A direct measurement of the polyion conformation in aqueous solutions at different temperatures. Small angle neutron scattering of PSSNa using zero average and full contrast

Dilute polyelectrolyte solutions: recent progress and open questions

Polyelectrolytes are a class of polymers possessing ionic groups on their repeating units. Since counterions can dissociate from the polymer backbone, polyelectrolyte chains are strongly influenced by electrostatic interactions. As a result, the physical properties of polyelectrolyte solutions are significantly different from those of electrically neutral polymers. The aim of this article is to highlight key results and some outstanding questions in the polyelectrolyte research from recent literature. We focus on the influence of electrostatics on conformational and hydrodynamic properties of polyelectrolyte chains. A compilation of experimental results from the literature reveals significant disparities with theoretical predictions. We also discuss a new class of polyelectrolytes called poly(ionic liquid)s that exhibit unique physical properties in comparison to ordinary polyelectrolytes. We conclude this review by listing some key research challenges in order to fully understand the conformation and dynamics of polyelectrolytes in solutions.

Structures of cationic and anionic polyelectrolytes in aqueous solutions: the sign effect

In this study, we use molecular dynamics simulation to explore the structures of anionic and cationic polyelectrolytes in aqueous solutions. We first confirm the significantly stronger solvation effects of single anions compared to cations in water at the fixed ion radii, due to the reversal orientations of asymmetric dipolar H₂O molecules around the ions. Based on this, we demonstrate that the solvation discrepancy of cations/anions and electrostatic correlations of ionic species can synergistically cause the nontrivial structural difference between single anionic and cationic polyelectrolytes. The cationic polyelectrolyte shows an extended structure whereas the anionic polyelectrolyte exhibits a collapsed structure, and their structural differences decline with increasing the counterion size. Furthermore, we corroborate that multiple cationic polyelectrolytes or multiple anionic polyelectrolytes can exhibit largely differential molecular architectures in aqueous solutions. In the solvation dominant regime, the polyelectrolyte solutions exhibit uniform structures; whereas, in the electrostatic correlation dominant regime, the polyelectrolyte solutions exhibit heterogeneous structures, in which the likely charged chains microscopically aggregate through counterion condensations. Increasing the intrinsic chain rigidity causes polyelectrolyte extension and hence moderately weakens the inter-chain clustering. Our work highlights the various, unique structures and molecular architectures of polyelectrolytes in solutions caused by the multi-body correlations between polyelectrolytes, counterions and asymmetric dipolar solvent molecules, which provides insights into the fundamental understanding of ion-containing polymers.

Polyelectrolyte association and solvation

There has been significant interest in the tendency of highly charged particles having the same charge to form dynamic clusters in solution, but an accepted theoretical framework that can account for this ubiquitous phenomenon has been slow to develop. The theoretical difficulties are especially great for flexible polyelectrolytes due to the additional complex coupling between the polyelectrolyte chain configurations and the spatial distribution of the ionic species in solution. For highly charged polyelectrolytes, this leads to the formation of a diffuse "polarizable" cloud of counter-ions around these polymers, an effect having significant implications for the function of proteins and other natural occurring polyelectrolytes, as emphasized long ago by Kirkwood and co-workers. To investigate this phenomenon, we perform molecular dynamics simulations of a minimal model of polyelectrolyte solutions that includes an explicit solvent and counter-ions, where the relative affinity of the counter-ions and the polymer for the solvent is tunable through the variation of the relative strength of the dispersion interactions of the polymer and ions. In particular, we find that these dispersion interactions can greatly influence the nature of the association between the polyelectrolyte chains under salt-free conditions. We calculate static and dynamic correlation functions to quantify the equilibrium structure and dynamics of these complex liquids. Based on our coarse-grained model of polyelectrolyte solutions, we identify conditions in which three distinct types of polyelectrolyte association arise. We rationalize these types of polyelectrolyte association based on the impact of the selective solvent affinity on the charge distribution and polymer solvation in these solutions. Our findings demonstrate the essential role of the solvent in the description of the polyelectrolyte solutions, as well as providing a guideline for the development of a more predictive theory of the properties of the thermodynamic and transport properties of these complex fluids.

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.

SANS from Salt-Free Aqueous Solutions of Hydrophilic and Highly Charged Star-Branched Polyelectrolytes

Scattering functions of sodium sulfonated polystyrene (NaPSS) star-branched polyelectrolytes with high sulfonation degrees were measured from their salt-free aqueous solutions, using the Small Angle Neutron Scattering (SANS) technique. Whatever the concentration c, they display two maxima. The first, of abscissa q₁*, is related to a position order between star cores and scales as q₁* ∝ c^1/3. The second, of abscissa q₂*, is also observed in the scattering function of a semi-dilute solution of NaPSS linear polyelectrolytes. In the dilute regime (c < c*, non-overlapping stars), peak abscissa does not depend on concentration c and is just an intramolecular characteristic associated with the electrostatic repulsion between arms of the same star. In the semi-dilute regime, due to the star interpenetration, the scattering function – through the peak position, reflects repulsion between arms of the same star or of different stars. The c threshold between these distinct c-dependencies of q₂* in the dilute and semi-dilute regimes is estimated as c*. Just as simple is the measurement of the geometrical radius R of the star obtained from the q₁* value at c* through the relation 2R = 2π/q₁*. By considering NaPSS stars of the same functionality with different degrees of polymerization per arm N_a, we find R scaling linearly with N_a, suggesting an elongated average conformation of the arms. This is in agreement with theoretical predictions and simulations. Meanwhile the value of q₂* measured in the dilute regime does not allow any inhomogeneous counterion distribution inside the stars to be revealed.

