Nonlinear Screening Research Articles

Model of large volumetric capacitance in graphene supercapacitors based on ion clustering

Electric double-layer supercapacitors (SCs) are promising devices for high-power energy storage based on the reversible absorption of ions into porous conducting electrodes. Graphene is a particularly good candidate for the electrode material in SCs due to its high conductivity and large surface area. In this paper, we consider SC electrodes made from a stack of graphene sheets with randomly inserted spacer molecules. We show that the large volumetric capacitances $C\ensuremath{\gtrsim}100\phantom{\rule{0.28em}{0ex}}\mathrm{F}/{\mathrm{cm}}^{3}$ observed experimentally can be understood as a result of collective intercalation of ions into the graphene stack and the accompanying nonlinear screening by graphene electrons that renormalizes the charge of the ion clusters.

Charge inhomogeneities and transport in semiconductor heterostructures with a Mnδ-layer

We study experimentally and theoretically the effects of disorder, nonlinear screening, and magnetism in semiconductor heterostructures containing a $\delta$-layer of Mn, where the charge carriers are confined within a quantum well and hence both ferromagnetism and transport are two-dimensional (2D) and differ qualitatively from their bulk counterparts. Anomalies in the electrical resistance observed in both metallic and insulating structures can be interpreted as a signature of significant ferromagnetic correlations. The insulating samples turn out to be the most interesting as they can give us valuable insights into the mechanisms of ferromagnetism in these heterostructures. At low charge carrier densities, we show how the interplay of disorder and nonlinear screening can result in the organization of the carriers in the 2D transport channel into charge droplets separated by insulating barriers. Based on such a droplet picture and including the effect of magnetic correlations, we analyze the transport properties of this set of droplets, compare it with experimental data, and find a good agreement between the model calculations and experiment. Our analysis shows that the peak or shoulder-like features observed in temperature dependence of resistance of 2D heterostructures $\delta$-doped by Mn lie significantly below the Curie temperature $T_{C}$ unlike the three-dimensional case, where it lies above and close to $T_{C}$. We also discuss the consequences of our description for understanding the mechanisms of ferromagnetism in the heterostructures under study.

Theory of volumetric capacitance of an electric double-layer supercapacitor

Electric double-layer supercapacitors are a fast-rising class of high-power energy storage devices based on porous electrodes immersed in a concentrated electrolyte or ionic liquid. As yet there is no microscopic theory to describe their surprisingly large capacitance per unit volume (volumetric capacitance) of ~100 F/cm(3), nor is there a good understanding of the fundamental limits on volumetric capacitance. In this paper we present a non-mean-field theory of the volumetric capacitance of a supercapacitor that captures the discrete nature of the ions and the exponential screening of their repulsive interaction by the electrode. We consider analytically and via Monte Carlo simulations the case of an electrode made from a good metal and show that in this case the volumetric capacitance can reach the record values. We also study how the capacitance is reduced when the electrode is an imperfect metal characterized by some finite screening radius. Finally, we argue that a carbon electrode, despite its relatively large linear screening radius, can be approximated as a perfect metal because of its strong nonlinear screening. In this way the experimentally measured capacitance values of ~100 F/cm(3) may be understood.

State Dependent Regenerative Effect in Milling Processes

The governing equation of milling processes is generalized with the help of accurate chip thickness derivation resulting in a state dependent delay model. This model is valid for large amplitude machine tool vibrations and uses accurate nonlinear screen functions describing the entrance and exit positions of the cutting edges of the milling tool relative to the workpiece. The periodic motions of this nonlinear system are calculated by a shooting method. The stability calculation is based on the linearization around these periodic solutions by means of the semidiscretization method applied for the corresponding time-periodic delay system. Predictor-corrector method is developed to continue the periodic solutions as the bifurcation parameter, that is, the axial immersion is varied. It is observed that the influence of the state dependent delay on linear stability can be significant close to resonance where large amplitude forced vibrations occur. The existence of an unusual fold bifurcation is shown where a kind of hysteresis phenomenon appears between two different stable periodic motions.

