Polyelectrolyte solutions + multivalent salts = phase separation

Summary A queous solutions of highly charged flexible polyelectrolytes phase separate in the presence of multivalent counterions. We present a theoretical model which explains this behavior in terms of electrostatic bridging between monomers via the condensed counterions. The ?Polymer Reference Interaction Site Model? with the Debye-Hückel closure (equivalent to the ?Random Phase Approximation?) is sufficient to understand the crucial role of the valency of the counterions, to predict a demixion above a given valency and a redissolution of the precipitate in excess of added salt. The model successfully reproduces the different experimental phase diagrams of polystyrene sulfonate suspensions with different added electrolytes. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Counterion condensation theory of attraction between like charges in the absence of multivalent counterions

There is abundant experimental evidence suggesting the existence of attractive interactions among identically charged polyelectrolytes in ordinary salt solutions. The presence of multivalent counterions is not required. We review the relevant literature in detail and conclude that it merits more attention than it has received. We discuss also some recent observations of a low ionic strength attraction of negatively charged DNA to the region of a negatively charged glass nanoslit where the floor of the nanoslit meets the walls, again in the absence of multivalent ions. On the theoretical side, it has become clear that purely electrostatic interactions require the presence of multivalent counterions if they are to generate like-charge attraction. Any theory of like-charge attraction in the absence of multivalent counterions must therefore contain a non-electrostatic component. We point out that counterion condensation theory, which has predicted like-charge polyelectrolyte attraction in an intermediate range of distances in ordinary 1:1 salt conditions, contains both electrostatic and non-electrostatic elements. The non-electrostatic component of the theory is the modeling constraint that the counterions fall into two explicit populations, condensed and uncondensed. As reviewed in the paper, this physically motivated constraint is supported by strong experimental evidence. We proceed to offer an explanation of the nanoslit observations by showing in an idealized model that the line of intersection of two intersecting planes is a virtual polyelectrolyte. Since we have previously developed a counterion condensation theory of attraction of two like-charged polyelectrolytes, our suggestion is that the DNA is attracted to the virtual polyelectrolytes that may be located in the nanoslit where floor meets walls. We present the detailed calculations needed to document this suggestion: an extension of previous theory to the case of polyelectrolytes with like but not identical charges; the demonstration of counterion condensation on a plane with bare charge density greater than an explicitly exhibited critical value; a calculation of the free energy of the plane; a calculation of the interaction of a line charge polyelectrolyte with a like-charged plane; and the detailed demonstration that the line of intersection of two planes is a virtual polyelectrolyte.     

Weakly charged lamellar bilayer system: Interplay between thermal undulations and electrostatic repulsion

We study the interplay between thermal undulations and electrostatic interactions for weakly charged surfactant bilayers by measuring the backscattering of light from very dilute lamellar phases of the non-ionic surfactant triethylene glycol monodecyl ether (C₁₀E₃) doped with small amounts of the anionic surfactant sodium dodecyl sulphate (SDS), both with and without added electrolyte. Upon charging, the lamellar phases show a transition from undulation to electrostatic stabilization. Non-lamellar structures develop if the molar mixing ratio exceeds . Deviations from ideal swelling, , where is the lamellar repeating distance and the membrane volume fraction, were detected for all lamellar phases. Salt-free lamellar phases with charge densities below , as well as more highly charged lamellar phases at high ionic strength show a universal logarithmic deviation from ideal swelling that was analyzed using theories for undulation stabilized lamellar phases. Deviations from ideal swelling for electrostatically stabilized lamellar phases were analyzed using theories recently developed for undulations in charged lamellar phases. The fits to the various theories yield a value of for the bending modulus of the C₁₀E₃ bilayers. Received 21 June 1999 and Received in final form 25 August 1999     

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.     

Semi-analytical method of calculating the electrostatic interaction of colloidal solutions

We present a semi-analytical method of calculating the electrostatic interaction of colloid solutions for confined and unconfined systems. We expand the electrostatic potential of the system in terms of some basis functions such as spherical harmonic function and cylinder function. The expansion coefficients can be obtained by solving the equations of the boundary conditions, combining an analytical translation transform of the coordinates and a numerical multipoint collection method. The precise electrostatic potential and the interaction energy are then obtained automatically. The method is available not only for the uniformly charged colloids but also for nonuniformly charged ones. We have successfully applied it to unconfined diluted colloid system and some confined systems such as the long cylinder wall confinement, the air–water interfacial confinement and porous membrane confinement. The consistence checks of our calculations with some known analytical cases have been made for all our applications. In theory, the method is applicable to any dilute colloid solutions with an arbitrary distribution of the surface charge on the colloidal particle under a regular solid confinement, such as spherical cavity confinement and lamellar confinement.     

