The low-frequency limit of the electrical conductivity (d.c. conductivity) of differently flexible polyions in aqueous solutions has been measured over an extended polyion concentration range, covering both the dilute and semidilute (entangled and unentangled) regime, up to the concentrated regime. The data have been analyzed taking into account the different flexibility of the polymer chains according to the scaling theory of polyion solutions, in the case of flexible polyions, and according to the Manning model, in the case of rigid polyions. In both cases, the fraction f of free counterions, released into the aqueous phase from the ionizable polyion groups, has been evaluated and its dependence on the polyion concentration determined. Our results show that the counterion condensation follows at least three different regimes in dependence on the polyion concentration. The fraction f of free counterions remains constant only in the semidilute regime (a region that we have named the Manning regime), while there is a marked dependence on the polyion concentration both in the dilute and in the concentrated regime. These results are briefly discussed at the light of the aqueous ionic solutions.
Molecular dynamics simulations are used to study the local dynamics of counterion-charged polymer association at charge densities above and below the counterion condensation threshold. Surprisingly, the counterions form weakly-interacting clusters which exhibit short range orientational order, and which decay slowly due to migration of ions across the diffuse double layer. The cluster dynamics are insensitive to an applied electric field, and qualitatively agree with the available experimental data. The results are consistent with predictions of the classical theory only over much longer time …
A model of rod-like polyelectrolyte brushes in the presence of monovalent and multivalent counterions but with no added-salt is studied using Monte Carlo simulation. The average height of the brush, the histogram of rod conformations, and the counterion density profile are obtained for different values of the grafting density of the charge-neutral wall. For a domain of grafting densities, the brush height is found to be relatively insensitive to the density due to a competition between counterion condensation and inter-rod repulsion. In this regime, multivalent counterions collapse the brush i…
We present results of molecular dynamics simulations of strong, flexible polyelectrolyte chains in solution with added salt. The effect of added salt on the polyelectrolyte chain structure is fully treated for the first time as a function of polymer density. Systems above and below the Manning condensation limit are studied. The chain contraction due to added salt is weaker than expected from simple screening arguments. The chain structure is intimately tied to the ion density near the chain even for chains in the counterion condensation regime. In contradiction to Manning counterion condensat…
The collapse kinetics of strongly charged polyelectrolytes in poor solvents is investigated by Langevin simulations and scaling arguments. The rate of collapse increases sharply as the valence of counterions, z, increases from one to four. The combined system of the collapsed chain and the condensed counterions forms a Wigner crystal when the solvent quality is not too poor provided z >= 2. For very poor solvents the morphology of the collapsed structure resembles a Wigner glass. For a fixed z and quality of the solvent the efficiency of collapse decreases dramatically as the size of the count…
Multivalent counterions can induce an effective attraction between like-charged rodlike polyelectrolytes, leading to the formation of polelectrolyte bundles. In this paper, we calculate the equilibrium bundle size using a simple model in which the attraction between polyelectrolytes (assumed to be pairwise additive) is treated phenomenologically. If the counterions are point-like, they almost completely neutralize the charge of the bundle, and the equilibrium bundle size diverges. When the counterions are large, however, steric and short-range electrostatic interactions prevent charge neutrali…
Knots on ring polymers tend to be tight. For knots on charged polymers (polyelectrolytes), electrostatic repulsion among the monomers is considered to enhance the persistence length and further localize the knots. However, the effects of counterion condensation on knots behavior are not clear. Here we use molecular dynamics simulations to systematically study the effect of counterion condensation on the knot behavior under different electrostatic strength and solvent quality conditions, with the focus on the knot sizes. We show that generally counterion condensation \emph{delocalizes} the knot…
