Charged Plane Research Articles

Influence of the dielectrophoretic force in mixed electrical double layers

The equilibrium properties of a charged plane immersed in an aqueous electrolyte solution are examined using a generalized Poisson–Boltzmann equation that takes into account the finite ion size by modeling the solution as a suspension of polarizable insulating spheres in water. This formalism is applied to a general solution composed of two or more counterion species with different valences, sizes, and effective permittivity values. It is shown that, due to the dependence of the dielectrophoretic force on the ion size and effective permittivity value, the concentration of the smaller counterion strongly increases while that of the larger one decreases in the immediate vicinity of the charged surface. As a result the surface potential value strongly increases as compared to the usual modified Poisson–Boltzmann theory that only includes steric interactions among ions. This effect is particularly important in the case of mixtures of univalent and divalent counterions, being significant even for relatively low surface charge values.

Force exerted on a conducting spherical particle near the plate of a plane capacitor

The potential energy and the interaction force of a conducting spherical particle and a similarly charged plane plate are calculated for relatively small distances. The force is calculated from the potential energy and the plate is represented as a conducting sphere whose radius is 100 times greater than the radius of the particle. It is assumed that the particle is not charged by the plate. The domains of parameters in which the particle is always repulsed from the plate and in which the attraction takes place are determined.

The Conditions of Stability of Two-Dimensional Quantum Systems of Three Charged Particles

For a two-dimensional Coulomb system of three charged particles, among which two particles are identical and the third particle is of different nature, we study the conditions of existence for symmetric and antisymmetric bound energy states (conditions of stability) in the mass–charge (m;Z) plane. High-precision three-body numerical calculations based on a stochastic variational method with Gaussian bases are performed. Several anomalous effects in the behavior of the characteristic distances between particles are revealed, and the nonzero quadrupole moment is found in a two-dimensional polar-symmetric field. The systematic comparison of the results for two- and three-dimensional systems is performed. The values of energy and size, the density distributions, and the correlation functions for the various reference three-particle systems are obtained.

Algebraic Repulsions between Charged Planes with Strongly Overlapping Electrical Double Layers

Langmuir's disjoining pressure between two flat, charged planes was calculated analytically for strongly overlapping double layers in the limit of zero electric field between the planes. The resulting repulsion has a long-range algebraic decay that stems from the thermodynamic equilibrium between homogeneously distributed interplate ions and ions in the surrounding electrolyte reservoir. Together with the van der Waals attraction, the repulsion forms the zero-field pendant of the exponentially screened DLVO potential, a pendant that is always repulsive at large plate-plate distances. The experimental occurrence of algebraic repulsions can be simply predicted from surface charge density and ionic strength.

Current Oscillations in the Layer-by-Layer Electrochemical Deposition of Vertically Aligned Nanosheets of Zinc Hydroxide Nitrate

Large scale, vertically aligned nanosheets of zinc hydroxide nitrate [Zn5(OH)8(NO3)2·2H2O] were synthesized by electrochemical deposition in a methanol solution containing a small fraction of water. Structural analysis by X-ray diffraction and scanning electron microscopy reveal that the nanosheets are layered zinc hydroxide nitrate grown on top of a polycrystalline ZnO layer, forming a two layer structure. During the nanosheet growth, well defined current oscillations were observed at a constant voltage. It was determined that the current oscillations are associated with the layer-by-layer growth of the nanosheets. The alternative stacking of positive and negatively charged polar planes of zinc hydroxide nitrate causes the current fluctuation. Each current oscillation cycle represents one monolayer addition to the existing nanosheets. With a mild annealing treatment, the obtained nanosheets may be transformed to porous ZnO, a more appropriate and useful material for various technological applications. This study provides a new route to precisely control the growth of nanostructures in solution as well as the type of polar surface via current monitoring during deposition. Although layer-by-layer deposition has been extensively studied in vacuum such as atomic layer deposition, it has rarely been reported for solution growth which may have potential applications in materials research.

Electron excess in alkaline earth sub-nitrides: 2D electron gas or 3D electride?

Alkaline earth sub-nitrides were synthesised more than five decades ago, but their potential for high-performance electronics was only recently demonstrated [Lee et al., Nature, 2013]. Based on the formal valence of the elements, there is an intrinsic excess of electrons, which is unusual for a chemically stable compound. We report an electrostatic and electronic analysis of Ca2N, Sr2N and Ba2N, which reveals a highly anisotropic electronic band structure, with a subtle balance between localisation and delocalisation of excess electrons in between positively charged planes of [M2N]+. A deep potential well is found at empty crystallographic positions, which are occupied by anions in the structurally analogous ternary nitrides. A greater degree of delocalisation (conductivity) is predicted for heavier metals.

