Self-similarity of nonlinear screening in asymmetric complex plasmas

In this paper, two-component electroneutral systems of finite-sized macroions and oppositely charged point-like microions in the average spherical electroneutral Wigner–Seitz cell with a central macroion are studied. We investigate the self-similarity of nonlinear screening of highly charged macroions by microions in a classical asymmetrically charged complex plasma. This work is devoted to the problem of the relationship between the effective (‘visible’) charge of the macroion Z^* and its initial charge Z taking into account the effect of the nonlinear screening. It is analysed how the form of the dependence Z^*(Z) changes. The self-similarity of this dependence has been demonstrated for various characteristic system temperatures, macroion concentrations, and macroion sizes.     

Salt-modulated structure of polyelectrolyte-macroion complex fibers

The structure and stability of strongly charged complex fibers, formed by complexation of a single long semi-flexible polyelectrolyte chain and many oppositely charged spherical macroions, are investigated numerically at the ground-state level using a chain-sphere cell model. The model takes into account chain elasticity as well as electrostatic interactions between charged spheres and chain segments. Using a numerical optimization method based on a periodically repeated unit cell, we obtain fiber configurations that minimize the total energy. The optimal fiber configurations exhibit a variety of helical structures for the arrangement of macroions including zig-zag, solenoidal and beads-on-a-string patterns. These structures result from the competition between attraction between spheres and the polyelectrolyte chain (which favors chain wrapping around the spheres), chain bending rigidity and electrostatic repulsion between chain segments (which favor unwrapping of the chain), and the interactions between neighboring sphere-chain complexes which can be attractive or repulsive depending on the system parameters such as salt concentration, macroion charge and chain length per macroion (linker size). At about physiological salt concentration, dense zig-zag patterns are found to be energetically most stable when parameters appropriate for the DNA-histone system in the chromatin fiber are adopted. In fact, the predicted fiber diameter in this regime is found to be around 30 nanometers, which roughly agrees with the thickness observed in in vitro experiments on chromatin. We also find a macroion (histone) density of 5–6 per 11nm which agrees with results from the zig-zag or cross-linker models of chromatin. Since our study deals primarily with a generic chain-sphere model, these findings suggest that structures similar to those found for chromatin should also be observable for polyelectrolyte-macroion complexes formed in solutions of DNA and synthetic nano-colloids of opposite charge. In the ensemble where the mean linear density of spheres on the chain is fixed, the present model predicts a phase separation at intermediate salt concentrations into a densely packed complex phase and a dilute phase.     

Macroion effective charge in complex plasmas with regard to microion correlations

In the present paper, features of high-charged macroions screening by microions are analysed in classical asymmetrically charged complex plasmas. We consider a two-component electroneutral system of classical macroions and oppositely charged microions in a spherically symmetrical electroneutral Wigner–Seitz cell with a central macroion in its centre. The present paper is devoted to a problem of a relation between the effective macroion charge and an initial one with regard to a non-linear screening effect and microions correlations. We show how this relation changes with the number of the central macroion charge value on the rise. Characteristics of two different parts of the relation between the effective charge and the initial one are calculated.     

Bending of charged flexible membranes due to the presence of macroions

We investigate the bending of flexible charged membranes due to the presence of rigid rodlike macroions in the framework of the Debye-Hückel approximation. When the macroions are fixed in space at some distance from the bilayer the membrane bends towards them; we calculate the exact deformation profile. On the other hand a macroion which is adsorbed on the membrane causes a deflection of the bilayer. Finally, we consider swollen lamellar polyanion/charged-lipid complexes where the macroions are intercalated between charged lipid bilayers. We predict the occurrence of a double adsorption (pinching effect) of the macroion for sufficiently flexible membranes. Received: 9 February 1998 / Revised: 9 June 1998 / Accepted: 2 July 1998     

Solvent and nonlinear effects on the charge renormalization of nanoparticles within a molecular electrolyte model

A general analysis of the effect of the molecular structure of a polar solvent on the effective interactions among suspended charged nanoparticles (macroions up to 30 nm in size) is performed using a simple molecular model for the solvent in the supporting electrolyte. The solvent molecules are modeled as small rods with end point charges of opposite sign and equal magnitude, whereas the small ions are assumed to be point-like. We compare the renormalized charges of the effective pair potentials (EPPs) among the spherical nanoparticles, obtained after contracting the supporting electrolyte, with those obtained from a similar model, which does not include the solvent molecules. The parameters of both models have been adjusted to give the same screening length. The comparison shows that the renormalized charges are overestimated when the molecular structure of the solvent is neglected. This is in agreement with the image charge effect induced by the different permittivities inside and outside the nanoparticles for the model with explicit solvent molecules; an effect that is missing in the model without solvent molecules. A new numerical method allows us to explore macroion diameters much larger than the solvent molecular size.     

