Like-charged Polyelectrolytes Research Articles

Analytical ultracentrifugation study of complex formation between like-charged glycinin and polyelectrolytes: Impact of ionic strength and chain length

In food systems, complexes formed between soybean protein and polyelectrolytes are extensively utilized. However, the mechanisms governing their interactions remain elusive, especially when they possess similar net charges. This study investigates the complexation between like-charged glycinin (11S) and diblock copolymers of polyethylene glycol-block-poly(sodium styrene sulfonate) (PEG-b-PSS) using analytical ultracentrifugation (AUC), a first-principle technique that examines macromolecular characteristics such as molecular weight, stoichiometry, and binding properties. The results reveal that 11S can interact with polyelectrolytes of the same net charges. At ionic strengths above 0.1 M, under a specific concentration of PEG-b-PSS with a PSS degree of polymerization of 33, reducing ionic strength augments the binding strength between PEG-b-PSS and 11S while enhancing the electrostatic repulsion between complexes. Consequently, association occurs as ionic strength decreases from 0.5 to 0.3 M due to the predominance of binding strength, and the association disappears at 0.1 M because electrostatic repulsion becomes predominant. Moreover, PEG-b-PSS with a higher degree of polymerization in the PSS blocks facilitates the formation of insoluble complexes of 11S via soluble intermediates. At an ionic strength of 0.025 M, PEG-b-PSS induces the dissociation of 11S into subunits and peptides. This study demonstrates that by controlling the ionic strength and the degree of polymerization of the polyelectrolyte, it is possible to regulate the binding strength between 11S and polyelectrolyte, as well as the structural changes during binding. Furthermore, this study contributes to understanding the complex formation mechanism between soybean protein and polyelectrolytes, and further expands the application of AUC in studying their binding.

Interactions between Rigid Polyelectrolytes Mediated by Ordering and Orientation of Multivalent Nonspherical Ions in Salt Solutions.

Multivalent ions in solutions with polyelectrolytes (PEs) induce electrostatic correlations that can drastically change ion distributions around the PEs and their mutual interactions. Using coarse-grained molecular dynamics simulations, we show how in addition to valency, ion shape and concentration can be harnessed as tools to control rigid like-charged PE-PE interactions. We demonstrate a correlation between the orientational ordering of aspherical ions and how they mediate the effective PE-PE attraction induced by multivalency. The interaction type, strength, and range can thus be externally controlled in ionic solutions. Our results can be used as generic guidelines to tune the self-assembly of like-charged polyelectrolytes by variation of the characteristics of the ions.

Crystallization of charged gold particles mediated by nonadsorbing like-charged polyelectrolyte.

We report that the aqueous dispersions of negatively charged submicron-sized colloidal Au particles formed non-close-packed colloidal crystals by the addition of a like-charged linear polyelectrolyte, sodium polyacrylate (NaPAA). Au particles often form irregular aggregates in dispersions because of a strong van der Waals force acting between them. To prevent aggregation, we introduced negative electric charges on particle surfaces. By the addition of NaPAA, colloidal crystals were formed on the bottom of a sample cell because of the supply of Au particles by sedimentation and 2D diffusion even under very dilute conditions. Interparticle potential calculations demonstrated that the addition of NaPAA caused depletion attraction between the particles as well as a significant reduction in the interparticle repulsion because of the electrostatic screening effect. However, the electrostatic repulsion was strong enough to prevent the direct contact of particles in the excluded region between Au particles. Large-area crystals could be obtained by tilting the sample cell. By drying the sample, the Au particles came into contact and the non-space-filling crystals changed into closest packed crystals. These closest packed crystals exhibited a significant enhancement of Raman scattering intensity because of high hot-spot density.

Ion-mediated interactions between like-charged polyelectrolytes with bending flexibility

Ion-mediated interactions between polyelectrolytes (PEs) are crucial to the properties of flexible biopolymers such as nucleic acids and proteins but the effect of PE flexibility on such interactions has not been explicitly addressed until now. In this work, the potentials of mean force (PMFs) between like-charged PEs with different bending flexibility have been investigated by Monte Carlo simulations and a cylindrical confinement around each PE was involved to model two PEs in an array. We found that in the absence of trivalent salt, the PMFs between like-charged PEs in an array are apparently repulsive while the bending flexibility can visibly decrease the repulsive PMFs. With the addition of high trivalent salt, the PMFs become significantly attractive whereas the attractive PMFs can be apparently weakened by the bending flexibility. Our analyses reveal that the effect of bending flexibility is attributed to the increased PE conformational space, which allows the PEs to fluctuate away to decrease the monovalent ion-mediated repulsion or to weaken the trivalent ion-mediated attraction through disrupting trivalent ion-bridging configuration. Additionally, our further calculations show that the effect of bending flexibility on the ion-mediated interactions is less apparent for PEs without cylindrical confinement.

