Analytical modeling of static behavior of electrostatically actuatednano/micromirrors considering van der Waals forces

In this paper, the effect of van der Waals （vdW） force on the pull-in behavior of electrostatically actuated nano/micromirrors is investigated. First, the minimum po- tential energy principle is utilized to find the equation gov- erning the static behavior of nano/micromirror under electro- static and vdW forces. Then, the stability of static equilib- rium points is analyzed using the energy method. It is found that when there exist two equilibrium points, the smaller one is stable and the larger one is unstable. The effects of dif- ferent design parameters on the mirror＇s pull-in angle and pull-in voltage are studied and it is found that vdW force can considerably reduce the stability limit of the mirror. At the end, the nonlinear equilibrium equation is solved numer- ically and analytically using homotopy perturbation method （HPM）. It is observed that a sixth order perturbation approx- imation can precisely model the mirror＇s behavior. The re- suits of this paper can be used for stable operation design and safe fabrication of torsional nano/micro actuators.

STATIC STUDY OF CANTILEVER BEAM STICTION UNDER ELECTROSTATIC FORCE INFLUENCE

The model and analysis of the cantilever beam adhesion problem under the action of electrostatic force are given. Owing to the nonlinearity of electrostatic force, the analytical solution for this kind of problem is not available. In this paper, a systematic method of generating polynomials which are the exact beam solutions of the loads with di?erent distributions is provided. The polynomials are used to approximate the beam displacement due to electrostatic force. The equilibrium equation o?ers an answer to how the beam deforms but no information about the unstuck length. The derivative of the functional with respect to the unstuck length o?ers such information. But to compute the functional it is necessary to know the beam deformation. So the problem is iteratively solved until the results are converged. Galerkin and Newton-Raphson methods are used to solve this nonlinear problem. The e?ects of dielectric layer thickness and electrostatic voltage on the cantilever beam stiction are studied. The method provided in this paper exhibits good convergence. For the adhesion problem of cantilever beam without electrostatic voltage, the analytical solution is available and is also exactly matched by the computational results given by the method presented in this paper.

Axial control for nonlinear resonances of electrostatically actuated nanobeam with graphene sensor

The nonlinear resonance response of an electrostatically actuated nanobeam is studied over the near-half natural frequency with an axial capacitor controller. A graphene sensor deformed by the vibrations of the nanobeam is used to produce the voltage signal. The voltage of the vibration graphene sensor is used as a control signal input to a closed- loop circuit to mitigate the nonlinear vibration of the nanobeam. An axial control force produced by the axial capacitor controller can transform the frequency-amplitude curves from nonlinear to linear. The necessary and sufficient conditions for guaranteeing the system stability and a saddle-node bifurcation are studied. The numerical simulations are conducted for uniform nanobeams. The nonlinear terms of the vibration system can be transformed into linear ones by applying the critical control voltage to the system. The nonlinear vibration phenomena can be avoided, and the vibration amplitude is mitigated evidently with the axial capacitor controller.

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.

Electrostatic force on the rectangular shield wall of a strip transmission line

For a strip transmission line shielded by rectangular walls, the Green抯 function is helpful to construct the variation expression of the electrostatic energy. Thomson theorem is employed to determine the charge distribution on the strip. The electrostatic force on each side of the rectangular shield wall is achieved by using the principle of virtual work. The result is easy to be obtained by computerized calculation.

A New Electrostatic Generator Driven by Only an Electric Field of an Electret

Today, the sun is a very useful source of energy because it continuously radiates energy. An electron is radiating energy continuously, too. A new electrostatic generating method using this electric field energy from electrons as a driving force of charge carriers was invented, and its success was presented on ESA 2017 and ESA 2019. This new electrostatic generator was realized by asymmetric electrostatic force, which is a new phenomenon. Unfortunately, its experimental success rate was rare. Therefore, the cause was searched by many experiments. Finally, it became apparent that the acceleration force of the charge carrier was not stronger than the deceleration force of the charge carrier with this experimental equipment. Therefore, the electrode arrangement of this equipment was improved. As a result, the acceleration force was increased, and the deceleration force was decreased. Then, the experimental success rate became 100%.

