Comparison of complex coacervate core micelles from two diblock copolymers or a single diblock copolymer with a polyelectrolyte

With light scattering titrations, we show that complex coacervate core micelles (C3Ms) form from a diblock copolymer with a polyelectrolyte block and either an oppositely charged polyelectrolyte, a diblock copolymer with an oppositely charged polyelectrolyte or a mixture of the two. The effect of added salt and pH on both types of C3Ms is investigated. The hydrodynamic radius of mixed C3Ms can be controlled by varying the percentage of oppositely charged polyelectrolyte or diblock copolymer. A simple core-shell model is used to interpret the results from light scattering, giving the same trends as the experiments for both the hydrodynamic radii and the relative scattering intensities. Temperature has only a small effect on the C3Ms. Isothermal titration calorimetry shows that the complexation is mainly driven by Coulombic attraction and by the entropy gain due to counterion release.     

Theory of competitive counterion adsorption on flexible polyelectrolytes: divalent salts

The counterion distribution around an isolated flexible polyelectrolyte in the presence of a divalent salt is evaluated using the adsorption model [M. Muthukumar, J. Chem. Phys. 120, 9343 (2004)] that considers the Bjerrum length, salt concentration, and local dielectric heterogeneity as physical variables in the system. Self-consistent calculations of effective charge and size of the polymer show that divalent counterions replace condensed monovalent counterions in competitive adsorption. The theory further predicts that at modest physical conditions for a flexible polyelectrolytes such as sodium polystyrene sulfonate in aqueous solutions polymer charge is compensated and reversed with increasing divalent salt. Consequently, the polyelectrolyte shrinks and reswells. Lower temperatures and higher degrees of dielectric heterogeneity between chain backbone and solvent enhance condensation of all species of ions. Complete diagrams of states for the effective charge calculated as functions of the Coulomb strength and salt concentration suggest that (a) overcharging requires a minimum Coulomb strength and (b) progressively higher presence of salt recharges the polymer due to either electrostatic screening (for low Coulomb strengths) or coion condensation (for high Coulomb strengths). Consideration of ion-bridging by divalent counterions leads to a first-order collapse of polyelectrolytes in modest presence of divalent salts and at higher Coulomb strengths. The authors' theoretical predictions are in agreement with the generic results from experiments and simulations.     

Interfacial tension in polyelectrolyte systems exhibiting associative liquid–liquid phase separation

A continued interest in polyelectrolyte phase diagrams guides the study of interfacial phenomena driven by polyelectrolyte complexation. The liquid–liquid interfaces formed by associative phase separation of oppositely charged synthetic and natural polyelectrolytes provide measurement challenges addressed by force-sensitive methods and deformed droplet retraction. The ultralow interfacial tension, typical of these systems, is sensitive to salt concentration and temperature and displays universal features described by mean-field theory. Several areas of fundamental development and novel applications of charge complexation for interfacial study and examples from membraneless organelles and biomolecular condensates are described.     

One‐Step Microfluidic Fabrication of Polyelectrolyte Microcapsules in Aqueous Conditions for Protein Release

We report a microfluidic approach for one‐step fabrication of polyelectrolyte microcapsules in aqueous conditions. Using two immiscible aqueous polymer solutions, we generate transient water‐in‐water‐in‐water double emulsion droplets and use them as templates to fabricate polyelectrolyte microcapsules. The capsule shell is formed by the complexation of oppositely charged polyelectrolytes at the immiscible interface. We find that attractive electrostatic interactions can significantly prolong the release of charged molecules. Moreover, we demonstrate the application of these microcapsules in encapsulation and release of proteins without impairing their biological activities. Our platform should benefit a wide range of applications that require encapsulation and sustained release of molecules in aqueous environments.     

Poisson-Boltzmann theory of the charge-induced adsorption of semi-flexible polyelectrolytes

