Debye Screening Length Research Articles

On the nature of screening in Voorn–Overbeek type theories

By using a recently formulated Legendre transform approach to the thermodynamics of charged systems, we explore the general form of the screening length in the Voorn-Overbeek-type theories, which remains valid also in the cases where the entropy of the charged component(s) is not given by the ideal gas form as in the Debye-Hückel theory. The screening length consistent with the non-electrostatic terms in the free energy ansatz for the Flory-Huggins and Voorn-Overbeek type theories, derived from the local curvature properties of the Legendre transform, has distinctly different behavior than the often invoked standard Debye screening length, though it reduces to it in some special cases.

A model for the electric field-driven flow and deformation of a drop or vesicle in strong electrolyte solutions

A model is constructed to describe the flow field and arbitrary deformation of a drop or vesicle that contains and is embedded in an electrolyte solution, where the flow and deformation are caused by an applied electric field. The applied field produces an electrokinetic flow, which is set up on the charge-up time scale $\tau _{*c}=\lambda _{*} a_{*}/D_{*}$ , where $\lambda _{*}$ is the Debye screening length, $a_{*}$ is the inclusion length scale and $D_{*}$ is an ion diffusion constant. The model is based on the Poisson–Nernst–Planck and Stokes equations. These are reduced or simplified by forming the limit of strong electrolytes, for which dissolved salts are completely ionised in solution, together with the limit of thin Debye layers. Debye layers of opposite polarity form on either side of the drop interface or vesicle membrane, together forming an electrical double layer. Two formulations of the model are given. One utilises an integral equation for the velocity field on the interface or membrane surface together with a pair of integral equations for the electrostatic potential on the outer faces of the double layer. The other utilises a form of the stress-balance boundary condition that incorporates the double layer structure into relations between the dependent variables on the layers’ outer faces. This constitutes an interfacial boundary condition that drives an otherwise unforced Stokes flow outside the double layer. For both formulations relations derived from the transport of ions in each Debye layer give additional boundary conditions for the potential and ion concentrations outside the double layer.

Electroviscous drag on squeezing motion in sphere-plane geometry.

Theoretically and experimentally, we study electroviscous phenomena resulting from charge-flow coupling in a nanoscale capillary. Our theoretical approach relies on Poisson-Boltzmann mean-field theory and on coupled linear relations for charge and hydrodynamic flows, including electro-osmosis and charge advection. With respect to the unperturbed Poiseuille flow, we define an electroviscous coupling parameter ξ, which turns out to be maximum where the film height h_{0} is comparable to the Debye screening length λ. We also present dynamic atomic force microscopy data for the viscoelastic response of a confined water film in sphere-plane geometry; our theory provides a quantitative description for the electroviscous drag coefficient and the electrostatic repulsion as a function of the film height, with the surface charge density as the only free parameter. Charge regulation sets in at even smaller distances.

Universal Casimir Interaction between Two Dielectric Spheres in Salted Water.

We study the Casimir interaction between two dielectric spheres immersed in a salted solution at distances larger than the Debye screening length. The long distance behavior is dominated by the nonscreened interaction due to low-frequency transverse magnetic thermal fluctuations. It shows universality properties in its dependence on geometric dimensions and independence of dielectric functions of the particles, with these properties related to approximate conformal invariance. The universal interaction overtakes nonuniversal contributions at distances of the order of or larger than 0.1 μm, with a magnitude of the order of the thermal scale k_{B}T such as to make it important for the modeling of colloids and biological interfaces.

Universal Casimir interactions in the sphere–sphere geometry

We study universal Casimir interactions in two configurations which appear as dual to each other. The first involves spheres described by the Drude model and separated by vacuum while the second involves dielectric spheres immersed in a salted solution at distances larger than the Debye screening length. In both cases, the long-distance limit, equivalently the high-temperature limit, is dominated by the effect of low-frequency transverse magnetic thermal fluctuations. They are independent of the details of dielectric functions of materials, due to the finite conductivity of metals in the former case and of salted water in the latter one. They also show universality properties in their dependence on geometric dimensions in relation to an approximate conformal invariance of the reduced free energy.

