Debye Screening Length Research Articles

Partially auxetic behavior in fcc crystals of hard-core repulsive Yukawa particles

Elastic properties of the face centered cubic (fcc) phase of particles, interacting through hard-core repulsive Yukawa potential are determined by Monte Carlo (MC) simulations in the NpT ensemble with variable shape of the periodic box. The effects of the Debye screening length () and contact value of the potential () on elastic properties of the system are studied. It is found that the hard-core repulsive Yukawa system is partially auxetic. The Poisson's ratio of the system in the direction is negative and decreases with increasing the Debye screening length. Poisson's ratio of the hard-core repulsive Yukawa system measured in the directions at versus density.

Electrical Biomolecule Detection Using Nanopatterned Silicon via Block Copolymer Lithography

An electrical biosensor exploiting a nanostructured semiconductor is a promising technology for the highly sensitive, label-free detection of biomolecules via a straightforward electronic signal. The facile and scalable production of a nanopatterned electrical silicon biosensor by block copolymer (BCP) nano-lithography is reported. A cost-effective and large-area nanofabrication, based on BCP self-assembly and single-step dry etching, is developed for the hexagonal nanohole patterning of thin silicon films. The resultant nanopatterned electrical channel modified with biotin molecules successfully detects the two proteins, streptavidin and avidin, down to nanoscale molarities (≈1 nm). The nanoscale pattern comparable to the Debye screening length and the large surface area of the three-dimensional silicon nanochannel enable excellent sensitivity and stability. A device simulation confirms that the nanopatterned structure used in this work is effective for biomolecule detection. This approach relying on the scalable self-assembly principle offers a high-throughput manufacturing process for clinical lab-on-a-chip diagnoses and relevant biomolecular studies.

Debye–Falkenhagen dynamics of electric double layer in presence of electrode heterogeneities

A phenomenological theory of electric double layer (EDL) polarization of an electrode (in the absence and presence of electroactive species) is obtained using the Debye–Falkenhagen equation for the potential. The influence of surface heterogeneities on the compact layer causes the distribution in relaxation time, resulting in constant phase element (CPE) response. This contribution of the compact layer is included through the current balance boundary constraint at the outer Helmholtz plane. The results for the impedance and the capacitance are obtained in terms Debye screening length and dynamic polarization length which is dependent on the surface heterogeneity parameter. At frequencies less than the characteristic compact layer relaxation frequency, the EDL is controlled by the compact layer dynamics and shows CPE response. The intermediate frequencies show the emergence of pseudo-Gerischer and pseudo-Warburg like behavior for systems with lower concentration and lower diffusion coefficients of ions. EDL behaves like a resistor at larger frequencies. Theoretical results capture various observations in the experimental capacitance dispersion data.

D3-D7 holographic dual of a perturbed 3D CFT

An appropriately oriented D3-D7-brane system is the holographic dual of relativistic Fermions occupying a 2+1-dimensional defect embedded in 3+1-dimensional spacetime. The Fermions interact via fields of ${\mathcal N}=4$ Yang-Mills theory in the 3+1-dimensional bulk. Recently, using internal flux to stabilize the system in the probe $N_7<<N_3$ limit, a number of solutions which are dual to conformal field theories with Fermion content have been found. We use holographic techniques to study perturbations of a particular one of the conformal field theories by relevant operators. Generally, the response of a conformal field theory to such a perturbation grows and becomes nonperturbative at low energy scales. We shall find that a perturbation which switches on a background magnetic field $B$ and Fermion mass $m$ induces a renormalization group flow that can be studied perturbatively in the limit of small $m^2/B$. We solve the leading order explicitly. We find that, for one particular value of internal flux, the system exhibits magnetic catalysis, the spontaneous breaking of chiral symmetry enhanced by the presence of the magnetic field. In the process, we derive formulae predicting the Debye screening length of the Fermion-antiFermion plasma at finite density and the diamagnetic moment of the ground state of the Fermion system in the presence of a magnetic field.