A model is suggested for the structure of an adsorbed layer of a highly charged semi-flexible polyelectrolyte on a weakly charged surface of opposite charge sign. The adsorbed phase is thin, owing to the effective reversal of the charge sign of the surface upon adsorption, and ordered, owing to the high surface density of polyelectrolyte strands caused by the generally strong binding between polyelectrolyte and surface. The Poisson-Boltzmann equation for the electrostatic interaction between the array of adsorbed polyelectrolytes and the charged surface is solved for a cylindrical geometry, both numerically, using a finite element method, and analytically within the weak curvature limit under the assumption of excess monovalent salt. For small separations, repulsive surface polarization and counterion osmotic pressure effects dominate over the electrostatic attraction and the resulting electrostatic interaction curve shows a minimum at nonzero separations on the Angstrom scale. The equilibrium density of the adsorbed phase is obtained by minimizing the total free energy under the condition of equality of chemical potential and osmotic pressure of the polyelectrolyte in solution and in the adsorbed phase. For a wide range of ionic conditions and charge densities of the charged surface, the interstrand separation as predicted by the Poisson-Boltzmann model and the analytical theory closely agree. For low to moderate charge densities of the adsorbing surface, the interstrand spacing decreases as a function of the charge density of the charged surface. Above about 0.1 M excess monovalent salt, it is only weakly dependent on the ionic strength. At high charge densities of the adsorbing surface, the interstrand spacing increases with increasing ionic strength, in line with the experiments by Fang and Yang [J. Phys. Chem. B 101, 441 (1997)].     

Electrostatic free energy of weakly charged macromolecules in solution and intermacromolecular complexes consisting of oppositely charged polymers

When oppositely charged polyelectrolytes are mixed in water, attraction between oppositely charged groups may lead to the formation of polyelectrolyte complexes (associative phase separation, complex coacervation, interpolymer complexes). Theory is presented to describe the electrostatic free energy change when ionizable (annealed) (macro-)molecules form a macroscopic polyelectrolyte complex. The electrostatic free energy includes an electric term as well as a chemical term that is related to the dissociation of the ionic groups in the polymer. An example calculation for complexation of polyacid with polybase uses a cylindrical diffuse double layer model for free polymer in solution and electroneutrality within the complex and calculates the free energy of the system when the polymer is in solution or in a polyelectrolyte complex. Combined with a term for the nonelectrostatic free energy change upon complexation, a theoretical stability diagram is constructed that relates pH, salt concentration, and mixing ratio, which is in qualitative agreement with an experimental diagram obtained by Bungenberg de Jong (1949) for complex coacervation of arabic gum and gelatin. The theory furthermore explains the increased tendency toward phase separation when the polymer becomes more strongly charged and suggests that complexation of polyacid or polybase with zwitterionic polymer (e.g., protein) of the same charge sign (at the "wrong side" of the iso-electric point) may be due (in part) to an induced charge reversal of the protein.     

Proteins and polyelectrolytes: A charged relationship

We review the interaction of charged polymeric systems with proteins. In solutions of low ionic strength there are many examples of proteins attracted to polyelectrolytes even if both systems carry the same overall charge. This attractive interaction is widespread, having been observed for single polyelectrolyte chains as well as for polyelectrolytes grafted to surfaces (polyelectrolyte brushes) and charged polymeric networks. In all cases, adding salt weakens the interaction considerably. We discuss the suggestion that the attractive force at low salinity originates from the asymmetry of interaction between charged polymer segments and charged patches on the surface of the protein globule. This can be explained if the attractive force is mainly due to a counterion release force, i.e., the polyelectrolyte chains become the multivalent counterions for the patches of opposite charge localized on the surface of the proteins. We review a selection of simple models that lead to semi-quantitative estimates of this force as the function of salt concentration.     

Mixed systems of hydrophobically modified polyelectrolytes: controlling rheology by charge and hydrophobe stoichiometry and interaction strength

Rheology and phase separation were investigated for aqueous mixtures of two oppositely charged hydrophobically modified polyelectrolytes. The typical phase separation, normally seen for oppositely charged polymer mixtures, is dramatically reduced by the presence of hydrophobic modification, and phase separation is only detected close to the point of charge neutralization. While the two polyelectrolytes separately can give high viscosities and a gel-like behavior, a pronounced maximum in viscosity and storage modulus with the mixing ratio of the polyelectrolytes is observed; the maximum is located between the points of charge and hydrophobe stoichiometry and reflects a combination of hydrophobic and electrostatic association. Lowering the charge density of the anionic polymer leads to a strengthened association at first, but at lower charge densities there is a weakened association due to the onset of phase separation. The strength of the electrostatic interaction was modified by adding salt. Increased ionic strength can lead to phase separation and to increased or decreased viscosity depending on the polyelectrolyte mixing ratio.     

