Theory of polyzwitterion conformations

A model for zwitterionic polymers and their capacitance applications

Zwitterions have been shown experimentally to enhance the dielectric constant of ionic media, owing to their large molecular dipole. Many studies since explored the enhancement of ionic conductivity with zwitterion additives as well as bulk behavior of zwitterions. Here, we examine the capacitance behavior of zwitterions between charged parallel plates using a mean-field theory. Employing only chain connectivity of a cation and anion with neutral monomers in between with mean-field electrostatics, we show that our model captures the high-dielectric behavior of zwitterions. We also predict an optimum in the capacitance of zwitterionic media as a function of chain length. To address the issue of zwitterion screening near charged surfaces, we demonstrate that zwitterions simultaneously partially screen charged walls and act as a pure dielectric that propagates the electric field far from the surface. Moreover, we show that salt solutions with zwitterionic additives outperform the energy density of both salt-only and zwitterion-only capacitors. We find that salt-only capacitors perform better at low applied potential, whereas salt capacitors with zwitterionic additives perform better at high applied potential.

Characterizing Hygroscopic Films of Polyzwitterions in Electric Fields Using Neutron and X-ray Reflectometries: Electrostriction or Mass Loss?

We study responses of thermally annealed ultrathin films deposited on silicon substrates and containing polyzwitterions to applied electric fields by using specular neutron reflectometry (NR). In particular, we applied 7 kV under vacuum at 150 °C on the films containing poly(1-(3-sulfonatopropyl)-2-vinylpyridinium) (P2VPPS) and its blends with either a deuterated ionic liquid (EMIMBF4-d11), potassium bromide (KBr), or deuterated sodium polystyrenesulfonate (NaPSS-d7). The voltage was applied over an air gap, and the in situ neutron reflectivity measurements allowed us to measure changes in the films. In all the cases, we measured decreases in thicknesses of the films, which varied up to ∼8% depending on the added salt. Posteriori X-ray reflectivity (XRR) measurements on the same films at room temperature reveal that these films were highly hygroscopic, which led to the presence of water in these films. Analysis of the NR and the XRR revealed that the decrease in the thickness of the films in the neutron reflectivity experiments on heating resulted from the loss of water and the ionic liquid but not from electrostrictive effects. The in situ NR and posteriori XRR experiments revealed not only the hygroscopic nature of these films but also depth-resolved structural rearrangements due to the applied electric fields in the films containing electrolytes and polyelectrolytes. This work shows that a combination of NR and XRR can be used to distinguish between mass loss and electrostriction in films containing charged polymers such as polyzwitterions.

Theory of thermoreversible gelation and anomalous concentration fluctuations in polyzwitterion solutions

We present a theoretical framework to investigate thermoreversible phase transitions within polyzwitterion systems, encompassing macrophase separations (MPS) and gelation. In addition, we explore concentration fluctuations near critical points associated with MPS, as well as tricritical and bicritical points at the intersection of MPS and gelation. By utilizing mean-field percolation theory and field theory formalism, we derive the Landau free energy in terms of polyzwitterion concentration with fixed dipole strengths and other experimental variables, such as temperatures and salt concentrations. As the temperature decreases, the dipoles can form cross-links, resulting in polyzwitterion associations. The associations can grow to a gel network and enhance the propensity for MPS, including liquid-liquid, liquid-gel, and gel-gel phase separations. Remarkably, the associations also impact critical behaviors. Using the renormalization group technique, we find that the critical exponents of the polyzwitterion concentration correlation functions significantly deviate from those in the Ising universality class due to the presence of polyzwitterion associations, leading to crossover critical behaviors.

Dipole Theory of Polyzwitterion Microgels and Gels

The behavior of polyzwitterions, constituted by dipole-like zwitterionic monomers, is significantly different from that of uniformly charged polyelectrolytes. The origin of this difference lies in the intrinsic capacity of polyzwitterions to self-associate intramolecularly and associate with interpenetrating chains driven by dominant dipolar interactions. Earlier attempts to treat polyzwitterions implicitly assume that the dipoles of zwitterion monomers are randomly oriented. At ambient temperatures, the dipolar zwitterion monomers can readily align with each other generating quadrupoles and other multipoles and thus generating heterogeneous structures even in homogeneous solutions. Towards an attempt to understand the role of such dipolar associations, we present a mean field theory of solutions of polyzwitterions. Generally, we delineate a high-temperature regime where the zwitterion dipoles are randomly oriented from a low-temperature regime where quadrupole formation is significantly prevalent. We present closed-form formulas for: (1) Coil-globule transition in the low-temperature regime, the anti-polyelectrolyte effect of chain expansion upon addition of low molar mass salt, and chain relaxation times in dilute solutions. (2) Spontaneous formation of a mesomorphic state at the borderline between the high-temperature and low-temperature regimes and its characteristics. A universal law is presented for the radius of gyration of the microgel, as a proportionality to one-sixth power of the polymer concentration. (3) Swelling equilibrium of chemically cross-linked polyzwitterion gels in both the high temperature and low-temperature regimes. Addressing the hierarchical internal dynamics of polyzwitterion gels, we present a general stretched exponential law for the time-correlation function of gel displacement vector, that can be measured in dynamic light scattering experiments. The present theory is of direct experimental relevance and additional theoretical developments to all polyzwitterion systems, and generally to biological macromolecular systems such as intrinsically disordered proteins.

