Counterion release from adsorbed highly charged polyelectrolyte: an electrooptical study

The adsorption of sodium poly(4-styrene sulfonate) on oppositely charged beta-FeOOH particles is studied by electrooptics. The focus of this paper is on the release of condensed counterions from adsorbed polyelectrolyte upon surface charge overcompensation. The fraction of condensed Na+ counterions on the adsorbed polyion surface is estimated according to the theory of Sens and Joanny and it is compared with the fraction of condensed counterions on nonadsorbed polyelectrolyte. The relaxation frequency of the electrooptical effect from the polymer-coated particle is found to depend on the polyelectrolyte molecular weight. This is attributed to polarization of the layer from condensed counterions on the polyion surface, being responsible for creation of the effect from particles covered with highly charged polyelectrolyte. The number of the adsorbed chains is calculated also assuming counterion condensation on the adsorbed polyelectrolyte and semiquantative agreement is found with the result obtained from the condensed counterion polarizability of the polymer-coated particle. Our findings are in line with theoretical predictions that the fraction of condensed counterions remains unchanged due to the adsorption of highly charged polyelectrolyte onto weakly charged substrate.     

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.     

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.     

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.     

dc Electrokinetics for spherical particles in salt-free concentrated suspensions including ion size effects

We study the electrophoretic mobility of spherical particles and the electrical conductivity in salt-free concentrated suspensions including finite ion size effects. An ideal salt-free suspension is composed of just charged colloidal particles and the added counterions that counterbalance their surface charge. In a very recent paper [Roa et al., Phys. Chem. Chem. Phys., 2011, 13, 3960-3968] we presented a model for the equilibrium electric double layer for this kind of suspensions considering the size of the counterions, and now we extend this work to analyze the response of the suspension under a static external electric field. The numerical results show the high importance of such corrections for moderate to high particle charges, especially when a region of closest approach of the counterions to the particle surface is considered. The present work sets the basis for further theoretical models with finite ion size corrections, concerning particularly the ac electrokinetics and rheology of such systems.     

Ion size effects on the electrokinetics of salt-free concentrated suspensions in ac fields

We analyze the influence of finite ion size effects in the response of a salt-free concentrated suspension of spherical particles to an oscillating electric field. Salt-free suspensions are just composed of charged colloidal particles and the added counterions released by the particles to the solution that counterbalance their surface charge. In the frequency domain, we study the dynamic electrophoretic mobility of the particles and the dielectric response of the suspension. We find that the Maxwell-Wagner-O’Konski process associated with the counterions condensation layer is enhanced for moderate to high particle charges, yielding an increment of the mobility for such frequencies. We also find that the increment of the mobility grows with ion size and particle charge. All these facts show the importance of including ion size effects in any extension attempting to improve standard electrokinetic models.     

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.     

Explicit ions condensation around strongly charged polyelectrolytes and spherical macroions: the influence of salt concentration and chain linear charge density. Monte Carlo simulations

The condensation of monovalent counterions and trivalent salt particles around strong rigid and flexible polyelectrolyte chains as well as spherical macroions is investigated by Monte Carlo simulations. The results are compared with the condensation theory proposed by Manning. Considering flexible polyelectrolyte chains, the presence of trivalent salt is found to play an important role by promoting chain collapse. The attraction of counterions and salt particles near the polyelectrolyte chains is found to be strongly dependent on the chain linear charge density with a more important condensation at high values. When trivalent salt is added in a solution containing monovalent salt, the trivalent cations progressively replace the monovalent counterions. Ion condensation around flexible chains is also found to be more efficient compared with rigid rods due to monomer rearrangement around counterions and salt cations. In the case of spherical macroions, it is found that a fraction of their bare charge is neutralized by counterions and salt cations. The decrease of the Debye length, and thus the increase of salt concentration, promotes the attraction of counterions and salt particles at the macroion surface. Excluded volume effects are also found to significantly influence the condensation process, which is found to be more important by decreasing the ion size.     

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.     