Force Interactions of Nonagglomerating Polylactide Particles Obtained through Covalent Surface Grafting with Hydrophilic Polymers

Nonagglomerating polylactide (PLA) particles with various interaction forces were designed by covalent photografting. PLA particles were surface grafted with hydrophilic poly(acrylic acid) (PAA) or poly(acrylamide) (PAAm), and force interactions were determined using colloidal probe atomic force microscopy. Long-range repulsive interactions were detected in the hydrophilic/hydrophilic systems and in the hydrophobic/hydrophilic PLA/PLA-g-PAAm system. In contrast, attractive interactions were observed in the hydrophobic PLA/PLA and in the hydrophobic/hydrophilic PLA/PLA-g-PAA systems. AFM was also used in the tapping mode to determine the surface roughness of both neat and surface-grafted PLA film substrates. The imaging was performed in the dry state as well as in salt solutions of different concentrations. Differences in surface roughness were identified as conformational changes induced by the altered Debye screening length. To understand the origin of the repulsive force, the AFM force profiles were compared to the Derjaguin, Landau, Verwey, and Overbeek (DLVO) theory and the Alexander de Gennes (AdG) model. The steric repulsion provided by the different grafted hydrophilic polymers is a useful tool to inhibit agglomeration of polymeric particles. This is a key aspect in many applications of polymer particles, for example in drug delivery.

Macro- versus Microscopic View on the Electrokinetics of a Water–Membrane Interface

Electrophoresis is an experimental method widely used to study electrostatic properties of interfaces. Here, we question the validity of the macroscopic theory for the planar geometry by Helmholtz and Smoluchowski by considering a POPC bilayer in an aqueous solution with 500 mM NaCl, using molecular dynamics simulations. We find that POPC shows positive electrophoretic mobility due to adsorption of sodium ions at the lipid headgroups. The theory assumes that the region in which the water density undergoes a transition from the bulk value to zero (interfacial width) is small compared to the Debye screening length. This separation of length scale is not fullfilled in the present case. Hence, contrasting the theory, we observe that the surface is not sharply defined, continuum hydrodynamics is not applicable, the effective viscosity in the double layer is increased compared to the bulk, and the zeta potential is dominated by the dipole potential. Our results might have widespread implications for interpretation of electrokinetic studies in general.

When and Why Like-Sized, Oppositely Charged Particles Assemble into Diamond-like Crystals

Like-sized, oppositely charged nanoparticles are known to assemble into large crystals with diamond-like (ZnS) ordering, in sharp contrast to analogous molecular ions and micrometer-scale colloids, which invariably favor more closely packed structures (NaCl or CsCl). Here, we show that these experimental observations can be understood as a consequence of ionic screening and the slight asymmetry in surface charge present on the assembling particles. With this asymmetry taken into account, free-energy calculations predict that the diamond-like ZnS lattice is more favorable than other 1:1 ionic structures, namely, NaCl or CsCl, when the Debye screening length is considerably larger than the particle size. A thermodynamic model describes how the presence of neutralizing counterions within the interstitial regions of the crystal acts to bias the formation of low-volume-fraction structures. The results provide general insights into the self-assembly of non-close-packed structures via electrostatic interactions.

Effect of size polydispersity on the crystal-fluid and crystal-glass transition in hard-core repulsive Yukawa systems

We investigated the effect of size polydispersity on the crystal-fluid transition in hard-core repulsive Yukawa systems by means of Monte Carlo simulations for several state points in the Yukawa parameter space. Size polydispersity was introduced in the system only with respect to the hard particle cores; particles with different diameters had the same surface potential ψ0, but the charge per particle was not varied with packing fraction or distance. We observed a shift to higher packing fraction of the crystal-fluid transition of bulk crystals with a fixed log-normal size distribution upon increasing the polydispersity, which was more pronounced for weakly charged particles (ψ0 ≈ 23 mV) compared to more highly charged particles (ψ0 ≈ 46 mV), and also more pronounced for larger Debye screening length. At high polydispersities (≥0.13) parts of the more highly charged systems that were initially crystalline became amorphous. The amorphous parts had a higher polydispersity than the crystalline parts, indicating the presence of a terminal polydispersity beyond which the homogeneous crystal phase was no longer stable.

Computation of screened two‐electron matrix elements

Computational studies are presented for atoms in screening environments. Numerical solution of atomic Hartree–Fock equations in the Slater type orbitals basis are presented for screened Debye electron–electron as well as electron–nucleus interaction. Slater integrals are evaluated using a Gauss–Laguerre quadrature. Detailed numerical results are presented for various atoms and Debye lengths establishing the method as well as showing the opposing effects of electron–nucleus and electron–electron screening that may induce ambiguity in physical properties extracted from experimental plasma data. A detailed discussion of convergence properties is given. The relevant outcome of the present study revealed the fact that the present expansion method and the previously published Legendre expansion method (Winkler, Int. J. Quantum Chem. 2010, 110, 3129) have their best convergence properties in different regions of the Debye screening length. This is important for applications. In addition, the new expansion method can be implemented for other screening potentials, where other approaches fail. © 2013 Wiley Periodicals, Inc.

