Flexible Polyelectrolytes Research Articles

The microrheology of polystyrene sulfonate combs in aqueous solution

Video particle tracking (VPT) and diffusing wave spectroscopy were used to characterize the microrheology of polystyrene sulfonate combs in aqueous solutions. At low frequencies VPT demonstrated predominantly viscous behavior. The manner in which the viscosity scaled as a function of monomer concentration was a sensitive function of the comb architecture. Densely branched combs or combs with long side chains demonstrated entangled polyelectrolyte scaling above the overlap concentration, whereas sparsely branched combs had unentangled polyelectrolyte scaling. A dynamic scaling model was developed for the viscosity of unentangled semidilute solutions of comb polyelectrolytes. Diffusing wave spectroscopy demonstrated Rouse modes (G' approximately G" approximately omega12) for the high-frequency dynamics of the semidilute comb solutions. The form of the high-frequency viscoelasticity was independent of the chain architecture and the modulus scaled as expected for linear flexible polyelectrolytes.

Layer-by-Layer Electrostatic Self-Assembly of Single-Wall Carbon Nanotube Polyelectrolytes

We have used anionic and cationic single-wall carbon nanotube polyelectrolytes (SWNT-PEs), prepared by the noncovalent adsorption of ionic naphthalene or pyrene derivatives on nanotube sidewalls, for the layer-by-layer self-assembly to prepare multilayers from carbon nanotubes with polycations, such as poly(diallyldimethylammonium) or poly(allylamine hydrochloride) (PDADMA or PAH, respectively), and polyanions (poly(styrenesulfonate), PSS). This is a general and powerful technique for the fabrication of thin carbon nanotube films of arbitrary composition and architecture and allows also an easy preparation of all-SWNT (SWNT/SWNT) multilayers. The multilayers were characterized with vis-near-IR spectroscopy, X-ray photoelectron spectroscopy (XPS), surface plasmon resonance (SPR) measurements, atomic force microscopy (AFM), and imaging ellipsometry. The charge compensation in multilayers is mainly intrinsic, which shows the electrostatic nature of the self-assembly process. The multilayer growth is linear after the initial layers, and in SWNT/polyelectrolyte films it can be greatly accelerated by increasing the ionic strength in the SWNT solution. However, SWNT/SWNT multilayers are much more inert to the effect of added electrolyte. In SWNT/SWNT multilayers, the adsorption results in the deposition of 1-3 theoretical nanotube monolayers per adsorbed layer, whereas the nominal SWNT layer thickness is 2-3 times higher in SWNT/polyelectrolyte films prepared with added electrolyte. AFM images show that the multilayers contain a random network of nanotube bundles lying on the surface. Flexible polyelectrolytes (e.g., PDADMA, PSS) probably surround the nanotubes and bind them together. On macroscopic scale, the surface roughness of the multilayers depends on the components and increases with the film thickness.

Effective Charges of Polyelectrolytes in a Salt-Free Solution Based on Counterion Chemical Potential

The phenomenon of counterion condensation around a flexible polyelectrolyte chain with N monomers is investigated by Monte Carlo simulations in terms of the degree of ionization alpha, which is proportional to the effective charge. It is operationally defined as the ratio of observed to intrinsic counterion concentration, alpha = co/ci. The observed counterion concentration in the dilute polyelectrolyte solution is equivalent to an electrolyte solution of concentration co with the same counterion chemical potential. It can be determined directly by thermodynamic experiments such as ion-selective electrode. With the polyelectrolyte fixed at the center of the spherical Wigner-Seitz cell, the polymer conformation, counterion distribution, and chemical potential can be obtained. Our simulation shows that the degree of ionization rises as the polymer concentration decreases. This behavior is opposite to that calculated from the infinitely long charged rod model, which is often used to study counterion condensation. Moreover, we find that, for a specified line charge density, alpha decreases with an increment in chain length and chain flexibility. In fact, the degree of ionization is found to decline with increasing polymer fractal dimension, which can be tuned by varying bending modulus and solvent quality. Those results can be qualitatively explained by a simple model of two-phase approximation.

