Salt-free Polyelectrolyte Research Articles

Coarse-grained explicit-solvent molecular dynamics simulations of semidilute unentangled polyelectrolyte solutions.

We present results from explicit-solvent coarse-grained molecular dynamics (MD) simulations of fully charged, salt-free, and unentangled polyelectrolytes in semidilute solutions. The inclusion of a polar solvent in the model allows for a more physical representation of these solutions at concentrations, where the assumptions of a continuum dielectric medium and screened hydrodynamics break down. The collective dynamic structure factor of polyelectrolytes, S(q,t), showed that at [Formula: see text], where [Formula: see text] is the polyelectrolyte peak in the structure factor S(q) and [Formula: see text] is the correlation length, the relaxation time obtained from fits to stretched exponential was [Formula: see text], which describes unscreened Zimm-like dynamics. This is in contrast to implicit-solvent simulations using a Langevin thermostat where [Formula: see text]. At [Formula: see text], a crossover region was observed that eventually transitions to another inflection point [Formula: see text] at length scales larger than [Formula: see text] for both implicit- and explicit-solvent simulations. The simulation results were also compared to scaling predictions for correlation length, [Formula: see text], specific viscosity, [Formula: see text], and diffusion coefficient, [Formula: see text], where [Formula: see text] is the polyelectrolyte concentration. The scaling prediction for [Formula: see text] holds; however, deviations from the predictions for [Formula: see text] and D were observed for systems at higher [Formula: see text], which are in qualitative agreements with recent experimental results. This study highlights the importance of explicit-solvent effects in molecular dynamics simulations, particularly in semidilute solutions, for a better understanding of polyelectrolyte solution behavior.

Isotropic-to-Nematic Transition in Salt-Free Polyelectrolyte Coacervates from Coarse-Grained Simulations

Recent interest in complex coacervation between oppositely charged polyelectrolytes (PEs) has been fueled by its relevance to biology in the context of membraneless organelle formation within living cells. For PEs with limited flexibility (such as double-stranded DNA), theoretical treatments and recent experiments have reported the emergence of liquid crystalline order (LCO) within the resulting coacervate phases. In this work, we study the underlying physics of this phenomenon using coarse-grained molecular dynamics simulations of symmetric semiflexible–semiflexible and asymmetric semiflexible–flexible coacervates. By comparing coacervates with the corresponding semidilute solutions of neutral polymers, we demonstrate that the presence of Coulomb interactions in coacervates facilitates orientational ordering, in agreement with theoretical predictions. Quantitative comparisons between our simulations and theory indicate that, for asymmetric nematic coacervates, the strong orientational ordering of stiff polyanions induces a weak ordering of the flexible polycations─an effect that was not anticipated by available theoretical studies. Simulations reveal that, for nematic coacervates, the preferred orientation of the PE chains at the liquid–liquid coacervate–supernatant interface is parallel, and the alignment of semiflexible PEs is homogeneous. The results presented here provide new molecular-level insights into the intra-coacervate LCO and will help motivate further experimental and theoretical activities in this area.

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.

Microrheological Approach for Probing the Entanglement Properties of Polyelectrolyte Solutions.

The entanglement dynamics and viscoelasticity of polyelectrolyte solutions remain active research topics. Previous studies have reported conflicting experimental results when compared to Dobrynin's scaling predictions derived from the Doi-Edwards (DE) tube model for entangled polymers. Herein, by combining classical bulk shear rheometry with diffusing wave spectroscopy (DWS) microrheometry, we investigate how the key viscoelastic parameters (the specific viscosity ηsp, the plateau modulus Ge, and the ratio of the reptation time to the Rouse time of an entanglement strand τrep/τe) depend on the polymer concentration for semidilute entangled (SE) solutions containing poly(sodium styrenesulfonate) with high molecular weight. Our experimental measurements yield Ge ∝ c1.51±0.04, in good agreement with the scaling of Ge ∝ c1.5 predicted by Dobrynin's model for salt-free polyelectrolyte SE solutions, suggesting that the electrostatic interaction influences the viscoelastic properties of polyelectrolyte SE solutions. On the other hand, the deviation in the scaling exponent for ηsp ∝ c2.56±0.04 and τrep/τe ∝ c1.82±0.28 is observed between our DWS experiments and Dobrynin's model prediction (∝ c1.5), likely due to the fact that Dobrynin's scaling model does not account for mechanisms such as the contour length fluctuation, the constraint release, and the retardation of solvent dynamics, which are known to occur for SE solutions of neutral polymers. Our results demonstrate that DWS serves as a powerful rheological tool to study the entanglement dynamics of polyelectrolyte solutions. The scaling relationships obtained in this study provide new insights to the long-standing debate on the entanglement dynamics of polyelectrolyte solutions.