Nonlinear Screening in Multilayer Graphene Systems

Electrostatic screening in multilayer graphene is highly nonlinear due to the vanishing density of states at the Fermi level. Using a discrete model we study the charge screening normal to the layers. Our model shows a strong charge and temperature dependence and has a simple continuum limit at T=0 for undoped systems. Doped systems can exhibit more complex behavior due to minority-carrier screening. Most importantly we find that the screening length can vary more than an order of magnitude depending on the experimental conditions, reconciling the large range of screening lengths reported in previous experiments. This has important consequences for technological applications of multilayer graphene used in electrodes or transistor channels.

Nonlinear screening of charged macromolecules

We present several aspects of the screening of charged macromolecules in an electrolyte. After a review of the basic mean field approach, based on the linear Debye-Hückel theory, we consider the case of highly charged macromolecules, where the linear approximation breaks down and the system is described by the full nonlinear Poisson-Boltzmann equation. Some analytical results for this nonlinear equation give some interesting insight on physical phenomena like the charge renormalization and the Manning counterion condensation.

Nonlinear screening of charges induced in graphene by metal contacts

To understand the band bending caused by metal contacts, we study the potential and charge density induced in graphene in response to contact with a metal strip. We find that the screening is weak by comparison with a normal metal as a consequence of the ultra-relativistic nature of the electron spectrum near the Fermi energy. The induced potential decays with the distance from the metal contact as x^{-1/2} and x^{-1} for undoped and doped graphene, respectively, breaking its spatial homogeneity. In the contact region the metal contact can give rise to the formation of a p-p', n-n', p-n junction (or with additional gating or impurity doping, even a p-n-p' junction) that contributes to the overall resistance of the graphene sample, destroying its electron-hole symmetry. Using the work functions of metal-covered graphene recently calculated by Khomyakov et al. [Phys. Rev. B 79, 195425 (2009)] we predict the boundary potential and junction type for different metal contacts.

Poisson–Boltzmann theory of charged colloids: limits of the cell model for saltysuspensions

Thermodynamic properties of charge-stabilized colloidal suspensions and polyelectrolytesolutions are commonly modelled by implementing the mean-field Poisson–Boltzmann(PB) theory within a cell model. This approach models a bulk system by a singlemacroion, together with counterions and salt ions, confined to a symmetricallyshaped, electroneutral cell. While easing numerical solution of the nonlinear PBequation, the cell model neglects microion-induced interactions and correlationsbetween macroions, precluding modelling of macroion ordering phenomena. Analternative approach, which avoids the artificial constraints of cell geometry, exploitsthe mapping of a macroion–microion mixture onto a one-component model ofpseudo-macroions governed by effective interparticle interactions. In practice,effective-interaction models are usually based on linear-screening approximations,which can accurately describe strong nonlinear screening only by incorporatingan effective (renormalized) macroion charge. Combining charge renormalizationand linearized PB theories, in both the cell model and an effective-interaction(cell-free) model, we compute osmotic pressures of highly charged colloids andmonovalent microions, in Donnan equilibrium with a salt reservoir, over a range ofconcentrations. By comparing predictions with primitive model simulation data for salt-freesuspensions, and with predictions from nonlinear PB theory for salty suspensions, wechart the limits of both the cell model and linear-screening approximations inmodelling bulk thermodynamic properties. Up to moderately strong electrostaticcouplings, the cell model proves accurate for predicting osmotic pressures of deionized(counterion-dominated) suspensions. With increasing salt concentration, however, therelative contribution of macroion interactions to the osmotic pressure grows, leadingpredictions from the cell and effective-interaction models to deviate. No evidence isfound for a liquid–vapour phase instability driven by monovalent microions. Theseresults may guide applications of PB theory to colloidal suspensions and other softmaterials.

Electric field emission of electrons from negatively charged spherical particles in a dusty plasma in the regime of nonlinear screening

This note presents a discussion of the electric field emission from negatively charged spherical particles in a dusty plasma in the regime of nonlinear screening. Using the appropriate representation of the nonlinear screening by Gurevich and the matrix method, the tunneling probability of an electron through the potential energy barrier around the particle has been evaluated as a function of its radial energy; corresponding values of the current density have also been obtained. A discussion of numerical results, thus obtained concludes the presentation.

