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 entropy of the small ions, and their correlated density fluctuations. Degree of ionization computed from SCFT is significantly lower than that from the variational formalism. The difference is entirely due to the density fluctuations of the small ions in the system, which are accounted for in the variational procedure. When these fluctuations are deliberately suppressed in the truncated variational procedure, there emerges a remarkable quantitative agreement in the various contributing factors to the equilibrium degree of ionization, in spite of the fundamental differences in the approximations and computational procedures used in these two schemes. Nevertheless, since the significant effects from density fluctuations of small ions are not captured by the SCFT, and due to the close agreement between SCFT and the other contributing factors in the more transparent variational procedure, the latter is a better computational tool for obtaining the degree of ionization.
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.
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.
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.
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.
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…
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…
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…
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…
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…
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 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…
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…
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…
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…
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…
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…
In a recent Letter, Gurovitch and Sens studied the adsorption of a weakly charged polyelectrolyte chain onto an oppositely charged colloidal particle. By using a variational technique they found that the colloidal particle can adsorb a polymer of higher charge than its own, and thus be ``overcharged.'' I argue that the observed overcharging by a factor of 16/5 is indeed an artifact of the approximations involved in the study. Moreover, I show that the existence of overcharging depends crucially on the choice of the trial wave function, contrary to their claim.
Understanding the behavior of charged complex fluids is crucial for a plethora of important industrial, technological, and medical applications. Using coarse-grained molecular dynamics simulations, here we investigate the properties of a polyelectrolyte solution, with explicit counterions and implicit solvent, that is driven by a steady electric field. By properly tuning the interplay between interparticle electrostatics and the applied electric field, we uncover two nonequilibrium continuous phase transitions as a function of the driving field. The first transition occurs from a homogeneously…
The adsorption of flexible and highly charged polyelectrolytes onto oppositely charged planar surfaces is investigated by means of Monte Carlo simulations. The effect of image forces stemming from the dielectric discontinuity at the substrate interface is considered. The influence, at fixed polyelectrolyte volume fraction, of chain length and surface-charge density is also considered. A detailed structural study, including monomer and fluid charge distributions, is provided. It is demonstrated that image forces can considerably reduce the degree of polyelectrolyte adsorption and concomitantly …
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 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…
Mean-field theory and scaling arguments are presented to model polyelectrolyte adsorption from semi-dilute solutions onto charged surfaces. Using numerical solutions of the mean-field equations, we show that adsorption exists only for highly charged polyelectrolytes in low salt solutions. Simple scaling laws for the width of the adsorbed layer and the amount of adsorbed polyelectrolyte are obtained. In other situations the polyelectrolyte chains will deplete from the surface. For fixed surface potential conditions, the salt concentration at the adsorption--depletion crossover scales as the pro…
A theory is presented which quantitatively accounts for the cooperative adsorption of cationic surfactants to anionic polyelectrolytes. For high salt concentration we find that the critical adsorption concentration (CAC) is a bilinear function of the polyion monomer and salt concentrations, with the coefficients dependent only on the type of surfactant used. The results presented in the paper might be useful for designing more efficient gene delivery systems.
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…
The problem of charged polymer chains (polyelectrolytes) as they adsorb on a planar surface is addressed theoretically. We review the basic mechanisms and theory underlying polyelectrolyte adsorption on a single surface in two situations: adsorption of a single charged chain, and adsorption from a bulk solution in $θ$ solvent conditions. The behavior of flexible and semi-rigid chains is discussed separately and is expressed as function of the polymer and surface charges, ionic strength of the solution and polymer bulk concentration. We mainly review mean-field results and briefly comment about…
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 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…
The charge of a polyelectrolyte (PE) controls myriads of phenomena in biology, biotechnology, and materials science, but still remains elusive from an understanding. Considering the adsorption of counterions on an isolated PE chain, an analytical expression for the effective charge - valid for all chain flexibility, for variable salt, in good solvents at all conditions, in poor solvents in the expanded (coil) state away from the critical point, and for gels, brushes and other PE systems in their expanded state - is derived. Phase boundaries and the critical point for the I-st order collapse tr…
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…
A lattice of uniformly charged, infinitesimally thin, rods decorated with an ordered array of counterions exhibits anomalous behavior as the spacing between the rods is varied. In particular, the counterion lattice undergoes a sequence of structural shearing, or "tilting," phase transformations as the spacing between the rods decreases. The potential implications of this behavior with respect to the packaging of biologically relevant polyelectrolytic molecules are commented upon.
