Debye Screening Length Research Articles

Enhanced thermoelectric performance in the n-type NbFeSb half-Heusler compound with heavy element Ir doping

The p-type NbFeSb half-Heusler compound has been proved to be a promising thermoelectric (TE) material with a figure of merit zT > 1. However, the corresponding n-type (V,Nb)FeSb solid solutions show poor TE performance. Here, we report the enhanced TE performance of n-type NbFe1-xIrxSb (0.01 < x < 0.08) by band modification and heavy element doping compared with that of the state-of-the-art n-type Co-doped (V,Nb)FeSb. The band effective mass m* b is reduced to 0.76 me, and the high-temperature carrier mobility increases obviously. Debye screening length calculation and model analysis show the additional introduced grain boundary scattering, due to small grain sizes, which deteriorates the room temperature carrier mobility. The heavier doping element Ir not only optimizes the carrier concentration but also introduces strong point defect scattering on phonons, resulting in a minimum thermal conductivity of 3.7 Wm−1K−1 at 1000 K for the NbFe0.92Ir0.02Sb sample. The larger bandgap of NbFeSb effectively suppresses minority carrier excitation. A maximum zT value of 0.5 is obtained at 1000 K for the NbFe0.94Ir0.06Sb sample, almost a 50% increase compared with that of the n-type (V0.6Nb0.4)FeSb samples.

Formation, Charge Transfer, Structural and Morphological Characteristics of ZnO Fractal-Percolation Nanosystems

Structural and morphological characteristics of ZnO nanosystems in the form of three-dimensional network-like systems have been investigated. Current–voltage (I–V) characteristics and charge transfer parameters of ZnO fractal-percolation nanosystems have been studied both in air and in vacuum at different temperatures and voltage sweep rates. The charge transfer characteristics show the presence of RαCiCαi chains in the nanosystems. The RC chains are formed because the Debye screening length has the same order of magnitude as the local values of ZnO nanowires radii. Gas-sensing tests based on I–V characteristics investigation have shown a possibility of distinguishing between reducing gases such as CH4 or C2H5OH.

Nanoporous Polymer Films with a High Cation Transference Number Stabilize Lithium Metal Anodes in Light-Weight Batteries for Electrified Transportation.

To suppress dendrite formation in lithium metal batteries, high cation transference number electrolytes that reduce electrode polarization are highly desirable, but rarely available using conventional liquid electrolytes. Here, we show that liquid electrolytes increase their cation transference numbers (e.g., ∼0.2 to >0.70) when confined to a structurally rigid polymer host whose pores are on a similar length scale (0.5-2 nm) as the Debye screening length in the electrolyte, which results in a diffuse electrolyte double layer at the polymer-electrolyte interface that retains counterions and reject co-ions from the electrolyte due to their larger size. Lithium anodes coated with ∼1 μm thick overlayers of the polymer host exhibit both a low area-specific resistance and clear dendrite-suppressing character, as evident from their performance in Li-Li and Li-Cu cells as well as in post-mortem analysis of the anode's morphology after cycling. High areal capacity Li-S cells (4.9 mg cm-2; 8.2 mAh cm-2) implementing these high transference number polymer-hosted liquid electrolytes were remarkably stable, considering ∼24 μm of lithium was electroreversibly deposited in each cycle at a C-rate of 0.2. We further identified a scalable manufacturing path for these polymer-coated lithium electrodes, which are drop-in components for lithium metal battery manufacturing.

Resonances in nonrelativistic free-free Gaunt factors with screened Coulomb interaction

The effect of Coulomb interaction screening on nonrelativistic free-free absorption is investigated by integrating the numerical continuum wave functions. The screened potential is taken to be in Debye-H\"uckel (Yukawa) form with a screening length $D$. It is found that the values of the free-free Gaunt factors for different Debye screening lengths $D$ for a given initial electron energy ${\ensuremath{\varepsilon}}_{i}$ and absorbing photon energy $\ensuremath{\omega}$ generally lie between those of the pure Coulomb field and field-free case. However, for initial electron energies below 0.1 Ry and fixed photon energy, the Gaunt factors show dramatic enhancements (broad and narrow resonances) in the vicinities of the critical screening lengths, ${D}_{nl}$, at which the energies of $nl$ bound states in the potential merge into the continuum. These enhancements of the Gaunt factors can be significantly higher than their values in the unscreened (Coulomb) case over a broad range of ${\ensuremath{\varepsilon}}_{i}$. The observed broad and narrow resonances in the Gaunt factors are related to the temporary formation of weakly bound (virtual) and resonant (quasibound) states of the low-energy initial electron on the Debye-H\"uckel potential when the screening length is in the vicinity of ${D}_{nl}$.