Nonlinear Screening Indexes of Drought Resistance at Rice Seedling Stage Based on Support Vector Machine

Screening indexes of drought resistance in crops is a puzzler with a few samples,multi-index and non-linear characteristics.Rationality of linear regression model and the indexes obtained by linear screening based on empirical risk minimization are debated.On the contrary,support vector machine based on structural risk minimization has the advantages of non-linear characteristics,fitting for a few samples,avoiding the over-fit,strong generalization ability and high prediction precision,etc.In this paper,setting the survival percentage under repeated drought condition as the target and support vector regression as the nonlinear screen tool,six integrated indicators including plant height,proline,malondialdehyde,leaf age,area of the first leaf under the central leaf and ascorbic acid,were highlighted from 24 morphological and physiological indicators in 15 paddy rice cultivars.The results showed that support vector regression model with the six integrated indicators had a more distinct improvement in fitting and prediction precision than the linear reference models.Considering the simplicity of indicators measurement,the support vector regression model with the only six morphological indicators including shoot dry weight,area of the second leaf under the central leaf,root shoot ratio,leaf age,leaf fresh weight and area of the first leaf under the central leaf was also feasible.Furthermore,an explanatory system including the significance of regression model and the importance of single indicator was established based on support vector regression and F-test.

Nonlinear Screening Indicators of Drought Resistance at Seedling Stage of Rice Based on Support Vector Machine

Screening indexes for drought resistance in crops is a puzzler characterized with a few samples, multiple indexes, and nonlinear. Rationality of linear regression model and indexes obtained by linear screening based on empirical risk minimization are controversal. On the contrary, support vector machine based on structural risk minimization has the advantages of nonlinear characteristics, fitting for a few samples, avoiding the over-fit, strong generalization ability, and high prediction precision. In this paper, setting the survival percentage under repeated drought condition as the target and support vector regression as the nonlinear screen tool, 6 integrated indexes including plant height, proline content, malondialdehyde content, leaf age, area of the first leaf under the central leaf and ascorbic acid were highlighted from 24 morphological and physiological indexes in 15 paddy rice cultivars. The results showed that support vector regression model with the 6 integrated indexes had a more distinct improvement in fitting and prediction precision than the linear reference models. Considering the simplicity of indexes measurement, the support vector regression model with only 6 morphological indexes including shoot dry weight, area of the second leaf under the central leaf, root shoot ratio, leaf age, leaf fresh weight, and area of the first leaf under the central leaf was also feasible. Furthermore, an explanatory system including the significance of regression model and the importance of single index was established based on support vector regression and F-test.

Ferroelectric Domain Shape: Can C3 Symmetry Be Distinguished from C6 Symmetry?

It is shown that arising of regular triangular isolated domains in lithium niobate and lithium tantalate can be attributed to nonlinear bulk screening currents. Their role in restoration of C3 symmetry and time reversion violation is revealed. Various physical consequences of the presence of nonlinear currents during polarization reversal are discussed.

Screening of heterogeneous surfaces: charge renormalization of Janus particles

Nonlinear ionic screening theory for heterogeneously charged spheres is developed in termsof a mode decomposition of the surface charge. A far-field analysis of the resultingelectrostatic potential leads to a natural generalization of charge renormalization frompurely monopolar to dipolar, quadrupolar, etc, including ‘mode couplings’. Ournovel scheme is generally applicable to large classes of surface heterogeneities, andis explicitly applied here to Janus spheres with differently charged upper andlower hemispheres, revealing strong renormalization effects for all multipoles.

Nonlinear screening of external charge by doped graphene

We solve a nonlinear integral equation for the electrostatic potential in doped graphene due to an external charge, arising from a Thomas-Fermi (TF) model for screening by graphene's $\pi$ electron bands. In particular, we study the effects of a finite equilibrium charge carrier density in graphene, non-zero temperature, non-zero gap between graphene and a dielectric substrate, as well as the nonlinearity in the band density of states. Effects of the exchange and correlation interactions are also briefly discussed for undoped graphene at zero temperature. Nonlinear results are compared with both the linearized TF model and the dielectric screening model within random phase approximation (RPA). In addition, image potential of the external charge is evaluated from the solution of the nonlinear integral equation and compared to the results of linear models. We have found generally good agreement between the results of the nonlinear TF model and the RPA model in doped graphene, apart from Friedel oscillations in the latter model. However, relatively strong nonlinear effects are found in the TF model to persist even at high doping densities and large distances of the external charge.

