Debye Screening Length Research Articles

Size, shape, and diffusivity of a single Debye-Hückel polyelectrolyte chain in solution.

Brownian dynamics simulations of a coarse-grained bead-spring chain model, with Debye-Hückel electrostatic interactions between the beads, are used to determine the root-mean-square end-to-end vector, the radius of gyration, and various shape functions (defined in terms of eigenvalues of the radius of gyration tensor) of a weakly charged polyelectrolyte chain in solution, in the limit of low polymer concentration. The long-time diffusivity is calculated from the mean square displacement of the centre of mass of the chain, with hydrodynamic interactions taken into account through the incorporation of the Rotne-Prager-Yamakawa tensor. Simulation results are interpreted in the light of the Odjik, Skolnick, Fixman, Khokhlov, and Khachaturian blob scaling theory (Everaers et al., Eur. Phys. J. E 8, 3 (2002)) which predicts that all solution properties are determined by just two scaling variables-the number of electrostatic blobs X and the reduced Debye screening length, Y. We identify three broad regimes, the ideal chain regime at small values of Y, the blob-pole regime at large values of Y, and the crossover regime at intermediate values of Y, within which the mean size, shape, and diffusivity exhibit characteristic behaviours. In particular, when simulation results are recast in terms of blob scaling variables, universal behaviour independent of the choice of bead-spring chain parameters, and the number of blobs X, is observed in the ideal chain regime and in much of the crossover regime, while the existence of logarithmic corrections to scaling in the blob-pole regime leads to non-universal behaviour.

Scattering of Electrons/positrons by H-atoms and H$_2$ Molecules under Weakly Coupled Plasmas

In this paper we have examined the screening effects of weak Debye plasma on elastic scattering of electrons (e‒) or positrons (e+) by atomic as well molecular hydrogen at intermediate and high incident energies Ei ≥50 eV. The present theoretical work aims at investigating how plasma influences the angular and total scattering, in the background of free or no-plasma situation. The basic calculations are carried out in the 'eikonal-Born-series' (EBS) approach suitable for atomic hydrogen, along with the 'Independent Atom-in-Molecule' (IAiM) model for the H2 molecular target. Debye screening length ΛD is adopted as the parameter to assess the effect of the plasma environment on the scattering. Reduction in the forward differential cross sections (FDCS) and the total (complete) cross sections (TCS) is studied at typical values ΛD = 5, 7.5 and 10 Bohr radii a0. Our results show that, compared to the TCS, the FDCS are more sensitive to the plasma effects, for both H and H2 targets. Further for both these targets, differences between electron and positron scattering are also observed in our theoretical results.

Effect of Enzymes on Serum and Particle Properties of Carrot Cell Suspensions

Rheological properties of cell wall suspensions strongly depend on particle size and particle-particle interactions. In the present study, an experimental method was developed to study the effect of particle elasticity and electrostatic interactions on the rheological properties of cell suspensions. Enzymes were used to selectively depolymerize the pectin (backbone) and proteins in suspensions. The enzymatic treatments affected the physical properties, thus a hypothesis for the structure-function relationship of these biopolymers was formulated. The enzymatic treatment directly affected particle properties, resulting in looser cell walls as visualized by cryo-SEM. The effect of the enzymatic treatment on the storage modulus was measured as a function of total solid content (below critical packing fraction). Furthermore, experiments were performed in the presence of varying concentrations of sodium chloride in order to change the Debye screening length. Such method assisted in decoupling the electrostatic effects from particle elasticity. In addition, particle properties were measured directly by applying a compressive strain on the particles and measuring the normal force. By fitting the normal stress relaxation with a Maxwell model, particle properties such as time scale of relaxation and elasticity were obtained. It is suggested that for carrot suspensions, pectins on the cell walls could contribute to the particle hardness. The pectins on carrot cell walls are responsible for electrostatic interactions between particles.

Photoexcitation and ionization of hydrogen atom confined in Debye environment

The dynamics of a hydrogen atom confined in an impenetrable spherical box and under the effect of Debye screening, in the presence of intense short laser pulses of few femtosecond (fs) is studied in detail. The energy spectra and wave functions have been calculated using Bernstein polynomial (B-polynomial) method. Variation of transition probabilities for various transitions due to changes in Debye screening length, confinement radius as well as the parameters characterizing applied laser pulse is studied and explained.