Regulation of the Stability of Titania Nanosheet Dispersions with Oppositely and Like-Charged Polyelectrolytes.

Charging and aggregation processes of titania nanosheets (TNS) were extensively studied in the presence of oppositely charged or like-charged polyelectrolytes in aqueous dispersions. The surface charge of the TNS was systematically varied by the pH; therefore, positive nanosheets were obtained at pH 4 and negative ones at pH 10. Strong adsorption of poly(styrene sulfonate) (PSS) of high negative line charge density on the TNS was observed at pH 4, leading to charge neutralization and reversal of the original sign of charge of the nanosheets. The adsorption of like-charged poly(diallyldimethylammonium chloride) (PDADMAC) was also feasible through a hydrophobic interaction. The predominating interparticle forces were mainly of the DLVO-type, but additional patch-charge attraction also took place in the case of PSS at low surface coverage. The TNS was found to be hydrophilic at pH 10 and no adsorption of like-charged PSS was possible because of strong electrostatic repulsion between the polyelectrolyte and the surface. The PDADMAC showed high affinity to the oppositely charged TNS surface in alkaline dispersions, giving rise to neutral and positively charged nanosheets at appropriate polyelectrolyte doses. Formation of a saturated PDADMAC layer on the TNS led to high resistance against salt-induced aggregation through the electrosteric stabilization mechanism. These results shed light on the importance of polyelectrolyte concentration, ionic strength, and charge balance on the colloidal stability of TNS, which is especially important in applications, where the nanosheets are dispersed in complex solution containing polymeric compounds and electrolytes.

Effect of Polyelectrolyte Mono- and Bilayer Formation on the Colloidal Stability of Layered Double Hydroxide Nanoparticles.

Sequential adsorption of polyelectrolytes on nanoparticles is a popular method to obtain thin films after deposition. However, the effect of polyelectrolyte multilayer formation on the colloidal stability of the nanoparticles has not been studied in detail. In the present work, layered double hydroxides (LDH) were synthesized and interaction with oppositely and like-charged polyelectrolytes was investigated. Electrophoretic and light scattering measurements revealed that colloidal stability of LDH can be tuned by adsorption of poly(styrene sulfonate) (PSS) on the oppositely charged LDH surface in appropriate doses and thus, unstable or stable dispersions can be designed. Negatively charged LDH of adsorbed PSS monolayer was obtained and a poly(diallyldimethyl ammonium chloride) (PDADMAC) second layer was systematically built on the particles. The obtained polyelectrolyte bilayer provided high colloidal stability for the LDH-PSS-PDADMAC dispersions due to the presence of repulsive interparticle forces of electrostatic and steric origin. The results provide crucial quantitative information on designing highly stable particle-polyelectrolyte systems for the preparation of thin films or immobilization of guest substances between the layers for delivery processes.

Exploring the interactions in binary mixtures of polyelectrolytes: Influence of mixture composition, concentration, and temperature on counterion condensation

The counterion condensation in the binary mixtures of like-charged polyelectrolytes with two different molecular weights, where both are negatively charged, has been studied by conductance measurement in aqueous medium. Sodium polystyrenesulfonate with two different chain lengths have been selected as model polyelectrolyte and the investigation has been carried out in the absence of any added salt. The specific conductance-polyelectrolyte concentration data were analyzed in the light of the scaling argument for the conformation of polyion chains in solutions to quantify the fractions of free counterions. Effects of polyelectrolyte concentration, molecular weights of the components of the mixture, and solution temperature on the condensation of counterions have been investigated to explore polyion–counterion interaction, and inter- and intra-chain interactions in these polyelectrolyte mixtures. This investigation revealed that the extent of counterion condensation is significantly influenced by the mixture composition, the polyelectrolyte concentration and the temperature. Evaluation of the polyion transference numbers provided important information as to the direction of the motion of the counterions under the action of the applied electric field.

