Electro-optics of colloid-polyelectrolyte complexes: counterion release from adsorbed macromolecules

Complexation between sodium carboxymethylcellulose (NaCMC) and ellipsoidal particles of oppositely charged beta-FeOOH is studied using electric light scattering and electrophoresis. We focus on the complex behavior for overcharging of the particle surface. In this case, the fraction of condensed counterions on NaCMC is found to remain unchanged during polymer adsorption onto a weakly charged particle surface. Using the theory of Sens and Joanny, we evaluate the fraction of condensed counterions and compare it with results for nonadsorbed NaCMC. The polarization of condensed counterions along the chain of the adsorbed macromolecule is proved to create the electro-optical effect in suspensions stabilized by NaCMC adsorption.     

Complexation of ferric oxide particles with pectins of different charge density

The effect of polyelectrolyte charge density on the electrical properties and stability of suspensions of oppositely charged oxide particles is followed by means of electro-optics and electrophoresis. Variations in the electro-optical effect and the electrophoretic mobility are examined at conditions where fully ionized pectins of different charge density adsorb onto particles with ionizable surfaces. The charge neutralization point coincides with the maximum of particle aggregation in all suspensions. We find that the concentration of polyelectrolyte, needed to neutralize the particle charge, decreases with increasing charge density of the pectin. The most highly charged pectin presents an exception to this order, which is explained with a reduction of the effective charge density of this pectin due to condensation of counterions. The presence of condensed counterions, remaining bound to the pectin during its adsorption on the particle surface, is proved by investigation of the frequency behavior of the electro-optical effect at charge reversal of the particle surface.     

Counterion condensation on charged spheres, cylinders, and planes

We use the framework of counterion condensation theory, in which deviations from linear electrostatics are ascribed to charge renormalization caused by collapse of counterions from the ion atmosphere, to explore the possibility of condensation on charged spheres, cylinders, and planes immersed in dilute solutions of simple salt. In the limit of zero concentration of salt, we obtain Zimm-Le Bret behavior: a sphere condenses none of its counterions regardless of surface charge density, a cylinder with charge density above a threshold value condenses a fraction of its counterions, and a plane of any charge density condenses all of its counterions. The response in dilute but nonzero salt concentrations is different. Spheres, cylinders, and planes all exhibit critical surface charge densities separating a regime of counterion condensation from states with no condensed counterions. The critical charge densities depend on salt concentration, except for the case of a thin cylinder, which exhibits the invariant criticality familiar from polyelectrolyte theory.     

pePC-SAFT: Modeling of polyelectrolyte systems: 1. Vapor–liquid equilibria

A molecular thermodynamic model for polyelectrolyte systems—called pePC-SAFT—is proposed. The effect of charged monomers within the polyelectrolyte chain is explicitly taken into account in the reference term by replacing the hard-chain contribution of the PC-SAFT model by a charged-hard-chain contribution. Moreover, counterion condensation is accounted for to determine the effective number of charges along the polyion as well as of free counterions. The electrostatic contribution of the free counterions is described by a Debye–Hückel term.     

Anionic polyelectrolyte adsorption on mica mediated by multivalent cations: a solution to DNA imaging by atomic force microscopy under high ionic strengths

Adsorption of DNA molecules on mica, a highly negatively charged surface, mediated by divalent or trivalent cations is considered. By analyzing atomic force microscope (AFM) images of DNA molecules adsorbed on mica, phase diagrams of DNA molecules interacting with a mica surface are established in terms of concentrations of monovalent salt (NaCl) and divalent (MgCl2) or multivalent (spermidine, cobalt hexamine) salts. These diagrams show two transitions between nonadsorption and adsorption. The first one arises when the concentration of multivalent counterions is larger than a limit value, which is not sensitive to the monovalent salt concentration. The second transition is due to the binding competition between monovalent and multivalent counterions. In addition, we develop a model of polyelectrolyte adsorption on like-charged surfaces with multivalent counterions. This model shows that the correlations of the multivalent counterions at the interface between DNA and mica play a critical role. Furthermore, it appears that DNA adsorption takes place when the energy gain in counterion correlations overcomes an energy barrier. This barrier is induced by the entropy loss in confining DNA in a thin adsorbed layer, the entropy loss in the interpenetration of the clouds of mica and DNA counterions, and the electrostatic repulsion between DNA and mica. The analysis of the experimental results provides an estimation of this energy barrier. We then discuss some important issues, including DNA adsorption under physiological conditions.     