Effect of the non‐linear screening on a modification of the Debye–Hückel plus hole approximation in complex plasma

The authors analyse two‐component electroneutral systems of classical macroions of finite size and point‐like oppositely charged microions. This article deals with the modification of the Debye–Hückel plus hole approximation when a non‐linear screening effect is taken into account in a complex plasma. Parameters of non‐linear screening of the macroions by surrounding microions are calculated within the framework of the Poisson–Boltzmann approximation. Two effects are found as a result of such calculations: (a) subdivision of all microions into two subclasses, free microions and bound microions and (b) a significant reduction of an effective charge Z^* of the macroion in comparison with its true value Z due to the non‐linear screening by a thin high‐density envelope of the bound microions. We show that the value of a non‐ideal portion of an internal energy differs considerably in the case when the non‐linear screening effect is taken into account in the vicinity of the macroion.     

The Laplace transform of the MSA pair distribution functions between macroions in an ion-dipole fluid

The Laplace transform is obtained for the pair distribution function between a pair of ions, an ion and a macroion, and a pair of macroions in an ion-dipole fluid. This fluid is a simplified model of an electrolyte with a discrete model of solvent (hard spheres with embedded point dipoles). From these results, an expression for the solvation force between macroions is obtained. This result consists of the classical DLVO result plus a series of corrections.     

Rescaled mean spherical approximation structure factor for an aqueous suspension of polystyrene spheres

Rescaled mean spherical approximation (RMSA) has been used to calculate the structure factor for the aqueous suspension of polystyrene macroions with the interaction potential taken according to Derjaguin and Landau (1941) and Verwey and Overbeek (1948) (DLVO) model. The effects of charge over the macroion and size on the surface potential and therefore, the structure factor have been studied. The breakdown of the DLVO potential with an excess charge over the macroion (⩾800e) has been reported. The oscillation in the first peak height of structure factor versus wave vector curve with size has been correlated with the Debye length.     

Strong attraction between charged spheres due to metastable ionized states

We report a mechanism which can lead to long-range attractions between like-charged spherical macroions, stemming from the existence of metastable ionized states. We show that the ground state of a single highly charged colloid plus a few excess counterions is overcharged. For the case of two highly charged macroions in their neutralizing divalent counterion solution we demonstrate that, in the regime of strong Coulomb coupling, the counterion clouds are very likely to be unevenly distributed, leading to one overcharged and one undercharged macroion. This long-living metastable configuration in turn leads to a long-range Coulomb attraction.     

Macroion-induced compositional instability of binary fluid membranes

Macroion adsorption on a mixed, fluid, lipid membrane containing oppositely charged lipids induces local changes in lipid composition at the interaction zones, and gradients at their boundaries. Including these effects in the free energy of the macroion-dressed membrane we derive its spinodal equation, and show that nonideal lipid mixing can lead to (lipid-mediated) attraction between macroions and lateral phase separation in the composite membrane. The critical nonideality for this transition is substantially smaller than that of the bare lipid membrane, decreasing with macroion size and charge. That is, the lipid membrane is destabilized by macroion adsorption.     

Landau–Ginzburg theory for ‘star’-shaped droplets

ABSTRACT

Molecular simulations have shown that when a nano-drop comprising a single spherical central ion and a dielectric solvent is charged above a well-defined threshold, it acquires a stable star morphology. A linear continuum model of the ‘star’-shapes comprised electrostatic and surface energy is not sufficient to describe these shapes. We employ combined molecular dynamics, continuum electrostatics and macroscopic modelling in order to construct a unified free energy functional that describes the observed star-shaped droplets. We demonstrate that the Landau free energy coupled to the third-order Steinhardt invariant mimics the shapes of droplets detected in molecular simulations. Using the maximum likelihood technique we build a universal free energy functional that describes droplets for a range of Rayleigh fissility parameter. The analysis of the macroscopic free energy demonstrates the origin of the finite amplitude perturbations just above the Rayleigh limit. We argue that the presence of the finite amplitude perturbations precludes the use of the small parameter perturbation method for the analysis of the shapes above the Rayleigh limit of the corresponding spherical shape.     

