Effective Screening Length Research Articles

Selective protein and DNA adsorption on PLL-PEG films modulated by ionic strength

We describe a soft thin film which selectively adsorbs DNA but averts the non-specific binding of proteins. Indium tin oxide (ITO) substrates were surface-modified with a poly(L-lysine)-g-poly(ethylene glycol) (PLL-PEG) film which carries an outer protein-repelling PEG layer and an underlying positively charged PLL layer that attracts DNA. Binding of DNA could be tuned by a factor of over 90 by varying the salt concentration. The dependence of DNA binding on ionic strength was described with a physicochemical model which led to the conclusion of an unexpectedly high enrichment of salt inside the PEG layer. In addition, the model led to an expanded definition of the Debye-Huckel type effective screening length parameter z. Our new findings on a film with dual passivation/attraction properties can find applications in biopolymer-specific coatings useful in bioseparation and biosensing. In addition, the physicochemical characterisation provides new insight into the interactions between biopolymers and polymer-coated interfaces.

Effective Screening Length of Isotropic Liquid Samples Submitted to an Applied Voltage

A cell of isotropic liquid in the shape of a slab of thickness d and containing ionic impurities is considered. It is shown that the screening effect produced by the ionic charges on the external field is characterized by an effective surface length, lambda(S)(U), depending on the applied voltage U. The analysis indicates that lambda(S)(U)) << lambda(D) when the applied voltage is very large, and lambda(S)(U) --> lambda(D) for very small values of the applied voltage, where lambda(D) is the Debye screening length. The presence of the ions is responsible also for a counterpotential, v, that for small U is such to cancel the effective electric field in the sample, whereas in the opposite limit it is inversely proportional to the applied difference of potential.

Classical charged fluids at equilibrium near an interface: Exact analytical density profiles and surface tension

The structure of equilibrium density profiles in an electrolyte in the vicinity of an interface with an insulating or conductive medium is of crucial importance in chemical physics and colloidal science. The Coulomb interaction is responsible for screening effects, and in dilute solutions the latter effects give rise to universal leading corrections to nonideality, which distinguish electrolyte from nonelectrolyte solutions. An example is provided by the excess surface tension for an air-water interface, which is determined by the excess particle density, and which was first calculated by Onsager and Samaras. Because of the discrepancy between the dielectric constants on both sides of the interface, every charge in the electrolyte interacts with an electrostatic image, and the Boltzmann factor associated with the corresponding self-energy has an essential singularity over the length scalel from the wall. Besides Coulomb interactions, short-range repulsions must be taken into account in order to prevent the collapse between charges with opposite signs or between each charge and its image when the solvent dielectric constant is lower than that of the continuous medium on the other side of the interface. For a dilute and weaklycoupled electrolyte,l is negligible with respect to the bulk Debye screening length ξD. In the framework of the grand-canonical ensemble, systematic partial resummations in Mayer diagrammatics allow one to exhibit that, in this regime, the exact density profiles at leading order are the same as if they were calculated in a partially-linearized mean-field theory, where the screened pair interaction obeys an inhomogeneous Debye equation. In the latter equation the effective screening length depends on the distancex from the interface: it varies very fast over the lengthl and tends to its bulk value over a few ξDs. The equation can be solved iteratively at any distancex, and the exact density profiles are calculated analytically up to first order in the coupling parameter l/ξD. They show the interplay between three effects: (1) the geometric repulsion from the interface associated with the deformation of screening clouds, (2) the polarization effects described by the images on the other side of the interface, (3) the interaction between each charge and the potential drop created by the electric layer which appears as soon as the fluid has not a charge-symmetric composition. Moreover, the expressions allow us to go beyond Onsager-Samaras theory: the surface tension is calculated for charge-asymmetric electrolytes and for any value of the ratio between the dielectric constants on both sides of the interface. Similar diagrammatic techniques also allow one to investigate the charge renormalization in the dipolar effective pair interaction along the interface with an insulating medium.

Hybrid approach to the ion drag force

A detailed calculation of the ion drag force acting on a single grain in a collisionless Maxwellian plasma with an arbitrary velocity of the ion flow is carried out. The traditional binary collision approach to the problem is combined with the linear kinetic formalism. It is shown that for a pointlike particle the binary collision approach yields correct results provided that the effective plasma screening length is chosen appropriately. The correct choice follows from the self-consistent kinetic theory. On the other hand, the binary collision approach accounts consistently for the effects of finite grain size and grain charging. Taking these effects into account an expression for the ion drag force is obtained. Calculations are performed for a typical (exemplary) set of complex plasma parameters. The relevance for recent complex plasma experiments is briefly discussed.

