Phase separation in salt-free symmetric mixtures of oppositely charged rodlike polyelectrolytes is studied using quasi-analytical calculations. Stability analyses for the isotropic-isotropic and the isotropic-nematic phase transitions in the mixtures are carried out and demonstrate that electrostatic interactions favor nematic ordering. Coexistence curves for the symmetric mixtures are also constructed and are used to examine the effects of linear charge density and electrostatic interaction strength on rodlike polyelectrolyte complexation. It is found that the counterions are uni- formly distributed in the coexisting phases for low electrostatic interaction strengths dictated by the linear charge density of the polyelectrolytes and Bjerrum's length. However, the counterions also partition along with the rodlike polyelectrolytes with an increase in the electrostatic interaction strength. It is shown that the number density of the counterions is higher in the concentrated (or "coacervate") phase than in the dilute (or supernatant) phase. In contrast to such rodlike mixtures, flexible polyelectrolyte mixtures can undergo only isotropic-isotropic phase separation. A comparison of the coexistence curves for weakly-charged rodlike mixtures with those of analogous flexible polyelectrolyte mixtures reveals that the electrostatic driving force for the isotropic-isotropic phase separation is stronger in the flexible mixtures.
We study the effect of electrostatic interactions on the distribution function of the end-to-end distance of a single polyelectrolyte chain in a rodlike configuration. We investigate the validity of the concept of electrostatic persistence length for uniformly charged wormlike chains for both screened and unscreened Coulomb interactions. We find that the distribution function of a polyelectrolyte often differs significantly from the distribution function of a wormlike chain.
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…
The interplay between electrostatic interactions and orientational correlations is studied for a model system of charged rods positioned on a chain, using Monte Carlo simulation techniques. It is shown that the coupling brings about the notion of {\em electrostatic frustration}, which in turn results in: (i) a rich variety of novel orientational orderings such as chiral phases, and (ii) an inherently slow dynamics characterized by stretched-exponential behavior in the relaxation functions of the system.
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…
In solutions of star-branched polyelectrolytes, electrostatic interactions between charged arms on neighboring stars can compete with intra-star interactions and rotational entropy to induce anisotropy in the orientational distribution of arms. For model stars comprising rigid rodlike arms with evenly spaced charged monomers interacting via an effective screened-Coulomb (Yukawa) potential, we explore the influence of arm orientational anisotropy on effective star-star interactions. Monte Carlo simulation and density-functional theory are used to compute arm orientational distributions and effe…
The ubiquitous biomacromolecule DNA has an axial rigidity persistence length of ~50 nm, driven by its elegant double helical structure. While double and multiple helix structures appear widely in nature, only rarely are these found in synthetic non-chiral macromolecules. Here we describe a double helical conformation in the densely charged aromatic polyamide poly(2,2'-disulfonyl-4,4'-benzidine terephthalamide) or PBDT. This double helix macromolecule represents one of the most rigid simple molecular structures known, exhibiting an extremely high axial persistence length (~1 micrometer). We pre…
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.