The Effect of Block Ratio and Structure on the Thermosensitivity of Double and Triple Betaine Block Copolymers

AB-type and BAB-type betaine block copolymers composed of a carboxybetaine methacrylate and a sulfobetaine methacrylate, PGLBT-b-PSPE and PSPE-b-PGLBT-b-PSPE, respectively, were synthesized by one-pot RAFT polymerization. By optimizing the concentration of the monomer, initiator, and chain transfer agent, block extension with precise ratio control was enabled and a full conversion (~99%) of betaine monomers was achieved at each step. Two sets (total degree of polymerization: ~300 and ~600) of diblock copolymers having four different PGLBT:PSPE ratios were prepared to compare the influence of block ratio and molecular weight on the temperature-responsive behavior in aqueous solution. A turbidimetry and dynamic light scattering study revealed a shift to higher temperatures of the cloud point and micelle formation by increasing the ratio of PSPE, which exhibit upper critical solution temperature (UCST) behavior. PSPE-dominant diblocks created spherical micelles stabilized by PGLBT motifs, and the transition behavior diminished by decreasing the PSPE ratio. No particular change was found in the diblocks that had an identical AB ratio. This trend reappeared in the other set whose entire molecular weight approximately doubled, and each transition point was not recognizably impacted by the total molecular weight. For triblocks, the PSPE double ends provided a higher probability of interchain attractions and resulted in a more turbid solution at higher temperatures, compared to the diblocks which had similar block ratios and molecular weights. The intermediates assumed as network-like soft aggregates eventually rearranged to monodisperse flowerlike micelles. It is expected that the method for obtaining well-defined betaine block copolymers, as well as the relationship of the block ratio and the chain conformation to the temperature-responsive behavior, will be helpful for designing betaine-based polymeric applications.

Polyzwitterion fast and slow mode behavior are coupled to phase separation as observed by dynamic laser light scattering

A model zwitterionic polysulfobetaine, poly(3-(acrylamidopropyl-dimethyl-ammonium) propyl-1-sulfonate) (pAPAPS), phase separates upon cooling and exhibits an upper critical solution temperature (UCST) behavior with no added salt in deuterium oxide solutions. Dynamic light scattering measurements indicate the presence of distinct fast and slow diffusive modes, where the fast mode is interpreted as a collective diffusion coefficient and the slow mode is attributed to the diffusion of multi-chain dynamic clusters. The relative population of fast and slow modes varies systematically with temperature and concentration. A clustering temperature (T*) was assigned when the slow mode first appeared upon cooling. The slow mode then increases in relative scattering amplitude as the phase boundary is approached. The fast mode exhibits a concentration dependence above T* consistent with the virial expansion in the collective diffusion. The sign of the virial coefficient (kd) is negative, even in the good solvent region above the expected Flory temperature (Θ ≈ 39 °C), a behavior distinct from synthetic neutral polymers in organic solvents. The onset of multi-chain clustering at T < T* coincides with the poor solvent regime (T < Θ). Attractive dipolar interactions due to the zwitterionic sulfobetaine groups in pAPAPS are suggested as the origin of the multi-chain clusters with no salt. Upon the addition of 100 mM NaCl, the slow mode is suppressed, and the hydrodynamic radius is consistent with polyzwitterion chain dimensions in a dilute solution. We find that concentration dependent diffusion is highly linked to the theta temperature and the emergence of dynamic clusters as the polymer goes from good to poor solvent on approach to the UCST. The slow mode in the semidilute regime is reported along with preliminary small-angle neutron scattering data that show salt reduces clustering and leads to predominantly chain scattering.

Anti-polyelectrolyte and polyelectrolyte effects on conformations of polyzwitterionic chains in dilute aqueous solutions

Polyzwitterions (PZs) are considered as model synthetic analogs of intrinsically disordered proteins. Based on this analogy, PZs in dilute aqueous solutions are expected to attain either globular (i.e. molten, compact) or random coil conformations. Addition of salt is expected to open these conformations. To the best of our knowledge, these hypotheses about conformations of PZs have never been verified. In this study, we test these hypotheses by studying effects of added salt [potassium bromide (KBr)] on gyration and hydrodynamic radii of poly(sulfobetaine methacrylate) in dilute aqueous solutions using dynamic light scattering and small-angle X-ray scattering, respectively. Effects of zwitteration are revealed by direct comparisons of the PZs with the polymers of the same backbone but containing (1) no explicit charges on side groups such as poly(2-dimethylaminoethyl methacrylate)s and (2) explicit cationic side groups with tertiary amino bromide pendants. Zeta-potential measurements, transmission electron microscopy, and ab initio molecular dynamics simulations reveal that the PZs acquire net positive charge in near salt-free conditions due to protonation but retain coiled conformations. Added KBr leads to nonmonotonic changes exhibiting an increase followed by a decrease in radius of gyration (and hydrodynamic radius), which are called antipolyelectrolyte and polyelectrolyte effects, respectively. Charge regulation and screening of charge-charge interactions are discussed in relation to the antipolyelectrolyte and polyelectrolyte effects, respectively, which highlight the importance of salt in affecting net charge and conformations of PZs.

