Domain Structures in Low Ionic Strength Polyelectrolyte Solutions

Organization of hyaluronic acid molecules in solutions

The organization of hyaluronic acid (HA) solutions was investigated by small angle neutron scattering (SANS). It was demonstrated that HA formed clusters greater than several hundred nanometers. The SANS response revealed a weak correlation peak, corresponding to ordering over a distance scale of about 80 nm. At higher wave vectors, the SANS response indicated the presence of rod-like structures. Addition of calcium ions only weakly affects the structure of the HA solution, but significantly reduces its osmotic pressure. The osmotic component of the SANS response is in good agreement with the intensity obtained from direct osmotic pressure measurements. The results are consistent with the rigid structure of the HA molecule.

Graphical abstract

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.

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.

Development of a coarse-grained model for surface-functionalized gold nanoparticles: towards an accurate description of their aggregation behavior

Understanding the dispersion stability and aggregation propensity of self-assembled monolayer gold NPs at a molecular level is crucial to guide their rational design and to inform about the optimal surface functionalization for specific applications. To reach this goal, in silico modeling via coarse-grained (CG) molecular dynamics (MD) simulations is a fundamental tool to complement the information acquired from experimental studies since CG modeling allows to get a deep knowledge of the molecular interactions that take place at the nanoscale in this kind of systems. Unfortunately, current CG models of monolayer-protected AuNPs present several drawbacks that limit their accuracy in certain scenarios. We here develop a CG model that is fully compatible and extends the SPICA/SDK (Shinoda-DeVane-Klein) force field. Our model allows reproducing the behavior of AuNPs functionalized with hydrophobic as well as charged and more hydrophilic ligands. This model improves upon results obtained with previously derived CG force fields and successfully describes NPs aggregation and self-assembly in aqueous solution.

Pectin self-assembly and its disruption by water: Insights into plant cell wall mechanics

Plant cell walls undergo multiple cycles of dehydration and rehydration during their life. Cal- cium crosslinked low methoxy pectin is a major constituent of plant cell walls. Understanding the dehydration-rehydration...

Oscillatory structural forces between charged interfaces in solutions of oppositely charged polyelectrolytes

Forces between negatively charged micron-sized silica particles were measured in aqueous solutions of cationic polyelectrolytes with an atomic force microscope (AFM). In these oppositely charged systems, damped oscillatory force profiles were systematically observed in systems at higher polyelectrolyte concentrations, typically around few g L-1. The wavelength of these oscillations is decreasing with increasing concentration. When the wavelength and concentration are normalized with the cross-over concentration, universal power-law dependence is found. Thereby, the corresponding scaling exponent changes from 1/3 in the dilute regime to 1/2 in the semi-dilute regime. This dependence is the same as in the like-charged systems, which were described in the literature earlier. This common behavior suggests that these oscillatory forces are related to the structuring of the polyelectrolyte solutions. The reason that the oppositely charged systems behave similarly to like-charged ones is that the former systems undergo a charge reversal due to the adsorption of the polyelectrolytes to the oppositely charged surface, whereby sufficiently homogeneous adsorbed layers are being formed. The main finding of the present study is that at higher polyelectrolyte concentrations such oscillatory forces are the rule, including the oppositely charged ones.

SAXS methods for investigating macromolecular and self-assembled polyelectrolyte complexes

Polyelectrolyte complexation is driven by associative interactions between oppositely charged polyelectrolytes, resulting in formation of a macroscopic polymer dense phase and a polymer dilute phase with applications in coatings, adhesives, and purification membranes. Beyond macroscale phase separation, precision polymer synthesis has enabled further development of polyelectrolyte complex (PEC)-based self-assembled micelles and hydrogels with applications in biotechnology. Interestingly, it has been suggested that mechanisms similar to polyelectrolyte complexation drive formation of biological condensates that play an indispensable role in cellular biogenesis. The formation pathways and functionality of these complex materials is dependent on the physical properties that are built into polymer structure and the resulting physical conformation in the dilute and dense phase. Scattering techniques have enabled in situ investigation of structure-function relationships in PEC materials that may address unresolved biophysical questions in cellular processes as well as catalyze the development of novel materials for diverse applications. We describe preparation of PEC materials with controlled polymer characteristics (length, blockiness, charge density), small-angle X-ray scattering (SAXS) techniques employed to probe appropriate length scales, and the data analysis routines from a practical standpoint for new users. This article deals with bulk complexes and not with the related, important and interesting area of non-equilibrium layer-by-layer assembly of polyelectrolytes.

