Polyelectrolyte brushes in monovalent and multivalent salt solutions

Underscreening in concentrated electrolytes: re-entrant swelling in polyelectrolyte brushes

Hypersaline environments are ubiquitous in nature and are found in myriad technological processes. Recent empirical studies have revealed a significant discrepancy between predicted and observed screening lengths at high salt concentrations, a phenomenon referred to as underscreening. Herein we investigate underscreening using a cationic polyelectrolyte brush as an exemplar. Poly(2-(methacryloyloxy)ethyl)trimethylammonium (PMETAC) brushes were synthesised and their internal structural changes and swelling response was monitored with neutron reflectometry and spectroscopic ellipsometry. Both techniques revealed a monotonic brush collapse as the concentration of symmetric monovalent electrolyte increased. However, a non-monotonic change in brush thickness was observed in all multivalent electrolytes at higher concentrations, known as re-entrant swelling; indicative of underscreening. For all electrolytes, numerical self-consistent field theory predictions align with experimental studies in the low-to-moderate salt concentration regions. Analysis suggests that the classical theory of electrolytes is insufficient to describe the screening lengths observed at high salt concentrations and that the re-entrant polyelectrolyte brush swelling seen herein is consistent with the so-called regular underscreening phenomenon.

Study on the Mechanism of the Reversible Color Change of Polyacrylic Acid Modified Gold Nanoparticles Responding to pH

In view of various explanations regarding the pH response of the nanocomposite of gold nanoparticles (AuNPs) modified with polyacrylic acid (PAA) molecules in reported literature, in this work, AuNPs with a size of 20 nm saturatedly loaded with PAA molecules (AuNPs-PAAs) were used to investigate the following aspects of this issue. We investigated the effects of pH on the stability of AuNPs-PAAs in the presence of salt, CTAB, poly (sodium styrenesulfonate) (PSS), ethanol, and free PAA, respectively. Common techniques were undertaken to evaluate the stability, including UV-Vis spectroscopy, Zeta potential analysis, and TEM. The results show that AuNPs-PAAs could respond to pH variations, having a reversible aggregation-to-disaggregation, accompanying their Zeta potential change. The proposed corresponding mechanism was that this reversible change was attributes to the net charge variation of AuNPs-PAAs induced by a reversible protonation-to-deprotonation of PAA rather than the conformational change. It was found that salt, CTAB, PSS, and free PAA could strengthen the dispersity of AuNPs-PAAs, even though their absolute Zeta potential values were decreased to small values or dropped to nearly zero. This abnormal phenomenon was explained by solvation. It was also found that AuNPs-PAAs have an opposite pH response in aqueous and ethanol solutions, justifying the solvation effect. All these results revealed the conformational stability of PAAs immobilized on AuNPs. The methods and the findings of this investigation give some new insights to understand the pH-response of AuNPs-PAAs composites and the design of AuNPs-PAAs-based functional sensors.

Theoretical Modeling of Chemical Equilibrium in Weak Polyelectrolyte Layers on Curved Nanosystems

Surface functionalization with end-tethered weak polyelectrolytes (PE) is a versatile way to modify and control surface properties, given their ability to alter their degree of charge depending on external cues like pH and salt concentration. Weak PEs find usage in a wide range of applications, from colloidal stabilization, lubrication, adhesion, wetting to biomedical applications such as drug delivery and theranostics applications. They are also ubiquitous in many biological systems. Here, we present an overview of some of the main theoretical methods that we consider key in the field of weak PE at interfaces. Several applications involving engineered nanoparticles, synthetic and biological nanopores, as well as biological macromolecules are discussed to illustrate the salient features of systems involving weak PE near an interface or under (nano)confinement. The key feature is that by confining weak PEs near an interface the degree of charge is different from what would be expected in solution. This is the result of the strong coupling between structural organization of weak PE and its chemical state. The responsiveness of engineered and biological nanomaterials comprising weak PE combined with an adequate level of modeling can provide the keys to a rational design of smart nanosystems.

