Electrostatic potential of point charges inside dielectric prolate spheroids

The exact solution to an electrostatic problem of finding the electric potential of point charges inside a dielectric prolate spheroid is discussed in this note by using the classical electrostatic theory, where the prolate spheroid is embedded in a dissimilar dielectric medium. Such a problem may find its application in hybrid solvent biomolecular simulations, in which biomolecules and a part of solvent molecules within a dielectric cavity are explicitly modeled while a surrounding dielectric continuum is used to model bulk effects of the solvent beyond the cavity. Numerical experiments have demonstrated the convergence of the proposed series solutions.     

Extending the fast multipole method for charges inside a dielectric sphere in an ionic solvent: High-order image approximations for reaction fields

As a sequel to our previous paper on extending the Fast Multipole Method (FMM) for charges inside a dielectric sphere [J. Comput. Phys. 223 (2007) 846–864], this paper further extends the FMM to the electrostatic calculation for charges inside a dielectric sphere immersed in an ionic solvent, a scenery with more relevance in biological applications. The key findings include two fourth-order multiple discrete image approximations in terms of u = λa to the reaction field induced by the ionic solvent, provided that u = λa < 1 where λ is the inverse Debye screening length of the ionic solvent and a is the radius of the dielectric sphere. A 10⁻⁴ relative accuracy in the reaction field of a source charge within the sphere can be achieved with only 3–4 point image charges. Together with the image charges, the FMM can be used to speed up the calculation of electrostatic interactions of charges in a dielectric sphere immersed in an ionic solvent.     

Extending the Fast Multipole Method for Charges inside a Dielectric Sphere in an Ionic Solvent: High Order Image Approximations for Reaction Fields

As a sequel to our previous paper on extending the Fast Multipole Method (FMM) for charges inside a dielectric sphere [J. Comput. Phys. 223 (2007) 846–864], this paper further extends the FMM to the electrostatic calculation for charges inside a dielectric sphere immersed in an ionic solvent, a scenery with more relevance in biological applications. The key findings include two fourth-order multiple discrete image approximations in terms of u = λa to the reaction field induced by the ionic solvent, provided that u = λa < 1 where λ is the inverse Debye screening length of the ionic solvent and a is the radius of the dielectric sphere. A 10⁻⁴ relative accuracy in the reaction field of a source charge within the sphere can be achieved with only 3–4 point image charges. Together with the image charges, the FMM can be used to speed up the calculation of electrostatic interactions of charges in a dielectric sphere immersed in an ionic solvent.     

Conductance of ion channels and nanopores with charged walls: a toy model

We consider ion transport through protein ion channels in lipid membranes and water-filled nanopores in silicon films. It is known that, due to the large ratio of dielectric constants of water and the surrounding material, an ion placed inside the channel faces a large electrostatic self-energy barrier. The barrier leads to an exponentially large resistance of the channel. We study reduction of the electrostatic barrier by immobile charges located on the internal walls of the channel. We show that the barrier practically vanishes already at relatively small concentration of wall charges.     

极化电荷与自由电荷之间区别的演示实验

通过将导体放入静电场发生的静电感应现象和将绝缘体（电介质）放入静电场发生的极化现象,演示一组实验,生动地显示了电介质被极化出的正、负电荷,既不能离开电介质,也不能在电介质中自由移动,就是将带有极化电荷的电介质与导体接触,极化电荷也不会与导体上的自由电荷中和,即极化电荷牢固地束缚在介质上．说明极化电荷与自由电荷之间的本质区别,加深学生对这些概念的理解和运用．     

Electrostatic potential in cylindrical dielectric media using the image charge method

We derive a simple analytical expression for the electric potential produced by a point charge in a cylindrical pore with relative permittivity different from that of the surrounding medium. The interface between the pore and the surrounding media may contain electric charge or be electrically neutral. The expression reduces to the known solutions when the surrounding dielectric medium is identical to the pore or an electric conductor. We discuss the convergence of the series expansion and numerically evaluate the electrostatic potential inside the cylindrical pore. The calculated potential shows the effect of the dielectric permittivity difference of the media. The results demonstrate that the expression can be implemented in a numerical dynamic simulation of charged systems in cylindrical geometry. We also give an expression for the case when the source charge is in the medium outside the cylinder.     