Flexible Charged Macromolecules on Mixed Fluid Lipid Membranes: Theory and Monte Carlo Simulations

Fluid membranes containing charged lipids enhance binding of oppositely charged proteins by mobilizing these lipids into the interaction zone, overcoming the concomitant entropic losses due to lipid segregation and lower conformational freedom upon macromolecule adsorption. We study this energetic-entropic interplay using Monte Carlo simulations and theory. Our model system consists of a flexible cationic polyelectrolyte, interacting, via Debye-Hückel and short-ranged repulsive potentials, with membranes containing neutral lipids, 1% tetravalent, and 10% (or 1%) monovalent anionic lipids. Adsorption onto a fluid membrane is invariably stronger than to an equally charged frozen or uniform membrane. Although monovalent lipids may suffice for binding rigid macromolecules, polyvalent counter-lipids (e.g., phosphatidylinositol 4,5 bisphosphate), whose entropy loss upon localization is negligible, are crucial for binding flexible macromolecules, which lose conformational entropy upon adsorption. Extending Rosenbluth’s Monte Carlo scheme we directly simulate polymer adsorption on fluid membranes. Yet, we argue that similar information could be derived from a biased superposition of quenched membrane simulations. Using a simple cell model we account for surface concentration effects, and show that the average adsorption probabilities on annealed and quenched membranes coincide at vanishing surface concentrations. We discuss the relevance of our model to the electrostatic-switch mechanism of, e.g., the myristoylated alanine-rich C kinase substrate protein.

Electrostatic Persistence Length of Semiflexible and Flexible Polyelectrolytes

I have calculated the dependence of the electrostatic persistence length on the Debye screening length for semiflexible, strongly and weakly charged flexible polyelectrolytes. For semiflexible and strongly charged flexible polyelectrolytes the electrostatic part of the chain persistence length is proportional to the Debye screening length. This result is obtained by evaluating the bending angle fluctuations and in the framework of the Gaussian variational principle. A polyelectrolyte chain with linear dependence of the electrostatic persistence length on the Debye screening length has a lower free energy than that of a chain with the Odijk−Skolnick−Fixman electrostatic persistence length. In the case of weakly charged chains the electrostatic persistence length has a sublinear dependence on the Debye screening length which is due to inverse logarithmic dependence of the linear charge density of the chain of electrostatic blobs on the Debye screening length. This result was derived by applying a coarse-graining procedure to an initially flexible polyelectrolyte chain by representing it as a chain of electrostatic blobs. The blob size and chain persistence length are then found self-consistently by minimizing the chain's variational free energy.

Charge Inversion by Flexible Polyelectrolytes on Flat Surfaces from Self-Consistent Field Calculations

We have applied a continuum self-consistent field (SCF) theory to flexible polyelectrolytes on flat surfaces either uncharged or carrying charges opposite to the polyelectrolytes. We examined in detail the effects of various parameters on the polyelectrolyte adsorption and surface charge compensation by the adsorbed polyelectrolytes. The ground-state dominance approximation (GSDA) was used to explore the large parameter space involved, including the charge distribution and degree of ionization of the polyelectrolytes, surface charge density, short-range (non-Coulombic) surface−polymer interactions, solvent quality, and bulk polymer and salt concentrations. The numerical results under GSDA were also compared with full SCF calculations to examine the effects of molecular weight of the polyelectrolytes. Strong charge inversion is found for relatively long polyelectrolytes on oppositely charged, attractive surfaces in poor solvent at high salt concentrations. At the mean-field level, the adsorption behavior of polyelectrolytes at high salt concentrations can be understood by that of neutral polymers in good solvent.

Langevin dynamics of semiflexible polyelectrolytes: Rod-toroid–globule-coil structures and counterion distribution

We have investigated the nature of counterion condensation on uniformly charged semiflexible polyelectrolyte chains and the concomitant configurations by monitoring the role of chain stiffness, chain length, counterion valency, and the strength of electrostatic interaction. The counterion condensation is seen to follow the adsorption process and the effective polymer charge increases with chain stiffness. Size and shape, as calculated through the radius of gyration, effective persistence length, and hydrodynamic radius, are studied. Stable coil-like, globular, folded-chain, toroidal, and rodlike configurations are possible at suitable combinations of values of chain stiffness, chain length, electrostatic interaction strength, and the valency of counterion. For high strengths of electrostatic interactions, sufficiently stiff polyelectrolytes form toroids in the presence of multivalent counterions, whereas flexible polyelectrolytes form disordered globules. The kinetic features of the nucleation and growth of toroids are monitored. Several metastable structures are found to frustrate the formation of toroids. The generic pathway involves the nucleation of one primary loop somewhere along the chain contour, followed by a growth process where the rest of the chain is folded continuously on top of the primary loop. The dependence of the average radii of toroids on the chain length is found to be roughly linear, in disagreement with existing scaling arguments.