STRUCTURE SCALARS IN CHARGED PLANE SYMMETRY

We consider non-adiabatic flow of the fluid possessing dissipation in the form of shearing viscosity in electromagnetic field. The scalar functions (structure scalars) for charged plane symmetry are formulated and are related with the physical variables of the fluid. We also develop a relationship between the Weyl tensor and other physical variables by using Taub mass formalism. The role of electric charge as well as its physical significance for the evolution of the shear tensor and expansion scalar are also explored. Finally, we discuss a special case for dust with cosmological constant.

Potential profile of the quantum step in semiconductors and the example of GaN

It is usually assumed that the quantum step (QS), quantum well (QW) and quantum barrier (QB) have the rectangular potential profiles. We show that the potential profiles are not really rectangular. A QS is actually a smooth, gradual change of potential over a distance larger than one monolayer. For a narrow QW, instead of the QW, a more appropriate term is the quantum valley. We study the dipole layers formed by the ions and calculate the electrostatic contribution to the potential. Notably, the minimal thickness of the QS is not determined by the distance between the charged planes, but by the lateral spacing between ions of the same polarity. In the example of GaN, the QS cannot be thinner than about 3 Å.

Clay Particles Destabilize Engineered Nanoparticles in Aqueous Environments

Given the ubiquity of natural clay minerals, the most likely interaction of nanoparticles released into an aquatic environment will be with suspended clay minerals. Thus, the transport of engineered nanoparticles in the subsurface and the water column will most likely be altered by their interaction with these minerals. We studied the interactions of two of the most produced nanoparticles, Ag and TiO(2), and montmorillonite to determine how heteroaggregation can alter the stability of nanoparticle/clay mineral mixtures. Since at low pH montmorillonite has a negatively charged basal plane and positively charged edges, its interaction with these nanoparticles at different pH lead to unusual behaviors. There are six different interactions for each clay-nanoparticle pair. At pH values below the IEP of montmorillonite edge site, montmorillonite reduced the stability of both negatively charged Ag and positively charged TiO(2) nanoparticles. Surprisingly this enhanced coagulation only occurs within an intermediate ionic strength range. The spillover of the montmorillonite basal plane electric double layer to the montmorillonite edge may screen the electrostatic attraction between Ag and the montmorillonite edge at low ionic strength, whereas a repulsion between TiO(2) and montmorillonite face sites may restabilize the mixture.

Effect of polycarboxylate ether comb-type polymer on viscosity and interfacial properties of kaolinite clay suspensions

The interactions between kaolinite clay particles and a comb-type polymer (polycarboxylate ether or PCE), so-called PCE super-plasticizer, were investigated through viscosity and surface forces measurements by a rheometer and a Surface Forces Apparatus (SFA). The addition of PCE shows a strong impact on the viscosity of concentrated kaolinite suspensions in alkaline solutions (pH=8.3) but a weak effect under acidic conditions (pH=3.4). In acidic solutions, the high viscosity measured is attributed to the strong electrostatic interaction between negatively charged basal planes and positively charged edge surfaces of clay particles. Under the alkaline condition, the suspension viscosity was found to first increase significantly and then decrease with increasing PCE dosages. The results from surface forces measurement show that PCE molecules at low dosages can bridge the kaolinite particles in the concentrated suspensions via hydrogen bonding, leading to the formation of a kaolinite-PCE “network” and hence an increased suspension viscosity. At high PCE dosages, clay particles are fully covered by PCE molecules, leading to a more dispersed kaolinite suspensions and hence lower suspension viscosity due to steric repulsion between the adsorbed PCE molecules. The insights derived from measuring viscosity and interfacial properties of kaolinite suspensions containing varying amount of comb-type super-plasticizer PCE at different pH provide the foundation for many engineering applications and optimizing industrial processes.