We consider the phase behavior of polymeric systems by calculating the structure factors beyond the Random Phase Approximation. The effect of this correction to the mean-field RPA structure factor is shown to be important in the case of coulombic systems. Two examples are given: simple electrolytes and mixtures of incompatible oppositely charged polyelectrolytes. In this last case, all former studies predicted an enhancement of compatibility for increasing charge densities; we also describe the complexation transition between the polyelectrolytes. We determine a phase diagram of the polyelectr…
The complexation of a polyelectrolyte with an oppositely charged spherical macroion is studied for both salt free and salty solutions. When a polyelectrolyte winds around the macroion, its turns repel each other and form an almost equidistant coil. It is shown that this repulsive correlations of turns lead to the charge inversion: more polyelectrolyte winds around the macroion than it is necessary to neutralize it. The charge inversion becomes stronger with increasing concentration of salt and can exceed 100%. This paper confirms that correlations are the universal mechanism of charge inversio…
In many biological processes highly charged biomolecules are adsorbed into oppositely charged surfaces of macroions and membranes. They form strongly correlated structures close to the surface which can not be explained by the conventional Poisson-Boltzmann theory. Many of the flexible biomolecules can be described by Gaussian polymers. In this work strong coupling theory is used to study the adsorption of highly charged Gaussian polyelectrolytes. Two cases of adsorptions are considered, when the Gaussian polyelectrolytes are confined a) by one charged wall, and b) between two charged walls. T…
We propose a detailed description of the structure of the layer formed by polyelectrolyte chains adsorbed onto an oppositely charged surface in the semi-dilute regime. We combine the mean-field Poisson-Boltzmann-Edwards theory and the scaling functional theory to describe the variations of the monomer concentration, the electrostatic potential, and the local grafting density with the distance to the surface. For long polymers, we find that the effective charge of the decorated surface (surface plus adsorbed polyelectrolytes) can be much larger than the bare charge of the surface at low salt co…
The behavior of highly charged short rod-like polyelectrolytes near oppositely charged planar surfaces is investigated by means of Monte Carlo simulations. A detailed microstructural study, including monomer and fluid charge distribution, and chain orientation, is provided. The influence of chain length, substrate's surface-charge-density and image forces is considered. Due to the lower chain-entropy (compared to flexible chains), our simulation data show that rod-like polyelectrolytes can, in general, better adsorb than flexible ones do. Nonetheless, at low substrate-dielectric-constant, it i…
Complexation in symmetric solutions of oppositely charged polyelectrolytes is studied theoretically. We include polyion crosslinking due to formation of thermoreversible ionic pairs. The electrostatic free energy is calculated within the Random Phase Approximation taking into account the structure of thermoreversible polyion clusters. The degree of ion association is obtained self-consistently from a modified law of mass action, which includes long-range electrostatic contributions. We analyze the relative importance of the three complexation driving forces: long-range electrostatics, ion asso…
We study by Small Angle Neutron Scattering (SANS) the structure of Hyaluronan -Lysozyme complexes. Hyaluronan (HA) is a polysaccharide of 9 nm intrinsic persistence length that bears one negative charge per disaccharide monomer (Mmol = 401.3 g/mol); two molecular weights, Mw = 6000 and 500 000 Da were used. The pH was adjusted at 4.7 and 7.4 so that lysozyme has a global charge of +10 and + 8 respectively. The lysozyme concentration was varied from 3 to 40 g/L, at constant HA concentration (10 g/L). At low protein concentration, samples are monophasic and SANS experiments reveal only fluctuati…
Complexation of a Thermoresponsive Brush-Type Polyelectrolyte with an Oppositely Charged Surfactant: Effect of Temperature and Surfactant Concentration
The transport of polyelectrolytes confined by oppositely charged surfaces and driven by a constant electric field is of interest in studies of DNA separation according to size. Using molecular dynamics simulations that include surface polarization effect, we find that the mobilities of the polyelectrolytes and their counterions change non-monotonically with the confinement surface charge density. For an optimum value of the confinement charge density, efficient separation of polyelectrolytes can be achieved over a wide range of polyelectrolyte charge due to the differential friction imparted b…
We present a simple model to study micellization of amphiphiles condensed on a rodlike polyion. Although the mean field theory leads to a first order micellization transition for sufficiently strong hydrophobic interactions, the simulations show that no such thermodynamic phase transition exists. Instead, the correlations between the condensed amphiphiles can result in a structure formation very similar to micelles.
