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     

Effects of counterion fluctuations in a polyelectrolyte brush

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 solvent, while for multivalent counterions, the transition is generally continuous. For collapsed brushes, the brush height is not independent of grafting density as it is for osmotic brushes, but scales linear with it.Received: 26 November 2003, Published online: 11 May 2004PACS: 61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling - 61.20.Qg Structure of associated liquids: electrolytes, molten salts, etc.     

Non-linear osmotic brush regime: Simulations and mean-field theory

We investigate polyelectrolyte brushes in the osmotic regime using both theoretical analysis and molecular dynamics simulation techniques. In the simulations at moderate Bjerrum length, we observe that the brush height varies weakly with grafting density, in contrast to the accepted scaling law, which predicts a brush thickness independent of the grafting density. We show that such behavior can be explained by considering lateral electrostatic effects (within the non-linear Poisson-Boltzmann theory) combined with the coupling between lateral and longitudinal degrees of freedom due to the conserved polymer volume (which are neglected in scaling arguments). We also take the non-linear elasticity of polyelectrolyte chains into consideration, which makes significant effects as chains are almost fully stretched in the osmotic regime. It is shown that all these factors lead to a non-monotonic behavior for the brush height as a function of the grafting density. At large grafting densities, the brush height increases with increasing the grafting density due to the volume constraint. At small grafting densities, we obtain a re-stretching of the chains for decreasing grafting density, which is caused by lateral electrostatic contributions and is controlled by the counterion-condensation process around polyelectrolyte chains. These results are obtained assuming all counterions to be trapped within the brush, which is valid for sufficiently long chains of large charge fraction.Received: 14 May 2003, Published online: 11 November 2003PACS: 61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling - 36.20.-r Macromolecules and polymer molecules - 61.20.Qg Structure of associated liquids: electrolytes, molten salts, etc.     

Repulsion between oppositely charged surfaces in multivalent electrolytes

In answer to recent experimental force measurements between oppositely charged surfaces we here reproduce the repulsion in the presence of multivalent salt using Monte Carlo simulations within the primitive model. Our osmotic pressure curves are in good agreement with experimental results. In contrast with Poisson-Boltzmann calculations, both repulsion and charge inversion are seen in the simulations. Repulsion is observed only for conditions under which there is charge inversion at large separations. However, in these cases, the repulsion is present also at intermediate separations, where there is no charge inversion. The charge inversion is thereby not the cause of the repulsion. Instead the repulsion appears to be an effect of the large amount of excess salt in the slit. Both phenomena, however, are closely linked and a consequence of ion-ion correlations, promoted by a strong electrostatic coupling.     

Beyond Poisson-Boltzmann: Fluctuation effects and correlation functions

We formulate the exact non-linear field theory for a fluctuating counter-ion distribution in the presence of a fixed, arbitrary charge distribution. The Poisson-Boltzmann equation is obtained as the saddle-point of the field-theoretic action, and the effects of counter-ion fluctuations are included by a loop-wise expansion around this saddle point. The Poisson equation is obeyed at each order in this loop expansion. We explicitly give the expansion of the Gibbs potential up to two loops. We then apply our field-theoretic formalism to the case of a single impenetrable wall with counter ions only (in the absence of salt ions). We obtain the fluctuation corrections to the electrostatic potential and the counter-ion density to one-loop order without further approximations. The relative importance of fluctuation corrections is controlled by a single parameter, which is proportional to the cube of the counter-ion valency and to the surface charge density. The effective interactions and correlation functions between charged particles close to the charged wall are obtained on the one-loop level. Received 8 February 1999 and Received in final form 15 May 1999     

Numerical solution of a modified Poisson-Boltzmann equation for 1 : 2 and 2 : 1 electrolytes in the diffuse layer

A modified Poisson-Boltzmann (MPB) equation for an unsymmetrically charged electrolyte in the diffuse part of the electric double layer at a plane charged wall is solved numerically using a quasi-linearization procedure. Computations are carried out for 1 : 2 and 2 : 1 restricted primitive model electrolytes with no imaging and for a metallic wall and the results compared with the classical Gouy-Chapman-Stern theory. Except for negligible surface charge, the system with a divalent counter ion is the most sensitive to any change in its physical parameters. In general the MPB mean electrostatic potential, in contrast to the Gouy-Chapman-Stern potential, is not a monotonic decreasing function. The asymptotic behaviour of the MPB equation implies charge oscillations above a critical electrolyte concentration (?0·23 M) while below this concentration imaging or surface charge-ion interactions can produce a charge inversion. Charge separation is found for no surface charge with a metallic wall. The point ion limit is briefly considered.     

Nonlinear screening and gas-liquid separation in suspensions of charged colloids

We calculate phase diagrams of charged colloidal spheres (valency Z and radius a) in a 1:1 electrolyte from multicentered nonlinear Poisson-Boltzmann theory. Our theory takes into account charge renormalization of the colloidal interactions and volume terms due to many-body effects. For valencies as small as Z = 1 and as large as 10(4) we find a gas-liquid spinodal instability in the colloid-salt phase diagram provided Z lambdaB/a > or similar 24+/-1, where lambdaB is the Bjerrum length.     