Precise and Prompt Analyte Detection via Ordered Orientation of Receptor in WSe2-Based Field Effect Transistor.

Field-effect transistors (FET) composed of transition metal dichalcogenide (TMDC) materials have gained huge importance as biosensors due to their added advantage of high sensitivity and moderate bandgap. However, the true potential of these biosensors highly depends upon the quality of TMDC material, as well as the orientation of receptors on their surfaces. The uncontrolled orientation of receptors and screening issues due to crossing the Debye screening length while functionalizing TMDC materials is a big challenge in this field. To address these issues, we introduce a combination of high-quality monolayer WSe2 with our designed Pyrene-based receptor moiety for its ordered orientation onto the WSe2 FET biosensor. A monolayer WSe2 sheet is utilized to fabricate an ideal FET for biosensing applications, which is characterized via Raman spectroscopy, atomic force microscopy, and electrical prob station. Our construct can sensitively detect our target protein (streptavidin) with 1 pM limit of detection within a short span of 2 min, through a one-step functionalizing process. In addition to having this ultra-fast response and high sensitivity, our biosensor can be a reliable platform for point-of-care-based diagnosis.

The electrochemical impedance spectrum of asymmetric electrolytes across low to moderate frequencies

• New mathematical analysis for the electrochemical impedance spectrum of asymmetric electrolytes. • Double plateau behavior in the real part of impedance predicted across low to moderate frequencies. • Low frequency response is caused transient bulk diffusion, or concentration polarization, of salt across an electrochemical cell. We develop new mathematical expressions for the electrochemical impedance spectrum of an asymmetric electrolyte. Specifically, we consider the Poisson-Nernst-Planck (PNP) equations governing ion transport in a binary asymmetric electrolyte with unequal valences and diffusivities, flanked by planar, parallel, blocking electrodes. The electrodes are subject to an oscillating voltage of small amplitude comparable to the thermal voltage scale. We further consider the limit practically applicable to liquid electrolytes of thin Debye layers ∊ = 1 / ( κ L ) ≪ 1 , where κ - 1 is the Debye screening length and L is the length of the half cell. The impedance is then obtained from the current in the external circuit, defined as the rate of change of electric field at either electrode. We identify two distinct asymptotic regimes for the frequency ( ω ) in the limit ∊ → 0 : low frequencies, on the order of the inverse bulk diffusion time ω = O ( D A / L 2 ) ; and moderate frequencies, on the order of the inverse RC charging time scale ω = O ( D A κ / L ) . Here D A = ( z + + z - ) D + D - / ( z + D + + z - D - ) is the ambipolar diffusion coefficient of the salt, z ± are the ionic valences, and D ± are the ionic diffusivities. Our analysis provides new, concise expressions for the impedance at low and moderate frequencies, that account for ionic valence asymmetry. Further, in the moderate frequency analysis, higher order contributions (in ∊ ) to the impedance reveal that the real part (i.e. the resistance) appears to diverge as ω - 1 / 2 in the limit ω L / ( κ D A ) → 0 , akin to a semi-infinite Warburg element. We determine that this occurs due to the existence of oscillating diffusion layers, O ( ∊ 1 / 2 L ) in width, that bridge the ion transport between the O ( ∊ L ) wide Debye layers adjacent to each electrode and the O ( L ) wide bulk electro-neutral electrolyte. In the low frequency regime, however, these diffusion layers relax, and effectively merge across the bulk of the cell; consequently, the resistance spectrum attains a plateau in the limit of zero frequency ω L 2 / D A → 0 . Thus, our asymptotic analysis discerns the electrochemical processes that dictate the impedance of asymmetric electrolytes at the low and moderate frequency regimes.

