Surface charge estimation on hemispherical dielectric samples from EFM force gradient measurements

A numerical model capable of estimating the surface charge density(σ_S) and the dielectric constant(k_e) of a hemispherical sample from force gradient measurements is proposed. Force gradients are commonly detected by a biased conductive tip during electrostatic force microscopy(EFM) probing but provide limited quantitative assessment of the charge in the sample. The proposed model gives an analytical solution for the force exerted over a biased conical tip. Theoretical numerical results, presented in the form of multitraces of minimum force gradients for fixed bias voltages and tip-sample distances allow the translation of EFM force gradient measurements into functions of σ_S and k_e.     

Electrostatic transport of regolith particles for sample return mission from asteroids

To achieve reliable and autonomous regolith sampling from asteroids in space, the authors have developed a new sampling system that utilizes electrostatic force. This system consists of electrostatic capture and transport subsystems. Regolith particles on an asteroid are captured through parallel screen electrodes activated by the application of an alternating high voltage. The captured particles are then transported to a collection capsule from side to side basically along the electric flux lines in a zigzag path where an alternating electrostatic field is applied. It has been demonstrated that glass and sand particles can be transported in the horizontal direction that imitates micro-gravity on asteroids. The transport rate was increased by applying a high voltage of appropriate frequency. The demonstrated transport rate was approximately 3 g/min. The configuration of the path was improved to increase the transport performance. Numerical calculation using the discrete element method predicted that the transport of particles is successful if the gravity is less than 0.02-G. The process of sampling particles on asteroids will be easier than that on the Earth, because gravity is extremely low on small asteroids, particles are assumed to be highly charged because of cosmic rays, no air drag is exerted on the particles, and high voltage can be applied in vacuum where no gas discharge occurs.     

Magnetic force microscopy signal of flux line above a semi-infinite type II-superconductor

We have examined a single flux line in the semi-infinite type-II superconductor. The stray magnetic field of the flux line has been calculated. We have found that the vertical force exerted on a magnetic force microscopy (MFM) tip from the flux line is measurable by currently existing MFM. Two types of magnetic tips were taken into consideration, solid and thin film tips. For example, with a Cobalt film of the thickness of 100 nm and 30 nm on a tip, we found a vertical force of 4*10^–10 N and 1.5*10^–10 N, respectively. The lateral force exerted on a tip by the flux line was also calculated. The lateral force must be small enough to prevent the flux line from becoming depinned.     

A pseudopotential based theory of the driving forces for electromigration in metals

We present a pseudopotential calculation of the driving forces for atomic migration in metals in the presence of electron currents. When electrons are scattered by impurities in a metal, we find that a force is generally exerted on each atom in the vicinity of the scattering center. Because the scattering is predominantly elastic, it is possible to express this force field as the classical electrostatic force arising from the total electronic charge, as has been assumed by Friedel and Bosvieux. The electron charge density is determined from a pseudopotential calculation, and the resulting force is expressed as a sum of effective interactions between the diffusing atom and all crystal defects.The forces on an atom arising from the electron scattering and from the applied electric field together comprise the driving force which causes a net current of atoms. The driving forces are calculated for intestitial and vacancy migration in several metals, and the results are found to compare favorably with most experimental data.     

An overlooked electrostatic force that acts on a non-charged asymmetric conductor in a symmetric (parallel) electric field

Usually, when a material that has charge Q is placed in an electric field E, an electrostatic force F = QE acts on the material. This force does not act on a non-charged material. Nevertheless, when a non-charged material is placed in a convergent field, another electrostatic force acts. This force is called the gradient force. If the material is small and the shape is a sphere, the gradient force can be calculated by an approximate formula, but it cannot be calculated for other shapes. In this paper the gradient force that acts on a symmetric rod conductor in a convergent (asymmetric) field was simulated by an axis symmetry finite difference method.Under same simulation conditions without the next two points, the shape of the conductor and the form of the field were reversed. The shape of the conductor was changed into an asymmetric shape (e.g. bat shape), and the form of the field was changed into a symmetric (parallel) one. The electrostatic force that acts on the asymmetric conductor in the symmetric (parallel) field was simulated. It was found that approximately the same intensity force as in the first simulation also acts on this conductor. This force is thought to be an overlooked electrostatic force. I provisionally call it the asymmetric force in this paper.The asymmetric force with differently shaped conductors was simulated and it was found that the asymmetric force was maximized for a cup shaped conductor.Finally, the asymmetric force with the cup shaped conductor in normal and reversed parallel (symmetric) fields was simulated, and it was confirmed that the asymmetric force remains the same in both fields.     

