Diffusion of cationic polyelectrolytes into cellulosic fibers

The penetration of cationic polyelectrolytes into anionic cellulosic fibers was evaluated with fluorescent imaging techniques in order to clarify the mechanism and time scales for the diffusion process. The bulk charge of the cellulosic fibers indirectly creates a driving force for diffusion into the porous fiber wall, which is entropic in nature due to a release of counterions as the polyelectrolyte adsorbs. The individual bulk charges in the fiber cell wall also interact with the diffusing polyelectrolyte, such that the polyelectrolyte diffuses to the first available charge and consequently adsorbs and remains fixed. Thus, subsequent polyelectrolyte chains must first diffuse through the adsorbed polyelectrolyte layer before adsorbing to the next available bulk charges. This behavior differs from earlier suggested diffusion mechanisms, by which polyelectrolytes were assumed to first adsorb to the outermost surface and then reptate into the pore structure. The time scales for polyelectrolyte diffusion were highly dependent on the flexibility of the chain, which was estimated from calculations of the persistence length. The persistence length ultimately depended on the charge density and electrolyte concentration. The charge density of the polyelectrolyte had a greater influence on the time scales for diffusion. High charge density polyelectrolytes were observed to diffuse on a time scale of months, whereas the diffusion of low charge density polyelectrolytes was measured on the order of hours. An influence of the chain length, that is, steric interactions due the persistence length of the polyelectrolyte and to the tortuosity of the porous structure of the fiber wall, could only be noted for low charge density polyelectrolytes. Increasing the electrolyte concentration increased the chain flexibility by screening the electrostatic contribution to the persistence length, in turn inducing a faster diffusion process. However, a significant change in the diffusion behavior was observed at high electrolyte concentrations, at which the interaction between the polyelectrolyte charges and the fiber charges was almost completely screened.     

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.     

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.     

Electrophoretic mobility of a particle covered with an ion-penetrable membrane

The electrophoretic behavior of a planar particle covered by an ion-penetrable membrane, which simulates a biological entity, is investigated. We show that, in general, a point charge model will overestimate the electrophoretic mobility of a particle and the deviation increases with the increase in the concentration of fixed charge and with the decrease in the thickness of membrane layer. As in the case of a point charge model, the present model also predicts a local maximum in the absolute mobility as the thickness of membrane layer varies. If the sizes of counterions of various valences are the same, then the lower the valence of counterions, the larger the mobility, and the larger the counterions, the greater the mobility. The latter is consistent with the experimental observations in the literature. For the level of the concentration of fixed charge examined, the effect of coions on the mobility is negligible.     

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.     

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.     

A Monte Carlo study of spherical electrical double layer of macroions-polyelectrolytes systems in salt free solutions

A canonical Monte Carlo simulation is performed to investigate the microstructure and the electrical double layer (EDL) of polyelectrolytes around macroions in the bulk systems based on the primitive model. We explore the influences of particles size, chain length, and charge density of polyelectrolytes on the microscopic behavior of the macroions-polyelectrolytes systems. The simulation results show that the surface charge density and the chain length of the polyelectrolytes are two key factors that affect the microstructure of polyelectrolytes around the macroions and potential of mean force between the macroions as well as the zeta potential of the spherical EDL constructed by polyelectrolytes. The high surface charge density of a polyelectrolyte leads to the polyelectrolyte acting as a bridge for the aggregation of macroions, causing the presence of the attraction between macroions. The polyelectrolytes with a long chain length present a cooperativity effect for the adsorption of the polyelectrolytes on the surface of the macroions. Furthermore, the two key factors both induce the overcharge of the macroions. The longer the chain length and the higher surface charge density of the polyelectrolytes, the stronger is the overcharge.     

Mean field theory of charged dendrimer molecules

Using self-consistent field theory (SCFT), we study the conformational properties of polyelectrolyte dendrimers. We compare results for three different models of charge distributions on the polyelectrolytes: (1) a smeared, quenched charge distribution characteristic of strong polyelectrolytes; (2) a smeared, annealed charge distribution characteristic of weak polyelectrolytes; and (3) an implicit counterion model with Debye-Huckel interactions between the charged groups. Our results indicate that an explicit treatment of counterions is crucial for the accurate characterization of the conformations of polyelectrolyte dendrimers. In comparing the quenched and annealed models of charge distributions, annealed dendrimers were observed to modulate their charges in response to the density of polymer monomers, counterions, and salt ions. Such phenomena is not accommodated within the quenched model of dendrimers and is shown to lead to significant differences between the predictions of quenched and annealed model of dendrimers. In this regard, our results indicate that the average dissociated charge α inside the dendrimer serves as a useful parameter to map the effects of different parametric conditions and models onto each other. We also present comparisons to the scaling results proposed to explain the behavior of polyelectrolyte dendrimers. Inspired by the trends indicated by our results, we develop a strong segregation theory model whose predictions are shown to be in very good agreement with the numerical SCFT calculations.     