Charge renormalization of charged spheres based on thermodynamic properties

At strong electrostatic coupling, counterions are accumulated in the vicinity of the surface of the charged particle with intrinsic charge Z. In order to explain the behavior of highly charged particles, effective charge Z(*) is therefore invoked in the models based on Debye-Huckel approximation, such as the Derjaguin-Landau-Verwey-Overbeek potential. For a salt-free colloidal suspension, we perform Monte Carlo simulations to obtain various thermodynamic properties omega in a spherical Wigner-Seitz cell. The effect of dielectric discontinuity is examined. We show that at the same particle volume fraction, counterions around a highly charged sphere with Z may display the same value of omega as those around a weakly charged sphere with Z(*), i.e., omega(Z)=omega(Z(*)). There exists a maximally attainable value of omega at which Z=Z(*). Defining Z(*) as the effective charge, we find that the effective charge passes through a maximum and declines again due to ion-ion correlation as the number of counterions is increased. The effective charge is even smaller if one adopts the Debye-Huckel expression omega(DH). Our results suggest that charge renormalization can be performed by chemical potential, which may be observed in osmotic pressure measurements.     

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.     

Chain stiffness, salt valency, and concentration influences on titration curves of polyelectrolytes: Monte Carlo simulations

Monte Carlo simulations have been used to study two different models of a weak linear polyelectrolyte surrounded by explicit counterions and salt particles: (i) a rigid rod and (ii) a flexible chain. We focused on the influence of the pH, chain stiffness, salt concentration, and valency on the polyelectrolyte titration process and conformational properties. It is shown that chain acid-base properties and conformational properties are strongly modified when multivalent salt concentration variation ranges below the charge equivalence. Increasing chain stiffness allows to minimize intramolecular electrostatic monomer interactions hence improving the deprotonation process. The presence of di and trivalent salt cations clearly promotes the chain degree of ionization but has only a limited effect at very low salt concentration ranges. Moreover, folded structures of fully charged chains are only observed when multivalent salt at a concentration equal or above charge equivalence is considered. Long-range electrostatic potential is found to influence the distribution of charges along and around the polyelectrolyte backbones hence resulting in a higher degree of ionization and a lower attraction of counterions and salt particles at the chain extremities.     

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.     

Polyelectrolyte–particle complex formation. Polyelectrolyte linear charge density and ionic concentration effects. Monte Carlo simulations

The influence of the linear charge density (LCD) of a polyelectrolyte on its adsorption on an oppositely charged colloidal particle is investigated by Monte Carlo simulations. Adsorption characteristics are studied at different linear charge densities and ionic concentrations and for a given polyelectrolyte/particle size ratio so that particle curvature has full effect. The isolated polyelectrolyte goes through a smooth transition from a collapsed structure to an extended rod-like conformation with increasing the linear charge density in the low ionic concentration regime. In the high ionic concentration regime, the polyelectrolyte is less sensitive to the increase in the linear charge density and adopts a coil conformation. We found that complex formation is promoted by decreasing the ionic concentration and increasing the linear charge density and that large changes in the polymer dimensions are observed at the adsorption-desorption limit. By adjusting the linear charge density and ionic strength, we demonstrate that the adsorption-desorption limit corresponds to a sharp transition from non-adsorbed to adsorbed conformations and that the mean adsorption energy per monomer has to be less than -0.4 kT to achieve adsorption. We calculated that the linear charge density at the adsorption-desorption limit is related to the Debye-Hückel length according to LCD^crit ~3². At small values of the linear charge density and low ionic strength (no adsorption is observed at high ionic strength), a large amount of monomers are present in loops and tails. By increasing LCD, the amount of monomers in trains reaches a maximum value and the polyelectrolyte adopt flat conformation at the surface of the particle.     

