Conformation Of Polyelectrolyte Research Articles

Conformational Transition of Semiflexible Ring Polyelectrolyte in Tetravalent Salt Solutions: A Simple Numerical Modeling without the Effect of Twisting.

In this work, the conformational behaviors of ring polyelectrolyte in tetravalent salt solutions are discussed in detail through molecular dynamics simulation. For simplification, here we have neglected the effect of the twisting interaction, although it has been well known that both bending and twisting interactions play a deterministic in the steric conformation of a semiflexible ring polymer. The salt concentration CS and the bending energy b take a decisive role in the conformation of the ring polyelectrolyte (PE). Throughout our calculations, the b varies from b = 0 (freely joint chain) to b = 120. The salt concentration CS changes in the range of 3.56 × 10-4 M ≤ CS ≤ 2.49 × 10-1 M. Upon the addition of salt, ring PE contracts at first, subsequently re-expands. More abundant conformations are observed for a semiflexible ring PE. For b = 10, the conformation of semiflexible ring PE shifts from the loop to two-racquet-head spindle, then it condenses into toroid, finally arranges into coil with the increase of CS. As b increases further, four phase transitions are observed. The latter two phase transitions are different. The semiflexible ring PE experiences transformation from toroid to two racquet head spindle, finally to loop in the latter two phase transitions. Its conformation is determined by the competition among the bending energy, cation-bridge, and entropy. Combined, our findings indicate that the conformations of semiflexible ring PE can be controlled by changing the salt concentration and chain stiffness.

Unveiling the transition of tumbling and tank-treading dynamics of star-shaped polyelectrolytes in shear flow by modulating the solution's dielectric properties.

The effects of the solution's dielectric properties on the conformation and dynamics of star-shaped polyelectrolytes in shear flow are investigated using a hybrid simulation method coupling multi-particle collision dynamics and molecular dynamics. The simulation results showed that by modulating the dielectric properties of the solution, star-shaped polyelectrolytes showed a three-step dynamic behavior transition from tumbling to tank-treading to tumbling dynamics under shear flow. The analysis indicated that this distinct transition in dynamics could be attributed to the uneven distribution of counterions induced by shear on the chain, resulting in a change in the polyelectrolyte conformation and degree of segmental alignment in arms. These findings contribute to a comprehensive understanding of the non-equilibrium dynamics of star-shaped polyelectrolytes in shear flow and offer a viable approach for controlling the dynamic behavior of star-shaped polyelectrolytes by adjusting the dielectric properties of the solution.

Effect of Counterion Size on Knotted Polyelectrolyte Conformations.

Using Langevin dynamics simulations and a coarse-grained primitive model of electrolytes, we show that the behavior of knotted circular strong polyelectrolytes (PEs) in diluted aqueous solution is largely affected by the diameter of the counterions (CIs), σCI. Indeed, we observe that both gyration radius and knot length vary nonmonotonically with σCI, with both small and bulky CIs favoring knot localization, while medium-sized ones promote delocalized knots. We also show that the conformational change from delocalized to tight knots occurs via the progressive coalescence of the knot's essential crossings. The emerging conformers correspond to the minima of the free energy landscape profiled as a function of the knot length or PE size. We demonstrate that different conformational states can coexist, the transition between them appearing first-order-like and controlled by the enthalpic and entropic trade-off of the amount of CIs condensed on the PE. Such balance can be further altered by varying CI concentrations, thus providing an additional and more convenient tuning parameter for the system properties. Our results lay the foundation for achieving broader and more precise external adjustability of knotted PE size and shape by choosing the nature of its CIs. Thus, they offer new intriguing possibilities for designing novel PE-based materials that are capable of responding to changes in ionic solution properties.

Effect of counterion size on polyelectrolyte conformations and thermodynamics.