Effect of photovoltaic panel electric field on the wind speed required for dust removal from the panels

Methods to remove dust deposits by high-speed airflow have significant potential applications,with optimal design of flow velocity being the core technology.In this paper,we discuss the wind speed required for particle removal from photovoltaic(PV)panels by compressed air by analyzing the force exerted on the dust deposited on inclined photovoltaic panels,which also included different electrification mechanisms of dust while it is in contact with the PV panel.The results show that the effect of the particle charging mechanism in the electric field generated by the PV panel is greatly smaller than the effect of the Van der Waals force and gravity,but the effect of the particle charged by the contact electrification mechanism in the electrostatic field is very pronounced.The wind speed required for dust removal from the PV panel increases linearly with the PV panel electric field,so we suggest that the nighttime,when the PV electric field is relatively small,would be more appropriate time for dust removal.The above results are of great scientific importance for accurately grasping the dust distribution law and for achieving scientific removal of dust on PV panels.

The Whole Theory of This Universe—A Step Forward to Einstein, Part-3rd: “The Universal Theory of Visible and Invisible Universe”

We believe that the universe is of two types: visible and invisible. Nothing is at rest between the invisible and visible universes. All microscopic bodies as well as all macroscopic bodies are in motion along curved paths (i.e. in circles). The universe inside an atom is as vast as the visible universe. An atom consists of millions of particles or particle galaxies which contain central energy pools or central energy cores. Energy pools present in the centre of the invisible universe inside atomic or subatomic particles from which particles and energy are continuously interconverting. In a dense central energy pool, two opposite charges are created due to the swirling motion of microscopic energy droplets. Small microscopic energy droplets may swirl either clockwise or anti-clockwise to produce microscopic tornadoes which are non-superimposable mirror images of each other and gain the property of positive and negative charges. Hence, the electrostatic force is originated between these two opposite charges, which are then changed into a pair of particles, i.e. catitron, which carries a positive charge, and anitron which carries a negative charge. All the other millions of subatomic particles or particle galaxies are produced in the same way. So, the electrostatic force is the basic force, and all other forces originate from this basic electrostatic force of attraction. When charged particles move, they produce an oscillating electric field, and the spinning of these particles produces oscillating magnetic fields. These oscillating electric and magnetic fields are perpendicular to each other and, by their interaction, an oscillating gravitational field is produced which is also perpendicular to both the oscillating electric field and the oscillating magnetic field. The Earth’s axial tilt, which causes the Earth’s precessional motion, is caused by the parallel alignment of the Earth’s magnetic field with the magnetic field of the Sun. Gravity is not a cause of space-time curvature, but gravity causes space-time curvature. Space-time curvature is nothing but a curved path around a heavy object. The Universal Theory of Visible and Invisible Universe—The Whole Theory of This Universe—A Step Forward to Einstein, opens new windows in the challenging fields of science and research, i.e. visible and invisible universe, universe inside an atom, what is the stuff of the entire universe? What will happen at the end of this whole universe?

Dynamics simulation of tertiary amines adsorbing on kaolinite(001) plane

The collecting power of tertiary amines（DRN,DEN and DPN） on kaolinite follows the order of DENDPNDRN.After reacting with DRN,DEN and DPN,the surface potentials of kaolinite increase remarkably,and the recruitments caused by collectors also follow the order of DENDPNDRN.The results of dynamics simulation show that the geometries of substituent groups bonding to N are deflected and twisted,and some of bond angles are changed when tertiary amines cations adsorb on kaolinite（001） surface.Based on the results of dynamics simulations and quantum chemistry calculations,the electrostatic forces between three tertiary amines cations and 4×4×3（001） plane of kaolinite are 1.38×10？7 N（DRN12H＋）,1.44×10-6 N（DEN12H＋）,1.383×10-6 N（DPN12H＋）,respectively.

RF MEMS Switch on Poly-Silicon Substrate

The improvements of the design and the compatibility with silicon IC of RF MEMS switch are presented.The compatibility with silicon IC is realized by dielectric isolation technology,and the decrease of the pull voltage of the switch is done by etching some holes on the metal membrane.The preliminary test results are as follows: C off and C on are 0 32pF,6pF,respectively;the pull down voltage is about 25V.The package of the RF MEMS switch is done by micro stripline,and the isolation and the insertion loss are 35dB,2dB,respectively at 1 5GHz;the switching speed is about 3μs by oscilloscope.

