Self-organization of grafted polyelectrolyte layers via the coupling of chemical equilibrium and physical interactions

Induced phase transformation in ionizable colloidal nanoparticles

Acid-base equilibria directly influence the functionality and behavior of particles in a system. Due to the ionizing effects of acid-base functional groups, particles will undergo charge exchange. The degree of ionization and their intermolecular and electrostatic interactions are controlled by varying the pH and salt concentration of the solution in a system. Although the pH can be tuned in experiments, it is hard to model this effect using simulations or theoretical approaches. This is due to the difficulty in treating charge regulation and capturing the cooperative effects in a colloidal suspension with Coulombic interaction. In this work, we analyze a suspension of ionizable colloidal particles via molecular dynamics (MD) simulations, along with Monte Carlo simulations for charge regulation (MC-CR) and derive a phase diagram of the system as a function of pH. It is observed that as pH increases, particles functionalized with acid groups change their arrangement from face-centered cubic (FCC) packing to a disordered state. We attribute these transitions to an increase in the degree of charge polydispersity arising from an increase in pH. Our work shows that charge regulation leads to amorphous solids in colloids when the mean nanoparticle charge is sufficiently high.

Aggregation-Induced Asymmetric Charge States of Amino Acids in Supramolecular Nanofibers

Electrostatic interactions contribute critically to the kinetic pathways and thermodynamic outcomes of peptide self-assembly involving one or more than one charged amino acids. While it is well understood in protein folding that those amino acids with acidic/basic side chains could shift their pKas when placed in a hydrophobic microenvironment, to what extent aggregation of monomeric peptide units from the bulk solution could alter their charged status and how this change in pKa values would reciprocally impact their assembly outcomes. Here, we design and analyze two solution systems containing peptide amphiphiles with hydrocarbon chains of different lengths to determine the factor of deprotonation on assembly. Our results suggest that models of supramolecular nanofibers with uniformly distributed, fully charged amino acids are oversimplified. We demonstrate, with molecular dynamics simulations, and validate with experimental results that asymmetric, different protonation states of the peptides lead to distinct nanostructures after self-assembly. The results give estimates on the electrostatic interactions in peptide amphiphiles required for their self-assembly and shed light on modeling molecular assembly systems containing charged amino acids.

Charge fluctuations in charge-regulated systems: dependence on statistical ensemble

We investigate charge regulation of nanoparticles in concentrated suspensions, focusing on the effect of different statistical ensembles. We find that the choice of ensemble does not affect the mean charge of nanoparticles, but significantly alters the magnitude of its fluctuation. Specifically, we compared the behaviors of colloidal charge fluctuations in the semi-grand canonical and canonical ensembles and identified significant differences between the two. The choice of ensemble-whether the system is isolated or is in contact with a reservoir of acid and salt-will, therefore, affect the Kirkwood-Shumaker fluctuation-induced force inside concentrated suspensions. Our results emphasize the importance of selecting an appropriate ensemble that accurately reflects the experimental conditions when studying fluctuation-induced forces between polyelectrolytes, proteins, and colloidal particles in concentrated suspensions.

Phase Behavior of Ion-Containing Polymers in Polar Solvents: Predictions from a Liquid-State Theory with Local Short-Range Interactions

The thermodynamic phase behavior of charged polymers is a crucial property underlying their role in biology and various industrial applications. A complete understanding of the phase behaviors of such polymer solutions remains challenging due to the multi-component nature of the system and the delicate interplay among various factors, including the translational entropy of each component, excluded volume interactions, chain connectivity, electrostatic interactions, and other specific interactions. In this work, the phase behavior of partially charged ion-containing polymers in polar solvents is studied by further developing a liquid-state (LS) theory with local shortrange interactions. This work is based on the LS theory developed for fully-charged polyelectrolyte solutions. Specific interactions between charged groups of the polymer and counterions, between neutral segments of the polymer, and between charged segments of the polymer are incorporated into the LS theory by an extra Helmholtz free energy from the perturbed-chain statistical associating fluid theory (PC-SAFT). The influence of the sequence structure of the partially charged polymer is modeled by the number of connections between bonded segments. The effects of chain length, charge fraction, counterion valency, and specific short-range interactions are explored. A computational App for salt-free polymer solutions is developed and presented, which allows easy computation of the binodal curve and critical point by specifying values for the relevant model parameters.

