Nonlinear Screening Research Articles

Phase separation in charge-stabilized colloidal suspensions: Influence of nonlinear screening

The phase behavior of charge-stabilized colloidal suspensions is modeled by a combination of response theory for electrostatic interparticle interactions and variational theory for free energies. Integrating out degrees of freedom of the microions (counterions, salt ions), the macroion-microion mixture is mapped onto a one-component system governed by effective macroion interactions. Linear response of microions to the electrostatic potential of the macroions results in a screened-Coulomb (Yukawa) effective pair potential and a one-body volume energy, while nonlinear response modifies the effective interactions [A. R. Denton, Phys. Rev. E 70, 031404 (2004)]. The volume energy and effective pair potential are taken as input to a variational free energy, based on thermodynamic perturbation theory. For both linear and first-order nonlinear effective interactions, a coexistence analysis applied to aqueous suspensions of highly charged macroions and monovalent microions yields bulk separation of macroion-rich and macroion-poor phases below a critical salt concentration, in qualitative agreement with predictions of related linearized theories [R. van Roij, M. Dijkstra, and J.-P. Hansen, Phys. Rev. E 59, 2010 (1999); P. B. Warren, J. Chem. Phys. 112, 4683 (2000)]. It is concluded that nonlinear screening can modify phase behavior but does not necessarily suppress bulk phase separation of de-ionized suspensions.

Effects of interactions and disorder on the compressibility of two-dimensional electron and hole systems

The compressibility χ of dilute two-dimensional electron and hole gases in GaAs semiconductor structures has been studied in the ranges of the interaction parameter r s = 1 –2.5 and r s = 10 –30 for the electron and hole system, respectively. Nonmonotonic dependence of χ - 1 with an upturn at low carrier densities is observed. Despite the large difference in r s the behavior of χ - 1 in both systems can be accurately described by the theory of nonlinear screening of disorder by the carriers.

Collective Grain Interactions for Constant Ionization Source

AbstractThe dust screening and dust attraction in plasmas is considered for the constant ionization source. Both limits of linear and nonlinear screening are considered. It is shown that the non‐linear screening changes substantially the collective dust screening and collective dust attraction. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

New paradigm for plasma crystal formation

The major properties of complex (dusty) plasmas as a new state of matter are shown to be determined by the collective interaction of two coupled fields, the electrostatic field and the flux field. Both fields determine the grain collective nonlinear screening and grain attraction. Collective interactions together with nonlinear screening are used in the formulation of a new paradigm for plasma crystal formation.

Nonequilibrium Green's function theory of resonant steady state photoconduction in a double quantum well FET subject to THz radiation at plasmon frequency

Recent experimental observations by X.G. Peralta and S.J. Allen, et al. of dc photoconductivity resonances in steady source-drain current subject to terahertz radiation in a grid-gated double-quantum well FET suggested an association with plasmon resonances. This association was definitively confirmed for some parameter ranges in our detailed electrodynamic absorbance calculations. In this paper we propose that the reason that the dc photoconductance resonances match the plasmon resonances in semiconductors is based on a nonlinear dynamic screening mechanism. In this, we employ a shielded potential approximation that is nonlinear in the terahertz field to determine the nonequilibrium Green's function and associated density perturbation that govern the nonequilibrium dielectric polarization of the medium. This ‘‘conditioning’’ of the system by the incident THz radiation results in resonant polarization response at the plasmon frequencies which, in turn, causes a sharp drop of the resistive shielded impurity scattering potentials and attendant increase of the dc source-drain current. This amounts to disabling the impurity scattering mechanism by plasmon resonant behavior in nonlinear screening.