Electrostatic properties of mercaptoundecanoic-acid-coated-gold surfaces interacting with TiO2 surfaces

We studied electrostatic properties of the MUA-coated-gold surface and the TiO₂ surface for design of gold–TiO₂ distribution, which may be controlled with electrostatic interactions. The forces between the surfaces were measured as a function of the salt concentration and pH value using the AFM. By applying the DLVO theory to the forces, the potential and charge density of the surfaces were quantitatively acquired for each salt concentration and each pH value. The potential and charge density dependences on the salt concentrations and the pH values were explained with the law of mass action and the ionizable groups on the surface.     

混合电解质溶液中考虑介电饱和度的表面电位评估原理

基于非线性泊松-玻尔兹曼方程，推导了混合电解质溶液中考虑介电饱和度的表面电位的解析表达式. 近似解析解和精确数值解计算出的表面电位在很大范围的电荷密度和离子强度条件下均具有很好的一致性. 当表面电荷密度大于0.30 C/m^{2 时，介电饱和度对表面电位的影响变得尤为重要；当表面电荷密度小于0.30 C/m2时，可忽略介电饱和度的影响，即基于经典泊松-玻尔兹曼方程可获得有效的表面电位解析模型. 因此，0.3 C/m2可作为是否考虑介电饱和度的颗粒临界表面电荷密度值. 在低表面电荷密度时，考虑介质饱和度的表面电位解析模型可自然回归到经典泊松-玻尔兹曼理论的结果，得到的表面电位可以正确地预测一价和二价反离子之间的吸附选择性.}     

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。     

Revisiting the Poisson-Boltzmann theory: Charge surfaces, multivalent ions and inter-plate forces

The Poisson-Boltzmann (PB) theory is extensively used to gain insight on charged colloids and biological systems as well as to elucidate fundamental properties of intermolecular forces. Many works have been devoted in the past to study PB-related features and to confirm them experimentally. In this work we explore the properties of inter-plate forces in terms of different boundary conditions. We treat the cases of constant surface charge, constant surface potential and mixed boundaries. The interplay between electrostatic interactions, attractive counter-ion release, and repulsive van ’t Hoff contribution is discussed separately for each case. Finally, we discuss how the crossover between attractive and repulsive interactions for constant surface charge case is influenced by the presence of multivalent counter-ions, where it is shown that the range of the attractive interaction grows with the valency.     

Electrostatics of DNA-cationic lipid complexes: isoelectric instability

We propose a Poisson-Boltzmann electrostatic theory for DNA/cationic lipid complexes modeled as a stack of aligned DNA chains intercalated with lipid bilayers, a structure suggested by the recent X-ray synchrotron studies of Radler et al. Poisson-Boltzmann theory is shown to predict that the isoelectric point - where the DNA and cationic lipid charges are in balance - is unstable against absorption of extra DNA or lipid material. The instability is caused by the entropy gain obtained following the release of small ions inside the complex and is manifested by singular behavior of the rod-rod spacing near the isoelectric point. We apply the theory to a discussion of the results of Radler et al. Received: 21 July 1997 / Received in final form: 19 January 1998 /Accepted: 5 March 1998     

Structure of peptide solutions: A light scattering and numerical study

We investigated the interactions between protein molecules in solution, in particular for low salt concentrations and thus strong electrostatic interactions where a treatment based on the second virial coefficient is not sufficient. Static and dynamic light scattering experiments on solutions containing the peptide human calcitonin (hCT) were combined with calculations based on the Ornstein-Zernike equation with the hypernetted chain (HNC) closure and computer simulations within the primitive electrolyte model. The simulation illustrates the distribution of proteins in solution and the formation of (transient) protein aggregates. It furthermore allows us to predict the physical stability of hCT solutions in dependence of ionic strength, pH and hCT concentration.Received: 26 December 2003, Published online: 25 March 2004PACS: 87.15.Nn Properties of solutions; aggregation and crystallization of macromolecules - 61.20.Qg Structure of associated liquids: electrolytes, molten salts, etc. - 87.14.Ee ProteinsV. Lobaskin: Present address: Max-Planck-Institut für Polymerforschung, 55128 Mainz, Germany     

Numerical study of a modified BBGY integral equation for the primitive model of an electrolyte solution

A modified Poisson-Boltzmann equation derived from the BBGY hierarchy of equations is solved numerically for the restricted primitive model of an electrolyte solution. Computations are carried out for 1 : 1 and 2 : 2 electrolytes, and results compared with 1 : 1 Monte Carlo data and results from the Poisson-Boltzmann extensions arising from the Kirkwood hierarchy. Satisfactory agreement with the Monte Carlo results are found in the 1 : 1 case, and the correct qualitative behaviour of thermodynamic properties obtained in the 2 : 2 case. At low concentrations in the 2 : 2 case the modified Poisson-Boltzmann equations from the Kirkwood and BBGY hierarchies predict the anomalous behaviour found in the thermodynamic properties of real electrolytes. The behaviour of the mean electrostatic potential changes from a damped exponential to a damped oscillatory form for 1·2 < κa < 1·3 (where κ is the Debye-Hückel constant and a is an ionic diameter) in the 1 : 1 case and at κa ～ 0·8 in the 2 : 2 case for the parameters considered.     