Complexation of a long flexible polyelectrolyte (PE) molecule with oppositely charged spherical particles such as colloids, micelles, or globular proteins in a salty water solution is studied. PE binds spheres winding around them, while spheres repel each other and form almost periodic necklace. If the total charge of PE is larger than the total charge of spheres, repulsive correlations of PE turns on a sphere lead to inversion of the net charge of each sphere. In the opposite case, we predict another correlation effect: under-screened by PE spheres bind to PE in such a great number that they …
We study the effect of electrostatic interactions on the distribution function of the end-to-end distance of a single polyelectrolyte chain in the rodlike limit. The extent to which the radial distribution function of a polyelectrolyte is reproduced by that of a wormlike chain with an adjusted persistence length is investigated. Strong evidence is found for a universal scaling formula connecting the effective persistence length of a polyelectrolyte with its linear charge density and the Debye screening of its self-interaction. An alternative definition of the electrostatic persistence length i…
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 …
Interplay of Coulomb interaction energy, free ion entropy, and conformational elasticity is a fascinating aspect in polyelectrolytes (PEs). We develop a theory for complexation of two oppositely charged PEs, a process known to be the precursor to the formation of complex coacervates in PE solutions, to explore the underlying thermodynamics of complex formation, at low salts. Explicit calculation of the free energy of complexation and its components indicates that the entropy of free counterions and salt ions and the Coulomb enthalpy of bound ion-pairs dictate the equilibrium of PE complexation…
The adsorption of three different polycations at the negatively charged surface of tubular J-aggregates of the amphiphilic cyanine dye 3,3'-bis(2-sulfopropyl)-5,5',6,6'-tetrachloro-1,1'-dioctylbenzimidacarbocyanine (C8S3) is investigated by means of cryogenic electron microscopy and optical absorption spectroscopy. All three polycations could be adsorbed at the aggregates without flocculation or precipitation when added in molar amounts of monomers sufficiently smaller than of the dye molecules. Preferably the aggregates are either coated by the polycations in total or left completely uncoated…
The "polymer reference interaction site model" (PRISM) integral equation formalism is used to determine the pair structure of binary colloidal dispersions involving large and small polyions of opposite charge. Two examples of such bidisperse suspensions are considered in detail, namely mixtures of charged spherical colloids and oppositely charged polyelectrolyte chains, and binary mixtures of oppositely charged large and small clay platelets. In both cases clear evidence is found for aggregation of the larger particles induced by the polyionic counterions, signalled by a strong enhancement of …
Using self-assembly techniques, x-ray reflectivity measurements, and computer simulations, we study the effective interaction between charged polymer rods and surfaces. Long-time Brownian dynamics simulations are used to measure the effective adhesion force acting on the rods in a model consisting of a planar array of uniformly positively charged, stiff rods and a negatively charged planar substrate in the presence of explicit monovalent counterions and added monovalent salt ions in a continuous, isotropic dielectric medium. This electrostatic model predicts an attractive polymer-surface adhes…
We investigate theoretically polyelectrolyte bridging interactions on the two-body level. The model system is composed of two macroions with two oppositely charged flexible chains. The electrostatic interactions are treated on the Debye - H\" uckel level. The formal level of the theory is provided by the Feynman-Kleinert variational method generalized to include also self-interactions between polyelectrolyte segments. The variational equations are shown to exhibit two solution branches corresponding to {\sl strong} and {\sl weak} coupling, whereas conformations of the chain can be described as…
The formation of inter-polyelectrolyte complexes from the association of oppositely charged polymers in an electrolyte is studied. The charged polymers are linear oppositely charged polyelectrolytes, with possibly a neutral block. This leads to complexes with a charged core, and a more dilute corona of dangling chains, or of loops (flower-like structure). The equilibrium aggregation number of the complexes (number of polycations m+ and polyanions m-) is determined by minimizing the relevant free energy functional, the Coulombic contribution of which is worked out within Poisson-Boltzmann theor…
We study the complex formation between one long polyanion chain and many short oligocation chains by computer simulations. We employ a coarse-grained bead-spring model for the polyelectrolyte chains, and model explicitly the small salt ions. We systematically vary the concentration and the length of the oligocation, and examine how the oligocations affects the chain conformation, the static structure factor, the radial and axial distribution of various charged species, and the number of bound ions in the complex. At low oligocation concentration, the polyanion has an extended structure. Upon i…
We analyze, by means of an RPA calculation, the conditions under which a mixture of oppositely charged polyelectrolytes can micro-segregate in the neighborhood of a charged surface creating a layered structure. A number of stable layers can be formed if the surface is sufficiently strongly charged even at temperatures at which the bulk of the mixture is homogeneous.
Based on extensive Monte Carlo simulations and analytical considerations we study the electrostatically driven adsorption of flexible polyelectrolyte chains onto charged Janus nanospheres. These net-neutral colloids are composed of two equally but oppositely charged hemispheres. The critical binding conditions for polyelectrolyte chains are analysed as function of the radius of the Janus particle and its surface charge density, as well as the salt concentration in the ambient solution. Specifically for the adsorption of finite-length polyelectrolyte chains onto Janus nanoparticles, we demonstr…
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.