We investigate electro-osmosis in aqueous solutions of polyelectrolytes using mean-field equations. A solution of positively charged polyelectrolytes is confined between two negatively charged planar surfaces, and an electric field is applied parallel to the surfaces. When electrostatic attraction between the polymer and the surface is strong, the polymers adhere to the surface, forming a highly viscous adsorption layer that greatly suppresses the electro-osmosis. Conversely, electro-osmosis is enhanced by depleting the polymers from the surfaces. We also found that the electro-osmotic flow is…
We formulate a self-consistent field theory for polyelectrolyte brushes in the presence of counterions. We numerically solve the self-consistent field equations and study the monomer density profile, the distribution of counterions, and the total charge distribution. We study the scaling relations for the brush height and compare them to the prediction of other theories. We find a weak dependence of the brush height on the grafting density.We fit the counterion distribution outside the brush by the Gouy-Chapman solution for a virtual charged wall. We calculate the amount of counterions outside…
Bending rigidity of a charged membrane or a charged polyelectrolyte screened by monovalent counterions is known to be enhanced by electrostatic effects. We show that in the case of screening by multivalent counterions the electrostatic effects reduce the bending rigidity. This inversion of the sign of the electrostatic contribution is related to the formation of two-dimensional strongly correlated liquids (SCL) of counterions at the charged surface due to strong lateral repulsion between them. When a membrane or a polyelectrolyte is bent, SCL is compressed on one side and stretched on the othe…
A simple electrostatic theory of condensation of rod-like polyelectrolytes under influence of polyvalent ions is proposed. It is based on the idea that Manning condensation of ions results in formation of the Wigner crystal on a background of a bundle of rods. It is shown that, depending on a single dimensionless parameter, this can be the densely packed three-dimensional Wigner crystal or the two-dimensional crystal on the rod surfaces. For DNA the location of charge on the spiral results in a model of the one-dimensional Wigner crystal. It is also argued that the Wigner crystal idea can be a…
In this paper we perform molecular dynamics simulations of a spherical polyelectrolyte brush and counterions in a salt-free medium. The dielectric discontinuity on the grafted nanoparticle surface is taken into account by the method of image charges. Properties of the polyelectrolyte brush are obtained for different parameters, including valency of the counterions, radius of the nanoparticle, and the brush total charge. The monovalent counterions density profiles are obtained and compared with a simple mean-field theoretical approach. The theory allows us to obtain osmotic properties of the sy…
Using molecular dynamics simulations, it is demonstrated that monovalent counterions can induce aggregation of similarly charged rod-like polyelectrolyte chains. The critical value of the linear charge density for aggregation is shown to be close to the critical value for the extended-collapsed transition of a single flexible polyelectrolyte chain, and decreases with increasing valency of the counterions. The effective interaction potential between two rod-like polyelectrolyte chains is measured, and is related to the angular distribution of the condensed counterions.
We study the equilibrium conformations of a grafted polyelectrolyte (PE) in the presence of explicit counterions (CI) using Monte Carlo simulations. The interplay between attractive Lennard-Jones interactions (parametrized by epsilon), and electrostatics (parametrized by A = q^2l_B/a, where q =counterion valency, l_B = Bjerrum length and a = monomer diameter), results in a variety of conformations, characterized as extended (E), pearls with m beads (P_m), sausage (S) and globular (G). For large epsilon, we observe a transition from G -> P_2 -> P_3 -> . . . -> S -> G with increasing A, i.e., a …
We discuss recent investigations of the interaction of polyelectrolytes with proteins. In particular, we review our recent studies on the interaction of simple proteins such as human serum albumin (HSA) or lysozyme with linear polyelectrolytes, charged dendrimers, charged networks, and polyelectrolyte brushes. In all cases discussed here we combined experimental work with molecular dynamics (MD) simulations and mean-field theories. In particular, isothermal titration calorimetry (ITC) has been employed to obtain the respective binding constants Kb and the Gibbs free energy of binding. MD-simul…
In order to understand how live matter functions one needs to understand the interaction between polyelectrolytes. We discover a general dependence of polyelectrolyte conductivity valid in at least nine decades of polyelectrolyte concentration spanning dilute and semidilute pure water solutions. Furthermore, we showed that current state of the art theories can not explain polyelectrolyte conductivity and suggest the path in transport theories which needs to be taken in order to explain polyelectrolyte conductivity.