Bicontinuous Microemulsions in Partially Charged Ternary Polymer Blends

We describe the phase behavior of a partially charged ternary polymer blend model system, comprising a compositionally symmetric poly[(oligo(ethylene glycol) methyl ether methacrylate-co-oligo(ethylene glycol) propyl sodium sulfonate methacrylate)]-b-polystyrene (POEGMA23-PS) diblock polymer and the constituent POEGMA23 and PS homopolymers, along the volumetrically symmetric isopleth, where 23 denotes the percentage of charged monomers in the POEGMA chain. Small-angle neutron and X-ray scattering and dynamic mechanical spectroscopy measurements reveal morphological transitions from a layered superlattice to swollen lamellae to a bicontinuous microemulsion (BμE), followed by macroscopic phase separation, with increasing homopolymer content. The BμE channel occurs between 85 and 90% homopolymer addition, positioned approximately at the isotropic Lifshitz composition predicted by mean-field theory for neutral systems. The resulting BμE morphology exhibits a periodicity of 26 nm, yielding a mesoscopically structured but macroscopically disordered bicontinuous structure. That this structure can be achieved in a charged polymer system is surprising, given the huge asymmetries typically induced by adding charge to either diblock copolymers or binary polymer blends.

Block copolymers as bile salt sequestrants: intriguing structures formed in a mixture of an oppositely charged amphiphilic block copolymer and bile salt

To study the formation and characterize the structure of mixed complexes of oppositely charged block copolymers and surfactants are of great significance for practical applications, e.g., in drug carrier formulations that are based on electrostatically assisted assembly. In this context, biocompatible block copolymers and biosurfactants (like bile salts) are particularly interesting. In this work, we report on the co-assembly in dilute aqueous solution between a cationic poly(N-isopropyl acryl amide) (PNIPAM) diblock copolymer and the oppositely charged bile salt surfactant sodium deoxycholate at ambient temperature. The cryogenic transmission electron microscopy (cryo-TEM) experiments revealed the co-existence of two types of co-assembled complexes of radically different morphology and inner structure. They are formed mainly as a result of the electrostatic attraction between the positively charged copolymer blocks and bile salt anions and highlight the potential of using linear amphiphilic block copolymers as bile salt sequestrants in the treatment of bile acid malabsorption and hypercholesterolemia. The first complex of globular morphology has a coacervate core of deoxycholate anions and charged copolymer blocks surrounded by a PNIPAM corona. The second complex has an intriguing tape-like supramolecular morphology of several micrometer in length that is striped in the direction of the long axis. A model is presented in which the stretched cationic blocks of several block copolymers interact electrostatically with the bile salt molecules that are associated to form a zipper-like structure. The tape is covered on both sides by the PNIPAM chains that stabilize the overall complex in solution. In addition to cryo-TEM, the mixed system was investigated in a range of molar charge fractions at a constant copolymer concentration by static light scattering, small angle X-ray scattering, and electrophoretic mobility measurements.

Solution properties of imidazolium-based amphiphilic polyelectrolyte in pure- and mixed-solvent media

Mixed solvents that are selectively attractive to different parts of an amphiphilic polyelectrolyte lead to exceptional and promoted solution properties.