Beyond the Tradeoff: Dynamic Selectivity in Ionic Transport and Current Rectification.

Traditionally, ion selectivity in nanopores and nanoporous membranes is understood to be a consequence of Debye overlap, in which the Debye screening length is comparable to the nanopore radius somewhere along the length of the nanopore(s). This criterion sets a significant limitation on the size of ion-selective nanopores, as the Debye length is on the order of 1-10 nm for typical ionic concentrations. However, the analytical results we present here demonstrate that surface conductance generates a dynamical selectivity in ion transport, and this selectivity is controlled by so-called Dukhin, rather than Debye, overlap. The Dukhin length, defined as the ratio of surface to bulk conductance, reaches values of hundreds of nanometers for typical surface charge densities and ionic concentrations, suggesting the possibility of designing large-nanopore (10-100 nm), high-conductance membranes exhibiting significant ion selectivity. Such membranes would have potentially dramatic implications for the efficiency of osmotic energy conversion and separation techniques. Furthermore, we demonstrate that this mechanism of dynamic selectivity leads ultimately to the rectification of ionic current, rationalizing previous studies, showing that Debye overlap is not a necessary condition for the occurrence of rectifying behavior in nanopores.

An introduction to the physics of the Coulomb logarithm, with emphasis on quantum-mechanical effects

An introduction to the physical interpretation of the Coulomb logarithm is given with particular emphasis on the quantum-mechanical corrections that are required at high temperatures. Excerpts from the literature are used to emphasize the historical understanding of the topic, which emerged more than a half-century ago. Several misinterpretations are noted. Quantum-mechanical effects are related to diffraction by scales of the order of the Debye screening length; they are not due to quantum uncertainty related to the much smaller distance of closest approach.

Modeling the influence of effective oil volume fraction and droplet repulsive interaction on nanoemulsion gelation

The aim of this work was to test the applicability of the Mason-Scheffold model, developed for monodispersed systems, on predicting the storage modulus of sodium dodecyl sulfate-stabilized polydisperse canola oil nanoemulsion gels as a function of oil volume fraction (ϕ) and average droplet size. The storage moduli increased with ϕ, but at a constant ϕ they increased with a decrease in droplet size. An effective oil volume fraction (ϕeff) was calculated by combining the effects of ϕ, average droplet size, their inter-droplet repulsive interaction using the Debye screening length and the counterion dissociation factor (f). With increasing ϕeff, storage modulus rapidly increased at the onset of jamming, followed by a gradual increase at higher ϕeff where gelation is controlled by deformation of droplets and their surrounding charge cloud. The model fits the data well, although, the values of critical volume fraction for jamming (ϕc) did not seem appropriate for the polydisperse nanoemulsions. It was proposed that the influence of f on ϕc could be significant and values lower than 0.1 could be more appropriate for high concentration of ionic emulsifier.

High Partial Auxeticity Induced by Nanochannels in [111]-Direction in a Simple Model with Yukawa Interactions.

Computer simulations using Monte Carlo method in the isobaric-isothermal ensemble were used to investigate the impact of nanoinclusions in the form of very narrow channels in the -direction on elastic properties of crystals, whose particles interact via Yukawa potential. The studies were performed for several selected values of Debye screening length (). It has been observed that introduction of the nanoinclusions into the system reduces the negative value of Poisson’s ratio towards , maintaining practically constant values of Poisson’s ratio in the directions and . These studies also show that concentration of particles forming the nanoinclusions in the system has a significant effect on the value of Poisson’s ratio in the -direction. A strong (more than fourfold) decrease of Poisson’s ratio in this direction was observed, from (system without inclusions) to (system with nanoinclusions) at when the inclusion particles constituted about 10 percent of all particles. The research also showed an increase in the degree of auxeticity in the system with increasing concentration of nanoinclusion particles for all the screening lengths considered.

Selective enhancement of auxeticity through changing a diameter of nanochannels in Yukawa systems

A new effect of selective enhancement of auxeticity through the changes of nanochannels’ diameter in Yukawa systems is reported. Elastic properties of the model of Yukawa crystals with narrow nanochannels in the [001] crystallographic direction have been studied by Monte Carlo simulations in the isobaric–isothermal ensemble. It has been found that the choice of nanochannels’ diameter allows one to decrease the Poissons ratio value of the system in one of two selected crystallographic directions. The value of Poisson’s ratio in those directions can be changed in a wide range, e.g. from −0.061(9) to −0.625(44) in the -direction, depending on the nanochannels’ type and the Debye screening length.