We present a theoretical model to study the effect of counterion size on the effective charge, size, and thermodynamic behavior of a single, isolated, and flexible polyelectrolyte (PE) chain. We analyze how altering counterion size modifies the energy and entropy contributions to the system, including the ion-pair free energy, excluded volume interactions, entropy of free and condensed ions, and dipolar attraction among monomer-counterion pairs, which result in competing effects challenging intuitive predictions. The PE self-energy is calculated using the Edwards-Muthukumar Hamiltonian, considering a Gaussian monomer distribution for the PE. The condensed ions are assumed to be confined within a cylindrical volume around the PE backbone. The dipolar and excluded volume interactions are described by the second and third virial coefficients. The assumption of freely rotating dipoles results in a first-order coil-globule transition of the PE chain. A more realistic, weaker dipolar attraction, parameterized in our theory, shifts it to a second-order continuous transition. We calculate the size scaling-exponent of the PE and find exponents according to the relative dominance of the electrostatic, excluded volume, or dipolar effects. We further identify the entropy- and energy-driven regimes of the effective charge and conformation of the PE, highlighting the interplay of free ion entropy and ion-pair energy with varying electrostatic strengths. The crossover strength, dependent on the counterion size, indicates that diminishing sizes favor counterion condensation at the expense of free ion entropy. The predictions of the model are consistent with trends in simulations and generalize the findings of the point-like counterion theories.

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.

Electrically Mediated Static Contact Angle and Hysteresis of Polyelectrolyte Solutions.

Manipulating a droplet by electrowetting-on-dielectric (EWOD) is vital in various fields ranging from industrial applications to life sciences. As of now, EWOD research has focused primarily on aqueous electrolytes and ionic liquids. This paper investigates the electrowetting behavior of weak polyelectrolyte solutions containing poly(acrylic acid) (PAA). The study reveals distinct wetting behavior of weakly and fully charged PAA droplets controlled by their solution pH. Under an applied electric field, strongly ionized PAA wets more effectively than weakly charged PAA. The electrowetting hysteresis of fully ionized PAA droplets was also higher than that of weakly charged droplets. The reason may be the suppression of retraction flow near the contact line. In this thin region, the electric field aligns the stretched polymer chains perpendicular to the dielectric surface, thus affecting the bulk rheological properties. The results reveal how charge-connectivity and polyelectrolyte conformation under an external electric field can control the electrowetting gain and the hysteresis. This previously unexplored electrowetting mechanism of polyelectrolyte solutions might help order and manipulate biological polyelectrolytes, such as deoxyribonucleic acid (DNA), polypeptides, and glycosaminoglycans.

Molecular conformation of polyelectrolytes inside Layer-by-Layer assembled films

Among all methods available for the preparation of multifunctional nanostructured composite materials with remarkable functional properties, Layer-by-Layer (LbL) assembly is currently one of the most widely used techniques due to its environmental friendliness, its ease of use and its versatility in combining a plethora of available colloids and macromolecules into finely tuned multicomponent architectures with nanometer scale control. Despite the importance of these systems in emerging technologies, their nanoscopic 3D structure, and thus the ability to predict and understand the device performance, is still largely unknown. In this article, we use neutron scattering to determine the average conformation of individual deuterated polyelectrolyte chains inside LbL assembled films. In particular, we determine that in LbL-films composed of poly(sodium 4-styrenesulfonate) (PSS) and poly(allylamine hydrochloride) (PAH) multilayers prepared from 2 M sodium chloride solutions the PSS chains exhibit a flattened coil conformation with an asymmetry factor of around seven. Albeit this highly non-equilibrium state of the polymer chain, its density profiles follow Gaussian distributions occupying roughly the same volume as in the bulk complex.

Adsorption kinetics of polyacrylamide-based polyelectrolyte onto a single silica particle studied using microfluidics and optical tweezers.

Polyelectrolyte adsorption is considered important in tuning the surface property and the fate of particles; however, often studied on macroscopic surfaces. To gain insights into how polyelectrolytes are adsorbed onto a single particle, it is imperative to utilize techniques capable of elucidating adsorption kinetics on a single-particle level in a controlled flow field. The polyelectrolyte adsorption kinetics was investigated by electrophoretic mobility measurements combined with the kinetics study onto a single-particle viewpoint using microfluidics and optical tweezers. We directly evaluated the thickness, δH, of adsorbed polyelectrolyte onto a negatively-charged silica particle to deduce the adsorbed polyelectrolyte's conformation. The effect of charge density and salt concentrations were studied. All polyelectrolytes exhibited dependence of δH on salt concentration. The attractive interactions control the cationic polyelectrolytes adsorption process. The δH depends on charge density indicating more loops and tail confirmation for the weakly-charged polyelectrolytes. The anionic polyelectrolytes showed a dependence of the initial rate and saturation value of δH on salt concentrations, attributed to the repulsion between charged segments and the silica surfaces. Here, we present new insights into the polyelectrolyte adsorption kinetics, particularly the influence of electrostatic interaction from the single-particle perspective, inaccessible to conventional bulk measurements.

