Electrostatic Image Research Articles

Models for the Charging of Particles in Liquid Toners: A Summary

Liquid toners have been used in the development of electrostatic images in digital printing since the midfifties. In this article, several models are discussed that were introduced to explain the processes responsible for charging toner particles. The acid-base models had to be extended by equilibrium models describing dynamic dissociation, adsorption and desorption. The important role of water traces in non-aqueous media for the dissociation of molecules and stabilization of ions was investigated. Later, electrical conditions were considered to explain specific high field effects by additional charge generation and relaxation processes. The focus of this article is on the models developed for the charging mechanisms. The enormous progress in measurement techniques that was necessary for improving and, in some cases, correcting the models is not described in detail here nor are models concerning practical issues in printing.

Electrostatic image theory for an anisotropic boundary

An image theory for electrostatic problems involving the anisotropic impedance boundary is introduced through Heaviside operator calculus. The image of a point charge in front of an anisotropic boundary plane is given in terms of a combination of point charge and a surface-charge distribution consisting of a planar angular sector of exponentially decaying surface charge bounded by two line charges. The angle of the sector depends on the anisotropy of the boundary. For vanishing anisotropy the sector contracts to an exponentially decaying line charge coinciding with the result derived previously for the isotropic boundary. The theory is validated numerically by computing potential values from the image and through inverse Fourier transform techniques.

Computing induced charges in inhomogeneous dielectric media: application in a Monte Carlo simulation of complex ionic systems.

The efficient calculation of induced charges in an inhomogeneous dielectric is important in simulations and coarse-grained models in molecular biology, chemical physics, and electrochemistry. We present the induced charge computation (ICC) method for the calculation of the polarization charges based on the variational formulation of Allen et al. [Phys. Chem. Chem. Phys. 3, 4177 (2001)]. We give a different solution for their extremum condition that produces a matrix formulation. The induced charges are directly calculated by solving the linear matrix equation Ah=c, where h contains the discretized induced charge density, c depends only on the source charges-the ions moved in the simulation-and the matrix A depends on the geometry of dielectrics, which is assumed to be unchanged during the simulation. Thus, the matrix need be inverted only once at the beginning of the simulation. We verify the efficiency and accuracy of the method by means of Monte Carlo simulations for two special cases. In the simplest case, a single sharp planar dielectric boundary is present, which allows comparison with exact results calculated using the method of electrostatic images. The other special case is a particularly simple case where the matrix A is not diagonal: a slab with two parallel flat boundaries. Our results for electrolyte solutions in these special cases show that the ICC method is both accurate and efficient.

Inverse Dirichlet problem and conformal mapping

In this exposition we consider an inverse Dirichlet problem for harmonic functions that arises in the mathematical modelling of electrostatic imaging methods. In the first part we will survey the main ideas of some reconstruction procedures that have been employed for the numerical solution of this nonlinear and ill-posed inverse boundary value problem. In the second part we will outline a recently developed method that is based on conformal mapping techniques. By some numerical examples we will illustrate the feasibility of this new method.

Electrostatic force acting on a spherically symmetric charge distribution in contact with a conductive plane

A spherically symmetric charge distribution is a useful, first-order model of a charged insulating particle, such as a toner particle used in electrostatic imaging technologies. The electrostatic force of adhesion between a spherically symmetric charge distribution in contact with a conductive ground plane is derived using the method of images. Finite element analysis is used, with the uniformly charged sphere of charge Q modeled with K charge points, each of which has a charge of magnitude Q/ K. Both a closed form solution and a numerical calculation are used to derive the total force. It is found that the electrostatic image force acting on the few charge points located in proximity to the conductive plane (the proximity charge) is comparable to the electrostatic force acting on a single charge point of magnitude Q located in the center of the sphere. This is a surprising result since it is conventionally assumed that a spherically symmetric charge distribution can be modeled by a single charge point Q located in the center of the sphere. However, this assumption is only valid at distances far from any conductive planes. When all pairs of charge points and their charge images are considered, the total electrostatic force acting on a sphere of charge Q in contact with a conductive plane is larger than the conventionally assumed electrostatic image force by a correction factor (1+4/ π). The additional force, that we call the proximity force which is primarily due to the proximity charge (the 4/ π term), is independent of the number of K charge points assumed, suggesting it is model independent at contact. The proximity force's functional dependence on the separation between the bottom of the charged sphere and the conductive plane depends on the distribution of the charge points near the contact point. Implications of the existence of the electrostatic proximity force are discussed.