Counterion release and electrostatic adsorption

The effective charge of a rigid polyelectrolyte (PE) approaching an oppositely charged surface is studied. The cases of a weak (annealed) and strongly charged PE with condensed counterions (such as DNA) are discussed. In the most interesting case of the adsorption onto a substrate of low dielectric constant (such as a lipid membrane or a mica sheet) the condensed counterions are not always released as the PE approaches the substrate, because of the major importance of the image-charge effect. For the adsorption onto a surface with freely moving charges, the image-charge effect becomes less important and full release is often expected.     

A counterion condensation theory for the relaxation,rise, and frequency dependence of the parallel polarization of rodlike polyelectrolytes

We calculate the relaxation, rise, and frequency dependence of the parallel polarization of counterions condensed on rodlike polyelectrolytes and charged colloids. Emphasis is placed on an effective counterion mobility along the rod as strongly influenced by electrostatic interactions.     

Elastically driven linker aggregation between two semiflexible polyelectrolytes

The behavior of mobile linkers connecting two semiflexible charged polymers, such as polyvalent counterions connecting DNA or F-actin chains, is studied theoretically. The chain bending rigidity induces an effective repulsion between linkers at large distances while the interchain electrostatic repulsion leads to an effective short-range interlinker attraction. We find a rounded phase transition from a dilute linker gas where the chains form large loops between linkers to a dense disordered linker fluid connecting parallel chains. The onset of chain pairing occurs within the rounded transition.     

Charged particles on surfaces: coexistence of dilute phases and periodic structures at interfaces

We consider a mixture of two immiscible oppositely charged molecules strongly adsorbed to an interface, with a neutral nonselective molecular background. We determine the coexistence between a high density ionic periodic phase and a dilute isotropic ionic phase. We use a strong segregation approach for the periodic phase and determine the one-loop free energy for the dilute phase. Lamellar and hexagonal patterns are calculated for different charge stoichiometries of the mixture. Molecular dynamics simulations exhibit the predicted phase behavior. The periodic length scale of the solid phase is found to scale as epsilon/(lB psi3/2), where psi is the effective charge density, lB is the Bjerrum length, and epsilon is the cohesive energy.     

Simple model for attraction between like-charged polyions

We present a simple model for the possible mechanism of appearance of attraction between like charged polyions inside a polyelectrolyte solution. The attraction is found to be short ranged, and exists only in the presence of multivalent counterions. It is produced by the correlations in layers of condensed counterions surrounding each polyion and is only weakly temperature dependent. We find the attraction to be maximum at zero temperature and dimish as the temperature is raised. The attraction is only possible if the number of condensed counterions exceeds the threshold, , where is the valence of counterions and Z is the polyion charge. Received 10 March 1999 and Received in final form 20 April 1999     

Salt-induced counterion-mobility anomaly in polyelectrolyte electrophoresis

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 the chain and counterions.     

Salt-induced collapse and reexpansion of highly charged flexible polyelectrolytes

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-induced complexation phenomena.     

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.     

二维情况下两组分带电囊泡形变耦合相分离的理论模拟研究

结合离散空间变分方法和耗散动力学研究了二维两组分带电囊泡的形变耦合相分离,系统地考察了囊泡带电量组分含量、带电组分的电荷密度、两组分间的相容性和温度等因素对形变耦合相分离动力学的影响.模拟结果表明电荷引入可增加不同组分间的表观相溶性.当温度较高时,静电相互作用可直接抑制囊泡相分离,避免了同种组分的团聚;当温度较低时,静电相互作用则可明显增加分相相区数目,使其呈微观相分离,从而避免了同种组分大范围的团聚.     

Variational charge renormalization in charged systems

We apply general variational techniques to the problem of the counterion distribution around highly charged objects where strong condensation of counterions takes place. Within a field-theoretic formulation using a fluctuating electrostatic potential, the concept of surface-charge renormalization is recovered within a simple one-parameter variational procedure. As a test, we reproduce the Poisson-Boltzmann surface potential for a single-charged planar surface both in the weak-charge and strong-charge regime. We then apply our techniques to non-planar geometries where closed-form solutions of the non-linear Poisson-Boltzmann equation are not available. In the cylindrical case, the Manning charge renormalization result is obtained in the limit of vanishing salt concentration. However, for intermediate salt concentrations a slow crossover to the non-charged-renormalized regime (at high salt) is found with a quasi-power-law behavior which helps to understand conflicting experimental and theoretical results for the electrostatic persistence length of polyelectrolytes. In the spherical geometry charge renormalization is only found at intermediate salt concentrations, in agreement with previous numerical results.Received: 16 December 2002, Published online: 22 July 2003PACS: 82.70.-y Disperse systems; complex fluids - 61.20.Ja Computer simulation of liquid structure - 61.20.Qg Structure of associated liquids: electrolytes, molten salts, etc.     

