Surface-Immobilized Interpolyelectrolyte Complexes Formed by Polyelectrolyte Brushes.

A scaling theory of interaction and complex formation between planar polyelectrolyte (PE) brush and oppositely charged mobile linear PEs is developed. Counterion release is found to be the main driving force for the complexation. An interpolyelectrolyte coacervate complex (IPEC) between the brush and oppositely charged mobile PEs is formed at moderate grafting density and low salt concentration. At higher grafting density mobile chains penetrate the brush, but the brush structure is controlled by the balance between entropic elasticity and nonelectrostatic short-range interactions, as happens in a neutral brush. An increase in salt concentration beyond the theoretically predicted threshold leads to the release of the guest polyions from the brush. For brushes with moderate grafting density, complexation with oppositely charged guest polyions is predicted to trigger lateral microphase separation and formation of the finite-size surface IPEC clusters. Power law dependencies for the cluster dimensions on the brush grafting density, PE length, and salt concentration are provided.

Structure and Dynamics of Hybrid Colloid-Polyelectrolyte Coacervates: Insights from Molecular Simulations.

Electrostatic interactions in polymeric systems are responsible for a wide range of liquid-liquid phase transitions that are of importance for biology and materials science. Such transitions are referred to as complex coacervation, and recent studies have sought to understand the underlying physics and chemistry. Most theoretical and simulation efforts to date have focused on oppositely charged linear polyelectrolytes, which adopt nearly ideal-coil conformations in the condensed phase. However, when one of the coacervate components is a globular protein, a better model of complexation should replace one of the species with a spherical charged particle or colloid. In this work, we perform coarse-grained simulations of colloid-polyelectrolyte coacervation using a spherical model for the colloid. Simulation results indicate that the electroneutral cell of the resulting (hybrid) coacervates consists of a polyelectrolyte layer adsorbed on the colloid. Power laws for the structure and the density of the condensed phase, which are extracted from simulations, are found to be consistent with the adsorption-based scaling theory of hybrid coacervation. The coacervates remain amorphous (disordered) at a moderate colloid charge, Q, while an intra-coacervate colloidal crystal is formed above a certain threshold, at Q > Q*. In the disordered coacervate, if Q is sufficiently low, colloids diffuse as neutral nonsticky nanoparticles in the semidilute polymer solution. For higher Q, adsorption is strong and colloids become effectively sticky. Our findings are relevant for the coacervation of polyelectrolytes with proteins, spherical micelles of ionic surfactants, and solid organic or inorganic nanoparticles.

Scattering evidence of positional charge correlations in polyelectrolyte complexes.

Polyelectrolyte complexation plays an important role in materials science and biology. The internal structure of the resultant polyelectrolyte complex (PEC) phase dictates properties such as physical state, response to external stimuli, and dynamics. Small-angle scattering experiments with X-rays and neutrons have revealed structural similarities between PECs and semidilute solutions of neutral polymers, where the total scattering function exhibits an Ornstein-Zernike form. In spite of consensus among different theoretical predictions, the existence of positional correlations between polyanion and polycation charges has not been confirmed experimentally. Here, we present small-angle neutron scattering profiles where the polycation scattering length density is matched to that of the solvent to extract positional correlations among anionic monomers. The polyanion scattering functions exhibit a peak at the inverse polymer screening radius of Coulomb interactions, q* ≈ 0.2 Å-1. This peak, attributed to Coulomb repulsions between the fragments of polyanions and their attractions to polycations, is even more pronounced in the calculated charge scattering function that quantifies positional correlations of all polymer charges within the PEC. Screening of electrostatic interactions by adding salt leads to the gradual disappearance of this correlation peak, and the scattering functions regain an Ornstein-Zernike form. Experimental scattering results are consistent with those calculated from the random phase approximation, a scaling analysis, and molecular simulations.

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.

Sequence Blockiness Controls the Structure of Polyampholyte Necklaces.

A scaling theory of statistical (Markov) polyampholytes is developed to understand how sequence correlations, that is, the blockiness of positive and negative charges, influences conformational behavior. An increase in the charge patchiness leads to stronger correlation attractions between oppositely charged monomers, but simultaneously, it creates a higher charge imbalance in the polyampholyte. A competition between effective short-range attractions and long-range Coulomb repulsions induces globular, pearl-necklace, or fully stretched chain conformations, depending on the average length of the block of like charges. The necklace structure and the underlying distribution of the net charge are also controlled by the sequence. Sufficiently long blocks allow for charge migration from globular beads (pearls) to strings, thereby providing a nonmonotonic change in the number of necklace beads as the blockiness increases. The sequence-dependent structure of polyampholyte necklaces is confirmed by molecular dynamics simulations. The findings presented here provide a framework for understanding the sequence-encoded conformations of synthetic polyampholytes and intrinsically disordered proteins (IDPs).