Theory of boundary-free two-dimensional dust clusters

It is shown theoretically that a stable two-dimensional (2D) grain cluster can exist in plasmas without external confinement if the shadow attraction of grains is taken into account. These are considered as boundary-free clusters. The equilibrium radius of the clusters is investigated numerically. It is found that it is rapidly decreasing with an increase of the attraction coefficient and with an increase of the number of grains N in the cluster. Comparison of energies of one shell cluster containing N grains with the energies of a cluster with N−1 grains in the shell and an additional one grain in the center as functions of the attraction coefficient is used to find the magic numbers for new shell creation. It is demonstrated that a dissociation of the cluster in several smaller clusters requires less energy than a removal of one of the grains from the cluster. The computations were performed for the Debye screening and for the nonlinear screening models and show that the structure of the clusters is sensitive to the type of screening. Frequencies of all collective modes of the 2D boundary-free clusters are calculated up to N=7 grains in the cluster for the case where all grains form one shell cluster and for the case where N=6 grains form one shell cluster and one of the grains is located at the center of the cluster. The frequencies of the modes increase with a decrease of the cluster radius. Stable and unstable modes are investigated as a function of the attraction coefficient. The presence of instability indicates that this type of equilibrium cluster does not correspond to the minimum energy in all directions and will be converted into another stable configuration. The universal magic number Nm of grains in one shell cluster, such that for N=Nm+1 the modes of the shell start to be unstable and the cluster converts to the cluster with Nm grains in the shell and one grain in the center, is found for both the Yukawa screening and for the nonlinear screening. A new experimental setup with remote hard-wall confinement is proposed for possible experimental investigation of boundary-free 2D clusters.

A novel aspect of dust in plasma

Nonlinear screening of the dust grains immersed in a homogenous fully ionized electron-ion plasma is investigated. Assuming conservation of entropy, an important relation is obtained between the maximum potential (and therefore the charge) of the dust grain and the temperature of the electrons. The Thomas-Fermi equation is derived for the potential of a dust grain in a nondegenerate plasma suggesting the existence of dust atom with a well defined atomic radius. Furthermore, based on the Born-Oppenheimer approximation, the notion of a dust-grain molecule is introduced in which the protons act like a kind of “glue” which binds two negatively charged dust grains together, and the motion of the grains have little influence on that binding force. Finally, considering the weak interaction between the proton clouds of two dust grains, an expression of exchange energy is obtained.

Effects of interactions and disorder on the compressibility of two‐dimensional electron and hole systems

AbstractWe have studied the thermodynamic compressibility of 2D electron and 2D hole gases near the apparent metal‐insulator transition, in the ranges of the interaction parameter rs =1–2.5 and rs =10–30, respectively. Nonmonotonic dependence of the inverse compressibility on the carrier density is observed with an upturn at low densities. Despite the large difference in rs , this behaviour of inverse compressibility in both electron and hole systems can be quantitatively accounted for by a nonlinear screening of disorder by the carriers, in particular, by the disorder‐driven proliferation of depletion regions in the 2D channel. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Collective Grain Interactions II. Non‐linear Collective Drag Force

AbstractIt is found that the collective effects operating at large distances from the grain surface can produce substantial scattering of the ion flux and create an additional collective drag force dominant for large grain densities. The consideration is restricted to large grain charges β = Zde 2a /TiλDi ≫ 1 and Ti /Te ≪ 1 (–eZd being the grain charge in units of electron charge, a being the grain size, λDi being the ion Debye radius and Te,i being electron and ion temperatures, respectively). For present dusty plasma experiments β ≈ 10–50, the large charges of grains are screened non‐linearly and the ion scattering creates non‐linear drag force. The present investigation considers effects of scattering by collective grain fields at large distances from the grains. It is found that the physical reason of the importance of collective drag force, calculated in this paper, is related to presence of weakly screened collective field of grains outside the non‐linear screening distance depending on grain densities. The amplitude of this collective fields of the grains is determined by non‐linear screening at non‐linear screening radius. It is shown that for dust densities of present experiments the collective drag force related to this scattering can be of the order of the non‐linear drag force caused by scattering inside the non‐linear screening radius or even larger. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Nonlinear drag force in dusty plasmas

