The effect of multivalent counterions to the structure of highly dense polystyrene sulfonate brushes

Unexpected Two-Stage Swelling of Weak Polyelectrolyte Brushes with Divalent Counterions

We use particle-based, coarse-grained simulations to study the influence of divalent counterions on a weak polyelectrolyte brush. Our simulations show a profound influence of even small concentrations of divalent salt on the titration behavior of the brush, which is shown to be a combined effect of electrostatic interactions and the Donnan effect. Furthermore, we examine the partitioning of mono- and divalent counterions into the brush. We demonstrate the preferred uptake of divalent ions by the brush, which is further enhanced by electrostatic correlation effects. Finally, our simulations reveal a hitherto unobserved two-stage swelling of the brush as a function of the pH in the presence of divalent salt. This phenomenon arises as a consequence of charge regulation and ion partitioning.

Hydrophilic and Apolar Hydration in Densely Grafted Cationic Brushes and Counterions with Large Mobilities

We employ an all-atom molecular dynamics (MD) simulation framework to unravel water microstructure and ion properties for cationic [poly(2-(methacryloyloxy)ethyl) trimethylammonium chloride] (PMETAC) brushes with chloride ions as counterions. First, we identify locally separate water domains (or first hydration shells) each around {N(CH3)3}+ and the C═O functional groups of the PMETAC chain and one around the Cl- ion. These first hydration shells around the respective moieties overlap, and the extent of the overlap depends on the nature of the species triggering it. Second, despite the overlap, the water molecules in these domains demonstrate disparate properties dictated by the properties of the atoms and groups around which they are located. For example, the presence of the methyl groups makes the {N(CH3)3}+ group trigger apolar hydration as evidenced by the corresponding orientation of the dipole of the water molecules around the {N(CH3)3}+ moiety. These water molecules around the {N(CH3)3}+ group also have enhanced tetrahedrality compared to the water molecules constituting the hydration layer around the C═O group and the Cl- counterion. Our simulations also identify that there is an intervening water layer between the Cl- ion and {N(CH3)3}+ group: this layer prevents the Cl- ion from coming very close to the {N(CH3)3}+ group. As a consequence, there is a significantly large mobility of the Cl- ions inside the PMETAC brush layer. Furthermore, the C═O group of the polyelectrolyte (PE) chain, due to the partial negative charge on the oxygen atom and the specific structure of the PMETAC brush system, demonstrates strongly hydrophilic behavior and enforces a specific dipole response of water molecules analogous to that experienced by water around anionic species of high charge density. In summary, our findings confirm that PMETAC brushes undergo hydrophilic hydration at one site and apolar hydration at another site and ensure large mobility of the supported Cl- counterions.

Adsorption of Mono- and Divalent Ions onto Dendritic Polyglycerol Sulfate (dPGS) as Studied Using Isothermal Titration Calorimetry

The effective charge of highly charged polyelectrolytes is significantly lowered by a condensation of counterions. This effect is more pronounced for divalent ions. Here we present a study of the counterion condensation to dendritic polyglycerol sulfate (dPGS) that consists of a hydrophilic dendritic scaffold onto which sulfate groups are appended. The interactions between the dPGS and divalent ions (Mg²⁺ and Ca²⁺) were analyzed using isothermal titration calorimetry (ITC) and showed no ion specificity upon binding, but clear competition between the monovalent and divalent ions. Our findings, in line with the latest theoretical studies, demonstrate that a large fraction of the monovalent ions is sequentially replaced with the divalent ions.

Rheological properties of polymer chains at a copper oxide surface: Impact of the chain length, surface coverage, and grafted polymer shape

We employ a recently derived semirealistic set of coarse-grained interactions to simulate polymer brushes of cis-1,4-polybutadiene grafted on a cuprous-oxide surface within the framework of dissipative particle dynamics. We consider two types of brushes, I and Y, that differ in the way they are connected to the surface. Our model explores the impact of free polymer chain length, grafting density of the brush, and imposed shear rate on the structural and dynamic properties of complex metal oxide polymer interfaces.