The persistence length of a single, strongly charged, stiff polyelectrolyte chain is investigated theoretically. Path integral formulation is used to obtain the effective electrostatic interaction between the monomers. We find significant deviations from the classical Odijk, Skolnick and Fixman (OSF) result. An induced attraction between monomers is due to thermal fluctuations and correlations between bound counterions. The electrostatic persistence length is found to be smaller than the OSF value and indicates a possible mechanical instability (collapse) for highly charged polyelectrolytes wi…
We study the electrokinetics of a single polyelectrolyte chain in salt solution using hydrodynamic simulations. The salt-dependent chain mobility compares well with experimental DNA data. The mobility of condensed counterions exhibits a salt-dependent change of sign, an anomaly that is also reflected in the counterion excess conductivity. Using Green's function techniques this anomaly is explained by electrostatic screening of the hydrodynamic interactions between chain and counterions.
We explore, using the recently developed efficient Monte Carlo simulation method, the interaction of an anionic polyelectrolyte solution with a like-charged dielectric surface. In addition to polyions, the solution also contains salt with either monovalent, divalent, or trivalent counterions. In agreement with recent experimental observations, we find that multivalent counterions can lead to strong adsorption of polyions onto the surface. On the other hand, addition of a 1:1 electrolyte diminishes the adsorption induced by the multivalent counterions. Dielectric discontinuity at the interface …
We demonstrate that a highly charged polyelectrolyte confined in a spherical cavity undergoes reversible transformations between amorphous conformations to a four-fold symmetry morphology as a function of dielectric mismatch between the media inside and outside the cavity. Surface polarization due to dielectric mismatch exhibits an extra "confinement" effect, which are most pronounced within a certain range of the cavity radius and the electrostatic strength between the monomers and counterions and multivalent counterions. For cavities with a charged surface, surface polarization leads to an i…
A new quantitative theory for polyelectrolytes in salt free dilute solutions is developed. Depending on the electrostatic interaction strength, polyelectrolytes in solutions can undergo strong stretching (with polyelectrolyte dimension R_g\sim l_B^{1/3}N, where l_B is the Bjerrum length and N is the number of the chain segments) or strong compression (with R_g\sim l_B^{-1/2}N^{1/3}). A strong polymer collapse occurs as a first-order phase transition due to accompanying counterion condensation.
The osmotic coefficient of B-DNA in water may, in moderately dilute solutions, deviate as much as 100 % from predictions based on a simple 'counterion condensation' theory. We determine the results for osmotic properties via a cell model description of the ionic atmosphere near a cylindrical polyelectrolyte. The cell model predictions for the osmotic properties disagree with predictions based on simple condensation theory, but are in surprisingly good harmony with experimental findings. We argue that the neglect of finite-radius effects makes simple condensation theory inapplicable at all but …
We perform extensive molecular dynamics simulations of a highly charged flexible polyelectrolyte (PE) chain in a poor solvent for the case when the chain is in a collapsed state and the electrostatic interactions, characterized by the reduced Bjerrum length $\ell_B$, are strong. We detect the existence of several sub-regimes, $R_g \sim \ell_B^{-γ}$, in the dependence of the gyration radius of the chain $R_g$ on $\ell_B$. In contrast to a good solvent, the exponent $γ$ for a poor solvent crucially depends on the size and valency of counterions. To explain the different sub-regimes we generalize…
We investigate the effect of counterion fluctuations in a single polyelectrolyte brush in the absence of added salt by systematically expanding the counterion free energy about Poisson-Boltzmann mean field theory. We find that for strongly charged brushes, there is a collapse regime in which the brush height decreases with increasing charge on the polyelectrolyte chains. The transition to this collapsed regime is similar to the liquid-gas transition, which has a first-order line terminating at a critical point. We find that for monovalent counterions the transition is discontinuous in theta so…
Counterion distributions and effective electrostatic interactions between spherical macroions in polyelectrolyte solutions are calculated via second-order perturbation (linear response) theory. By modelling the macroions as continuous charge distributions that are permeable to counterions, analytical expressions are obtained for counterion profiles and effective pair interactions in solutions of star-branched and microgel macroions. The counterions are found to penetrate stars more easily than microgels, with important implications for screening of bare macroion interactions. The effective pai…