Viscometric and conductometric study of polyelectrolytes of low charge density in salt free aqueous solutions

Viscometric and conductometric measurements have been performed on dilute, salt free solutions of poly(vinyl alcohol) (PVA) and poly(vinyl alcohol, vinyl sulphate ester) copolymer salts in order to get information on transition from a neutral to charged macromolecules. With increasing linear charge density from a very low value to a moderate one a non linear dependence of polyelectrolyte effect on copolymer composition was observed. A comparison has shown that there is a close analogy between the expansion of polyanions and swelling of polyelectrolyte networks at comparable linear charge density range. Due to the intra- and inter-molecular mobile ionic bridges a considerable contraction was pointed out by viscometry for barium, magnesium and copper salts. However, the differences in properties of counterions of higher charge number indicates that in addition to the valency, there is a definite chemical effect, too. It has been revealed by the electric conductance measurements that the transition from a neutral to charged macromolecules could be a very complex one calling for a new and more detailed theoretical consideration of polyelectrolyte solutions.     

Dynamics and stability of dispersions of polyelectrolyte-filled multilayer microcapsules

The authors report dynamic and coagulation properties of a dispersion of polyelectrolyte multilayer microcapsules filled with solutions of a strong polyelectrolyte. Microcapsules are shown to take a charge of the sign of encapsulated polyions and are characterized by a nonuniform distribution of inner polyions, which indicates a semipermeability of the shell and a leakage of counterions. The capsule self-diffusion coefficient in the vicinity of the similarly charged wall is measured using a particle tracking procedure from confocal images of the dispersion. The diffusion of capsules in the force field suggests that the effective interaction potential contains an electrostatic barrier, so that we deal with the same types of interaction forces as for solid particles. The theoretical estimates of the authors show that when microcapsules are in close proximity, their interaction should even be quantitatively the same as that of colloids with the same surface potential. However, due to the mobility of inner polyions they might repel stronger at large distances. The authors thus conclude that the encapsulation of charged polymers is an important factor in determining the adhesion and interaction properties of multilayer microcapsules.     

The Effect of Surface Charge on Adsorption of a Cationic Polyelectrolyte

The regularities of adsorption of a cationic polyelectrolyte, poly(diallyldimethylammonium chloride), on the surface of fused quartz are studied at different values of solution pH by capillary electrokinetics. It is shown that the polyelectrolyte adsorption on a negatively charged surface depends on the value of the surface charge and increases with its growth. At a low charge value (pH 3.8), the polyelectrolyte adsorption increases the quartz surface charge. The driving forces of the adsorption are both electrostatic interaction and forces of nonelectrostatic nature, probably hydrophobic interactions and a change in entropy due to the displacement of counterions from a double layer. The adsorption of poly(diallyldimethylammonium chloride) on quartz from alkaline and neutral solutions is irreversible, which indicates the key role of the electrostatic interaction. At low values of the surface charge, the nonelectrostatic interactions play the main role, thereby resulting in polyelectrolyte desorption.     

Loose complexation of weakly charged microemulsion droplets and a polyelectrolyte

The effect of polyelectrolyte addition on the properties of an oil-in-water (O/W) microemulsion of weakly charged spherical micelles is studied. The 81 A radius O/W droplets in this system can be charged by the partial substitution of the nonionic surfactant by a cationic surfactant. The effect of the addition of poly(acrylic acid) (PAA), which is a charged pH-dependent polyelectrolyte, on the interactions between charged or noncharged droplets has been investigated using SANS. We have characterized the phase behavior of this pH-smart system as a function of the microemulsion and the polyelectrolyte concentration and the number of charges per droplet at three pH values: pH = 2, 4.5, and 12. In particular, an associative phase separation due to the bridging of the droplets by the neutral PAA chains through H-bonds is observed with extremely low PAA addition at low pH. At the opposite, an addition of PAA at pH = 4.5 generates a strong repulsive contribution between neutral droplets. Electrostatic bonds between charged droplets and PAA, controlled by the number of charges per droplet, are responsible for a pH drift and then for an associative phase separation similar to that observed at low pH. Finally, at high pH, the creation of electrostatic bonds between fully charged PAA and charged droplets liberates sufficiently counterions in solution at high droplet charge density to screen the electrostatic interactions and to allow an associative phase separation.     

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.