Thermodynamic non-ideality in charge regulation of weak polyelectrolytes

Molecular control via dynamic bonding enables material responsiveness in additively manufactured metallo-polyelectrolytes

Metallo-polyelectrolytes are versatile materials for applications like filtration, biomedical devices, and sensors, due to their metal-organic synergy. Their dynamic and reversible electrostatic interactions offer high ionic conductivity, self-healing, and tunable mechanical properties. However, the knowledge gap between molecular-level dynamic bonds and continuum-level material properties persists, largely due to limited fabrication methods and a lack of theoretical design frameworks. To address this critical gap, we present a framework, combining theoretical and experimental insights, highlighting the interplay of molecular parameters in governing material properties. Using stereolithography-based additive manufacturing, we produce durable metallo-polyelectrolytes gels with tunable mechanical properties based on metal ion valency and polymer charge sparsity. Our approach unveils mechanistic insights into how these interactions propagate to macroscale properties, where higher valency ions yield stiffer, tougher materials, and lower charge sparsity alters material phase behavior. This work enhances understanding of metallo-polyelectrolytes behavior, providing a foundation for designing advanced functional materials.

Dilute polyelectrolyte solutions: recent progress and open questions

Polyelectrolytes are a class of polymers possessing ionic groups on their repeating units. Since counterions can dissociate from the polymer backbone, polyelectrolyte chains are strongly influenced by electrostatic interactions. As a result, the physical properties of polyelectrolyte solutions are significantly different from those of electrically neutral polymers. The aim of this article is to highlight key results and some outstanding questions in the polyelectrolyte research from recent literature. We focus on the influence of electrostatics on conformational and hydrodynamic properties of polyelectrolyte chains. A compilation of experimental results from the literature reveals significant disparities with theoretical predictions. We also discuss a new class of polyelectrolytes called poly(ionic liquid)s that exhibit unique physical properties in comparison to ordinary polyelectrolytes. We conclude this review by listing some key research challenges in order to fully understand the conformation and dynamics of polyelectrolytes in solutions.

Single-chain simulation of Ising density functional theory for weak polyelectrolytes

Conventional theories of weak polyelectrolytes are either computationally prohibitive to account for the multidimensional inhomogeneity of polymer ionization in a liquid environment or oversimplistic in describing the coupling effects of ion-explicit electrostatic interactions and long-range intrachain correlations. To bridge this gap, we implement the Ising density functional theory (iDFT) for ionizable polymer systems using the single-chain-in-mean-field algorithm. The single-chain-in-iDFT (sc-iDFT) shows significant improvements over conventional mean-field methods in describing segment-level dissociation equilibrium, specific ion effects, and long-range intrachain correlations. With an explicit consideration of the fluctuations of polymer configurations and the position-dependent ionization of individual polymer segments, sc-iDFT provides a faithful description of the structure and thermodynamic properties of inhomogeneous weak polyelectrolyte systems across multiple length scales.

Electroresponse of weak polyelectrolyte brushes

End-tethered polyelectrolytes are widely used to modify substrate properties, particularly for lubrication or wetting. External stimuli, such as pH, salt concentration, or an electric field, can induce profound structural responses in weak polyelectrolyte brushes, which can be utilized to further tune substrate properties. We study the structure and electroresponsiveness of weak polyacid brushes using an inhomogeneous theory that incorporates both electrostatic and chain connectivity correlations at the Debye-Hückel level. Our calculation shows that a weak polyacid brush swells under the application of a negative applied potential, in agreement with recent experimental observation. We rationalize this behavior using a scaling argument that accounts for the effect of the surface charge. We also show that the swelling behavior has a direct influence on the differential capacitance, which can be modulated by the solvent quality, pH, and salt concentration.

A Molecular Theory of Polypeptide Adsorption at Inorganic Surfaces

A faithful description of polypeptide adsorption at ionizable surfaces remains a theoretical challenge from a molecular perspective due to the strong coupling of local thermodynamic nonideality and ionizations of both the adsorbate and substrate that are sensitive to the solution condition such as pH, ion valence, and salt concentration. Building upon a recently developed coarse-grained model for natural amino acids in bulk electrolyte solutions, here we report a molecular theory applicable to polypeptide adsorption on ionizable inorganic surfaces over a broad range of inhomogeneous conditions. Our thermodynamic model is able to account for diverse solution effects as well as the amino-acid sequence on polypeptide adsorption and surface association such as hydrogen bonding or bidentate coordination. The theoretical predictions have been validated by extensive comparison with experimental data for the adsorption isotherms of three representative polypeptides at a titanium surface.

Surface charge regulation using classical density functional theory: the effect of divalent potential determining ions

The charge regulation approach has been used to describe the charge of surfaces susceptible to the presence of protons and other ions. Conventionally, this model is used with the Poisson-Boltzmann equation, which generally neglects the finite size of the ions and the electrostatic correlations. Recently, progress has been made by coupling charge regulation with classical density functional theory (DFT), which explicitly includes these correlations. However, little is known about charge regulation at surfaces with both acid-base equilibria and complexation with multivalent ions. The main purpose of this work is to investigate the role divalent ions play in charge regulation. Using DFT, we show that the size of the divalent ion has significant consequences on the surface charge density and it should not be neglected. For the surface reactions investigated, the larger the size of the divalent cation, the greater the charge on the surface due to higher divalent concentration there. At low divalent concentration, the ion correlations play a second-order but non-negligible role; using Poisson-Boltzmann theory with point ions cannot recover the DFT surface charge. At high concentrations, ion correlations play a dominant role by creating charge inversion.

Ising density functional theory for weak polyelectrolytes with strong coupling of ionization and intrachain correlations

We report a theoretical framework for weak polyelectrolytes by combining the polymer density functional theory with the Ising model for charge regulation. The so-called Ising density functional theory provides an accurate description of the effects of polymer conformation on the ionization of individual segments and is able to account for both the intra- and interchain correlations due to the excluded-volume effects, chain connectivity, and electrostatic interactions. Theoretical predictions of the titration behavior and microscopic structure of ionizable polymers are found to be in excellent agreement with the experiment.