Polyelectrolytes are charged polymers comprising macromolecules in which substantial portions of the constituent units contain cationic (e.g., pyridinium, ammonium) or anionic (e.g., sulfonate, carboxylate) groups, which possess special functions from the features of counterions, such as dissociation to charged species, mechanical stability, phase behavior, etc. Therefore, functional polyelectrolytes have been widely applied in many fields. In this perspective, we present some progresses in the studies of poly(polyoxometalate)s, denoted as poly(POM)s, as a kind of new charged polymers/polyelectrolytes, by covalent bonding between the inorganic polyoxometalate (POM) clusters and the organic polymer chains. According to the distinct positions of POMs in polymer chain and functions of poly(POM)s, they are divided into the following four categories: crosslinked poly(POM); side-chain poly(POM); backbone poly(POM), including poly(POM)-conjugated polymer hybrid and block poly(POM)-polymer; and POM-based covalent organic framework (PCOF). This perspective introduces the synthesis methods of poly(POM) polyelectrolytes and their macromolecular and aggregate structural characteristics, while also focusing on their properties and functions. Their application areas include catalysis, thermal resistance, optical functions, fuel cells and batteries, etc.

The counterion-mediated hydrogen bonding (CMHB) is related to the hydrogen bonding between bound counterions and polyelectrolyte chains in polyelectrolyte systems, where the counterions can both electrostatically bind to the charged groups of polyelectrolyte chains and act as hydrogen bond donors or acceptors to form hydrogen bonds with the hydrogen bond sites associated with polyelectrolyte chains simultaneously. A large number of literatures illustrate that strong polyelectrolytes (SPs) are insensitive to pH, which severely limmits the applications of SPs as smart materials. However, our studies have demonstrated that the CMHB makes SPs pH-responsive. This perspective discusses the mechanism of pH responsiveness of SPs and the pH-tunable properties of SPs, based on the pH-controlled CMHB effect. The future research directions on the pH responsiveness of SPs are also discussed here. It is anticipated that the study of the pH responsiveness of SPs not only will provide a new understanding of the fundamental properties of SPs, but also will greatly expand the applications of SPs in the field of smart materials.

Polyelectrolyte solutions are more variable than uncharged macromolecule due to electrical interaction between charged molecules and surrounding counterions. Therefore, the subject of polyelectrolyte solutions has attracted a wide range of interests in both basic and applied research, and has also been extensively explored. However, the understanding of the molecular dynamics and conformation of polyelectrolytes in solution remains to be deepened, and universal consensus on some key issues have not been reached. Many methods have contributed to solving the above problems in different ways, including dielectric relaxation spectroscopy (DRS). In this perspective, we briefly reviewed the history of dielectric spectroscopic research on polyelectrolyte solution, with emphasis on summarizing our efforts. In particular, we expound the characteristics of DRS and its ability to obtain the internal information of the system of interest. Finally, we evaluate the advantages and limitations of the dielectric method and discussed future prospects of this field.

Polymer density-functional theories (PDFTs) have distinct advantages in the study of polyelectrolyte (PE) systems over experiments and molecular simulations. Here we give an introductory review of some PDFTs recently developed for PE systems. We start with a general formalism of PDFTs and its relation to the widely used polymer self-consistent field theory (SCFT), then explain the various correlations that are neglected in SCFT but can be accounted for in PDFTs, including those due to the excluded-volume interaction and chain connectivity of uncharged polymers, the electrostatic correlations of small ions, and the chain correlations in PEs. We also list some applications of PDFTs for PE systems, and finally give some perspectives on future work. We hope that our review can attract more researchers to apply and further develop PDFTs as a promising class of theoretical and computational tools.

Polyelectrolyte brushes (PEBs) are commonly used to modify surface that have attracted great research interest. The dielectric permittivity of the grafted surface is typically significantly different from that of solution, which results in surface polarization (SP) effect with a jump of electric field. It is thus important to study how SP alters the PEB’s structure and properties. In this work, the SP effects on PEB structure was studied using a statistical thermodynamic theory. The free energy functional to describe SP effect was constructed by using the image-charge method. Meanwhile, the electrostatic potential was solved from a modified Poisson-Boltzmann equation taking the ion solvation effect into consideration. In the absence of SP, the thickness of PEB exhibited a continuous collapse transition when decreasing the solvent quality. In the presence of SP, the collapse became a jump-like transition. Free energy analysis showed that the long-range Coulombic interaction dominated the transition because of the enhanced counterion condensation in the presence of SP. The theory provides an effective tool to study SP effect on PEBs, and the results explain the underlying physics in PEB collapse transition.