Simulation Study of the Conformational Properties of Diblock Polyelectrolytes in Salt Solutions

Coarse-grained molecular dynamics simulations are performed to understand the behavior of diblock polyelectrolytes in solutions of divalent salt by studying the conformations of chains over a wide range of salt concentrations. The polymer molecules are modeled as bead spring chains with different charged fractions and the counterions and salt ions are incorporated explicitly. Upon addition of a divalent salt, the salt cations replace the monovalent counterions, and the condensation of divalent salt cations onto the polyelectrolyte increases, and the chains favor to collapse. The condensation of ions changes with the salt concentration and depends on the charged fraction. Also, the degree of collapse at a given salt concentration changes with the increasing valency of the counterion due to the bridging effect. As a quantitative measure of the distribution of counterions around the polyelectrolyte chain, we study the radial distribution function between monomers on different polyelectrolytes and the counterions inside the counterion worm surrounding a polymer chain at different concentrations of the divalent salt. Our simulation results show a strong dependence of salt concentration on the conformational properties of diblock copolymers and indicate that it can tune the self-assembly behaviors of such charged polyelectrolyte block copolymers.     

Release of lysozyme from the branched polyelectrolyte-lysozyme complexation

On the basis of the discretely charged sphere model of lysozyme, the release behavior of lysozyme from the branched polyelectrolyte-lysozyme complexation is investigated by adding salt and changing the pH values of the solution. It is found that, with the increase of the salt ionic strength of the solution, the lysozymes are gradually released from the oppositely charged polyelectrolyte as a result of the screening of electrostatic attraction between the two ionic species by adding the salt. Interestingly, there exists a critical salt ionic strength at which all proteins are released from the branched polyelectrolyte, and the polyelectrolyte-protein complexation is broken completely. Beyond the critical value, the increase of the salt ionic strength causes self-association of the proteins released from the branched polyelectrolyte-protein complexation. The self-association of the protein is detrimental in biological systems. By calculating the second virial coefficient, we found that the optimal salt content for the dispersion of proteins coincides with the critical ionic strength, because the second virial coefficient reaches its maximum at the critical ionic strength. Similarly, increasing the pH value of the solution can also release the lysozymes from the polyelectrolyte, because the increase of pH value of the solution changes the charge distribution and net charge of the lysozyme, weakens the attraction between lysozymes mediated by polyelectrolyte, and finally leads to the dissolution of the complexation of branched polyelectrolyte with lysozymes in strong alkaline solution. In addition, by exploring the effect of architecture of the polyelectrolyte on the release behavior of proteins, we found that it is more difficult to release proteins from the branched polyelectrolyte than from the linear polyelectrolyte.     

Fluorescence and ESR studies of the conformational behavior of oppositely charged polyelectrolytes at solid/liquid interfaces

The conformational behavior of oppositely charged polyelectrolytes on alumina in solutions was investigated by means of excimer fluorescence and electron spin resonance spectroscopy using maleic acid-propene copolymer labeled with pyrene or TEMPO. It was found that the ability of the polyanion at the surface for conformational rearrangements is strongly influenced by the constraints of the adsorbed state that restrict its complexation. Polyelectrolyte complexes (PEC) formed by mixing of the oppositely charged polyelectrolytes exhibited extreme coiling due to the screening of the charged groups. The polyelectrolytes undergo spreading during the adsorption process due to the electrostatic attraction. Surface binding can irreversibly limit the flexibility for the reconformation process to a great extent. It is also shown here that a flatter adsorbed state could be reached by sequential adsorption of polyanion and polycation than could be reached by the direct adsorption of the polyelectrolyte complex itself.     

Cylindrical cell model for the electrostatic free energy of polyelectrolyte complexes

Associative phase separation (complex coacervation) in a mixture of oppositely charged polyelectrolytes can lead to different types of (inter-)polyelectrolyte complexes (soluble micelles, macroscopic precipitation). In a previous report [Langmuir 2004, 20, 2785-2791], we presented a model for the electrostatic free energy change when (weakly charged) polyelectrolyte forms a homogeneous complex phase. The influence of ionization of the polymer on the electrostatic free energy of the complex was incorporated but the influence of complex density neglected. In the present effort, cylindrical cells are assumed around each polyelectrolyte chain in the complex, and on the basis of the Poisson-Boltzmann equation, the electrostatic free energy is calculated as a function of the complex density. After combination with Flory-Huggins mixing free energy terms and minimization of the total free energy, the equilibrium complex density is obtained, for a given ratio of polycations to polyanions in the complex. The analysis is used in an example calculation ofpolyelectrolyte film formation by alternatingly applying a polycation and a polyanion solution. The calculation suggests that the often observed exponential growth of a polyelectrolyte film when the polymer is weakly charged has a thermodynamic origin: the polyelectrolyte complex shifts repeatedly between two equilibrium states of different densities and compositions. However, when the polyelectrolytes are strongly charged the difference in the compositions between the two equilibrium states is very small, and exponential growth by an absorption mechanism is no longer possible.     