Polyelectrolyte Complex Coacervation across a Broad Range of Charge Densities.

Polyelectrolyte complex coacervates of homologous (co)polyelectrolytes with a near-ideally random distribution of a charged and neutral ethylene oxide comonomer were synthesized. The unique platform provided by these building blocks enabled an investigation of the phase behavior across charge fractions 0.10 ≤ f ≤ 1.0. Experimental phase diagrams for f = 0.30-1.0 were obtained from thermogravimetric analysis of complex and supernatant phases and contrasted with molecular dynamics simulations and theoretical scaling laws. At intermediate to high f, a dependence of polymer weight fraction in the salt-free coacervate phase (w P,c) of w P,c ∼ f 0.37±0.01 was extracted; this trend was in good agreement with accompanying simulation predictions. Below f = 0.50, w P,c was found to decrease more dramatically, qualitatively in line with theory and simulations predicting an exponent of 2/3 at f ≤ 0.25. Preferential salt partitioning to either coacervate or supernatant was found to be dictated by the chemistry of the constituent (co)polyelectrolytes.

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.

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.

Temperature-Induced Re-Entrant Morphological Transitions in Block-Copolymer Micelles.

Using a combination of a mean-field theoretical method and the numerical Scheutjens-Fleer self-consistent field approach, we predict that it is possible to have re-entrant morphological transitions in nanostructures of diblock copolymers upon variation in temperature-mediated solubility of the associating blocks. This peculiar effect is explained by the different rates in variation of the density of the collapsed core domains and the corresponding interfacial energy as a function of the temperature. The theoretical findings are supported by existing experimental observations of reversed sequences of the morphological transitions occurring upon temperature variation in solutions of amphiphilic block copolymers.

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.

Explicit description of complexation between oppositely charged polyelectrolytes as an advantage of the random phase approximation over the scaling approach.

A polyelectrolyte complex (PEC) of oppositely charged linear chains is considered within the Random Phase Approximation (RPA). We study the salt-free case and use the continuous model assuming a homogeneous distribution of the charges throughout the polyions. The RPA correction to the PEC free energy is renormalized via subtraction of polyion self-energy in order to find the correlation free energy of the complex. An analogous procedure is usually carried out in the case of the Debye-Hückel (DH) plasma (a gas of point-like ions), where the infinite self-energy of point-like charges is subtracted from the diverging RPA correction. The only distinction is that in the PEC both the RPA correction and chain self-energy of connected like charges are convergent. This renormalization allows us to demonstrate that the correlation free energy of the PEC is negative, as could be expected, while the scaling approach postulates rather than proving the negative sign of the energy of interactions between the blobs. We also demonstrate that the increasing concentration of oppositely charged polyions in the solution first results in the formation of neutral globules of the PEC consisting of two polyions as soon as the concentration reaches a certain threshold value, cgl, whereas solution macroscopic phase separation (precipitation of globules) occurs at a much higher concentration, ccoac, ccoac ≫ cgl. Partitioning of polyions between different states is calculated and analytical dependencies of cgl and ccoac on the polyion length, degree of ionization and solvent polarity are found.

Two regions of microphase separation in ion-containing polymer solutions.

The phenomenon of spinodal decomposition in weakly charged polyelectrolyte solutions is studied theoretically within the random phase approximation. A novel feature of the theoretical approach is that it accounts for the effects of ionic association, i.e. ion pair and multiplet formation between counterions and ions in polymer chains, as well as the dependence of local dielectric permittivity on the polymer volume fraction Φ. The main focus is on the spinodal instability of polyelectrolyte solutions towards microscopic phase separation. It has been shown that increasing the binding energy of ions decreases the classical microphase separation region (possible at low polymer concentrations) due to the effective neutralization of the chains. A qualitatively new type of microphase separation is found in the presence of a dielectric mismatch between polymer and solvent. This new branch of microphase separation is realized at high polymer concentrations where ion association processes are the most pronounced. Typical microstructures are shown to have a period of a few nanometers like in ionomers. The driving force for the microphase formation of a new type is more favourable ion association in polymer-rich domains where ionomer-type behavior takes place. Effective attraction due to ion association promotes microscopic as well as macroscopic phase separation, even under good solvent conditions for uncharged monomer units of polymer chains. Polyelectrolyte-type behavior at low Φ and ionomer-type behavior at high Φ result in the presence of two critical points on the phase diagrams of polyelectrolyte solutions as well as two separate regions of possible microscopic structuring. Our predictions on the new type of microphase separation are supported by experimental data on polymer solutions, membranes and gels.

