Two Sides of the Same Coin: A Unified Theoretical Treatment of Polyelectrolyte Complexation in Solution and Layer-by-Layer Films

Polyelectrolyte coacervates, obtained by mixing solutions of oppositely charged polyions, and layer-by-layer films, produced by sequential adsorption of polyelectrolytes on a surface, are two types of closely related soft materials. While both types of materials are produced by polyelectrolyte complexation, their theoretical description had so far followed divergent paths. This work reports a unifying theoretical treatment of polyelectrolyte complexation in solution and layer-by-layer self-assembled thin films using a molecular theory that describes polyelectrolyte complexation by using a chemical-equilibrium formalism. The theory is shown to predict both the phase diagrams of polyelectrolyte mixtures in solution and the formation of layer-by-layer thin films in good agreement with experimental evidence. In the latter case, the theory correctly captures the effects of solution pH and ionic strength on the mass of the deposited films as well as the possibility of layer-by-layer deposition without full charge reversal at extreme pHs. The theory is then used to revisit the “universal curve” for the effect of salt concentration on layer-by-layer deposition previously proposed on experimental grounds by Salehi et al. [Macromolecules 2015, 48, 400–409]. This universal curve makes predictions about the growth rate of a layer-by-layer film for a given polyanion/polycation pair by using only information obtained from a mixture of the same polyelectrolytes in solution, thereby linking both phenomena. Our theoretical results confirm the validity of the curve. This achievement demonstrates the practical importance of describing polyelectrolyte coacervates and multilayer films within a unified theoretical framework

Responsive Polymers End-Tethered in Solid-State Nanochannels: When Nanoconfinement Really Matters

Solid state nanochannels modified with supramolecular architectures are a new and interesting class of stimuli-responsive nanofluidic element. Their fundamental understanding requires describing the behavior of soft-materials in confined geometries and its responses to changes in solution conditions. Here, a nanochannel modified with a polyelectrolyte brush is studied with a molecular theory that incorporates the conformational behavior of the polymers, electrostatic, van der Waals, and repulsive interactions coupled with the ability of the polymer segments to regulate their charge through acid−base equilibrium. The theory predicts pH-dependent ionic conductivity in excellent agreement with experimental observations. The polymer chains undergo large conformational changes triggered by variations in the outer solution environment and the conductivity of the device is shown to be controlled by the charge state of the polymer. The degree of polymer charge is largely affected by charge regulation and nanoconfinement effects. The molecular calculations show that the apparent pKa inside the pore departs from that in solution when increasing the curvature of the nanochannel

Transport Rectification in Nanopores with Outer Membranes Modified with Surface Charges and Polyelectrolytes

This work reports a comprehensive theoretical study of the transport-rectification properties of cylindrical nanopores with neutral inner walls and chemically modified outer membrane. The chemical species on the two outer sides of the membrane have charges of opposite sign and can be either surface-confined species (<i>i.e.</i>, surface charges) or polyelectrolyte brushes. The advantage of this design over other types of rectifying nanopores is that it requires controlling the composition of the outer walls of the pore (which are easy to access) rather than the inner walls, thus simplifying the fabrication process. Ion-current rectification in nanopores with charged outer walls is ascribed to applied-potential-induced changes in the ionic concentration within the pore. The rectification efficiency is studied as a function of pore length, radius, surface charge and bulk electrolyte concentration. An analytical model is derived for the case of surface-confined charges that predicts the current–potential curves in very good agreement with the numerical calculations. Neutral nanopores with polyelectrolyte-modified outer walls have two distinct advantages compared to surface-charged systems: (i) they exhibit higher rectification factors due to the large charge density immobilized by the polyelectrolyte brushes, and (ii) the applied potential deforms the polyelectrolyte chains toward the oppositely charged electrode. This deformation brings the polyelectrolyte brushes into the pore in the low conductivity state and expels them from the pore in the high conductivity regime. Calculations of the potentials of mean-force suggest that the applied-field-induced conformational changes can be used to control the translocation of cargoes larger than ions, such as proteins and nanoparticles

Ion Transport and Molecular Organization Are Coupled in Polyelectrolyte-Modified Nanopores

Chemically modified nanopores show a strong and nontrivial coupling between ion current and the structure of the immobilized species. In this work we study theoretically the conductance and structure in polymer modified nanopores and explicitly address the problem of the coupling between ion transport and molecular organization. Our approach is based on a nonequilibrium molecular theory that couples ion conductivity with the conformational degrees of freedom of the polymer and the electrostatic and nonelectrostatic interactions among polyelectrolyte chains, ions, and solvent. We apply the theory to study a cylindrical nanopore between two reservoirs as a function of pore diameter and length, the length of the polyelectrolyte chains, their grafting density, and whether they are present or not on the outer reservoir walls. In the very low applied potential regime, where the distribution of polyelectrolyte and ions is similar to that in equilibrium, we present a simple analytical model based on the combination of the different resistances in the system that describes the conductance in excellent agreement with the calculations of the full nonequilibrium molecular theory. On the other hand, for a large applied potential bias, the theory predicts a dramatic reorganization of the polyelectrolyte chains and the ions. This reorganization results from the global optimization of the different interactions in the system under nonequilibrium conditions. For nanopores modified with long chains, this reorganization leads to two interesting physical phenomena: (i) control of polyelectrolyte morphology by the direction and magnitude of ion-fluxes and (ii) an unexpected decrease in system resistance with the applied potential bias for long chains due to the coupling between polyelectrolyte segment distribution and ion currents