Iron oxide nanoparticles grafted with sulfonated copolymers are stable in concentrated brine at elevated temperatures and weakly adsorb on silica

Magnetic nanoparticles that can be transported in subsurface reservoirs at high salinities and temperatures are expected to have a major impact on enhanced oil recovery, carbon dioxide sequestration, and electromagnetic imaging. Herein we report a rare example of steric stabilization of iron oxide (IO) nanoparticles (NPs) grafted with poly(2-acrylamido-2-methylpropanesulfonate-co-acrylic acid) (poly(AMPS-co-AA)) that not only display colloidal stability in standard American Petroleum Institute (API) brine (8% NaCl + 2% CaCl2 by weight) at 90 °C for 1 month but also resist undesirable adsorption on silica surfaces (0.4% monolayer NPs). Because the AMPS groups interacted weakly with Ca(2+), they were sufficiently well solvated to provide steric stabilization. The PAA groups, in contrast, enabled covalent grafting of the poly(AMPS-co-AA) chains to amine-functionalized IO NPs via formation of amide bonds and prevented polymer desorption even after a 40,000-fold dilution. The aforementioned methodology may be readily adapted to stabilize a variety of other functional inorganic and organic NPs at high salinities and temperatures.

Behavior of hydrophobic polyelectrolyte solution in mixed aqueous/organic solvents revealed by neutron scattering and viscosimetry

We investigate in this paper the influence of the improvement of the solvent quality on the structure and the viscous properties of solutions of an hydrophobic polyelectrolyte, poly(styrene-co-sodium styrenesulfonate): PSS. The solvent used is a mixture of water and an organic solvent, THF, which is also slightly polar. We use small angle neutron scattering in the semidilute regime and viscosimetry as a function of concentration in dilute and semidilute unentangled regime. The structure, namely the scattering from all chains, is characterized by a maximum ("polyelectrolyte peak"). Its position and amplitude depends, at a given sulfonation rate of PSS, on the solvent quality through the added amount of organic solvent (THF). These evolutions with the THF amount are more pronounced when the sulfonation rate f is low (more hydrophobic polyelectrolyte) and the amount of added THF is high. Adding THF to hydrophobic PSS (f = 0.50 or f = 0.38), diminishes also the "shoulder" visible in the log I - log q plot and associated with the pearl size. It is therefore proposed that when THF is added to aqueous polyelectrolyte solutions, the pearls are dissolved and the chain conformation evolves from the pearl-necklace shape already reported in pure water toward the string-like conformation in pure water for fully sulfonated PSS. An addition of THF also reduces the important low q upturn found with hydrophobic polyelectrolyte solutions: the large aggregates are dissolved by THF. The upturn can become for PSSNa f = 0.38, after adding enough THF (50%), even smaller than that for the charged hydrophilic case PSSNa f = 0.82, in water. This can mean that in the quasi-fully charged PSS at f = 0.82 there are still hydrophobic effects in water, which is disagreeing with our recent reports, or that the electrostatics contribution to the upturn is reduced due to a lower dielectric permittivity. Concerning the hydrophilic polyelectrolyte, poly(sodium-2-acrylamido-2-methylpropanesulfonate)-co-(acrylamide): AMAMPS, no evolution in structure occurs until 25% THF. The viscosimetry variation with THF fraction is in good agreement with the scattering one up to 25%: though little dependent on THF for AMAMPS, and for hydrophilic PSSNa, it increases for hydrophobic PSSNa in agreement with the chain expansion signaled by scattering. At 50% THF concentration, the hydrophilic polyelectrolyte shows new surprising behaviors: the scattering of PSSNa is no longer characteristic of polyelectrolytes, and AMAMPS solutions display an unexpected viscosity decrease.