Indentation of Highly Charged PSPM Brushes Measured by Force Spectroscopy: Application of a Compressible Fluid Model

Highly charged dense poly(sulfopropyl methacrylate) polyelectrolyte brushes were indented with an atomic force microscopy (AFM) tip as well as with an 8 μm silica colloidal probe at different ionic strengths ranging from Millipore water to 1 M NaCl. The force response during indentation was fitted to a phenomenological equation analogous to the equation of state of a compressible fluid. In this way, internal energy and brush thickness were obtained as a function of ionic strength. Long-range forces decayed exponentially with distance. The characteristic decay lengths were much larger than the Debye screening lengths at the respective ionic strengths. It was therefore concluded that long-range repulsion was due to compression of a loose corona of polymers in front of the dense part of the brush. The size of the indentor determines which region of the brush can be explored by AFM. The tip probes the denser parts of the brush, while with the colloidal probe the corona of the brush can be investigated. The obtained fits of the experimentally measured force distance curves were used as regularization tools for obtaining the brush swelling pressure or “force per unit area” as a function of brush compression. The swelling pressure as a function of brush thickness, h, followed over a wide range a power law close to ∼h–2. This approach allowed deriving fundamental brush parameters on a thermodynamical basis like the compressibility as a function of thickness.

Liquid-vapor phase diagram and surface properties in oppositely charged colloids represented by a mixture of attractive and repulsive Yukawa potentials

The liquid-vapor phase diagrams of equal size diameter σ binary mixtures of screened potentials have been reported for several ranges of interaction using Monte Carlo simulation methods [J. B. Caballero, A. M. Puertas, A. Ferńandez-Barbero, F. J. de las Nieves, J. M. Romero-Enrique, and L. F. Rull, J. Chem. Phys. 124, 054909 (2006); A. Fortini, A.-P. Hynninen, and M. Dijkstra, J. Chem. Phys. 125, 094502 (2006)]. Both works report controversial results about the stability of the phase diagram with the inverse Debye screening length κ. Caballero found stability for values of κσ up to 20 while Fortini reported stability for κσ up to 20 while Fortini reported stability for κσ ≤ 4. In this work a spinodal decomposition process where the liquid and vapor phases coexist through an interface in a slab geometry is used to obtain the phase equilibrium and surface properties using a discontinuous molecular dynamics simulations for mixtures of equal size particles carrying opposite charge and interacting with a mixture of attractive and repulsive Yukawa potentials at different values of κσ. An crude estimation of the triple point temperatures is also reported. The isothermal-isobaric method was also used to determine the phase stability using one phase simulations. We found that liquid-vapor coexistence is stable for values of κσ > 20 and that the critical temperatures have a maximum value at around κσ = 10, in agreement with Caballero et al. calculations. There also exists a controversy about the liquid-vapor envelope stability of the pure component attractive Yukawa model which is also discussed in the text. In addition, details about the equivalence between continuous and discontinuous molecular dynamics simulations are given, in the Appendix, for Yukawa and Lennard-Jones potentials.

Investigation of charge transfer and ionization in He-like systems (Li+, Be2+, B3+, C4+, N5+, O6+)-hydrogen atom collisions in Debye plasmas

The charge transfer and ionization cross sections have been calculated for He-like system (Li+, Be2+, B3+, C4+, N5+, O6+) and hydrogen atom collisions in Debye plasmas for energies ranging from 1 to 500 keV using the classical trajectory Monte Carlo method. Interactions of the active electrons with the projectile ions have been described by model potentials. Cross sections are determined in both screening and unscreening environments, and a comparative study between both environments has been carried out. In particular, an interesting feature of sudden increase in the ionization cross sections at lower velocities is also observed in all the systems like pandey et al. [M. K. Pandey et al., Phys. Plasmas 19, 062104 (2012)] calculations for O8+ + H collision. The feature of sudden increase in ionization cross sections at lower velocities and the effect of plasmas condition on it are explained in terms of the classical trajectory framework. We have found the cross sections for both capture and ionization are dependence on Debye screening lengths throughout the collision energies range, but are particularly pronounced at low projectile collisions energies. The calculated cross sections for the unscreened case are found in reasonable agreement with available experimental and theoretical results.