Effects of Non-Ionic Micelles on the Acid-Base Equilibria of a Weak Polyelectrolyte

Weak polyelectrolytes (WPEs) are widely used as pH-responsive materials, pH modulators and charge regulators in biomedical and technological applications that involve multi-component fluid environments. In these complex fluids, coupling between (often weak) interactions induced by micelles, nanoparticles and molecular aggregates modify the pKa as compared to that measured in single component solutions. Here we investigated the effect of coupling between hydrogen bonding and excluded volume interactions on the titration curves and pKa of polyacrylic acid (PAA) in solutions comprising PEO-based micelles (Pluronics and Brij-S20) of different size and volume fraction. Titration experiments of dilute, salt-free solutions of PAA (5 kDa, 30 kDa and 100 kDa) at low degree of polymer ionization (α < 0.25) drive spatial re-organization of the system, reduce the degree of ionization and consequentially increase the pKa by up to ~0.7 units. These findings indicate that the actual degree of ionization of WPEs measured in complex fluids is significantly lower (at a given pH) than that measured in single-component solutions.

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.

Design of Multifunctional Nanopore Using Polyampholyte Brush with Composition Gradient

Molecular organizations and charge patterns inside biological nanopores are optimized by evolution to enhance ionic and molecular transport. Inspired by the nuclear pore complex that employs asymmetrically arranged disordered proteins for its gating, we here design an artificial nanopore coated by an asymmetric polyampholyte brush as a model system to study the asymmetric mass transport under nanoconfinement. A nonequilibrium steady-state molecular theory is developed to account for the intricate charge regulation effect of the weak polyampholyte and to address the coupling between the polymer conformation and the external electric field. On the basis of this state-of-the-art theoretical method, we present a comprehensive theoretical description of the stimuli-responsive structural behaviors and transport properties inside the nanopore with all molecular details considered. Our model demonstrates that by incorporating a gradient of pH sensitivity into the polymer coatings of the nanopore, a variety of asymmetric charge patterns and functional structures can be achieved, in a pH-responsive manner that allows for multiple functions to be implemented into the designed system. The asymmetric charge pattern inside the nanopore leads to an electrostatic trap for major current carriers, which turns the nanopore into an ionic rectifier with a rectification factor above 1000 at optimized pH and salt concentration. Our theory further predicts that the nanopore design behaves like a double-gated nanofluidic device with pH-triggered opening of the gates, which can serve as an ion pump and pH-responsive molecular filter. These results deepen our understanding of asymmetric transport in nanoconfined systems and provide guidelines for designing polymer-coated smart nanopores.

Structure and dynamics of nanoconfined water and aqueous solutions

This review is devoted to discussing recent progress on the structure, thermodynamic, reactivity, and dynamics of water and aqueous systems confined within different types of nanopores, synthetic and biological. Currently, this is a branch of water science that has attracted enormous attention of researchers from different fields interested to extend the understanding of the anomalous properties of bulk water to the nanoscopic domain. From a fundamental perspective, the interactions of water and solutes with a confining surface dramatically modify the liquid's structure and, consequently, both its thermodynamical and dynamical behaviors, breaking the validity of the classical thermodynamic and phenomenological description of the transport properties of aqueous systems. Additionally, man-made nanopores and porous materials have emerged as promising solutions to challenging problems such as water purification, biosensing, nanofluidic logic and gating, and energy storage and conversion, while aquaporin, ion channels, and nuclear pore complex nanopores regulate many biological functions such as the conduction of water, the generation of action potentials, and the storage of genetic material. In this work, the more recent experimental and molecular simulations advances in this exciting and rapidly evolving field will be reported and critically discussed.

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.

Body centered tetragonal nanoparticle superlattices: why and when they form?