Charge renormalization and other exact coupling corrections to the dipolar effective interaction in an electrolyte near a dielectric wall

The aim of the paper is to study the renormalizations of the charge and screening length that appear in the large-distance behavior of the effective pairwise interaction w(alphaalpha') between two charges e(alpha) and e(alpha') in a dilute electrolyte solution, both along a dielectric wall and in the bulk. The electrolyte is described by the so-called primitive model in the framework of classical statistical mechanics and the electrostatic response of the wall is characterized by its dielectric constant. In a previous paper [Phys. Rev. E 68, 022133 (2003)] a graphic reorganization of resummed Mayer diagrammatics has been devised in order to exhibit the general structure of the 1/y3 leading tail of w(alphaalpha') (x,x',y) for two charges located at distances x and x' from the wall and separated by a distance y along the wall. When all species have the same closest approach distance b to the wall, the coefficient of the 1/y3 tail is the product Dalpha(x)Dalpha'(x') of two effective dipoles. Here we use the same graphic reorganization in order to systematically investigate the exponential large-distance behavior of w(alphaalpha') in the bulk. (We show that the reorganization also enables one to derive the basic screening rules in both cases.) Then, in a regime of high dilution and weak coupling, the exact analytical corrections to the leading tail of w(alphaalpha'), both in the bulk or along the wall, are calculated at first order in the coupling parameter epsilon and in the limit where b becomes negligible with respect to the Debye screening length. (Epsilon is proportional to the so-called plasma parameter.) The structure of corrections to the terms of order epsilon is exhibited, and the scaling regime for the validity of the Debye limit is specified. In the vicinity of the wall, we use the density profiles calculated previously [J. Stat. Phys. 105, 211 (2001)] up to order epsilon and a method devised [J. Stat. Phys. 105, 245 (2001)] for the determination of the corresponding correction in the auxiliary screened potential, which also appears in the linear-response theory. The first coupling correction to the effective dipole Dalpha(x) is a function (not a mere exponential decay) determined by the nonuniformity of the density profiles as well as by three- and four-body screened interactions in w(alphaalpha'). Though the effective screening length (beyond the Debye value) in the direction perpendicular to the wall is the same as in the bulk, the bare solvated charges are not renormalized by the same quantity as in the bulk, because of combined steric and electrostatic effects induced by the wall.

Micron-sized particle-charge measurements in an inductive rf gas-discharge plasma using gravity-driven probe grains

A method for measuring the interactions of charged dust particles within a three-dimensional dust cloud in a plasma is presented. The measurements have been performed with the help of gravity-driven heavy charged probe particles, which moved through a dust cloud levitating at the diffuse edge of an inductively coupled rf discharge plasma. Assuming a screened Coulomb potential surrounding each particle, both the particle charge and the effective screening length were calculated from an analysis of the elastic particle interactions for 20, 30, and 50 Pa of neon pressure. The basic parameters of the bulk discharge plasma have been diagnosed with a Langmuir probe to compare the experimental data with those deriving from different theoretical approaches. The observed discrepancies are discussed.

Adsorption of Divalent Cations on DNA

The distribution of divalent ions in semidilute solutions of high-molecular-mass DNA containing both sodium chloride and strontium chloride in near-physiological conditions is studied by small-angle x-ray scattering and by small-angle neutron scattering. Both small-angle neutron scattering and small-angle x-ray scattering reveal a continuous increase in the scattering intensity at low q with increasing divalent ion concentration, while at high q the scattering curves converge. The best fit to the data is found for a configuration in which DNA strands of cross-sectional radius 10 Å are surrounded by a counterion sheath of outer radius ∼13.8 Å, independent of the strontium chloride concentration. When the strontium chloride is replaced by calcium chloride, similar results are obtained, but the thickness of the sheath increases when the divalent salt concentration decreases. These results correspond in both cases to partial localization of the counterions within a layer that is thinner than the effective Debye screening length.