Potential-Dependent Adhesion Forces between dsDNA and Electroactive Surfaces

A promising approach to regulating the interactions between polyelectrolytes and materials is the use of electroactive surfaces that can change their charge state. However, common electroactive groups are too unstable to be practical for this purpose. Here we have performed a single molecule force spectroscopy study of the interactions between dsDNA and an 1,1'-biferrocenylene (BFD = bis(fulvalene)diiron)-terminated self-assembled monolayer surface that allows us to reversibly change the charge state. We found that the interaction force between DNA and the surface is correlated to the oxidation state of the BFD groups, which is conveniently controlled by the electrochemical potentials. We discovered that the electroactive SAM produces much stronger interaction forces than its nonelectroactive counterpart. A model based on the Grahame equation was able to quantitatively reproduce the experimentally observed relation between the applied potentials and adhesion forces. Our electroactive surface provides a model system for quantitative studies of the interactions between polyelectrolyte and charged surfaces in liquid. These insights may enable new opportunities for actively manipulating the binding, orientations, and conformations of polyelectrolytes for biosensing, nanomotors, and other applications.

Weak Polyelectrolytes as Nanoarchitectonic Design Tools for Functional Materials: A Review of Recent Achievements.

The ionization degree, charge density, and conformation of weak polyelectrolytes can be adjusted through adjusting the pH and ionic strength stimuli. Such polymers thus offer a range of reversible interactions, including electrostatic complexation, H-bonding, and hydrophobic interactions, which position weak polyelectrolytes as key nano-units for the design of dynamic systems with precise structures, compositions, and responses to stimuli. The purpose of this review article is to discuss recent examples of nanoarchitectonic systems and applications that use weak polyelectrolytes as smart components. Surface platforms (electrodeposited films, brushes), multilayers (coatings and capsules), processed polyelectrolyte complexes (gels and membranes), and pharmaceutical vectors from both synthetic or natural-type weak polyelectrolytes are discussed. Finally, the increasing significance of block copolymers with weak polyion blocks is discussed with respect to the design of nanovectors by micellization and film/membrane nanopatterning via phase separation.

Stable Vesicles Formed by a Single Polyelectrolyte in Salt Solutions

The conformation of polyelectrolyte (PE) affects a wealth of structural and dynamic properties of PE solutions and is also fundamental to the study of the folding and aggregation of proteins. Here, we theoretically investigate the classical problem of the conformation of a single homogeneous PE in salt solutions. We predict the formation of a stable vesicle structure at intermediate salt concentrations which is beyond the well-accepted framework of globule to pearl-necklace transition. The vesicle formed by a single PE is electrostatic in origin where salt ions play the role of surfactant. We demonstrate that the transitions from vesicle to both spherical globule and pearl-necklace are discontinuous; the latter involves a two-step nucleation with an intermediate vesicle-necklace state. We also calculate the full diagram of state and show the existence of a critical quadruple point that is uniquely determined for PE with a given chain length. The vesicle structure can be well-controlled by the external salt concentration, which facilitates the design of ionic-responsive single-chain nanoparticles.

Equilibrium Conformations and Surface Charge Regulation of Spherical Polymer Brushes in Stretched Regimes

In the present work, we study the equilibrium conformations of linear polyelectrolytes tethered onto a spherical, oppositely charged core in equilibrium with an ionic reservoir of fixed concentration. Particular focus is placed on the situation of stretched chains, where the monomer concentration is known to display an inverse square-law decay far away from the spherical surface, which is then further extrapolated all the way down to the grafting core. While the equilibrium distributions of mobile ions are computed in the framework of a classical Density Functional Theory (cDFT) that incorporates both their size and electrostatic correlations within the grafted polyelectrolyte, the equilibrium configuration of the latter is described by its averaged radius of gyration, which is taken as a variational parameter that guarantees mechanical equilibrium across the polymer-solvent interface. The averaged particle size is then analyzed over a wide range of polymerization degrees, ionic concentrations and functionality of the polymer backbones. Two distinct regimes can be identified: at high ionic strengths, swelling of the grafted polymers is dominated by ionic entropic contribution as well as polymer size effects, whereas at low ionic concentrations a balance between electrostatic and entropic effects is the main driven mechanism for particle stretching. Using Monte Carlo simulations, we then proceed to investigate the effects of charge regulation when the brush core is further decorated with active functional sites randomly distributed over its surface, which act as receptors onto which dissolved acidic ions can be adsorbed.