A proposed voltage dependence of the ionic strength of a confined electrolyte based on a grand canonical ensemble model

Electrodes with highly porous morphologies are of great technological interest, as their exceptionally high specific surface areas make them ideal for use in capacitors, battery electrodes and electrochemical sensors. There is a large body of research focusing on the structure of confined electrolytes in these systems, but the majority of these studies focus on cases where the length scale of the porous domain is equal to or less than the Debye screening length of the electrolyte. In this work, we use a thermodynamic model to consider the structure of electrolytes in mesoscale domains, where the pore dimensions are significantly larger than the Debye screening length. In this limit, the interface is screened by the electrochemical double layer and the enclosed volume primarily consists of an electroneutral ‘bulk liquid’ domain. Despite the absence of direct interactions between ions in the bulk domain and the charged interface, we show that minimization of the free energy of the system leads to a reduction in the ionic strength of the electrolyte within the bulk liquid domain of the pore. Based on our model studies, we anticipate that this depletion will apply for porous domains with widths of the order of 50–200 nm even under mild experimental conditions and low applied voltages. The results imply relationships between electrolyte strength, surface morphology and applied voltage that may be important in device design.

Effect of static carrier screening on the energy relaxation of electrons in polar-semiconductor multiple-quantum-well superlattices

An electro-static model has been formalized to analyze the effect of carrier screening on the energy relaxation of electrons in polar-semiconductor multiple-quantum-well superlattices. The screened polar potential in this structure has been obtained in terms of its 0th order and 1st order Fourier components. The 1st order correction gives a further reduction of the coupling strength due to the uneven spatial distribution of carriers, and it heavily depends on the relative bi-layer thickness compared to the Debye screening length. The reductions of electron energy relaxation in In0.25GaAs/GaAsP0.33 multiple-quantum-well superlattices have been numerically analyzed yielding conclusions which agree with the recent experiments. The model provides a quantified approach to optimize the structure configuration in terms of the carrier cooling rate, allowing the multiple-quantum-well superlattice to be an ideal absorber candidate for realizing the hot carrier solar cell.

Persistence length of polyelectrolytes with precisely located charges

The conformation of polyelectrolytes in aqueous salt solutions is closely related to their self-assembly properties. In particular, the persistence length has a large impact on how the chain can arrange itself. In this work, biomimetic poly N-substituted glycines (polypeptoids) have been designed to position charged side chains at precise distances from each other to elucidate the relationship between the spacing of the charges along the backbone, the ionic strength, and the persistence length. Using small angle neutron scattering (SANS), it is shown that at low ionic strength, polypeptoids with charged groups located closer to each other along the polymer backbone are stiffer than those with the charged groups spaced further apart. At high ionic strength, the total persistence length decreases for both macromolecules because the electrostatic repulsions between ionized groups are screened. The measured persistence lengths were compared to those calculated using a discrete chain model with bending rigidity, and it is shown that the electrostatic persistence length scales quadratically with the Debye screening length. It is also shown that the bare persistence length of a molecule with alternating ionizable and hydrophilic groups is larger than that of a molecule containing 100% ionizable groups. This difference can be attributed to the longer hydrophilic side chains that may induce local chain stiffening.

Spectroscopic assessment of the role of hydrogen in surface defects, in the electronic structure and transport properties of TiO2, ZnO and SnO2nanoparticles

