Non-monotonic swelling of a macroion due to correlation-induced charge inversion

It is known that a large, charged body immersed in a solution of multivalent counterions may undergo charge inversion as the counterions adsorb to its surface. We use the theory of charge inversion to examine the case of a deformable, porous macroion which may adsorb multivalent ions into its bulk to form a three-dimensional strongly-correlated liquid. This adsorption may lead to non-monotonic changes in the size of the macroion as multivalent ions are added to the solution. The macroion first shrinks as its bare charge is screened and then reswells as the adsorbed ions invert the sign of the net charge. We derive a value for the outward pressure experienced by such a macroion as a function of the ion concentration in solution. We find that for small deviations in the concentration of multivalent ions away from the neutral point (where the net charge of the body is zero), the swollen size grows parabolically with the logarithm of the ratio of multivalent ion concentration to the concentration at the neutral point.     

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.     

Flexible linear polyelectrolytes in multivalent salt solutions: Solubility conditions

Single- and double-stranded DNA and many biological and synthetic polyelectrolytes undergo two structural transitions upon increasing the concentration of multivalent salt or molecules. First, the expanded-stretched chains in low monovalent salt solutions collapse into nearly neutral compact structures when the density of multivalent salt approaches that of the monomers. With further addition of multivalent salt the chains redissolve acquiring expanded-coiled conformations. We study the redissolution transition using a two-state model (F.J. Solis, M. Olvera de la Cruz, J. Chem. Phys. 112, 2030 (2000)). The redissolution occurs when there is a high degree of screening of the electrostatic interactions between monomers, thus reducing the energy of the expanded state. The transition is determined by the chemical potential of the multivalent ions in the solution, μ and the inverse screening length, κ. The transition point also depends on the charge distribution along the chain but is nearly independent of the molecular weight and degree of flexibility of the polyelectrolytes. We generate a diagram of μversusκ² where we find two regions of expanded conformations, one with charged chains and the other with overcharged (inverted charge) chains, separated by a collapsed nearly neutral conformation region. The collapse and redissolution transitions occur when the trajectory of the properties of the salt crosses the boundaries between these regions. We find that in most cases the redissolution occurs within the same expanded branch from which the chain precipitates. Received 15 May 2000 and Received in final form 28 June 2000     

Equilibrium charge distribution on annealed polyelectrolytes

Monte Carlo simulations are used to study the non-uniform equilibrium charge distribution along a single annealed polyelectrolyte chain under θ solvent conditions and with added salt. Within a range of the order of the Debye length charge accumulates at chain ends while a slight charge depletion appears in the central part of the chain. The simulation results are compared with theoretical predictions recently given by Castelnovo et al. In the parameter range where the theory can be applied we find almost perfect quantitative agreement. Received 7 March 2002 and Received in final form 28 May 2002     

Stretching DNA: Role of electrostatic interactions

The effect of electrostatic interactions on the stretching of DNA is investigated using a simple worm like chain model. In the limit of small force there are large conformational fluctuations which are treated using a self-consistent variational approach. For small values of the external force f, we find the extension scales as where is the Debye screening length. In the limit of large force the electrostatic effects can be accounted for within the semiflexible chain model of DNA by assuming that only small excursions from rod-like conformations are possible. In this regime the extension approaches the contour length as where f is the magnitude of the external force. The theory is used to analyze experiments that have measured the extension of double-stranded DNA subject to tension at various salt concentrations. The theory reproduces nearly quantitatively the elastic response of DNA at small and large values of f and for all concentration of the monovalent counterions. The limitations of the theory are also pointed out. Received 13 October 1998 and Received in final form 9 June 1999     

Adsorption of hydrophobic polyelectrolytes at the air/water interface: Conformational effect and history dependence

We present an experimental study of the adsorption of hydrophobic highly charged polyelectrolytes on a neutral and hydrophobic surface, the air/water interface. The polymer was a randomly sulphonated polystyrene with charge fractions between 0.3 and 0.9 and the adsorbed layers were characterised by Langmuir through measurements, ellipsometry and X-ray reflectivity. The adsorption rate is always very slow and the resulting layers are very thin (< 3 nm). A maximum of adsorption with the charge fraction is observed which we relate to the conformation of the chains in solution. We show that adsorption is partially irreversible, strongly hysteretic and that the state of an adsorbed layer depends on its history. Received 16 June 2000     