Orientational effect of the dynamical interaction of circular dislocation loops with a moving edge dislocation

The glide of an edge dislocation in a crystal containing circular dislocation loops is studied theoretically. An analytical expression is obtained for the drag force exerted on a dislocation by various types of dislocation loops, and it is shown that this force depends significantly on the orientation of the Burgers vector of immobile dislocation loops with respect to the gliding dislocation line. The F _‖/F _⊥ ratio of the drag force for the parallel orientation of the Burgers vectors of the loops with respect to the gliding dislocation line (F _‖) and the drag force for the perpendicular orientation (F _⊥) is equal to K(v/c)², where v is the velocity of the dislocation; c is the velocity of acoustic waves in the crystal; and K is a dimensionless coefficient, whose value is of the order of the ratio of the concentrations of dislocation loops with parallel and perpendicular orientations of the Burgers vector.     

Electrostatic force of dust deposition originating from contact between particles and photovoltaic glass

Charged photovoltaic glass produces an electrostatic field. The electrostatic field exerts an electrostatic force on dust particles, thus making more dust particles deposited on the glass. In this paper, the contact electrification between the deposited dust particles and the photovoltaic glass is studied. Meanwhile, the surface charge density model of the photovoltaic glass and the electrostatic force of charged particles are analyzed. The results show that with the increasing of the particle impact speed and the inclination angle of the photovoltaic panel, the charges on particles increase to different degrees.Under a given condition, the electrostatic forces acting on the charged particles at different positions above the glass plate form a bell-shaped distribution at a macro level, and present a maximum value in the center of the plate. As the distance between the particle and the charged glass decreases, the electrostatic force exerted on the particle increases significantly and fluctuates greatly. However, its mean value is still higher than the force caused by gravity and the adhesion force,reported by some studies. Therefore, we suggest that photovoltaic glass panels used in the severe wind-sand environment should be made of an anti-static transparent material, which can lessen the dust particles accumulated on the panels.     

Kinetic and theoretical studies of metal ion adsorption in KDP solution

Metal ion adsorption in saturated aqueous potassium dihydrogen phosphate solution was analyzed using kinetic, equilibrium model and computational chemistry approaches. The isotherm constants (K_F and n) in the Freundlich model and the first order Lagergren kinetic model parameter k assist with a general understanding of the fundamental adsorption behavior of trivalent and divalent metal ions. The electrostatic force based on electrostatic potential distribution was found to be an essential feature for metal ion adsorption via a correlation between the ESP values of each metal ion and these experimental parameters.     

Relaxation at clean metal surfaces

An electrostatic model of the energy of the surface layers of a metal is shown to describe in detail complex phenomena of surface relaxation in clean metals. The model accounts for relaxation effects that go many layers deep, that have both parallel and perpendicular components and that show large variations from surface to surface of the same metal. The model adds a new physically plausible assumption to the simple electrostatic model previously proposed by Finnis and Heine, which increases the force binding each ion to its bulk position by an amount fixed empirically for each metal. The equilibrium configuration of surface layers is found by minimizing the energy with respect to rigid translations of ion nets in a fixed electronic background density. The many surface structure parameters thus determined fit low-energy electron diffraction data on six surfaces of bcc Fe and six of fcc Al well in almost all cases.     

Sensing dipole fields at atomic steps with combined scanning tunneling and force microscopy

The electric field of dipoles localized at the atomic steps of metal surfaces due to the Smoluchowski effect were measured from the electrostatic force exerted on the biased tip of a scanning tunneling microscope. By varying the tip-sample bias the contribution of the step dipole was separated from changes in the force due to van der Waals and polarization forces. Combined with electrostatic calculations, the method was used to determine the local dipole moment in steps of different heights on Au(111) and on the twofold surface of an Al-Ni-Co decagonal quasicrystal.     

