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.     

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.     

General solvation motifs of a charged linear macroion in an aqueous droplet

ABSTRACT

We explore the solvation patterns of a charged rigid and semi-rigid linear macroion in an aqueous droplet. The solvation patterns are summarised in an empirical ‘phase diagram’ on the parameter space defined by the length of the macroion and its charge density. In the study, we employ molecular dynamics and atomistic modelling. The macroion is represented by a positively charged carbon nanotube. Linear macroion-solvent interactions in droplets are distinct from those of spherical ions because of the interplay among several factors such as the tendency of the solvent to form spherical droplets in order to minimise the surface energy, the constraint on the charge of a spherical droplet imposed by the Rayleigh limit, the solvation energy of the macroion and its length. The combination of all these factors may lead to a variety of solvent distributions along the rigid rod such as asymmetric solvation of the linear macroion, formation of spiky ‘star’-like distribution of solvent, partial wetting of the rod by a droplet. The study provides insight into the solvation of macroions in droplets with applications in electrosprayed macroions and atmospheric aerosols. We also propose a possible path of generating a sequence of nanoparticles of different shapes (spheres, multi-point stars) along a linear macromolecule by exploiting the various solvation patterns.     

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.     

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     

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     

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     

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.     

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.     

Experimental observation of excited state muon transfer in mixtures of hydrogen isotopes

Molecular dynamic (MD) computer simulations are used to investigate the stopping of heavy ions in strongly coupled electron plasmas. Our results show, that in this regime collisions between the electrons as well as non-linear screening effects yield at low ion velocities a dependence of the stopping power on the ion chargeZ which scales like Z^1.43 instead of the usual Z² ln(const/Z)-scaling for weak coupling. This is connected with an enhanced local density of electrons around a highly charged, slow ion.Supported by the Bundesministerium für Bildung und Forschung (BMBF), the Gesellschaft für Schwerionenforschung Darmstadt (GSI) and the European Community.     

Dielectrophoresis of nanocolloids: A molecular dynamics study

Dielectrophoresis (DEP), the motion of polarizable particles in non-uniform electric fields, has become an important tool for the transport, separation, and characterization of microparticles in biomedical and nanoelectronics research. In this article we present, to our knowledge, the first molecular dynamics simulations of DEP of nanometer-sized colloidal particles. We introduce a simplified model for a polarizable nanoparticle, consisting of a large charged macroion and oppositely charged microions, in an explicit solvent. The model is then used to study DEP motion of the particle at different combinations of temperature and electric field strength. In accord with linear response theory, the particle drift velocities are shown to be proportional to the DEP force. Analysis of the colloid DEP mobility shows a clear time dependence, demonstrating the variation of friction under non-equilibrium. The time dependence of the mobility further results in an apparent weak variation of the DEP displacements with temperature.     

Rotational bands in 169Re

Based on the systematic investigation of the data available for nuclei with A≥ 40, a Z ^1/3-dependence for the nuclear charge radii is shown to be superior to the generally accepted A ^1/3 law. A delicate scattering of data around R _c/Z ^1/3 is inferred as owing to the isospin effect and a linear dependence of R _c/Z ^1/3 on N/Z (or (N - Z)/2) is found. This inference is well supported by the microscopic Relativistic Continuum Hartree-Bogoliubov (RCHB) calculation conducted for the proton magic Ca, Ni, Zr, Sn and Pb isotopes including the exotic nuclei close to the neutron drip line. With the linear isospin dependence provided by the data and RCHB theory, a new isospin-dependent Z ^1/3 formula for the nuclear charge radii is proposed. Received: 23 September 2001 / Accepted: 21 January 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.     