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 ...

Crossover from Rouse to Reptation Dynamics in Salt-Free Polyelectrolyte Complex Coacervates.

Considerable interest in the dynamics and rheology of polyelectrolyte complex coacervates has been motivated by their industrial application as viscosity modifiers. A central question is the extent to which classical Rouse and reptation models can be applied to systems where electrostatic interactions play a critical role on the thermodynamics. By relying on molecular simulations, we present a direct analysis of the crossover from Rouse to reptation dynamics in salt-free complex coacervates as a function of chain length. This crossover shifts to shorter chain lengths as electrostatic interactions become stronger, which corresponds to the formation of denser coacervates. To distinguish the roles of Coulomb interactions and density, we compare the dynamics of coacervates to those of neutral, semidilute solutions at the same density. Both systems exhibit a universal dynamical behavior in the connectivity-dominated (subdiffusion and normal diffusion) regimes, but the monomer relaxation time in coacervates is much longer and increases with increasing Bjerrum length. This is similar to the cage effect observed in glass-forming polymers, but the local dynamical slowdown is caused here by strong Coulomb attractions (ion pairing) between oppositely charged monomers. Our findings provide a microscopic framework for the quantitative understanding of coacervate dynamics and rheology.

Effect of external salt addition on the structural, morphological and electrochemical properties of flexible PEDOT:PSS based LbL multilayered films

This article concerns with the effect of external salt addition on the structural, morphological and electrochemical properties of linear poly(ethylene imine) (LPEI) and poly(3,4-ethylenedioxythiophene)-poly(styrenesulfonate) (PEDOT:PSS) based LbL assembled films that is a cathodic color changing electrode for electrochromic device. For this purpose, cationic and anionic commercial polyelectrolytes (PEs) with/without 0.3 M NaCl were deposited on PET-ITO with automatized dip coating system. From QCM-D, it was found that the multilayer deposition became larger for LbL assembled films obtained from salt-free PEs. While the dissipation change (ΔD) of (LPEI/PEDOT:PSS)10/NaCl (150 × 10−6) exhibited relatively soft/flexible structure compared to the (LPEI/PEDOT:PSS)10 (110 × 10−6), ΔD changes became more obvious during PEDOT:PSS adsorption. Furthermore, it was determined that the film thickness and surface roughness values were highly dependent on the number of deposited bilayers whereas they dropped with the addition of salt to LPEI. The root mean square roughness (Rq) of (LPEI/PEDOT:PSS)10, (LPEI/PEDOT:PSS)20 and (LPEI/ PEDOT:PSS)40 were found to be 28 nm, 41.7 nm and 61.5 nm, respectively, while Rq of (LPEI/PEDOT:PSS)20/NaCl was 14.2 nm. All LbL mutilayered films had hydrophilic character and the average contact angle value of (LPEI/PEDOT:PSS)20/NaCl was found to be 66° due to the presence of salt within the multilayers. In addition, ion transport rate increased if the external salt was added to PE. Concerning the salt effect on colorancy of LbL multilayers, all films showed reversible color changes between blue and transparent/pale blue and (LPEI/PEDOT:PSS)20 exhibited darker blue in the colored state whereas (LPEI/PEDOT:PSS)20/NaCl had more translucent in the bleached state.

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.

Counter-ion solution modeling in salt-free polyelectrolytes depicts clustering mystery

Polymer chains modeled in a counter-ion solvation lead to polyelectrolyte clustering that is observed in solution, but has so far been mysterious in origin.

Phase Behavior of Salt-Free Polyelectrolyte Gel-Surfactant Systems.