The adsorption of highly \textit{oppositely} charged flexible polyelectrolytes (PEs) on a charged planar substrate is investigated by means of Monte Carlo (MC) simulations. We study in detail the equilibrium structure of the first few PE layers. The influence of the chain length and of a (extra) non-electrostatic short range attraction between the polycations and the negatively charged substrate is considered. We show that the stability as well as the microstructure of the PE layers are especially sensitive to the strength of this latter interaction. Qualitative agreement is reached with some …
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…
Complex coacervation, known as the liquid-liquid phase separation of solutions with oppositely charged polyelectrolytes, has attracted substantial interest in recent years. We study the effect of the charge regulation (CR) mechanism on the complex coacervation by including short-range interactions between the charged sites on the polymer chains as well as an association-dissociation energy parameter in the CR mechanism. We investigate the phase diagrams of two CR models: (i) the hopping CR model (HCR) and (ii) the asymmetric CR model (ACR). It is shown that during the phase separation that the…
We briefly discuss our recent field-theoretic study of polyelectrolyte complexation, which occurs in solutions of two oppositely charged polyelectrolytes. Charged systems require theoretical methods beyond the mean-field (or self-consistent field) approximation; indeed, mean-field theory is qualitatively incorrect for such polyelectrolyte solutions. Both analytical (one-loop) and numerical (complex Langevin) methods to account for charge correlations are discussed. In particular, the first application of field-theoretic simulations to polyelectrolyte systems is reported. The polyelectrolyte ch…
We present real-time observations by confocal microscopy of the dynamic behavior of multilamellar vesicles (MLVs), composed of charged synthetic lipids, when put in contact with oppositely charged polyelectrolyte (PE) molecules. We find that the MLVs exhibit astonishing morphological transitions, which result from the discrete and progressive binding of the charged bilayers induced by a high PE concentration gradient. Our physical picture is confirmed by quantitative measurements of the fluorescence intensity as the bilayers bind to each other. The shape transitions lead eventually to the spon…
The adsorption of highly \textit{oppositely} charged flexible polyelectrolytes onto a charged spherical surface is investigated by means of Monte Carlo simulations in a fashion which resembles the layer-by-layer deposition technique introduced by Decher. Electroneutrality is insured at each step by the presence of monovalent counterions (anions and cations). We study in detail the structure of the \textit{equilibrium} complex. Our investigations of the first few layer formations strongly suggest that multilayering in spherical geometry is not possible as an equilibrium process with purely elec…
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 distrib…
In systems of highly charged linear polyelectrolytes and oppositely charged colloidal particles, long-lived clusters of polyelectrolyte-decorated particles form in an interval of concentrations around the isoelectric point, where reentrant condensation connected to charge inversion of cluster is observed. The mechanisms that drive the aggregation and stabilize, at the different polymer/particle ratios, a well defined size of the aggregates are not completely understood. Moreover, a central question still remains unanswered, i.e., whether the clusters are true equilibrium or metastable aggregat…
We study the adsorption-desorption transition of polyelectrolyte chains onto planar, cylindrical and spherical surfaces with arbitrarily high surface charge densities by massive Monte Carlo computer simulations. We examine in detail how the well known scaling relations for the threshold transition-demarcating the adsorbed and desorbed domains of a polyelectrolyte near weakly charged surfaces-are altered for highly charged interfaces. In virtue of high surface potentials and large surface charge densities, the Debye-Hueckel approximation is often not feasible and the nonlinear Poisson-Boltzmann…
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…
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…
Study of the Liquid/Vapor Interfacial Properties of Concentrated Polyelectrolyte-Surfactant Mixtures Using Surface Tensiometry and Neutron Reflectometry: Equilibrium, Adsorption Kinetics and Dilational Rheology
We study mixtures of charged surfactants, which alone in solution form uni- and multilamellar vesicles, and oppositely charged polyelectrolytes (PEs). The phase behavior is investigated at fixed surfactant concentration as a function of the PE-to-surfactant charge ratio $x$. We find that, for $x>0$, aggregates form. Light microscopy and X-ray scattering experiments show that the isoelectric point plays a crucial role since the morphology and the microscopic structure of the aggregates are different before ($x\leq1$) and after the isoelectric point ($x>1$). To better understand the dynamics for…