The model Lysozyme-PSSNa system for electrostatic complexation: Similarities and differences with complex coacervation

We review, based on structural information, the mechanisms involved when putting in contact two nano-objects of opposite electrical charge, in the case of one negatively charged polyion, and a compact charged one. The central case is mixtures of PSS, a strong flexible polyanion (the salt of a strong acid, and with high linear charge density), and Lysozyme, a globular protein with a global positive charge. A wide accurate and consistent set of information in different situations is available on the structure at local scales (5-1000Å), due to the possibility of matching, the reproducibility of the system, its well-defined electrostatics features, and the well-defined structures obtained. We have related these structures to the observations at macroscopic scale of the phase behavior, and to the expected mechanisms of coacervation. On the one hand, PSS/Lysozyme mixtures show accurately many of what is expected in PEL/protein complexation, and phase separation, as reviewed by de Kruif: under certain conditions some well-defined complexes are formed before any phase separation, they are close to neutral; even in excess of one species, complexes are only modestly charged (surface charges in PEL excess). Neutral cores are attracting each other, to form larger objects responsible for large turbidity. They should lead the system to phase separation; this is observed in the more dilute samples, while in more concentrated ones the lack of separation in turbid samples is explained by locking effects between fractal aggregates. On the other hand, although some of the features just listed are the same required for coacervation, this phase transition is not really obtained. The phase separation has all the macroscopic aspects of a fluid (undifferentiated liquid/gas phase) - solid transition, not of a fluid-fluid (liquid-liquid) one, which would correspond to real coacervation). The origin of this can be found in the interaction potential between primary complexes formed (globules), which agrees qualitatively with a potential shape of the type repulsive long range attractive very short range. Finally we have considered two other systems with accurate structural information, to see whether other situations can be found. For Pectin, the same situation as PSS can be found, as well as other states, without solid precipitation, but possibly with incomplete coacervation, corresponding to differences in the globular structure. It is understandable that these systems show smoother interaction potential between the complexes (globules) likely to produce liquid-liquid transition. Finally, we briefly recall new results on Hyaluronan/Lysozyme, which present clear signs of coacervation in two liquid phases, and at the same time the existence of non-globular complexes, of specific geometry (thin rods) before any phase separation. These mixtures fulfill many of the requirements for complex coacervation, while other theories should also be checked like the one of Shklovskii et al.

Effect of crowding on the conformation of interwound DNA strands from neutron scattering measurements and Monte Carlo simulations

With a view to determining the distance between the two opposing duplexes in supercoiled DNA, we have measured small angle neutron scattering from pHSG298 plasmid (2675 base pairs) dispersed in saline solutions. Experiments were carried out under full and zero average DNA neutron scattering contrast using hydrogenated plasmid and a 1:1 mixture of hydrogenated and perdeuterated plasmid, respectively. In the condition of zero average contrast, the scattering intensity is directly proportional to the single DNA molecule scattering function (form factor), irrespective of the DNA concentration and without complications from intermolecular interference. The form factors are interpreted with Monte Carlo computer simulation. For this purpose, the many body problem of a dense DNA solution was reduced to the one of a single DNA molecule in a congested state by confinement in a cylindrical potential. It was observed that the interduplex distance decreases with increasing concentration of salt as well as plasmid. Therefore, besides ionic strength, DNA crowding is shown to be important in controlling the interwound structure and site juxtaposition of distal segments of supercoiled DNA. This first study exploiting zero average DNA contrast has been made possible by the availability of perdeuterated plasmid.

The microrheology of polystyrene sulfonate combs in aqueous solution

Video particle tracking (VPT) and diffusing wave spectroscopy were used to characterize the microrheology of polystyrene sulfonate combs in aqueous solutions. At low frequencies VPT demonstrated predominantly viscous behavior. The manner in which the viscosity scaled as a function of monomer concentration was a sensitive function of the comb architecture. Densely branched combs or combs with long side chains demonstrated entangled polyelectrolyte scaling above the overlap concentration, whereas sparsely branched combs had unentangled polyelectrolyte scaling. A dynamic scaling model was developed for the viscosity of unentangled semidilute solutions of comb polyelectrolytes. Diffusing wave spectroscopy demonstrated Rouse modes (G' approximately G" approximately omega12) for the high-frequency dynamics of the semidilute comb solutions. The form of the high-frequency viscoelasticity was independent of the chain architecture and the modulus scaled as expected for linear flexible polyelectrolytes.

Effective interaction of charged platelets in aqueous solution: investigations of colloid laponite suspensions by static light scattering and small-angle x-ray scattering

We study dilute aqueous solutions of charged disklike mineral particles (laponite) by a combination of static light scattering (SLS) and small-angle x-ray scattering (SAXS). Laponite solutions are known to form gels above a certain critical concentration that must be described as nonequilibrium states. Here we focus on the investigation by SLS and SAXS at concentrations below gelation (c<0.016 g/L) and at low concentrations of added salt (0.001M and 0.005M). Thus, we have obtained the scattering function of single Laponite platelets as well as the structure factor describing their interaction at finite concentration. A detailed analysis of the combined sets of data proves that the solutions are in a well-defined equilibrium state. Moreover, this analysis demonstrates the internal consistency and accuracy of the scattering functions obtained at finite concentrations. We find that laponite particles interact through an effective pair potential that is attractive on short range but repulsive on longer range. This finding demonstrates that Laponite solutions exhibit only a limited stability at the concentration of added salt used herein. Raising the ionic strength to 0.005M already leads to slow flocculation as is evidenced from the enhanced scattering intensity at smallest scattering angles. All data strongly suggest that the gelation occurring at higher concentration is related to aggregation.