Electrical conductivity of some cationic polysaccharides. I. Effects of polyelectrolyte concentration,charge density,substituent at the ionic group,and solvent polarity

Electrolytic conductivity behavior of some cationic polysaccharides in water, methanol, and the mixtures water/methanol is presented. The polyelectrolytes investigated contain quaternary ammonium salt groups, N‐alkyl‐N,N‐dimethyl‐2‐hydroxypropyleneammonium chloride, attached to a dextran backbone. This study considers the influences of polymer concentration (1 × 10^?6 < C < 1 × 10^?2 monomol L^?1) and the charge density (ξ = 0.48–3.17) modified either by changing charge distance (b) or dielectric constant of the solvent (ε) on polyion–counterion interaction in salt‐free solutions. Above the critical value, ξ_c = 1, the variation of the equivalent conductivity (Λ) as a function of concentration is typical for a polyelectrolyte behavior. The conductometric data in water were analyzed in terms of the Manning's counterion condensation theory. The presence of longer alkyl chains at quaternary N atoms was found to have a negligible influence on the Λ values. The results show that the decrease of the medium polarity results in the decrease of the number of free ions and, consequently, of the equivalent conductivity values. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 3584–3590, 2005     

Polyelectrolyte conductivity

Using the de Gennes scaling model for the configuration of a polyelectrolyte chain in semidilute solution, we construct a simple model of AC conductivity for semidilute solutions of strongly charged polyelectrolytes without added salt. We compare the predictions of this model with literature data and new data on two polyelectrolytes with very different affinities for water. The sodium salt of sulfonated polystyrene in water is a hydrophobic polyelectrolyte (the uncharged monomer does not dissolve in water), where the chain is locally collapsed. The sodium salt of poly(2-acrylamido-2-methylpropanesulfonate), is a much more hydrophilic polyelectrolyte, making the chain quite expanded locally. The model describes the conductivity of both cases reasonably for concentrations below 10⁻² M (mol of monomer per liter). Deviations between experiment and theory at higher concentrations lead us to conclude that counterion condensation decreases as concentration is increased. This is qualitatively consistent with the experimental observation that the dielectric constant of the polyelectrolyte solution increases as polyelectrolyte is added. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2951–2960, 1997     

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.     

The effect of electrosteric interactions on the effective charge of thermoresponsive ionic microgels: Theory and experiments

In this work, the influence of counterion valence and salt concentration on the effective charge of two types of thermoresponsive ionic microgel particles has been studied. The effective charge of the microgel at different swelling states has been experimentally determined from electrophoretic mobility measurements by solving the electrokinetic equations of the solvent for a single polyelectrolyte brush in the presence of an electric field, taking into account the friction of the solvent inside the polymer network. The experimental results have been compared to those obtained by means of the Ornstein‐Zernike integral formalism within the HNC relation. Results show that microgel bare charge is screened by the combined effect of counterion condensation and permeation inside the microgel particle. In addition to the electrostatic interaction, the steric exclusion exerted by the polymer plays an important role on the local ionic concentrations, especially for shrunken configurations. This steric term is responsible for the strong increase of the microgel effective charge experimentally observed when particles shrink for temperatures above the lower critical solution temperature. We also observe that, in the internal region of the microgel, charge electroneutrality is fulfilled, so the effective charge mainly arises from the region close to the microgel surface. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 2038–2049.     

Effective charges of polyelectrolytes in a salt-free solution based on counterion chemical potential

The phenomenon of counterion condensation around a flexible polyelectrolyte chain with N monomers is investigated by Monte Carlo simulations in terms of the degree of ionization alpha, which is proportional to the effective charge. It is operationally defined as the ratio of observed to intrinsic counterion concentration, alpha = co/ci. The observed counterion concentration in the dilute polyelectrolyte solution is equivalent to an electrolyte solution of concentration co with the same counterion chemical potential. It can be determined directly by thermodynamic experiments such as ion-selective electrode. With the polyelectrolyte fixed at the center of the spherical Wigner-Seitz cell, the polymer conformation, counterion distribution, and chemical potential can be obtained. Our simulation shows that the degree of ionization rises as the polymer concentration decreases. This behavior is opposite to that calculated from the infinitely long charged rod model, which is often used to study counterion condensation. Moreover, we find that, for a specified line charge density, alpha decreases with an increment in chain length and chain flexibility. In fact, the degree of ionization is found to decline with increasing polymer fractal dimension, which can be tuned by varying bending modulus and solvent quality. Those results can be qualitatively explained by a simple model of two-phase approximation.     