Direct Observation of Charge Inversion in Divalent Nanofluidic Devices.

Solid-state nanofluidic devices have proven to be ideal systems for studying the physics of ionic transport at the nanometer length scale. When the geometrical confining size of fluids approaches the ionic Debye screening length, new transport phenomena occur, such as surface mediated transport and permselectivity. Prior work has explored these effects extensively in monovalent systems (e.g., predominantly KCl and NaCl). In this report, we present a new characterization method for the study of divalent ionic transport and have unambiguously observed divalent charge inversion at solid/fluid interfaces. This observation has important implications in applications ranging from biology to energy conversion.

Interfacial Water Structure at Surfactant Concentrations below and above the Critical Micelle Concentration as Revealed by Sum Frequency Generation Vibrational Spectroscopy

Interfacial water in close proximity to an adsorbed surfactant layer plays an important role in many areas. Here, we systematically investigate the interfacial water structure at the adsorption layer of cetyltrimethylammonium bromide (CTAB) from low concentrations to its critical micelle concentration. Our sum frequency generation (SFG) spectroscopy results show that, with increasing CTAB concentration, the water SFG signals first increase, reaching maximum intensities at 0.1 mM, and then drop, whereas the ppp SFG signals of the terminal-methyl asymmetric stretch reach maximum intensities and saturate at 1 mM, which is the critical micelle concentration of CTAB. Our analysis reveals that the interfacial water layer adopts the most orderly arrangement when the interfacial potential of the adsorption layer reaches saturation and not at the surfactant concentration of adsorption saturation. Most importantly, our SFG data provide direct evidence for the antagonistic effects of the interfacial potential and thickness compression of the electrostatic field of the surfactant adsorption layer, leading to the strongest water SFG signals at 0.1 mM. Below 0.1 mM, the increased interfacial potential can have a pronounced effect on the increase of the overall dipole moment of the interfacial water layers. Above 0.1 mM, the decreased Debye screening length significantly reduces the water dipole moment. Finally, the newly proposed adsorption model cannot explain our SFG results.

Elastic properties of mono‐ and polydisperse two‐dimensional crystals of hard‐core repulsive Yukawa particles

AbstractMonte Carlo simulations of mono‐ and polydisperse two‐dimensional crystals are reported. The particles in the studied system, interacting through hard‐core repulsive Yukawa potential, form a solid phase of hexagonal lattice. The elastic properties of crystalline Yukawa systems are determined in the NpT ensemble with variable shape of the periodic box. Effects of the Debye screening length (), contact value of the potential (), and the size polydispersity of particles on elastic properties of the system are studied. The simulations show that the polydispersity of particles strongly influences the elastic properties of the studied system, especially on the shear modulus. It is also found that the elastic moduli increase with density and their growth rate depends on the screening length. Shorter screening length leads to faster increase of elastic moduli with density and decrease of the Poisson's ratio. In contrast to its three‐dimensional version, the studied system is non‐auxetic, i.e., shows positive Poisson's ratio.

An investigation of antiprotons collisions with positronium atom in Debye plasma environments

The effects of Debye plasmas on antihydrogen formation and ionization processes are investigated in antiprotons ( p¯) and positronium (Ps) collisions. The classical trajectory Monte Carlo method with Debye Huckel potentials has been used for cross section calculations. In this process, antihydrogen formation and ionization cross sections have been calculated in unscreened as well as in Debye plasmas conditions in energies ranging from 1 to 500 keV. Partial cross sections for antihydrogen formation are also calculated which show the largest cross sections correspond to production of antihydrogen in the n = 2 (2s, 2p) states. Comparative study has been carried out to determine the differences of cross sections in screening and unscreening cases. The results show that the cross sections for both antihydrogen formation and positronium ionization depend on Debye screening lengths as well as on collision energies. The effects of plasmas conditions on antihydrogen formation and positronium ionization are explain...