Electrostatic proximity force,toner adhesion,and a new electrophotographic development system

It has recently been shown that the electrostatic adhesion of a discrete distribution of charge points that are uniformly distributed around a sphere in contact with a conductive plane is larger than the conventional result, (1/4πε₀)(Q²/4r²), by (1+4/π), where Q is the total charge and r is the radius of the spherical particle. This new electrostatic force, the 4/π term, is due to discrete nature of charge and is called the electrostatic proximity force. This electrostatic proximity force is active at every contact point between a real, charged insulating particle and a conductive plane. By minimizing the number of contact points, the adhesion of electrophotographic toner particles to a conductive surface has been reduced by at least a factor of 10 compared to commercially available toners, allowing the viability of a new electrophotographic development system: a dc-jump, non-magnetic, monocomponent development system.     

Forces and charges on a slightly deformed droplet in the DC field of a plate condenser

A conducting drop in partial wetting on the lower electrode of a plate condenser and surrounded by a dielectric fluid is considered. When a DC field is applied the drop, acquiring electric charges, is subjected to an electrostatic force normal to the electrode. The force exerted on undeformable drops was previously calculated. In this paper, the distortion from a spherical shape is asymptotically calculated at low electric Bond numbers to generalize previous developments. A mechanism is proposed to explain the drop detachment, leading to an electrical field strength threshold. Some experiments were performed confirming the mechanism.     

Multifrequency radiation force of acoustic waves in fluids

In this article we introduce the concept of multifrequency radiation force produced by a polychromatic acoustic beam propagating in a fluid. This force is a generalization of dynamic radiation force due to a bichromatic wave. We analyse the force exerted on a rigid sphere by a plane wave with N frequency components. Our approach is based on solving the related scattering problem, taking into account the nonlinearity of the fluid. The radiation force is calculated by integrating the excess of pressure in the quasilinear approximation over the surface of the sphere. Results reveal that the spectrum of the multifrequency radiation force is composed of up to N(N−1)/2 distinct frequency components. In addition, the radiation force generated by plane progressive waves is predominantly caused by parametric amplification. This is a phenomenon due to the nonlinear nature of wave propagation in fluids.     

An improved proximity force approximation for electrostatics

A quite straightforward approximation for the electrostatic interaction between two perfectly conducting surfaces suggests itself when the distance between them is much smaller than the characteristic lengths associated with their shapes. Indeed, in the so called “proximity force approximation” the electrostatic force is evaluated by first dividing each surface into a set of small flat patches, and then adding up the forces due two opposite pairs, the contributions of which are approximated as due to pairs of parallel planes. This approximation has been widely and successfully applied in different contexts, ranging from nuclear physics to Casimir effect calculations. We present here an improvement on this approximation, based on a derivative expansion for the electrostatic energy contained between the surfaces. The results obtained could be useful for discussing the geometric dependence of the electrostatic force, and also as a convenient benchmark for numerical analyses of the tip–sample electrostatic interaction in atomic force microscopes.     

The effect of electrostatic force on the evolution of sand saltation cloud

In a wind-blown sand layer, it has been found that wind transport of particles is always associated with separation of electric charge. This electrification in turn produces some electrostatic forces in addition to the gravitational and fluid friction forces that affect the movement of saltating sand particles, further, the wind-blown sand saltation. To evaluate this effect quantitatively, this paper presents a simulation of evolution of wind-blown sand grains after the electrostatic forces exerted on the grains are taken into account in the wind feedback mechanism of wind-blown saltation. That is, the coupling interaction between the wind flow and the saltating sand particles is employed in the simulation to the non-stationary wind and sand flows when considering fluid drag, gravitation, and a kind of electrostatic force generated from a distribution of electric field changing with time in the evolution process of the sand saltation. On the basis of the proposed simulation model, a numerical program is given to perform the simulation of this dynamic process and some characteristic quantities, e.g., duration of the system to reach the steady state, and curves of the saltating grain number, grain transport rate, mass-flux profile, and wind profile varying with time during the non-stationary evolution are displayed. The obtained numerical results exhibit that the electrostatic force is closely related to the average charge-to-mass ratio of sand particles and has obvious influence on these characteristic quantities. The obtained results also show that the duration of the system to reach the steady state, the sand transport rate and the mass flux profile coincide well with experimental results by Shao and Raupach (1992) when the average charge-to-mass ratio of sand particles is 60 μC/kg for the sand particles with average diameter of 0.25 mm. When the average charge-to-mass ratios of sand particles are taken as some other certain values, the calculation results still show that the mass flux profiles are well in agreement with the experimental data by Rasmussen and Mikkelsen (1998) for another category of sand particles, which tell us that the electrostatic force is one of main factors that have to be considered in the research of mechanism of wind-blown sand saltation.     