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 cylinders and spheres: Ion size effects

The effect of the counterion size on the degree of counterion condensation onto a cylindrical macroion and a spherical one in the absence of salt is studied theoretically within a modified Poisson–Boltzmann approach. We find that excluded volume interactions reduce the degree of condensation. Using a simple variational free energy we show that this reduction can be attributed to an effective increase in the macroion size due to the contribution of the condensed counterions. We also find that for a charged cylinder, the reduction in charge renormalization vanishes at infinite dilution because of the extended nature of the condensed layer. In contrast, excluded volume interactions can reduce the degree of charge renormalization of a sphere even at high dilutions. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3598–3615, 2004     

Aqueous solutions of ionenes: interactions and counterion specific effects as seen by neutron scattering

Aqueous solutions of ionenes with bromide and fluoride counterions have been investigated using small angle neutron scattering for the first time. Ionenes are a class of cationic polyelectrolytes based on quaternary ammonium atoms and, considering the very low solubility of their uncharged part (hydrocarbon chain), would be formally classified as hydrophobic. Ionenes present important structural differences over previously studied polyelectrolytes: (a) charge is located on the polyelectrolyte backbone, (b) the distance between charges is regular and tunable by synthesis, (c) hydrophobicity comes from methylene groups of the backbone and not from bulky side groups. Results for Br ionenes feature a disappearance of the well-known polyelectrolyte peak beyond a given monomer concentration. Below this concentration, the position of the peak depends on the chain charge density, f(chem), and scales as f(chem)(0.30±0.04). This is an indication of a hydrophilic character of the ionene backbone. In addition, osmotic coefficients of ionene solutions resemble again other hydrophilic polyelectrolytes, featuring no unusual increase in the water activity (or a significant counterion condensation). We conclude that despite the hydrophobicity of the hydrocarbon chain separating charged centers on ionenes, these chains behave as hydrophilic. In contrast to Br ionenes, the polyelectrolyte peak remains at all concentrations studied for the single F ionene investigated. This strong counterion effect is rationalized in terms of the different hydrating properties and ion pairing in the case of bromide and fluoride ions.     

Nonstoichiometric polyelectrolyte complexes: A mathematical model and some experimental results

A mathematical model is presented to describe nonstoichiometric water‐soluble polyelectrolyte complexes, and the predictions are compared with some experimental results. The theory is a mixture of Madelung's theory for ionic crystals and Manning's counterion condensation theory. The central parameters are the degree of complexation, φ, and the degree of counterion binding, θ. All other quantities are known in principle. It is found that there is a competition between complexation and counterion binding. When φ is large, θ is small, or vice versa. The degree of complexation, φ, depends sensibly on the concentration, c_s, of the added low molecular salt, the polyanion chain length, N, and the dielectric constant, ϵ, of the solvent. There exists a critical salt concentration, c_s,c, at which the complexes salt out and where for c_s > c_s,c the complexes dissociate back into their single strands, the polyanions, and polycations. Further, φ is larger the smaller the polyanion length and the smaller the solvent dielectric constant are. To prove these predictions we have formed nonstoichiometric complexes between IONENE and PAA and IONENE and PMAA, respectively. The degree of complexation was determined by ultracentrifugation and checked by viscometry. The accord found between theory and experiment is both qualitatively as well quantitatively quite well. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 335–348, 1999     

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.     

Theory of volume transition in polyelectrolyte gels with charge regularization

We present a theory for polyelectrolyte gels that allow the effective charge of the polymer backbone to self-regulate. Using a variational approach, we obtain an expression for the free energy of gels that accounts for the gel elasticity, free energy of mixing, counterion adsorption, local dielectric constant, electrostatic interaction among polymer segments, electrolyte ion correlations, and self-consistent charge regularization on the polymer strands. This free energy is then minimized to predict the behavior of the system as characterized by the gel volume fraction as a function of external variables such as temperature and salt concentration. We present results for the volume transition of polyelectrolyte gels in salt-free solvents, solvents with monovalent salts, and solvents with divalent salts. The results of our theoretical analysis capture the essential features of existing experimental results and also provide predictions for further experimentation. Our analysis highlights the importance of the self-regularization of the effective charge for the volume transition of gels in particular, and for charged polymer systems in general. Our analysis also enables us to identify the dominant free energy contributions for charged polymer networks and provides a framework for further investigation of specific experimental systems.     