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…
We consider the complexation of highly charged semiflexible polyelectrolytes with oppositely charged macroions. On the basis of scaling arguments we discuss how the resulting complexes depend on the persistence length of the polyelectrolyte, the salt concentration, and the sizes and charges of the chain and the macroions. We study first the case of complexation with a single sphere and calculate the wrapping length of the chain. We then extend our considerations to complexes involving many wrapped spheres and study cooperative effects. The mechanical properties of such a complex under an exter…
We study the structure of complexes formed between ionic surfactants (SF) and a single oppositely charged polyelectrolyte (PE) chain. For our computer simulation we use the ``primitive'' electrolyte model: while the polyelectrolyte is modeled by a tethered chain of charged hard sphere beads, the surfactant molecules consist of a single charged head bead tethered to a tail of tethered hard spheres. A hydrophobic attraction between the tail beads is introduced by assuming a Lennard-Jones potential outside the hard-sphere diameter. As a function of the strengths of both the electrostatic and the …
We study the effective interaction between differently charged polyelectrolyte-colloid complexes in electrolyte solutions via Monte Carlo simulations. These complexes are formed when short and flexible polyelectrolyte chains adsorb onto oppositely charged colloidal spheres, dispersed in an electrolyte solution. In our simulations the bending energy between adjacent monomers is small compared to the electrostatic energy, and the chains, once adsorbed, do not exchange with the solution, although they rearrange on the particles surface to accomodate further adsorbing chains or due to the electros…
When polyelectrolyte-neutral block copolymers are mixed in solutions to oppositely charged species (e.g. surfactant micelles, macromolecules, proteins etc), there is the formation of stable supermicellar aggregates combining both components. The resulting colloidal complexes exhibit a core-shell structure and the mechanism yielding to their formation is electrostatic self-assembly. In this contribution, we report on the structural properties of supermicellar aggregates made from yttrium-based inorganic nanoparticles (radius 2 nm) and polyelectrolyte-neutral block copolymers in aqueous solution…
We theoretically study the polarizability and the interactions of neutral complexes consisting of a semi-flexible polyelectrolyte adsorbed onto an oppositely charged spherical colloid. In the systems we studied, the bending energy of the chain is small compared to the Coulomb energy and the chains are always adsorbed on the colloid. We observe that the polarizability is large for short chains and small electrical fields and shows a non-monotonic behavior with the chain length at fixed charge density. The polarizability has a maximum for a chain length equal to half of the circumference of the …
Controlling the assembly of polyelectrolytes and surfactant at liquid-liquid interfaces offers new ways to fabricate soft materials with specific physical properties. However, little is known of the relationships between the kinetics of interfacial assembly, structural and rheological properties of such interfaces. We studied the kinetics at water-oil interface of the assembly of a positively charged biopolymer, chitosan, with an anionic fatty acid using a multi-scale approach. The growth kinetics of the membrane was followed by interfacial rheometry and space- and time- resolved dynamic light…
We report on the electrostatic complexation between polyelectrolyte-neutral copolymers and oppositely charged 6 nm-crystalline nanoparticles. For two different dispersions of oxide nanoparticles, the electrostatic complexation gives rise to the formation of stable nanoparticle clusters in the range 20 - 100 nm. It is found that inside the clusters, the particles are pasted together by the polyelectrolyte blocks adsorbed on their surface. Cryo-transmission electronic microscopy allows to visualize the clusters and to determine the probability distributions functions in size and in aggregation n…
We predict the nature (attractive or repulsive) and range (exponentially screened or long-range power law) of the electrostatic interactions of oppositely charged and planar plates as a function of the salt concentration and surface charge densities (whose absolute magnitudes are not necessarily equal). An analytical expression for the crossover between attractive and repulsive pressure is obtained as a function of the salt concentration. This condition reduces to the high-salt limit of Parsegian and Gingell where the interaction is exponentially screened and to the zero salt limit of Lau and …