Kinetically Controlled Self-Assembly of Latex–Microgel Core–Satellite Particles

Latex–microgel core–satellite particles were prepared by electrostatic assembly of negatively charged polystyrene latex and positively charged microgels of a poly­(<i>N</i>-isopropylmethacrylamide) (pNIPMAM) and poly­[2-methacryloyloxy)­ethyl] trimethylammonium chloride (pMETAC) copolymer. The number of satellites per core, determined by scanning electron microscopy, varied from 3 to 10 depending on the sizes of the microgel and latex microparticles. The numbers of satellites per core for different size ratios were compared with the predictions for thermodynamically controlled (maximum packing) and kinetically controlled (random sequential adsorption) assembly, and it was shown that the assembly of latex and microgel proceeds through a random sequential adsorption mechanism. The charges of the microgels and latex particles were retained within the assemblies; therefore, the core–satellite particles have well-defined regions of positive and negative charge. These regions were used to direct the adsorption of gold and latex nanoparticles of opposite charge in order to create multicomponent colloids

Twisting of Charged Nanoribbons to Helicoids Driven by Electrostatics

Charged amphiphiles in solution usually self-assemble into flat nanoribbons that spontaneously twist into different shapes. The role of electrostatics in this process is still under strong debate. This work studies the electrostatic free energy of twisting a nanoribbon at the level of the nonlinear Poisson–Boltzmann approximation. It is shown that helicoid-shaped ribbons are more stable than flat ribbons, while other shapes under consideration (cylindrical helixes and bent ribbons) are always less stable than the flat ribbon. The unexpected electrostatics-driven twisting of the ribbon into a helicoid is ascribed to the increase in its perimeter with increasing degree of twisting, as charges near the edge of the ribbon are electrostatically more stable than those near its center. This argument successfully explains the effects of salt concentration and the width of the ribbon on the optimal twisting period and allows us to approximately describe the problem of ribbon twisting in terms of two dimensionless variables that combine the helicoid twisting period, the Debye length of the solution, and the width of the ribbon. The magnitude of the electrostatic twisting energy predicted by our calculations is comparable to that of restoring elastic forces for typical ribbons of self-assembled amphiphiles, which indicates that electrostatics plays an important role in determining the equilibrium shape of charged nanoribbons

Redox and Acid−Base Coupling in Ultrathin Polyelectrolyte Films

A single layer of poly(allylamine) with a covalently attached osmium pyridine−bipyridine complex adsorbed onto a Au surface modified by mercaptopropanesulfonate has been studied theoretically with a molecular approach and experimentally by cyclic voltammetry. These investigations have been carried out at different pHs and ionic strengths of the electrolyte solution in contact with the redox polyelectrolyte modified electrode. The theory predicts strong coupling between the acid−base and redox equilibria, particularly for low ionic strength, pH close to the pKa, and high concentration of redox sites. The coupling leads to a decrease in the peak potential at pH values above the apparent pKa of the weak polyelectrolyte, in good agreement with the experimental pH dependence at 4 mM NaNO3. Theoretical calculations suggest that the inflection point in the peak position versus pH curves can be used to estimate the apparent pKa of the amino groups in the polymer. Comparison of the apparent pKa for PAH-Os in the film with that of poly(allylamine) reported in the literature shows that the underlying charged thiol strongly influences charge regulation in the film. A systematic study of the film thickness and the degree of protonation in sulfonate and amino groups for solutions of different pH and ionic strength shows the coupling between the different interactions. It is found that the variation of the film properties has a non-monotonic dependence on bulk pH and salt concentration. For example, the film thickness shows a maximum with electrolyte ionic strength, whose origin is attributed to the balance between electrostatic amino−amino repulsions and amino−sulfonate attractions

Molecular Theory of Chemically Modified Electrodes by Redox Polyelectrolytes under Equilibrium Conditions: Comparison with Experiment

A molecular theory is presented to describe chemically modified electrodes by redox polymers. The theory is based on writing the free energy functional of the system which includes the size, shape, charge distribution, and conformations of all of the molecular species as well as all of the inter and intramolecular interactions, the acid−base equilibrium for the ionizable groups of the weak polyelectrolyte, and the redox equilibrium of the electrochemical active sites with the metal. The minimization of the free energy leads to the molecular organization of the film as a function of bulk pH, salt concentration, and applied electrode potential. The approach is applied to the experimental system composed by osmium pyridine−bipyridine complex covalently bound to poly(allylamine) backbone, which is adsorbed onto a mercapto-propane sulfonate thiolated gold electrode. The redox and nonredox capacity of the electrode and its dependence on the electrode potential calculated with the molecular theory shows very good agreement with linear scan voltammetric experiments under reversible conditions (equilibrium scans) without the use of any free adjustable parameter. The predicted film thickness is in line with ellipsometric measurements. Further, the theory predicts the swelling of the film as a function of the electrode potential. The molecular theory provides the link between the molecular organization within the film and the electrochemical behavior. It is shown that the electrostatic, excluded volume, and van der Waals interaction fields are strongly coupled in a nontrivial way. Furthermore, the degree of charge regulation and distribution of oxidized states couples to the molecular distributions and the interaction fields. The application of the theory to different model systems demonstrates the importance of incorporating molecular information into the theoretical approach and the very strong coupling that exists between molecular structure, film organization, interactions fields, and electrochemical behavior