Dependence of polyelectrolyte apparent persistence lengths, viscosity, and diffusion on ionic strength and linear charge density

Modelling effluent reuse in the pulp and paper industry to predict consequences on conductivity

The objective of this study was to assess, through simulation, conductivity variations in pulp and paper circuits when recycling waste water treatment plant (WWTP) effluent with a view to reducing fresh water use in a tissue mill. WWTP effluent was recycled in the process for different uses. A PS2000 digital model coupled with the PHREEQC chemical simulation engine was used to identify and quantify the main sources of conductivity: caustic soda, sodium bisulphite and acetate production through anaerobic microbial activity. Recycling WWTP effluent enables fresh water uptake to be reduced by 50% when used for pulp dilution or white water, by 81% when used in paper machine showers, and up to 96% for all uses combined. As fresh water use decreases, circuit closure increases along with, consequently, COD and conductivity. COD build-up can be controlled by best available techniques application. Recycling WWTP effluent has a strong impact on conductivity. However, the impact of high conductivity levels on additives performance is limited in the case of the mill studied. Acetate concentration could be controlled by better agitation of tanks or the introduction of air by pumps. Furthermore, limiting acetate production can reduce the need for caustic soda to control the pH.

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.

Hydrodynamic and conformational characterization of aqueous sodium alginate solutions with varying salinity

Insight into the role of electrostatic interactions on the hydrodynamics and conformation of aqueous sodium alginate was gained through viscometry. Alginate chains are found to shrink in salt-free solutions more rapidly with increasing polymer concentration compared to salt-solutions. For salt-free solutions, a reduced polymer concentration of less than 1 suffices to make the alginate coil volume half of that at infinite dilution which becomes invariant when the reduced concentration exceeds 8. In saline media having salt concentration greater than 0.1 mol·L^-1, the chains become more flexible, caused by the shielding of intra-chain repulsions. The chains effectively reached unperturbed state when the added salt concentration becomes ≥0.5 mol·L^-1. Alginate chains are shown to remain stiff up to about 8-10 monomers within the investigated temperature range. This study explores the possible modification of the individual chain behavior induced by the neighboring chains or by the variation of temperature.

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.

Neutralization and Salt Effect on the Structure and Mechanical Properties of Polyacrylic Acid Gels under Equivolume Conditions

The effects of neutralization and salt on the structure and mechanical properties of polyacrylic acid (PAA) gels under equivolume conditions were investigated by small-angle X-ray scattering (SAXS) measurements and tensile tests. We attained the equivolume condition by immersing a piece of PAA gel sample in an ion reservoir containing linear PAA, NaOH, and NaCl at prescribed concentrations (post-ion-tuning). The volume fraction of the linear polymer was set to be the same as that of the gel so as to satisfy the iso-osmotic pressure at the reference state. Various types of reservoirs were prepared by adding NaOH and/or NaCl with different concentrations to the reference reservoir, followed by immersing a PAA gel piece. In the SAXS measurements, a scattering peak appeared, and the scattering intensity at q = 0 decreased by neutralization, while the addition of salt increased the scattering intensity. On the other hand, Young’s modulus measured with the tensile test decreased with neutralization; however, it scarcely changed with the addition of salt. The newly developed equivolume post-ion-tuning technique may serve as a new standard scheme to study polyelectrolyte gels.

Physicochemical Properties and Biological Performance of Polymethacrylate Based Gene Delivery Vector Systems: Influence of Amino Functionalities

Physicochemical characteristics and biological performance of polyplexes based on two identical copolymers bearing tertiary amino or quaternary ammonium groups are evaluated and compared. Poly(2-(dimethylamino)ethyl methacrylate)-b-poly(oligo(ethylene glycol) methyl ether methacrylate) block copolymer (PDMAEMA-b-POEGMA) is synthesized by reversible addition fragmentation chain transfer polymerization. The tertiary amines of PDMAEMA are converted to quaternary ammonium groups by quaternization with methyl iodide. The two copolymers spontaneously formed well-defined polyplexes with DNA. The size, zeta potential, molar mass, aggregation number, and morphology of the polyplex particles are determined. The parent PDMAEMA-b-POEGMA exhibits larger buffering capacity, whereas the corresponding quaternized copolymer (QPDMAEMA-b-POEGMA) displays stronger binding affinity to DNA, yielding invariably larger in size and molar mass particles bearing greater number of DNA molecules per particle. Experiments revealed that QPDMAEMA-b-POEGMA is more effective in transfecting pEGFP-N1 than the parent copolymer, attributed to the larger size, molar mass, and DNA cargo, as well as to the effective cellular traffic, which dominated over the enhanced ability for endo-lysosomal escape of PDMAEMA-b-POEGMA.