Communication: Light driven remote control of microgels' size in the presence of photosensitive surfactant: Complete phase diagram.

Here we report on a light triggered remote control of microgel size in the presence of photosensitive surfactant. The hydrophobic tail of the cationic surfactant contains azobenzene group that undergoes a reversible photo-isomerization reaction from a trans- to a cis-state accompanied by a change in the hydrophobicity of the surfactant. We have investigated light assisted behaviour and the complex formation of the microgels with azobenzene containing surfactant over the broad concentrational range starting far below and exceeding several times of the critical micelle concentration (CMC). At small surfactant concentration in solution (far below CMC), the surfactant in the trans-state accommodates within the microgel causing its compaction, while the cis-isomer desorbs out of microgel resulting in its swelling. The process of the microgel size change can be described as swelling on UV irradiation (trans-cis isomerization) and shrinking on irradiation with blue light (cis-trans isomerization). However, at the surfactant concentrations larger than CMC, the opposite behaviour is observed: the microgel swells on blue irradiation and shrinks during exposure to UV light. We explain this behaviour theoretically taking into account isomer dependent micellization of surfactant within the microgels.

Photosensitive microgels containing azobenzene surfactants of different charges.

We report on light sensitive microgel particles that can change their volume reversibly in response to illumination with light of different wavelengths. To make the anionic microgels photosensitive we add surfactants with a positively charged polyamine head group and an azobenzene containing tail. Upon illumination, azobenzene undergoes a reversible photo-isomerization reaction from a trans- to a cis-state accompanied by a change in the hydrophobicity of the surfactant. Depending on the isomerization state, the surfactant molecules are either accommodated within the microgel (trans-state) resulting in its shrinkage or desorbed back into water (cis-isomer) letting the microgel swell. We have studied three surfactants differing in the number of amino groups, so that the number of charges of the surfactant head varies between 1 and 3. We have found experimentally and theoretically that the surfactant concentration needed for microgel compaction increases with decreasing number of charges of the head group. Utilization of polyamine azobenzene containing surfactants for the light triggered remote control of the microgel size opens up a possibility for applications of light responsive microgels as drug carriers in biology and medicine.

A polymer microgel at a liquid-liquid interface: theory vs. computer simulations.

We propose a mean-field theory and dissipative particle dynamics (DPD) simulations of swelling and collapse of a polymer microgel adsorbed at the interface of two immiscible liquids (A and B). The microgel reveals surface activity and lowers A-B interfacial tension. Attempting to occupy as large an interfacial area as possible, the microgel undergoes anisotropic deformation and adopts a flattened shape. Spreading over the interface is restricted by polymer subchain elasticity. The equilibrium shape of the microgel at the interface depends on its size. Small microgels are shown to be more oblate than the larger microgels. Increasing microgel cross-link density results in stronger reduction of the surface tension and weaker flattening. As the degree of immiscibility of A and B liquids increases, the microgel volume changes in a non-monotonous fashion: the microgel contraction at moderate immiscibility of A and B liquids is followed by its swelling at high incompatibility of the liquids. The segregation regime of the liquids within and outside the microgel is different. Being segregated outside the microgel, the liquids can be fully (homogeneously) mixed or weakly segregated within it. The density profiles of the liquids and the polymer were plotted under different conditions. The theoretical and the DPD simulation results are in good agreement. We hope that our findings will be useful for the design of stimuli responsive emulsions, which are stabilized by the microgel particles, as well as for their practical applications, for instance, in biocatalysis.

Polymer gels with associating side chains and their interaction with surfactants.

