Structure of Polyelectrolyte Brushes on Polarizable Substrates

Structure of a Grafted Polyelectrolyte Layer at the Dielectric Interface: Coupling Effects of Dielectric Contrast, Ionic Strength, and Excluded Volume

A statistical thermodynamic theory is employed to study the grafted polyelectrolyte layers (GPELs) at dielectric interfaces, focusing on the coupling effects of dielectric contrast (Δε), ionic strength, and excluded volume. The dielectric contrast induces an image-charge effect near the interface, whose influence on GPELs remains to be further explored, especially when combined with ionic strength and excluded volume effects. With increasing grafting density (ρg), GPELs exhibit four distinct regimes: isotropic, stretched, collapsed, and re-stretched. In the isotropic regime, all three effects are weak, making GPELs insensitive to Δε variations. In the stretched and collapsed regimes, high ionic strength shifts dominance to the entropic effect of mobile ions. Here, mobile ions respond strongly to Δε, while PE chains remain insensitive. A jump-like decrease in layer thickness occurs at the stretch-collapse transition due to counterion accumulation near the surface, enhancing electrostatic interactions. In the re-stretched regime, GPELs behave like neutral polymer brushes, with excluded volume effects becoming crucial, rendering both PE chains and mobile ions insensitive to Δε. Reducing the charge density of PE chains further diminishes the response of mobile ions to Δε. The interplay of these effects results in a "roller coaster" trend in brush height with increasing ρg. This study underscores the necessity of considering all three effects to fully understand GPEL behavior at dielectric interfaces, as neglecting any one may lead to incomplete insights into swelling/shrinking behaviors. While some findings align with experimental results, others warrant further exploration.

Unveiling the Electrostatically Driven Collapsing and Relaxation of Polyelectrolyte-Colloid Complexes: A Tunable Pathway to Colloidal Assembly

Polyelectrolyte-colloid (PEC) complexes, ubiquitous across diverse fields, exhibit remarkable phase transitions, mimicking intricate biological assemblies. While the role of electrostatic forces in the PEC complex assembly is undeniable, achieving a holistic comprehension remains an elusive goal. This study unveils a fascinating phenomenon: the formation of highly collapsed coacervate structures in PEC complexes at elevated polyelectrolyte concentrations, followed by the swelling of complexes at even higher concentrations. Employing anionic silica colloids and cationic chitosan as a model system, small-angle X-ray/neutron (SAXS/SANS) elucidates the transition from a bead-on-a-necklace-like phase to a dense packed coacervate state (with volume fraction ∼0.62) until 3 wt % concentration of the polyelectrolyte. However, beyond 3 wt %, swelling of the dense collapsed assembly is observed. This structural evolution of PEC complexes as a function of chitosan concentration is attributed to the interplay of electrostatically driven interactions and the Donnan effect. Notably, the critical concentration for coacervation, Cs*, demonstrates a linear dependence on the initial colloid concentration. Interestingly, a complete expansion of the coacervate is observed at a high polyelectrolyte concentration, particularly for dilute colloid solutions (2 wt %). Furthermore, the addition of an electrolyte sheds light on the delicate interplay of forces. While a low electrolyte concentration partially screens charges, leading to a shift in phase diagram, higher concentrations trigger complete coacervate dissolution beyond the critical electrolyte concentration of 0.2 M, due to the complete screening of electrostatic charges.

Adsorption of polyelectrolytes in the presence of varying dielectric discontinuity between solution and substrate