In Situ Formation of Covalent Second Network in a DNA Supramolecular Hydrogel and Its Application for 3D Cell Imaging

DNA hydrogels have been demonstrated with important applications in three-dimensional cell culture in vitro due to their good biocompatibility, biodegradability, and permeability. In these applications, to observe the cell morphology and functions in situ, immobilization, labeling, and imaging processes are involved, which requires good stability of the hydrogels during washing and immersion. To improve the stability of the hydrogels for better imaging, here we built a covalent second network in a DNA supramolecular hydrogel by in situ polymerization and successfully constructed a stable three-dimensional transparent system for cell culture and observation. This strategy has been proved to be efficient in enhancing the mechanical properties and immobilizing the cells inside the hydrogel, which can be applied for immunostaining and cell imaging.

Modulation of the Electrochemical Reactivity of Solubilized Redox Active Polymers via Polyelectrolyte Dynamics

Redox active polymers (RAPs) are electrochemically versatile materials that find key applications in energy storage, sensing, and surface modification. In spite of the ubiquity of RAP-modified electrodes, a critical knowledge gap exists in the understanding of the electrochemistry of soluble RAPs and their relation to polyelectrolyte dynamics. Here, we explore for the first time the intersection between polyelectrolyte behavior and the electrochemical response that highly soluble and highly substituted RAPs with viologen, ferrocene, and nitrostyrene moieties elicit at electrodes. This comprehensive study of RAP electrolytes over several orders of magnitude in concentration and ionic strength reveals distinct signatures consistent with surface confined, colloidal, and bulk-like electrochemical behavior. These differences emerge across polyelectrolyte packing regimes and are strongly modulated by changes in RAP coil size and electrostatic interactions with the electrode. We found that, unlike monomer motifs, simple changes in the ionic strength caused variations over 1 order of magnitude in the current measured at the electrode. In addition, the thermodynamics of adsorbed RAP films were also affected, giving rise to standard reduction potential shifts leading to redox kinetic effects as a result of the mediating nature of the RAP film in equilibrium with the solution. Full electrochemical characterization via transient and steady-state techniques, including the use of ultramicroelectrodes and the rotating disk electrode, were correlated to dynamic light scattering, ellipsometry, and viscometric analysis. These methods helped elucidate the relationship between electrochemical behavior and RAP coil size, film thickness, and polyelectrolyte packing regime. This study underscores the role of electrostatics in modulating the reactivity of redox polyelectrolytes.

Molecular Processes Leading to "Necking" in Extensional Flow of Polymer Solutions: Using Microfluidics and Single DNA Imaging

We study the necking and pinch-off dynamics of liquid droplets that contain a semidilute polymer solution of polyacrylamide close to overlap concentration by combining microfluidics and single DNA observation. Polymeric droplets are stretched by passing them through the stagnation point of a T-shaped microfluidic junction. In contrast with the sudden breakup of Newtonian droplets, a stable neck is formed between the separating ends of the droplet which delays the breakup process. Initially, polymeric filaments experience exponential thinning by forming a stable neck with extensional flow within the filament. Later, thin polymeric filaments develop a structure resembling a series of beads-on-a-string along their length and finally rupture during the final stages of the thinning process. To unravel the molecular picture behind these phenomena, we integrate a T-shaped microfluidic device with advanced fluorescence microscopy to visualize stained DNA molecules at the stagnation point within the necking region. We find that the individual polymer molecules suddenly stretch from their coiled conformation at the onset of necking. The extensional flow inside the neck is strong enough to deform and stretch polymer chains; however, the distribution of polymer conformations is broad, and it remains stationary in time during necking. Furthermore, we study the dynamics of single molecules during formation of beads-on-a-string structure. We observe that polymer chains gradually recoil inside beads while polymer chains between beads remain stretched to keep the connection between beads. The present work effectively extends single molecule experiments to free surface flows, which provides a unique opportunity for molecular-scale observation within the polymeric filament during necking and rupture.