Langevin dynamics of semiflexible polyelectrolytes: rod-toroid-globule-coil structures and counterion distribution

We have investigated the nature of counterion condensation on uniformly charged semiflexible polyelectrolyte chains and the concomitant configurations by monitoring the role of chain stiffness, chain length, counterion valency, and the strength of electrostatic interaction. The counterion condensation is seen to follow the adsorption process and the effective polymer charge increases with chain stiffness. Size and shape, as calculated through the radius of gyration, effective persistence length, and hydrodynamic radius, are studied. Stable coil-like, globular, folded-chain, toroidal, and rodlike configurations are possible at suitable combinations of values of chain stiffness, chain length, electrostatic interaction strength, and the valency of counterion. For high strengths of electrostatic interactions, sufficiently stiff polyelectrolytes form toroids in the presence of multivalent counterions, whereas flexible polyelectrolytes form disordered globules. The kinetic features of the nucleation and growth of toroids are monitored. Several metastable structures are found to frustrate the formation of toroids. The generic pathway involves the nucleation of one primary loop somewhere along the chain contour, followed by a growth process where the rest of the chain is folded continuously on top of the primary loop. The dependence of the average radii of toroids on the chain length is found to be roughly linear, in disagreement with existing scaling arguments.     

Peculiarities of the formation of polyacrylamide compound-based polyelectrolyte complexes in the course of the flocculation of clay-salt dispersions

Peculiarities of the formation of polyelectrolyte complexes based on cationic and anionic copolymers of acrylamide having different macromolecule charge densities on the surfaces of kaolin particles in highly concentrated salt solution are investigated. The interactions of the copolymers with the clay particle surface and with each other are studied by electrokinetic and IR spectroscopy methods. The rheological properties of kaolin suspensions are investigated in a salt solution in the presence of the polyelectrolytes. The flocculation ability of the polyelectrolytes and their binary mixtures with respect to clay-salt dispersion is estimated. The mechanism for the formation of polyelectrolyte complexes on the surface of clay particles is discussed. It is shown that the complexation of oppositely charged polyelectrolytes on the surfaces of clay particles intensifies the flocculation of clay-salt dispersions.     

Time-dependent conformational changes of polyelectrolyte complexes in solution

Changes in the conformation of the polyelectrolytes when contacted with oppositely charged polyelectrolytes or when subjected to shifts in solution conditions (pH), have been studied in this work along with reversibility of the changes using fluorescence spectroscopy. While changes due to both of the above are marked, they are measurably different from each other. Thus, the extent of coiling of the complexes formed between the anionic polyelectrolyte, maleicacid anhydride–propene and the cationic polyelectrolytes was much higher than that achieved by the change in pH alone. Also, while the changes due to pH shifts were fast and reversible, that due to complexation between oppositely charged ones involved first a rapid uncoiling followed by slow recoiling to a new structure. Interestingly, shifting the coiled conformation to an even more coiled one resulted in a new reversible state, but shifting to a stretched state by complexation led to a somewhat irreversible structure. Also maximum interaction obtained between the anionic and one cationic polyelectrolyte was markedly higher than that between the former and another cationic polymer. These observations using fluorescence spectroscopy was consistent with that obtained by the potentiometric titration. The study clearly shows the importance of the manner in which the polyelectrolytes are equilibrated to desired solution conditions. These results are interpreted here in terms of deprotonation/protonation of the polyelectroytes upon pH change and complexation with oppositely charged ones resulting in screening of charges as well as stiffening.     

Monte Carlo simulation and molecular theory of tethered polyelectrolytes

We investigate the structure of end-tethered polyelectrolytes using Monte Carlo simulations and molecular theory. In the Monte Carlo calculations we explicitly take into account counterions and polymer configurations and calculate electrostatic interaction using Ewald summation. Rosenbluth biasing, distance biasing, and the use of a lattice are all used to speed up Monte Carlo calculation, enabling the efficient simulation of the polyelectrolyte layer. The molecular theory explicitly incorporates the chain conformations and the possibility of counterion condensation. Using both Monte Carlo simulation and theory, we examine the effect of grafting density, surface charge density, charge strength, and polymer chain length on the distribution of the polyelectrolyte monomers and counterions. For all grafting densities examined, a sharp decrease in brush height is observed in the strongly charged regime using both Monte Carlo simulation and theory. The decrease in layer thickness is due to counterion condensation within the layer. The height of the polymer layer increases slightly upon charging the grafting surface. The molecular theory describes the structure of the polyelectrolyte layer well in all the different regimes that we have studied.     