The condition for large angle scattering in ion-grain collisions, which determine the nonlinear part of the ion drag force, coincides with the condition for the grain screening to be nonlinear (∣eϕ∣∕Ti>1 where ϕ is the electrostatic grain potential and Ti is the ion mean energy), a condition met in many laboratory experiments. A self-consistent treatment of the nonlinear ion-drag force therefore requires a correct treatment of nonlinear screening. A model to account for the nonlinearity is presented and the drag force calculated, showing that it can be substantially larger than that for linear screening. An important physical feature found in the present investigation is that nonlinear screening corresponds to almost full screening inside a finite radius and that large angle scattering occurs only inside this radius. The nonlinear ion-drag force is found to have a strong dependence on the grain size, ratio of ion to electron temperatures, and ion density.

Routes Towards Anderson-Like Localization of Bose-Einstein Condensates in Disordered Optical Lattices

We investigate, both experimentally and theoretically, possible routes towards Anderson-like localization of Bose-Einstein condensates in disordered potentials. The dependence of this quantum interference effect on the nonlinear interactions and the shape of the disorder potential is investigated. Experiments with an optical lattice and a superimposed disordered potential reveal the lack of Anderson localization. A theoretical analysis shows that this absence is due to the large length scale of the disorder potential as well as its screening by the nonlinear interactions. Further analysis shows that incommensurable superlattices should allow for the observation of the crossover from the nonlinear screening regime to the Anderson localized case within realistic experimental parameters.

Nonlinear screening on the charged surfaces with trivalent and tetravalent salt ions: Monte Carlo simulations

We investigate the electrostatic screening phenomena with divalent, trivalent and tetravalent salt ions on charged surfaces. The integrated charge distribution function is studied to clarify the structure of the electric double-layers on spherical colloids and charged rods by Monte Carlo simulations. The profiles of electric double-layers show that the charge inversion phenomena with divalent salt are sensitive to the size of microions. These results reflect the importance of the nonlinearity and excluded-volume effect on strongly charged systems in an aqueous solution.

Role of effective potential barriers in the nonlinear screening regime: Grain charging and ion drag force

The effects of barriers in the effective potential of ion-grain interaction on grain charging and ion drag force are investigated in the nonlinear regime of grain screening. The use of analytical fittings of the numerical solutions to the Poisson’s equation for the electrostatic potential around a dust grain assuming nonlinear dependence of polarization charge around the grain on electrostatic potential allows us to present the results in analytical form. This can be useful since the previous investigations use complex numerical calculations.

Nonohmic quasi-2D hopping conductance and the kinetics of its relaxation

The nonohmic properties of a quasi-2D hopping-conductance channel are studied. The channel is formed in a p-Si layer by a field effect in the region where the Fermi level crosses the impurity band. It is shown that the dependence of conductance σ on a longitudinal electric field E has a threshold character and obeys the law lnσ(E) ∝ E1/2. The dependences of the conductance of the quasi-2D channel on temperature and the electric field are satisfactorily explained using the concepts of nonlinear screening and of nonohmic properties of disordered systems with a random Coulomb potential. This mechanism of nonlinearity is confirmed by specific features of the mesoscopic fluctuations in the off-diagonal component of resistance, which reflect the reconstruction of a percolation cluster under the action of the longitudinal electric field. A long-term relaxation in conductance is observed during transition from a nonohmic to ohmic mode, which indicates that the system exhibits properties corresponding to electronic glass and that the current paths are significantly modified in a strong electric field.

Screening of a Test Charge in Plasma

Nonlinear screening of a test charge in plasma by electronstrapped or untrapped is studied. The obtained results are inrigorous estimations mathematically in comparison with thecorresponding Debye screening forms. Meanwhile their validity is physically discussed and some confusions in literature are clarified.