Molecular dynamics simulation of discontinuous volume phase transitions in highly-charged crosslinked polyelectrolyte networks with explicit counterions in good solvent

The volumetric properties of highly-charged defect-free polyelectrolyte networks with tetrafunctional crosslinks are studied through molecular dynamics simulations in the canonical ensemble. The network backbone monomers, which are monovalent, and the counterions, which are mono-, di-, or trivalent, are modeled explicitly in the simulations, but the solvent is treated implicitly as a dielectric medium of good solvation quality. The osmotic pressure of the network-solvent system is found to depend greatly on the strength of electrostatic interactions. Discontinuous volume phase transitions are observed when the electrostatic interactions are strong, and the onset of these transitions shifts to higher solvent dielectricity as the counterion valency increases. The roles of the various virial contributions to the osmotic pressure are examined. The network elasticity entropy is found to behave nearly classically. As the network contracts and collapses with increasing strength of electrostatic interactions, the loss of counterion entropy leads to increased counterion osmotic pressure contributions via two mechanisms. The reduction in available configurational space increases the counterion translational entropy contribution to the ideal part of the osmotic pressure, and the greater number of counterion-monomer contacts formed due to counterion condensation and confinement increases the counterion excluded-volume entropy contribution to the excess part of the osmotic pressure. These observations contrast the decrease in the single ideal-gas-like counterion translational entropy contribution to the osmotic pressure predicted by the counterion condensation-charge renormalization theory. An accompanying decrease in the total electrostatic energy balances the loss of counterion excluded-volume entropy as the polyelectrolyte networks collapse in low-dielectric solvents. This interplay between the electrostatic energy and the counterion excluded-volume entropy appears to be responsible for the discontinuous volume phase transitions that are observed in polyelectrolyte networks. The structure of the polyelectrolyte network is also found to be affine in the swollen state, with constituent chains nearly fully extended, and nonaffine in the collapsed state, with the chains adopting a Gaussian conformation.     

Solution properties of ion-containing polymers in polar solvents

The placement of ionic groups within the molecular structure of a polymer produces marked modification in physical properties. A large number of studies have been performed on these ion-containing polymers, but few have focused on the effects of anion–cation interactions (i.e., counterion binding or ionization) on hydrodynamic volume, especially as the molecular structure of the solvent and nature of counterion are varied. In this study changes in hydrodynamic volume are followed through reduced viscosity measurements as a function of the abovementioned molecular parameters. The dilute solution properties of various polyelectrolytes that contain sulfonate and carboxylate groups were investigated as a function of the counterion structure, charge density, molecular weight, and solvent structure. The polymeric materials were selected because of their specific chemical structure and physical properties. In the first instance a (2-acrylamide-2 methylpropanesulfonic acid)-acrylamide-sodium vinyl sulfonate terpolymer was synthesized and subsequently neutralized with a series of bases. Viscometric measurements on these materials indicate that the nature of the cation affects the ability of the polyelectrolyte to expand its hydrodynamic volume at low polymer levels. The magnitude of the molecular expansion is shown to be due in part to the ability of the counterion to dissociate from the backbone chain, which, in turn, is directly related to the solvent structure. The changes in solution behaviour of these inomers lend support for the existence of ion pairs (i.e., site binding) and ionized moieties on the polymer chains. Measurements performed in a variety of solvent systems further confirm this interpretation. In addition, and acrylamide-sodium vinyl sulfonate copolymer was partially hydrolyzed with sodium hydroxide to study the effect of varying the charge density at a constant degree of polymerization and counterion structure. The results show that the charge density has a significant effect on the magnitude of the reduced viscosity and dilute solution behaviour. These observations, made in aqueous and nonaqueous solvents, are related to the interrelation of hydrodynamic volume, counterion concentration, and site binding. Again the controlling factor is the degree of site binding of the counterion onto the polymer backbone. Finally, we observe that the increased hydrodynamic volume affects viscosity behavior beyond the polyelectrolyte effect regime. If the average charge density on the macromolecule is relative high and/or the molecular weight is large (≥ 10⁶) sufficient intermolecular interactions will occur to produce rapid changes in reduced viscosity.     

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)].     

