Salt-free Polyelectrolyte Solutions Research Articles

Depletion of Polyelectrolytes near Like-Charged Substrates Probed by Optical Reflectivity

Salt-free polyelectrolyte solutions form a polyelectrolyte-free depletion layer near like-charged solid interfaces. This evidence is provided by optical reflectivity measurements from planar silica substrates in contact with aqueous solutions of sodium poly(styrene sulfonate). Analysis of the observed reflectivity signal, which features unusual negative signals and optical matching points, with a two-slab model demonstrates the existence of such a polyelectrolyte-free depletion layer. Moreover, the applied model permits the extraction of the corresponding layer thickness, which typically is several tenths of nanometers. This thickness decreases as the inverse square root of the polyelectrolyte concentration, but the actual values exceed the expected Debye length substantially. These results clearly provide independent evidence for the existence of a polyelectrolyte-free depletion layer, as previously suggested on the basis of direct force measurements with the atomic force measurement.

Overlap Concentration in Salt-Free Polyelectrolyte Solutions

For strongly charged polyelectrolytes in salt-free solutions, we use molecular dynamics simulations of a coarse-grained bead-spring model to calculate overlap concentrations c* and chain structure ...

Entanglement Properties of Polyelectrolytes in Salt-Free and Excess-Salt Solutions.

We study the entanglement properties of polyelectrolytes in salt-free and excess-salt solutions, corresponding to rod-like and expanded coil conformations, respectively. While the solvent's ionic strength has a large impact on the conformation of polyelectrolytes, it does not affect its entanglement density and entanglement crossover. This contradicts current models of polymer entanglement and suggests that the density of binary contacts in solution is not affected by the solvent quality. Based on this observation, we work out the reptation dynamics of polyelectrolytes in salt-free solution, which differ appreciably from earlier models.

Viscosity of Semidilute and Concentrated Nonentangled Flexible Polyelectrolytes in Salt-Free Solution.

We report viscosity data of nonentangled sodium polystyrene sulfonate (NaPSS) in salt-free aqueous solution as a function of polymer concentration ( c) and degree of polymerization ( N). Different empirical equations are examined and found not to describe the semidilute solution viscosity over a wide concentration range and/or to yield values of [η] that do not match dilute solution measurements. Deviations from the scaling prediction of ηsp ∝ c1/2 (Fuoss' law) are observed at high concentrations. Specifically, we find ηsp ≈ N1.26 c1/2 e1.4 c in the semidilute regime, which agrees with the scaling prediction only for c ≲ 0.02 M. The viscosity data presented in this study and in earlier reports show a high degree of consistency. A comparison with diffusion measurements for NaPSS in salt-free solution by Oostwal and co-workers suggests that the disagreement between the scaling theory and experiments does not arise solely from the concentration dependence of the monomeric friction coefficient.

Communication: Counter-ion solvation and anomalous low-angle scattering in salt-free polyelectrolyte solutions.

We investigate the influence of counter-ion solvation on the homogeneity of salt-free polyelectrolyte solutions based on a coarse-grained model that includes an explicit solvent. We show that the solvation of the counter-ions can cause a transformation between a nearly homogeneous to a non-uniform polymer solution, in which there is both a chain clustering and the formation of large charge-free domains, i.e., "voids." The emergence of these heterogeneous structures induced by counter-ion solvation is accompanied by the localization and formation of counter-ion rich domains that are symptomatic of emergent effective long-range attractive interchain interactions.

Barrier-induced dielectric counterion relaxation at super-low frequencies in salt-free polyelectrolyte solutions.

Based on the thermally activated diffusion of counterions over the barrier of the electrostatic binding potential, we construct a scaling theory for the slow dielectric response in dilute and semi-dilute polyelectrolyte solutions. The theory is based on an analytic evaluation of the mean-escape time of a single counterion from the surface of a polyelectrolyte chain and uses a variational expression for the electrostatic potential of a charged cylinder including counterion condensation. This mean-escape time shows a range of characteristic power-law dependencies on the polyelectrolyte length and the polyelectrolyte monomer concentration. The existence of this novel dielectric mode at super-low frequencies reflects the wide spectrum of experimental findings for the super-low-frequency dielectric relaxation mode and thereby helps to reconcile conflicting interpretations of experimental data in terms of conventional scaling laws. We also devise a scaling theory for the counterion condensation of finite-length polyelectrolyte chains at finite concentration, which allows us to include polyelectrolyte charge renormalization in dilute as well as semi-dilute solutions in a unified theoretical framework.