Diffusiophoresis of a Charged Porous Particle in a Charged Cavity.

The quasi-steady diffusiophoresis of a charged porous sphere situated at the center of a charged spherical cavity filled with a liquid solution of a symmetric electrolyte is analyzed. The porous particle can represent a solvent-permeable and ion-penetrable polyelectrolyte molecule or floc of nanoparticles in which fixed charges and frictional segments are uniformly distributed, whereas the spherical cavity can denote a charged pore involved in microfluidic or drug-delivery systems. The linearized electrokinetic differential equations governing the ionic concentration, electric potential, and fluid velocity distributions in the system are solved by using a perturbation method with the fixed charge density of the particle and the ζ-potential of the cavity wall as the small perturbation parameters. An expression for the diffusiophoretic (electrophoretic and chemiphoretic) mobility of the confined particle with arbitrary values of a/ b, κ a, and λ a is obtained in closed form, where a and b are the radii of the particle and cavity, respectively; κ and λ are the reciprocals of the Debye screening length and the length characterizing the extent of flow penetration into the porous particle, respectively. The presence of the charged cavity wall significantly affects the diffusiophoretic motion of the particle in typical cases. The diffusio-osmotic (electro-osmotic and chemiosmotic) flow occurring at the cavity wall can substantially alter the particle velocity and even reverse the direction of diffusiophoresis. In general, the particle velocity decreases with an increase in a/ b, increases with an increase in κ a, and decreases with an increase in λ a, but exceptions exist.

Complex electric double layers in charged topological colloids

Charged surfaces in contact with liquids containing ions are accompanied in equilibrium by an electric double layer consisting of a layer of electric charge on the surface that is screened by a diffuse ion cloud in the bulk fluid. This screening cloud determines not only the interactions between charged colloidal particles or polyelectrolytes and their self-assembly into ordered structures, but it is also pivotal in understanding energy storage devices, such as electrochemical cells and supercapacitors. However, little is known to what spatial complexity the electric double layers can be designed. Here, we show that electric double layers of non-trivial topology and geometry -including tori, multi-tori and knots- can be realised in charged topological colloidal particles, using numerical modelling within a mean-field Poisson-Boltzmann theory. We show that the complexity of double layers -including geometry and topology- can be tuned by changing the Debye screening length of the medium, or by changing the shape and topology of the (colloidal) particle. More generally, this work is an attempt to introduce concepts of topology in the field of charged colloids, which could lead to novel exciting material design paradigms.

A graphene aptasensor for biomarker detection in human serum

This paper presents an affinity graphene nanosensor for detection of biomarkers in undiluted and non-desalted human serum. The affinity nanosensor is a field-effect transistor in which graphene serves as the conducting channel. The graphene surface is sequentially functionalized with a nanolayer of the polymer polyethylene glycol (PEG) and a biomarker-specific aptamer. The aptamer is able to specifically bind with and capture unlabeled biomarkers in serum. A captured biomarker induces a change in the electric conductivity of the graphene, which is measured in a buffer of optimally chosen ionic strength to determine the biomarker concentration. The PEG layer effectively rejects nonspecific adsorption of background molecules in serum while still allowing the aptamer to be readily accessible to serum-borne biomarkers and increases the effective Debye screening length on the graphene surface. Thus, the aptamer-biomarker binding sensitively changes the graphene conductivity, thereby achieving specific and label-free detection of biomarkers with high sensitivity and without the need to dilute or desalt the serum. Experimental results demonstrate that the graphene nanosensor is capable of specifically capturing human immunoglobulin E (IgE), used as a representative biomarker, in human serum in the concentration range of 50 pM–250 nM, with a resolution of 14.5 pM and a limit of detection of 47 pM.

Ionic current magnetic fields in a two dimensional nanoslit

Internal and external magnetic fields due to pressure-driven ionic currents inside a two- dimensional nanoslit are obtained theoretically and numerically by finite element solution of governing equations, i.e., Poisson-Nernst-Planck, Ampere, and Navier-Stokes equations. The transport governing equations in this study are non-dimensionalized by Debye screening length, and discretized in a two dimensional finite length nanoslit. The magnetic field components have opposite signs above and below the nanoslit due to opposite directions of the Amperian closed path. Within the nanoslit the non-uniformity of ionic currents resulted in non-uniform magnetic fields however outside the nanoslit, magnetic fields remain relatively constant, independent of the distance from a sufficiently long and wide nanoslit. It is anticipated that non-invasive ionic/streaming current measurements can be conducted by external magnetic fields readouts in sufficiently long and wide nanoslits. For instance, to estimate electrical properties (zeta potential) of solid-liquid interface, and to accurately sequence DNA and biomolecules.