We investigate the solution self-assembly of a mixture of positively charged homopolymers and AB diblock copolymers, in which the A blocks are negatively charged, and the B blocks are neutral. The electrostatic complexation between oppositely charged polymers drives the formation of many ordered phases. The microstructures and phase diagrams are calculated using self-consistent field theory (SCFT) based on an ion-pair model with an equilibrium constant $ K $ to characterize the strength of binding between positively and negatively charged monomers. The effects of the charge ratio, representing the ratio of charges from the homopolymer over all charges from polymers in the system, on the ordered structure are systematically studied, both for hydrophobic and hydrophilic A blocks. The charge ratio plays an important role in determining the phase boundaries in the phase diagram of salt concentration versus polymer concentration. We also provide information about the varying tendency of the domain spacing and core size of the spherical phase when the charge ratio is changed, and the results are in good agreement with experiments. These studies provide a deep understanding of the self-assembled microstructures of oppositely charged diblock copolymer-homopolymer systems.

The liquid-liquid phase separation of biopolymers in living cells contains multiple interactions and occurs in a dynamic environment. Resolving the regulation mechanism is still a challenge. In this work, we designed a series of peptides (XXLY)₆SSSGSS and studied their complexation and coacervation behavior with single-stranded oligonucleotides. The “X” and “Y” are varied to combine known amounts of charged and non-charged amino acids, together with the introduction of secondary structures and pH responsiveness. Results show that the electrostatic interaction, which is described as charge density, controls both the strength of complexation and the degree of chain relaxation, and thus determines the growth and size of the coacervates. The hydrophobic interaction is prominent when the charges are neutralized. Interestingly, the secondary structures of peptides exhibit profound effect on the morphology of the phases, such as solid phase to liquid phase transition. Our study gains insight into the phase separation under physiological conditions. It is also helpful to create coacervates with desirable structures and functions.

We utilize molecular dynamics simulations to investigate the microstructures of ions and polyelectrolytes in aqueous solutions under external electric fields. By focusing on the multi-body interactions between ionic components and H₂O molecules, as well as their responses to the external electric fields, we clarify several nontrivial molecular features of the ionic and polyelectrolyte solutions, such as the solvations of cations and anions, clustering of the ions, and dispersions/aggregations of polyelectrolyte chains, as well as the corresponding responses of H₂O molecules in these contexts. Our simulations illustrate the variations in structures of ionic solutions caused by reversing the charge sign of the ions, and elucidate the disparity in structures between anionic and cationic polyelectrolyte solutions in the presence of the external electric fields. This work clarifies the mechanism for the alternations in complex multi-body interactions in aqueous solutions caused by the application electric field, which can contribute to the fundamental understanding of the physical and chemical natures of ion-containing and charged polymeric systems.

Understanding how supercoiled DNA releases intramolecular stress is essential for its functional realization. However, the molecular mechanism underlying the relaxation process remains insufficiently explored. Here we employed MD simulations based on the oxDNA2 model to investigate the relaxation process of a 336-base pair supercoiled minicircular DNA under double-strand breaks with two fixed endpoints. Our simulations show that the conformational changes in the DNA occur continuously, with intramolecular stress release happening abruptly only when the DNA chain traverses the breakage site. The relaxation process is influenced not only by the separation distance between the fixed ends but also their angle. Importantly, we observe an inhibitory effect on the relaxation characterized by small angles, where short terminal loops impede DNA conformational adjustments, preserving the supercoiled structure. These findings elucidate the intricate interplay between DNA conformational change, DNA motion and intramolecular stress release, shedding light on the mechanisms governing the relaxation of supercoiled DNA at the molecular level.

Polyampholyte gels, which have hierarchical structures, exhibit excellent self-healing properties and have great promise for biomaterials and bioengineering. We investigated the relationship between microscopic structures and macroscopic viscoelastic properties of polyampholyte gels and found three factors influencing their viscoelastic properties, including the chemical crosslinking bonds, topological entanglements controlled by monomer concentration, and the ionic bonds. Ionic strength plays a major role on the strength of ionic bonds. A crossover point of elastic modulus and loss modulus was observed in the dynamic frequency sweeps at low monomer concentration or low chemical crosslinking density for gels with intermediate strength of ionic bonds. The solid-liquid transition signaled by the crossover point is a typical feature of dynamic associated gels, representing the dynamical association-dissociation of the ionic bonds and full relaxation of the topological entanglements in the gel network. While the crossover point disappears when the ionic bonds are too weak or too strong to form “permanent” bonds. Consistently, in the non-linear yielding measurement, gels with intermediate strength of the ionic bonds are ductile and yield at very large shear strain due to the self-healing properties and the dynamic association-dissociation of the ionic bonds. But the self-healing properties disappear when the ionic bond strength is too weak or too strong. Our work reveals the mechanism of how the dynamic association-dissociation of ionic bonds influences both the linear and non-linear viscoelastic properties of the polyampholyte gels.