Scattering Functions of Flexible Polyelectrolytes in the Presence of Mixed Valence Counterions: Condensation and Scaling

We have investigated by small-angle X-ray and neutron scattering the structure of salt-free aqueous solutions of sulfonated polystyrene with variable fractions of monovalent (sodium, Na) and divalent (calcium, Ca) counterions. We follow the variation of the position of the maximum in the scattered intensity, q*, as a function of the concentration, c, and the fraction of Ca counterions. A relevant parameter is the degree of condensation of Na and Ca counterions in the different mixtures. We survey the literature and check that, in the case of monovalent counterions, the variation of q* with c can be described by the scaling theory of Dobrynin, Colby, and Rubinstein, provided the counterion condensation is included according to the Manning-Oosawa approach. Scattering data from mixed valence systems are still in agreement with this scaling model at lower concentrations, except for pure CaPSS 2 aqueous solutions. For increasing concentration, a discrepancy is enhanced that extends toward higher Ca fractions. This indicates that counterion condensation is not the only process. Another possible one is a retraction of the macroions due to divalent counterions that induce bridging-type correlations between monomers, as already observed on the form factors of CaPSS 2 and NaPSS plus added CaCl 2 salt. Such a retraction modifies the scaling, in particular, via a change in the overlap concentration c*. Furthermore, it is noticeable that q* measurements have to be handle with care. We show that misinterpretation of the characteristic maximum in the small-angle scattering of polyelectrolyte solutions may occur, especially at high concentration, if the contribution of the condensed counterions to the total scattering function is predominant.

Flexible polyelectrolytes with monovalent salt

We present a model for describing flexible polyelectrolytes in a good solvent and in the presence of monovalent salt. The molecule composed by N monomers is characterized by the end-to-end distance R e = b ( Z - 1 ) γ and the number of associated counterions n. At high temperatures the polyelectrolyte behaves as a neutral polymer ( γ = 0.588 ). Decreasing the temperature, the macromolecule changes from this extended configuration ( γ = 0.588 ) to a stretched form ( γ ≈ 1 ). At even lower temperatures, above the Manning condensation threshold, the polyelectrolyte collapses ( γ ≈ 0.3 ). Our results show good agreement with simulations.

Molecular Dynamics Simulations of Layer-by-Layer Assembly of Polyelectrolytes at Charged Surfaces: Effects of Chain Degree of Polymerization and Fraction of Charged Monomers

We performed molecular dynamics simulations of the electrostatic assembly of multilayers of flexible polyelectrolytes at a charged surface. The multilayer build-up was achieved through sequential adsorption of oppositely charged polymers in a layer-by-layer fashion from dilute polyelectrolyte solutions. The steady-state multilayer growth proceeds through a charge reversal of the adsorbed polymeric film which leads to a linear increase in the polymer surface coverage after completion of the first few deposition steps. Moreover, substantial intermixing between chains adsorbed during different deposition steps is observed. This intermixing is consistent with the observed requirement for several deposition steps to transpire for completion of a single layer. However, despite chain intermixing, there are almost perfect periodic oscillations of the density difference between monomers belonging to positively and negatively charged macromolecules in the adsorbed film. Weakly charged chains show higher polymer surface coverage than strongly charged ones.

Multilayer DNA/Poly(allylamine hydrochloride) Microcapsules: Assembly and Mechanical Properties

We report the preparation, characterization, and mechanical properties of DNA/poly(allylamine hydrochloride) (PAH) multilayer microcapsules. The DNA/PAH multilayers were first constructed on a planar support to examine their layer-by-layer buildup. Surface plasmon resonance spectroscopy (SPR) showed a nonlinear growth of the assembly upon each bilayer deposited independently on a concentration of salt. A weak increase in the film thickness with the DNA concentration was, however, detected. A post-treatment of the multilayers in the salt solutions has shown a thinning of the film. The optimal conditions of the planar film growth were used to deposit the same multilayers on the surface of colloidal templates and to study their roughness and morphology with the atomic force microscope (AFM) imaging. When an outer layer is formed by DNA, we observe large domains of oriented parallel DNA loops, while an outer layer formed by PAH shows highly porous morphology. The dissolution of colloidal templates led to a formation of highly porous DNA/PAH microcapsules. We probe their mechanical properties by measuring force-deformation curves with the AFM-related setup. The experiment suggests that the DNA/PAH capsules are softer than capsules made from the flexible polyelectrolytes studied before. The softening is due to both higher permeability and smaller Young's modulus of the shell material. The Young's modulus of the DNA/PAH shells increases after post-treatment in salt solutions of relatively low concentration.