Theory of self-coacervation in semi-dilute and concentrated zwitterionic polymer solutions

Based on the random phase approximation, we develop a molecular theory of self-coacervation in zwitterionic polymer solutions. We show that the interplay between the volume interactions of the monomeric units and electrostatic correlations of charged groups on a polymer backbone can result in liquid-liquid phase separation (self-coacervation). We analyse the behavior of the coacervate phase polymer concentration depending on the electrostatic interaction strength - the ratio of the Bjerrum length to the bond length of the chain. We establish that in a wide range of polymer concentration values - from a semi-dilute to a rather concentrated solution - the chain connectivity and excluded volume interaction of the monomeric units have an extremely weak effect on the contribution of the electrostatic interactions of the dipolar monomeric units to the total free energy. We show that for rather weak electrostatic interactions, the electrostatic correlations manifest themselves as Keesom interactions of point-like freely rotating dipoles (Keesom regime), while in the region of strong electrostatic interactions the electrostatic free energy is described by the Debye-Hückel limiting law (Debye regime). We show that for real zwitterionic coacervates the Keesom regime is realized only for sufficiently small polymer concentrations of the coacervate phase, while the Debye regime is approximately realized for rather dense coacervates. Using the mean-field variant of the density functional theory, we calculate the surface tension (surface free energy) of the "coacervate-solvent" interface as a function of the bulk polymer concentration. Obtained results can be used to estimate the parameters of the polymer chains needed for practical applications such as drug encapsulation and delivery, as well as the design of adhesive materials.

An Introduction to the Stickers-and-Spacers Framework as Applied to Biomolecular Condensates

Cellular organization is determined by a combination of membrane-bound and membrane-less biomolecular assemblies that range from clusters of tens of molecules to micrometer-sized cellular bodies. Over the last decade, membrane-less assemblies have come to be referred to as biomolecular condensates, reflecting their ability to condense specific molecules with respect to the remainder of the cell. In many cases, the physics of phase transitions provides a conceptual framework and a mathematical toolkit to describe the assembly, maintenance, and dissolution of biomolecular condensates. Among the various quantitative and qualitative models applied to understand intracellular phase transitions, the stickers-and-spacers framework offers an intuitive yet rigorous means to map biomolecular sequences and structure to the driving forces needed for higher-order assembly. This chapter introduces the fundamental concepts behind the stickers-and-spacers model, considers its application to different biological systems, and discusses limitations and misconceptions around the model.

Competing interactions give rise to two-state behavior and switch-like transitions in charge-rich intrinsically disordered proteins

The most commonly occurring intrinsically disordered proteins (IDPs) are polyampholytes, which are defined by the duality of low net charge per residue and high fractions of charged residues. Recent experiments have uncovered nuances regarding sequence–ensemble relationships of model polyampholytic IDPs. These include differences in conformational preferences for sequences with lysine vs. arginine and the suggestion that well-mixed sequences form a range of conformations, including globules, conformations with ensemble averages that are reminiscent of ideal chains, or self-avoiding walks. Here, we explain these observations by analyzing results from atomistic simulations. We find that polyampholytic IDPs generally sample two distinct stable states, namely, globules and self-avoiding walks. Globules are favored by electrostatic attractions between oppositely charged residues, whereas self-avoiding walks are favored by favorable free energies of hydration of charged residues. We find sequence-specific temperatures of bistability at which globules and self-avoiding walks can coexist. At these temperatures, ensemble averages over coexisting states give rise to statistics that resemble ideal chains without there being an actual counterbalancing of intrachain and chain-solvent interactions. At equivalent temperatures, arginine-rich sequences tilt the preference toward globular conformations whereas lysine-rich sequences tilt the preference toward self-avoiding walks. We also identify differences between aspartate- and glutamate-containing sequences, whereby the shorter aspartate side chain engenders preferences for metastable, necklace-like conformations. Finally, although segregation of oppositely charged residues within the linear sequence maintains the overall two-state behavior, compact states are highly favored by such systems.

Recent Advances in Zwitterionic Hydrogels: Preparation, Property, and Biomedical Application

Nonspecific protein adsorption impedes the sustainability of materials in biologically related applications. Such adsorption activates the immune system by quick identification of allogeneic materials and triggers a rejection, resulting in the rapid failure of implant materials and drugs. Antifouling materials have been rapidly developed in the past 20 years, from natural polysaccharides (such as dextran) to synthetic polymers (such as polyethylene glycol, PEG). However, recent studies have shown that traditional antifouling materials, including PEG, still fail to overcome the challenges of a complex human environment. Zwitterionic materials are a class of materials that contain both cationic and anionic groups, with their overall charge being neutral. Compared with PEG materials, zwitterionic materials have much stronger hydration, which is considered the most important factor for antifouling. Among zwitterionic materials, zwitterionic hydrogels have excellent structural stability and controllable regulation capabilities for various biomedical scenarios. Here, we first describe the mechanism and structure of zwitterionic materials. Following the preparation and property of zwitterionic hydrogels, recent advances in zwitterionic hydrogels in various biomedical applications are reviewed.