Role of electrostatic interactions in the adsorption of dye molecules by Ti3C2-MXenes

MXenes, a new class of 2D materials, have recently attracted increasing attention as promising adsorbents for environmental remediation. It has been previously demonstrated that MXenes can successfully capture selected organic dyes from aqueous media; however, to date, the adsorption performance of MXenes for a wide variety of dyes in simulated real-life aquatic environments other than clean laboratory deionized (DI) water has not been systematically investigated. In this study, we systematically investigated the adsorption performance of delaminated Ti3C2-MXenes for six different organic dyes in aquatic media at different pH levels and ionic strengths. Our results strongly suggest the importance of the electrostatic interactions between the ionizable functional groups of MXenes and dyes for removal efficiency. The electrostatic repulsions between negatively charged MXenes and certain anionic dyes reduced the removal efficiencies of MXenes for these dyes in DI water; however, the presence of divalent cations significantly improved the removal efficiencies, possibly owing to the charge screening effects and like-charge attractions mediated by cation binding to the functionalities of dyes and MXenes. These results provide a rational strategy for optimizing the conditions for efficient removal of different types of organic dyes using MXenes.

All-atom molecular dynamics simulations of weak polyionic brushes: influence of charge density on the properties of polyelectrolyte chains, brush-supported counterions, and water molecules

All atom molecular dynamics (MD) simulations of planar Na+-counterion-neutralized polyacrylic acid (PAA) brushes are performed for varying degrees of ionization (and thereby varying charge density) and varying grafting density. Variation in the PE charge density (or degree of ionization) and grafting density leads to massive changes of the properties of the PE molecules (quantified by the changes in the height and the mobility of the PE brushes) as well as the local arrangement and distribution of the brush-supported counterions and water molecules within the brushes. The effect on the counterions is manifested by the corresponding variation of the counterion mobility, counterion concentration, extent of counterion binding to the charged site of the PE brushes, water-in-salt-like structure formation, and counterion-water-oxygen radial distribution function within the PE brushes. On the other hand, the effect on water molecules is manifested by the corresponding variation of water-oxygen-water-oxygen RDF, local water density, water-water and water-PE functional group hydrogen bond networks, static dielectric constant of water molecules, orientational tetrahedral order parameter, and water mobility. Enforcing such varying degree of ionization of weak polyelectrolytes is possible by changing the pH of the surrounding medium. Thus, our results provide insights into the changes in microstructure (at the atomistic level) of weak polyionic brushes at varying pH. We anticipate that this knowledge will prove to be vital for the efficient design of several nano-scale systems employing PE brushes such as nanomechanical gates, current rectifiers, etc.

Conformational Characterization of Polyelectrolyte Oligomers and Their Noncovalent Complexes Using Ion Mobility-Mass Spectrometry

Poly-l-lysine (PLL), polystyrenesulfonate (PSS), and a mixture of these polyelectrolytes were investigated by electrospray ionization ion mobility mass spectrometry. The IM step confirmed the formation of noncovalent (i.e., supramolecular) complexes between these polyelectrolytes, which were detected in various charge states and stoichiometries in the presence of their constituents. Experimental and theoretical collision cross sections (CCSs) were derived for both PLL and PSS oligomers as well as their noncovalent assemblies. PSS chains showed higher compactness with increasing size as compared to PLL chains, indicating that the intrinsic conformations of the polyelectrolytes depend on the nature of the functional groups on their side chains. The CCS data for the noncovalent complexes further revealed that assemblies with higher PLL content have higher CCS values than other compositions of similar mass and that PLL-PSS complex formation is accompanied by significant size contraction.

Enrichment and Distribution of Pb2+ Ions in Zwitterionic Poly(cysteine methacrylate) Brushes at the Solid-Liquid Interface

Cysteine-based polyzwitterionic brushes have been prepared via a two-step route. First, poly(allyl methacrylate) (PAMA) brushes have been grown from the surface of silicon substrates using surface-initiated atom transfer radical polymerization. The obtained PAMA brushes with free pendant vinyl groups were further modified via radical thiol-ene addition reaction to attach l-cysteine moieties. Surface ζ potential investigations on pH-responsiveness of these poly(cysteine methacrylate) (PCysMA) brushes confirm their zwitterionic character at intermediate pH range, while at pH values either below pH 3.50 or above pH 8.59, they exhibit polyelectrolyte character. Under acid (pH < 3.50) or base (pH > 8.59) conditions, they possess either cationic or anionic character, respectively. In the zwitterionic region, these PCysMA brushes show positive surface ζ potential in the presence of Pb(CH₃COO)₂ solutions of various concentrations. The results are in line with microscopic investigations using anomalous X-ray reflectivity (AXRR) carried out along the absorption edge of Pb²⁺ ions. When the photon energies were varied around the absorption L3 edge of lead (13037 eV), the Pb²⁺ concentration normal to the silicon substrates, as a function of depth inside PCysMA brushes, could be revealed at the nanoscale. Both ζ potential and AXRR measurements confirm the enrichment of Pb²⁺ ions inside PCysMA brushes, indicating the potential of PCysMA to be used as a water purification material.