Collective Electrostatic Interaction of Particles in a Complex Plasma with Ion Flow

Linearized electrostatic potential of a test charge in a complex (dusty) plasma with ion flow is found. Dust component is treated as a continuous medium. Positions of dust particles are assumed to be fixed (unperturbed by the test charge). Calculations are performed using the static dielectric response function found in the framework of the fluid model. The model includes ion loss and ion creation caused respectively by absorption on dust particles and ionization. Dust charge variations and friction force on ions (ion‐neutral and ion‐dust friction) are also present in the model. The main point of the paper is the potential distribution in the plane containing the test charge and oriented perpendicular to the ion flow. The possibility of the electrostatic attraction of two same sign charges in the plane perpendicular to the ion flow is investigated. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Giant enhancement of noncontact friction between closely spaced bodies by dielectric films and two-dimensional systems

The effect of an external bias voltage and spatial variations of the surface potential on the damping of cantilever vibrations in an atomic force microscope (AFM) is considered. The damping is due to an electrostatic friction that arises due to dissipation of the energy of an electromagnetic field generated in the sample by oscillating static charges induced on the surface of the AFM probe tip by the bias voltage or spatial variations of the surface potential. A similar effect appears when the tip is oscillating in an electrostatic field created by charged defects present in the dielectric sample. The electrostatic friction is compared to the van der Waals (vdW) friction between closely spaced bodies, which is caused by a fluctuating electromagnetic field related to the quantum and thermal fluctuations of current density inside the bodies. It is shown that the electrostatic friction and the vdW friction can be strongly enhanced in the presence of dielectric films or two-dimensional (2D) structures—such as a 2D electron system or an incommensurate layer of adsorbed ions exhibiting acoustic oscillations—on the probe tip and sample surfaces. It is also shown that the damping of cantilever oscillations caused by the electrostatic friction in the presence of such 2D structures can have the same order of magnitude and the same dependence on the distance as observed in experiment by Stipe et al. [Phys. Rev. Lett. 87, 096801 (2001)]. At small distances, the vdW friction can be large enough to be measured in experiment. In interpreting the experimental data that obey a quadratic dependence on the bias voltage, one can reject a phonon mechanism according to which the friction depends on the fourth power of the voltage.     

Charge interaction in layered systems with spatial dispersion

The potential electrostatic energy of a charge near the surface of a metal with a metal or a dielectric coating (adsorbate), on the interface between metal (semimetal) and insulator (electrolyte) and in layered thin-film sandwich-type systems (MIS structures) has been calculated. The influence of the metal and the dielectric epitaxial coatings of the metal surface upon the interaction of charges is investigated. Taking into account the spatial dispersion effects, it is shown that in thin films surrounded by a medium with a large dielectric constant, the Coulomb repulsion between electrons decreases.     

点电荷在拓扑绝缘体和导体中感应磁单极

利用电势和磁标势的第一类零阶贝塞尔函数的公式及拓扑绝缘体材料的本构关系, 推导了点电荷在电介质、 拓扑绝缘体和接地导体三个区域的感应电势及感应磁标势. 研究表明: 点电荷 在电介质、 拓扑绝缘体和接地导体中感应了像电荷和像磁单极; 感应像电荷和感应像磁单极的大小和正负除了与场源电荷、 拓扑绝缘体材料参数等因素有关外, 还与像电荷和像磁单极所处的空间位置有关.     

The electrostatic potential in a crystalline slab

The electrostatic potential in a crystalline slab of point charges is expressed as a sum of three types of terms, an intrinsic term, microscopic fringing terms and a macroscopic term.     

静电场强化介电流体冷凝换热实验研究

本文以电绝缘性低沸点介电流体R11为实验工质,利用自行设计和制作的电流体力学实验模型,对介电流体进 行静电场强化冷凝换热实验研究。实验结果表明:静电场对模型内介电流体的凝结换热有很好的强化作用,其换热系数主 要与外加电场强度、热通量及电极相对位置等因素有关,这种电场强化凝结换热技术对制冷和热传递工程具有参考价值。     

电偶极子位于均匀介质球中时球外电场的研究

采用分离变量法求解了电偶极子位于均匀介质球中时复连通域的拉普拉斯方程和泊松方程,求出了球内外两种不同介质的电势分布和球面上的极化电荷分布;通过求解二阶非线性微分方程得到了球外的电场线函数;利用计算软件Math-ematica 5.0,作出了相应的相互正交的等势线簇图形和电场线簇图形,并且进行了必要的讨论.     