We examine the interactions between polyelectrolytes (PEs) and uncharged substrates under conditions corresponding to a dielectric discontinuity between the aqueous solution and the substrate. To this end, we vary the relevant system characteristics, in particular the substrate dielectric constant ɛs under different salt conditions. We employ coarse-grained molecular dynamics simulations with rodlike PEs in salt solutions with explicit ions and implicit water solvent with dielectric constant ɛw = 80. As expected, at low salt concentrations, PEs are repelled from the substrates with ɛs < ɛw but are attracted to substrates with a high dielectric constant due to image charges. This attraction considerably weakens for high salt and multivalent counterions due to enhanced screening. Furthermore, for monovalent salt, screening enhances adsorption for weakly charged PEs, but weakens it for strongly charged ones. Meanwhile, multivalent counterions have little effect on weakly charged PEs, but prevent adsorption of highly charged PEs, even at low salt concentrations. We also find that correlation-induced charge inversion of a PE is enhanced close to the low dielectric constant substrates, but suppressed when the dielectric constant is high. To explore the possibility of a PE monolayer formation, we examine the interaction of a pair of like-charged PEs aligned parallel to a high dielectric constant substrate with ɛs = 8000. Our main conclusion is that monolayer formation is possible only for weakly charged PEs at high salt concentrations of both monovalent and multivalent counterions. Finally, we also consider the energetics of a PE approaching the substrate perpendicular to it, in analogy to polymer translocation. Our results highlight the complex interplay between electrostatic and steric interactions and contribute to a deeper understanding of PE-substrate interactions and adsorption at substrate interfaces with varying dielectric discontinuities from solution, ubiquitous in biointerfaces, PE coating applications, and designing adsorption setups.

Broken symmetries in quasi-2D charged systems via negative dielectric confinement

We report spontaneous symmetry breaking (SSB) phenomena in symmetrically charged binary particle systems under planar nanoconfinement with negative dielectric constants. The SSB is triggered solely via the dielectric confinement effect, without any external fields. The mechanism of SSB is found to be caused by the strong polarization field enhanced by nanoconfinement, giving rise to charge/field oscillations in the transverse directions. Interestingly, dielectric contrast can even determine the degree of SSB in transverse and longitudinal dimensions, forming charge-separated interfacial liquids and clusters on square lattices. Furthermore, we analytically show that the formed lattice constant is determined by the dielectric mismatch and the length scale of confinement, which is validated via molecular dynamics simulations. The novel broken symmetry mechanism may provide new insights into the study of quasi-2D systems and the design of future nanodevices.

Collapse and expansion kinetics of a single polyelectrolyte chain with hydrodynamic interactions

We investigate the collapse and expansion dynamics of a linear polyelectrolyte (PE) with hydrodynamic interactions. Using dissipative particle dynamics with a bead-spring PE model, long-range electrostatics, and explicit ions, we examine how the timescales of collapse tcol and expansion texp depend on the chain length N and obtain scaling relationships tcol ∼ Nα and texp ∼ Nβ. For neutral polymers, we derive values of α = 0.94 ± 0.01 and β = 1.97 ± 0.10. Interestingly, the introduction of electrostatic interaction markedly shifts α to α ≈ 1.4 ± 0.1 for salt concentrations within c = 10-4 to 10-2 M. A reduction in the ion-to-monomer size ratio noticeably reduces α. On the other hand, the expansion scaling remains approximately constant, β ≈ 2, regardless of the salt concentration or ion size considered. We find β > α for all conditions considered, implying that expansion is always slower than collapse in the limit of long polymers. This asymmetry is explained by distinct kinetic pathways of collapse and expansion processes.

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.

Enabling High-Capacitance Supercapacitors by Polyelectrolyte Brushes

Polyelectrolyte brushes (PEBs) hold excellent potential for designing high-capacitance electrical double-layer capacitors (EDLCs), a crucial component of supercapacitors. Both experiments and computational simulations have shown their energy-storage advantage. However, the effect of PEBs on the energy storage of EDLCs is not yet fully understood. Herein, we systematically study the energy-storage effects of polyanionic (PA) and polycationic (PC) brushes using polymer density functional theory (DFT). First, the application of polymer DFT in polyelectrolyte-grafted EDLCs is successfully validated using molecular dynamics simulations. With the help of polymer DFT, an interfacial adhesion microstructure of the PA/PC brushes is observed. Most importantly, the results show that polyelectrolyte-grafted EDLCs achieve a significant increase in capacitance at low salt concentrations and surface voltages, offering an excellent energy-storage advantage over traditional EDLCs. However, this advantage is considerably diminished at high salt concentrations or surface voltages, showing unusual salt- and voltage-dependent behaviors of energy-storage capacity. Nonetheless, the PC-grafted EDLCs maintain their outstanding energy-storage performance, even at relatively high salt concentrations and surface voltages. These findings deepen our comprehension of PEBs at the molecular level and provide insights for the molecular design of high-capacitance supercapacitors.