Analysis of coherent Thomson scattering from a low temperature plasma

The spectrum of coherent Thomson scattering (CTS) induced by a periodic ponderomotive perturbation in a low-density low temperature plasma is considered. The analysis is performed for the case when the period of the resulting optical lattice is less than the Debye screening length in the plasma by solving an electron Boltzmann equation, where the total force is the sum of the periodic force due to the optical lattice and the electrostatic force due to self-consistent electric field in the plasma. An analogy between the CTS spectra calculated here and coherent Rayleigh scattering spectra in a neutral gas is established. For relatively low intensity for the optical lattice, the calculated CTS spectra are nearly Gaussian with widths slightly wider than the incoherent Thomson widths. We demonstrate that at higher intensities the line shape narrows and saturates to a width approximately half of that found at low lattice intensities. The proportionality of the spectral width to the square root of the electron temperature allows one to extract the electron temperature from the saturated spectra. Possible application of CTS for remote measuring the electron temperature in plasma is discussed.

Study of the Transport Properties of the Critical Binary Mixture Triethylamine − Water with an Ionic Impurity

The binary liquid mixture of triethylamine + water (TEA–W) has a lower consolute point at a critical composition of 32.27 mass. % triethylamine. The shear viscosity (η) and the electrical conductivity (σ) in the single phase region of this system with added (K+, Cl–) ions at various concentrations are measured in the vicinity and far from the critical temperature TC. For the pure system without KCl salt, the viscosity measurements yield an enhancement, as expected, for the Ising criticality with a crossover to a regular behavior. Shear viscosity data are consistent with a power-law divergence η = η0(Qζ0)zt–y predicted by the mode-coupling and dynamic renormalization group theories. In the temperature range ∆T = TC – T < 2 ºC, the electrical conductivity (σ) exhibits a monotonous deviation from the Vogel–Fulcher–Tammann (VFT) behavior. This anomaly is described by a power law t1 –α, where t is the reduced temperature (T –TC)/TC, and α is the critical exponent of the specific heat anomaly at constant pressure. For the electrolyte mixtures, the obtained critical exponent values are in the range of those expected by the theoretical calculations for the Ising 3D universality class. By combining the viscosity and the electrical conductivity data, the value of the computed Walden product has been determined, and the salt dissociation degrees, as well as the Debye screening length, have been estimated.

A new approach towards the Debye length challenge for specific and label-free biological sensing based on field-effect transistors.

Biologically-modified field-effect transistors (BioFETs) are promising platforms for specific and label-free biosensing due to their sub-micron footprint suitable for multiplexing in ultra-small samples, low noise levels, inherent amplification, etc. Debye screening length is a well-recognized challenge for any BioFET-based technology. The screening length is the smallest at the double layer, where the solution ion population is higher than the bulk population. One way to address the small double layer screening length is to electrostatically modify the potential drop across the solution such as to minimize the potential drop over the double layer. This will decrease the population of the double layer ions and increase the screening length. However, this is not possible with BioFETs as voltage application to the reference electrode simultaneously affects both the double layer and the BioFET conducting channel. The current study addresses the screening length challenge with the novel Meta-Nano-Channel (MNC) BioFET. The MNC BioFET, which is fabricated in a complementary-metal-oxide-silicon (CMOS) process, allows decoupling of the electrostatics of the double layer from the electrodynamics of the conducting channel. The study explores the mechanism of sensing with the MNC BioFET, and demonstrates how the double layer can be electrostatically tuned in order to optimize the screening length without affecting the conducting channel. Finally, specific and label-free sensing of 10 ng ml-1 prostate specific antigen (PSA) is demonstrated. It is shown that by electrostatically increasing the double layer screening length, the sensing signal increases from 70 mV to 133 mV.

Fully differential analysis of the electron impact ionization of hydrogen in Debye plasmas

In this work, electron impact ionizing collisions on atomic hydrogen embedded in weakly coupled plasmas are studied at impact energies of 80 and 150 eV. Fully differential cross sections calculated by means of a distorted wave model which explicitly considers the screening effect among the three interacting particles in the final state are presented and analyzed. Compared to the unscreened case, clear differences in shape and magnitude are found for the dominant structures, the binary and recoil peaks, suggesting that the role played in the collision by the different particles varies with the Debye screening length. A scaling law for the fully differential cross section in terms of the nuclear charge Z, first proposed by Kornberg and Miraglia in the photo-double ionization context, is shown to also hold for the electron impact ionization of hydrogenic ions in the present screened context.