Importance of varying permittivity on the conductivity of polyelectrolyte solutions.

Dissolved ions can alter the local permittivity of water; nevertheless most theories and simulations ignore this fact. We present a novel algorithm for treating spatial and temporal variations in the permittivity and use it to measure the equivalent conductivity of a salt-free polyelectrolyte solution. Our new approach quantitatively reproduces experimental results unlike simulations with a constant permittivity that even qualitatively fail to describe the data. We can relate this success to a change in the ion distribution close to the polymer due to the buildup of a permittivity gradient.

A new equation of state of a flexible-chain polyelectrolyte solution: Phase equilibria and osmotic pressure in the salt-free case.

We develop a first-principle equation of state of salt-free polyelectrolyte solution in the limit of infinitely long flexible polymer chains in the framework of a field-theoretical formalism beyond the linear Debye-Hueckel theory and predict a liquid-liquid phase separation induced by a strong correlation attraction. As a reference system, we choose a set of two subsystems-charged macromolecules immersed in a structureless oppositely charged background created by counterions (polymer one component plasma) and counterions immersed in oppositely charged background created by polymer chains (hard-core one component plasma). We calculate the excess free energy of polymer one component plasma in the framework of modified random phase approximation, whereas a contribution of charge densities' fluctuations of neutralizing backgrounds we evaluate at the level of Gaussian approximation. We show that our theory is in a very good agreement with the results of Monte Carlo and MD simulations for critical parameters of liquid-liquid phase separation and osmotic pressure in a wide range of monomer concentration above the critical point, respectively.

Low-frequency collective exchange mode in the dielectric spectrum of salt-free dilute polyelectrolyte solutions

We study the frequency-dependent dielectric response of flexible polyelectrolyte chains in aqueous salt-free dilute solution as a function of polymer concentration and length by means of Brownian dynamics simulations including hydrodynamic interactions. We show that condensed and uncondensed counter ions are characterized by different dielectric response spectra and thus confirm long-held scaling assumptions used for the interpretation of experimental data. In addition to the well-known relaxation modes of condensed and uncondensed counter ions we observe for a single polyelectrolyte chain, we find in many-chain simulations a novel spectral feature at low frequencies that essentially corresponds to an exchange of counter ions between neighboring polyelectrolytes. Our results suggest that the experimental low-frequency dielectric mode might not be due to condensed counter ions, as is commonly assumed, but rather due to a collective many-chain process. This could resolve a long-standing puzzle in the comparison of experimental results and scaling predictions.

Conformational effect on small angle neutron scattering behavior of interacting polyelectrolyte solutions: A perspective of integral equation theory

We present small angle neutron scattering (SANS) measurements of deuterium oxide (D(2)O) solutions of linear and star sodium poly(styrene sulfonate) (NaPSS) as a function of polyelectrolyte concentration. Emphasis is on understanding the dependence of their SANS coherent scattering cross section I(Q) on the molecular architecture of single polyelectrolyte. The key finding is that for a given concentration, star polyelectrolytes exhibit more pronounced characteristic peaks in I(Q), and the position of the first peak occurs at a smaller Q compared to their linear counterparts. Based on a model of integral equation theory, we first compare the SANS experimental I(Q) of salt-free polyelectrolyte solutions with that predicted theoretically. Having seen their satisfactory qualitative agreement, the dependence of counterion association behavior on polyelectrolyte geometry and concentration is further explored. Our predictions reveal that the ionic environment of polyelectrolyte exhibits a strong dependence on polyelectrolyte geometry at lower polyelectrolyte concentration. However, when both linear and star polyelectrolytes exceed their overlap concentrations, the spatial distribution of counterion is found to be essentially insensitive to polyelectrolyte geometry due to the steric effect.

Electrical Conductances of Sodium Carboxymethylcellulose in Acetonitrile (1) + Water (2) Mixed Solvent Media in the Presence of Sodium Chloride at 308.15 K

The electrical conductances of solutions of an anionic polyelectrolyte sodium carboxymethylcellulose in acetonitrile (1) + water (2) mixed solvent media containing 0.10, 0.20, and 0.40 volume fractions of acetonitrile (v1) have been reported at 308.15 K in the presence of sodium chloride. The conductance data have been analyzed on the basis of an equation recently developed by us (J. Chem. Eng. Data, 2010, 55, 2108–2115) following the model for the electrical conductivity of salt-free polyelectrolyte solutions using the scaling description for the configuration of a polyion chain according to Dobrynin et al. (Macromolecules, 1995, 28, 1859–1871). Excellent quantitative agreement between the experimental results and those obtained using the equation developed here was observed. This provides further support in favor of the approach developed. Influences of the solvent composition and the concentration of the added salt were also examined.