Potential of mean force between oppositely charged nanoparticles: A comprehensive comparison between Poisson\u2013Boltzmann theory and Monte Carlo simulations

Ion-mediated interactions between like-charged polyelectrolytes have been paid much attention, and the Poisson–Boltzmann (PB) theory has been shown to fail in qualitatively predicting multivalent ion-mediated like-charge attraction. However, inadequate attention has been paid to the ion-mediated interactions between oppositely charged polyelectrolytes. In this work, the potentials of mean force (PMF) between oppositely charged nanoparticles in 1:1 and 2:2 salt solutions were investigated by Monte Carlo simulations and the PB theory. Our calculations show that the PMFs between oppositely charged nanoparticles are generally attractive in 1:1 and 2:2 salt solutions and that such attractive PMFs become weaker at higher 1:1 or 2:2 salt concentrations. The comprehensive comparisons show that the PB theory can quantitatively predict the PMFs between oppositely charged nanoparticles in 1:1 salt solutions, except for the slight deviation at very high 1:1 salt concentration. However, for 2:2 salt solutions, the PB theory generally overestimates the attractive PMF between oppositely charged nanoparticles, and this overestimation becomes more pronounced for nanoparticles with higher charge density and for higher 2:2 salt concentration. Our microscopic analyses suggest that the overestimation of the PB theory on the attractive PMFs for 2:2 salt solutions is attributed to the underestimation of divalent ions bound to nanoparticles.

Complex between cationic like-charged polyelectrolytes/surfactants systems

We report for the first time the complex formation between cationic like-charged polyelectrolytes and surfactant systems. The mechanism of attraction has been investigated through extensive course-grained molecular dynamic simulations and atomic force microscopy (AFM) experiments. The addition of a tetravalent salt is found to play a crucial role in the polyelectrolyte backbone properties. We found extended structures at low and high salt concentration values, whereas, for intermediate ones, the chains condensate. The combination of elements with the same charge has been investigated in three different regimes depending on the tetrasalt concentration: before condensation; at the condensation point and during the re-expansion. The mixture of polyelectrolytes and surfactants in salt free is also studied and compared to the mixture in a tetrasalt solution.

Depletion and double layer forces acting between charged particles in solutions of like-charged polyelectrolytes and monovalent salts.

Interaction forces between silica particles were measured in aqueous solutions of the sodium salt of poly(styrene sulphonate) (PSS) and NaCl using the colloidal probe technique based on an atomic force microscope (AFM). The observed forces can be rationalized through a superposition of damped oscillatory forces and double layer forces quantitatively. The double layer forces are modeled using Poisson-Boltzmann (PB) theory for a mixture of a monovalent symmetric electrolyte and a highly asymmetric electrolyte, whereby the multivalent coions represent the polyelectrolyte chains. The effective charge of the polyelectrolyte is found to be smaller than the bare number of charged groups residing on one polyelectrolyte molecule. This effect can be explained by counterion condensation. The interplay between depletion and double layer forces can be further used to predict the phase of the depletion force oscillations. However, this picture holds only at not too elevated concentrations of the polyelectrolyte and salt. At higher salt concentrations, attractive van der Waals forces become important, while at higher polyelectrolyte concentrations, the macromolecules adsorb onto the like-charged silica interface.

Interaction of Charged Patchy Protein Models with Like-Charged Polyelectrolyte Brushes.

We study the adsorption of charged patchy particle models (CPPMs) on a thin film of a like-charged and dense polyelectrolyte (PE) brush (of 50 monomers per chain) by means of implicit-solvent, explicit-salt Langevin dynamics computer simulations. Our previously introduced set of CPPMs embraces well-defined one- and two-patched spherical globules, each of the same net charge and (nanometer) size, with mono- and multipole moments comparable to those of small globular proteins. We focus on electrostatic effects on the adsorption far away from the isoelectric point of typical proteins, i.e., where charge regulation plays no role. Despite the same net charge of the brush and globule, we observe large binding affinities up to tens of the thermal energy, kBT, which are enhanced by decreasing salt concentration and increasing charge of the patch(es). Our analysis of the distance-resolved potentials of mean force together with a phenomenological description of all leading interaction contributions shows that the attraction is strongest at the brush surface, driven by multipolar, Born (self-energy), and counterion-release contributions, dominating locally over the monopolar and steric repulsions.