We demonstrated recently that polyelectrolytes with cationic moieties along the chain and a single anionic head are able to form physical hydrogels due to the reversible nature of the head-to-body ionic bond. Here we generate a variety of such polyelectrolytes with various cationic moieties and counterion combinations starting from a common polymeric platform. We show that the rheological properties (shear modulus, critical strain) of the final hydrogels can be modulated over three orders of magnitude depending on the cation/anion pair. Our data fit remarkably well within a scaling model invol…
The modification of the boundary condition for polyelectrolyte adsorption on charged surface with short-ranged interaction is investigated under two regimes. For weakly charged Gaussian polymer in which the short-ranged attraction dominates, the boundary condition is the same as that of the neutral polymer adsorption. For highly charged polymer (compressed state) in which the electrostatic interaction dominates, the linear relationship (electrostatic boundary condition) between the surface monomer density and the surface charge density needs to be modified.
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…
In the present study, we have investigated, using Monte Carlo simulations (MC), the adsorption of polyelectrolytes on the charged nanopatterned surfaces. Different surface patterns were considered and we noticed that the amount of adsorption is directly dependent on the size of the domains. Also in the case of checkerboard configuration, it was observed that the polyelectrolytes are aligned along the diagonal of square domains.
Understanding and controlling polyelectrolyte adsorption onto carbon nanotubes is a fundamen- tal challenge in nanotechology. Polyelectrolytes have been shown to stabilise nanotube suspensions through adsorbing onto the nanotube surface, and polyelectrolyte-coated nanotubes are emerging as building blocks for complex and addressable self-assembly. The conventional wisdom suggests that polyelectrolyte adsorption onto nanotubes is driven by specific chemical or van der Waals interac- tions. We develop a simple mean-field model and show that ion-image attraction is a significant effect for adsorp…
The collapse of flexible polyelectrolytes in a solution of multivalent counterions is studied by means of a two state model. The states correspond to rod-like and spherically collapsed conformations respectively. We focus on the very dilute monomer concentration regime where the collapse transition is found to occur when the charge of the multivalent salt is comparable (but smaller) to that of the monomers. The main contribution to the free energy of the collapsed conformation is linear in the number of monomers $N$, since the internal state of the collapsed polymer approaches that of an amorp…
Adsorption of charged polymers (polyelectrolytes) from a semi-dilute solution to a charged surface is investigated theoretically. We obtain simple scaling laws for (i) the amount of polymer adsorbed to the surface, Gamma, and (ii) the width of the adsorbed layer D, as function of the fractional charge per monomer p and the salt concentration c_b. For strongly charged polyelectrolytes (p<1) in a low-salt solution, both Gamma and D scale as p^{-1/2}. In salt-rich solutions D~c_b^{1/2}/p whereas the scaling behavior of Gamma depends on the strength of the polymer charge. For weak polyelectrolytes…
The adsorption of highly charged flexible polycations and polyanions on a charged cylindrical substrate is investigated by means of Monte Carlo (MC) simulations. A detailed structural study, including monomer and fluid charge distributions, is provided. The influence of a short range attraction between the polycations and the negatively charged substrate is also considered. We demonstrate that the building up of multilayer structures is highly prohibited mainly due to the high entropy penalty stemming from the low dimensionality of the substrate at strong curvature.
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…
We studied polyelectrolyte adsorption on a repulsive charged surface by scaling analysis. At low ionic strength and low surface charge density in which a single polyelectrolyte is able to be adsorbed onto the surface, different regimes in the phase diagram are identified. The possibility of multi-layer structure formed by polyelectrolytes of like charge is also investigated.