A MEMS micromirror driven by electrostatic force

A microelectromechanical systems (MEMS) micromirror is demonstrated in this paper. The micromirror is actuated by an electrostatic force and can achieve a large out of plane stroke by eliminating the electrostatic pull-in effect. The micromirror consists of a mirror of 400 μm by 400 μm in the center, a spring and three fixed bottom electrodes each side. Design principles and the analytical model are both developed, and they are verified by finite element analysis (FEA). The resonant frequency for the piston movement of the designed micromirror is about 2.5 kHz by FEA simulation. The micromirror prototype has been fabricated by a surface micromachining process and it is successfully tested using a microsystem analyzer. An out of plane stroke of 1.65 μm is observed at 100 V and it agrees well with the predicted result from analytical model.     

Electrostatic force acting on conductive ball between electrodes

To advance electrostatic applications such as novel printing technologies and solder ball control for LSI bumping, the electrostatic force acting on a conductive ball between two electrodes is calculated. The electrostatic force increases as the ratio of the ball diameter to the electrode separation increases. The electrostatic force is also calculated for the case when a charge pattern is formed on the insulating layer on the upper electrode. In this case, the electrostatic force initially varies as the square of the charge pattern area but eventually plateaus to a constant value as the area increases. Experiments investigating the force acting on the ball are performed. The force estimated from these experiments agrees with the value obtained by electric field analysis.     

Self-consistent calculation of electrostatic force for two kinds of mesoscopic surface structures

The scanning electrostatic force microscopy (SEFM) can acquire information of surface structures in a non-contact way. We calculate the electrostatic force between the charged tip and polarized surface structure in SEFM in the framework of self-consistent integral equation formalism (SCIEF), incorporating the image method to treat the electrostatic coupling of substrate and tip. We consider two kinds of surface structures, one is the topographic structure on the surface, the other is the dielectric structure embedded in the substrate. The force pattern of the topographic structure shows a protrusion around the surface structure. However, the force pattern displays a hollow around an embedded structure with a dielectric constant less than that of substrate medium. For an embedded structure with a larger dielectric constant, the force pattern exhibits a protrusion, and the force signal is much weaker than that of the topographic structure. Therefore, it is expected that one may identify these surface structures from the pure electrostatic force information in SEFM. The force signal of the densely arranged dielectric pads is simply the superposition of force signal of each pad individually, the interference effect of electric field is not remarkable. Received: 26 March 1998 / Accepted: 9 June 1998     

Limiting phenomena for the spreading of water on polymer films by electrowetting

This paper is about fundamental limitations in electrowetting, used as a tool for spreading water solutions on hydrophobic surfaces, like the surface of a polymer film. Up to which point can an electric voltage decrease the contact angle? The first limitation comes when using pure water, above a threshold voltage, little droplets are emitted at the perimeter of the mother drop. We present an analysis of the drop contour line stability, involving competition between electrostatic and capillary forces, which is compatible with observations. The use of salted water solutions suppresses this instability, then one faces a second limitation: the evolution of the contact angle saturates before complete wetting. We show that this saturation is caused by ionisation of the air in the vicinity of the drop edge. We analyse the luminescence induced by gas ionization and measure the related electrical discharges. We explain how air ionization suppresses the driving force for electrowetting and how it induces the formation of an hydrophillic ring around the drop.     

Electrostatic interaction between two conducting spheres

In the paper we consider the problem of the electrostatic interaction between two charged conducting spheres with arbitrary electrical charges and radiuses. Using the image charges method we determine exact analytical formulas for the force F and for the potential energy W of the interaction between these two spheres as well as for the potential V of the electromagnetic field in an arbitrary point created by them. Our formulas lead to Coulomb’s law for point charges.We theoretically prove the experimentally shown fact that two spheres with the same type (positive or negative) of charges can also attract each other.