Orientation Behavior of Polyelectrolyte in Solution under an External Electric Field. A Coarse Grain Molecular Dynamics Simulation Study

Abstract A coarse grain molecular dynamics simulation method was applied to polystyrenesulfonate in aqueous solution to investigate the conformational and orientational behavior of flexible polyion under an external electric field. When the electric field was applied, the deviation of the counter-ion distribution and the rotational orientation of the polyion toward the direction of the electric field were observed. The orientation behavior of flexible polyelectrolytes depended on the field strength, and two typical orientational motions were detected. That is, at low electric field strength, elongation of the whole polyion chain conformation occurs at first stage and subsequently rotationally orients toward the field direction. On the other hand, segment orientation occurs at the high field because of the fast displacement of the counter ions on each polymer segment. The ionic polarization of the flexible polyion was evaluated by the component analysis of the counter-ion deviation. Results showed that the loosely-bound counter ions contribute largely to the ionic polarization.

Molecular Dynamics Simulations of Polyelectrolyte Multilayering on a Charged Particle

Molecular dynamics simulations of polyelectrolyte multilayering on a charged spherical particle revealed that the sequential adsorption of oppositely charged flexible polyelectrolytes proceeds with surface charge reversal and highlighted electrostatic interactions as the major driving force of layer deposition. Far from being completely immobilized, multilayers feature a constant surge of chain intermixing during the deposition process, consistent with experimental observations of extensive interlayer mixing in these films. The formation of multilayers as well as the extent of layer intermixing depends on the degree of polymerization of the polyelectrolyte chains and the fraction of charge on its backbone. The presence of ionic pairs between oppositely charged macromolecules forming layers seems to play an important role in stabilizing the multilayer film.

Structure formation in films of weakly charged block polyelectrolyte solutions

A mean-field dynamic density functional theory is used to describe a phase diagram of concentrated solutions of weakly charged flexible block polyelectrolytes in a film. Electrostatics is taken into account by applying the local electroneutrality constraint (the Donnan membrane equilibrium approach). In the Donnan limit it is assumed that a salt added to the solution perfectly screens long-range electrostatic interactions. The phase diagram of a solution of a triblock polyelectrolyte in a film as a function of the solvent concentration and the charge of the polyelectrolyte (solvophilic) block is calculated for a given film thickness. The phase behavior of the block polyelectrolyte film arises from the interplay between surface-induced alignment and the electrostatically-driven structure formation. The observed mesoscopic structures (lamellar, perforated lamellar, cylindrical, micellar, and mixed phases) are oriented parallel to the surfaces for the considered case of morphologies unfrustrated by the film thickness. Structures with connections between parallel layers (bicontinuous, etc.) are not formed. As a result of surface-induced ordering, the region of ordered phases in a film is wider than in bulk and the phase boundary between ordered and disordered phases is more diffuse. As in the case of unconfined block polyelectrolyte solution, the solution in a film does not follow the lyotropic sequence of phases of such a block copolymer upon increase in the charge of the polyelectrolyte block. Upon changing the charge of the solvophilic copolymer block, transformations of copolymer morphology take place via change in curvature of polymeric domains. Due to confinement of a polyelectrolyte film, no swelling of solvophilic domains is observed.

Adsorption of Weak Polyelectrolytes to an Oppositely Charged Langmuir Film: Change in the Conformation of the Adsorbed Molecules and Saturation of the Ionization Degree

We have studied the adsorption of a weak flexible polyelectrolyte, poly(acrylic acid), at an oppositely charged surface, the surface of water covered with a Langmuir film of dimethyldioctadecylammonium bromide. The surface charge density and the polymer ionization degree α were conveniently varied by varying respectively the density σ of the Langmuir film and the pH of the polyelectrolyte solution. By infrared spectroscopy we evidenced a change in the mean orientation of the adsorbed chains when increasing the surface charge density, from parallel to the surface for σ < σ0 to perpendicular to the surface for σ > σ0. A signature of this regime change also appears in the compression elastic modulus. The value of σ0 scales as α at low α, as predicted by theory, but saturates when increasing α, presumably because of a saturation of the polyelectrolyte charge fraction.

Optimal linearized Poisson-Boltzmann theory applied to the simulation of flexible polyelectrolytes in solution.