Effect of Charge, Size and Temperature on Stability of Charged Colloidal Nano Particles

Molecular simulation of charged colloidal suspension is performed in NVT canonical ensemble using Monte Carlo method and primitive model. The well-known Derjaguin-Landau-Verwey- Overbeek theory is applied to account for effective interactions between particles. Effect of temperature, valance of micro-ions and the size of colloidal particles on the phase stability of the solution is investigated. The results indicate that the suspension is more stable at higher temperatures. On the other hand, for a more stable suspension to exist, lower micro- ion valance is favorable. For micro-ions of higher charge the number of aggregates and the number of particle in each of aggregate on average is higher. However for the best of our results larger colloidal particle are less stable. Comparing the results with theoretical formula considering the influence of surface curvature shows qualitative consistency.

A kinematic model describing particle movement near a surface as effected by Brownian motion and electrostatic and Van der Waals forces

Nanoparticle movement near a surface is greatly influenced by electrostatic and Van der Waals forces between the particle and the surface,as well as by Brownian motion.In this paper,several precise equations are derived to describe the Van der Waals and electrostatic forces between a particle and a surface when the particle is removed from the surface.These include an equation for particle displacement under the electrostatic force,and a numerical calculation for particle displacement under the Van der Waals force.Finally,a kinematic model is constructed to describe the particle distribution under the effects of the electrostatic and Van der Waals forces,as well as the particle’s Brownian motion.The results show that increasing the multiply of the particle and surface zeta potential values and decreasing the ionic strength of the detergent can prevent a particle from redepositing onto a surface.

Deactivating Metal Particle by Optimizing Insulation Configuration in Spark Gap Switch

As a new method to protect the spark gap from metal particle contamination, the effect of the metal inserted insulator on the controlling behavior of metal particles was investigated in a quasi-uniform electric field. Considering that the inserted metal electrodes can decrease the electric field around the insulator and divert the electrostatic force away from the insulator, the method can be used to prevent the particles from moving toward the insulator so as to reduce the possibility of a breakdown. The inserted metal electrodes can reverse the direction of the particles＇ horizontal motion. A study on the insulator shape indicates that the inserted metal electrodes can repulse the particle and improve the particle lifting voltage significantly near the vertical surface of the insulator or ribbed insulator. For the insulator with a tilting surface the inserted metal electrodes have little influence on the particle motion. In addition, the size of the inserted electrodes shows a significant effect on the control of particle motion.

A Fully Differential Interface Circuit of Closed-loop Accelerometer with Force Feedback Linearization

In this paper,a fifth-order fully differential interface circuit( IC) is presented to improve the noise performance for micromechanical sigma-delta( Σ-Δ) accelerometer. A lead compensator is adopted to ensure the stability of the closed-loop high-order system. A low noise capacitance detection circuit is described with a correlated-double-sampling( CDS) technique to decrease 1 /f noise and offset of the operational amplifier. This paper also proposes a self-test technique for the interface circuit to test the harmonic distortion. An electrostatic force feedback linearization circuit is presented to reduce the harmonic distortion resulting in larger dynamic range( DR). The layout of the IC is implemented in a standard 0. 6 μm CMOS technology and operates at a sampling frequency of 250 kHz. The interface consumes 20 mW from a 5 V supply. The post-simulation results indicate that the noise floor of the digital accelerometer is about- 140 dBV /Hz1 /2at low frequency. The sensitivity is 2. 5 V /g and the nonlinearity is 0. 11%. The self-test function is achieved with 98. 2 dB thirdorder harmonic distortion detection based on the electrostatic force feedback linearization.

One Method to Derivate Coulomb’s Law between Two Charges

In electromagnetics, Coulomb’s law is a very classic formula. Almost all textbooks give this formula, but none of them give a detailed corresponding theoretical derivation. In order for beginners of physics to better understand the physical meaning of this formula, we explored the source, the physical model and mechanism of this formula. Based on the principle that the interaction between two different fields can generate energy density, which is equal to the pressure, we analyzed the distribution of the electric field energy density as well as the corresponding pressure on the charged surface. Through the rigorous mathematical derivation, we give the theoretical derivation of this formula.