强电解质凝胶的溶胀平衡与体积相变

以作者近年来对强电解质凝胶的研究结果为中心,介绍了磺酸基凝胶和丙烯酸基凝胶在纯水,缓冲溶液中溶胀比与电荷密度的关系及其差异,揭示了磺酸基凝胶中的反离子凝聚现象和在有机溶剂中体积相变,还讨论了体积相变的滞后现象及其成因,最后就体积相变的驱动力,统一认识电解质和离聚体以及有关的实验结果阐述了作者的见解。     

Interacting nanoparticles with functional surface groups

Functionalized nanoparticles with ionizable groups have generated a large variety of structures with important potential applications in technology. The nature of their interactions is crucial to determining their solubility and to exploring assemblies with diverse symmetries. Here, we use a molecular theory to describe the interactions between two nanoparticles coated with short polymer chains that contain ionizable (functional) end‐groups immersed in aqueous salt solution. It is shown here that the fraction of ionized functional groups in the system depends on factors such as the ionic strength and pH of solution, grafting density of polymer chains, the chain length, as well as the separation distance between the nanoparticles. The interactions between two neighboring nanoparticles influence the charge regulation of the end‐groups, which consequently induces an asymmetric distribution of these charged end‐groups on the nanoparticles, and thus confers a preferred directionality in nanoparticle–nanoparticle interactions. We show that the charge regulating system is less repulsive than an equivalent system with a fixed charge distribution. This is due to a decrease in the charge density of the weak acid end‐groups, to avoid a local increase in counterion confinement (condensation) in the region between neighboring nanoparticles, when their separation decreases. The anisotropic degree of ionization found in our results can be used to design aggregates of nanoparticles with reduced symmetries. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

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.     

Single ion diffusive transport within a Poly(styrene sulfonate) polymer brush matrix probed by fluorescence correlation spectroscopy

Diffusive transport within complex environments is a critical piece of the chemistry occurring in such diverse membrane systems as proton exchange and bilayer lipid membranes. In the present study, fluorescence correlation spectroscopy was used to evaluate diffusive charge transport within a strong polyelectrolyte polymer brush. The fluorescent cation rhodamine-6G was used as a counterion probe molecule, and the strong polyelectrolyte poly(styrene sulfonate) was the polymer brush. Such strong polyelectrolyte brushes show promise for charge storage applications, and thus it is important to understand and tune their transport efficiencies. The polymer brush demonstrated preferential solvation of the probe counterion as compared to solvation by the aqueous solvent phase. Additionally, diffusion within the polymer brush was strongly inhibited, as evidenced by a decrease in diffusion constant of 4 orders of magnitude. It also proved possible to tune the transport characteristics by controlling the solvent pH, and thus the ionic strength of the solvent. The diffusion characteristics within the charged brush system depend on the brush density as well as the effective interaction potential between the probe ions and the brush. In response to changes in ionic strength of the solution, it was found that these two properties act in opposition to each other within this strong polyelectrolyte polymer brush environment. A stochastic random walk model was developed to simulate interaction of a diffusing charged particle with a periodic potential, to show the response of characteristic diffusion times to electrostatic field strengths. The combined results of the experiments and simulations demonstrate that responsive diffusion characteristics in this brush system are dominated by changes in Coulombic interactions rather than changes in brush density. More generally, these results support the use of FCS to evaluate local charge transport properties within polyelectrolyte brush systems, and demonstrate that the technique shows promise in the development of novel polyelectrolyte films for charge storage/transport materials.     

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.     

The pH inside a swollen polyelectrolyte gel: poly(N-vinylimidazole)

The pH inside a dissolved polyelectrolyte coil or a swollen ionic polymer network is not accessible to direct measurement. It is here calculated through a simple model, based on Donnan equilibrium, counterion condensation (for charge density exceeding the critical value), and balance of mobile ions, without any assumption on the pKa of the ionizable groups. The data needed for the calculation with this model are polymer concentration, pH value in the initial solution, and pH value in the bath at equilibrium. All three can be determined experimentally by a batch method where the polymer is immersed in a different pot for each starting pH. The model is applied to a sample system, namely, chemically cross-linked poly(N-vinylimidazole) immersed in acidic baths of different pH values. The imidazole units are basic and become protonated by the acid, thus changing the pH of the initial bath. The model shows how the pH developed inside the swollen gel is several units higher than the pH of the bath at equilibrium, both with or without the correction for counterion condensation. Consequently, when the pKa of the polyelectrolyte is determined in the usual way (with the pH measured in the external bath), it gives an apparent value that is several units below the pKa determined from the actual pH inside the swollen gel at equilibrium. The inclusion of the counterion condensation decreases very slightly the polymer basicity. Surface effects and intramolecular association between protonated and unprotonated imidazole rings are discussed to explain the pKa behavior in the limit of low degree of ionization.