Screening and sheath formation in a nonequilibrium mixed Cairns-Tsallis electron distribution

The effects of electron nonextensivity for a given nonthermality state, on Debye shielding and electrostatic sheath formation are examined. A physically meaningful Cairns-Tsallis distribution is outlined and a generalized expression for the Debye screening length λDq,α is obtained. It is shown that an increase of the entropic index q causes λDq,α to decrease whatever the amount of plasma nonthermality α. In addition, smaller pertinent values of q along with relatively higher values of α provide larger values of λDq,α. The shielded electrostatic potential falls off as a function of distance more slowly as α increases, a result somewhat analogous to the dynamical shielding decrease (albeit in a different context) of a free charge as it begins to move. Moreover, smaller pertinent values of q along with relatively higher values of α are found to involve higher ion drift speed vi0 for proper sheath formation. As α increases, the sheath electrostatic potential-gradient dΨs/dξ becomes abruptly steep slowing down the energetic electrons leakage to the wall. Moreover, the sheath thickness broadens as the electron nonthermality strengthens.

Long-Ranged Oppositely Charged Interactions for Designing New Types of Colloidal Clusters

Getting control over the valency of colloids is not trivial and has been a long-desired goal for the colloidal domain. Typically, tuning the preferred number of neighbors for colloidal particles requires directional bonding, as in the case of patchy particles, which is difficult to realize experimentally. Here, we demonstrate a general method for creating the colloidal analogs of molecules and other new regular colloidal clusters without using patchiness or complex bonding schemes (e.g., DNA coating) by using a combination of long-ranged attractive and repulsive interactions between oppositely charged particles that also enable regular clusters of particles not all in close contact. We show that, due to the interplay between their attractions and repulsions, oppositely charged particles dispersed in an intermediate dielectric constant (4 <epsilon <10) provide a viable approach for the formation of binary colloidal clusters. Tuning the size ratio and interactions of the particles enables control of the type and shape of the resulting regular colloidal clusters. Finally, we present an example of clusters made up of negatively charged large and positively charged small satellite particles, for which the electrostatic properties and interactions can be changed with an electric field. It appears that for sufficiently strong fields the satellite particles can move over the surface of the host particles and polarize the clusters. For even stronger fields, the satellite particles can be completely pulled off, reversing the net charge on the cluster. With computer simulations, we investigate how charged particles distribute on an oppositely charged sphere to minimize their energy and compare the results with the solutions to the well-known Thomson problem. We also use the simulations to explore the dependence of such clusters on Debye screening length kappa(-1) and the ratio of charges on the particles, showing good agreement with experimental observations.

Wave interaction of electrons in cryogenic plasma-like medium with degenerate electrons

The general expression of the interaction potential between electrons in a plasma-like medium (gas plasma, semiconductor plasma) with degenerate electrons (light negative charge carriers) is calculated. It is shown that the electron-electron interaction at short distances (smaller than or of the order of the Debye screening length) is described by the ordinary Coulomb potential with Debye field screening. At distances far exceeding the Debye screening length, the electron repulsion weakens and attraction becomes dominant, which is caused by the wave interaction of electrons due to the ion-acoustic wave exchange. It is shown that the wave interaction potential decreases with distance as 1/r 3. The possibility of forming the bound state of two electrons (Cooper pair) in the field of such a potential in indicated media is discussed.

Anomalous stiffening and ion-induced coil-helix transition of carrageenans under monovalent salt conditions.

The macromolecular conformations of anionic polysaccharides with decreasing linear charge densities—lambda, iota, and kappa carrageenan—, at varying NaCl concentrations, are studied by single-chain statistical analysis of high-resolution atomic force microscopy (AFM) images. Lambda remains in the random coil conformation, whereas iota and kappa undergo ion-induced coil-helix transitions, with a 2-3-fold increase in chain rigidity. At low ionic strengths, I, the polymer chains sequester Na⁺, leading to a greater flexibility, and beyond a critical I to the formation of an intramolecular single helix. The persistence length exhibits a sublinear dependence on the Debye screening length, κ⁻¹, L(p)(e) ∼ κ(-y) (with 0 < y < 1), deviating from the classical polyelectrolyte behavior expressed by Odijk-Skolnick-Fixman or Barrat-Joanny models. Above a certain I, the L(p) shows an upturn, resulting in polymer stiffening and nonmonotonic behavior. This phenomenon is inferred from specific ion-polymer interactions and/or nonlinear electrostatic physics involving ion-ion correlations.