Stable, Single-Layer MX2 Transition-Metal Oxides and Dichalcogenides in a Honeycomb-Like Structure

Recent studies have revealed that single-layer transition-metal oxides and dichalcogenides (MX2) might offer properties superior to those of graphene. So far, only very few MX2 compounds have been synthesized as suspended single layers, and some of them have been exfoliated as thin sheets. Using first-principles structure optimization and phonon calculations based on density functional theory, we predict that, out of 88 different combinations of MX2 compounds, several of them can be stable in free-standing, single-layer honeycomb-like structures. These materials have two-dimensional hexagonal lattices and have top-view appearances as if they consisted of either honeycombs or centered honeycombs. However, their bonding is different from that of graphene; they can be viewed as a positively charged plane of transition-metal atoms sandwiched between two planes of negatively charged oxygen or chalcogen atoms. Electron correlation in transition-metal oxides was treated by including Coulomb repulsion through LDA...

Three region model and quantum enhancement of thermionic and photoelectric electron emission from negatively charged metallic surfaces

In this paper the authors have evaluated the transmission coefficient of electrons across a negatively charged plane metallic surface on the basis of a three region model for variation of the poten...

A Design and Numerical Study of Flying-Plate Initiating System

In order to form plane shock wave in explosive charge after detonation ,a flying-plate initiating system was put forward. The principle of material selection, the shape and incline angle of flying-plate were defined by theoretical analysis and calculations. The velocity of flying-plate, distance of between flying-plate and driving charge was analyzed and calculated according one-dimensional driving theory. The working process of flying-plate initiating system was studied by numerical simulation and the simulation results show flying-plate initiating system is reliable way to initiate main charge and form good plane wave.

Impact of Micelle Ionic Electrical Double Layer Structure on the Excited State Protolytic Reaction in the Fluorescent Probe Bound to the Colloidal Nanoparticles

The fluorescent probe, 2-hydroxynaphthalene(dodecylo)-6-sulfonamide (NSDA) bound selectively to shear plane of various electrostatic charges was synthesized and its photophysical properties have been investigated by means of steady state fluorescence and nanosecond time-resolved spectroscopy. Our experimental data allowed us to determine the excited state proton transfer (ESPT) rate and equilibrium constants of NSDA bound to micelles and to estimate the electric potential value (Ψ) at the particle surface. The spatial dependence of proton movement velocity through electric double layer (EDL) of micelles has been thoroughly analyzed. In this article, a new approach of estimating the values of the micelle potential (Ψ(R)) from the excited state proton transfer rate constant of the fluorescent probe bound at a certain distance (R) to a micellar surface has been proposed. The Ψ(R) values, obtained in this way, are compared with electrophoretic values of the particle potential (ζ). Our results on electrophoretic potentials and the reaction course of the ESPT in colloidal environment may contribute to a deeper understanding of micellar interactions and behavior of the living cells in contact with various diluted substances such as pharmacological drugs, hormones, proteins, and other colloidal particles.

Interaction of bentonite colloids with Cs, Eu, Th and U in presence of humic acid: A flow field-flow fractionation study

The interaction of Cs(I), Eu(III), Th(IV) and U(VI) with montmorillonite colloids was investigated in natural Grimsel Test Site groundwater over a 3 years period. The asymmetric flow field-flow fractionation combined with various detectors was applied to study size variations of colloids and to monitor colloid association of trace metals. The colloids suspended directly in the low ionic strength ( I), slightly alkaline granitic groundwater ( I = 10 −3 mol/L, pH 9.6) showed a gradual agglomeration with a size distribution shift from initially 10–200 nm to 50–400 nm within over 3 years. The Ca 2+ concentration of 2.1 × 10 −4 mol/L in the ground water is believed to be responsible for the slow agglomeration due to Ca 2+ ion exchange against Li + and Na + at the permanently charged basal clay planes. Furthermore, the Ca 2+ concentration lies close to the critical coagulation concentration (CCC) of 10 −3 mol L −1 for clay colloids. Slow destabilization may delimit clay colloid migration in this specific groundwater over long time scales. Eu(III) and Th(IV) are found predominantly bound to clay colloids, while U(VI) prevails as the UO 2(OH) 3 − complex and Cs(I) remains mainly as aquo ion under our experimental conditions. Speciation calculations qualitatively represent the experimental data. A focus was set on the reversibility of metal ion-colloid binding. Addition of humic acid as a competing ligand induces rapid metal ion dissociation from clay colloids in the case of Eu(III) even after previous aging for about 3 years. Interestingly only partial dissociation occurs in the case of Th(IV). Experiments and calculations prove that the humate complexes dominate the speciation of all metal ions under given conditions. The partial irreversibility of clay bound Th(IV) is presently not understood but might play an important role for the colloid-mediated transport of polyvalent actinides over wide distances in natural groundwater.