Entropy and enthalpy of polyelectrolyte complexation: Langevin dynamics simulations

We report a systematic study by Langevin dynamics simulation on the energetics of complexation between two oppositely charged polyelectrolytes of same charge density in dilute solutions of a good solvent with counterions and salt ions explicitly included. The enthalpy of polyelectrolyte complexation is quantified by comparisons of the Coulomb energy before and after complexation. The entropy of polyelectrolyte complexation is determined directly from simulations and compared with that from a mean-field lattice model explicitly accounting for counterion adsorption. At weak Coulomb interaction strengths, e.g., in solvents of high dielectric constant or with weakly charged polyelectrolytes, complexation is driven by a negative enthalpy due to electrostatic attraction between two oppositely charged chains, with counterion release entropy playing only a subsidiary role. In the strong interaction regime, complexation is driven by a large counterion release entropy and opposed by a positive enthalpy change. The addition of salt reduces the enthalpy of polyelectrolyte complexation by screening electrostatic interaction at all Coulomb interaction strengths. The counterion release entropy also decreases in the presence of salt, but the reduction only becomes significant at higher Coulomb interaction strengths. More significantly, in the range of Coulomb interaction strengths appropriate for highly charged polymers in aqueous solutions, complexation enthalpy depends weakly on salt concentration and counterion release entropy exhibits a large variation as a function of salt concentration. Our study quantitatively establishes that polyelectrolyte complexation in highly charged Coulomb systems is of entropic origin.     

Transport,and thermodynamic investigations on sodium polystyrenesulfonate in ethylene glycol–water media

Polyion–counterion interactions in sodium polystyrenesulfonate dissolved in (ethylene glycol + water) mixed solvent media have been investigated conductometrically with special reference to their variations as functions of polyelectrolyte concentration, relative permittivity and temperature. Manning counterion condensation theory for polyelectrolyte solutions failed to describe the present experimental results. The data have, therefore, been analyzed using a new model for semidilute polyelectrolyte conductivity which takes into account the scaling arguments proposed by Dobrynin et al. The fractions of uncondensed counterions were found to depend on the polyelectrolyte concentration varying from 0.27 to 0.37, within the concentration range investigated here, indicating a strong interaction between counterions and polyion. A considerable fraction of the counterions is shown to migrate in the same direction as the polyions. The results further demonstrate that the monomer units experience more frictional resistance in solutions as the ethylene glycol content of the mixture increases or as the temperature decreases.     

Molecular dynamics and neutron scattering study of the dependence of polyelectrolyte dendrimer conformation on counterion behavior

Atomistic molecular dynamics (MD) simulations and contrast variation small angle neutron scattering (SANS) have been combined to investigate the Generation-5 polyelectrolyte polyamidoamine starburst dendrimer. This work reveals the dendrimer conformational dependence on counterion association at different levels of molecular charge. The accuracy of the simulations is verified through satisfactory comparison between modeled results, such as excess intra-dendrimer scattering length density distribution and hydration level, and their experimental counterparts. While the counterion distributions are not directly measureable with SANS, the spatial distribution of the counterions and their dendrimer association are extracted from the validated MD equilibrium trajectories. It is found that the conformation of the charged dendrimer is strongly dependent on the counterion association. Sensitivity of the distribution of counterions around charged amines to the counterion valency is qualitatively explained by adopting Langmuir adsorption theory. Moreover, via extending the concept of electrical double layer for compact charged colloids, we define an effective radius of a charged dendrimer including the spatial distribution of counterions in its vicinity. Within the same framework, the correlation between the strength of intra-dendrimer electrostatic repulsion and the counterion valency and dynamics is also addressed.     