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.     

Transport properties of some cationic polysaccharides 2. Charge density effect

The charge density effect on the behavior of some cationic polysaccharides in aqueous and nonaqueous (methanol) solutions was studied by viscometric and conductometric measurements. The polyelectrolytes investigated contain quaternary ammonium salt groups, N-alkyl-N,N-dimethyl-2-hydroxypropylene ammonium chloride, attached to a dextran backbone. This new class of polyelectrolytes has various linear charge density parameters, xi, located below and above the critical threshold value of counterions condensation, xi(c)=1(xi=0.25-3.18). The viscometric data revealed that all copolymers exhibit a polyelectrolyte behavior and were plotted in the terms of Rao equation. The conductometric measurements of solutions of these copolymers were presented as a function of polymer concentration and charge density. The results were analyzed within the Manning's theory and lower experimental values of the equivalent conductivity than the theoretical ones were found. Possible reasons of this discrepancy have been discussed. The interaction parameters were evaluated and these were found to depend on both the polymer concentration and the charge density. The conductometric behavior of these cationic polysaccharides has shown that counterion condensation is not a threshold phenomenon, their association to the charged groups of the polyions taking place for xi>1 as well as xi<1.     

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.     

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.     

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.     

Influence of weak groups on polyelectrolyte mobilities

The ionization of dissociable groups in weak polyelectrolytes does not occur in a homogenous fashion. Monomer connectivity imposes constraints on the localization of the dissociated (charged) monomers that affect the local electric potential. As a result, the mean bare charge along a weak polyelectrolyte can vary depending on the proximity to topological features (e.g. presence of crosslinks or dangling ends). Using reaction‐ensemble Monte‐Carlo simulations we calculate the dissociation inhomogeneities for a few selected PE configurations, linear, rod‐like, flexible four‐arm star, and a star with stiff arms. An ensemble preaverage is used to obtain the annealed bare charge profile for these different polymer configurations. Using molecular dynamics simulations within a Lattice‐Boltzman fluid, we investigate how the electrophoretic mobility is affected by the bare charge inhomogeneities arising from the annealed weak polyelectrolytes. Surprisingly, the mobility obtained for the situations corresponding to the predicted charge profile for annealed weak polyelectrolytes are not significantly different than the mobility obtained when all the monomers have an identical charge (under the constraint that the total polyelectrolyte bare charge is the same). This is also true for the stiff rod‐like variants where conformational changes induced from the localization of the monomer charges are negligible. In salty solutions, we find that counterions are affected by the electric potential modulations induced by the topological features. Since the counterions crowd in regions where the electric potential caused by the dissociated monomers is highest, they wash‐out the bare charge inhomogeneities and contribute to a more uniform effective backbone charge.     

Linear polyelectrolytes in tetravalent salt solutions

The effect of adding tetravalent salt of different sizes to a solution of linear and flexible polyelectrolytes is investigated by molecular dynamics simulations. Upon the addition of salt, a chain reexpansion takes place, following a well-known collapsed conformation. The degrees of collapse and reexpansion increase with ion size. In the solution, tetravalent counterions replace monovalent ones and condense onto the chains. The condensation for small ions displays a profile different from that for large ones. In a high-salt region, ions can form layering orders around a polyelectrolyte and locally overcompensate the charge inside. Consequently, the integrated charge distribution reveals an oscillatory behavior away from a chain. By studying the radial distribution function between monomers on different polyelectrolytes, like-charge attraction between chains is demonstrated. This attraction is a prerequisite to chain aggregation or precipitation. The results show a strong dependence of salt concentration and ion size on the properties of polyelectrolyte solutions.     