A model of wetting on quasicrystals in ambient air

Water does not wet well-polished quasicrystal surfaces, in strong contrast to the behavior observed on aluminum metal in ambient atmosphere. Contact angle measurements combined with a determination of the electronic partial density of states and of oxide layer thicknesses demonstrate that this unexpected wetting property is related to the electronic density of states within the bulk material, underneath the oxide layer, and to the thickness of the oxide layer. A model is derived in this paper that aims at an interpretation of these results in terms of electrostatic image forces developed in the conduction electron cloud by the dipoles of the water molecules.

Reversible short-range electrostatic imaging in frequency modulation atomic forcemicroscopy on metallic surfaces

The mechanism of atomic-scale image formation in non-contact AFM on metallic surfacesis analysed using total-energy pseudopotential calculations. Depending on thetip–apex configuration, we find two different imaging modes. Both clean and metalcontaminated Si tips provide atomic resolution arising from the very strong covalenttip–sample interaction, in striking similarity with the imaging mechanism found onsemiconductor surfaces. A completely new mechanism, reversible short-range electrostaticimaging, due to subtle charge-transfer interactions is identified for oxidized Si tips.Contrary to the strong covalent-bond imaging, this new mechanism causes onlynegligible surface perturbation and can account for recent experimental results.

First-Principles Characterization of Atomic Structure of Al<SUB>2</SUB>O<SUB>3</SUB>(0001)/Cu Nano-Hetero Interface

Atomic structures characterization of Al 2 O 3 (0001)/Cu nano-hetero interfaces has been performed by the first-principles pseudopotential method and in cooperation with HRTEM observations. The physical properties of the interfaces depend strongly on the interface stoichiometry. Bonding nature of the O-rich (O-terminated) interface is explained as strong covalent and ionic interactions, whereas that of the stoichiometric (Al-terminated) interface is weak covalent and electrostatic image interactions. The O-terminated interface has quite larger adhesive energy than that of the stoichiometric one. Recent HRTEM observations of the Al 2 O 3 (0001)/Cu interface have confirmed the O-terminated interlace. However, the observed incoherent interface is not the same as an ideal coherent interface obtained by the first-principles. We explain the relationship between the present coherent interface and the practical incoherent one.

Covalent and reversible short-range electrostatic imaging in noncontact atomic force microscopy.

We present a computational study of atomic-scale image formation in noncontact atomic force microscopy on metallic surfaces. We find two imaging scenarios: (1). atomic resolution arising due to very strong covalent tip-sample interaction exhibiting striking similarity with the imaging mechanism found on semiconductor surfaces, and (2). a completely new mechanism, reversible short-range electrostatic imaging, arising due to subtle charge-transfer interactions. Contrary to the strong covalent-bond imaging, the newly identified mechanism causes only negligible surface perturbation and can account for results recently observed experimentally.

Intermolecular Forces between the n-Alkanes Methane to Butane Adsorbed at the Water/Vapor Interface

Experimental data on the dependence of the surface tension of water on the adsorption of n-alkanes (methane to butane) from the vapor phase over a range of temperatures are re-interpreted to obtain improved estimates of the two-dimensional second virial coefficients for comparison with calculations based on the Lennard−Jones (L−J) formalism in two dimensions. The analysis includes the fugacity corrections for the alkane gases and takes the L−J parameters as known for the three-dimensional gases. The new L−J calculations use a closed-form analytical solution of the basic equation for the two-dimensional second virial coefficient. These older published computations are correct and, as expected, are in complete agreement with the results by numerical integration with modern computer software. Together with estimates of the standard entropies of adsorption, the results indicate that no significant structuring of the surface water molecules occurs upon adsorption of the alkanes. The two-dimensional second virial coefficients are in fair accord with the L−J predictions, except for butane. The reduction of the attractive component of the potentials of mean force between physisorbed molecules arising from the frequency-dependent interaction with their electrostatic images in the bulk aqueous phase, as described by McLachlan (Mol. Phys. 1964, 7, 381), or from the polarization of the adsorbates by a surface electric field (surface field polarization) is minor for methane, ethane, and propane. For butane, these effects may be significant but possible changes in conformation upon adsorption may weaken the validity of the gas-phase L−J parameters in estimating the two-dimensional virial coefficients for this alkane.

Relationship between charge distribution and its image by electrostatic force microscopy

We shall demonstrate in this article that characterization of the charge distribution by electrostatic force microscopy is not straightforward: we will stress the important role played by the electrostatic images of the scanned charge distribution in the tip and by the operating mode in the formation of extra features in images obtained with this instrument. To illustrate this, we will describe two models that correspond to the scanning of small and extended charge distributions. These models will be compared with experimental images.

Phase imaging of buried structures

We report magnetic and electrostatic phase imaging of micron-scale metallic lines covered with 525 nm of SiO 2. Magnetic force microscopy (MFM) has been used to image a buried current-carrying line, to resolve its micron-scale defects, and characterize current crowding around those defects. The MFM phase signal from this structure compares quantitatively to the MFM signal from the same structure, taken prior to deposition of the oxide layer when transformed by a Green’s function propagation to account for the oxide thickness. The alternative use of electric force microscopy (EFM) to find the location of a break and identify void defects in buried lines is contrasted with MFM.