Electric double layer for spherical particles in salt-free concentrated suspensions including ion size effects

The equilibrium electric double layer (EDL) that surrounds colloidal particles is essential for the response of a suspension under a variety of static or alternating external fields. An ideal salt-free suspension is composed of charged colloidal particles and ionic countercharges released by the charging mechanism. Existing macroscopic theoretical models can be improved by incorporating different ionic effects usually neglected in previous mean-field approaches, which are based on the Poisson-Boltzmann equation (PB). The influence of the finite size of the ions seems to be quite promising because it has been shown to predict phenomena like charge reversal, which has been out of the scope of classical PB approximations. In this work we numerically obtain the surface electric potential and the counterion concentration profiles around a charged particle in a concentrated salt-free suspension corrected by the finite size of the counterions. The results show the high importance of such corrections for moderate to high particle charges at every particle volume fraction, especially when a region of closest approach of the counterions to the particle surface is considered. We conclude that finite ion size considerations are obeyed for the development of new theoretical models to study non-equilibrium properties in concentrated colloidal suspensions, particularly salt-free ones with small and highly charged particles.     

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.     

Counterion condensation in hydrosols of single-crystalline detonation nanodiamond particles obtained by air annealing of their agglomerates

The pattern of previously recorded dependences of the specific surface charge and electrophoretic mobility of monodisperse detonation nanodiamond particles on pH of aqueous KCl solutions suggests that counterions are condensed on the particle surface. Counterion condensation is considered in terms of the Levin model, and the experimental ratios between the densities of the electrokinetic and surface charges of dispersed particles, as well as the fractions of condensed counterions, are calculated as depending on pH and KCl concentration in nanodiamond hydrosols. The obtained dependences lead to the conclusion that counterion condensation on the surface of detonation nanodiamond particles does indeed take place.     

Increased layer interdiffusion in polyelectrolyte films upon annealing in water and aqueous salt solutions

As-deposited films of multilayered polyelectrolytes are considered to be non-equilibrium structures. Due to the strong attraction between oppositely charged polyions, polyelectrolyte interdiffusion is thought to be suppressed during the adsorption process. Equilibration is promoted by a decrease of the electrostatic attraction between polyion pairs. We have used neutral impact collision ion scattering spectroscopy to investigate the influence of polyelectrolyte multilayer annealing in water and aqueous 1 M NaCl solutions at different temperatures (20 and 70 degrees C) on the increase in interpenetration of a single polyelectrolyte layer throughout the whole film. The multilayers were composed of poly(4-vinylpyridinium) and poly(4-styrenesulfonate). Contrast between neighboring layers was established by labelling the layer in question with the heavy atom ruthenium. It is found that both temperature and salt increase layer interpenetration, whereas salt has a stronger influence than temperature. From numerical simulations polyelectrolyte diffusion coefficients were evaluated for the different annealing conditions. The influence of temperature and salt on the equilibration of the film is interpreted in terms of increased screening of polyion charges and binding of small counterions to polyion monomeric units.     

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)].     

Potential distribution around a polyelectrolyte-coated spherical particle in a salt-free medium

Simple analytic approximate expressions for the solution to the Poisson-Boltzmann equation around a spherical particle coated with an ion-penetrable polyelectrolyte layer in a salt-free medium containing counterions only are derived. The results of the calculation of the potential distribution using the approximate solution are found to be in good agreement with exact numerical results. It is shown that as in the case of a charged rigid particle, there is a certain critical value of the particle charge, separating two cases, that is, the low-particle-charge case and the high-particle-charge case. In the low-charge case the potential is essentially the same as if counterions were absent and thus the potential is proportional to the particle charge. In the high-charge case counterion condensation occurs in the polyelectrolyte layer region, so that the dependence of the potential on the particle charge is considerably suppressed.     