The effective elasticity of highly charged stiff polyelectrolytes is studied in the presence of counterions, with and without added salt. The rigid polymer conformations may become unstable due to an effective attraction induced by counterion density fluctuations. Instabilities at the longest, or intermediate length scales may signal collapse to globule, or necklace states, respectively. In the presence of added-salt, a generalized electrostatic persistence length is obtained, which has a nontrivial dependence on the Debye screening length. It is also found that the onset of conformational ins…
We explore the mechanical response of a single polyelectrolyte chain under tension in good and poor solvents using a combination of simulation and theory. In poor solvents, where the equilibrium state of the chain is a collapsed globule, we find that the chain undergoes a globule-coil transition, as the magnitude of the force is increased beyond a critical value. This transition, where the polymer size changes discontinuously from a small to a large value, is accompanied by release of bound counterions from the chain. We explain these results by adhering to a statistical mechanical theory of c…
Using molecular dynamics simulations we study the behavior of a dilute solution of strongly charged polyelectrolytes in poor solvents, where we take counterions explicitly into account. We focus on the chain conformational properties under conditions where chain-chain interactions can be neglected, but the counterion concentration remains finite. We investigate the conformations with regard to the parameters chain length, Coulomb interaction strength, and solvent quality, and explore in which regime the competition between short range hydrophobic interactions and long range Coulomb interaction…
Similarly-charged polyelectrolytes are known to attract each other and aggregate into bundles when the charge density of the polymers exceeds a critical value that depends on the valency of the counterions. The dynamics of aggregation of such rigid polyelectrolytes are studied using large scale molecular dynamics simulations. We find that the morphology of the aggregates depends on the value of the charge density of the polymers. For values close to the critical value, the shape of the aggregates is cylindrical with height equal to the length of a single polyelectrolyte chain. However, for lar…
Dendritic polyelectrolytes constitute high potential drugs and carrier systems for biomedical purposes, still their biomolecular interaction modes, in particular those determining the binding affinity to proteins, have not been rationalized. We study the interaction of the drug candidate dendritic polyglycerol sulfate (dPGS) with serum proteins using Isothermal Titration Calorimetry (ITC) interpreted and complemented with molecular computer simulations. Lysozyme is first studied as a well-defined model protein to verify theoretical concepts, which are then applied to the important cell adhesio…
Light scattering and viscometric measurements on weak polyelectrolytes show two important aspects of counterion condensation, namely, non-monotonic variation in the polyelectrolyte size with the increase in the electrostatic strength, and, monovalent counterion selectivity in determining the nature of collapse transition at high electrostatic strengths. Here, we present a self-consistent variational theory for weak polyelectrolytes which includes the effects of the polarizability of monovalent counterions. Our theory reproduces several experimental findings including non-monotonic conformation…
Interplay between counterion-mediated interaction and stiffness inherent to polymer chain can bring substantial complexity to the morphology and dynamics of polyelectrolyte brush condensates. Trivalent counterions induce collapse of flexible polyelectrolyte brushes, over a certain range of grafting density, into octopus-like surface micelles; however, if individual chains are rigid enough, the ion-mediated local nematic ordering assembles the brush chains into fractal-like dendritic condensates whose relaxation dynamics is significantly slower than that in the surface micelles. Notably, the tr…
Conformational properties of a single flexible polyelectrolyte chain in a poor solvent are studied using constant temperature molecular dynamics simulation. The effects of counterions are explicitly taken in to account. Structural properties of various phases and the transition between these phases are studied by tracking the values of asphericity, radius of gyration, fraction of condensed counterions, number of non-bonded neighbours and Coulomb interaction energies. From our simulations, we find strong evidence for a first-order phase transition from extended to collapsed phase consistent wit…
The effective elasticity of highly charged stiff polyelectrolytes is studied in the presence of counterions, with and without added salt. The rigid polymer conformations may become unstable due to an effective attraction induced by counterion density fluctuations. Instabilities at the longest, or intermediate length scales may signal collapse to globule, or necklace states, respectively. In the presence of added-salt, a generalized electrostatic persistence length is obtained, which has a nontrivial dependence on the Debye screening length.