Ion-Specific Effects of Divalent Ions on the Structure of Polyelectrolyte Brushes

Polyelectrolyte brushes consist of charged polymer chains attached on one end to a surface at high densities. They are relevant for many practical applications ranging from biosensors to drug delivery to colloidal stability. Their structure and functionality can be dramatically influenced by multivalent counterions in the solution environment. In this work, the surface forces apparatus (SFA) and atomic force microscopy (AFM) were used to investigate the effects of three alkaline earth divalent cations, Mg²⁺, Ca²⁺, and Ba²⁺, on the structures of polystyrenesulfonate (PSS) brushes tethered to mica and silicon oxide surfaces. While all these ions caused significant shrinkage of the height of the PSS brushes, strong ion-specific effects were observed. Mg²⁺ and Ca²⁺ caused homogeneous shrinkage; Ba²⁺ led to pinned-micelle like inhomogeneous structures. Isothermal titration calorimetry (ITC) demonstrated that this ion specificity was mainly caused by the difference in binding energy between sulfonate groups and the divalent cations. Considering the abundance of divalent cations in industrial processes, natural environments, and biological systems, the understanding of strong ion-specific effects of divalent counterions is of great importance for theoretical studies and various applications involving polyelectrolytes.

Giant Hyaluronan Polymer Brushes Display Polyelectrolyte Brush Polymer Physics Behavior

Polyelectrolyte brushes are important stimuli-responsive materials in a variety of technological applications as well as in biological systems. Their small size, however, introduces characterization challenges, particularly in studying 3D structure and time-dependent behavior. In this Letter, we report on the polyelectrolyte brush behavior of extra-large hyaluronan brushes (∼15 μm) recently developed using an enzyme-mediated growth process. In response to increasing ionic strength, the brush displays the osmotic brush regime and the salted brush regime. We also show a collapse of 96% when the brush is placed in a poor solvent. This collapse is rapid when changing from a good to poor solvent, but re-expansion is slow when changing back to a good solvent. The observed brush behavior described in this Letter is similar to that seen for smaller polyelectrolyte brushes, indicating that these larger brushes may serve as model systems to study more complex phenomena through confocal microscopy.

Salt- and pH-induced swelling of a poly(acrylic acid) brush via quartz crystal microbalance w/dissipation (QCM-D)

We infer the swelling/de-swelling behavior of weakly ionizable poly(acrylic acid) (PAA) brushes of 2-39 kDa molar mass in the presence of KCl concentrations from 0.1-1000 mM, pH = 3, 7, and 9, and grafting densities σ = 0.12-2.15 chains per nm2 using a Quartz Crystal Microbalance with Dissipation (QCM-D), confirming and extending the work of Wu et al. to multiple chain lengths. At pH 7 and 9 (above the pKa ∼ 5), the brush initially swells at low KCl ionic strength (<10 mM) in the "osmotic brush" regime, and de-swells at higher salt concentrations, in the "salted brush" regime, and is relatively unaffected at pH 3, below the pKa, as expected. At pH 7, at low and moderate grafting densities, our results in the high-salt "salted brush" regime (Cs > 10 mM salt) agree with the predicted scaling H ∼ Nσ+1/3Cs-1/3 of brush height H, while in the low-salt "osmotic brush" regime (Cs < 10 mM salt), we find H ∼ Nσ+1/3Cs+0.28-0.38, whose dependence on Cs agrees with scaling theory for this regime, but the dependence on σ strongly disagrees with it. The predicted linearity in the degree of polymerization N is confirmed. The new results partially confirm scaling theory and clarify where improved theories and additional data are needed.

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.

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.