Enhanced scattering induced by electrostatic correlations in concentrated solutions of salt-free dipolar and ionic polymers

We present a generalized theory for studying the static monomer density-density correlation function (structure factor) in concentrated solutions and melts of dipolar as well as ionic polymers. The theory captures effects of electrostatic fluctuations on the structure factor and provides insights into the origin of experimentally observed enhanced scattering at ultralow wavevectors in salt-free ionic polymers. It is shown that the enhanced scattering can originate from a coupling between the fluctuations of electric polarization and monomer density. Local and non-local effects of the polarization resulting from finite sized permanent dipoles and ion-pairs in dipolar and charge regulating ionic polymers, respectively, are considered. Theoretical calculations reveal that, similar to the salt-free ionic polymers, the structure factor for dipolar polymers can also exhibit a peak at a finite wavevector and enhanced scattering at ultralow wavevectors. Although consideration of dipolar interactions leads to attractive interactions between monomers, the enhanced scattering at ultralow wavevectors is predicted solely on the basis of the electrostatics of weakly inhomogeneous dipolar and ionic polymers without considering the effects of any aggregates or phase separation. Thus, we conclude that neither aggregation nor phase separation is necessary for observing the enhanced scattering at ultralow wavevectors in salt-free dipolar and ionic polymers. For charge regulating ionic polymers, it is shown that electrostatic interactions between charged monomers get screened with a screening length, which depends not only on the concentration of "free" counterions and coions, but also on the concentration of "adsorbed" ions on the polymer chains. Qualitative comparisons with the experimental scattering curves for ionic and dipolar polymer melts are presented using the theory developed in this work.

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.

Liquid-liquid phase separation in dilute solutions of poly(styrene sulfonate) with multivalent cations: Phase diagrams, chain morphology, and impact of temperature

The dilute solution behavior of sodium poly(styrene sulfonate) is studied in the presence of trivalent Al³⁺ and bivalent Ba²⁺ cations at various levels of excess NaCl. The study evaluates the phase behavior and the morphology of the polyelectrolyte chains with increasing extent of decoration with the Al³⁺ and Ba²⁺ cations and analyses the effect of temperature on these decorated chains. The phase behavior is presented in the form of the cation concentration versus the respective poly(styrene sulfonate) concentration, recorded at the onset of precipitation. Whereas poly(styrene sulfonate) with Al³⁺ exhibits a linear phase boundary, denoted as the "threshold line," which increases with increasing poly(styrene sulfonate) concentration, Ba²⁺ cations show a threshold line which is independent of the poly(styrene sulfonate) concentration. An additional re-entrant phase, at considerably higher cation content than those of the threshold lines, is observed with Al³⁺ cations but not with Ba²⁺ cations. The threshold line and the re-entrant phase boundary form parts of the liquid-liquid phase boundary observed at the limit of low polymer concentration. The dimensions of the polyelectrolyte chains shrink considerably while approaching the respective threshold lines on increase of the Al³⁺ and Ba²⁺ cation content. However, subtle differences occur between the morphological transformation induced by Al³⁺ and Ba²⁺. Most strikingly, coils decorated with Al³⁺ respond very differently to temperature variations than coils decorated with Ba²⁺ do. As the temperature increases, the poly(styrene sulfonate) chains decrease their size in the presence of Al³⁺ cations but increase in size in the presence of Ba²⁺ cations.

The Influence of Polymer and Ion Solvation on the Conformational Properties of Flexible Polyelectrolytes

The study of the coupling between the conformational properties of a polyelectrolyte chain and the distribution of counter-ions surrounding the chain is important in developing predictive theories for more complex polymer materials, such as polyelectrolyte gels. We investigated the influence of solvent affinity to counter-ions and the polyelectrolyte backbone on the conformational properties of highly charged flexible polymer chains using molecular dynamics simulations that include both ions and an explicit solvent. We find that the solvation of the polyelectrolyte backbone can be achieved by either increasing the solvent affinity for the polyelectrolyte segments or by increasing the solvent affinity for the counter-ions. However, these two mechanisms influence the conformational properties of the polyelectrolyte chain in rather different ways, suggesting the inadequacy of polyelectrolyte solution models that treat the solvent as a continuum medium.