Dynamic analysis of Bernoulli-Euler piezoelectric nanobeam with electrostatic force

The effect of electrostatic force on the dynamic response of a Bernoulli-Euler piezoelectric nanobeam is analyzed in this paper.The governing equations with the electrostatic stress are derived based on a variational principle.Static bending problem of simply supported and cantilever beam is considered.The influence of the electrostatic force on the first four natural frequencies is discussed.It is shown that when the beam thickness is small,the effect of the electrostatic force is significant.When the beam thickness is large,the electrostatic force is insignificant and can be neglected.The results also indicate that one can adjust the natural frequency of a nanobeam by applying appropriate voltage.

A novel measuring method of clamping force for electrostatic chuck in semiconductor devices

Electrostatic chucks are one of the core components of semiconductor devices. As a key index of electrostatic chucks, the clamping force must be controlled within a reasonable range. Therefore, it is essential to accurately measure the clamping force. To reduce the negative factors influencing measurement precision and repeatability, this article presents a novel method to measure the clamping force and we elaborate both the principle and the key procedure. A micro-force probe component is introduced to monitor, adjust, and eliminate the gap between the wafer and the electrostatic chuck. The contact force between the ruby probe and the wafer is selected as an important parameter to characterize de-chucking, and we have found that the moment of de-chucking can be exactly judged. Moreover, this article derives the formula calibrating equivalent action area of backside gas pressure under real working conditions, which can effectively connect the backside gas pressure at the moment of de-chucking and the clamping force. The experiments were then performed on a self-designed measuring platform.The de-chucking mechanism is discussed in light of our analysis of the experimental data. Determination criteria for de-chucking point are summed up. It is found that the relationship between de-chucking pressure and applied voltage conforms well to quadratic equation. Meanwhile, the result reveals that actual de-chucking behavior is much more complicated than the description given in the classical empirical formula.

Recent Progress in Numerical Methods for the Poisson-Boltzmann Equation in Biophysical Applications

Efficiency and accuracy are two major concerns in numerical solutions of the Poisson-Boltzmann equation for applications in chemistry and biophysics.Recent developments in boundary element methods,interface methods,adaptive methods,finite element methods,and other approaches for the Poisson-Boltzmann equation as well as related mesh generation techniques are reviewed.We also discussed the challenging problems and possible future work,in particular,for the aim of biophysical applications.

Scalable gas-phase processes to create nanostructured particles

The properties of nanoparticles are often different from those of larger grains of the same solid material because of their very large specific surface area. This enables many novel applications, but properties such as agglomeration can also hinder their potential use. By creating nanostructured particles one can take optimum benefit from the desired properties while minimizing the adverse effects. We aim at developing high-precision routes for scalable production of nanostructured particles. Two gas-phase synthesis routes are explored. The first one - covering nanoparticles with a continuous layer - is carried out using atomic layer deposition in a fluidized bed. Through fluidization, the full surface area of the nanoparticles becomes available. With this process, particles can be coated with an ultra-thin film of constant and well-tunable thickness. For the second route - attaching nanoparticles to larger particles - a novel approach using electrostatic forces is demonstrated. The micron-sized particles are charged with one polarity using tribocharging. Using electrospraying, a spray of charged nanoparticles with opposite polarity is generated. Their charge prevents agglomeration, while it enhances efficient deposition at the surface of the host particle. While the proposed processes offer good potential for scale-up, further work is needed to realize large-scale processes.

Quasi-static motion of microparticles at the depinning contact line of an evaporating droplet on PDMS surface

In this paper, evaporation of sessile water droplets containing fluorescent polystyrene （PS） microparticles on polydimethylsiloxane （PDMS） surfaces with different curing ratios was studied experimentally using laser confocal microscopy. At the beginning, there were some microparticles located at the contact line and some microparticles moved towards the line. Due to contact angle hysteresis, at first both the contact line and the microparticles were pinned. With the depinning contact line, the microparticles moved together spontaneously. Using the software Image J, the location of contact lines at different time were acquired and the circle centers and radii of the contact lines were obtained via the least square method. Then the average distance of two neighbor contact lines at a certain time interval was obtained to characterize the motion of the contact line. Fitting the distance-time curve at the depinning contact line stage with polynomials and differentiating the polynomials with time, we obtained the velocity and acceleration of both the contact line and the microparticles located at the line. The velocity and the maximum acceleration were, respectively, of the orders of 1 p.m/s and 20-200 nm/s2, indicating that the motion of the microparticles located at the depinning contact line was quasi-static. Finally, we presented a theoretical model to describe the quasi-static process, which may help in understanding both self-pinning and depinning of microparticles.