Experimental study for rheological property of exhaustively deionized aqueous suspension of very small colloidal spheres (diameter < ca. 60 nm)

The rheological properties of aqueous suspensions of small silica spheres (18–56nm in diameter), in an exhaustively deionized state and the presence of a salt, have been investigated. In a deionized state, the suspensions of larger spheres, 29nm and 56nm in diameter, were Newtonian fluids at sphere volume fraction ϕ=0.10, although the suspension of the smallest spheres, 18nm, showed shear thinning at ϕ=0.087. Debye screening lengths were calculated based on electrical conductivity. The effective volume fractions, including the electrical double layers, of suspensions in the above condition were 0.37, 0.23, and 0.21 for spheres of 18nm, 29nm, and 56nm in diameter, respectively. Experiments provide strong evidence that all of the small spheres form steady electrical double layers in water and that the suspension of 18-nm spheres was in a glassy state.

General strategy for biodetection in high ionic strength solutions using transistor-based nanoelectronic sensors.

Transistor-based nanoelectronic sensors are capable of label-free real-time chemical and biological detection with high sensitivity and spatial resolution, although the short Debye screening length in high ionic strength solutions has made difficult applications relevant to physiological conditions. Here, we describe a new and general strategy to overcome this challenge for field-effect transistor (FET) sensors that involves incorporating a porous and biomolecule permeable polymer layer on the FET sensor. This polymer layer increases the effective screening length in the region immediately adjacent to the device surface and thereby enables detection of biomolecules in high ionic strength solutions in real-time. Studies of silicon nanowire field-effect transistors with additional polyethylene glycol (PEG) modification show that prostate specific antigen (PSA) can be readily detected in solutions with phosphate buffer (PB) concentrations as high as 150 mM, while similar devices without PEG modification only exhibit detectable signals for concentrations ≤10 mM. Concentration-dependent measurements exhibited real-time detection of PSA with a sensitivity of at least 10 nM in 100 mM PB with linear response up to the highest (1000 nM) PSA concentrations tested. The current work represents an important step toward general application of transistor-based nanoelectronic detectors for biochemical sensing in physiological environments and is expected to open up exciting opportunities for in vitro and in vivo biological sensing relevant to basic biology research through medicine.

Electrophoresis of electrically neutral porous spheres induced by selective affinity of ions.

I investigate the possibility that electrically neutral porous spheres electrophorese in electrolyte solutions with asymmetric affinity of ions to spheres on the basis of electrohydrodynamics and the Poisson-Boltzmann and Debye-Bueche-Brinkman theories. Assuming a weak electric field and ignoring the double-layer polarization, I obtain analytical expressions for electrostatic potential, electrophoretic mobility, and flow field. In the equilibrium state, the Galvani potential forms across the interface of the spheres. Under a weak electric field, the spheres show finite mobility with the same sign as the Galvani potential. When the radius of the spheres is significantly larger than the Debye and hydrodynamic screening length, the mobility monotonically increases with increasing salinity.

Controlling self-assembly of reduced graphene oxide at the air-water interface: quantitative evidence for long-range attractive and many-body interactions.

Industrial-scale applications of two-dimensional materials are currently limited due to lack of a cost-effective and controlled synthesis method for large-area monolayer films. Self-assembly at fluid interfaces is one promising method. Here, we present a quantitative analysis of the forces governing reduced graphene oxide (rGO) assembly at the air-water interface using two unique approaches: area-based radial distribution functions and a theoretical Derjaguin-Landau-Verwey-Overbeek (DLVO) interaction potential for disks interacting edge-to-edge. rGO aggregates at the air-water interface when the subphase ionic strength results in a Debye screening length equal to the rGO thickness (∼1 mM NaCl), which is consistent with the DLVO interaction potential. At lower ionic strengths, area-based radial distribution functions indicate that rGO-rGO interactions at the air-water interface are dominated by long-range (tens of microns) attractive and many-body repulsive forces. The attractive forces are electrostatic in nature; that is, the force is weakened by minor increases in ionic strength. A quantitative understanding of rGO-rGO interactions at the air-water interface may allow for rational synthesis of large-area atomically thin films that have potential for planar electronics and membranes.