The flocculation of kaolin aqueous dispersion by two cationic polyelectrolytes

The flocculation by compositions, based on synthetic poly-1,2-dimethyl-5-vinylpyridinium methyl sulfate (K1),poly-trimethyl(methacryloyloxyethyl)-ammonium methyl sulfate (K2) and natural polyelectrolyte (chitosan, Cs) using an aqueous kaolin dispersion was studied. Floccule formation parameters and sedimentation rates were determined by optical microscopy, turbidimetry and microelectrophoresis. The synergistic effect is observed using the polyelectrolyte compositions, it appears in 40% increase of the floccule sedimentation rates and promotes the formation of two times more dense floccules compared to using individual flocculants. The synergistic effect of two cationic polyelectrolytes was confirmed by the flocculation research results in aqueous-salt solutions at various NaCl salt concentrations. A study of the behavior of the two polyelectrolytes macromolecules in solution was performed to explain the observed synergistic effect. The decrease of macromolecules hydrodynamic radius in the joint presence of two like-charged polyelectrolytes was revealed by the capillary viscometry, dynamic and static light scattering. It was determined, that the behavior of two cationic polyelectrolytes in the common solution determines the character of their behavior on the dispersed phase surface in the flocculation process.

Interplay between Depletion and Double-Layer Forces Acting between Charged Particles in Solutions of Like-Charged Polyelectrolytes.

Direct force measurements between negatively charged silica particles in the presence of a like-charged strong polyelectrolyte were carried out with an atomic force microscope. The force profiles can be quantitatively interpreted as a superposition of depletion and double-layer forces. The depletion forces are modeled with a damped oscillatory profile, while the double-layer forces with the mean-field Poisson-Boltzmann theory for a strongly asymmetric electrolyte, whereby an effective valence must be assigned to the polyelectrolyte. This effective valence is substantially smaller than the bare valence due to ion condensation effects. The unusual aspect of the electrical double layer in these systems is the exclusion of the like-charged polyelectrolyte from the vicinity of the surface, leading to a strongly nonexponential diffuse ionic layer that is dominated by counterions and has a well-defined thickness. As the oscillatory depletion force sets in right after this layer, this condition can be used to predict the phase of the oscillatory depletion force.

Complexation and coacervation of like-charged polyelectrolytes inspired by mussels

It is well known that polyelectrolyte complexes and coacervates can form on mixing oppositely charged polyelectrolytes in aqueous solutions, due to mainly electrostatic attraction between the oppositely charged polymers. Here, we report the first (to the best of our knowledge) complexation and coacervation of two positively charged polyelectrolytes, which provides a new paradigm for engineering strong, self-healing interactions between polyelectrolytes underwater and a new marine mussel-inspired underwater adhesion mechanism. Unlike the conventional complex coacervate, the like-charged coacervate is aggregated by strong short-range cation-π interactions by overcoming repulsive electrostatic interactions. The resultant phase of the like-charged coacervate comprises a thin and fragile polyelectrolyte framework and round and regular pores, implying a strong electrostatic correlation among the polyelectrolyte frameworks. The like-charged coacervate possesses a very low interfacial tension, which enables this highly positively charged coacervate to be applied to capture, carry, or encapsulate anionic biomolecules and particles with a broad range of applications.

Shell formation in short like-charged polyelectrolytes in a harmonic trap.

Inspired by recent experiments and simulations on pattern formation in biomolecules by optical tweezers, a theoretical description based on the reference interaction site model (RISM) is developed to calculate the equilibrium density profiles of small polyelectrolytes in an external potential. The formalism is applied to the specific case of a finite number of Gaussian and rodlike polyelectrolytes trapped in a harmonic potential. The density profiles of the polyelectrolytes are studied over a range of lengths and numbers of polyelectrolytes in the trap, and the strength of the trap potential. For smaller polymers we recover the results for point charges. In the mean field limit the longer polymers, unlike point charges, form a shell at the boundary layer. When the interpolymer correlations are included, the density profiles of the polymers show sharp shells even at weaker trap strengths. The implications of these results are discussed.

Like-charged protein-polyelectrolyte complexation driven by charge patches.

We study the pair complexation of a single, highly charged polyelectrolyte (PE) chain (of 25 or 50 monomers) with like-charged patchy protein models (CPPMs) by means of implicit-solvent, explicit-salt Langevin dynamics computer simulations. Our previously introduced set of CPPMs embraces well-defined zero-, one-, and two-patched spherical globules each of the same net charge and (nanometer) size with mono- and multipole moments comparable to those of globular proteins with similar size. We observe large binding affinities between the CPPM and the like-charged PE in the tens of the thermal energy, kBT, that are favored by decreasing salt concentration and increasing charge of the patch(es). Our systematic analysis shows a clear correlation between the distance-resolved potentials of mean force, the number of ions released from the PE, and CPPM orientation effects. In particular, we find a novel two-site binding behavior for PEs in the case of two-patched CPPMs, where intermediate metastable complex structures are formed. In order to describe the salt-dependence of the binding affinity for mainly dipolar (one-patched) CPPMs, we introduce a combined counterion-release/Debye-Hückel model that quantitatively captures the essential physics of electrostatic complexation in our systems.