Self-assembly of polyelectrolyte diblock copolymers within mixtures of monovalent and multivalent counterions

In this study, the self-assembly behavior of polyelectrolyte (PE) diblock copolymers in solutions containing mixtures of monovalent and multivalent counterions was investigated using molecular dynamics simulation. The properties of the assembled micelles and counterion condensations at different charge fractions of multivalent ions have been discussed. The bridging effect of multivalent ions induces the electrostatic correlations of the PE chains, leading to the fusion of large micelles and the formation of bulky aggregates. Notably, lamellar and well-organized face-centered cubic (FCC) arrangements of the assembled micelles were observed in the mixture of monovalent and trivalent ions. At large fractions of multivalent ions, cylindrical and lamellar precipitates composed of the assembled micelles were formed owing to the inter-connecting coronas. The mixtures of monovalent and multivalent counterions allow the regulation of the electrostatic interactions and tuning of the properties in assembled micelles.

Morphologies of a polyelectrolyte brush grafted onto a cubic colloid in the presence of trivalent ions

We study the morphologies of a polyelectrolyte brush grafted onto a surface of cubic geometry under good solvent conditions in the presence of trivalent counterions, using molecular dynamics simulations. The electrostatic correlation effect and excluded volume effect on the morphologies are studied through varying the charge fraction and grafting density, respectively. Combining snapshots of surface morphologies, brush height, distribution profiles of polymer monomers, and monomer-monomer/counterion pair correlation functions, it is clearly shown that the electrostatic correlation effect, represented by the trivalent-counterion-mediated bridging effect, can induce lateral microphase separation of the cubic polyelectrolyte brush, resulting in the formation of pinned patches. These structures then lead to multi-scale ordering in the brush system and, thereby, a non-monotonic dependence of the brush height, corresponding to a collapse-to-swell transition, on the grafting density. Our simulation results demonstrate that, with the sequence of surface morphologies responsive to adjusting external parameters, the cubic polyelectrolyte brush can serve as a candidate system for the manufacturing of smart stimuli-responsive materials.

Self-assembly of polyelectrolyte diblock copolymers at monovalent and multivalent counterions

In this work, the self-assembly behaviors of diblock copolymers consisting of one hydrophobic block and one ionizable polyelectrolyte (PE) block in the presence of monovalent and multivalent counterions are systematically discussed through molecular dynamics simulation. Copolymers are molded as bead-spring chains and the ions are explicitly considered. First, the self-assembled structures of symmetrical block copolymers at different charge fractions are analyzed in detail. Spherical hydrophobic cores are favored by all of the micelles. The effect of counterion valence is much more noticeable at high values of charge fraction. When the PE blocks are fully charged, the presence of multivalent counterions preferably provokes the formation of macroscopic structures. A precipitant spherical micelle is generated in the presence of divalent counterions. Special shapes of coronas are created in the presence of trivalent ions, and a remarkable one dimensional macroscopic cylindrical aggregation of micelles forms; the whole assembly is not typical core-shell micelles, but rather a cylinder with alternating spherical micelles arranged perpendicular to the cylinder axis. The self-assemblies with different lengths of fully charged PE blocks are also discussed. Surprisingly, in the presence of divalent counterions, two dimensional in-plane macroscopic aggregation of micelles is realized when the proportion of PE blocks is larger than 1/2; the self-assembled spherical micelles locate approximately in the same plane to form an inter-linked network. One dimensional aggregation of micelles in the presence of trivalent counterions is maintained with an increased proportion of the PE block. Owing to the dominant intra- and inter-condensation of divalent and trivalent counterions, respectively, two and one dimensional macroscopic aggregation of the micelles is achieved. Our findings indicate that varying the counterion valence is a powerful mechanism to tune the properties of self-assemblies, and the bridging effect introduced by multivalent counterions is the key parameter for the aggregation of the micelles.