Solution Properties of Polyelectrolytes with Divalent Counterions

Divalent ions are known to strongly influence the phase behavior, conformation, and flow properties of polyelectrolytes in solution. Here, we report small-angle neutron scattering and viscosity data for the magnesium salt of polystyrene sulfonate (MgPSS) in salt-free water and compare these results with analogous measurements for NaPSS. In a dilute solution, both salts are found to exhibit a rod-like conformation for high degrees of polymerization, but the chain dimensions of MgPSS are significantly smaller than for NaPSS, which is consistent with the lower charge density of MgPSS found from conductivity data. In the semidilute regime, the correlation length scales as ξ ≃ 3.7c–1/2 nm for NaPSS and ξ ≃ 5.4c–1/2 nm for MgPSS. At high concentrations, deviations to weaker power laws are observed for both salts. The variation of the viscosity with the degree of polymerization (ηsp ∼ N) is consistent with unentangled, Rouse-like dynamics. Fuoss-law-type behavior (ηsp ∼ c1/2) is observed at low polymer concentrations, which turns into a stretched exponential dependence at high c, perhaps due to an increase in the local friction experienced by polymer segments.

Reversible ion binding for polyelectrolytes with adaptive conformations

AbstractPolyelectrolytes may adopt rod‐ or coil‐like conformations depending on the strength of intrachain repulsion and the effective charge density. The charge density of polyelectrolytes is influenced not only by the binding of small ions, but also by the binding with oppositely charged chains. We introduce a coupled variational approach that treats reversible ion binding, adaptive chain structure, and electrostatic correlations simultaneously. This approach captures the swelling and deswelling of single polyelectrolyte chains, and the competition between interchain cross‐linking and ion binding in mixtures of polyelectrolytes. Applying our theory to study polyelectrolyte coacervation, we identify two distinct regimes. In the weak binding regime, the charge density is high and the solution properties are dependent on the conformations of polyelectrolytes. In the strong binding regime, this dependence is weakened and the solution thermodynamics are dominated by the short‐range ion‐binding equilibrium.

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.

Flexible, charged biopolymers in monovalent and mixed-valence salt: Regimes of anomalous electrostatic stiffening and of salt insensitivity.

The conformations of biological polyelectrolytes (PEs), such as polysaccharides, proteins, and nucleic acids, affect how they behave and interact with other biomolecules. Relative to neutral polymers, PEs in solution are more locally rigid due to intrachain electrostatic repulsion, the magnitude of which depends on the concentration of added salt. This is typically quantified using the Odijk-Skolnick-Fixman (OSF) electrostatic-stiffening model, in which salt-dependent Debye-Hückel (DH) screening modulates intrachain repulsion. However, the applicability of this approach to flexible PEs has long been questioned. To investigate this, we use high-precision single-molecule elasticity measurements to infer the scaling with salt of the local stiffness of three flexible biopolymers (hyaluronic acid, single-stranded RNA, and single-stranded DNA) in both monovalent and mixed-valence salt solutions. In monovalent salt, we collapse the data across all three polymers by accounting for charge spacing, and find a common power-law scaling of the electrostatic persistence length with ionic strength with an exponent of 0.66±0.02. This result rules out simple OSF pictures of electrostatic stiffening. It is roughly compatible with a modified OSF picture developed by Netz and Orland; alternatively, we posit the exponent can be explained if the relevant electrostatic screening length is the interion spacing rather than the DH length. In mixed salt solutions, we find a regime where adding monovalent salt, in the presence of multivalent salt, does not affect PE stiffness. Using coarse-grained simulations, and a three-state model of condensed, chain-proximate, and bulk ions, we attribute this regime to a "jacket" of ions surrounding the PE that regulates the chain's effective charge density as ionic strength varies. The size of this jacket in simulations is again consistent with a screening length controlled by interion spacing rather than the DH length. Taken together, our results describe a unified picture of the electrostatic stiffness of polyelectrolytes in the mixed-valence salt conditions of direct relevance to cellular and intercellular biological systems.

