Thermodynamic properties of a polyelectrolyte solution containing a mixture of counterions of the same charge

Electrostatic internal and free energies are calculated for the cell model of a polyelectrolyte solution having two kinds of counterions of the same charge but different size. The calculation is based on the solution of the Poisson–Boltzmann equation obtained previously. The electrostatic contributions to the internal and free energies are presented as functions of valences, radii, and mole fractions of counterions, and their application to interpretation of experimental results is discussed.     

Rod-like polyelectrolyte adsorption onto charged surfaces in monovalent and divalent salt solutions

We analyze the adsorption of strongly charged polyelectrolytes onto weakly charged surfaces in divalent salt solutions. We include short-range attractions between the monomers and the surface and between condensed ions and monomers, as well correlations among the condensed ions. Our results are compared with the adsorption in monovalent salt solutions. Different surface charge densities (σ), and divalent (m) and monovalent (s) salt concentrations are considered. When the Wigner-Seitz cells diameter (2R) is larger than the length of the rod, the maximum amount of adsorption scales like n_max ∼ σ^4/3 in both monovalent and divalent solutions. For homogeneously charged surfaces, the maximum adsorption occurs at s* ∼ σ² when s* > ϕ, where ϕ is the monomer concentration, the counterpart for divalent salt solution, m* roughly scales as σ^2.2 when m* > ϕ. The effective surface charge density has a maximum absolute value at m′ < m*. A discrete surface charge distribution and short-range attractions between monomers and surface charge groups can greatly enhance surface charge inversion especially for high salt concentration. The critical salt concentration for adsorption in divalent salt solution roughly scales as m_c ∼ bσ^1.9, where b is the distance between two neighboring charged monomers. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3642–3653, 2004     

Electrochemical characteristics of polyelectrolyte brushes with electroactive counterions

Cyclic voltammetry (CV) was employed to characterize the electrochemical behavior of polyelectrolyte brushes with immobilized electroactive counterions in response to external changes in concentration and composition of the supporting electrolyte and as a function of brush thickness. Poly(methacryloyloxy)ethyl-trimethyl-ammonium chloride (PMETAC) brushes were synthesized on Au substrates via atom transfer radical polymerization followed by ion-exchange with ferricyanide ions ([Fe(CN)6]3-) as redox probes. CV measurements of the modified PMETAC brushes showed the typical electrochemical response corresponding to a surface-confined electroactive species and the redox counterions, as [Fe(CN)6]3- species form stable ion pairs with the quaternary ammonium groups of the brush. The electron-transfer features of PMETAC brushes with different thicknesses, as characterized by CV and UV-vis spectroscopy, revealed that the charge density probed by CV was lower than the charge density measured by UV-vis spectroscopy. The electrode current decreased significantly with increasing concentration of supporting electrolyte due to the effect of the Donnan potential. Hydrophobic counterions, ClO4-, which induced brush collapse, lead to significantly reduced electrode currents.     

Bipolar reverse osmosis membrane for separating mono-and divalent ions

Bipolar reverse osmosis membranes that have both negatively and positively charged layers have been prepared to enhance the selectivity towards mono- and divalent ions in respect of both cations and anions. Positively charged layers are formed on low pressure reverse osmosis membranes having negative charge (NTR-7410 and 7450) by an adsorption method using polyethyleneimine (PEI) or a quaternary ammonium polyelectrolyte (QAP). These layers attach to the membrane's dense layer, which is made of sulfonated polyether sulfone. The selectivity of mono- and divalent ions is proven by experimental results for single electrolytes (NaCl, Na₂SO₄ and MgCl₂). Although negatively charged membranes repulse divalent anions more strongly than cations and monovalent anions, bipolar reverse osmosis membranes reject both divalent cations and divalent anions better than monovalent ions. An optimal preparation method for bipolar membranes showing selectivity towards mono- and divalent ions were developed. The bipolar membranes showed good ion selectivity for artificial sea water.     