In-situ investigation of the adsorption of globular model proteins on stimuli-responsive binary polyelectrolyte brushes

Binary brushes constituted from two incompatible polymers can be used in the form of ultrathin polymeric layers as a versatile tool for surface engineering to tune physicochemical surface characteristics such as wettability, surface charge, chemical composition, and morphology and furthermore to create responsive surface properties. Mixed brushes of oppositely charged weak polyelectrolytes represent a special case of responding surfaces that are sensitive to changes in the pH value of the aqueous environment and therefore represent interesting tools for biosurface engineering. The polyelectrolyte brushes used for this study were composed of two oppositely charged polyelelctrolytes poly(2-vinylpyridine) (P2VP) and poly(acrylic acid) (PAA). The in-situ properties and surface characteristics such as as surface charge, surface tension, and extent of swelling of these brush layers are functions of the pH value of the surrounding aqueous solution. To test the behavior of the mixed polylelctrolyte brushes in contact with biosystems, protein adsorption experiments with globular model proteins were performed at different pH values and salt concentrations (confinement of counterions) of the buffer solutions. The influence of the pH value, buffer salt concentration, and isoelectric points (IEP) of the brush and protein on the adsorbed amount and the interfacial tension during protein adsorption as well as the protein adsorption mechanism postulated in reference to recently developed theories of protein adsorption on polyelectrolyte brushes is discussed. In the salted regime, protein adsorption was found to be similar to the often-described adsorption at hydrophobic surfaces. However, in the osmotic regime the balance of electrostatic repulsion and a strong entropic driving force, "counterion release", was found to be the main influence on protein adsorption.     

Ionic effects in collapse of polyelectrolyte brushes

We investigated the effect of counterion valence on the structure and swelling behavior of polyelectrolyte brushes using a nonlocal density functional theory that accounts for the excluded-volume effects of all ionic species and intrachain and electrostatic correlations. It was shown that charge correlation in the presence of multivalent counterions results in collapse of a polyelectrolyte brush at an intermediate polyion grafting density. At high grafting density, the brush reswells in a way similar to that in a monovalent ionic solution. In the presence of multivalent counterions, the nonmonotonic swelling of a polyelectrolyte brush in response to the increase of the grafting density can be attributed to a competition of the counterion-mediated electrostatic attraction between polyions with the excluded-volume effect of all ionic species. While a polyelectrolyte brush exhibits an "osmotic brush" regime at low salt concentration and a "salted brush" regime at high salt concentration regardless of the counterion valence, we found a smoother transition as the valence of the counterions increases. As observed in recent experiments, a quasi-power-law dependence of the brush thickness on the concentration ratio can be identified when the monovalent counterions are replaced with trivalent counterions at a fixed ionic strength.     

Electrophoretic mobility of a highly charged colloidal particle in a solution of general electrolytes.

For a highly charged particle in an electrolyte solution, counterions are condensed very near the particle surface. The electrochemical potential of counterions accumulated near the particle surface is thus not affected by the applied electric field, so that the condensed counterions do not contribute to the particle electrophoretic mobility. In the present paper we derive an expression for the electrophoretic mobility mu(infinity) of a highly charged spherical particle of radius a and zeta potential zeta in the limit of very high zeta in a solution of general electrolytes with large ka (where k is the Debye-Hückel parameter) on the basis of our previous theory for the case of symmetrical electrolytes (H. Ohshima, J. Colloid Interface Sci. 263 (2003) 337). It is shown that zeta can formally be expressed as the sum of two components: the co-ion component, zetaco-ion, and the counterion component, zetacounterion (where zeta = zetaco-ion + zetacounterion) and that the limiting electrophoretic mobility mu(infinity) is given by mu(infinity) = epsilonr epsilon0 zetaco-ion(infinity)/eta + 0(1/ka), where zetaco-ion(infinity) is the high zeta-limiting form of zetaco-ion, epsilonr and eta are, respectively, the relative permittivity and viscosity of the solution, and epsilon0 is the permittivity of a vacuum. That is, the particle behaves as if its zeta potential were zetaco-ion(infinity), independent of zeta. For the case of a positively charged particle in an aqueous electrolyte solution at 25 degrees C, the value of zetaco-ion(infinity) is 35.6 mV for 1-1 electrolytes, 46.0 mV for 2-1 electrolytes, and 12.2 mV for 1-2 electrolytes. It is also found that the magnitude of mu(infinity) increases as the valence of co-ions increases, whereas the magnitude of mu(infinity) decreases as the valence of counterions increases.     