By molecular dynamics simulation, we study the charge inversion phenomenon of a rod macroion in the presence of polyelectrolyte counterions. We simulate electrophoresis of the macroion under an applied electric field. When both counterions and coions are polyelectrolytes, charge inversion occurs if the line charge density of the counterions is larger than that of the coions. For the macroion of surface charge density equal to that of the DNA, the reversed mobility is realized either with adsorption of the multivalent counterion polyelectrolyte or the combination of electrostatics and other mec…
The article presents a comprehensive study of counterion dynamics around a generic linear polyelectrolyte (PE) chain with the help of coarse-grained computer simulations. The ion-chain coupling is discussed in the form of binding time, mean-square-displacement (MSD) relative to the chain, local ion transport coefficient, and spatio-temporal correlations in the effective charge. We have shown that a counterion exhibits sub-diffusive behavior $\langle δR^2 \rangle \sim t^δ$, $δ\approx0.9$ w.r.t. chain's centre of mass (COM). The MSD of ions perpendicularly outwards from the chain segment exhibit…
Counterion distribution around an isolated flexible polyelectrolyte in the presence of a divalent salt is evaluated using the adsorption model [M. Muthukumar, J. Chem. Phys. {\bf 120}, 9343 (2004)] that considers Bjerrum length, salt concentration, and local dielectric heterogeneity as physical variables in the system. Self consistent calculations of effective charge and size of polymer show that divalent counterions replace condensed monovalent counterions in competitive adsorption. The theory further predicts that at modest physical conditions, polymer charge is compensated and reversed with…
Strong coupling phenomena, such as the like charged macroions attraction, opposite charged macroions repulsion, charge renormalization or charge inversion, are known to be mediated by multivalent counterions. Most theories treat the counterions as point charges, and describe the system by a single coupling parameter that measures the strength of the Coulomb interactions. In many biological systems, the counterions are highly charged and have finite sizes and can be well-described by polyelectrolytes. The shapes and orientations of these polymer counterions play a major role in the thermodynami…
In this paper we analyze the behavior of hydrophobic polyelectrolytes. It has been proposed that this system adopts a pearl-necklace structure reminiscent of the Rayleigh instability of a charged droplet. Using a Poisson-Boltzmann approach, we calculate the counterion distribution around a given pearl assuming the latter to be penetrable for the counterions. This allows us to calculate the effective electric charge of the pearl as a function of the chemical charge. Our predictions are in very good agreement with the recent experimental measurements of the effective charge by Essafi et al. (Eur…
The concentration profiles of monomers and counterions in star-branched polyelectrolyte micelles are calculated through Monte-Carlo simulations, using the simplest freely-jointed chain model. We have investigated the onset of different regimes corresponding to the spherical and Manning condensation of counterions as a function of the strength of the Coulomb coupling. The Monte-Carlo results are in fair agreement with the predictions of Self-Consistent-Field analytical models. We have simulated a real system of diblock copolymer micelles of (sodium-polystyrene-sulfonate)(NaPSS)-- (polyethylene-…
We perform extensive molecular dynamics simulations of a charged polymer in a good solvent in the regime where the chain is collapsed. We analyze the dependence of the gyration radius $R_g $ on the reduced Bjerrum length $\ell_B$ and find two different regimes. In the first one, called as a weak electrostatic regime, $R_g \sim \ell_B^{-1/2}$, which is consistent only with the predictions of the counterion-fluctuation theory. In the second one, called a strong electrostatic regime, we find $R_g \sim \ell_B^{-1/5}$. To explain the novel regime we modify the counterion-fluctuation theory.