Density Profiles in a Quantum Coulomb Fluid Near a Hard Wall

Equilibrium particle densities near a hard wall are studied for a quantum fluid made of point charges which interact via Coulomb potential without any regularization. In the framework of the grand-canonical ensemble, we use an equivalence with a classical system of loops with random shapes, based on the Feynman-Kac path-integral representation of the quantum Gibbs factor. After systematic resummations of Coulomb divergences in the Mayer fugacity expansions of loop densities, there appears a screened potential $\phi$. It obeys an inhomogeneous Debye-H\"uckel equation with an effective screening length which depends on the distance from the wall. The formal solution for $\phi$ can be expanded in powers of the ratios of the de Broglie thermal wavelengths $\laa$'s of each species $\alpha$ and the limit of the screening length far away from the wall. In a regime of low degeneracy and weak coupling, exact analytical density profiles are calculated at first order in two independent parameters. Because of the vanishing of wave-functions close to the wall, density profiles vanish gaussianly fast in the vicinity of the wall over distances $\laa$'s, with an essential singularity in Planck constant $\hbar$. When species have different masses, this effect is equivalent to the appearance of a quantum surface charge localized on the wall and proportional to $\hbar$ at leading order. Then, density profiles, as well as the electrostatic potential drop created by the charge-density profile, also involve a term linear in $\hbar$ andwhich decays exponentially fast over the classical Debye screening length $\xid$. The corresponding contribution to the global surface charge exactly compensates the charge in the very vicinity of the surface, so that the net electric field vanishes in the bulk, as it should.

Asymptotically exact dispersion relations for collective modes in a confined charged Fermi liquid

Using general local conservations laws we derive dispersion relations for edge modes in a slab of electron liquid confined by a symmetric potential. The dispersion relations are exact up to $\lambda^{2} q^{2}$, where $q$ is a wave vector and $\lambda$ is an effective screening length. For a harmonic external potential the dispersion relations are expressed in terms of the {\em exact} static pressure and dynamic shear modulus of a homogeneous liquid with the density taken at the slab core. We also derive a simple expression for the frequency shift of the dipole (Kohn) modes in nearly parabolic quantum dots in a magnetic field.

Magnetic-field-induced anisotropic curvature elasticity of a vesicle membrane containing magnetic polyions.

Interaction between a charged membrane and the electrolyte solution containing magnetic polyions is considered. A self-magnetic field, which arises due to the nonhomogeneous magnetic particle distribution near a charged membrane increases the effective charge screening length for the parts of a membrane normal to a magnetic field. The anisotropy of elastic properties of a membrane depending on the screening length is calculated on the basis of the curvature expansion. It is shown that due to diminishing of the spontaneous curvature for the parts of a membrane normal to a magnetic field there are two competing mechanisms of the ferrovesicle shape transformation under the influence of a magnetic field-the formation of a prolate shape orientated along a field due to the diminishing action of the demagnetizing field energy and the deformation to a oblate shape due to the decrease in the spontaneous curvature of the parts of a membrane normal to a field.

Magnetic response of the superconducting thin film

Based on the London theory, the supercurrent density and penetrating magnetic field in response to an applied perpendicular magnetic are calculated for a superconducting thin film (strip or disk). Using the method of the Hankel transform, the formulations for the supercurrent density and penetrating magnetic field are given in two limits: a⪢ Λ and a⪡ Λ ( a is the width of the superconducting thin film and Λ is the effective screening length). From these formulations it is shown that the supercurrent density and penetrating magnetic field decrease by a power law with the distance from the edge of a superconducting thin film, unlike the exponential decrease in bulk superconductors.

Thermodynamics of electrolyte solutions in the modified mean spherical approximation

The exact Ornstein–Zernike formalism for ionic fluids is seen to be equivalent to the dressed-ion theory (DIT), therefore proving the exact character of this mean-field formalism. The modified mean spherical approximation (MMSA) [Varela et al., J. Chem. Phys. 109, 1930 (1998)] is a modified version of the mean spherical approximation, which corrects some of the deficiencies of the original version of this closure relation in the prediction of the effective screening length. The MMSA effective non-Debye decay length, developed in the framework of the dressed-ion transport theory (DIT) of Kjellander and Mitchell, is an improvement on those of other theoretical and numerical schemes, which include self-consistent second moment approaches, asymptotic expansions, and nonlinear Debye–Hückel approximations. The MMSA screening length is used to analyze thermodynamic magnitudes of the charged fluid such as the internal energy and the osmotic coefficient and the results are seen to fit accurately to hypernetted chain calculations.