Origin of Sr segregation at La1−xSrxMnO3surfaces

A uniform distribution of La and Sr in lanthanum-strontium manganites would lead to charged crystal planes, a charged surface, and arbitrarily large surface energy for a bulk crystal. This divergent energy can be eliminated by depleting the La concentration near the surface. Assuming an exponential form for segregation suggested by experiment, the total electrostatic energy is calculated, depending only upon the decay length and on an effective charge ${Z}^{*}$ associated with the La ion. It is found to be lower in energy than neutralization of the surface by changing Mn charge states or simply readjusting the La concentration in the surface plane, though the energy minimum is found at a shorter decay length than that observed. The extension of this mechanism to segregation near the surface in other systems is discussed.

Numerical computer calculation of distribution of similar point charges at the dielectric surface

Results of numerical calculation of the distribution of similar point charges over a uniformly charged dielectric plane are presented for different surface charge densities and surface temperatures. It is shown that, in the case of the surface charge density ranging from 2 × 10−6 to 7 × 10−5 C/m2 and temperatures ranging from 300 to 800 K, the Lindemann criterion is fulfilled for the average deviation of the point charge from the equilibrium position, and the collection of point charges at the dielectric surface can be regarded as a 2D Coulomb crystal.

Polyelectrolyte adsorption onto oppositely charged interfaces: unified approach for plane, cylinder, and sphere

A universal description is presented for weak adsorption of flexible polyelectrolyte chains onto oppositely charged planar and curved surfaces. It is based on the WKB (Wentzel-Kramers-Brillouin) quantum mechanical method for the Green function equation in the ground state dominance limit. The approach provides a unified picture for the scaling behavior of the critical characteristics of polyelectrolyte adsorption and the thickness of the adsorbed polymer layer formed adjacent to the interface. We find, particularly at low-salt conditions, that curved convex surfaces necessitate much larger surface charge densities to trigger polyelectrolyte adsorption, as compared to a planar interface in the same solution. In addition, we demonstrate that the different surface geometries yield very distinct scaling laws for the critical surface charge density required to initiate chain adsorption. Namely, in the low-salt limit, the surface charge density scales cubical with the inverse Debye screening length for a plane, quadratic for an adsorbing cylinder, and linear for a sphere. As the radius of surface curvature grows, the parameter of critical chain adsorption onto a rod and a sphere turns asymptotically into that of a planar interface. The transition occurs when the radius of surface curvature becomes comparable to the Debye screening length. The general scaling trends derived appear to be consistent with the complex-formation experiments of polyelectrolyte chains with oppositely charged spherical and cylindrical micelles. Finally, the WKB results are compared with the existing theories of polyelectrolyte adsorption and future perspectives are outlined.

Built-in and induced polarization across LaAlO3/SrTiO3 heterojunctions

Ionic crystals terminated at oppositely charged polar surfaces are inherently unstable and expected to undergo surface reconstructions to maintain electrostatic stability. Essentially, an electric field that arises between oppositely charged atomic planes gives rise to a built-in potential that diverges with thickness. In ultra thin film form however the polar crystals are expected to remain stable without necessitating surface reconstructions, yet the built-in potential has eluded observation. Here we present evidence of a built-in potential across polar \lao ~thin films grown on \sto ~substrates, a system well known for the electron gas that forms at the interface. By performing electron tunneling measurements between the electron gas and a metallic gate on \lao ~we measure a built-in electric field across \lao ~of 93 meV/\AA. Additionally, capacitance measurements reveal the presence of an induced dipole moment near the interface in \sto, illuminating a unique property of \sto ~substrates. We forsee use of the ionic built-in potential as an additional tuning parameter in both existing and novel device architectures, especially as atomic control of oxide interfaces gains widespread momentum.

Effects of Discrete Charge Clustering in Simulations of Charged Interfaces.

A system of counterions between charged surfaces is investigated, with the surfaces represented by uniform charged planes and three different arrangements of discrete surface charges - an equispaced grid and two different clustered arrangements. The behaviors of a series of systems with identical net surface charge density are examined, with particular emphasis placed on the long ranged corrections via the method of "charged slabs" and the effects of the simulation cell size. Marked differences are observed in counterion distributions and the osmotic pressure dependent on the particular representation of the charged surfaces; the uniformly charged surfaces and equispaced grids of discrete charge behave in a broadly similar manner, but the clustered systems display a pronounced decrease in osmotic pressure as the simulation size is increased. The influence of the long ranged correction is shown to be minimal for all but the very smallest of system sizes.