Adsorption of highly charged polyelectrolytes onto an oppositely charged porous substrate

The adsorption behavior of highly charged cationic polyelectrolytes onto porous substrates is electrostatic in nature and has been shown to be highly dependent on the polyelectrolyte properties. Copolymers of acrylamide (AM) and diallyldimethylammonium chloride (DADMAC) were synthesized to have a range of macromolecular properties (i.e., charge density and molecular mass). Traditional titration methods have been complemented by fluorescence labeling techniques that were developed to directly observe the extent that fluorescently labeled poly(AM- co-DADMAC) adsorbs into the pore structure of a cellulosic substrate. Although contributing to the electrostatic driving force, the charge density acts to limit adsorption to the outermost surface under electrolyte-free conditions. However, adsorption into the pores can occur if both the molecular mass and charge density of poly(AM- co-DADMAC) are sufficiently low. Adsorption initially increases as the electrolyte concentration is increased. However, the electrostatic persistence length of poly(AM- co-DADMAC) restricts the polyelectrolyte from entering the pores. Therefore, changes in the adsorption behavior at moderate electrolyte concentrations have been attributed to swelling of the polyelectrolyte layer at the fiber exterior. The adsorption behavior changes again at high electrolyte concentrations such that poly(AM- co-DADMAC) could adsorb into the pore structure. This occurred when the electrolyte concentration was sufficient to screen the electrostatic persistence length of poly(AM- co-DADMAC), provided that the entropic driving force for adsorption still existed. It is suggested that adsorption into the pore structure is a kinetic process that is governed by localized electrostatic interactions between poly(AM- co-DADMAC) and the charges located within the pores.     

Counterions in layer-by-layer films--influence of the drying process

The amount of counterions, measured by means of X-ray photoelectron spectroscopy (XPS), in layer-by-layer (LbL) films of poly(allylamine hydrochloride) (PAH) and poly(styrene sulfonate) (PSS), prepared from solutions with various NaCl concentrations, is shown to be greatly influenced by the film drying process: a smaller amount of counterions is observed in films dried after adsorption of each layer, when compared with films that were never dried during the film preparation. This is attributed to the formation of NaCl nanocrystals during the drying process which dissolve when the film is again immersed in the next polyelectrolyte solution. The presence of bonded water molecules was confirmed in wet films indicating that the counterions near the ionic groups are immersed in a water network. The number of counterions is dependent on the amount of salt in polyelectrolyte solutions in such a way that for a concentration of 0.2 M the relative amount of counterions attains saturation for both dried and wet samples, indicating that the process which leads the aggregation of counterions near of the ionic groups is not influenced by the drying process. Moreover, it is proven for wet samples that the increase in salt concentration leads to a decrease in the number of PAH ionized groups as predicted by the Muthukumar theory [J. Chem. Phys. 120 (2004) 9343] accounting for the counterion condensation on flexible polyelectrolytes.     

Electrostatic-interaction-induced phase separation in solutions of flexible-chain polyelectrolytes

A model of a polyelectrolyte solution has been formulated on the basis of the formalism of the thermodynamic perturbation theory. Macromolecules have been described in terms of the model of a flexible chain with an excluded volume and a variable electrical charge. During construction of the thermodynamic perturbation theory, a set of three independent subsystems—polyelectrolyte macromolecules placed in a structureless charge background of counterions, counterions placed in a structureless charge background of macromolecules, and Coulomb gas ions of a low-molecular-mass salt—has been taken as the reference system. In the framework of this model, liquid-liquid phase separation due to strong correlation-induced attraction has been predicted. The behavior of the degree of ionization over a wide monomer concentration range, including the region of phase separation either in a salt-free solution or in the presence of univalent ions of a low-molecular-mass salt in the solution, has been studied. It has been shown that macromolecules in the coexisting phases should have different degrees of ionization. The occurrence of phase separation under normal conditions in the case when dimethylformamide is taken as a solvent and the nonoccurrence of this phase separation in the case of aqueous solutions of flexible-chain polyelectrolytes are predicted.     

Counterion localization in solutions of starlike polyelectrolytes and colloidal polyelectrolyte brushes: a self-consistent field theory

A quantitative analysis of the distribution of counterions in salt-free solutions of colloidal polyelectrolyte brushes and starlike polyelectrolytes is performed on the level of the Poisson-Boltzmann approximation. Exact numerical solutions are obtained for starlike polyelectrolyte molecules composed of f = 20, . . ., 50 arms with a fixed fractional charge alpha per segment by applying the self-consistent field method of Scheutjens and Fleer (SF-SCF). The Wigner-Seitz cell dimension defines the concentration of polyelectrolyte stars in the system. The numerical results are compared to predictions of an analytical mean field theory and related to experimental observations on the osmotic pressure in solutions of starlike polyelectrolytes and colloidal polyelectrolyte brushes.     

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.