We study the bending rigidity of highly charged stiff polyelectrolytes, for both a single chain and many chains forming a bundle. A theory is developed to account for the interplay between competitive binding of counterions and charge correlations in softening the polyelectrolyte (PE) chains. The presence of even a small concentration of multivalent counterions leads to a dramatic reduction in the bending rigidity of the chains that are nominally stiffened by the repulsion between their backbone charges. The variation of the bending rigidity as a function of $f_{0}$, the fraction of charged mo…
Structural and thermodynamic properties of the model solution containing charged oligomers and the equivalent number of counterions were studied by means of the canonical Monte Carlo simulation technique. The oligomers are represented as (flexible) freely jointed chains or as a linear (rigid) array of charged hard spheres. In accordance with the primitive model of electrolyte solutions, the counterions are modeled as charged hard spheres and the solvent as dielectric continuum. Significant differences in the pair distribution functions, obtained for the rigid (rod-like) and flexible model are …
Recent experiments have shown that trivalent ion, spermidine$^{3+}$, can provoke lateral microphase segregation in DNA brushes. Using molecular simulations and simple theoretical arguments, we explore the effects of trivalent counterions on polyelectrolyte brushes. At a proper range of grafting density, polymer size, and ion concentration, the brush polymers collapse heterogeneously into octopus-like surface micelles. Remarkably, the heterogeneity in brush morphology is maximized and the relaxation dynamics of chain and condensed ion are the slowest at the 1:3 stoichiometric concentration of t…
We study the attractive interactions between rod-like charged polymers in solution that appear in the presence of multi-valence counterions. The counterions condensed to the rods exhibit both a strong transversal polarization and a longitudinal crystalline arrangement. At short distances between the rods, the fraction of condensed counterions increases, and the majority of these occupy the region between the rods, where they minimize their repulsive interactions by arranging themselves into packing structures. The attractive interaction is strongest for multivalent counterions. Our model takes…
Size Effect of Monovalent Ions on Polyelectrolyte Brushes
South China Advanced Institute for Soft Matter Science and Technology, School of Emergent Soft Matter, South China University of Technology（华南软物质科学与技术高等研究院， emergent soft matter 学院，华南理工大学）
Dilute solutions of strongly charged polymer electrolytes undergo, upon addition of multivaltent salt to the solutions, a phase transition from extended conformations to collapsed or bundled ones. Upon further addition of salt they experience a second transition, a redissolution back into extended conformations. This paper presents a theoretical study of the structure and properties of the phase diagram of these solutions. On the basis of simple phenomenological observations a schematic phase diagram is constructed that allows a simple and explicit determination of the direction of the tie lin…
We report results from a molecular dynamics (MD) simulation on the conformations of a long flexible polyelectrolyte complexed to a charged sphere, \textit{both negatively charged}, in the presence of neutralizing counterions in the strong Coulomb coupling regime. The structure of this complex is very sensitive to the charge density of the polyelectrolyte. For a fully charged polyelectrolyte the polymer forms a dense two-dimensional "disk", whereas for a partially charged polyelectrolyte the monomers are spread over the colloidal surface. A mechanism involving the \textit{overcharging} of the p…
The association between polyelectrolytes (PEs) of the same size but opposite charge is systematically studied in terms of the potential of mean force (PMF) along their center-of-mass reaction coordinate via coarse-grained, implicit-solvent, explicit-salt computer simulations. The focus is set on the onset and the intermediate, transient stages of complexation. At conditions above the counterion-condensation threshold, the PE association process exhibits a distinct sliding-rod-like behavior where the polymer chains approach each other by first stretching out at a critical distance close to thei…