Body centered tetragonal (BCT) phases are structural intermediates between body centered cubic (BCC) and face centered cubic (FCC) structures. However, BCC ↔ FCC transitions may or may not involve a stable BCT intermediate. Interestingly, nanoparticle superlattices usually crystallize in BCT structures, but this phase is much less frequent for colloidal crystals of micrometer-sized particles. Two origins have been proposed for the formation of BCT NPSLs: (i) the influence of the substrate on which the nanoparticle superlattice is deposited, and (ii) non-spherical nanoparticle shapes, combined with the fact that different crystal facets have different ligand organizations. Notably, none of these two mechanisms alone is able to explain the set of available experimental observations. In this work, these two hypotheses were independently tested using a recently developed molecular theory for nanoparticle superlattices that explicitly captures the degrees of freedom associated with the ligands on the nanoparticle surface and the crystallization solvent. We show that the presence of a substrate can stabilize the BCT structure for spherical nanoparticles, but only for very specific combinations of parameters. On the other hand, a truncated-octahedron nanoparticle shape strongly stabilizes BCT structures in a wide region of the phase diagram. In the latter case, we show that the stabilization of BCT results from the geometry of the system and it does not require different crystal facets to have different ligand properties, as previously proposed. These results shed light on the mechanisms of BCT stabilization in nanoparticle superlattices and provide guidelines to control its formation.

Charge Regulation Effects in Nanoparticle Self-Assembly

Nanoparticles in solution acquire charge through the dissociation or association of surface groups. Thus, a proper description of their electrostatic interactions requires the use of charge-regulating boundary conditions rather than the commonly employed constant-charge approximation. We implement a hybrid Monte Carlo/molecular dynamics scheme that dynamically adjusts the charges of individual surface groups of objects while evolving their trajectories. Charge regulation effects are shown to qualitatively change self-assembled structures due to global charge redistribution, stabilizing asymmetric constructs. We delineate under which conditions the conventional constant-charge approximation may be employed and clarify the interplay between charge regulation and dielectric polarization.

Polymer brushes with reversibly tunable grafting density

We propose a novel class of responsive polymer brushes, where the effective grafting density can be controlled by external stimuli. This is achieved by using end-grafted polymer chains that have an affinity to the substrate. For sufficiently strong surface interactions, a fraction of chains condenses into a near-surface layer, while the remaining ones form the outer brush. The dense layer and the more tenuous outer brush can be seen as coexisting microphases. The effective grafting density of the outer brush is controlled by the adsorption strength and can be changed reversibly and in a controlled way as a response to changes in environmental parameters. The effect is demonstrated by numerical self-consistent field calculations and analyzed by scaling arguments. Since the thickness of the denser layer is about a few monomer sizes, its capacity to form a microphase is limited by the product of the brush chain length and the grafting density. We explore the range of chain lengths and grafting densities where the effect is most pronounced. In this range, the SCF studies suggest that individual chains inside the brush show large rapid fluctuations between two states that are separated by only a small free energy barrier. The behavior of the brush as a whole, however, does not reflect these large fluctuations, and the effective grafting density varies smoothly as a function of the control parameters.

Microphase separation and aggregate self-assembly in brushes of oppositely charged polyelectrolytes triggered by ion pairing

This work applies a molecular theory to study the formation of lateral self-assembled aggregates in mixed brushes composed of polyanion and polycation chains. In order to overcome the well-known limitations of mean-field electrostatics to capture polyelectrolyte complexation, the formation of ion pairs between anionic and cationic groups in the polyelectrolytes is explicitly modeled in our theory as an association reaction. This feature is essential to capture the microphase separation of the mixed brush and the formation of lateral aggregates triggered by polyelectrolyte complexation. The effects of solution pH and ionic strength, surface coverage, and chain length on the morphology of the mixed brush are systematically explored. It is shown that increasing salt concentration leads to the rupture of polyelectrolyte complexes and the stabilization of the homogeneous, non-aggregated brush, providing that the formation of ion pairs between the polyelectrolytes and the salt ions in solution is explicitly accounted for by the theory. The inclusion of ion-pairing association reactions between oppositely charged polyelectrolytes within a mean-field description of electrostatics emerges from this work as a useful and simple theoretical approach to capture the formation of polyelectrolyte complexes and their responsiveness to solution ionic strength and pH.