Osmotic Pressure and Diffusion of Ions in Charged Nanopores.

The transport of ions and water in nanopores is of interest for a number of natural and technological processes. Due to their practically identical long straight cylindrical pores, nanoporous track-etched membranes are suitable materials for investigation of its mechanisms. This communication reports on simultaneous measurements of osmotic pressure and salt diffusion with a 24 nm pore track-etched membrane. Due to the use of dilute electrolyte solutions (1–4 mM KCl and LiCl), this pore size was commensurate with the Debye screening length. Advanced interpretation of experimental results using a full version of the space-charge model has revealed that osmotic pressure and salt diffusion can be quantitatively correlated with electrostatic interactions of ions with charged nanopore walls. The surface-charge density is shown to increase with electrolyte concentration in agreement with the mechanism of deprotonation of weakly acidic surface groups. Moreover, a lack of significant surface-charge dependence on the kind of cation (K+ or Li+) demonstrates that binding of salt counterions does not play a major role in this system.

Electrophoresis and electric conduction in a salt-free suspension of charged particles.

The electrophoresis and electric conduction of a suspension of charged spherical particles in a salt-free solution are analyzed by using a unit cell model. The linearized Poisson-Boltzmann equation (valid for the cases of relatively low surface charge density or high volume fraction of the particles) and Laplace equation are solved for the equilibrium electric potential profile and its perturbation caused by the imposed electric field, respectively, in the fluid containing the counterions only around the particle, and the ionic continuity equation and modified Stokes equations are solved for the electrochemical potential energy and fluid flow fields, respectively. Explicit analytical formulas for the electrophoretic mobility of the particles and effective electric conductivity of the suspension are obtained, and the particle interaction effects on these transport properties are significant and interesting. The scaled zeta potential, electrophoretic mobility, and effective electric conductivity increase monotonically with an increase in the scaled surface charge density of the particles and in general decrease with an increase in the particle volume fraction, keeping each other parameter unchanged. Under the Debye-Hückel approximation, the dependence of the electrophoretic mobility normalized with the surface charge density on the ratio of the particle radius to the Debye screening length and particle volume fraction in a salt-free suspension is same as that in a salt-containing suspension, but the variation of the effective electric conductivity with the particle volume fraction in a salt-free suspension is found to be quite different from that in a suspension containing added electrolyte.

Highly Sensitive DNA Detection Beyond the Debye Screening Length Using CMOS Field Effect Transistors

Field effect transistors are considered one of the key technologies to provide real-time and label-free biodetection. Direct detection in physiological solutions is, however, severely limited by the Debye charge-screening effect of the electrical double layer. Most measurements are therefore performed indirectly in diluted ionic-strength solutions. This study proposes a general technique based on modulation of the surface electric field of the CMOS (complementary metal oxide semiconductor) extended-gate field effect transistors (EGFETs) to investigate the screening effect on hybridized DNA (deoxyribonucleic acid) signals from 1 MHz to 15 MHz. The 32 EGFET sensor array exhibited a floating-gate potential change of 17.4 mV/log[DNA] from 1 fM to 100 pM with a near picomolar-level resolution and a response time below 8 minutes.

Conformation and persistence length of chitosan in aqueous solutions of different ionic strengths via asymmetric flow field-flow fractionation

Conformation of chitosan in acidic aqueous solutions is strongly influenced by ionic strength, but the conventional employed size exclusion chromatography is limited to high ionic strength. Here we show that conformation of chitosan in acetate buffer down to millimolar ionic strength can be studied via asymmetric flow field-flow fractionation (AF4), where the separation is governed by the diffusion properties of the chitosan molecules and assisted by the electrostatic repulsion of the polyelectrolyte from the channel membrane. The size of chitosan decreases with ionic strength due to increasing screening of the polyelectrolyte effect. The persistence length of chitosan in the solutions, obtained by fitting the conformation plot by the wormlike chain model, decreases linearly with the Debye screening length from 44.5 nm at a salt concentration of 1.25 mM dominated by the electrostatic contribution to 8.6 nm in 800 mM acetate buffer close to its intrinsic persistence length of 7.7 nm.