Unusual Salt and pH Induced Changes in Polyethylenimine Solutions

Linear PEI is a cationic polymer commonly used for complexing DNA into nanoparticles for cell-transfection and gene-therapy applications. The polymer has closely-spaced amines with weak-base protonation capacity, and a hydrophobic backbone that is kept unaggregated by intra-chain repulsion. As a result, in solution PEI exhibits multiple buffering mechanisms, and polyelectrolyte states that shift between aggregated and free forms. We studied the interplay between the aggregation and protonation behavior of 2.5 kDa linear PEI by pH probing, vapor pressure osmometry, dynamic light scattering, and ninhydrin assay. Our results indicate that:

At neutral pH, the PEI chains are associated and the addition of NaCl initially reduces and then increases the extent of association.

The aggregate form is uncollapsed and co-exists with the free chains.

PEI buffering occurs due to continuous or discontinuous charging between stalled states.

Ninhydrin assay tracks the number of unprotonated amines in PEI.

The size of PEI-DNA complexes is not significantly affected by the free vs. aggregated state of the PEI polymer.

Despite its simple chemical structure, linear PEI displays intricate solution dynamics, which can be harnessed for environment-sensitive biomaterials and for overcoming current challenges with DNA delivery.

The persistence length of adsorbed dendronized polymers

The persistence length of cationic dendronized polymers adsorbed onto oppositely charged substrates was studied by atomic force microscopy (AFM) and quantitative image analysis. One can find that a decrease in the ionic strength leads to an increase of the persistence length, but the nature of the substrate and of the generation of the side dendrons influence the persistence length substantially. The strongest effects as the ionic strength is being changed are observed for the fourth generation polymer adsorbed on mica, which is a hydrophilic and highly charged substrate. However, the observed dependence on the ionic strength is much weaker than the one predicted by the Odijk, Skolnik, and Fixman (OSF) theory for semi-flexible chains. Low-generation polymers show a variation with the ionic strength that resembles the one observed for simple and flexible polyelectrolytes in solution. For high-generation polymers, this dependence is weaker. Similar dependencies are found for silica and gold substrates. The observed behavior is probably caused by different extents of screening of the charged groups, which is modified by the polymer generation, and to a lesser extent, the nature of the substrate. For highly ordered pyrolytic graphite (HOPG), which is a hydrophobic and weakly charged substrate, the electrostatic contribution to the persistence length is much smaller. In the latter case, we suspect that specific interactions between the polymer and the substrate also play an important role.

Effects of solution conditions on characteristics and size exclusion chromatography of pneumococcal polysaccharides and conjugate vaccines

Molecular properties of bacterial polysaccharides and protein-polysaccharide conjugates play an important role in the efficiency and immunogenicity of the final vaccine product. Size exclusion chromatography (SEC) is commonly used to analyze and characterize biopolymers, including capsular polysaccharides. The objective of this work was to determine the effects of solution ionic strength and pH on the SEC retention of several capsular polysaccharides from S. pneumoniae bacteria in their native and conjugated forms. The retention time of the charged polysaccharides increased with increasing ionic strength and decreasing pH due to compaction of the polysaccharides associated with a reduction in the intramolecular electrostatic interactions. The calculated radius of gyration was in good agreement with model calculations based on the worm-like chain model accounting for the increase in chain stiffness and excluded volume of the charged polysaccharide at low ionic strength. These results provide important insights into the effects of solution ionic strength on physical properties and SEC behavior of capsular polysaccharides and their corresponding conjugates.

Unusual surface and solution behaviour of keratin polypeptides

Intermediate filament-like aggregation from keratin polypeptides upon increasing [NaCl] as revealed by SANS.

Surface adsorption of sulfonated poly(phenylene sulfone)/C14TAB mixtures and its correlation with foam film stability

Polyelectrolyte/surfactant mixtures of rigid monosulfonated poly(phenylene sulfone) (sPSO₂-220) and tetradecyl trimethylammonium bromide (C₁₄TAB) were investigated by surface tension, surface elasticity and foam film stability measurements.

Is DNA a Good Model Polymer?