Anomalously interacting new extra vector bosons and their first LHC constraints

In this review phenomenological consequences of the Standard Model extension by means of new spin-1 chiral fields with the internal quantum numbers of the electroweak Higgs doublets are summarized. The prospects for resonance production and detection of the chiral vector Z* and W*^± bosons at the LHC energies are considered on the basis of quantitative simulations within the CompHEP/CalcHEP package. The Z* boson can be observed as a Breit-Wigner resonance peak in the invariant dilepton mass distributions in the same way as the well-known extra gauge Z?? bosons. However, the Z* bosons have unique signatures in transverse momentum, angular and pseudorapidity distributions of the final leptons, which allow one to distinguish them from other heavy neutral resonances. In 2010, with 40 pb^?1 of the LHC proton-proton data at the energy 7 TeV, the ATLAS detector was used to search for narrow resonances in the invariant mass spectrum of e ⁺ e ^? and ??⁺??^? final states and high-mass charged states decaying to a charged lepton and a neutrino. No statistically significant excess above the Standard Model expectation was observed. The exclusion mass limits of 1.15 and 1.35 TeV/c ² were obtained for the chiral neutral Z* and charged W* bosons, respectively. These are the first direct limits on the W* and Z* boson production. Based on the above, a novel strategy for the chiral boson search in the LHC dijet data is discussed. For almost all currently considered exotic models the relevant signal is expected in the central dijet rapidity region y _1,2 ? 0 and |y ₁ ? y ₂| ? 0. On the contrary, the chiral bosons do not contribute to this region but produce an excess of dijet events far away from it. In particular, for these bosons the appropriate kinematical restrictions lead to a dip in the centrality ratio distribution over the dijet invariant mass instead of a bump expected in the most exotic models.     

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.     

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.     

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.     

Fragmentation of12C nuclei in emulsion at 50 GeV/c

A total of 852¹²C-emulsion nucleus interactions at 4.2 GeV/c per incident nucleon was investigated. At least one charged projectile fragment was observed in 733 events, in which the multiplicity and angular distributions ofZ=1,2, and ≧3 projectile fragments were studied. Five events were observed in which¹²C projectile nuclei were fragmented into twoZ=3 fragments. Thus the cross section of this process is about 6×10^?3 of the inelastic cross section. The angular distribution of projectile fragments becomes narrower as the fragment charge increases. At all values of fragment charges, a pronounced peak in the angular distribution can be observed at zero emission angle. In this paper, only the projectile-fragmentation events possessing no heavily ionizing particle (n _h =0 events) have been investigated. Our sample contains 84 of these events, i.e., about 10% of the total inelastic events. The number of events withZ _max, the charge of the emitted principal fragment, equal to 1, 2, 3, 4, and 5 are 11, 52, 13, 4, and 4, respectively. Of these 84 events, 36 interactions have a total charge of emitted projectile fragmentsZ ^* equal to 6, i.e., as much as the beam chargeZ _p . Of the 36 events, 17 produce no charged pions and of the 17 events, 10 only represent the dissociation of¹²C→3α, i.e., 1.2% of the total inelastic interactions. The number of events withZ ^*=5, 4, 3, 2, and 1 are 27, 14, 4, 2, and 1, respectively. The average number of produced charged pions per one interacting projectile nucleon was estimated to be 1.2±0.1. This value agrees with the corresponding one in elementary interaction at the same energy per nucleon, a result pertaining to the incoherent production model in collision of two nuclei. In this class of events,n _h =0, the number of stars in which H, He, Li, Be, and B isotopes were detected are 59, 58, 13, 4, and 4, respectively. The projected angular distributions ofZ=1 and 2 projectile fragments are Gaussian shaped, narrow, consistent with isotropy, and depend on the fragment. These distributions are consistent with quantum mechanical calculations using the sudden approximation and shell-model functions. From the angular measurements ofα-particle tracks in the dissociation¹²C→3α events, the distribution ofα-particle transverse momentum inside the carbon projectile nucleus was deduced. It seems that the dissociation of¹²C→3α happens via an intermediate⁸Be state.     

Contribution of superstring <Emphasis Type="Italic">Z</Emphasis>′ boson on the polarization effects in proton proton collisions

In this work we investigate the single- and the double-spin asymmetries at the collisions of polarized protons pp → (γ ^*, Z ⁰, Z′) + X within the scope of QCD, the electroweak interaction and superstring E ₆ theory. The helicity amplitude method is used. Analytical expressions for the single- and the double-spin asymmetries are obtained and their dependence on the transverse momentum of the lepton pair is investigated at the three different values of invariant masses of the lepton pair. The pure contribution coming from the superstring Z′ boson on the single- and double- spin asymmetries has been extracted. The results obtained allow investigation of the spin structure of the proton.     

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.