We investigate end-effects in the ion distribution around strongly charged, flexible polyelectrolytes with a quenched charge distribution by molecular dynamics simulations of dilute polyelectrolyte solutions. We take the counterions explicitly into account and calculate the full Coulomb interaction via an Ewald summation method. We find that the free counterions of the solution are distributed in such a way that a fraction of the chain charges is effectively neutralized. This in turn leads to an effective charge distribution which is similar to those found for weakly charged titrating polyelec…
Similarly-charged polymers in solution, known as polyelectrolytes, are known to form aggregated structures in the presence of oppositely charged counterions. Understanding the dependence of the equilibrium phases and the dynamics of the process of aggregation on parameters such as backbone flexibility and charge density of such polymers is crucial for insights into various biological processes which involve biological polyelectrolytes such as protein, DNA etc., Here, we use large-scale coarse-grained molecular dynamics simulations to obtain the phase diagram of the aggregated structures of fle…
We study the salt-dependent conformations of dilute flexible polyelectrolytes in solution via computer simulations. Low concentrations of multivalent salt induce the known conformational collapse of individual polyelectrolyte chains, but as the salt concentration is increased further this is followed by a reexpansion. We explicitly demonstrate that multivalent counterions can overcompensate the bare charge of the chain in the reexpansion regime. Both the degree of reexpansion and the occurrence of overcharging sensitively depend on ion size. Our findings are relevant for a wide range of salt-i…
The structure of polyelectrolytes is highly sensitive to small changes in the interactions between its monomers. In particular, interactions mediated by counterions play a significant role, and are affected by both specific molecular effects and generic concentration effects. The ability of coarse-grained models to reproduce the structural properties of an atomic model is thus a challenging task. Our present study compares the ability of different kinds of coarse-grained models: (i)~to reproduce the structure of an atomistic model of a polyelectrolyte (the sodium polyacrylate), (ii)~to reprodu…
We report chain self-diffusion and viscosity data for sodium polystyrene sulfonate (NaPSS) in semidilute salt-free aqueous solutions measured by pulsed field gradient NMR and rotational rheometry respectively. The observed concentration dependence of $η$ and $D$ are consistent with the Rouse-Zimm scaling model with a concentration dependent monomeric friction coefficient. The concentration dependence of the monomeric friction coefficient exceeds that expected from free-volume models of diffusion, and its origin remains unclear. Correlation blobs and dilute chains with equivalent end-to-end dis…
Counterion adsorption on a flexible polyelectrolyte chain in a spherical cavity is considered by taking a "permuted" charge distribution on the chain so that the "adsorbed" counterions are allowed to move along the backbone. We compute the degree of ionization by using self-consistent field theory (SCFT) and compare with the previously developed variational theory. Analysis of various contributions to the free energy in both theories reveals that the equilibrium degree of ionization is attained mainly as an interplay of the adsorption energy of counterions on the backbone, the translational en…
We develop a first-principle equation of state of salt-free polyelectrolyte solution in the limit of infinitely long flexible polymer chains in the framework of a field-theoretical formalism beyond the linear Debye-Hueckel theory and predict a liquid-liquid phase separation induced by a strong correlation attraction. As a reference system we choose a set of two subsystems - charged macromolecules immersed in a structureless oppositely charged background created by counterions (polymer one component plasma) and counterions immersed in oppositely charged background created by polymer chains (har…
We present a theory for the equilibrium structure of polyelectrolyte solutions. The main element is a simple, new optimization scheme that allows theories such as the random phase approximation (RPA) to handle the harsh repulsive forces present in such systems. Comparison is made with data from recent neutron scattering experiments of randomly charged, hydrophilic polymers in salt-free, semi-dilute solution at various charge densities. Models with varying degrees of realism are examined. The usual explanation of the invariance observed at high charge density has been counterion condensation. H…