Electrical Conductances of Sodium Polystyrenesulfonate in 2-Ethoxyethanol (1) + Water (2) Mixed Solvent Media in the Presence of Sodium Chloride at (308.15, 313.15, 318.15, and 323.15) K

The electrical conductances of solutions of an anionic polyelectrolyte sodium polystyrenesulfonate in 2-ethoxyethanol (1) + water (2) mixed solvent media containing (0.25, 0.40, and 0.50) mass fractions of 2-ethoxyethanol (w1) have been reported at (308.15, 313.15, 318.15, and 323.15) K in the presence of sodium chloride. The conductance data have been analyzed on the basis of an equation developed in this study following the model for the electrical conductivity of salt-free polyelectrolyte solutions using the scaling description for the configuration of a semidilute polyion chain according to Dobrynin et al. (Macromolecules 1995, 28, 1859−1871). Excellent quantitative agreement between the experimental results and those obtained using the equation developed here was observed.

Charge regularization in phase separating polyelectrolyte solutions

Theoretical investigations of phase separation in polyelectrolyte solutions have so far assumed that the effective charge of the polyelectrolyte chains is fixed. The ability of the polyelectrolyte chains to self-regulate their effective charge due to the self-consistent coupling between ionization equilibrium and polymer conformations, depending on the dielectric constant, temperature, and polymer concentration, affects the critical phenomena and phase transitions drastically. By considering salt-free polyelectrolyte solutions, we show that the daughter phases have different polymer charges from that of the mother phase. The critical point is also altered significantly by the charge self-regularization of the polymer chains. This work extends the progress made so far in the theory of phase separation of strong polyelectrolyte solutions to a higher level of understanding by considering chains which can self-regulate their charge.

Electrical conductivity of sodium polystyrenesulfonate in acetonitrile–water-mixed solvent media: experiment and data analysis using the Manning counterion condensation model and the scaling theory approach

Precise measurements on the electrical conductivity of sodium polystyrenesulfonate in acetonitrile–water-mixed solvent media containing 20 and 40 vol.% of acetonitrile at 308.15, 313.15, and 318.15 K are reported. The mobility of the polyelectrolyte solute was found to be influenced by the polyelectrolyte concentration, the relative permittivity of the medium, and the temperature. The Manning counterion condensation theory for salt-free polyelectrolyte solution failed to describe the experimental results. The data have, therefore, been analyzed on the basis of a new model for semidilute polyelectrolyte conductivity which takes into account the scaling arguments to obtain the fractions of uncondensed counterions which were found to depend on the polyelectrolyte concentration. The effects of the temperature and the relative permittivity of the medium on the equivalent conductivity as well as on the fraction of uncondensed counterions have also been discussed.

The effects of concentration, relative permittivity, and temperature on the transport properties of sodium polystyrenesulphonate in 2-ethoxyethanol–water mixed solvent media

Precise measurements on the electrical conductivity of solutions of sodium polystyrenesulphonate in 2-ethoxyethanol–water mixed solvent media containing 10, 25, 40 and 50 wt% of 2-ethoxyethanol at 308.15, 313.15, 318.15, and 323.15 K are reported here. The degree of substitution of sodium polystyrenesulphonate used was 1, and the concentrations were varied from ∼1 × 10 −4 to ∼1 × 10 −2 equiv. l −1. The results showed a slight and monotonous increase in the equivalent conductivity with decreasing polyelectrolyte concentration. The applicability of the Manning’s theory for salt-free polyelectrolyte solutions was examined and a major discrepancy against the theory was observed. The calculated values of the equivalent conductivity deduced on the basis of this theory were found to be lower than the experimental ones. Possible reasons for this discrepancy have been discussed. A semi quantitative description of the experimental data is, however, obtained by adjusting the charge density parameter. The effects of the temperature and relative permittivity of the medium on the equivalent conductivity were also investigated.