Charge regulation mechanism in end-tethered weak polyampholytes

Weak polyampholytes, containing oppositely charged dissociable groups, are expected to be responsive to changes in ionic conditions. Here, we determine structural and thermodynamic properties, including the charged groups' degrees of dissociation, of end-tethered weak polyampholyte layers as a function of salt concentration, pH, and the solvent quality. For diblock weak polyampholytes grafted by their acidic blocks, we find that the acidic monomers increase their charge while the basic monomers decrease their charge with decreasing salt concentration for pH values less than the pKa value of both monomers and vice versa when the pH > pKa. This complex charge regulation occurs because the electrostatic attraction between oppositely charged blocks is stronger than the repulsion between monomers with the same charge in both good and poor solvents when the screening by salt ions is weak. This is evidenced by the retraction of the top block into the bottom layer. In the case of poor solvent conditions to the basic block (the top block), we find lateral segregation of basic monomers into micelles, forming a two-dimensional hexagonal pattern on the surface at intermediate and high pH values for monovalent salt concentrations from 0.01 to 0.1 M. When the solvent is poor to both blocks, we find lateral segregation of the grafted acidic block into lamellae with longitudinal undulations of low and high acidic monomer density. By exploiting weak block polyampholytes, our work expands the parameter space for creating responsive surfaces stable over a wide range of pH and salt concentration.

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.

Weak polyelectrolyte brushes: re-entrant swelling and self-organization

We have studied the combined influence of pH and ionic strength on the properties of brushes of a weak polyion, poly(acrylic acid), in conditions of grafting density close to the mushroom-brush crossover. By combining atomic force microscopy AFM and quartz crystal microbalance, we show that at low ionic strengths the conformational change of grafted polyions is non-monotonic with increasing pH due to the counterintuitive variation of the ionization degree. Thus, reentrant swelling of the polymer chains is observed with increasing pH. This effect is more important at low polymer grafting densities, when it is accompanied by in-plane heterogeneous distribution at intermediate pH values. In addition, we observed self-assembly on the polymer brush (formation of holes and islands) at pH values below pKa, due to the short-range attractive interaction between uncharged grafted chains. The sensitivity of the ionization of grafted chains to the physicochemical environment was also studied by measuring the interaction force between a silica tip and polymer brushes by atomic force microscopy. The dependence of the ionization of polyions on the presence of the tip points toward important charge regulation effects, in particular at pH values corresponding to partial ionization of the polyion.

The Phase Behavior of Nanoparticle Superlattices in the Presence of a Solvent

Superlattices of nanoparticles coated by alkyl-chain ligands are usually prepared from a stable solution by evaporation, therefore the pathway of superlattice self-assembly critically depends on the amount of solvent present within it. This work addresses the role of the solvent on the structure and the relative stability of the different supercrystalline phases of single-component superlattices (simple cubic, body-centered cubic (BCC), face-centered cubic (FCC), and hexagonal close-packed). The study is performed with a molecular theory for nanoparticle superlattices introduced in this work, which predicts the structure and thermodynamics of the supercrystals explicitly treating the presence and molecular details of the solvent and the ligands. The theory predicts a FCC-BCC transition with decreasing solvent content due to the competition between the translational entropy of the solvent and the entropy and internal energy of the ligands. This result provides an explanation for recent experimental observations by in situ X-ray scattering, which reported a FCC-BCC transition during solvent evaporation. The theory also predicts the effects of the length and surface coverage of the ligands and the radius of the core on the phase behavior in agreement with experimental evidence and previous molecular dynamics simulations. These results validate the use of the dimensionless softness parameter λ (ratio of ligand length to core radius) to predict the phase behavior of wet superlattices. Our results stress the importance of explicitly considering the presence of the solvent in order to reach a complete picture of the mechanisms that mediate the self-assembly of nanoparticle superlattices.

Charge regulation radically modifies electrostatics in membrane stacks

Motivated by biological membrane-containing organelles in plants and photosynthetic bacteria, we study charge regulation in a model membrane stack. Considering (de)protonation as the simplest mechanism of charge equilibration between the membranes and with the bathing environment, we uncover a symmetry-broken charge state in the stack with a quasiperiodic effective charge sequence. In the case of a monovalent bathing salt solution our model predicts complex, inhomogeneous charge equilibria depending on the strength of the (de)protonation reaction, salt concentration, and membrane size. Our results shed light on the basic reorganization mechanism of thylakoid membrane stacks.