Range of Validity of a Simplified Model for Diffuse Charge Dynamics

AbstractThe modelling of electrochemical processes often requires the solution of the Poisson‐Nernst‐Planck (PNP) equations. In complex geometries, such as porous electrodes, that is challenging due to the presence of disparate length scales, ranging from the Debye screening length (∼nm) to the device length scale (∼cm). To overcome this difficulty, one often assumes that the electric double layer (EDL) is at quasi‐equilibrium to construct a simplified model that accounts for ion diffusion in the electro‐neutral bulk of the electrolyte while replacing the EDLs with appropriate boundary conditions. Various researchers have demonstrated that such an approach is valid in the asymptotic limit of a thin EDL and moderate electrode potentials. In this note, we explore the range of validity of this approximation by considering a one‐dimensional electrolytic cell with blocking electrodes subjected to a step change and time‐periodic alternations in the electrodes’ potentials by calculating the errors associated with the approximate approach as functions of the EDL thickness and electric field frequency and intensity. Additionally, we delineate numerical instabilities associated with the numerical solutions of the bulk equations with the nonlinear boundary condition peculiar to this problem.

Low‐Density Crystals in Charged Colloids: Comparison with Yukawa Theory

AbstractCharged colloids can behave as Yukawa systems, with similar phase behaviour. Using particle‐resolved studies, we consider a system with an unusually long Debye screening length which forms crystals at low colloid volume fraction φ ≈ 0.01. We quantitatively compare this system with the Yukawa model and find that its freezing point is compatible with the theoretical prediction but that the crystal polymorph is not always that expected. In particular we find body‐centred cubic crystals where face‐centred cubic crystals are expected. (© 2015 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Inverted critical adsorption of polyelectrolytes in confinement.

What are the fundamental laws for the adsorption of charged polymers onto oppositely charged surfaces, for convex, planar, and concave geometries? This question is at the heart of surface coating applications, various complex formation phenomena, as well as in the context of cellular and viral biophysics. It has been a long-standing challenge in theoretical polymer physics; for realistic systems the quantitative understanding is however often achievable only by computer simulations. In this study, we present the findings of such extensive Monte-Carlo in silico experiments for polymer-surface adsorption in confined domains. We study the inverted critical adsorption of finite-length polyelectrolytes in three fundamental geometries: planar slit, cylindrical pore, and spherical cavity. The scaling relations extracted from simulations for the critical surface charge density σc-defining the adsorption-desorption transition-are in excellent agreement with our analytical calculations based on the ground-state analysis of the Edwards equation. In particular, we confirm the magnitude and scaling of σc for the concave interfaces versus the Debye screening length 1/κ and the extent of confinement a for these three interfaces for small κa values. For large κa the critical adsorption condition approaches the known planar limit. The transition between the two regimes takes place when the radius of surface curvature or half of the slit thickness a is of the order of 1/κ. We also rationalize how σc(κ) dependence gets modified for semi-flexible versus flexible chains under external confinement. We examine the implications of the chain length for critical adsorption-the effect often hard to tackle theoretically-putting an emphasis on polymers inside attractive spherical cavities. The applications of our findings to some biological systems are discussed, for instance the adsorption of nucleic acids onto the inner surfaces of cylindrical and spherical viral capsids.

A self-amplified transistor immunosensor under dual gate operation: highly sensitive detection of hepatitis B surface antigen.

Ion-sensitive field-effect transistors (ISFETs), although they have attracted considerable attention as effective immunosensors, have still not been adopted for practical applications owing to several problems: (1) the poor sensitivity caused by the short Debye screening length in media with high ion concentration, (2) time-consuming preconditioning processes for achieving the highly-diluted media, and (3) the low durability caused by undesirable ions such as sodium chloride in the media. Here, we propose a highly sensitive immunosensor based on a self-amplified transistor under dual gate operation (immuno-DG ISFET) for the detection of hepatitis B surface antigen. To address the challenges in current ISFET-based immunosensors, we have enhanced the sensitivity of an immunosensor by precisely tailoring the nanostructure of the transistor. In the pH sensing test, the immuno-DG ISFET showed superior sensitivity (2085.53 mV per pH) to both standard ISFET under single gate operation (58.88 mV per pH) and DG ISFET with a non-tailored transistor (381.14 mV per pH). Moreover, concerning the detection of hepatitis B surface antigens (HBsAg) using the immuno-DG ISFET, we have successfully detected trace amounts of HBsAg (22.5 fg mL(-1)) in a non-diluted 1× PBS medium with a high sensitivity of 690 mV. Our results demonstrate that the proposed immuno-DG ISFET can be a biosensor platform for practical use in the diagnosis of various diseases.