Simulation of nonlinear shear rheology of dilute salt-free polyelectrolyte solutions

Brownian dynamics simulations are used to conduct a systematic analysis of the nonlinear shear rheology of dilute polyelectrolyte solutions, exploring its relationship to shear rate, Bjerrum length, and concentration. A simple coarse-grained bead-spring chain model that incorporates explicit counterions is used. It is found that the polyelectrolyte chains exhibit a shear thinning behavior at high shear rate (as characterized by bead Peclet number Pe) that is independent of the electrostatic strength due to the stripping of ions from close proximity to the chain caused by the flow. In contrast, at low values of Pe, the viscosity increases monotonically with increasing Bjerrum length over the range studied here, in contrast to the nonmonotonic trend displayed by the chain size. Furthermore, at fixed Bjerrum length, the reduced viscosity increases monotonically with concentration. The mechanism underlying these observations is essentially the primary electroviscous effect; the ion cloud surrounding a polyelectrolyte chain deforms in flow, causing a significant increase in viscosity as concentration increases. Finally, the authors have also considered the role of hydrodynamic interactions in these simulations, finding that for low concentration studies in shear flow, these do not qualitatively affect the results.

Determination of intrinsic viscosity of polyelectrolytes in salt-free solutions

Comparative analysis of the methods for determination of the intrinsic viscosity of both neutral and polyelectrolyte molecules is made.

The Effects of Concentration, Relative Permittivity and Temperature on the Transport Properties of Sodium Polystyrenesulphonate in Methanol–Water Mixed Solvent Media

Precise measurements on the electrical conductivity of solutions of sodium polystyrenesulphonate in methanol–water mixed solvent media containing 8, 16, 25, and 34 wt.% of methanol at 308.15, 313.15, 318.15, and 323.15 K are reported. The degree of substitution of sodium polystyrenesulphonate used was 1, and the concentrations were varied from ∼2.0 × 10−4 to ∼4.0 × 10−3 monomol l−1. The results showed a slight and monotonous increase in the equivalent conductivity with decreasing polyelectrolyte concentration. The applicability of the Manning’s theory for salt-free polyelectrolyte solution was examined and a major discrepancy against the theory was observed. The calculated values of the equivalent conductivity deduced on the basis of this theory were found to be lower than the experimental ones. Possible reasons for this discrepancy have been discussed. The effects of the temperature and relative permittivity of the medium on the equivalent conductivity were also investigated. Estimation of the fractions of uncondensed counterions provides important insight regarding the solution behavior of the polyelectrolyte in methanol–water mixtures.

Charge density threshold for LbL self-assembly and small molecule diffusion in polyelectrolyte multilayer films

Polyelectrolyte multilayer films were prepared via the layer-by-layer self-assembly using poly(diallydimethylammonium chloride) (PDADMAC) and pyrene labeled polyanions of 2-acrylamido-2-methylpropanesulfonic acid (AMPS) and N, N-dimethylacrylamide copolymers with different charge densities (AMPS mole fraction) F AMPS=0.20–0.999. Multilayer growth with alternating deposition from salt-free polyelectrolyte solutions was monitored by fluorescence intensity and film thickness, showing a charge density threshold between 0.574 and 0.711 for our polyanions, below which the multilayer cannot be formed due to desorption in the following depositions. For the fully charged polyanion, thickness of the multilayer film increased with increasing NaCl concentration in the deposition solution; while for other polyanions with lower F AMPS, little growth in multilayer films was found when NaCl concentration was 0.02 mol/L or higher. The quenching rate of nitromethane to the pyrene label in the multilayer film was adopted to detect the chain density and permeability of these films. Decreasing the charge density, increasing the salt concentration and reducing the layer number will accelerate the quenching rate. The former two is due to the formation of a looser structure in the multilayer films at low charge density of the polyelectrolytes or high salt concentration in the deposition solutions, while the last one is mainly due to the reduction of diffusion distance.

Effects of Concentration, Relative Permittivity, and Temperature on the Solution Behavior of Sodium Carboxymethylcellulose As Probed by Electrical Conductivity

Precise measurements on the electrical conductivity of solutions of sodium salt of carboxymethylcellulose in acetonitrile/water mixed-solvent media containing 10, 20, and 40 vol % of acetonitrile are reported as a function of temperature. The degree of substitution of carboxymethylcellulose used was 0.70, and the concentrations were varied from approximately 1 x 10(-4) to approximately 1 x 10(-2) equiv L(-1). The results showed a decrease in the equivalent conductivity with increasing polyelectrolyte concentration. The applicability of Manning's theory for salt-free polyelectrolyte solutions was examined, and a major discrepancy against the theory was observed. The calculated values of the equivalent conductivity deduced on the basis of this theory were found to be higher than the experimental ones. Possible reasons for this discrepancy have been discussed. The fractions of uncondensed counterions were evaluated, and these were found to depend on the polyelectrolyte concentration. The effects of the temperature and relative permittivity of the medium on the equivalent conductivity as well as on the fraction of uncondensed counterions were also investigated.