Conformational behaviour of hydrophobically modified (HM) polymer gels in solutions of nonionic surfactants is studied theoretically. A HM gel contains hydrophobic side chains (stickers) grafted to its subchains. Hydrophobic stickers are capable to aggregate into joint micelles with surfactant molecules. Micelles containing more than one sticker serve as additional physical cross-links of the network, and their formation causes gel shrinking. In the proposed theoretical model, the interior of the gel/surfactant complex is treated as an array of densely packed spherical polymer brushes consisting of gel subchains tethered to the surface of the spherical sticker/surfactant micelles. Effect of stickers length and grafting density, surfactant concentration and hydrophobicity on gel swelling as well as on hydrophobic association inside it is analyzed. It is shown that increasing surfactant concentration can result in a gel collapse, which is caused by surfactant-induced hydrophobic aggregation of stickers, and a successive gel reswelling. The latter should be attributed to a growing fraction of surfactants in joint aggregates and, hence, increasing number of micelles containing only one sticker and not participating in gel physical cross-linking. In polyelectrolyte (PE) gels hydrophobic aggregation is opposed by osmotic pressure of mobile counterions, so that at some critical ionization degree hydrophobic association is completely suppressed. Hydrophobic modification of polymers is shown to open new ways for controlling gel responsiveness. In particular, it is discussed that incorporation of photosensitive groups into gel subchains and/or surfactant tail could give a possibility to vary the gel volume by light. Since hydrophobic aggregation regularities in gels and solutions are common, we hope our findings will be useful for design of polymer based self-healing materials as well.

Mixing of Two Immiscible Liquids within the Polymer Microgel Adsorbed at Their Interface.

We report on the behavior of two immiscible liquids within polymer microgel adsorbed at their interface. By means of dissipative particle dynamics (DPD) simulations and theoretical analysis in the framework of the Flory-Huggins (FH) lattice theory, we demonstrate that the microgel acts as a "compatibilizer" of these liquids: their miscibility within the microgel increases considerably. If the incompatibility of the liquids is moderate, although strong enough to induce phase separation in their 1:1 composition, they form homogeneous mixture in the microgel interior. The mixture of highly incompatible liquids undergoes separation into two (micro)phases within the microgel likewise out of it; however, the segregation regime is weaker and the concentration profiles are characterized by a weaker decay (gradient) in comparison with those of two pure liquids. The enhanced miscibility is a result of the screening of unfavorable interactions between unlike liquid molecules by polymer subchains. We have shown that better miscibility of the liquids is achieved with densely cross-linked microgels. Our findings are very perspective for many applications where immiscible species have to be mixed at interfaces (like in heterogeneous catalysis).

Communication: Intraparticle segregation of structurally homogeneous polyelectrolyte microgels caused by long-range Coulomb repulsion.

Structurally homogeneous polyelectrolyte microgels in dilute aqueous solutions are shown to exhibit inhomogeneous density profile including intraparticle "phase" coexistence of hollow core and dense "skin." This effect is a consequence of long-range Coulomb repulsion of charged groups which appear because of entropy-driven escape of monovalent counterions into the outer solvent. Excess of the charged groups at the periphery of the microgel particle reduces electrostatic energy and overall free energy of the system despite a penalty in the elastic free energy of strongly stretched subchains in the hole. This finding can serve as additional tool controlling encapsulation, transport, and release of high- and low-molecular-weight species in processes where the microgels are used as delivery systems.

Polymer micelles with hydrophobic core and ionic amphiphilic corona. 1. Statistical distribution of charged and nonpolar units in corona.

Polymer micelles with hydrophobic polystyrene (PS) core and ionic amphiphilic corona from charged N-ethyl-4-vinylpyridinium bromide (EVP) and uncharged 4-vinylpyridine (4VP) units spontaneously self-assembled from PS-block-poly(4VP-stat-EVP) macromolecules in mixed dimethylformamide/methanol/water solvent. The fraction of statistically distributed EVP units in corona-forming block is ß = [EVP]/([EVP]+[4VP]) = 0.3-1. Micelles were transferred into water via dialysis technique, and pH was adjusted to 9, where 4VP is insoluble. Structural characteristics of micelles were investigated both experimentally and theoretically as a function of corona composition ß. Methods of dynamic and static light scattering, electrophoretic mobility measurements, sedimentation velocity, transmission electron microscopy, and UV spectrophotometry were applied. All micelles possessed spherical morphology. The aggregation number, structure, and electrophoretic mobility of micelles changed in a jumplike manner near ß ~ 0.6-0.75. Below and above this region, micelle characteristics were constant or insignificantly changed upon ß. Theoretical dependencies for micelle aggregation number, corona dimensions, and fraction of small counterions outside corona versus ß were derived via minimization the micelle free energy, taking into account surface, volume, electrostatic, and elastic contributions of chain units and translational entropy of mobile counterions. Theoretical estimations also point onto a sharp structural transition at a certain corona composition. The abrupt reorganization of micelle structure at ß ~ 0.6-0.75 entails dramatic changes in micelle dispersion stability in the presence of NaCl or in the presence of oppositely charged polymeric (sodium polymethacrylate) or amphiphilic (sodium dodecyl sulfate) complexing agents.