Dynamics of a single polyampholyte chain

Polymers that feature both positive and negative charges along chains, known as polyampholytes, represent a class of materials that hold promise for a new generation of energy storage devices, the design of which will require knowledge of the underlying structure and dynamics. Here, we develop a theory based on the Rouse model for the dynamic structure factor of a single polyampholyte chain in the weak coupling regime (negligible intramolecular electrostatics) or subjected to weak external electric fields (governed by linear response). Neglecting effects of small ions, we find deviations in scaling from the classic Rouse theory and make predictions for scattering experiments performed on polyampholytes. We find that, under weak coupling with arbitrarily strong fields, the dynamics are highly dependent on the charge distribution and consequently look at two representative examples-random charge densities and periodic charge densities-with different scaling properties. Under weak fields, the dynamics are largely independent of charge distribution. Finally, we investigate the influence of hydrodynamic effects and the implications of including inertial effects in the model.

Kinetics of charged polymer collapse in poor solvents

Extensive molecular dynamics simulations, using simple charged polymer models, have been employed to probe the collapse kinetics of a single flexible polyelectrolyte (PE) chain under implicit poor solvent conditions. We investigate the role of the charged nature of PE chain (A), valency of counterions (Z) on the kinetics of such PE collapse. Our study shows that the collapse kinetics of charged polymers are significantly different from those of the neutral polymer and that the finite-size scaling behavior of PE collapse times does not follow the Rouse scaling as observed in the case of neutral polymers. The critical exponent for charged PE chains is found to be less than that of neutral polymers and also exhibits dependence on counterion valency. The coarsening of clusters along the PE chain suggests a multi-stage collapse and exhibits opposite behavior of exponents compared to neutral polymers: faster in the early stages and slower in the later stages of collapse.

Simple synthesis route for fabrication of protective photo-crosslinked poly(zwitterionic) membranes for application in non-enzymatic glucose sensing

This work focuses on the fabrication of non-enzymatic glucose sensing materials based on laser-formed Au nanoparticles embedded in Ti-textured substrates. Those materials possess good catalytic activity toward glucose oxidation in 0.1 × phosphate buffered saline as well as resistance to some interferants, such as ascorbic acid, urea, and glycine. The electrodes are further coated with three different polymers, that is, Nafion, photo-crosslinked poly(zwitterions) based on sulfobetaine methacrylate, and a hybrid membrane consisting of both polymers. Both the optimal integrity of the material and its catalytic activity toward glucose oxidation were maintained by the hybrid membranes with a large excess of poly(zwitterions) (mass ratio 20:1). The chemical structures of the as-formed membranes are confirmed by Fourier transform infrared spectroscopy. Due to the zwitterionic nature of the coating, the electrodes are resistant to biofouling and maintain electrochemical activity toward glucose for 4 days. Moreover, due to the synergistic effect of both Nafion and poly(zwitterions), the interference from the two compounds, namely, from acetylsalicylic acid and acetaminophen, was diminished. Besides the presence of polymer membranes, the electrode possesses a sensitivity of 36.8 μA cm^-2  mM^-1 in the linear range of 0.4-12 mM, while the limit of detection was estimated to be 23 μM. Finally, the electrodes are stable, and their response is not altered even by 1,000 bending cycles.

Application of Zwitterionic Polymer Hydrogels to Optical Tissue Clearing for 3D Fluorescence Imaging

Zwitterionic polymers have both anion and cation groups in the side chain and have been used in various biomedical applications because of the unique properties. In this study, zwitterionic polymer hydrogels are applied to optical tissue clearing for 3D fluorescence imaging. Polyacrylamide hydrogels have been employed in Clear Lipid-exchanged Acrylamide-hybridized Rigid Imaging/Immunostaining/In situ-hybridization-compatible Tissue-hYdrogel method. Zwitterionic polymer hydrogels are produced using zwitterionic monomers, such as 3-[(3-acrylamidopropyl)dimethylammonio]propane-1-sulfonate (DAPS) and 2-methacryloyloxyethyl phosphorylcholine (MPC), and crosslinkers. The hydrogels made from poly(DAPS-co-acrylamide) and MPC homopolymers afford the most transparent tumor tissues. However, the tissues cleared using DAPS copolymers-containing hydrogels became turbid in a refractive index-matching solution, which are unable to obtain clear 3D fluorescence images. In contrast, the 3D fluorescence imaging is achieved in the MPC polymer-treated 2-mm-thick brain slices after immunostaining. The 3D fluorescence imaging of lung metastasis that is cleared by the MPC hydrogel to demonstrate the possible application to cancer diagnosis is performed. The results indicate the increased potentials of zwitterionic polymer hydrogels, especially MPC polymer hydrogels, in biomedical applications.