The current polarization rectification of the integer quantized Hall effect

We report on our theoretical investigation considering the widths of quantized Hall plateaus (QHPs) depending on the density asymmetry induced by the large current within the out-of-linear response regime. We solve the Schrödinger equation within the Hartree type mean field approximation using Thomas–Fermi–Poisson nonlinear screening theory. We observe that the two-dimensional electron system splits into compressible and incompressible regions for certain magnetic field intervals, where the Hall resistance is quantized and the longitudinal resistance vanishes, if an external current is imposed. We found that the strong current imposed induces an asymmetry on the widths of the incompressible strips (ISs) depending linearly on the current intensity and can be balanced by an inhomogeneous donor distribution.

Nonlinear screening effect in an ultrarelativistic degenerate electron-positron gas

Nonlinear screening process in an ultrarelativistic degenerate electron-positron gas has been investigated by deriving a generalized nonlinear Poisson equation for the electrostatic potential. In the simple one-dimensional case, the nonlinear Poisson equation leads to Debye-like (Coulomb-like) solutions at distances larger (less) than the characteristic length. When the electrostatic energy is larger than the thermal energy, this nonlinear Poisson equation converts into the relativistic Thomas–Fermi equation whose asymptotic solution in three dimensions shows that the potential field goes to zero at infinity much more slowly than the Debye potential. The possibility of the formation of a bound state in electron-positron plasma is also indicated. Further, it is investigated that the strong spatial fluctuations of the potential field may reduce the screening length and that the root mean square of this spatial fluctuating potential goes to zero for large r rather slowly as compared to the case of the Debye ...

Effects of charge screening and surface properties on signal transduction in field effect nanowire biosensors

A self-consistent numerical model for silicon-based field effect nanowire biosensors is developed to study the impact of various surface-related physical and chemical processes, including transport of semiconductor carriers and electrolyte mobile ions, protonation and deprotonation of surface charge groups, and charges, and orientations and surface binding dynamics of immobilized biomolecules. It is shown that the sensing signal levels are affected by the gate biasing points, nonlinear screening from both electrolytes and surface charge groups, as well as the biomolecule charges and orientations. The critical role of the nanowire surface heterogeneity in determining the sensing input dynamic range is indicated based on correlations with experimental data.

Effective medium theory for disordered two-dimensional graphene

We develop an effective medium theory to study the electrical transport properties of disordered graphene. The theory includes nonlinear screening and exchange-correlation effects allowing us to consider experimentally relevant strengths of the Coulomb interaction. Assuming random Coulomb impurities, we calculate the electrical conductivity as a function of gate voltage describing quantitatively the full cross over from the fluctuations dominated regime around the Dirac point to the large doping regime at high gate voltages. We find that the conductivity at the Dirac point is strongly affected by exchange-correlation effects.

Nonlinear screening of positive and negative point charges in GaAs

We have used a variational approach for approximately solving Resta's nonlinear Thomas-Fermi equation for the potential of (point) charges in GaAs. We have considered the cases of charges (in atomic units) Z = ±0.16, ±1.16, ±0.84. The charges Z = +0.16 and Z = −0.16 are the effective charges due to the partial ionicity of the chemical bonds on a Ga and As site, respectively. The charge Z = +0.84 corresponds to a Column VI donor on an As site, that of Z = +1.16 to a Column IV donor on a Ga site. Similarly, the charge of Z = −1.16 corresponds to a Column IV acceptor on an As site, that of Z = −0.84 to a Column II acceptor on a Ga site. As a result of our calculations, we have obtained site-dependent and charge-dependent spatial dielectric functions that describe the screening of the (point) charges by the valence electrons of (pure) GaAs.

Origin of the “0.25 anomaly” in the nonlinear conductance of a quantum point contact

We calculate the nonlinear conductance of a quantum point contact using the nonequilibrium Green's function technique within the Hartree approximation of spinless electrons. We quantitatively reproduce the ``0.25 anomaly'' in the differential conductance (i.e., the lowest plateau at $\ensuremath{\sim}0.25--0.3\ifmmode\times\else\texttimes\fi{}2{e}^{2}/h$) as well as an upward bending of higher conductance half-integer plateaus seen in the experiments, and relate these features to the nonlinear screening and pinning effects.