Thin layer analysis of a non-local model for the double layer structure

For the structure of the thin electrical double layer (EDL) and the property related to the EDL capacitance, we analyze boundary layer solutions (corresponding to the electrostatic potential) of a non-local elliptic equation which is a steady-state Poisson–Nernst–Planck equation with a singular perturbation parameter related to the small Debye screening length. Theoretically, the boundary layer solutions describe that those ions exactly approach neutrality in the bulk, and the extra charges are accumulated near the charged surface. Hence, the non-neutral phenomenon merely occurs near the charged surface. To investigate such phenomena, we develop new analysis techniques to investigate thin boundary layer structures. A series of fine estimates combining the Pohožaev's identity, the inverse Hölder type estimates and some technical comparison arguments are developed in arbitrary bounded domains. Moreover, we focus on the physical domain being a ball with the simplest geometry and gain a clear picture on the effect of the curvature on the boundary layer solutions. The content involves three contributions. The first one focuses mainly on the boundary concentration phenomena. We show that the net charge density behaves exactly as Dirac delta measures concentrated at boundary points. The second one is devoted to pointwise descriptions with curvature effects for the thin boundary layer. An interesting outcome shows that the significant curvature effect merely occurs in the part of the boundary layer close to the boundary, and this part is extremely thinner than the whole boundary layer. The third contribution gives a connection to the EDL capacitance. We provide a theoretical way to support that the EDL has higher capacitance in a quite thin region near the charged surface, not in the whole EDL. In particular, for the cylindrical electrode, our result has a same analogous measurement as the specific capacitance of the well-known Helmholtz double layer.

The Two-Particle Correlation Function for Systems with Long-Range Interactions

In this paper, we study the truncated two-particle correlation function in particle systems with long range interactions. For Coulombian and soft potentials, we define and give well-posedness results for the equilibrium correlations. In the Coulombian case, we prove the onset of the Debye screening length in the equilibrium correlations, for suitable velocity distributions. Additionally, we give precise estimates on the effective range of interaction between particles. In the case of soft potential interaction the equilibrium correlations and their fluxes in the space of velocities are shown to be linearly stable.

Dipole and generalized oscillator strength derived electronic properties of an endohedral hydrogen atom embedded in a Debye-Hückel plasma

We report electronic properties of a hydrogen atom encaged by an endohedral cavity under the influence of a weak plasma interaction. We implement a finite-difference approach to solve the Schrödinger equation for a hydrogen atom embedded in an endohedral cavity modeled by the Woods-Saxon potential with well depth V0, inner radius R0, thickness Δ, and smooth parameter γ. The plasma interaction is described by a Debye-Hückel screening potential that characterizes the plasma in terms of a Debye screening length λD. The electronic properties of the endohedral hydrogen atom are reported for selected endohedral cavity well depths, V0, and screening lengths, λD, that emulate different confinement and plasma conditions. We find that for low screening lengths, the endohedral cavity potential dominates over the plasma interaction by confining the electron within the cavity. For large screening lengths, a competition between both interactions is observed. We assess and report the photo-ionization cross section, dipole polarizability, mean excitation energy, and electronic stopping cross section as function of λD and V0. We find a decrease of the Generalized Oscillator Strength (GOS) when the final excitation is to an s state as the plasma screening length decreases. For a final excitation into a p state, we find an increase in the GOS as the endohedral cavity well-depth increases. For the case of the electronic stopping cross section, we find that the plasma screening and endohedral cavity effects are larger in the low-to-intermediate projectile energies for all potential well depths considered. Our results agree well to available theoretical and experimental data and are a first step towards the understanding of dipole and generalized oscillator strength dependent properties of an atom in extreme conditions encaged by an endohedral cavity immersed in a plasma medium.

On the Impact of Electrostatic Correlations on the Double-Layer Polarization of a Spherical Particle in an Alternating Current Field.