Perfect helical structure of semiflexible polyelectrolyte chain confined in a cylinder

Conformations of a semiflexible polyelectrolyte (SPE) chain with neutralizing charged counterions confined in a cylinder have been investigated by off-lattice Monte Carlo simulations. Effects of electrostatic interactions of different Bjerrum length lB between PEs and counterions, PEs of different chain stiffness b, and cylindrical confinement of different radius R on the conformations of SPEs have been examined. At suitable combinations of the above parameters of lB, b, and R, perfect helical structures are observed, which can be well characterized by the tangent correlation function. The number of turns in perfect helix can be read accurately through counting the number of oscillation periods of correlation function. The expanded confined space with a larger cylindrical radius leads the helix phase region into a smaller range of b and lB. The physical mechanism for the formation of perfect helical structures is further explored by the distribution of chain monomers and counterions. Although helix formation has been associated with the electrostatic interactions and chain stiffness, the cylindrical confinement promotes the formation of perfect helical structures driven by entropy. This study can provide a deeper insight about mechanisms behind the conformation of biological macromolecules with oppositely charged counterions in confinement cavity.

Linker histone defines structure and self-association behaviour of the 177\xa0bp human chromatosome

Linker histones play essential roles in the regulation and maintenance of the dynamic chromatin structure of higher eukaryotes. The influence of human histone H1.0 on the nucleosome structure and biophysical properties of the resulting chromatosome were investigated and compared with the 177-bp nucleosome using Cryo-EM and SAXS. The 4.5 Å Cryo-EM chromatosome structure showed that the linker histone binds at the nucleosome dyad interacting with both linker DNA arms but in a tilted manner leaning towards one of the linker sides. The chromatosome is laterally compacted and rigid in the dyad and linker DNA area, in comparison with the nucleosome where linker DNA region is more flexible and displays structural variability. In solution, the chromatosomes appear slightly larger than the nucleosomes, with the volume increase compared to the bound linker histone, according to solution SAXS measurements. SAXS X-ray diffraction characterisation of Mg-precipitated samples showed that the different shapes of the 177 chromatosome enabled the formation of a highly ordered lamello-columnar phase when precipitated by Mg2+, indicating the influence of linker histone on the nucleosome stacking. The biological significance of linker histone, therefore, may be affected by the change in the polyelectrolyte and DNA conformation properties of the chromatosomes, in comparison to nucleosomes.

Translational dielectric friction on a pearl-necklace-like polyelectrolyte chain

Translational dielectric friction effect on polyions is ignored by the literature. However, its contribution to the polyion conductibility is very sensitive to the configuration of the polyion chain, so that transition from coiled configurations to completely stretched configuration gives generally rise to a gap of the dielectric friction coefficient, βPdf. In the present work we analyze in details this effect in the case of slowly moving Pearl-Necklace-like Polyelectrolyte Chain of structural charge ZSe, and length L less than the structural length LS = ∣ZS∣bS, constituted by Nb beads separated alternatively by (Nb- 1) strings enclosing Ng groups (or small thermal blobs). The obtained practical results make possible, by comparing the experimental dielectric friction coefficient with its different possible theoretical values, to predict the chain conformation of the concerned polyelectrolyte.

Revisiting of the physico-chemical properties of polyelectrolyte multilayers for a fine tuning of the immobilization of bacteria or nanoparticles

Increasingly used in industrial coatings, polyelectrolytes multilayers (PEMs) are self-assembled systems made of the alternate deposition of oppositely charged polymers on substrates, usually built by the traditional layer-by-layer method. Their properties strongly depend on environmental physico-chemical parameters. Due to the variety of conditions used in the literature on the one hand and the diversity of polyelectrolytes systems on the other hand, it remains difficult to bring out general principles, leading now to a lack of a real understanding of the PEM buildup, from the macro- to the nanoscale. Here, combining acoustic and electrochemical methods with atomic force microscopy, in a systematic approach, we uncover the critical role of the deposition protocol in the growth regime of PEMs made of cationic poly (allylamine hydrochloride) and anionic poly(4-styrene sulfonate, sodium). Traditional dipping leads to thick, heterogeneous and relatively isolating PEMs whereas a spin-coating assisted method leads to thinner, homogeneous and more permeable PEMs. We also highlight that the pH and the ionic strength influence not only the electrostatic interactions and polyelectrolyte conformation in solution but also their organization after their adsorption on the substrate. Finally, our easily and rapidly adaptable protocol paves the way for promising potential bio-applications, since PEMs are applied to the bacterial immobilization on substrates or as a coating for nanostructured biosensor transducer.