Concentration Polarization Enabled Reactive Coating of Nanofiltration Membranes with Zwitterionic Hydrogel

In this study, the bottleneck challenge of membrane fouling is addressed via establishing a scalable concentration polarization (CP) enabled and surface-selective hydrogel coating using zwitterionic cross-linkable macromolecules as building blocks. First, a novel methacrylate-based copolymer with sulfobetain and methacrylate side groups was prepared in a simple three-step synthesis. Polymer gelation initiated by a redox initiator system (ammonium persulfate and tetramethylethylenediamine) for radical cross-linking was studied in bulk in order to identify minimum ("critical") concentrations to obtain a hydrogel. In situ reactive coating of a polyamide nanofiltration membrane was achieved via filtration of a mixture of the reactive compounds, utilizing CP to meet critical gelation conditions solely within the boundary layer. Because the feasibility was studied and demonstrated in dead-end filtration mode, the variable extent of CP was estimated in the frame of the film model, with an iterative calculation using experimental data as input. This allowed to discuss the influence of parameters such as solution composition or filtration rate on the actual polymer concentration and resulting hydrogel formation at the membrane surface. The zwitterionic hydrogel-coated membranes exhibited lower surface charge and higher flux during protein filtration, both compared to pristine membranes. Salt rejection was found to remain unchanged. Results further reveal that the hydrogel coating thickness and consequently the reduction in membrane permeance due to the coating can be tuned by variation of filtration time and polymer feed concentration, illustrating the novel modification method's promising potential for scale-up to real applications.

Conformational transitions and helical structures of a dipolar chain in external electric fields

The conformational behavior of a single dipolar chain in a uniform electric field is investigated by molecular dynamics simulations. The dipolar chain is modeled as a backbone bead-on-spring chain of equally charged beads, each connected by a rigid spring with an oppositely charged side bead that can freely rotate around the backbone bead. In the strong coupling regime, when the dipolar chain is in the globular state due to a strong electrostatic correlational attraction, the application of an electric field causes the chain swelling and elongation along the field direction. In the weak coupling regime, a qualitatively new regime is found when the swollen dipolar chain shrinks along the field direction adopting flattened conformations due to the field-induced anisotropy of the chain rigidity and the head-to-tail attraction of the dipoles orienting along the field lines. A novel helical conformation is detected for low-polar media and strong electric fields. An increasing rigidity of the backbone chain leads to some stabilization of the helical conformation and the formation of double and triple helices as well as flat spread springs. Fine tuning of the interplay between dipolar and volume interactions by external electric fields induces re-orientation of rod-like dipolar chains in dilute solutions. The obtained results can provide new ways to control dipolar polymer conformations and design materials with responsive properties.

Molecular theory of the electrostatic collapse of dipolar polymer gels

We develop a new quantitative molecular theory of liquid-phase dipolar polymer gels. We model monomer units of the polymer network as a couple of charged sites separated by a fluctuating distance. For the first time, within the random phase approximation, we have obtained an analytical expression for the electrostatic free energy of the dipolar gel. Depending on the coupling parameter of dipole-dipole interactions and the ratio of the dipole length to the subchain Kuhn length, we describe the gel collapse induced by electrostatic interactions in the good solvent regime as a first-order phase transition. This transition can be realized at reasonable physical parameters of the system (temperature, solvent dielectric constant, and dipole moment of monomer units). The obtained results could be potentially used in modern applications of stimuli-responsive polymer gels and microgels, such as drug delivery, nanoreactors, molecular uptake, coatings, superabsorbents, etc.

Hydration State Variation of Polyzwitterion Brushes through Interplay with Ions

Polyzwitterions have emerged as a new class of antifouling materials alternating poly(ethylene glycol). The exemplary biopassivation and lubrication behaviors are often attributed to the particular chemical structure of zwitterions, which involve a large dipole moment of the charged groups and a neutral net charge, while the hydration state and dynamics also associate with these characteristics. Polymer brushes composed of surface-tethered polyzwitterion chains produced by surface-initiated controlled radical polymerization have been developed as thin films which exhibit excellent antifouling and lubrication properties. In past decades, numerous studies have been devoted to examining the structure and dynamics of polyzwitterion brush chains in aqueous solutions. This feature article provides an overview of recent studies exploring the hydration state of polyzwitterion brushes with specular neutron reflectivity, highlights some newly published work on the nonuniform equilibrium structure, ion concentration dependence, ion specificity, and the effects of charge spacer length in the zwitterions, and discusses future perspective in this field.

Recent progress in the science of complex coacervation

Complex coacervation is an associative, liquid-liquid phase separation that can occur in solutions of oppositely-charged macromolecular species, such as proteins, polymers, and colloids. This process results in a coacervate phase, which is a dense mix of the oppositely-charged components, and a supernatant phase, which is primarily devoid of these same species. First observed almost a century ago, coacervates have since found relevance in a wide range of applications; they are used in personal care and food products, cutting edge biotechnology, and as a motif for materials design and self-assembly. There has recently been a renaissance in our understanding of this important class of material phenomena, bringing the science of coacervation to the forefront of polymer and colloid science, biophysics, and industrial materials design. In this review, we describe the emergence of a number of these new research directions, specifically in the context of polymer-polymer complex coacervates, which are inspired by a number of key physical and chemical insights and driven by a diverse range of experimental, theoretical, and computational approaches.