Variational approach to the scattering of charged particles by a many-electron system

We report a variational approach to the nonlinearly screened interaction of charged particles with a many-electron system. This approach has been developed by introducing a modification of the Schwinger variational principle of scattering theory, which allows to obtain nonperturbative scattering cross-sections of moving projectiles from the knowledge of the linear and quadratic density-response functions of the target. Our theory is illustrated with a calculation of the energy loss per unit path length of slow antiprotons moving in a uniform electron gas, which shows good agreement with a fully nonlinear self-consistent Hartree calculation. Since available self-consistent calculations are restricted to low heavy-projectile velocities, we expect our theory to have novel applications to a variety of processes where nonlinear screening plays an important role.

Nonlinear screening and stopping power in two-dimensional electron gases

We have used density-functional theory to study the nonlinear screening properties of a two-dimensional (2D) electron gas. In particular, we consider the screening of an external static point charge of magnitude $Z$ as a function of the distance of the charge from the plane of the gas. The self-consistent screening potentials are then used to determine the 2D stopping power in the low-velocity limit based on the momentum transfer cross section. Calculations as a function of $Z$ establish the limits of validity of linear and quadratic response theory calculations, and show that nonlinear screening theory already provides significant corrections in the case of protons. In contrast to the 3D situation, we find that the nonlinearly screened potential supports a bound state even in the high-density limit. This behavior is elucidated with the derivation of a high-density screening theorem which proves that the screening charge can be calculated perturbatively in the high-density limit for arbitrary dimensions. However, the theorem has particularly interesting implications in 2D where, contrary to expectations, we find that perturbation theory remains valid even when the perturbing potential supports bound states.

Nonlinear Screening Theory of the Coulomb Glass

A nonlinear screening theory is formulated to study the problem of gap formation and its relation to glassy freezing in classical Coulomb glasses. We find that a pseudogap ("plasma dip") in a single-particle density of states begins to open already at temperatures comparable to the Coulomb energy. This phenomenon is shown to reflect the emergence of short-range correlations in a liquid (plasma) phase, a process which occurs even in the absence of disorder. Glassy ordering emerges when disorder is present, but this occurs only at temperatures roughly an order of magnitude lower. Our result demonstrate that the formation of the plasma dip at high temperatures is a process distinct from the formation of the Efros-Shklovskii pseudogap, which in our model emerges only within the glassy phase.

Nonlinear Plasma Screening Effects on Elastic Electron-Dust Grain Collisions in Dusty Plasmas

Nonlinear plasma screening effects on elastic electron-dust grain collisions are investigated in dusty plasmas. The nonlinear screened interaction is considered to obtain the total interaction potential between the projectile electron and the dust grain. The semiclassical straightline trajectory analysis is applied to the path of the projectile electron in order to investigate the variation of the eikonal phase as functions of the impact parameter, dust charge, collision energy, and Debye length. The result shows that the nonlinear correction effects increase the magnitude of the eikonal phase as well as the total scattering cross section. It is found that the nonlinear effects on the eikonal phase are more significant for small impact parameters and decrease with increasing impact parameter.

On the theory of aggregation and micellization: PEO–PVP copolymer in water

We develop a theoretical approach to micellization of the PEO-PVP block-copolymer in water. This copolymer is a weak polyelectrolyte due to protonation of VP blocks. The theory accounts for non-linear ion screening, and predicts strong position dependence of both ion concentration and the effective Debye length. We consider both the case when the local Debye length is small compared to the core radius and the case when it is large. We found that the effective (local) pH is not uniform even inside one micellar core, hence non-uniform protonation of the core with higher charge density near the surface. In many cases the core charge is concentrated in a relatively thin surface layer. Considering statistical weights of non-equilibrium micelles and their continuous evolution we show that kinetics of both formation and dissociation of typical block-copolymer or surfactant micelles can be extremely slow. Thus micelle formation at the genuine (equilibrium) critical micelle concentration (c.m.c.) is totally suppressed (involves astronomical time scales) if the micelles are big enough. An 'apparent' critical micelle concentration (c.m.c.*) is introduced to account for this effect. The apparent c.m.c.* could be much higher than the genuine equilibrium c.m.c., i.e. a significant hysteresis is inherent in these systems. We also determine the ranges of meta-stability of micelles depending on the experimental time-scales.