Self-alignment of a polar molecule colliding with a solid surface

It is shown that polar molecules colliding with a solid are subject to efficient self-alignment caused by an interaction with their own electrostatic image dipole when the permanent dipole moment of the molecule exceeds 3 D.

ELECTROSTATIC IMAGE THEORY FOR TWO INTERSECTING CONDUCTING SPHERES

The classical electrostatic image principle for a perfectly conducting object consisting of two orthogonally intersecting spheres is revisited through vector analysis. A method for finding the image of a given charge distribution by splitting it in three virtual single-sphere problems is described. Also, a simple relation between the image charges of a given point charge is found. The method is applied to finding exact expressions for the polarizability dyadic of the object to be used as a bechmark for testing computing schemes on a nontrivial geometry. Application of the present object as a model for an oblong particle in a composite dielectric is also discussed.

Numerical computation of tunneling fluxes

The computation of tunneling probabilities in three dimensions is a numerical challenge, because the small transition probabilities associated with the overlap of exponentially vanishing wave function-tails require large computational accuracy. In scattering situations arising, e.g., in electron tunneling in metal-molecule-metal junctions, this is compounded by the need to provide a proper truncation procedure at the numerical boundaries of the computed system and by the need to account for electrostatic fields and image interactions. This paper describes a numerical methodology to deal with these problems. A pseudopotential that describes the underlying system is assumed given. Electrostatic fields and image interactions are evaluated for the given boundary conditions from numerically solving Laplace and Poisson equations. Tunneling probabilities are computed using a grid-based absorbing boundary conditions Green’s function method. An efficient and exact way to implement the absorbing boundary conditions by using the exact self-energy associated with separating the scattering system from the rest of the infinite space is described. This makes it possible to substantially reduce the size of the grid used in such calculations. Two applications, an examination of the possibility to resolve the spatial structure of an electron wave function in an electron cavity by scanning tunneling microscopy, and a calculation of electron tunneling probabilities through water, are presented.

Electrostatic imaging via conformal mapping

We present the solution of an inverse boundary value problem for harmonicfunctions arising in electrostatic imaging through conformal mapping techniques.The numerical method consists of two parts. In a first step, by successiveapproximations a nonlinear equation is solved to determine the boundary valuesof a holomorphic function on the outer boundary circle of an annulus. Then in asecond step an ill-posed Cauchy problem is solved to determine the holomorphicfunction in the annulus. The method extends and modifies an earlier analysis ofIdemen and Akduman (Idemen M and Akduman I 1988 SIAM J. Appl. Math. 48703–18). We establish a convergence result for the iteration procedure andthrough numerical examples we illustrate the feasibility of the method.

Simultaneous trapping and guiding of cold ions and electrons without externally applied fields

A new “external fields-free” trap capable of traping simultaneously cold paramagnetic positive and negative ions as well as electrons is proposed. Particles exhibit Zeeman repulsion from a periodically magnetized ferromagnetic film but are attracted to the same film due to the interaction with their own electrostatic image. It is shown that few millikelvin deep trapping can be realized with such an approach. Perspectives of using these traps as a quantum computer hardware and for the Wigner crystallization experiments are briefly discussed.

Electrostatic scanningforce microscopy images of long molecules: single-walled carbonnanotubes and DNA

Experimental measurements of the electrostaticproperties of long molecules are presented in this work. It isshown that, in the case of carbon nanotubes, the electrostaticforce between the scanning force microscopy tip and the sample enhances the network of nanotubes electrically connected to ametal electrode. On λ-DNA molecules the same kind ofexperiments result in essentially no measurable electrostaticforce due to the molecules. From this we conclude that λ-DNA has a negligible electronic conductivity.

Sampling-image streak framing technique and its special streak image tube

We designed a special electrostatic focusing streak image tube (SIT) with large magnification, tiny temporal distortion and large dynamic range for the application of the technique of sampling-image streaking frame (SISF) for plasma diagnostics in ICF. A proof-of-principle experiment of the technique is performed with the SIT, together with a picosecond laser and image reconstruction software. Using the digital image-processing program, the result gives 16 frames with an exposure time of better than 6.3 ps.

Heterodyne electrostatic imaging of polarization due to a surface acoustic wave

We describe a technique that enables us to obtain a stroboscopic image of surface polarization associated with a surface acoustic wave. The surface polarization has been imaged as it travels across the exposed substrate of a surface acoustic wave filter operating at 434 MHz. The high-frequency polarization signals were recovered using a heterodyne electrostatic force scanning probe microscopy technique.