The distribution of counterions around synthetic rod-like polyelectrolytes in solution

An investigation of the radial distribution of the counterions of a synthetic rodlike polyelectrolyte in aqueous solution is presented. The cationic polyelectrolyte used here has a poly(p-phenylene) backbone. For typical molecular weights the macroion comprises approximately one persistence length (ca. 20 nm) and effects of finite stiffness may be disregarded. Each repeating unit bears four charges which leads to a charge parameter of ξ = 6.65. The distribution of the iodide counterions around this highly charged macroion is studied by small-angle X-ray scattering (SAXS) in dilute aqueous solution. These investigations are supplemented by measurements using anomalous small-angle X-ray scattering (ASAXS) that furnishes additional information about the contrast of the macroion. Data taken at high scattering angles give indication for contributions caused by the longitudinal fluctuations of the counterions. After correction for this effect the experimental results are compared to intensities calculated by use of the Poisson-Boltzmann (PB)-cell model. It is found that the PB-cell model describes the corrected data at intermediate and high scattering angles. Deviations at low scattering angle are attributed to the mutual interaction of the rod-like polyelectrolyte that can be described in terms of an effective structure factor. Data taken at lowest scattering angles point to a weak attraction between the rod-like macroions. Received: 27 July 2001 and Received in final form 27 March 2002     

Zeta potential of colloidal particle in solvent primitive model electrolyte solution: a density functional theory study

A systematic study of zeta potential for a spherical double layer (SDL) around a colloidal particle in electrolyte solutions, is performed using density functional theory and Monte Carlo simulation. The usual recipe under the solvent primitive model is employed to model the system, where macroion, counterions, and coions are represented by charged hard spheres of uniform charge density and the presence of solvent is taken into account by modelling it as neutral hard spheres. All the components of the system are embedded in a dielectric continuum in order to consider the electrostatic effect of the solvent. The density functional theory employs a suitable weighted density approximation to calculate the hard-sphere contribution, whereas the residual electrostatic interactions are calculated as a small perturbation around the uniform fluid. The zeta potential profiles of a SDL in the presence of a number of electrolytes have been calculated and are found to be considerably influenced in the presence of solvent with an increase in the concentration of the electrolyte. The theory successfully predicts the maxima and sign reversal of the zeta potential profiles at high macroion surface charge density and in the presence of multivalent counterions, as obtained from the Monte Carlo simulation.     

Electrostatic field and charge distribution in small charged dielectric droplets

The charge distribution in small dielectric droplets is calculated on the basis of continuum medium approximation. There are considered charged liquid spherical droplets of methanol in the range of nanometer sizes. The problem is solved by the following way. We find the free energy of some ion in dielectric droplet, which is a function of distribution of other ions in the droplet. The probability of location of the ion in some element of volume in the droplet is a function of its free energy in this element of volume. The same approach can be applied to other ions in the droplet. The obtained charge distribution differs considerably from the surface distribution. The curve of the charge distribution in the droplet as a function of radius has maximum near the surface. Relative concentration of charges in the vicinity of the center of the droplet does not equal to zero, and it is the higher, the less is the total charge of the droplet. According to the estimates the model is applicable if the droplet radius is larger than 10 nm.     

Electrophoresis of a charge-inverted macroion complex: Molecular-dynamics study

We have performed molecular-dynamics simulations to study the effect of an external electric field on a macroion in the solution of multivalent Z : 1 salt. To obtain plausible hydrodynamics of the medium, we explicitly make the simulation of many neutral particles along with ions. In a weak electric field, the macroion drifts together with the strongly adsorbed multivalent counterions along the electric field, in the direction proving inversion of the charge sign. The reversed mobility of the macroion is insensitive to the external field, and increases with salt ionic strength. The reversed mobility takes a maximal value at intermediate counterion valence. The motion of the macroion complex does not induce any flow of the neutral solvent away from the macroion, which reveals screening of hydrodynamic interactions at short distances in electrolyte solutions. A very large electric field, comparable to the macroion unscreened field, disrupts charge inversion by stripping the adsorbed counterions off the macroion. Received 5 December 2001 and Received in final form 10 April 2002     

To what extent of ion neutralization can multivalent ion distributions around RNA-like macroions be described by Poisson-Boltzmann theory?