Non-steady-state photo-EMF in a PbNi1/3Nb2/3O3 crystal at λ=660 nm

Experiments on non-steady-state photoelectromotive force (photo-EMF) excitation are implemented with a P b N i 1 / 3 N b 2 / 3 O 3 crystal at wavelength λ = 660 n m . We study the paraelectric phase of the crystal, which belongs to a very peculiar class of materials—relaxor ferroelectrics. The dependencies of the signal amplitude on the frequency of phase modulation, light intensity, and spatial frequency are measured, and photoelectric parameters such as photoconductivity, diffusion, and Debye screening lengths are estimated from them. The signal characteristics demonstrate nonlinear dependencies on light intensity, which is explained by the laser heating of the medium. An unusual difference in the behavior of the photoconductivity response and non-steady-state photo-EMF is revealed.

Modeling the voltage distribution in a non-locally but globally electroneutral confined electrolyte medium: applications for nanophysiology.

The distribution of voltage in sub-micron cellular domains remains poorly understood. In neurons, the voltage results from the difference in ionic concentrations which are continuously maintained by pumps and exchangers. However, it not clear how electro-neutrality could be maintained by an excess of fast moving positive ions that should be counter balanced by slow diffusing negatively charged proteins. Using the theory of electro-diffusion, we study here the voltage distribution in a generic domain, which consists of two concentric disks (resp. ball) in two (resp. three) dimensions, where a negative charge is fixed in the inner domain. When global but not local electro-neutrality is maintained, we solve the Poisson-Nernst-Planck equation both analytically and numerically in dimension 1 (flat) and 2 (cylindrical) and found that the voltage changes considerably on a spatial scale which is much larger than the Debye screening length, which assumes electro-neutrality. The present result suggests that long-range voltage drop changes are expected in neuronal microcompartments, probably relevant to explain the activation of far away voltage-gated channels located on the surface membrane.

The Debye length and the running coupling of QCD: A potential and phenomenological approach

In this paper, one uses a damped potential to present a description of the running coupling constant of QCD in the confinement phase. Based on a phenomenological perspective for the Debye screening length, one compares the running coupling obtained here with both the Brodsky–de Téramond–Deur and the Richardson approaches. The results seem to indicate the model introduced here corroborate the Richardson approach. Moreover, the Debye screening mass in the confinement phase depends on a small parameter, which tends to vanish in the nonconfinement phase of QCD.

Structure and Dynamics of Electric-Field-Driven Convective Flows at the Interface between Liquid Electrolytes and Ion-Selective Membranes.

At voltages above a certain critical value, Vc ≈ 20 kT/e, a space charge layer forms near ion-selective interfaces in liquid electrolytes. Interactions between the space charge and an imposed electric field drives a hydrodynamic instability known as electroconvection. Through particle tracking velocimetry we experimentally study the structure and dynamics of the resultant electroconvective flow. Consistent with previous numerical simulations, we report that, following imposition of a sufficiently large voltage, electroconvection develops gradually as pairs of counter-rotating vortices, which nucleate at the interface between an ion-selective substrate and a liquid electrolyte. Depending on the imposed voltage and cell geometry, the vorticies grow to length scales of hundreds of micrometers. Electroconvective flows are also reported to be structured and multiscale, with the size ratio of the largest to the smallest observable vortices inversely proportional to the Debye screening length.

Introducing a Surface-Enhanced-Raman-Scattering Enhancer for Experimental Estimation of the Debye Screening Length in Organic Field-Effect Transistors

The Debye screening length LD is one of the key parameters for the field-effect channel geometry. However, to the best of our knowledge, there are little reports on the experimental estimation of L...