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.

Facile Control over the Supramolecular Ordering of Self-assembled Peptide Scaffolds by Simultaneous Assembly with a Polysacharride

Enabling control over macromolecular ordering and the spatial distribution of structures formed via the mechanisms of molecular self-assembly is a challenge that could yield a range of new functional materials. In particular, using the self-assembly of minimalist peptides, to drive the incorporation of large complex molecules will allow a functionalization strategy for the next generation of biomaterial engineering. Here, for the first time, we show that co-assembly with increasing concentrations of a highly charged polysaccharide, fucoidan, the microscale ordering of Fmoc-FRGDF peptide fibrils and subsequent mechanical properties of the resultant hydrogel can be easily and effectively manipulated without disruption to the nanofibrillar structure of the assembly.

Tunable Length of Cyclic Peptide-Polymer Conjugate Self-Assemblies in Water

Polymers conjugated to cyclic peptides capable of forming strong hydrogen bonds can self-assemble into supramolecular bottlebrushes even in aqueous solutions. However, controlling the aggregation of these supramolecular assemblies remains an obstacle that is yet to be overcome. By introducing pH-responsive poly(dimethylamino ethyl methacrylate) (pDMAEMA) arms, the repulsive forces were tuned by adjusting the degree of protonation on the polymer arms. Neutron scattering experiments demonstrated that conjugates in an uncharged state will self-assemble into supramolecular bottlebrushes. Reducing the pH in the system led to a decrease in the number of aggregation, which was reversible by addition of base. Potentiometric titration showed a correlation between the number of aggregation and the degree of ionization of the pDMAEMA arms. Hence, a balance between the strength of the hydrogen bonds and the repulsive electrostatic interactions determines the number of aggregation and extent of self-assembly. The presented work demonstrates that conjugate self-association can be controlled by tuning the charge density on the conjugated polymer arms, paving the way for the use of responsive cyclic peptide conjugates in pharmaceutical applications.

Unexpected Like-Charge Self-Assembly of a Biguanide-Based Antimicrobial Polyelectrolyte

Polyelectrolyte chains dissolved in good solvent are expected to collapse in compact configurations in the presence of multivalent ions. Here, we show that a weakly charged, hydrophilic polyelectrolyte containing biguanide groups self-assembles in water also in the presence of monovalent counterions, even at low salt concentrations. The polymer assembles in a compact, ordered, hairpin-like shape that, with increasing the ionic strength of the solution, can collapse further in three- or five-folded structures. Neither water nor ions mediate the self-assembly which, instead, is driven by the like-charge pairing of the biguanide units. The thermodynamics of the self-assembly show that the self-association is enthalpically driven, is isodesmic (at least at low aggregation number), and is favored by increasing salt concentration. This unique self-assembly behavior may be linked to the well-known polymer's antimicrobial properties and could help in rationalizing its biological activity.

Application of hydrophobically modified water-soluble polymers for the dispersion of hydrophobic magnetic nanoparticles in aqueous media

Oleylamine-coated CoFe₂O₄ magnetic nanoparticles were successfully encapsulated into hydrophobically modified water-soluble polymers. The resulting hydrophilic nanohybrids exhibit promising r₂-relaxivity properties.

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.

Counterion condensation theory of attraction between like charges in the absence of multivalent counterions