Ionic surfactants tend to collapse the outer parts of polyelectrolyte gels, forming shells that can be used to encapsulate other species including protein and peptide drugs. In this paper, the aqueous phase behavior of covalently cross-linked polyacrylate networks containing sodium ions and dodecyltrimethylammonium ions as counterions is investigated by means of swelling isotherms, dye staining, small-angle X-ray scattering, and confocal Raman spectroscopy. The equilibrium state is approached by letting the networks absorb pure water. With an increasing fraction of surfactant ions, the state of the water-saturated gels is found to change from being swollen and monophasic, via multiphasic states, to collapsed and monophasic. The multiphasic gels have a swollen, micelle-lean core surrounded by a collapsed, micelle-rich shell, or a collapsed phase forming a spheroidal inner shell separating two micelle-lean parts. It is shown that the transition between monophasic and core-shell states can be induced by variation of the osmotic pressure and variation of the charge of the micelles by forming mixed micelles with the nonionic surfactant octaethyleneglycol monododecylether. The experimental data are compared with theoretical predictions of a model derived earlier. In the calculations, the collapsed shell is assumed to be homogeneous, an approximation introduced here and shown to be excellent for a wide range of compositions. The theoretical results highlight the electrostatic and hydrophobic driving forces behind phase separation.

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.

Polyelectrolyte brushes in external fields: molecular dynamics simulations and mean-field theory.

A mean-field model is developed to predict the layer-thickness of sparse and salt-free polyelectrolyte brushes, exposed to an external electric field, which attracts the polyelectrolytes to the substrate. In molecular dynamics simulations, it is shown that a fraction of polymers collapses entirely to screen the charge of the substrate. The remaining brushes are then treated as field-free brushes at reduced grafting density. The mean-field model may thus be applied to field-free brushes, both in their osmotic and their weak charge regimes. It yields simple, closed equations for the brush height and for the partition of counterions in- and outside the brushes, and accurately reproduces simulation data of the collapse of the brushes during the crossover between both charge regimes.

Molecular dynamics simulations of polyelectrolyte brushes under poor solvent conditions: Origins of bundle formation

Molecular dynamics simulations are applied to investigate salt-free planar polyelectrolyte brushes under poor solvent conditions. Starting above the Θ-point with a homogeneous brush and then gradually reducing the temperature, the polymers initially display a lateral structure formation, forming vertical bundles of chains. A further reduction of the temperature (or solvent quality) leads to a vertical collapse of the brush. By varying the size and selectivity of the counterions, we show that lateral structure formation persists and therefore demonstrate that the entropy of counterions being the dominant factor for the formation of the bundle phase. By applying an external compression force on the brush we calculate the minimal work done on the polymer phase only and prove that the entropy gain of counterions in the bundle state, as compared to the homogeneously collapsed state at the same temperature, is responsible for the lateral microphase segregation. As a consequence, the observed lateral structure formation has to be regarded universal for osmotic polymer brushes below the Θ-point.

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.

Structure of Polyelectrolyte Brushes Subject to Normal Electric Fields

Molecular dynamic simulations of salt-free polyelectrolyte brushes subject to external fields applied normal to the grafting substrate reveal the three-dimensional monomer and counterion distributions. It is found that below a critical electric field, local electroneutrality holds for densely grafted brushes and the brush height remains independent of field intensity. Above this critical field (which scales as 1/3 with grafting density) brush height increases smoothly, and the fraction of condensed counterions decreases. The brush bifurcates into two subpopulations of stretched and collapsed chains when the grafting density is not low. At intermediate grafting densities, the majority of chains are stretched and the minority are nonstretched. At high grafting densities bifurcation and brush height growth occur consecutively. The majority of the chains are nonstretched at high grafting densities. Although not observed prior to overstretching of the chain model, it is predicted that the two subpopulations will re-merge to a single highly stretched phase when field intensity reaches a third critical value. The ability to control subpopulations of chains suggests that utilizing electric fields normal to polyelectrolyte brushes holds potential as controllable gates in microfluidic devices.

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.

Reduced viscosity, rheology and morphological properties of sulfonated poly (ether ether ketone): Polyetherimide blends

Blends of poly (ether ether ketone) (SPEEK) and polyetherimide (PEI) were prepared in five different weight ratios, using N, N-dimethylacetamide (DMAc) as solvent. Reduced viscosity and rheological parameters of these blends were investigated. Cannon–Fenske viscometer was used to study the viscoelastic parameters of the salt-free polyelectrolyte blends and the data obtained was fitted in Fuoss–Strauss equation. Effects of temperature and concentration have been investigated. It was observed that the storage modulus ( G′) and dynamic viscosity ( η′) of the blends varies significantly as compare to pure SPEEK and PEI. Surface morphology and thermal behavior of the membranes were studied using scanning electron microscopy (SEM) and differential scanning calorimetry (DSC). Form SEM results it was observed that the phase separation occurs at 25% PEI contents in blends.

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.