Geometrical evidence for long-range coupling in strongly anisotropic adsorbate systems: Sr and Li on Mo(211)

Alkali and earth alkali metals like Li and Sr adsorbed on the furrowed substrates Mo(211) and W(211) tend to form chain structures (1× n). These chains are oriented normal to the furrows, and n can reach values up to 8. In order to clarify the nature of the coupling along the furrows, we carried out a quantitative LEED–IV study in the energy range between 50 and 180 eV. We investigated the adsorption geometry of the Sr(1×5) structure on Mo(211) including the relaxations in the substrate. These results are compared with those obtained recently for the Li(1×4) structure on the same surface. The long-range indirect interactions between both types of adsorbate atoms that are responsible for ordering of the chains in the [01̄1] direction are correlated with substantial lateral substrate relaxations by up to 0.2 Å along the Mo(211) [1̄11] furrow direction. For both adsorbates, the relaxations form wave-like density modulations in the substrate that seem to be caused by Friedel oscillations of the substrate conduction electrons. These screen the local adsorbate-induced distortion of the electron density. The variation of periodicity and the corresponding change of effective screening length between the two adsorbates may be due to surface states involved in the bond formation. Whereas for Sr, the Langmuir–Gurney (LG) model still provides a consistent picture of bond formation compared with the observed bond lengths and changes of work function, the predictions of the LG model are inconsistent with the experimental findings for Li.

Conductance of symmetric electrolyte solutions: Formulation of the dressed-ion transport theory (DITT)

The concentration dependence of the electrical conductance of several symmetrical electrolytes is studied using the dressed-ion transport theory (DITT) formalism. This theoretical scheme is constructed from the Fuoss–Onsager theory using the equilibrium dressed-ion theory (DIT) distribution functions for electrolyte and colloid media. The conductance equation is constructed from previous results for the relaxation of the ionic atmosphere [Varela et al., J. Chem. Phys. 110, 4483 (1999)], now completed with the calculation of the concentration-dependent electrophoretic velocity of ions on the basis of a DIT in a hydrodynamic point of view. Onsager’s limiting law for the electrophoretic velocity based on the Debye–Hückel (DH) equilibrium distribution function is reformulated in terms of the DIT renormalized quantities, effective charges and effective screening length. The electrophoretic correction to the velocity calculated in the framework of this DITT is shown to exhibit a nontrivial dependence on the renormalized dielectric constant of the medium (ε*). The concentration dependence of both the deviations of the renormalized dielectric constant from the classical limit and the electrophoretic correction to the mobility is analyzed using the modified-mean spherical approximation (MMSA) value of the DIT linear response function α̂(k). The behavior of ε* and therefore of the electrophoretic correction to the ionic (or colloidal) mobilities is studied for both the random-phase approximation (RPA) and the MMSA and they are related to ionic association through the dimensionless coupling parameter, ζ, made up from the ratio between the Bjerrum length and the mean ionic radius. The expression for the conductance of the electrolyte solutions obtained in this new theoretical approach is cast in the form of a generalized Onsager’s limiting law with a concentration-dependent slope which is predicted in terms of the formation of DIT renormalized quasiparticles in the solution. Conductance predictions of several theoretical expressions for the renormalized magnitudes of electrolyte solutions are compared to direct experimental data of KCl, and are in very good agreement with the theoretical predictions of the mean-field DITT, which confirms the convenience of understanding transport processes in terms of effective dynamical entities with renormalized ionic charges interacting by means of a renormalized screened potential.

Relaxation of the ionic cloud on the basis of a dressed-ion theory

The dynamic response of a bulk electrolyte or colloid solution to an external field is investigated on the basis of a dressed-ion theory (DIT) in a hydrodynamic point of view. The radial part of the perturbed electric field acting on a given ion is explicitly calculated in terms of the DIT quantities derived from the linear response function calculated from the modified mean-spherical aproximation (MMSA) and its static and frequency-dependent limits are analyzed. In the static case, the asymptotic behavior is analyzed and Onsager’s result is reformulated in terms of the effective charges and effective screening length and in the limit of vanishing concentration Debye–Falkenhagen–Onsager results are recovered. In the frequency-dependent DIT transport theory a relation between the field frequency and the time of relaxation of the ionic atmosphere is shown to be needed in order to get real renormalized charges and screening lengths. A decay of the perturbed electrostatic field as the inverse square root of the field frequency is obtained at high frequency and vanishing concentration along with a model-independent phase factor between the external and internal fields. The radial dependence of the perturbed average potential in the neighborhood of a quasiparticle is also calculated in the static case and several behaviors ranging from classical Derjaguin–Landau–Verwey–Overbeek colloidal stability theory interaction to pure attraction and repulsion are obtained. The results are analyzed in terms of a splitting of the ionic cloud into three different parts each one contributing to the radial dependence of the perturbed potential.