Switchable Polyacrylic Acid Polyelectrolyte Brushes for Surface Plasmon Resonance Applications

Imaging wide-field surface plasmon resonance (SPR) microscopy sensors based on polyacrylic acid polyelectrolyte brushes (PAA PEBs) were designed to enhance the sensitivity of nano-object detection. The switching behavior of the PAA PEBs against changes in the pH values was investigated by analyzing the chemical, morphological, optical, and electrical properties. At pH ~1, the brushes collapse on the surface with the dominance of carboxylic groups (COOH). Upon the increase in the pH to nine, the switching process completes, and the brushes swell from dissociating most of the COOH groups and converting them into COO- groups. The domination of the negatively charged COO- groups increases the electrostatic repulsion in the polymer chains and stretches the brushes. The sensitivity of the SPR sensing device was investigated using a theoretical approach, as well as experimental measurements. The signal-to-noise ratio for a Au layer increases from six to eighteen after coating with PAA PEBs. In addition, the linewidth of the recorded image decreases from six pixels to five pixels by using the Au-PAA layers, which results from the enhanced spatial resolution of the recorded images. Coating a Au-layer with PAA PEBs enhances the sensitivity of the SPR sensing device, and improves the spatial resolution of the recorded image.

Effects of electrostatic coupling and surface polarization on polyelectrolyte brush structure

In this work, we perform molecular dynamics simulations to study a spherical polyelectrolyte brush. We explore the effects of surface polarization and electrostatic coupling on brush size and distribution of counterions. The method of image charges is considered to take into account surface polarization, considering a metallic, an unpolarizable, and a dielectric nano-core. It is observed that, for all cases, a moderate shrinking-swelling effect appears with an increase in the electrostatic coupling parameter. This effect occurs under high Manning ratios. The curves relating the average size of polyelectrolyte brush as a function of coupling show a minimum. The results show that the grafting density of polyelectrolytes on the nano-core surface plays an important role in the polarization effect. We consider a modified Poisson-Boltzmann theory to describe the counterion profiles around the brush in the case of unpolarizable nano-cores and weak electrostatic coupling.

Accelerated simulation method for charge regulation effects

The net charge of solvated entities, ranging from polyelectrolytes and biomolecules to charged nanoparticles and membranes, depends on the local dissociation equilibrium of individual ionizable groups. Incorporation of this phenomenon, charge regulation (CR), in theoretical and computational models requires dynamic, configuration-dependent recalculation of surface charges and is therefore typically approximated by assuming constant net charge on particles. Various computational methods exist that address this. We present an alternative, particularly efficient CR Monte Carlo method (CR-MC), which explicitly models the redistribution of individual charges and accurately samples the correct grand-canonical charge distribution. In addition, we provide an open-source implementation in the large-scale Atomic/Molecular Massively Parallel Simulator molecular dynamics (MD) simulation package, resulting in a hybrid MD/CR-MC simulation method. This implementation is designed to handle a wide range of implicit-solvent systems that model discreet ionizable groups or surface sites. The computational cost of the method scales linearly with the number of ionizable groups, thereby allowing accurate simulations of systems containing thousands of individual ionizable sites. By matter of illustration, we use the CR-MC method to quantify the effects of CR on the nature of the polyelectrolyte coil-globule transition and on the effective interaction between oppositely charged nanoparticles.

Conformation and Ionization Behavior of Charge-Regulating Polyelectrolyte Brushes in a Poor Solvent

Understanding the structural response of weak polyelectrolyte brushes upon external stimuli is crucial for their applications ranging from modifying surface properties to the development of smart and intelligent materials. In this work, coarse-grained molecular dynamics simulations were carried out to investigate the conformation and ionization behavior of charge-regulating polyelectrolyte brushes under poor solvent conditions, using an implicit solvent model. The results show that, while the thickness of a sparse polyelectrolyte brush shows a similar behavior to that of a single chain, namely, a monotonic change as a function of solvent quality (modeled by an effective segment-segment attraction strength parameter) and solution pH, a dense polyelectrolyte brush exhibits more complex behavior. An unexpected reexpansion is observed when the effective segment-segment attraction strength is further increased, especially in the case of a high pH. In the latter case, strong attraction in polymer segments promotes the formation of large, interchain, cylindrical aggregates, leading to an increase in brush thickness.