Optimal linearized Poisson-Boltzmann (OLPB) theory is applied to the simulation of flexible polyelectrolytes in solution. As previously demonstrated in the contexts of the cell model [H. H. von Grunberg, R. van Roij, and G. Klein, Europhys. Lett. 55, 580 (2001)] and a particle-based model [B. Beresfordsmith, D. Y. C. Chan, and D. J. Mitchell, J. Colloid Interface Sci. 105, 216 (1985)] of charged colloids, OLPB theory is applicable to thermodynamic states at which conventional, Debye-Huckel (DH) linearization of the Poisson-Boltzmann equation is rendered invalid by violation of the condition that the electrostatic coupling energy of a mobile ion be much smaller than its thermal energy throughout space, |nu(alpha)e psi(r)|<<k(B)T. As a demonstration of its applicability to flexible polyelectrolytes, OLPB theory is applied to a concentrated solution of freely jointed chains. The osmotic pressure is computed at various reservoir ionic strengths and compared with results from the conventional DH model for polyelectrolytes. Through comparison with the cylindrical cell model for polyelectrolytes, it is demonstrated that the OLPB model yields the correct osmotic pressure behavior with respect to nonlinear theory where conventional DH theory fails, namely at large ratios of mean counterion density to reservoir salt density, when the Donnan potential is large.

Structure and Dynamics in Aqueous Solutions of Amphiphilic Sodium Maleate-Containing Alternating Copolymers

The structure of aqueous solutions of sodium maleate copolymers with comonomers of variable hydrophobicity are examined using a combination of small-angle neutron scattering, small-angle X-ray scattering, and rheometry. Semidilute solutions of the copolymers made with mildly hydrophobic comonomers exhibit scattering and rheology that are typical of flexible polyelectrolytes, with a correlation length scaling with polymer concentration as c-α with α = 1/2 and specific viscosity scaling as c1/2/c3/2 when unentangled/entangled. In contrast, copolymers with more than eight carbons in their hydrocarbon comonomer form micelles (globules) at low concentrations and molecular weights. For these more hydrophobic copolymers, the correlation length scales as c-α with α < 1/3 and the viscosity remains small until a relatively high concentration at which the globules start to overlap. Once these more hydrophobic copolymers overlap, the micelles open up and allow intermolecular associations that cause the viscosity to i...

Soft effective interactions between weakly charged polyelectrolyte chains.

We apply extensive molecular dynamics simulations and analytical considerations in order to study the conformations and the effective interactions between weakly charged, flexible polyelectrolyte chains in salt-free conditions. We focus on charging fractions lying below 20%, for which case there is no Manning condensation of counterions and the latter can be thus partitioned in two states: those that are trapped within the region of the flexible chain and the ones that are free in the solution. We examine the partition of counterions in these two states, the chain sizes and the monomer distributions for various chain lengths, finding that the monomer density follows a Gaussian shape. We calculate the effective interaction between the centers of mass of two interacting chains, under the assumption that the chains can be modeled as two overlapping Gaussian charge profiles. The analytical calculations are compared with measurements from molecular dynamics simulations. Good quantitative agreement is found for charging fractions below 10%, where the chains assume coil-like configurations, whereas deviations develop for charge fraction of 20%, in which case a conformational transition of the chain towards a rodlike configuration starts to take place.

Ion Bridging Effects on the Electroviscosity of Flexible Polyelectrolytes

An experimental study is carried out to investigate the effect of added salt on the viscosity and microstructure of sodium polystyrenesulfonate solutions. The emphasis is placed on the valence of counterions to seek the existence of bridging effects associated with ion multivalence. To amplify the possible bridging effect, a mixture of water and glycerol is used as a solvent for viscosity experiments because of the lower dielectric constant of the mixture. The viscosity order with respect to the valence of added cations changes, depending on the polymer and salt concentrations. This is explained by the electroviscous effects along with the competition between the intra- and intermolecular association due to the bridging phenomenon.

Counterion associative behavior with flexible polyelectrolytes.

At low ionic strength, organic counterions dress a flexible charged polymer as measured directly by small-angle neutron scattering and neutron spin-echo spectroscopy. This dressed state, quantified by the concentration dependence of the static correlation length, illustrates the polymer-counterion coupled nature on the nanometer length scale. The counterions, made visible by selective hydrogen and deuterium labeling, undress from the polymeric template by addition of sodium chloride. The addition of this electrolyte leads to two effects: increased Debye electrostatic screening and decoupled organic counterion-polymer correlations. Neutron spin-echo spectroscopy measures a slowing down of the effective diffusion coefficient of the labeled counterions at the length scale of 8 nm, the static correlation length, indicating the nanosecond counterion dynamics mimics the polymer. These experiments, performed with semidilute solutions of tetramethylammonium poly(styrene sulfonate) [(h-TMA(+)) d-PSS], apply to relevant biopolymers including single and double stranded DNA and unfolded proteins, which undergo orchestrated dynamics of counterions and chain segments to fold, unfold, and assemble.