Surface morphologies of spherical polyelectrolyte brushes induced by trivalent salt ions

The surface morphologies of spherical polyelectrolyte brushes in salt solutions with opposite trivalent ions are studied using molecular dynamics (MD) simulations. The impact of salt concentration, grafting density, and charge fraction on brush morphologies is investigated systematically. A variety of surface patterns are predicted and the phase diagrams are presented. Both lateral and radial microphase separated structures in the brushes are observed upon varying the salt concentration. With low grafting density the spherical brush is separated into several patches, the number of which decreases with the addition of salt. At high grafting density, the polymer brush changes its morphology from an extended micelle to a 'carpet + brush' to the collapsed state upon increasing the salt concentration. Especially, the 'carpet + brush' structure consists of a core formed by partially collapsed brush chains and a corona formed by other stretched chains. The inter-chain 'bridging' interactions mediated by trivalent ions and the curvature effect play important roles in determining the chain conformations and brush structures.

Effect of Counterion Valence on Conformational Behavior of Spherical Polyelectrolyte Brushes Confined between Two Parallel Walls

We study the conformational behavior of spherical polyelectrolyte brushes in the presence of monovalent and trivalent counterions in a confined environment. The confinement is exerted by two parallel walls on the brushes. The enhancement of the confinement induces the extension of grafted chains. For the monovalent case, the increase of the charge fraction leads to extended brush conformation for different slit width (distance between two walls) but collapsed brush in the presence of trivalent counterions is observed. The confinement does not affect electrostatic correlation between trivalent counterions and charged monomers. However, it was found that narrow slit width contributes to stronger electrostatic correlation for the monovalent case. This is because more monovalent counterions are inside the brush at strong confinement, but almost all trivalent counterions are trapped into the brush independently of the slit width. The diffusion of counterions under the confinement is related to the electrostatic correlation. Our simulations also reveal that the brush thickness depends on the slit width nonlinearly.

Multivalent ions induce lateral structural inhomogeneities in polyelectrolyte brushes

Subtle details about a polyelectrolyte's surrounding environment can dictate its structural features and potential applications. Atomic force microscopy (AFM), surface forces apparatus (SFA) measurements, and coarse-grained molecular dynamics simulations are combined to study the structure of planar polyelectrolyte brushes [poly(styrenesulfonate), PSS] in a variety of solvent conditions. More specifically, AFM images provide a first direct visualization of lateral inhomogeneities on the surface of polyelectrolyte brushes collapsed in solutions containing trivalent counterions. These images are interpreted in the context of a coarse-grained molecular model and are corroborated by accompanying interaction force measurements with the SFA. Our findings indicate that lateral inhomogeneities are absent from PSS brush layers collapsed in a poor solvent without multivalent ions. Together, AFM, SFA, and our molecular model present a detailed picture in which solvophobic and multivalent ion-induced effects work in concert to drive strong phase separation, with electrostatic bridging of polyelectrolyte chains playing an essential role in the collapsed structure formation.

Comparing Solvophobic and Multivalent Induced Collapse in Polyelectrolyte Brushes

Coarse-grained molecular dynamics enhanced by free-energy sampling methods is used to examine the roles of solvophobicity and multivalent salts on polyelectrolyte brush collapse. Specifically, we demonstrate that while ostensibly similar, solvophobic collapsed brushes and multivalent-ion collapsed brushes exhibit distinct mechanistic and structural features. Notably, multivalent-induced heterogeneous brush collapse is observed under good solvent polymer backbone conditions, demonstrating that the mechanism of multivalent collapse is not contingent upon a solvophobic backbone. Umbrella sampling of the potential of mean-force (PMF) between two individual brush strands confirms this analysis, revealing starkly different PMFs under solvophobic and multivalent conditions, suggesting the role of multivalent "bridging" as the discriminating feature in trivalent collapse. Structurally, multivalent ions show a propensity for nucleating order within collapsed brushes, whereas poor-solvent collapsed brushes are more disordered; this difference is traced to the existence of a metastable PMF minimum for poor solvent conditions, and a global PMF minimum for trivalent systems, under experimentally relevant conditions.