Structure and Functionality of Polyelectrolyte Brushes: A Surface Force Perspective

The unique functionality of polyelectrolyte brushes depends on several types of specific interactions, including solvent structure effects, hydrophobic forces, electrostatic interactions, and specific ion interactions. Subtle variations in the solution environment can lead to conformational and surface structural changes of the polyelectrolyte brushes, which are mainly discussed from a surface-interaction perspective in this Focus Review. A brief overview is given of recent theoretical and experimental progress in the structure of polyelectrolyte brushes in various environments. Two important techniques for surface-force measurements are described, the surface forces apparatus (SFA) and atomic force microscopy (AFM), and some recent results on polyelectrolyte brushes are shown. Lastly, this Focus Review highlights the use of these surface-grafted polyelectrolyte brushes in the creation of functional surfaces for various applications, including nonfouling surfaces, boundary lubricants, and stimuli-responsive surfaces.

Multivalent counterions diminish the lubricity of polyelectrolyte brushes

Polyelectrolyte brushes provide wear protection and lubrication in many technical, medical, physiological, and biological applications. Wear resistance and low friction are attributed to counterion osmotic pressure and the hydration layer surrounding the charged polymer segments. However, the presence of multivalent counterions in solution can strongly affect the interchain interactions and structural properties of brush layers. We evaluated the lubrication properties of polystyrene sulfonate brush layers sliding against each other in aqueous solutions containing increasing concentrations of counterions. The presence of multivalent ions (Y³⁺, Ca²⁺, Ba²⁺), even at minute concentrations, markedly increases the friction forces between brush layers owing to electrostatic bridging and brush collapse. Our results suggest that the lubricating properties of polyelectrolyte brushes in multivalent solution are hindered relative to those in monovalent solution.

The interplay of nanointerface curvature and calcium binding in weak polyelectrolyte-coated nanoparticles

When engineering nanomaterials for application in biological systems, it is important to understand how multivalent ions, such as calcium, affect the structural and chemical properties of polymer-modified nanoconstructs. In this work, a recently developed molecular theory was employed to study the effect of surface curvature on the calcium-induced collapse of end-tethered weak polyelectrolytes. In particular, we focused on cylindrical and spherical nanoparticles coated with poly(acrylic acid) in the presence of different amounts of Ca2+ ions. We describe the structural changes that grafted polyelectrolytes undergo as a function of calcium concentration, surface curvature, and morphology. The polymer layers collapse in aqueous solutions that contain sufficient amounts of Ca2+ ions. This collapse, due to the formation of calcium bridges, is not only controlled by the calcium ion concentration but also strongly influenced by the curvature of the tethering surface. The transition from a swollen to a collapsed layer as a function of calcium concentration broadens and shifts to lower amounts of calcium ions as a function of the radius of cylindrical and spherical nanoparticles. The results show how the interplay between calcium binding and surface curvature governs the structural and functional properties of the polymer molecules. This would directly impact the fate of weak polyelectrolyte-coated nanoparticles in biological environments, in which calcium levels are tightly regulated. Understanding such interplay would also contribute to the rational design and optimization of smart interfaces with applications in, e.g., salt-sensitive and ion-responsive materials and devices.

Competitive calcium ion binding to end-tethered weak polyelectrolytes

We have developed a molecular model to describe the structural changes and potential collapse of weak polyelectrolyte layers end-tethered to planar surfaces and spherical nanoparticles as a function of pH and divalent ion concentration. In particular, we describe the structural changes of polymer-coated nanoparticles end-tethered to copolymers of poly(acrylic acid) (pAA) and poly arcrylamido-2-methylpropane sulfonate (pAMPS) in the presence of Ca²⁺ ions. We find that end-grafted poly(acrylic acid) layers will collapse in aqueous solutions containing sufficient amounts of Ca²⁺ ions, while polymers and copolymers with sufficient AMPS monomers will not collapse. The collapse of end-tethered pAA is due to the formation of calcium bridges between two acrylic acid monomers and one calcium ion. On the other hand pAMPS layers do not collapse due to the lack of calcium bridges. The collapse of pAA layers is strongly dependent on the pH as well as divalent and monovalent salt concentrations of the environment. The collapse is also strongly influenced by the curvature of the tethering surface.

Highly sensitive gating in pH-responsive nanochannels as a result of ionic bridging and nanoconfinement

Multivalent counterions can be used to control both the conductivity and opening of a nanogate functionalized with weak polyelectrolytes.

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.