Interpolymer complexes of poly(sulfonic acid)s and poly(ethylene oxide): an unexpected association

The formation of novel interpolymer complexes (IPCs) between poly(sulfonic acid)s and poly(ethylene oxide) (PEO) is reported. The complexes were precipitated from polymer mixtures in aqueous solution and deposited on surfaces as layer-by-layer films. Based on evidence from infrared spectroscopy, the interpolymer association in poly(sulfonic acid)/PEO IPCs is ascribed to hydrogen bonding between the sulfonic acid and the ether in PEO. This interaction is not anticipated because sulfonic acids are fully dissociated in aqueous solutions due to their strong acidity. Theoretical calculations suggest that the unexpected association of PEO and poly(sulfonic acid)s results from the formation of very strong sulfonic-acid/ether hydrogen bonds, which increase the apparent pK_as of the poly(sulfonic acid)s and, therefore, decrease the net charge of these polymers. It is shown that while poly(styrene sulfonic acid) (PSSA) and Nafion form IPCs with PEO, poly(vinyl sulfonic acid) (PVSA) does not. This result is explained in terms of the hydrodrophobic nature of PSSA and Nafion, which stabilizes their IPCs, and the fact that hydrogen bonds in PSSA/PEO IPCs are predicted to be stronger than in PVSA/PEO IPCs.

Charge Regulation of Colloidal Particles: Theory and Simulations

To explore charge regulation (CR) in physicochemical and biophysical systems, we present a model of colloidal particles with sticky adsorption sites which account for the formation of covalent bonds between the hydronium ions and the surface functional groups. Using this model and Monte Carlo simulations, we find that the standard Ninham and Parsegian (NP) theory of CR leads to results which deviate significantly from computer simulations. The problem with the NP approach is traced back to the use of a bulk equilibrium constant to account for surface chemical reactions. To resolve this difficulty we present a new theory of CR. The fundamental ingredient of the new approach is the sticky length, which is nontrivially related to the bulk equilibrium constant. The theory is found to be in excellent agreement with computer simulations, without any adjustable parameters. As an application of the theory we calculate the effective charge of colloidal particles containing carboxyl groups, as a function of pH and salt concentration.

Explicit Ion Effects on the Charge and Conformation of Weak Polyelectrolytes

The titration behavior of weak polyelectrolytes is of high importance, due to their uses in new technologies including nanofiltration and drug delivery applications. A comprehensive picture of polyelectrolyte titration under relevant conditions is currently lacking, due to the complexity of systems involved in the process. One must contend with the inherent structural and solvation properties of the polymer, the presence of counterions, and local chemical equilibria enforced by background salt concentration and solution acidity. Moreover, for these cases, the systems of interest have locally high concentrations of monomers, induced by polymer connectivity or confinement, and thus deviate from ideal titration behavior. This work furthers knowledge in this limit utilizing hybrid Monte Carlo⁻Molecular Dynamics simulations to investigate the influence of salt concentration, pK a , pH, and counterion valence in determining the coil-to-globule transition of poorly solvated weak polyelectrolytes. We characterize this transition at a range of experimentally relevant salt concentrations and explicitly examine the role multivalent salts play in determining polyelectrolyte ionization behavior and conformations. These simulations serve as an essential starting point in understanding the complexation between weak polyelectrolytes and ion rejection of self-assembled copolymer membranes.

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.

Routes for nanoparticle translocation through polymer-brush-modified nanopores

This work presents a theoretical study of the translocation routes of nanoparticles through polymer-brush modified nanopores. The calculations were performed with a molecular theory that explicitly accounts for the shape, size, conformations and interactions of all molecular species in the system. This work reports molecular-theory calculations allowing inhomogeneities in the three spatial dimensions, which allows us to study for the first time off-axis translocation routes, i.e. routes that do not coincide with the axis of the pore. Free-energy landscapes within the pore were obtained for particles of different sizes and affinity for the polymer brush. The minimum free-energy paths on these landscapes determine the translocation routes. Decreasing the size of the particle or increasing its affinity for the polymer, shifts the translocation route from the central axis of the pore towards its walls. Interestingly, for a given polymer-particle affinity, there exists an intermediate particle size that results in the most flat potential of mean force for translocation, therefore, that will optimize the rate of translocation.

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.