Stopping of heavy ions in plasmas at strong coupling

Standard approaches to the energy loss of ions in plasmas like the dielectric linear response or the binary collision model are strictly valid only in the regimes where the plasma is close to ideal and the coupling between projectile-ion and the plasma target is sufficiently weak. In this review we explore the stopping power in regimes where these conditions are not met. Actually relevant fields of application are heavy ion driven inertial fusion and the cooling of beams of charged particles by electrons. The conventional linear mean-field treatments are extended by many-body methods and particle simulations to account for strong correlations between the particles and for nonlinear coupling. We report the following important results in connection with the stopping at strong coupling: The energy loss of an ion scales with its charge approximately like Z 1.5, the effective screening length depends on Z and is larger than the Debye length. Slow highly charged ions are surrounded by a cloud of electrons trapped by many body collisions. Quantum effects like the wave nature of the electrons and Pauli-blocking reduce the stopping power by mollifying the effective interactions.

Solving the Poisson–Boltzmann equation to obtain interaction energies between confined, like-charged cylinders

We numerically solve the nonlinear Poisson–Boltzmann equation for two cylinders confined by two parallel charged plates. The repulsive electrical double layer component of the cylinder pair potential is substantially reduced by confinement between like-charged plates. While the effective cylinder surface charge is increased by the confinement, the effective interaction screening length is reduced, this effect being dominant so that the repulsive confined cylinder–cylinder interaction potential is reduced.

Effective ionic charges, permittivity and screening length: dressed ion theory applied to 1:2 electrolyte solutions

The concept of effective charges of charged particles in electrolyte solutions is discussed and defined in a general and exact way for cases with ‘exponential’ screening. The effective charges thus obtained are equivalent to those used in dressed ion theory (DIT) (Kjellander, R., and Mitchell, D. J., 1992, Chem. Phys. Lett., 200, 76; 1994, J. chem. Phys., 101, 603), which is an exact reformulation of the statistical mechanics of electrolytes, DIT is particularly suited for use in analyses of screening phenomena in electrolytes, and the reasons why it has this property are discussed in some detail. The DIT formalism is applied to obtain effective ionic charges q*, effective permittivity E, and screening length 1/K, of 1:2 aqueous electrolyte solutions in the hypernetted chain approximation. In the limit of infinite dilution q* → the actual charge, E → the permittivity of the solvent and 1/K ˜ the Debye length. The values of these quantities deviate much more from these limiting values compared with similar 1:1 and 2:2 electrolytes, and this is the case even at quite low concentrations.

Effective ionic charges, permittivity and screening length: dressed ion theory applied to 1:2 electrolyte solutions

Effective ionic charges, permittivity and screening length: dressed ion theory applied to 1:2 electrolyte solutions

Static structure of electrolyte systems and the linear response function on the basis of a dressed-ion theory

The static structure of a bulk electrolyte solution or colloid system is investigated in the framework of a dressed-ion theory (DIT). The number–number, charge–number, and charge–charge static structure factors are calculated and are seen to depend only on the linear response function of the DIT α̂(k), the α function therefore determining the charge structure of the fluid in what is an expression of the fluctuation–dissipation theorem. The expression of the static structure factors for one-component charged spheres (OCCS) is evaluated in the random-phase approximation and in a modified version of the mean-spherical approximation (MSA), using the hard-sphere fluid as a reference system, and an explicit expression for the linear response function and dielectric function is obtained. The effective screening length (κ−1) and the transition from monotonic exponential to oscillatory behavior obtained from the modified MSA expression of the α function are seen to improve the ones derived from the second moment condition at intermediate concentrations. The internal charge density distribution of a dressed ion and the renormalized ion charges (q*) are also investigated. The oscillatory behavior of the charge distributions suggests an “onionlike model,” with the central ion surrounded by spherical charge shells. The effective charges calculated from the modified MSA are seen to diverge in the neighborhood of the transition from the monotonic exponential regime to the oscillatory regime. In the limit of vanishing concentration, Debye–Hückel (DH) results are recovered.