The interaction of metal oxides with gases is very important for the operation of energy devices such as fuel cells and gas sensors, and also relevant for materials synthesis and processing. The electronic transport properties of metal oxides for the aforementioned devices strongly depend on the chemistry of these gases and on the presence or absence of defects on the surface and in the bulk. The Debye screening length is in this respect a material specific property which becomes particularly significant when the material is comprised of nanoparticles. In the present study, poly-crystalline TiO(2), ZnO and SnO(2) nanoparticles were synthesized by a high temperature flame spray combustion process and investigated for their interaction with hydrogen. The chemistry of the reduced and oxidized surfaces of these metal oxides, where the interaction with gases takes place, was investigated in detail with X-ray photoelectron spectroscopy (XPS). The transitions found near E(F) with XPS are consistent with those found by diffuse reflectance spectroscopy (DRS) and were assigned to surface states originating from non-equilibrium oxygen vacancies. We show how the non-stoichiometric character of the metal oxide surface constitutes electronic surface defects, in particular oxygen vacancies which allow for additional transitions near the Fermi energy (E(F)). The concentration of these surface defects can be strongly reduced by thermal after-treatment under air or increased by Ar(+)-sputtering, after which significant spectral features appear near E(F). Such prominent changes are particularly observed for TiO(2) and SnO(2), whereas the stoichiometry of the ZnO surface seems to be less responsive to such reducing and oxidizing conditions. Pronounced changes of the electrical conductivity upon changing from reducing to oxidizing conditions at elevated temperatures were monitored by electrochemical impedance spectroscopy (EIS). The lowering of the potential barrier for the charge transport particularly at lower temperatures already at reducing conditions is confirmed. The impedance response indicates that charge transfer is governed predominantly by one single process, i.e. by interaction of surface-like states localized within depletion layer with gas molecules. This implies that the free charge carriers in the material are determined by the intrinsic property like non-stoichiometry. Gas sensors made from such FSS nanoparticulate metal oxides showed well developed sensing characteristics of the hydrogen sensing at moderate temperatures.

Thermophoresis of charged colloidal rods

The thermal diffusion behavior of dilute solutions of very long and thin, charged colloidal rods (fd-virus particles) is studied using a holographic grating technique. The Soret coefficient of the charged colloids is measured as a function of the Debye screening length, as well as the rod-concentration. The Soret coefficient of the fd-viruses increases monotonically with increasing Debye length, while there is a relatively weak dependence on the rod-concentration when the ionic strength is kept constant. An existing theory for thermal diffusion of charged spheres is extended to describe the thermal diffusion of long and thin charged rods, leading to an expression for the Soret coefficient in terms of the Debye length, the rod-core dimensions, and the surface charge density. The thermal diffusion coefficient of a charged colloidal rod is shown to be accurately represented, for arbitrary Debye lengths, by a superposition of spherical beads with the same diameter of the rod and the same surface charge density. The experimental Soret coefficients are compared with this and other theories, and are contrasted against the thermal diffusion behaviour of charged colloidal spheres.

Light-induced phase transitions of colloidal monolayers with crystalline order

We experimentally study the phase behavior of a charge-stabilized two-dimensional colloidal crystal which is subjected to a one-dimensional periodic light field. Such light fields are created by a scanned optical line tweezer which allows the variation of the periodicity without optical realignments. In order to realize a wide range of line spacings relative to the lattice constant, we use a suspension of silica particles in bromobenzene. This colloidal system has a Debye screening length of about 4.6 μm which results in the formation of crystals with lattice constants up to 20 μm. Because the refractive index of bromobenzene is larger than that of the colloids, optical gradient forces lead to the attraction of particles at regions where the intensity is smallest. Depending on the depth and periodicity of the optical potential, we observe the light-induced assembly of colloids into triangular, rhombic and square phases.

Light intensity dependent Debye screening length in undoped photorefractive titanosillenite crystals

We report on the experimental evidence of the light intensity dependence of the Debye screening length ls in undoped photorefractive titanosillenite crystals (Bi12TiO20) by measuring the holographic gain and diffraction efficiency in a two-wave mixing experiment under 532 nm wavelength laser light. Debye length shows saturation at high values of the light intensity. Results are in agreement with the theoretical development.

Effects of electrostatic correlations on electrokinetic phenomena

The classical theory of electrokinetic phenomena is based on the mean-field approximation that the electric field acting on an individual ion is self-consistently determined by the local mean charge density. This paper considers situations, such as concentrated electrolytes, multivalent electrolytes, or solvent-free ionic liquids, where the mean-field approximation breaks down. A fourth-order modified Poisson equation is developed that captures the essential features in a simple continuum framework. The model is derived as a gradient approximation for nonlocal electrostatics of interacting effective charges, where the permittivity becomes a differential operator, scaled by a correlation length. The theory is able to capture subtle aspects of molecular simulations and allows for simple calculations of electrokinetic flows in correlated ionic fluids. Charge-density oscillations tend to reduce electro-osmotic flow and streaming current, and overscreening of surface charge can lead to flow reversal. These effects also help to explain the suppression of induced-charge electrokinetic phenomena at high salt concentrations.