Adsorption of a polyampholyte on a charged spherical particle

We develop a scaling theory for a single polyampholyte chain adsorbed on a charged spherical particle in a theta-solvent. Adsorption of a polyampholyte molecule is due to its polarization in the electrostatic field of the particle. For large particles with sizes exceeding the thickness of the adsorbed layer, the conformations of the chain are similar to the one found for polyampholyte adsorption on charged planar surface. However, an adsorbed polyampholyte chain forms a self-similar flower-like structure near the particles with sizes smaller than its Gaussian size. These self-similar structures result from the balance of the polarization energy of loops and the excluded volume interactions between monomers. The structure of an adsorbed polyampholyte in the flower-like conformation is similar to that of a neutral star polymer. Received 3 March 2000 and Received in final form 5 July 2000     

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     

Stability of charged metal clusters in the vicinity of an ionic charge

Stability of highly charged metal clusters in the electric field of an external ion is investigated with the classical liquid drop model. We study the optimum shape of the cluster which has a local minimum of the total energy, taking account of the effects of the surface charge polarization on the Coulomb energy and the cluster deformation on the surface energy. We find that the cluster deformation greatly affects the total energy of the system and that a cluster with a fissility larger than some critical value 0.7-0.8 can become unstable against deformation. We investigate the local competition between the Coulomb force and the surface tension at the cluster surface and show that the surface charge polarization which is induced by the external electric field significantly affects the shape of the cluster and its stability. Received 5 November 2002 / Received in final form 27 January 2003 Published online 11 March 2003 RID="a" ID="a"e-mail: hamada@konan-u.ac.jp     

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     

Virial expansion for charged colloids and electrolytes

Using a field-theoretic approach, we derive the first few coefficients of the exact low-density (“virial”) expansion of a binary mixture of positively and negatively charged hard spheres (two-component hard-core plasma, TCPHC). Our calculations are nonperturbative with respect to the diameters d₊ and d_- and charge valences q₊ and q_- of positive and negative ions. Consequently, our closed-form expressions for the coefficients of the free energy and activity can be used to treat dilute salt solutions, where typically d ₊∼d _- and q ₊∼q _-, as well as colloidal suspensions, where the difference in size and valence between macroions and counterions can be very large. We show how to map the TCPHC on a one-component hard-core plasma (OCPHC) in the colloidal limit of large size and valence ratio, in which case the counterions effectively form a neutralizing background. A sizable discrepancy with the standard OCPHC with uniform, rigid background is detected, which can be traced back to the fact that the counterions cannot penetrate the colloids. For the case of electrolyte solutions, we show how to obtain the cationic and anionic radii as independent parameters from experimental data for the activity coefficient. Received 6 September 2001 / Received in final form 20 May 2002 Published online 24 September 2002     

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     

Mean-field theory for polymer adsorption on curved surfaces

We discuss the influence of polymer adsorption on the curvature energy of an interface. Following an article by Clement and Joanny (J. Phys. II 7, 973 (1997)), a mean-field theory is used to calculate the surface tension, rigidity constants and spontaneous curvature associated with both reversible and irreversible polymer adsorption. In the case of irreversible polymer adsorption it is assumed that the amount of adsorbed polymer remains constant upon curving the interface. Unfortunately, constraining the amount of polymer by adding a Lagrange multiplier affects the thermodynamic state of the (free) polymer far away from the interface. Clement and Joanny solve this problem by removing the polymers in the bulk. We allow for the presence of free polymers, but to achieve this we have to apply a local external field to keep the adsorbed amount fixed. The results of the two approaches are compared and a physical interpretation is given. Received 25 July 2001 and Received in final form 5 December 2001     

Adsorption of polyampholytes on charged surfaces

We have studied the adsorption of neutral polyampholytes on model charged surfaces that have been characterized by contact angle and streaming current measurements. The loop size distributions of adsorbed polymer chains have been obtained using atomic-force microscopy (AFM) and compared to recent theoretical predictions. We find a qualitative agreement with theory; the higher the surface charge, the smaller the number of monomers in the adsorbed layer. We propose an original scenario for the adsorption of polyampholytes on surfaces covered with both neutral long-chain and charged short-chain thiols. Received 22 February 2002 and Received in final form 23 April 2002     