Dynamics of counterions in polyelectrolyte multilayers studied by electro-optics

The electro-optical behavior of a multilayer constructed via layer-by-layer deposition of poly(sodium 4-styrenesulfonate) (PSS) and poly(allylamine hydrochloride) (PAH) onto ellipsoidal β-FeOOH particles is examined using electric light scattering method. For fully charged polymers (at pH 4.5), the electro-optical effect is found to increase with polyelectrolyte layer number, showing a tendency to saturation in the linear growth regime. The effect is greater and of lower frequency of relaxation for the films ending with PAH in comparison to those with top PSS layer. Evidence is given that polarization of “condensed” counterions along the chains of the last-adsorbed polymer is mainly responsible for the observed electro-optical behavior of the polyelectrolyte multilayer. Although incorporation of “condensed” small ions into the film bulk seems probable for the PSS/PAH multilayer, their participation in the electro-optical effect is found negligible. The structural changes in the PSS/PAH multilayer due to the PAH deprotonation at pH 7.5 and the corresponding changes in the electro-optical effect confirm the key role of the last-adsorbed polymer for the behavior of the entire PSS/PAH film.     

Investigation of the interaction of a polyelectrolyte with low molecular weight electrolytes containing nonidentical counterions by differential refractometry

If the counterion of a polyelectrolyte is not identical with any of the ions of a low molecular weight electrolyte added to the solution, the system may be regarded as a four-component system. Relations for the refractive index increments have been derived which allow the determination of the coefficient of selective sorption of the added electrolyte from the refractive index increments of the components independent of the original counterion of the polyelectrolyte. Equilibrium dialysis and differential refractometry were used to study the interaction of KCl, KBr and NaI with poly[-1(2-hydroxyethyl)pyridiniumbenzenesulfonate methacrylate] or with an analogous polymer containing a toluenesulfonate counterion in aqueous solutions. The coefficient of selective sorption increases in the series Cl^? < Br^? < I^? from strongly negative to strongly positive values; the specific interaction of these counterions with the macroion increases in the same order.     

Conductivity spectra of polyphosphazene-based polyelectrolyte multilayers

Polyelectrolyte multilayers are built up from ionically modified polyphosphazenes by layer-by-layer assembly of a cationic (poly[bis(3-amino-N,N,N-trimethyl-1-propanaminium iodide)phosphazene] (PAZ+) and an anionic poly[bis(lithium carboxylatophenoxy)phosphazene] (PAZ-). In comparison, multilayers of poly(sodium 4-styrenesulfonate) (PSS) and poly(allylamine hydrochloride) (PAH) are investigated. Frequency-dependent conductivity spectra are taken in sandwich geometry at controlled relative humidity. Conductivity spectra of ion-conducting materials generally display a dc plateau at low frequencies and a dispersive regime at higher frequencies. In the present case, the dispersive regime shows a frequency dependence, which is deviating from the typical behavior found in most ion-conducting materials. Dc conductivity values, which can be attributed to long-range ionic transport, are on the order of sigmadc = 10-10-10-7 S.cm-1 and strongly depend on relative humidity. For PAZ+/PAZ- multilayers sigmadc is consistently larger by one decade as compared to PSS/PAH layers, while the humidity dependence is similar, pointing at general mechanisms. A general law of a linear dependence of log(sigmadc) on relative humidity is found over a wide range of humidity and holds for both multilayer systems. This very strong dependence was attributed to variations of the ion mobility with water content, since the water content itself is not drastically dependent on humidity.     

Interaction of monovalent and divalent counterions with some carboxylic polysaccharides

Eleven samples of carboxylic polysaccharides were studied. The activity coefficients γ have been measured for monovalent (Na⁺) and divalent (Ca²⁺) counterions. There is no specific influence of the structure of the chain on γ values. Agreement with theoretical values confirms the rigidity of the chain; for low charge density, the theoretical treatment seems to be incorrect. Selectivity is discussed in term of selectivity coefficient K and free energy of exchange ΔG; ΔG is linearly related to the charge density but K which characterizes the competition of the two counterions is sensitive to the nature of the chain. The carboxymethylamyloses present a larger selectivity whose origin is not discussed here. The last point treated is the intrinsic constant of dissociation of polyacids. The pK₀ values are practically independent of the nature of the polyelectrolyte and of the charge density; the values are close to the pK₀ of monomeric unit and are not affected by the position of ? COOH in the anhydroglucose ring.     