At concentrated electrolytes, the ion-ion electrostatic correlation effect is considered an important factor in electrokinetics. In this paper, we compute, in theory and simulation, the dipole moment for a spherical particle (charged, dielectric) under the action of an alternating electric field using the modified continuum Poisson-Nernst-Planck (PNP) model by Bazant et al. [ Double Layer in Ionic Liquids: Overscreening Versus Crowding . Phys. Rev. Lett. 2011 , 106 , 046102 ] We investigate the dependency of the dipole moment in terms of frequency and its variation with such quantities like ζ-potential, electrostatic correlation length, and double-layer thickness. With thin electric double layers, we develop simple models through performing an asymptotic analysis of the modified PNP model. We also present numerical results for an arbitrary Debye screening length and electrostatic correlation length. From the results, we find a complicated impact of electrostatic correlations on the dipole moment. For instance, with increasing the electrostatic correlation length, the dipole moment decreases and reaches a minimum and then it goes up. This is because of initially decreasing of surface conduction and finally increasing due to the impact of ion-ion electrostatic correlations on ion's convection and migration. Also, we show that in contrast to the standard PNP model, the modified PNP model can qualitatively explain the data from the experimental results in multivalent electrolytes.

Classical plasma dynamics of Mie-oscillations in atomic clusters

Mie plasmons are of basic importance for the absorption of laser light by atomic clusters. In this work we first review the classical Rayleigh-theory of a dielectric sphere in an external electric field and Thomson’s plum-pudding model applied to atomic clusters. Both approaches allow for elementary discussions of Mie oscillations, however, they also indicate deficiencies in describing the damping mechanisms by electrons crossing the cluster surface. Nonlinear oscillator models have been widely studied to gain an understanding of damping and absorption by outer ionization of the cluster. In the present work, we attempt to address the issue of plasmon relaxation in atomic clusters in more detail based on classical particle simulations. In particular, we wish to study the role of thermal motion on plasmon relaxation, thereby extending nonlinear models of collective single-electron motion. Our simulations are particularly adopted to the regime of classical kinetics in weakly coupled plasmas and to cluster sizes extending the Debye-screening length. It will be illustrated how surface scattering leads to the relaxation of Mie oscillations in the presence of thermal motion and of electron spill-out at the cluster surface. This work is intended to give, from a classical perspective, further insight into recent work on plasmon relaxation in quantum plasmas [1].

Pushing the Boundaries of Interfacial Sensitivity in Graphene FET Sensors: Polyelectrolyte Multilayers Strongly Increase the Debye Screening Length

Nanomaterial-based FET sensors represent an attractive platform for ultrasensitive, real-time, and label-free detection of chemical and biological species. Nevertheless, because their response is screened by mobile ions, it remains a challenge to use them to sense in physiological ionic strength solutions. In this work, it is demonstrated, both experimentally and theoretically, that polyelectrolyte multilayers are capable of increasing the sensing range of graphene-based FETs. Potential shifts at graphene surfaces and film thickness are recorded upon the construction of PDADMAC/PSS polyelectrolyte multilayer (PEM) films. By correlation of the potential shift with the film thickness, the electrostatic screening length and the concentration of mobile ion inside the films have been deduced. Across the polymer interface the Debye length is increased more than 1 order of magnitude. The fundamentals of this strategy are described by a conceptually simple thermodynamic model, which accounts for the entropy loss ...

A modified Poisson–Nernst–Planck model with excluded volume effect: theory and numerical implementation

The Poisson--Nernst--Planck (PNP) equations have been widely applied to describe ionic transport in ion channels, nanofluidic devices, and many electrochemical systems. Despite their wide applications, the PNP equations fail in predicting dynamics and equilibrium states of ionic concentrations in confined environments, due to the ignorance of the excluded volume effect. In this work, a simple but effective modified PNP (MPNP) model with the excluded volume effect is derived, based on a modification of diffusion coefficients of ions. At the steady state, a modified Poisson--Boltzmann (MPB) equation is obtained with the help of the Lambert-W special function. The existence and uniqueness of a weak solution to the MPB equation are established. Further analysis on the limit of weak and strong electrostatic potential leads to two modified Debye screening lengths, respectively. A numerical scheme that conserves total ionic concentration and satisfies energy dissipation is developed for the MPNP model. Numerical analysis is performed to prove that our scheme respects ionic mass conservation and satisfies a corresponding discrete free energy dissipation law. Positivity of numerical solutions is also discussed and numerically investigated. Numerical tests are conducted to demonstrate that the scheme is of second-order accurate in spatial discretization and has expected properties. Extensive numerical simulations reveal that the excluded volume effect has pronounced impacts on the dynamics of ionic concentration and flux. In addition, the effect of volume exclusion on the timescales of charge diffusion is systematically investigated by studying the evolution of free energies and diffuse charges.