用计算机模拟点电荷在二维平面上的静电场

二维平面上的点电荷的静电场是静电场问题的基础，作者独立开发了软件用以模拟，此程序由用户决定点电荷的所有参数，快速地生成视阈内的等势线与电场线，使用户方便的获得电场直观印象，并可以得到任意点的电势与场强，该程序操作简单，对于学生、教师的学与教都能起到很好的辅助作用。     

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.     

Classical and Quantum Algebraic Screening in a Coulomb Plasma near a Wall: A Solvable Model

The static position correlation in a quantum Coulomb plasma near a wall is studied by means of a model where two quantum charges are embedded in a classical plasma at equilibrium. Three kinds of walls are considered: a wall without electrostatic properties, a dielectric, and an ideal conductor. At large separations y along the wall, the correlation exactly decays as 1/y ³, though no algebraic tail exists for classical charges near an ideal conductor. This tail originates from thermal statistical and purely quantum fluctuations of polarization clouds which are deformed by the geometric constraint due to the wall and by the charges induced by influence inside a wall with electrical properties. The coefficient of the 1/y ³ tail can be calculated explicitly in a weak-coupling and low-delocalization regime. Then classical, diffraction, and purely quantum contributions are disentangled.     

Multiscale molecular dynamics using the matched interface and boundary method

The Poisson-Boltzmann (PB) equation is an established multiscale model for electrostatic analysis of biomolecules and other dielectric systems. PB based molecular dynamics (MD) approach has a potential to tackle large biological systems. Obstacles that hinder the current development of PB based MD methods are concerns in accuracy, stability, efficiency and reliability. The presence of complex solvent-solute interface, geometric singularities and charge singularities leads to challenges in the numerical solution of the PB equation and electrostatic force evaluation in PB based MD methods. Recently, the matched interface and boundary (MIB) method has been utilized to develop the first second order accurate PB solver that is numerically stable in dealing with discontinuous dielectric coefficients, complex geometric singularities and singular source charges. The present work develops the PB based MD approach using the MIB method. New formulation of electrostatic forces is derived to allow the use of sharp molecular surfaces. Accurate reaction field forces are obtained by directly differentiating the electrostatic potential. Dielectric boundary forces are evaluated at the solvent-solute interface using an accurate Cartesian-grid surface integration method. The electrostatic forces located at reentrant surfaces are appropriately assigned to related atoms. Extensive numerical tests are carried out to validate the accuracy and stability of the present electrostatic force calculation. The new PB based MD method is implemented in conjunction with the AMBER package. MIB based MD simulations of biomolecules are demonstrated via a few example systems.     

Density Profiles in a Classical Coulomb Fluid Near a Dielectric Wall. I. Mean-Field Scheme

The equilibrium density profiles in a classical multicomponent plasma near a hard wall made with a dielectric material characterized by a relative dielectric constant ∈_w are studied from the first Born–Green–Yvon (BGY) equation combined with Poisson equation in a regime where Coulomb coupling is weak inside the fluid. In order to prevent the collapse between charges with opposite signs or between each charge and its dielectric image inside the wall when ∈_w>1, hard-core repulsions are added to the Coulomb pair interaction. The charge-image interaction cannot be treated perturbatively and the density profiles vary very fast in the vicinity of the wall when ∈_w≠1. The formal solution of the associated inhomogeneous Debye–Hückel equations will be given in Paper II, together with a systematic fugacity expansion which allows to retrieve the results obtained from the truncated BGY hierarchy. In the present paper the exact density profiles are calculated analytically up to first order in the coupling parameter. The expressions show the interplay between three effects: the geometric repulsion from the impenetrable wall; the electrostatic effective attraction (∈_w>1) or repulsion (∈_w<1) due to its dielectric response; and the Coulomb interaction between each charge and the potential drop created by the electric layer which appears as soon as the system is not symmetric. We exhibit how the charge density profile evolves between a structure with two oppositely-charged layers and a three-layer organization when ∈_w varies. (The case of two ideally conducting walls will be displayed elsewhere).     

Beyond the method of images—the interaction of charged particles with real surfaces

A knowledge of the potential energy of a point charge outside a planar surface is important for understanding many charge transfer processes and surface spectroscopies. Whilst the ‘theory of images’ of classical electrostatics can be used to derive this potential, the result is valid only for static charges far from the surface. In this paper we describe recent attempts to consider moving charges near real surfaces, with particular reference to surfaces with dielectric overlayers, and we review experimental studies of the effects of the image force.