency. The phase behavior, interfacial structure, and coacervate composition are investigated by a classical density-functional theory. We find two types of coacervation that are different in their density. Supernatant phase in low-density coacervation (LDCA) fully consists of small ions, while in high-density coacervation (HDCA) it contains a considerable amount of PE chains. Asymmetric PE composition could generate an electric double layer at the interface of coacervate. For HDCA, ion density changes monotonically, while for LDCA it shows a global minimum at the double layer, giving a low tension value. Charged species of high charge valency enhance the existence of double layer. Our results explained the coacervate structure of low interfacial tension, which is important for experiments and industrial applications.

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.

Controlling Complex Coacervation via Random Polyelectrolyte Sequences

The utilization of chemical sequence control in polymeric materials is key to enabling material design on par with biomacromolecular systems. One important avenue for scalable sequence-controlled polymers leverages the random copolymerization of distinct monomers, with the statistical distribution of the monomeric sequence arising from reaction kinetics following a first-order Markov process. Here we utilize the framework of the random phase approximation (RPA) to develop a theory for the phase behavior of symmetric polyelectrolyte coacervates whose chemical sequences are dictated by simple statistical distributions. We find that a high charge "blockiness" within the random sequences favors the formation of denser and more salt-resistant coacervates while simultaneously increasing the width of the two-phase region. We trace these physical effects to the increased cooperativity of Coulomb interactions that results from increased charge blockiness in oppositely charged polyelectrolytes.

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.

An anionic shell shields a cationic core allowing for uptake and release of polyelectrolytes within core-shell responsive microgels

To realize carriers for drug delivery, cationic containers are required for anionic guests. Nevertheless, the toxicity of cationic carriers limits their practical use. In this study, we investigate a model system of polyampholyte N-isopropylacrylamide (NIPAM)-based microgels with a cationic core and an anionic shell to study whether the presence of a negative shell allows the cationic core to be shielded while still enabling the uptake and release of the anionic guest polyelectrolytes. These microgels are loaded with polystyrene sulfonate of different molecular weights to investigate the influence of their chain length on the uptake and release process. By means of small-angle neutron scattering, we evaluate the spatial distribution of polystyrene sulfonate within the microgels. The guest molecules are located in different parts of the core-shell microgels depending on their size. By combining these scattering results with UV-vis spectroscopy, electrophoretic mobility and potentiometric titrations we gain complementary results to investigate the uptake and release process of polyelectrolytes in polyampholyte core-shell microgels. Moreover, Brownian molecular dynamic simulations are performed to compare the experimental and theoretical results of this model. Our findings demonstrate that the presence of a shell still enables efficient uptake of guest molecules into the cationic core. These anionic guest molecules can be released through an anionic shell. Furthermore, the presence of a shell enhances the stability of the microgel-polyelectrolyte complexes with respect to the cationic precursor microgel alone.