Reversible electrochemical switching of polyelectrolyte brush surface energy using electroactive counterions

Polyelectrolyte brushes with electroactive counterions provide an effective platform for surfaces with electrochemically switchable wetting properties. Polycationic poly(2-(methacryloyloxy)-ethyl-trimethyl-ammonium chloride) (PMETAC) brushes with ferricyanide ions ([Fe(CN)6] 3-) were used as the electrochemically addressable surface. After a negative potential of -0.5 V was applied to the [Fe(CN)6](3-)-coordinated PMETAC brushes, the [Fe(CN)6](3-) species were reduced to [Fe(CN)6](4-), and the surface became more hydrophilic. By application of alternating negative and positive potentials, PMETAC brushes were switched reversibly between the reduced state ([Fe(CN)6]4-) and oxidized state ([Fe(CN)6]3-), resulting in reversible changes in water contact angles. The time required for a complete contact angle change can be tuned from 1 to 20 s, by changing the brush thickness and the concentration of supporting electrolyte. We present an electrochemical brush transport model that includes the electrochemical reaction at the charged electrode and describes ion transport through the brush phase covering the electrode. The model quantitatively describes the response of the contact angle (hydrophilicity) to the applied voltage as a function of background ionic strength and brush thickness, supporting the proposed mechanism of ion transport through the brush and electrochemical reaction at the electrode. A typical diffusion constant for ferricyanide in a PMETAC brush of any thickness in 5 mM KCl supporting electrolyte was found to be 2 x 10(-15) m2 s(-1), 5 to 6 orders of magnitude smaller than its bulk solution value.     

Monte Carlo simulations of charged dendrimer-linear polyelectrolyte complexes and explicit counterions

We study complexes composed of one dendrimer of generation G = 4 (G4 dendrimer) with N(t) = 32 charged terminal groups and an oppositely charged linear polyelectrolyte accompanied by neutralizing counterions in an athermal solvent using Monte Carlo simulations based on the bond fluctuation model. In our study both the full Coulomb potential and the excluded volume interactions are taken into account explicitly with the reduced temperature τ and the chain length N(ch) as the main simulation parameters. Our calculations indicate that there exist three temperature ranges that determine the behavior of such complexes. At τ(complex) stable charged dendrimer-linear polyelectrolyte complexes are formed first, which are subsequently accompanied by selective counterion localization within the complex interior at τ(loc) ≤ τ(complex), and counterion condensation as temperature is further decreased below τ(cond) < τ(loc). In particular, we observe that condensation takes place exclusively on the excess charges in the complex and thus no condensation is observed at the compensation point (N(ch) = N(t)), irrespective of τ. For N(ch) ≠ N(t) the complex is overally charged. Furthermore, we discuss the size and structure of the dendrimer and the linear polyelectrolyte within the complex, as well as spatial distributions of monomers and counterions. Conformations of the chain in the bound state are analysed in terms of loops, trains, and tails.     

Conductivity of nonaqueous solutions of aromatic polymers containing ionizable side groups

The concentration dependence of the equivalent conductivity has been measured for dilute DMAc solutions of K, Na, and Li salts of aromatic polymers with ionizable side groups [poly(diphenylenesulfophthalide) and poly(arylene ether ketone) with side COOH groups]. A correlation between the concentration dependences of the equivalent conductivity and reduced viscosity shows that the first parameter initially sharply decreases with an increase in concentration and then achieves a limiting value at a rather low concentration and that precisely in this concentration range the polyelectrolyte effect manifests itself in the concentration versus reduced viscosity curve. With an increasing amount of metal ions incorporated into the polymer, the equivalent conductivity grows. It was demonstrated that the type of counterion affects the reduced viscosity and equivalent conductivity of salt solutions. This effect depends on the structure of the polymer backbone: for poly(arylene ether ketone) salts, the reduced viscosity and the equivalent conductivity increase in the sequence Li → Na → K, while for poly(diphenylenesulfophthalide) salts, the reduced viscosity increases in the reverse order and the equivalent conductivity remains almost invariable. The limiting values of the equivalent conductivity and the degree of association of polyelectrolytes have been estimated in terms of the Arrhenius-Ostwald theory. It has been shown that, in the case of poly(diphenylenesulfophthalide) salts, the equivalent conductivity and the degree of association are higher than those for poly(arylene ether ketone) salts with side COOH groups. This finding is indicative of a stronger binding of counterions by poly(arylene ether ketone).     