Nucleic acids are negatively charged biomolecules, and metal ions in solutions are important to their folding structures and thermodynamics, especially multivalent ions. However, it has been suggested that the binding of multivalent ions to nucleic acids cannot be quantitatively described by the well-established Poisson-Boltzmann(PB) theory. In this work, we made extensive calculations of ion distributions around various RNA-like macroions in divalent and trivalent salt solutions by PB theory and Monte Carlo(MC) simulations. Our calculations show that PB theory appears to underestimate multivalent ion distributions around RNA-like macroions while can reliably predict monovalent ion distributions. Our extensive comparisons between PB theory and MC simulations indicate that when an RNA-like macroion gets ion neutralization beyond a "critical" value, the multivalent ion distribution around that macroion can be approximately described by PB theory.Furthermore, an empirical formula was obtained to approximately quantify the critical ion neutralization for various RNAlike macroions in multivalent salt solutions, and this empirical formula was shown to work well for various real nucleic acids including RNAs and DNAs.     

Macroions in salty water with multivalent ions: giant inversion of charge

Screening of a strongly charged macroion by oppositely charged colloidal particles, micelles, or short polyelectrolytes is considered. Because of strong lateral repulsion such multivalent counterions form a strongly correlated liquid at the surface of the macroion. This liquid provides correlation-induced attraction of multivalent counterions to the macroion surface. As a result even a moderate concentration of multivalent counterions in the solution inverts the sign of the net macroion charge. We show that at high concentration of monovalent salt the absolute value of inverted charge can be larger than the bare one. This giant inversion of charge can be observed in electrophoresis.     

Effect of size and charge on ordering of a highly charged concentrated macroions in suspension

An efficient fast Fourier transform method has been employed to determine correlation function [g(r*)] using the structure factor [S(Q*)] calculated with the rescaled mean spherical approximation (RMSA) and the DLVO potential. Based on this function a parametric (size and charge) study of the ordering in a highly charged and concentrated macroions (an ideal colloid) has been made. The strength of the correlation increases with the increase in the charge on macroions and it saturates after acertain value. Similarly, a critical diameter of the particle depending on the charge on it has been found at which normal feature of the ordering disappears.     

Rayleigh instability of charged droplets in the presence of counterions

The classical instability of a charged spherical droplet is reconsidered in the presence of counterions. An ensemble of such droplets is studied within a simplified cell model. Screening of the electric field by the counterions is found to increase the equilibrium droplet size. Furthermore, if the ions can enter the droplet, a first-order phase transition occurs upon increasing Bjerrum length, surface tension or droplet density, leading to a phase separation. Simple scaling properties of the free energy give the shape of the phase boundary and show the system to be scale-invariant there. Pearl-necklace structures of hydrophobic polyelectrolytes are discussed as an application. Received 30 August 2001     

Adsorption of hydrophobic polyelectrolytes onto oppositely charged surfaces

We present a scaling theory for the adsorption of a weakly charged polyelectrolyte chain in a poor solvent onto an oppositely charged surface. Depending on the fraction of charged monomers and on the solvent quality for uncharged monomers, the globule in the bulk of the solution has either a spherical conformation or a necklace structure. At sufficiently high surface charge density, a chain in the globular conformation adsorbs in a flat pancake conformation due to the Coulombic attraction to the oppositely charged surface. Different adsorption regimes are predicted depending on two screening lengths (the Debye screening length monitored by the salt concentration and the Gouy-Chapman length monitored by the surface charge density), on the degree of ionization of the polymer and on the solvent strength. At low bulk ionic strength, an increase in the surface charge density may induce a transition from an adsorbed necklace structure to a uniform pancake due to the enhanced screening of the intra-chain Coulombic repulsion by the counterions localized near the surface. Received 12 April 2001