Molecular dynamics studies of anchored polyelectrolytes

We study polyelectrolytes end-grafted to a surface in a model which includes counterions explicitly and treats the full long-range Coulomb interaction. For strongly charged polyelectrolytes the counterions are localized inside the brush and electroneutrality is satisfied locally. Under these conditions, we find that the brush thickness is linearly proportional to the chain length and the grafting density. The counterion distribution is strongly inhomogeneous, and counterion condensation can be observed although the Bjerrum length is smaller than the average bond length. Varying the Bjerrum length we find a non-monotonic behaviour of the brush height. Counterion diffusion is anisotropic, and is enhanced at higher grafting densities. For partially charged polyelectrolytes we obtain a crossover from quasi-neutral behaviour to the strongly charged behaviour reported above.     

Structure and mechanism formation of polyelectrolyte complex obtained from PSS/PAH system: effect of molar mixing ratio, base–acid conditions, and ionic strength

Colloidal dispersions of polyelectrolyte complexes were prepared in aqueous solutions. We have used mixtures containing the strongly charged anionic polyelectrolyte sodium polystyrene sulfonate (PSS) and the weak cationic polyelectrolyte polyallylamine hydrochloride (PAH). Both polymers have the same molecular weight. The complexes were obtained by adding drop by drop a solution of the anionic polyelectrolyte to excess cationic polyelectrolyte. In these conditions, sodium polystyrene sulfonate and polyallylamine hydrochloride self-assembled in nanometer-range complexes; the self-assembly is driven by electrostatic interactions, as well as by entropy changes due to counterion release. The electrostatic interactions were controlled in several ways: by changing the C _PSS/C _PAH concentration ratio, by modifying the pH (and thus the protonation degree of polyallylamine hydrochloride), and by adding sodium chloride (screened interactions). Dynamic light scattering experiments demonstrated that the hydrodynamics radius of the polyelectrolyte complex increases, changing from soluble to insoluble complex formation, when some physicochemical parameters are increased: the concentration ratio between polyelectrolytes, the sodium chloride concentration, and pH. Zeta potential measurements, as a function of the C _PSS/C _PAH concentration ratio, as well as of pH and ionic strength, allow us to state that the resulting particles have a structure constituted by a neutral core surrounded by a positively charged shell. The polyelectrolyte complexes have globular shapes, as observed by electron microscopy.     

Molecular bottle brushes in a solution of semiflexible polyelectrolytes and block copolymers with an oppositely charged block: a molecular dynamics simulation

Using a coarse-grained model, we performed molecular dynamics simulations of the electrostatically driven self-assembly of strongly charged polyelectrolytes and diblock copolymers composed of oppositely charged and neutral blocks. Stoichiometric micelle-like complexes formed in a dilute solution represent cylindrical brushes whose conformation is determined by the linear charge density on the polyelectrolyte and by temperature. The core-shell morphology of the cylindrical brushes is proven. The core of these anisotropic micelles consists of an insoluble complex coacervate formed by the ionic chains and a shell made up of the neutral solvophilic blocks. As the concentration of macromolecules increases, the orientational ordering of ionic micelles takes place. The complexation can induce effective steric stiffening of the polyelectrolyte chains.     

Thermodynamics of self-assembling of hydrophobically modified cationic polysaccharides and their mixtures with oppositely charged surfactants in aqueous solution

Microcalorimetric techniques, combined with turbidity measurements, were used to study the thermodynamics of self-assembling of hydrophobically modified cationic polysaccharides and their mixtures with oppositely charged surfactants in aqueous solution. The studied polyelectrolytes were a series of polymers based on dextran having pendant N-(2-hydroxypropyl)-N,N-dimethyl-N-alkylammonium chloride groups randomly distributed along the polymer backbone. The parameters for their micellization process are evaluated from the results of the observed dilution enthalpy curves and compared with those of the related cationic surfactants (DTAC and CTAC). The microcalorimetric results for the mixed systems (polyelectrolytes with oppositely charged surfactants) are used along with turbidity measurements to characterize systematically the thermodynamics of their interaction. The phase behavior is described and the interaction enthalpies are derived from the differences between the observed enthalpy curves with and without polyelectrolyte. Therefore, we discuss in detail the effect of changing the alkyl chain length of polyelectrolyte pendant groups, the molecular weight of the dextran backbone, and the temperature of the measurements on the interactions between polyelectrolyte and surfactant.