Surface potential of spherical polyelectrolyte brushes in the presence of trivalent counterions

We consider the ζ-potential and the effective charge of spherical polyelectrolyte brushes (SPBs) in aqueous solution in the presence of trivalent europium ions. The SPB consists of a polystyrene core of ca. 250 nm diameter onto which long chains of the strong polyelectrolyte poly(styrene sulfonate) are grafted (contour length: 82 nm). At low concentration of EuCl₃ the chains are stretched to nearly full length. If the concentration of the trivalent ions is raised, the surface layer of the polyelectrolyte chains collapses. The ζ-potential of the SPB is calculated from the electrophoretic mobilities measured at different concentrations of EuCl₃. At the collapse, ζ decreases by the partial neutralization of the charges by the trivalent ions. The experimental ζ-potential thus obtained agrees with the theoretical surface potential Ψ_theo calculated for the effective shear plane by a variational free energy model of the SPB.     

Osmotic coefficient of a polyelectrolyte solution with a mixture of monovalent counterions

An analytical solution of the Poisson-Boltzmann equation is presented for the cell model of a polyelectrolyte solution with two species of monovalent counterions of different size. On this basis the osmotic coefficient is calculated as a function of the mole fraction of counterions and their radii. It is shown that the degree of binding of the smaller ion species increases as its mole fraction decreases.     

Absence of charge inversion on rodlike polyelectrolytes with excess divalent counterions

Filamentous viruses such as fd and M13 are highly charged rodlike polyelectrolytes. In this study, we employ fd virus to test the recent prediction of charge inversion [Nguyen, Rouzina, and Shklovskii, J. Chem. Phys. 112, 2562 (2000)]. Light scattering measurements show bundle formation and resolubilization of fd viruses when MgCl(2) was added from 0 to 600 mM. The effective charge of fd was studied by measuring their electrophoretic mobility using a filament tracking method uniquely suited for the system. Monte Carlo simulations were performed under canonical ensemble to predict the charge distribution around the rodlike virus. Charge inversion, which has been suggested theoretically to accompany with bundle resolubilization, was not observed in either experiments or simulations. A modified analysis of force balance is called upon to account for these new findings.     

Osmotic coefficients of polystyrenesulphonates in dioxane-water mixtures—II. Divalent counterions and mixtures of mono- and divalent counterions

The osmotic pressures of solutions of magnesium and calcium polystyrenesulphonate in water and in 25 wt % mixture of dioxane in water have been measured for concentrations from 0?002 to 0?06 molal in monomer units. The osmotic coefficient derived from these measurements is almost independent of concentration. Its values for solutions in dioxane-water mixtures are much lower than for aqueous solutions. The osmotic coefficients of solutions containing mixtures of polystyrenesulphonic acid and its calcium salt in 25 wt % dioxane have also been determined. The osmotic coefficient of these solutions has a distinct maximum at a certain value of the equivalent fraction of the acid. The experimental results are compared with the predictions of the cylindrical cell model and infinite line charge model. Satisfactory agreement between theory and experiment is found.     

Enrichment and distribution of counterions in spherical polyelectrolyte brushes probed by SAXS

The spatial correlation of counterions [Li⁺, Na⁺, Rb⁺, Cs⁺, NH₄⁺, (CH₃)₄N⁺] with spherical polyelectrolyte brushes (SPBs), which consist of a PS core and chemically grafted PSS chains, was comprehensively studied through a combination of SAXS, DLS, and Zeta potential. Results show that the SAXS intensity profiles of the brush appears to be “insensitive” to the concentration of Na⁺. By contrast, introducing salt ions with a density lower than sodium [NH₄⁺, (CH₃)₄N⁺ and Li⁺] into the brush layer will cause a decrease in the scattering intensity while introducing those with a higher density than sodium (Rb⁺ and Cs⁺) will cause the opposite result. As verified by the combined results of SAXS, DLS, and Zeta potential, the collapse of the brush and the enrichment of the counterions in the brush layer occur simultaneously. It was further demonstrated that the concentration of counterions enriched in the innermost layer of the brush shell can be enhanced up to hundreds of times compared with the bulk concentration, and the counterion distribution in SPB shell follows a radial attenuation distribution. SAXS is confirmed to be powerful in probing the enrichment and distribution of counterions within SPB. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 738–747