Attractive instability of oppositely charged membranes induced by charge density fluctuations

We predict the conditions under which two oppositely charged membranes show a dynamic, attractive instability. Two layers with unequal charges of opposite sign can repel or be stable when in close proximity. However, dynamic charge density fluctuations can induce an attractive instability and thus facilitate fusion. We predict the dominant instability modes and time scales and show how these are controlled by the relative charge and membrane viscosities. These dynamic instabilities may be the precursors of membrane fusion in systems where artificial vesicles are engulfed by biological cells of opposite charge.     

Binding of oppositely charged membranes and membrane reorganization

We consider the electrostatic interaction between two rigid membranes, with different surface charge densities of opposite sign, across an aqueous solution without added salt. Exact solutions to the nonlinear Poisson-Boltzmann equation are obtained and their physical meaning discussed. We also calculate the electrostatic contribution to the free energy and discuss the renormalization of the area per head group of the charged lipids arising from the Coulomb interaction. Received 13 October 1998     

Elastic properties of polymer-doped dilute lamellar phases: A small-angle neutron scattering study

We investigate experimentally, using small-angle neutron scattering the elastic properties of polymer-doped dilute lamellar phases. In our system the polymer is water-soluble but nevertheless partially adsorbs onto the negatively charged surfactant bilayers. The effective polymer-mediated interaction between bilayers is less repulsive than the weakly screened electrostatic interaction that prevails at zero polymer content. It even becomes attractive in some regions of the phase diagram. Small-angle neutron scattering allows us to measure directly the Caillé exponent η characterizing the bilayer fluctuations in lamellar (smectic A) phases, and thus indirectly estimate the compression modulus as a measure of the strength of the bilayer-bilayer interactions. The compression modulus appears to be vanishing at a point located on the lamellar-lamellar phase separation boundary, a candidate critical point. Received: 7 August 2000     

Combined effects of headgroup charge and tail unsaturation of lipids on lateral organization and diffusion of lipids in model biomembranes

Lateral organization and dynamics of lipids in plasma membranes are crucial for several cellular processes such as signal transduction across the membrane and still remain elusive.In this paper,using coarse-grained molecular dynamics simulation,we theoretically study the combined effects of headgroup charge and tail unsaturation of lipids on the lateral organization and diffusion of lipids in ternary lipid bilayers.In neutral ternary lipid bilayers composed of saturated lipids,unsaturated lipids,and cholesterols,under the conditions of given temperature and components,the main factor for the phase separation is the unsaturation of unsaturated lipids and the bilayers can be separated into liquid-ordered domains enriched in saturated lipids and cholesterols and liquid-disordered domains enriched in unsaturated lipids.Once the headgroup charge is introduced,the electrostatic repulsion between the negatively charged lipid headgroups will increase the distance between the charged lipids.We find that the lateral organization and diffusion of the lipids in the(partially) charged ternary lipid bilayers are determined by the competition between the headgroup charge and the unsaturation of the unsaturated lipids.In the bilayers containing unsaturated lipids with lower unsaturation,the headgroup charge plays a crucial role in the lateral organization and diffusion of lipids.The headgroup charge may make the lipid domains unstable and even can suppress phase separation of the lipids in some systems.However,in the bilayers containing highly unsaturated lipids,the lateral organization and diffusion of lipids are mainly dominated by the unsaturation of the unsaturated lipids.This work may provide some theoretical insights into understanding the formation of nanosized domains and lateral diffusion of lipids in plasma membranes.     

盐离子对蛋白质带电特性的影响

本文应用分子理论,研究盐离子对蛋白质带电特性的影响,理论模型考虑蛋白质与阴离子的结合作用。研究发现,由于蛋白质与阴离子的结合,距离蛋白质表面附近处的阴离子被吸附在了蛋白质表面,在距离蛋白质表面附近区域,阴离子分布较少。通过计算体系中的静电势,我们发现,在距离蛋白质表面附近,静电势呈现了较大的负值,带正电荷的阳离子感受到静电吸引,会出现在距离蛋白质表面附近的区域,这会使得在距离蛋白质表面附近的区域,阳离子数目增多。这样,在不同阴离子浓度、以及阴离子与蛋白质不同结合能条件下,阴离子会在不同程度上影响蛋白质的带电特性、影响体系中的静电特性。通过考察不同结合能条件下,蛋白质表面电荷面密度随阴离子浓度的变化关系还发现,较大的结合能会使得阴离子与蛋白质结合增快,蛋白质表面会呈现从正电荷态向负电荷态的转变。理论结果符合实验观测,由此表明,盐离子与蛋白质的结合导致蛋白质表面带电特性的改变,是盐离子影响蛋白质带电特性的本质。