Self-assembly of model short triblock amphiphiles in dilute solution

In this work, a molecular theory is used to study the self-assembly of short diblock and triblock amphiphiles, with head-tail and head-linker-tail structures, respectively. The theory was used to systematically explore the effects of the molecular architecture and the affinity of the solvent for the linker and tail blocks on the relative stability of the different nanostructures formed by the amphiphiles in dilute solution, which include spherical micelles, cylindrical fibers and planar lamellas. Moreover, the theory predicts that each of these nanostructures can adopt two different types of internal organization: (i) normal nanostructures with a core composed of tail segments and a corona composed of head segments, and (ii) nanostructures with a core formed by linker segments and a corona formed by tail and head segments. The theory predicts the occurrence of a transition from micelle to fiber to lamella when increasing the length of the tail or the linker blocks, which is in qualitative agreement with the geometric packing theory and with experiments in the literature. The theory also predicts a transition from micelle to fiber to lamella as the affinity of the solvent for the tail or linker block is decreased. This result is also in qualitative agreement with experiments in the literature but cannot be explained in terms of the geometric packing theory. The molecular theory provides an explanation for this result in terms of the competition between solvophobic attractions among segments in the core and steric repulsions between segments in the corona for the different types of self-assembled nanostructures.

Determining the Potential of Mean Force for Amyloid-β Dimerization: Combining Self-Consistent Field Theory with Molecular Dynamics Simulation

Amyloid-β (Aβ) protein aggregates through a complex pathway to progress from monomers to soluble oligomers and ultimately insoluble fibrils. Because of the dynamic nature of aggregation, it has proven exceedingly difficult to determine the precise interactions that lead to the formation of transient oligomers. Here, a statistical thermodynamic model has been developed to elucidate these interactions. Aβ_1-42 was simulated using fully atomistic replica exchange molecular dynamics. We use an ensemble of approximately 5 × 10⁵ configurations taken from simulation as input in a self-consistent field theory that explicitly accounts for the size, shape, and charge distribution of both the amino acids comprising Aβ and all molecular species present in solution. The solution of the model equations provides a prediction of the probabilities of the configurations of the Aβ dimer and the potential of mean force between two monomers during the dimerization process. This model constitutes a reliable methodology to elucidate the underlying physics of the Aβ dimerization process as a function of pH, temperature, and salt concentration. The results obtained with this new model could be valuable in the design of Aβ oligomerization inhibitors, a prospective therapeutic for Alzheimer's disease.

Behavior of Weak Polyelectrolyte Brushes in Mixed Salt Solutions

Hydrophilic and hydrophobic weak polybasic brushes immersed in aqueous solutions of mixed salt counterions are considered using a mean-field numerical self-consistent field approach. On top of the solvent quality of the polymer, the counterion–solvent interactions are accounted for by implementing Flory–Huggins interaction parameters. We show that ion specificity within the brush can bring about large changes in conformation. It is found that the collapse transition of hydrophobic, weak polyelectrolyte brushes features an intermediate two-phase state wherein a subset of chains are collapsed in a dense layer at the substrate, while the remainder of chains are well-solvated and strongly stretched away from the it. Besides pH and ionic strength, solvent quality of counterions and the composition of ions in the solvent are important control parameters for the behavior of polyelectrolyte brushes. Increasingly hydrophobic counterions penetrate deeper within the brush and stabilize the collapsed region, while hydrophilic counterions do the opposite.

Polymer adsorption on curved surfaces

The conformational behavior of a coarse-grained finite polymer chain near an attractive spherical surface was investigated by means of multicanonical Monte Carlo computer simulations. In a detailed analysis of canonical equilibrium data over a wide range of sphere radius and temperature, we have constructed entire phase diagrams both for nongrafted and end-grafted polymers. For the identification of the conformational phases, we have calculated several energetic and structural observables such as gyration tensor based shape parameters and their fluctuations by canonical statistical analysis. Despite the simplicity of our model, it qualitatively represents in the considered parameter range real systems that are studied in experiments. The work discussed here could have experimental implications from protein-ligand interactions to designing nanosmart materials.