The details surrounding the cross-over from wormlike-specific to universal polymeric behavior has been the subject of debate and confusion even for the simple case of a dilute, unconfined wormlike chain. We have directly computed the polymer size, form factor, free energy and Kirkwood diffusivity for unconfined wormlike chains as a function of molecular weight, focusing on persistence lengths and effective widths that represent single-stranded and double-stranded DNA in a high ionic strength buffer. To do so, we use a chain-growth Monte Carlo algorithm, the Pruned-Enriched Rosenbluth Method (PERM), which allows us to estimate equilibrium and near-equilibrium dynamic properties of wormlike chains over an extremely large range of contour lengths. From our calculations, we find that very large DNA chains (≈ 1,000,000 base pairs depending on the choice of size metric) are required to reach flexible, swollen non-draining coils. Furthermore, our results indicate that the commonly used model polymer λ-DNA (48,500 base pairs) does not exhibit "ideal" scaling, but exists in the middle of the transition to long-chain behavior. We subsequently conclude that typical DNA used in experiments are too short to serve as an accurate model of long-chain, universal polymer behavior.

Detailed scaling analysis of low-force polyelectrolyte elasticity

Single-molecule force-extension data are typically compared to ideal models of polymer behavior that ignore the effects of self-avoidance. Here, we demonstrate a link between single-molecule data and the scaling pictures of a real polymer. We measure a low-force elasticity regime where the extension L of chemically denatured single-stranded DNA grows as a power law with force f : L approximately f;{gamma} , with gamma approximately 0.60-0.69 . This compares favorably with the "tensile-blob" model of a self-avoiding polymer, which predicts gamma=2/3 . We show that the transition out of the low-force regime is highly salt dependent, and use the tensile-blob model to relate this effect to the salt dependence of the polymer's Kuhn length and excluded-volume parameter. We find that, contrary to the well-known Odijk-Skolnick-Fixman theory, the Kuhn length of single-stranded DNA is linearly proportional to the Debye length of the solution. Finally, we show that the low-force elasticity becomes linear (gamma=1) at approximately 3 M salt, and interpret this as a Theta point of the polymer. At this point, the force-extension data is best described by the wormlike chain model, from which we estimate the bare (nonelectrostatic) persistence length of the polymer to be approximately 0.6 nm .

Critical exponents and self-similarity for sol-gel transition in aqueous alginate systems induced by in situ release of calcium cations

The sol-gel transition in aqueous alginate systems induced by in situ released calcium cations was monitored with rheology methods. Four alginate samples with different molecular weights and M/G ratios were used over the concentration C(Alg) of 2 approximately 6 wt % with different mole ratios f of Ca2+ to the alginate repeat unit. The scaling for the zero shear viscosity eta(0) before the gel point and the equilibrium modulus Ge after the gel point was described as eta(0) approximately epsilon(-k) and Ge approximately epsilon(z), respectively, where the relative distance to the gel point f(gel) was epsilon = (/f-f(gel)/)/f(gel). The relaxation critical exponent n was determined with Winter's criterion, and the critical exponents k and z estimated respectively from independent measurements of eta(0) and Ge gave n from z/(k + z). Before the gel point, the storage and loss moduli G' and G'' obtained at various epsilon can be superposed fairly well to form the master curve. The critical exponents n, k, and z were also evaluated from the shift factors and the structure self-similarity was found in the critical gel. The critical exponents evaluated with different methods agreed well with each other, suggesting two categories of the gelation as growth and cross-link. For the alginate with lower molecular weight, the critical exponents were almost independent of alginate concentration and close to the percolation prediction. For the alginate with higher molecular weight, the critical exponents, however, changed with alginate sample and concentration. The relative alginate concentration C(Alg)/C(Alg)* was found to serve as a criterion to divide these two transitions.

Strong and weak adsorptions of polyelectrolyte chains onto oppositely charged spheres

We investigate the complexation of long thin polyelectrolyte (PE) chains with oppositely charged spheres. In the limit of strong adsorption, when strongly charged PE chains adapt a definite wrapped conformation on the sphere surface, we analytically solve the linear Poisson-Boltzmann equation and calculate the electrostatic potential and the energy of the complex. We discuss some biological applications of the obtained results. For weak adsorption, when a flexible weakly charged PE chain is localized next to the sphere in solution, we solve the Edwards equation for PE conformations in the Hulthen potential, which is used as an approximation for the screened Debye-Huckel potential of the sphere. We predict the critical conditions for PE adsorption. We find that the critical sphere charge density exhibits a distinctively different dependence on the Debye screening length than for PE adsorption onto a flat surface. We compare our findings with experimental measurements on complexation of various PEs with oppositely charged colloidal particles. We also present some numerical results of the coupled Poisson-Boltzmann and self-consistent field equation for PE adsorption in an assembly of oppositely charged spheres.