(Vinyl amine)-(vinyl alcohol) copolymers Synthesis,characterization and potentiometric behaviour

Some copolymers of vinyl amine with vinyl alcohol have been synthesized by hydrolysis of copolymers of tert.-butyl vinyl carbamate with vinyl acetate. From reaction kinetics and counterion distribution, it can be concluded that the copolymers are random. The potentiometric titration behaviour indicates that the very marked dependence of the dissociation constant on the charge fraction, even at high ionic strength, for this polyelectrolyte system may result from a very specific solvation process i.e. a strong dependence on the charge state of the interactions between polyion with counterions and solvent molecules.     

Molecular dynamics simulations of polyelectrolyte adsorption

We have performed molecular dynamics simulations of polyelectrolyte adsorption at oppositely charged surfaces from dilute polyelectrolyte solutions. In our simulations, polyelectrolytes were modeled by chains of charged Lennard-Jones particles with explicit counterions. We have studied the effects of the surface charge density, surface charge distribution, solvent quality for the polymer backbone, strength of the short-range interactions between polymers and substrates on the polymer surface coverage, and the thickness of the adsorbed layer. The polymer surface coverage monotonically increases with increasing surface charge density for almost all studied systems except for the system of hydrophilic polyelectrolytes adsorbing at hydrophilic surfaces. In this case the polymer surface coverage saturates at high surface charge densities. This is due to additional monomer-monomer repulsion between adsorbed polymer chains, which becomes important in dense polymeric layers. These interactions also preclude surface overcharging by hydrophilic polyelectrolytes at high surface charge densities. The thickness of the adsorbed layer shows monotonic dependence on the surface charge density for the systems of hydrophobic polyelectrolytes for both hydrophobic and hydrophilic surfaces. Thickness is a decreasing function of the surface charge density in the case of hydrophilic surfaces while it increases with the surface charge density for hydrophobic substrates. Qualitatively different behavior is observed for the thickness of the adsorbed layer of hydrophilic polyelectrolytes at hydrophilic surfaces. In this case, thickness first decreases with increasing surface charge density, then it begins to increase.     

Entropic effects in the electric double layer of model colloids with size-asymmetric monovalent ions

The structure of the electric double layer of charged nanoparticles and colloids in monovalent salts is crucial to determine their thermodynamics, solubility, and polyion adsorption. In this work, we explore the double layer structure and the possibility of charge reversal in relation to the size of both counterions and coions. We examine systems with various size-ratios between counterions and coions (ion size asymmetries) as well as different total ion volume fractions. Using Monte Carlo simulations and integral equations of a primitive-model electric double layer, we determine the highest charge neutralization and electrostatic screening near the electrified surface. Specifically, for two binary monovalent electrolytes with the same counterion properties but differing only in the coion's size surrounding a charged nanoparticle, the one with largest coion size is found to have the largest charge neutralization and screening. That is, in size-asymmetric double layers with a given counterion's size the excluded volume of the coions dictates the adsorption of the ionic charge close to the colloidal surface for monovalent salts. Furthermore, we demonstrate that charge reversal can occur at low surface charge densities, given a large enough total ion concentration, for systems of monovalent salts in a wide range of ion size asymmetries. In addition, we find a non-monotonic behavior for the corresponding maximum charge reversal, as a function of the colloidal bare charge. We also find that the reversal effect disappears for binary salts with large-size counterions and small-size coions at high surface charge densities. Lastly, we observe a good agreement between results from both Monte Carlo simulations and the integral equation theory across different colloidal charge densities and 1:1-electrolytes with different ion sizes.