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     

Implementation of a sapphire cell with external electrodes for laser excitation of a forbidden atomic transition in a pulsed E-field

We demonstrate the production of an electric field inside a high temperature cesium vapor cell with external electrodes. This external control of the electric field, which is not possible with a glass cell in presence of a cesium vapor, is achieved using a cell made of sapphire, and is of particular interest for our ongoing Parity Violation experiment. We describe the main components and the implementation on the set-up, including the pulsed high voltage generator. With pulse duration not exceeding 200 ns the system provides a reversible longitudinal E-field of up to 2 kV/cm in the vapor at a density of ∼ 2×10¹⁴ at/cm³ without discharge. Atomic signals attest the application of the electric field in the cell, with the predicted value. Further improvements obtained with sapphire cells are also presented. Received 15 September 2000     

First principle theory for cavity solitons in semiconductor microresonators

Cavity solitons are similar to spatial solitons, appearing as localized bright dots in the transverse intensity profile of the electromagnetic field, but they arise in dissipative systems. In this paper we consider a broad-area vertical-cavity semiconductor microresonator, driven by an external coherent field, at room temperature. The active material is constituted by a Multiple Quantum Well GaAs/AlGaAs structure (MQW). We present a set of nonlinear dynamical equations for the electric field and the carrier density valid for both a passive and an active (i.e. with population inversion) configuration. The complex nonlinear susceptibility is derived on the basis of a full many-body theory, with the Coulomb enhancement treated in the Padé approximation. The linear stability analysis of the homogeneous steady states is performed with a generalised approach, and numerical simulations demonstrating the existence of spatial patterns and cavity solitons in experimentally achievable parameter regions are given for the two configurations. Received 18 January 2001     

Monte Carlo simulations of star-branched polyelectrolyte micelles

The concentration profiles of monomers and counterions in star-branched polyelectrolyte micelles are calculated through Monte Carlo simulations, using the freely jointed chain model. We have investigated the onset of different regimes corresponding to the spherical and Manning condensation of counterions as a function of the strength of the Coulomb coupling. The Monte Carlo results are in fair agreement with the predictions of Self-Consistent-Field analytical models. We have simulated a real system of diblock copolymer micelles of (sodium-polystyrene-sulfonate)(NaPSS)-(polyethylene-propylene)(PEP) with f = 54 hydrophilic branches of N = 251 monomers at room temperature in salt-free solution. The calculated form factor compares nicely with our neutron scattering data. Received 18 July 2002 and Received in final form 11 October 2002 RID="a" ID="a"e-mail: roger@drecam.saclay.cea.fr     

Quantum Brownian motion on potential surfaces coupled via tunneling in an external electric field[-2mm]

The present paper deals with the motion of a Brownian particle on two identical but shifted potential surfaces, coupled via a tunneling matrix element in an external electric field. Dissipation is induced by a heat bath represented by an infinite set of harmonic oscillators with a continuum range of frequencies. We derive a perturbative solution for the quantum coherence term of the particle system after performing a small-polaron-like transformation. This is subsequently necessary for the extraction of an equation that describes the reduced dynamics and the minimal action path of the Brownian particle. Finally we extract expressions for the population relaxation rate and the pure quantum-dephasing rate of the two-level system. Received 4 January 2001 and Received in final form 12 March 2001     

Interactions between isolated nucleosome core particles: A tail-bridging effect?

Interactions between isolated nucleosome core particles are studied as a function of the monovalent salt concentration by osmometry and by electrophoretic mobility measurements. The data are compared to the measurements performed on the protein-free DNA fragments and also analysed using the conventional theoretical approach. At low salt, an electrostatic screening effect accounts for the variation of the second virial coefficient whereas the simple hard-core contribution becomes predominant at high salt. In the intermediate range, an attraction occurs. In the light of previous results (Mangenot et al. Biophys. J. 82, 345 (2002)), we show that the flexible basic proteic tails are responsible for this attraction. A tail-bridging effect is discussed. Received 4 October 2001