A coarse-grained molecular model for glycosaminoglycans: application to chondroitin, chondroitin sulfate, and hyaluronic acid

A coarse-grained molecular model is presented for the study of the equilibrium conformation and titration behavior of chondroitin (CH), chondroitin sulfate (CS), and hyaluronic acid (HA)-glycosaminoglycans (GAGs) that play a central role in determining the structure and biomechanical properties of the extracellular matrix of articular cartilage. Systematic coarse-graining from an all-atom description of the disaccharide building blocks retains the polyelectrolytes' specific chemical properties while enabling the simulation of high molecular weight chains that are inaccessible to all-atom representations. Results are presented for the characteristic ratio, the ionic strength-dependent persistence length, the pH-dependent expansion factor for the end-to-end distance, and the titration behavior of the GAGs. Although 4-sulfation of the N-acetyl-D-galactosamine residue is found to increase significantly the intrinsic stiffness of CH with respect to 6-sulfation, only small differences in the titration behavior of the two sulfated forms of CH are found. Persistence length expressions are presented for each type of GAG using a macroscopic (wormlike chain-based) and a microscopic (bond vector correlation-based) definition. Model predictions agree quantitatively with experimental conformation and titration measurements, which support use of the model in the investigation of equilibrium solution properties of GAGs.

Electrostatic contribution to the persistence length of a semiflexible dipolar chain

We investigate the electrostatic contribution to the persistence length of a semiflexible polymer chain whose segments interact via a screened Debye-Hückel dipolar interaction potential. We derive the expressions for the renormalized persistence length on the level of a 1/D-expansion method already successfully used in other contexts of polyelectrolye physics. We investigate different limiting forms of the renormalized persistence length of the dipolar chain and show that, in, general, it depends less strongly on the screening length than in the context of a monopolar chain. We show that for a dipolar chain the electrostatic persistence length in the same regime of the parameter phase space as the original Odijk-Skolnick-Fixman (OSF) form for a monopolar chain depends logarithmically on the screening length rather than quadratically. This can be understood solely on the basis of a swifter decay of the dipolar interactions with separation compared to the monopolar electrostatic interactions. We comment also on the general contribution of higher multipoles to the electrostatic renormalization of the bending rigidity.

Variational theory for a single polyelectrolyte chain revisited

We reconsider the electrostatic contribution to the persistence length, le, of a single, infinitely long-charged polymer in the presence of screening. A Gaussian variational method is employed, taking le as the only variational parameter. For weakly charged and flexible chains, crumpling occurs at small length scales because conformational fluctuations overcome electrostatic repulsion. The electrostatic persistence length depends on the square of the screening length, le approximately kappa(-2), as first argued by Khokhlov and Khachaturian by applying the Odijk-Skolnick-Fixman (OSF) theory to a string of crumpled blobs. We compare our approach to previous theoretical works (including variational formulations) and show that the result le approximately kappa(-2), found by several authors comes from the improper use of a cutoff at small length scales. For highly charged and stiff chains, crumpling does not occur; here we recover the OSF result and validate the perturbative calculation for slightly bent rods.

Evaluation of Radius of Gyration and Intrinsic Viscosity Molar Mass Dependence and Stiffness of Hyaluronan

Nine hyaluronan (HA) samples were fractionated by size-exclusion chromatography, and molar mass (M), radius of gyration (Rg), and intrinsic viscosity ([eta]) were measured in 0.15 M NaCl at 37 degrees C by on-line multiangle light scattering and viscometer detectors. Using such method, we investigated the Rg and [eta] molar mass dependence for HA over a very wide range of molar masses: M ranging from 4 x 10(4) to 5.5 x 10(6) g/mol. The Rg and the [eta] molar mass dependence found for HA showed a meaningful difference. The Rg = f(M) power law was substantially linear in the whole range of molar masses explored with a constant slope of 0.6. In contrast, the [eta] = f(M) power law (Mark-Houwink-Sakurada plot) showed a marked curve shape, and a linear regression over the whole range of molar masses does not make sense. Also the persistence length (stiffness) for HA was estimated. The persistence length derived by using both the Odijk's model (7.5 nm from Rg vs M data) and the Bohdanecky's plot (6.8 nm from [eta] vs M data) were quite similar. These persistence length values are congruent with a semistiff conformation of HA macromolecules.