Structural behavior of competitive temperature and pH-responsive tethered polymer layers

Herein, we develop a molecular theory to examine a class of pH and temperature-responsive tethered polymer layers. The response of pH depends on intramolecular charge repulsion of weakly acidic monomers and the response of temperature depends on hydrogen bonding between polymer monomers and water molecules akin to the behavior of water-soluble polymers such as PEG (poly-ethylene glycol) or NIPAAm (n-isopropylacrylamide). We investigate the changes in structural behavior that result for various end-tethered copolymers: pH/T responsive monomers alone, in alternating sequence with hydrophobic monomers, and as 50/50 diblocks with hydrophobic monomers. We find that the sequence and location of hydrophobic units play a critical role in the thermodynamic stability and structural behavior of these responsive polymer layers. Additionally, the polymers exhibit tunable collapse when varying the surface coverage, location and sequence of hydrophobic units as a function of temperature and pH. As far as we know, our results present the first molecularly detailed theory for end-tethered polymers that are both pH and temperature-responsive via hydrogen bonding. We propose that this work holds predictive power for the guided design of future biomaterials.

Design of Multifunctional Nanogate in Response to Multiple External Stimuli Using Amphiphilic Diblock Copolymer

Nature uses the interplay between hydrophobic and electrostatic interactions of disordered proteins to orchestrate complicated molecular gates such as the nuclear pore complex to control the transport of biological masses. Inspired by nature, we here theoretically show that well-defined gate shape, sensitive response to pH and salt concentration, and selectivity in cargo transport can be simultaneously achieved by grafting amphiphilic diblock copolymers made of sequence-controlled hydrophobic and ionizable monomers on the inner surface of solid-state nanopore. As a result, multiple functions such as ionic gating and molecular filtering can be implemented into one single copolymer nanogate. The gate structure and thermodynamics is a result of the self-assembly of the sequence-designed copolymer in the confined geometry that minimizes the free energy of the system. Our theory further predicts a phase transition and discontinuous charge regulation of the confined copolymer that allows logical gating in biosensors and nanofluidic devices. As an example of application, a nanolocker with the potential of molecular pumping has also been designed with the cooperation of two amphiphilic copolymer gates. Our results highlight the importance of polymer sequence in nanogating, and these insights can be used to guide the rational design of polymer-coated smart nanopores.

Minimum free-energy paths for the self-organization of polymer brushes

A methodology to calculate minimum free-energy paths based on the combination of a molecular theory and the improved string method is introduced and applied to study the self-organization of polymer brushes under poor solvent conditions. Polymer brushes in a poor solvent cannot undergo macroscopic phase separation due to the physical constraint imposed by the grafting points; therefore, they microphase separate forming aggregates. Under some conditions, the theory predicts that the homogeneous brush and the aggregates can exist as two different minima of the free energy. The theoretical methodology introduced in this work allows us to predict the minimum free-energy path connecting these two minima as well as the morphology of the system along the path. It is shown that the transition between the homogeneous brush and the aggregates may involve a free-energy barrier or be barrierless depending on the relative stability of the two morphologies and the chain length and grafting density of the polymer. In the case where a free-energy barrier exists, one of the morphologies is a metastable structure and, therefore, the properties of the brush as the quality of the solvent is cycled are expected to display hysteresis. The theory is also applied to study the adhesion/deadhesion transition between two opposing surfaces modified by identical polymer brushes and it is shown that this process may also require surpassing a free-energy barrier.

Anisotropic surface functionalization of Au nanorods driven by molecular architecture and curvature effects

This work suggests a novel strategy to coat the caps and body of Au-nanorods (Au-NRs) with end-grafted polymer layers of different compositions by taking advantage of the different curvature of these two regions. A molecular theory was used to theoretically investigate the effect of local curvature and molecular architecture (intramolecular connectivity of the monomers) on the adsorption of polymer mixtures on cylindrical (Au-NR body) and spherical (Au-NR caps) surfaces. The adsorption process was systematically studied as a function of the backbone length, number and position of branches, quality of the solvent and total number of monomers of the polymer molecules in the mixture. The balance between repulsive forces and polymer-surface and polymer-polymer attractions governs the amount and composition of the adsorbed layer. This balance is in turn modulated by the architecture of the polymers, the curvature of the surface and the competition between the different polymers in the mixture for the available area. As a result, the equilibrium composition of the polymer layer on spheres and cylinders of the same radius differs, and in turn departs from that of the bulk solution. Curvature plays a major role: the available volume at a given distance from the surface is larger for spherical surfaces than for cylindrical ones, therefore the surface density of the bulkier (more branched) polymer in the mixture is larger on the Au-NR caps than on the Au-NR body. These results suggest that the combination of curvature at the nanoscale and tailored molecular architecture can confer anisotropic nanoparticles with spatially enriched domains and, therefore, lead to nanoconstructs with directional chemical interactions.