A statistical field theory of salt solutions of 'hairy' dielectric particles

In this paper, we formulate a field-theoretical model of dilute salt solutions of electrically neutral spherical colloid particles. Each colloid particle consists of a 'central' charge that is situated at the center and compensating peripheral charges (grafted to it) that are fixed or fluctuating relative to the central charge. In the framework of the random phase approximation, we obtain a general expression for electrostatic free energy of solution and analyze it for different limiting cases. In the limit of infinite number of peripheral charges, when they can be modelled as a continual charged cloud, we obtain an asymptotic behavior of the electrostatic potential of a point-like test charge in a salt colloid solution at long distances, demonstrating the crossover from its monotonic decrease to damped oscillations with a certain wavelength. We show that the obtained crossover is determined by certain Fisher-Widom line. For the same limiting case, we obtain an analytical expression for the electrostatic free energy of a salt-free solution. In the case of nonzero salt concentration, we obtain analytical relations for the electrostatic free energy in two limiting regimes. Namely, when the ionic concentration is much higher than the colloid concentration and the effective size of charge cloud is much bigger than the screening lengths that are attributed to the salt ions and the central charges of colloid particles. The proposed theory could be useful for theoretical description of the phase behavior of salt solutions of metal-organic complexes and polymeric stars.

Statistical field theory of ion–molecular solutions

Schematic representation of the multipolar molecule surrounded by salt ions in a dielectric solvent medium.

Binding without folding - the biomolecular function of disordered polyelectrolyte complexes

Recent evidence shows that oppositely charged intrinsically disordered proteins (IDPs) can form high-affinity complexes that involve neither the formation of secondary or tertiary structure nor site-specific interactions between individual residues. Similar electrostatically dominated interactions have also been identified for positively charged IDPs binding to nucleic acids. These highly disordered polyelectrolyte complexes constitute an extreme case within the spectrum of biomolecular interactions involving disorder. Such interactions are likely to be widespread, since sequence analysis predicts proteins with highly charged disordered regions to be surprisingly numerous. Here, we summarize the insights that have emerged from the highly disordered polyelectrolyte complexes identified so far, and we highlight recent developments and future challenges in (i) establishing models for the underlying highly dynamic structural ensembles, (ii) understanding the novel binding mechanisms associated with them, and (iii) identifying the functional consequences.

Conformational behavior of a semiflexible dipolar chain with a variable relative size of charged groups via molecular dynamics simulations

The conformational behavior of an isolated semiflexible dipolar chain has been studied by molecular dynamics simulations. The dipolar chain was modeled as a backbone chain of charged beads, each containing an oppositely charged unit connected to it by a rigid spring. The main focus was on the effect of the backbone chain rigidity and the size of the charged groups on the morphology of the collapsed states of the chain formed in low-polar media where the electrostatic interactions are essential. It has been found that the stable globular conformations of the long chain of N = 256 backbone beads are a toroid and an elliptical globule. The macroscopic parameters (such as the radius of gyration and shape factors) as well as the local characteristics of these conformations (radial density distributions of ions, orientational correlations of chain segments, dipoles etc.) are studied depending on the chain stiffness. The regions of stability of a torus and an elliptical globule are found for the dipolar chains with variable dipole length and stiffness, which depend on the strength of electrostatic interactions. It has been shown that a size asymmetry of oppositely charged beads destabilizes globular states favoring elongated chain conformations. A coexistence of various metastable states was demonstrated for shorter chains of N = 128, 64, and 32.

Ion-Specific Hydration States of Zwitterionic Poly(sulfobetaine methacrylate) Brushes in Aqueous Solutions

The ion-specific hydration states of zwitterionic poly(3-( N-2-methacryloyloxyethyl- N, N-dimethyl)ammonatopropanesulfonate) (PMAPS) brushes in various aqueous solutions were investigated by neutron reflectivity (NR) and atomic force microscopy (AFM). The asymmetric hydration state of the PMAPS brushes was verified from the NR scattering-length density profiles, while the variation in their swollen thickness was complementary as determined from AFM topographic images. PMAPS brushes got thicker in any salt solutions, while the extent of swelling and the dimensions of swollen chain structure were dependent on the ion species and salt concentration in the solutions. Anion specificity was clearly observed, whereas cations exhibited weaker modulation in ion-specific hydration states. The anion specificity could be ascribed to ion-specific interactions between the quaternary ammonium cation in sulfobetaine and the anions. The weak cation specificity was attributed to the intrinsically weak cohesive interactions between the weakly hydrated sulfonate anion in sulfobetaine and the strongly hydrated cations. The ion-specific hydration of PMAPS brushes was largely consistent with the ion-specific aggregation state of the PMAPS chains in aqueous solutions.