There is abundant experimental evidence suggesting the existence of attractive interactions among identically charged polyelectrolytes in ordinary salt solutions. The presence of multivalent counterions is not required. We review the relevant literature in detail and conclude that it merits more attention than it has received. We discuss also some recent observations of a low ionic strength attraction of negatively charged DNA to the region of a negatively charged glass nanoslit where the floor of the nanoslit meets the walls, again in the absence of multivalent ions. On the theoretical side, it has become clear that purely electrostatic interactions require the presence of multivalent counterions if they are to generate like-charge attraction. Any theory of like-charge attraction in the absence of multivalent counterions must therefore contain a non-electrostatic component. We point out that counterion condensation theory, which has predicted like-charge polyelectrolyte attraction in an intermediate range of distances in ordinary 1:1 salt conditions, contains both electrostatic and non-electrostatic elements. The non-electrostatic component of the theory is the modeling constraint that the counterions fall into two explicit populations, condensed and uncondensed. As reviewed in the paper, this physically motivated constraint is supported by strong experimental evidence. We proceed to offer an explanation of the nanoslit observations by showing in an idealized model that the line of intersection of two intersecting planes is a virtual polyelectrolyte. Since we have previously developed a counterion condensation theory of attraction of two like-charged polyelectrolytes, our suggestion is that the DNA is attracted to the virtual polyelectrolytes that may be located in the nanoslit where floor meets walls. We present the detailed calculations needed to document this suggestion: an extension of previous theory to the case of polyelectrolytes with like but not identical charges; the demonstration of counterion condensation on a plane with bare charge density greater than an explicitly exhibited critical value; a calculation of the free energy of the plane; a calculation of the interaction of a line charge polyelectrolyte with a like-charged plane; and the detailed demonstration that the line of intersection of two planes is a virtual polyelectrolyte.

Self-localization of polyacrylic acid molecules on polar ZnO(0001)-Zn surfaces

The adsorption of single polyacrylic acid (PAAc) molecules was investigated on stepped hydroxide-stabilized polar ZnO(0001)-Zn surfaces using atomic force microscope (AFM) topography and force distance spectroscopy. Stepped surfaces of ZnO(0001)-Zn were prepared by a wet chemical etching procedure and PAAc molecules were adsorbed from aqueous NaClO(4) solutions. AFM single molecule topography studies could be utilized to show that polyacrylic acid molecules specifically adsorb on the non-polar (10-10) step edge faces at low ionic strengths. The radius of gyration of the dissolved PAAc in aqueous solution was measured by means of static light scattering experiments yielding a radius of gyration of R(g)=136 nm at pH 7.4 in 50 mM NaClO(4)/NaOH solution, which is in good agreement with the size of the adsorbed PAAc molecules as measured using AFM. The obtained results could be rationalized in terms of binding-site configurations at step edges and the effect of the chemical environment on both local electric double layer charge and molecular conformation of the PAAc molecules. The point of zero charge of the ZnO(10-10) surface was measured with chemical force microscopy to be pH(PZC)=10.2 ± 0.2. The specific adsorption of polyacrylic acid at non-polar ZnO step-edges can be explained by coordinative bonds formed between the carboxylic acid group and the Zn-surface atoms. On the hydroxide stabilized polar surface only weak hydrogen bonds can be formed in addition to van-der-Waals forces. Thus a "diffusion and trapping" mechanism keeps the adsorbed PAAc molecules mobile on the ZnO(0001)-Zn surface terraces due to small interaction forces until they are trapped at the (10-10) step faces by stronger coordinative bonds from the carboxylic groups to zinc atoms located in the first atomic layer of the crystal structure.

Kinetic study on the reentrant condensation of oligonucleotide in trivalent salt solution

The reentrant condensation of 21-bp oligonucleotide in the presence of spermidine was investigated by laser light scattering and capillary electrophoresis. 21-bp oligonucleotide showed a bimodal distribution in 1 × TE buffer, with the slow mode being the characteristic diffusion of polyelectrolyte in solution without enough salt. At the fixed spermidine concentration, the reentry of oligonucleotide underwent aggregation, phase separation, and disassociation in sequence with time, and the kinetics was extremely slow. For example, it took more than 1200 h (50 days) for the reentry to complete at 21 mM spermidine. Higher spermidine concentration led to faster kinetics. After reentry, the slow mode disappeared, and the charges of oligonucleotide were at least partially neutralized. No prominent charge inversion was observed. The kinetics of oligonucleotide reentry in the presence of spermidine gained insight in the interactions of polyelectrolyte in aqueous solution.