Segregation in Like-Charged Polyelectrolyte–Surfactant Mixtures Can Be Precisely Tuned via Manipulation of the Surfactant Mass Ratio

In this study, we consider segregative phase separation in aqueous mixtures of quaternary ammonium surfactants didecyldimethylammonium chloride (DDQ) and alkyl (C12, 70%; C14 30%) dimethyl benzyl ammonium chloride (BAC) upon the addition of poly(diallyldimethylammonium) chloride (pDADMAC) as a function of both concentration and molecular weight. The nature of the surfactant type is dominant in determining the concentration at which separation into an upper essentially surfactant-rich phase and lower polyelectrolyte-rich phase is observed. However, for high-molecular-weight pDADMAC there is a clear indication of an additional depletion flocculation effect. When the BAC/DDQ ratio is tuned, the segregative phase separation point can be precisely controlled. We propose a phase separation mechanism for like-charged quaternary ammonium polyelectrolyte/surfactant/water mixtures induced by a reduction in the ionic atmosphere around the surfactant headgroup and possible ion pair formation. An additional polyelectrolyte-induced depletion flocculation effect was also observed.

Counterion condensation theory of attraction between like charges in the absence of multivalent counterions

There is abundant experimental evidence suggesting the existence of attractive interactions among identically charged polyelectrolytes in ordinary salt solutions. The presence of multivalent counterions is not required. We review the relevant literature in detail and conclude that it merits more attention than it has received. We discuss also some recent observations of a low ionic strength attraction of negatively charged DNA to the region of a negatively charged glass nanoslit where the floor of the nanoslit meets the walls, again in the absence of multivalent ions. On the theoretical side, it has become clear that purely electrostatic interactions require the presence of multivalent counterions if they are to generate like-charge attraction. Any theory of like-charge attraction in the absence of multivalent counterions must therefore contain a non-electrostatic component. We point out that counterion condensation theory, which has predicted like-charge polyelectrolyte attraction in an intermediate range of distances in ordinary 1:1 salt conditions, contains both electrostatic and non-electrostatic elements. The non-electrostatic component of the theory is the modeling constraint that the counterions fall into two explicit populations, condensed and uncondensed. As reviewed in the paper, this physically motivated constraint is supported by strong experimental evidence. We proceed to offer an explanation of the nanoslit observations by showing in an idealized model that the line of intersection of two intersecting planes is a virtual polyelectrolyte. Since we have previously developed a counterion condensation theory of attraction of two like-charged polyelectrolytes, our suggestion is that the DNA is attracted to the virtual polyelectrolytes that may be located in the nanoslit where floor meets walls. We present the detailed calculations needed to document this suggestion: an extension of previous theory to the case of polyelectrolytes with like but not identical charges; the demonstration of counterion condensation on a plane with bare charge density greater than an explicitly exhibited critical value; a calculation of the free energy of the plane; a calculation of the interaction of a line charge polyelectrolyte with a like-charged plane; and the detailed demonstration that the line of intersection of two planes is a virtual polyelectrolyte.

Phase behavior of crowded like-charged mixed polyelectrolytes in a cell-sized sphere

We studied the phase behavior of a mixture of two semiflexible negatively charged polyelectrolytes, giant DNA and alginate, under crowded condition in a cell-sized sphere (5-40 μm in diameter), where the persistence length of giant DNA is 50 nm and that of alginate is 5 nm. Through microscopic observation, we found that the polymer mixture exhibits a unique phase behavior, which depends on the size of the sphere, whereas the mixture remains homogeneous and isotropic in bulk solution. When the sphere is small, DNA is completely depleted on the surface. When the sphere is medium sized, a portion of the DNA is depleted on the surface, and the remainder stays within the sphere. By introducing a curvature-dependent term for the interaction between DNA and the surface into the Flory-Huggins model, we interpret the observed characteristics of the phase behavior in terms of the relative importance of the surface-to-volume effect.

Clusters in strong polyelectrolyte solutions in the condensation theory approach

The interaction free energy of parallel clusters of like-charged rod polyelectrolytes in solution is calculated in the framework of the extended condensation theory. For sufficiently high linear charge density of the polyelectrolyte, clustering takes place. The greater is the number of polyelectrolytes participating to the cluster, the smaller is the equilibrium interpolyelectrolyte distance, and the deeper is the corresponding free energy minimum. It is a counterintuitive organization due to the increasing of the counterion condensed charge and condensation volume, taking place as the polyelectyrolytes approach each other.