Molecular dynamics simulations of cylindrical polyelectrolyte brushes in monovalent and multivalent salt solutions

Molecular dynamics simulations are applied to investigate the cylindrical polyelectrolyte brushes in monovalent and multivalent salt solutions. By varying the salt valence and concentration, the brush thickness, shape factor of grafted chains, and distributions of monomers and ions in the solutions are studied. The simulation results show that the single osmotic pressure effect in the brush leads to changes in conformation in the presence of monovalent salt, while the ion exchange effect induces the collapse of the brushes in the multivalent salt solutions. Furthermore, the snapshots combined with the distributions of the end-monomers and the mean bond angles demonstrate a nonuniform stretching picture of the grafted chains, which is different with the chains tethered on the planar surface. The charge ratios between the ions trapped in the brush and the monomers are also calculated to elucidate the details of ion exchange process.

Anion-specific effects on the behavior of pH-sensitive polybasic brushes

The anion-specific solvation and conformational behavior of weakly basic poly(2-dimethylamino)ethyl methacrylate (poly(DMA)), poly(2-diethylamino)ethyl methacrylate (poly(DEA)), and poly(2-diisopropylamino)ethyl methacrylate (poly(DPA)) brushes, with correspondingly increasing inherent hydrophobicity, have been investigated using in situ ellipsometric and quartz crystal microbalance with dissipation (QCM-D) measurements. In the osmotic brush regime, as the initial low concentration of salt is increased, the brushes osmotically swell by the uptake of solvent as they become charged and the attractive hydrophobic inter- and intrachain interactions are overcome. With increased ionic strength, the brushes move into the salted brush regime where they desolvate and collapse as their electrostatic charge is screened. Here, as the brushes collapse, they transition to more uniform and rigid conformations, which dissipate less energy, than similarly solvated brushes at lower ionic strength. Significantly, in these distinct regimes brush behavior is not only ionic strength dependent but is also influenced by the nature of the added salt based on its position in the well-known Hofmeister or lyotropic series, with potassium acetate, nitrate, and thiocyanate investigated. The strongly kosmotropic acetate anions display low affinity for the hydrophobic polymers, and largely unscreened electrosteric repulsions allow the brushes to remain highly solvated at higher acetate concentrations. The mildly chaotropic nitrate and strongly chaotropic thiocyanate anions exhibit a polymer hydrophobicity-dependent affinity for the brushes. Increasing thiocyanate concentration causes the brushes to collapse at lower ionic strength than for the other two anions. This study of weak polybasic brushes demonstrates the importance of all ion, solvent, and polymer interactions.

Morphological transformations in polymer brushes in binary mixtures: DPD study

Morphological transformations in polymer brushes in a binary mixture of good and bad solvents are studied using dissipative particle dynamics simulations drawing on a characteristic example of polyisoprene natural rubber in an acetone-benzene mixture. A coarse-grained DPD model of this system is built based on the experimental data in the literature. We focus on the transformation of dense, collapsed brush in bad solvent (acetone) to expanded brush solvated in good solvent (benzene) as the concentration of benzene increases. Compared to a sharp globule-to-coil transition observed in individual tethered chains, the collapsed-to-expanded transformation in brushes is found to be gradual without a prominent transition point. The transformation becomes more leveled as the brush density increases. At low densities, the collapsed brush is highly inhomogeneous and patterned into bunches composed of neighboring chains due to favorable polymer-polymer interaction. At high densities, the brush is expanded even in bad solvent due to steric restrictions. In addition, we considered a model system similar to the PINR-acetone-benzene system, but with the interactions between the solvent components worsened to the limit of miscibility. Enhanced contrast between good and bad solvents facilitates absorption of the good solvent by the brush, shifting the collapsed-to-expanded transformation to lower concentrations of good solvent. This effect is especially pronounced for higher brush densities.