Enhanced scattering induced by electrostatic correlations in concentrated solutions of salt-free dipolar and ionic polymers

We present a generalized theory for studying the static monomer density-density correlation function (structure factor) in concentrated solutions and melts of dipolar as well as ionic polymers. The theory captures effects of electrostatic fluctuations on the structure factor and provides insights into the origin of experimentally observed enhanced scattering at ultralow wavevectors in salt-free ionic polymers. It is shown that the enhanced scattering can originate from a coupling between the fluctuations of electric polarization and monomer density. Local and non-local effects of the polarization resulting from finite sized permanent dipoles and ion-pairs in dipolar and charge regulating ionic polymers, respectively, are considered. Theoretical calculations reveal that, similar to the salt-free ionic polymers, the structure factor for dipolar polymers can also exhibit a peak at a finite wavevector and enhanced scattering at ultralow wavevectors. Although consideration of dipolar interactions leads to attractive interactions between monomers, the enhanced scattering at ultralow wavevectors is predicted solely on the basis of the electrostatics of weakly inhomogeneous dipolar and ionic polymers without considering the effects of any aggregates or phase separation. Thus, we conclude that neither aggregation nor phase separation is necessary for observing the enhanced scattering at ultralow wavevectors in salt-free dipolar and ionic polymers. For charge regulating ionic polymers, it is shown that electrostatic interactions between charged monomers get screened with a screening length, which depends not only on the concentration of "free" counterions and coions, but also on the concentration of "adsorbed" ions on the polymer chains. Qualitative comparisons with the experimental scattering curves for ionic and dipolar polymer melts are presented using the theory developed in this work.

Organic Salts Suppress Aggregation and Enhance the Hyperpolarizability of a π-Twisted Chromophore

Twisted intramolecular charge-transfer (TICT) chromophores exhibit extraordinary hyperpolarizabilities, β, and are therefore promising for electro-optic technologies. Nevertheless, centrosymmetric aggregate formation severely diminishes β in concentrated solutions or in polymer matrices. Herein, the remarkable effects of organic salts on the linear and nonlinear optical response of a high β benzimidazolium-based TICT chromophore, B2TMC-2, are reported. Addition of Bu₄ P⁺ Br^- to B2TMC-2 solution in CHCl₃ induces a halochromic blueshift, primarily reflecting interactions between Bu₄ P⁺ Br^- and the B2TMC-2 cationic portion. DC electric-field induced second-harmonic generation (EFISH) measurements on B2TMC-2+Bu₄ P⁺ Br^- solution reveal a large μβ=-22,160×10^-48  esu, unprecedented for any chromophore with such a broad optical transparency window. Moreover, Bu₄ P⁺ Br^- is shown to suppress B2TMC-2 aggregation, thereby preserving high μβ in concentrated solutions. This phenomenon should be applicable to many other NLO chromophores.

Response of a Permanently Charged Polyelectrolyte Brush to External Ions: The Aspects of Structure and Dynamics

Structure and dynamics inside permanently charged polyelectrolyte brushes, sodium polystyrene sulfonate brushes, during their response to the introduction of external ions (NaCl) are investigated by neutron reflectivity and dielectric spectroscopy. Neutron reflectivity measurements show that the segmental density of the inner part of the brushes decreases and that of the outer part increases when the salt level is tuned from the salt-free condition to a moderate level (<10^-2 M)-the brushes swell further compared with the salt-free condition. This is attributed to the breakup of the multiplets formed by dipole-dipole pairs, and by this process, the previously constrained chain segments by the multiplets are released. Dielectric spectroscopy discovers a giant dipole by the charge separation of the adsorbed counterions and the PSS^- chains, induced by electric field. The dynamics of the induced giant dipole is accelerated with the increase of external salt, as a result of the charge regularization by elevated salt level. At high-enough salt level, the screening effect reduces the electrostatic repulsion between the neighboring chains and makes the brushes shrink.

An interplay of electrostatic and excluded volume interactions in the conformational behavior of a dipolar chain: theory and computer simulations

The effect of an interplay between electrostatic and excluded volume interactions on the conformational behavior of a dipolar chain has been studied theoretically and by means of molecular dynamics simulations. Every monomer unit of the dipolar chain comprises a dipole formed by a charged group of the chain and an oppositely charged counterion. The counterion is assumed to freely move around the chain but keeping the distance between oppositely charged ions (the dipole length) fixed. The novelty of the developed mean-field theory is that variations of the dipole parameters (the dipole length and the counterion size) have been accounted for in both electrostatic and excluded volume contributions to the total free energy of the dipolar chain. It has been shown that conformational transitions between swollen and collapsed states of the chain can be induced by fine-tuning the balance between electrostatic and excluded volume interactions. In particular, in low-polar media not only globule but also extended coil conformations can be realized even under strong electrostatic attraction. The results of MD simulations of a dipolar chain with variable dipolar length support theoretical conclusions.

Flory-type theories of polymer chains under different external stimuli

In this Review, we present a critical analysis of various applications of the Flory-type theories to a theoretical description of the conformational behavior of single polymer chains in dilute polymer solutions under a few external stimuli. Different theoretical models of flexible polymer chains in the supercritical fluid are discussed and analysed. Different points of view on the conformational behavior of the polymer chain near the liquid-gas transition critical point of the solvent are presented. A theoretical description of the co-solvent-induced coil-globule transitions within the implicit-solvent-explicit-co-solvent models is discussed. Several explicit-solvent-explicit-co-solvent theoretical models of the coil-to-globule-to-coil transition of the polymer chain in a mixture of good solvents (co-nonsolvency) are analysed and compared with each other. Finally, a new theoretical model of the conformational behavior of the dielectric polymer chain under the external constant electric field in the dilute polymer solution with an explicit account for the many-body dipole correlations is discussed. The polymer chain collapse induced by many-body dipole correlations of monomers in the context of statistical thermodynamics of dielectric polymers is analysed.