We present the results of molecular dynamics simulations of steady shear between a pair of neutral polymer brushes, as well as a pair of charged polymer brushes in the strongly compressed regime. The results of the molecular dynamic simulations of neutral and polyelectrolyte brushes in implicit solvent including normal forces, shear forces, viscosities and friction coefficients as a function of separation between brushes, are presented in the study. The comparison of the simulation results of neutral and charged brushes shows that the charged brushes is in the quasi-neutral regime, and the dependence of viscosity on the separation distance show the similar power law of neutral brushes. Our simulation results confirm that the implicit solvent simulations of polyelectrolyte brushes that ignore hydrodynamics interaction are in agreement with the scaling predictions qualitatively because of screening of hydrodynamic interaction and long-range electrostatic interactions on the correlation length scale. Both of neutral and charged brushes show the lubrication properties that the friction coefficient decreases with the separation decreases at enough large loads. However, a maximum of friction coefficients is observed for polyelectrolyte brushes, which is in contrast to the neutral brushes with monotonical dependence.

Salt-doped block copolymers have widespread applications in batteries, fuel cells, semiconductors, and various industries, where their properties crucially depend on phase separation behavior. Traditionally, investigations into salt-doped diblock copolymers have predominantly focused on microphase separation, overlooking the segregation between ionic and polymeric species. This study employs weak segregation theory to explore the interplay between phase separation dominated by the polymer-modulated mode and the salt-out-modulated mode, corresponding to microscopic and macroscopic phase separations, respectively. By comparing diblock copolymers doped with salts to those doped with neutral solvents, we elucidate the significant role of charged species in modulating phase behavior. The phase separation mode exhibits a transition between the polymer-modulated and salt-out-modulated modes at different wavenumbers. In systems doped with neutral solvents, this transition is stepwise, while in salt-ion-doped systems, it is continuous. With a sufficiently large Flory-Huggins parameter between ions and polymers, the salt-out-modulated mode becomes dominant, promoting macrophase separation. Due to the solvation effect of salt ions, salt-doped systems are more inclined to undergo microphase separation. Furthermore, we explore factors influencing the critical wavenumber of phase separation, including doping level and the Flory-Huggins parameters between two blocks and between ions and polymeric species. Our findings reveal that in a neutral solvent environment, these factors alter only the boundary between micro- and macro-phase separations, leaving the critical wavenumber unchanged in microphase separation cases. However, in a salt-doped environment, the critical wavenumber of microphase separation varies with these parameters. This provides valuable insights into the pivotal role of electrostatics in the phase separation of salt-doped block copolymers.

Polyelectrolyte (PE) gels, distinguished by their unique stimuli-responsive swelling behavior, serve as the basis of broad applications, such as artificial muscles and drug delivery. In this work, we present a theoretical model to analyze the electrostatics and its contribution to the swelling behavior of PE gels in salt solutions. By minimizing the free energy of PE gels, we obtain two distinct scaling regimes for the swelling ratio at equilibrium with respect to the salt concentration. We compare our predictions for the swelling ratio with experimental measurements, which show excellent agreement. In addition, we employ a finite element method to assess the applicability range of our theoretical model and assumptions. We anticipate that our model will also provide valuable insights into drug adsorption and release, deformation of red blood cells, 4D printing and soft robotics, where the underlying mechanism of swelling remains enigmatic.

Titanium dioxide (TiO₂) hollow nanoparticles present significant potential for photocatalytic applications while their straightforward preparation with precise structure control is still challenging. This work reports the approach to preparing tunable hollow TiO₂ nanospheres by utilization of spherical polyelectrolyte brushes (SPB) as nanoreactors and templates. During the preparation, the evolution of the structure was characterized by small angle X-ray scattering (SAXS), and in combination with dynamic light scattering and transmission electron microscopy. The formation of TiO₂ shell within the brush (SPB@TiO₂) is confirmed by the significant increase of the electron density, and its internal structure has been analyzed by fitting SAXS data, which can be influenced by Titanium precursors and ammonia concentration. After calcining SPB@TiO₂ in a muffle furnace, hollow TiO₂ nanospheres are produced, and their transition to the anatase crystal form is triggered, as confirmed by X-ray diffraction analysis. Utilizing the advantages of their hollow structure, these TiO₂ nanospheres exhibit exceptional catalytic degradation efficiency of methylene blue (MB), tetracycline (TC), and 2,4-dichlorophenoxyacetic acid (2,4-D), and also demonstrate excellent recyclability.