Layer-by-Layer Self-Assembly of Polymers with Pairing Interactions

A molecular theory is introduced to model the layer-by-layer self-assembly (LbL-SA) of polymers with pairing interactions. Our theory provides a general framework to describe nonelectrostatic LbL-SA as the pairing interactions generically describe the formation of bonds between two complementary chemical species, for example, hydrogen donor and acceptor in hydrogen-bonding-LbL or host and guest in host-guest-LbL. The theory predicts fundamental observations related to LbL-SA: (i) phase separation of a mixture of polymers with pairing interactions in bulk solution, (ii) linear increase in film thickness with the number of LbL adsorption steps, (iii) stoichiometry overcompensation after each adsorption step, and (iv) interpenetration of polymer layers. Importantly, this study shows that the minimal requirement for nonelectrostatic LbL is the competition of a pairing interaction and an excluded-volume repulsion. A simple analytical model based on this competition predicts the volume fraction of the layers in good agreement with the numerical predictions of the molecular theory.

Probing the Inhomogeneous Charge Distribution on Annealed Polyelectrolyte Star Polymers in Dilute Aqueous Solutions

The conformational structure of a polyelectrolyte chain in dilute aqueous solution is strongly coupled with its surrounding electrostatic environment. With the introduction of branched topology, the distribution of counterions in the vicinity of a polyelectrolyte chain becomes highly inhomogeneous, giving rise to complex structures of branched polyelectrolytes in dilute aqueous solution. To directly probe the local electrostatic conditions near a branched polyelectrolyte in aqueous solutions, star-shaped poly(2-vinylpyridine) (P2VP) polymers with precise labeling of one single fluorophore at different locations, for example, the star center or the terminal group of one arm, were synthesized using reversible addition-fragmentation chain transfer (RAFT) polymerization of vinyl-terminated P2VP macromonomers. Using fluorescence correlation spectroscopy (FCS) combined with photon counting histogram (PCH) analysis, the conformational structures and local electric potential of P2VP star polyelectrolytes were investigated in dilute aqueous solutions of varied pH at a single molecule level. Despite the same hydrodynamic radius of P2VP stars, pH-sensitive fluorophores labeled at different locations sensitively differentiated the higher electric potential at the star center from the lower electric potential at the periphery in dilute aqueous solutions.

Prediction of solvent-induced morphological changes of polyelectrolyte diblock copolymer micelles

Self-assembly processes of polyelectrolyte block copolymers are ubiquitous in industrial and biological processes; understanding their physical properties can also provide insights into the design of polyelectrolyte materials with novel and tailored properties. Here, we report systematic analysis on how the ionic strength of the solvent and the length of the polyelectrolyte block affect the self-assembly and morphology of the polyelectrolyte block copolymer materials by constructing a salt-dependent morphological phase diagram using an implicit solvent ionic strength (ISIS) method for dissipative particle dynamics (DPD) simulations. This diagram permits the determination of the conditions for the morphological transition into a specific shape, namely vesicles or lamellar aggregates, wormlike/cylindrical micelles, and spherical micelles. The scaling behavior for the size of spherical micelles is predicted, in terms of radius of gyration (R(g,m)) and thickness of corona (Hcorona), as a function of solvent ionic strength (c(s)) and polyelectrolyte length (NA), which are R(g,m) ∼ c(s)(-0.06)N(A)(0.54) and Hcorona ∼ c(s)(-0.11)N(A)(0.75). The simulation results were corroborated through AFM and static light scattering measurements on the example of the self-assembly of monodisperse, single-stranded DNA block-copolynucleotides (polyT50-b-F-dUTP). Overall, we were able to predict the salt-responsive morphology of polyelectrolyte materials in aqueous solution and show that a spherical-cylindrical-lamellar change in morphology can be obtained through an increase in solvent ionic strength or a decrease of polyelectrolyte length.