Recent developments in smart antibacterial surfaces to inhibit biofilm formation and bacterial infections

Since their development over 70 years, antibiotics are still the most effective strategy to treat bacterial biofilms and infections.

Effect of Charged Group Spacer Length on Hydration State in Zwitterionic Poly(sulfobetaine) Brushes

Effect of alkyl chain spacer length between the charged groups (CSL) in zwitterionic poly(sulfobetaine) (PSB) brushes on the hydration state was investigated. PSB brushes with ethyl (PMAES), propyl (PMAPS), or butyl (PMABS) CSL were prepared by surface-initiated atom transfer radical polymerization on silicon wafers. Hydration states of the PSB brushes in aqueous solutions and/or humid vapor were investigated by contact angle measurement, infrared spectroscopy, AFM observation, and neutron reflectivity. The PSB brushes are swollen in humid air and deionized water due to the hydration of the charged groups leading to the reduction of hydrated PSB brushes/water interfacial free energy. The hydrated PSB brushes exhibit clear interface with low interfacial roughness due to networking of the PSB brush chains through association of the SBs. The hydrated PSB brushes produce diffusive swollen layer in the presence of NaCl because of the charge screening followed by SB dissociation by the bound ions. The ionic strength sensitivity in the hydration got more significant with increasing the CSL in SBs because of the augmentation in partial charge by charged group separation.

Polymer chain collapse induced by many-body dipole correlations

We present a simple analytical theory of a flexible polymer chain dissolved in a good solvent, carrying permanent freely oriented dipoles on the monomers. We take into account the dipole correlations within the random phase approximation (RPA), as well as a dielectric heterogeneity in the internal polymer volume relative to the bulk solution. We demonstrate that the dipole correlations of monomers can be taken into account as pairwise ones only when the polymer chain is in a coil conformation. In this case the dipole correlations manifest themselves through the Keesom interactions of the permanent dipoles. On the other hand, the dielectric heterogeneity effect (dielectric mismatch effect) leads to the effective interaction between the monomers of the polymeric coil. Both of these effects can be taken into account by renormalizing the second virial coefficient of the monomer-monomer volume interactions. We establish that in the case when the solvent dielectric permittivity exceeds the dielectric permittivity of the polymeric material, the dielectric mismatch effect competes with the dipole attractive interactions, leading to polymer coil expansion. In the opposite case, both the dielectric mismatch effect and the dipole attractive interaction lead to the polymer coil collapse. We analyse the coil-globule transition caused by the dipole correlations of monomers within the many-body theory. We demonstrate that accounting for the dipole correlations higher than the pairwise ones smooths this pure electrostatics driven coil-globule transition of the polymer chain.

Simulation of self-assembly of polyzwitterions into vesicles

Using the Langevin dynamics method and a coarse-grained model, we have studied the formation of vesicles by hydrophobic polymers consisting of periodically placed zwitterion side groups in dilute salt-free aqueous solutions. The zwitterions, being permanent charge dipoles, provide long-range electrostatic correlations which are interfered by the conformational entropy of the polymer. Our simulations are geared towards gaining conceptual understanding in these correlated dipolar systems, where theoretical calculations are at present formidable. A competition between hydrophobic interactions and dipole-dipole interactions leads to a series of self-assembled structures. As the spacing d between the successive zwitterion side groups decreases, single chains undergo globule → disk → worm-like structures. We have calculated the Flory-Huggins χ parameter for these systems in terms of d and monitored the radius of gyration, hydrodynamic radius, spatial correlations among hydrophobic and dipole monomers, and dipole-dipole orientational correlation functions. During the subsequent stages of self-assembly, these structures lead to larger globules and vesicles as d is decreased up to a threshold value, below which no large scale morphology forms. The vesicles form via a polynucleation mechanism whereby disk-like structures form first, followed by their subsequent merger.

Synthesis and application of polyzwitterionic and polyampholytic maleic acid-alt-(diallylamino)propylphosphonates

Ammonium persulfate-initiated alternate copolymerization of maleic acid with phosphonate ester monomer [(CH₂CH–CH₂)₂NH⁺(CH₂)₃PO₃Et₂Cl⁻] gave polyzwitterion A which upon ester hydrolysis afforded antiscalant polyampholyte B.

Polarizable polymer chain under external electric field: Effects of many-body electrostatic dipole correlations

We present a new simple self-consistent field theory of a polarizable flexible polymer chain under an external constant electric field with account for the many-body electrostatic dipole correlations. We show the effects of electrostatic dipole correlations on the electric-field-induced globule-coil transition. We demonstrate that only when the polymer chain is in the coil conformation, the electrostatic dipole correlations of monomers can be considered as pairwise. However, when the polymer chain is in a collapsed state, the dipole correlations have to be considered at the many-body level.