Simple approach for charge renormalization in highly charged macroions

We revisit the notion of renormalized charge, which is a concept of central importance in the field of highly charged colloidal or polyelectrolyte solutions. Working at the level of a linear Debye-Hückel-like theory only, we propose a versatile method to predict the saturated amount of charge renormalization, which is, however, a nonlinear effect arising at strong electrostatic coupling. The results are successfully tested against nonlinear Poisson-Boltzmann theory for polyions of various shapes (planar, cylindrical, and spherical), both in the infinite dilution limit or in confined geometry, with or without added electrolyte. Our approach, accurate for monovalent microions in solvents such as water, is finally confronted against experimental results on charged colloids and B-DNA solutions.     

Simulations of counterions at charged plates

Using Monte Carlo simulations, we study the counterion distribution close to planar charged walls in two geometries: i) when only one charged wall is present and the counterions are confined to one half-space, and ii) when the counterions are confined between two equally charged walls. In both cases the surface charge is smeared out and the dielectric constant is the same everywhere. We obtain the counterion density profile and compare it with both the Poisson-Boltzmann theory (asymptotically exact in the limit of weak coupling, i.e. low surface charge, high temperature and low counterion valence) and the strong-coupling theory (valid in the opposite limit of high surface charge, low temperature and high counterion valence) and with previously calculated correction terms to both theories for different values of the coupling parameter, thereby establishing the domain of validity of the asymptotic limits. Gaussian corrections to the leading Poisson-Boltzmann behavior (obtained via a systematic loop expansion) in general perform quite poorly: At coupling strengths low enough so that the Gaussian (or one-loop) correction does describe the numerical deviations from the Poisson-Boltzmann result correctly, the leading Poisson-Boltzmann term by itself matches the data within high accuracy. This reflects the slow convergence of the loop expansion. For a single charged plane, the counterion pair correlation function indicates a behavioral change from a three-dimensional, weakly correlated counterion distribution (at low coupling) to a two-dimensional, strongly correlated counterion distribution (at high coupling), which is paralleled by the specific-heat capacity which displays a rounded hump at intermediate coupling strengths. For the case of counterions confined between two equally charged walls, we analyze the inter-wall pressure and establish the complete phase diagram, featuring attraction between the walls for large enough coupling strength and at intermediate wall separation. Depending on the thermodynamic ensemble, the phase diagram exhibits a discontinuous transition where the inter-wall distance jumps to infinity (in the absence of a chemical potential coupling to the inter-wall distance, as for charged lamellae in excess solvent) or a critical point where two coexisting states with different inter-wall distance become indistinguishable (in the presence of a chemical potential, as for charged lamellae with a finite fixed solvent fraction). The attractive pressure decays with the inter-wall distance as an inverse cube, similar to analytic predictions, although the amplitude differs by an order of magnitude from previous theoretical results. Finally, we discuss in detail our simulation methods and compare the finite-size scaling behavior of different boundary conditions (periodic, minimal image and open). Received 6 November 2001     

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.     

Quantum phase transition in capacitively coupled double quantum dots

We investigate two equivalent, capacitively coupled semiconducting quantum dots, each coupled to its own lead, in a regime where there are two electrons on the double dot. With increasing interdot coupling, a rich range of behavior is uncovered: first a crossover from spin- to charge-Kondo physics, via an intermediate SU(4) state with entangled spin and charge degrees of freedom, followed by a quantum phase transition of Kosterlitz-Thouless type to a non-Fermi-liquid "charge-ordered" phase with finite residual entropy and anomalous transport properties. Physical arguments and numerical renormalization group methods are employed to obtain a detailed understanding of the problem.     

Renormalized tricritical behaviour for wetting transitions

In this paper we study tricritical wetting behaviour in three dimensions. In particular we concentrate on systems with short-ranged forces and apply linear functional renormalization group techniques to elucidate the effect of fluctuations upon tricriticality. In comparison with studies of critical wetting we identify an additional fluctuation regime which is relevant for values of the capillary parameter between 2/9 and 1/2. We demonstrate that this regime essentially provides a crossover from mean-field like behaviour, in which tricritical exponents are always distinct from their critical counterparts, from intermediate- and strong-fluctuation behaviour where the critical exponents for tricritical and critical wetting are found to always coincide. We conclude by discussing briefly the possible relevance of these results for experimental studies of wetting. Received 4 January 2001 and Received in final form 11 May 2001     

Streaming currents in a single nanofluidic channel

We report measurements of the streaming current, an electrical current generated by a pressure-driven liquid flow, in individual rectangular silica nanochannels down to 70 nm in height. The streaming current is observed to be proportional to the pressure gradient and increases with the channel height. As a function of salt concentration, it is approximately constant below approximately 10 mM, whereas it strongly decreases at higher salt. Changing the sign of the surface charge is found to reverse the streaming current. The data are best modeled using a nonlinear Poisson-Boltzmann theory that includes the salt-dependent hydration state of the silica surface.