Electrostatic Theory Research Articles

The comparative analysis of the two dimensional Laplace equation using the Galerkin finite element method with the exact solution for various domains (circular and rectangular) with triangular elemental meshing

Laplace Equation is used in many areas of studies such as potential theory and the fundamental forces of nature, Newtonian theory of gravity and electrostatics. It is used in Probability theory and Markov Chains as well as potential flows in fluid mechanics. Laplace Equation is used in various research areas and for this reason, to determine an accurate solution to this equation is of importance. In this study, the Finite Element Method is used to approximate the solution of the 2D Laplace Equation for two regions, circular and rectangular domains. These are compared to the exact solutions of the systems subjected to various physical restrictions; boundary conditions. This was done by using a mesh generator in Matlab, Distmesh, to obtain a mesh of triangular elements and then using Matlab to plot the exact and the approximated solutions as well as to determine the errors; norm. For these domains, the number of elements in the mesh was incremented and it was noted there was a convergence of the approximated to the actual solution. The boundary conditions were altered to observe the changes in the regions' field variable distribution (intensity values) of the Matlab plots.

A Deployment Algorithm for Mobile Wireless Sensor Networks based on the Electrostatic Field Theory

Abstract This paper proposes a deployment algorithm based on the electrostatic field theory for mobile wireless sensor networks. The nodes and obstacles in the deployment area are taken as the charged particles; and the particles will move due to the Coulomb’s force from other particles or obstacles. Finally, the nodes automatically spread to the whole area by the resultant action and complete the deployment. Four metrics, including coverage, uniformity, deployment time and average displacement distance, are used to evaluate the performance of the algorithm. The simulation results show that the proposed algorithm can give full play to its self-adaptive advantages and achieve the desired deployment effect; it is a kind of deployment algorithm with self-adaptive characteristics.

Charge distribution of Li-doped few-layer MoS2 and comparison to graphene and BN

According to first-principles calculation, we study the charge distribution of Li-doped few-layer (1-3 layers) MoS2 and compare it with the results of graphene and BN. It is found that the stable adsorption sites of Li are the top (Mo) site for MoS2 layer, and the hexagonal center for graphene and BN layers. Band structures of pristine MoS2 show that single-layer MoS2 is a direct band gap semiconductor while few-layer MoS2 is an indirect one. As MoS2 is doped, the Fermi level will shift to the conduction band, indicating a charge transfer between Li and MoS2. The charge transfer takes place mostly between Li and the topmost MoS2 layer, which is very similar to that happening between graphene and BN. However, the second and third layer of MoS2, which are far from Li, can acquire about 10% of transferred charges. In contrast, the second and third layer obtain no more than 2% of charges for graphene and BN. Based on the electrostatic theory, we derive for both double and triple layers the formulas of electrostatic energy, which show clearly that only charge transfer between Li and the topmost layer will give the lowest electrostatic energy. Moreover, we calculate the work functions of pristine MoS2, graphene and BN, and find that, despite similar work functions of MoS2 and BN, the larger band gap of BN will make charge transfer between Li and BN harder. The analyses of electrostatic energy and work function show that the charge distribution is dominated by both interlayer electrostatic interaction and work function of material. It is expected that the above results could be helpful for doping layered structures and designing devices.

Salt-specific effects observed in calorimetric studies of alkali and tetraalkylammonium salt solutions of poly(thiophen-3-ylacetic acid).

The enthalpies of dilution ΔHdil of aqueous solutions of a conjugated polyelectrolyte, poly(thiophen-3-ylacetic acid), neutralized by lithium, sodium, cesium, tetramethyl-, tetraethyl-, tetrapropyl-, and tetrabutylammonium hydroxides, were determined in the concentration range from cp = 2 × 10(-3) to 1 × 10(-1) monomol dm(-3) and for T = 278.15, 298.15, and 318.15 K. At low concentrations the dilution of the alkali PTAA salts yields an endothermic effect, which is in part a consequence of the hydrolysis. An exception is PTALi at 278.15 K, where ΔHdil < 0. In the case of tetraalkylammonium salts the enthalpies of dilution increase in the order TBA < TPA < TEA < TMA. Only the TBA salt of PTAA yields an exothermic effect upon dilution in the whole temperature range. In the second part of the study we measured the enthalpies of mixing, ΔHmix, of various salts of poly(thiophen-3-ylacetic acid) with LiCl, NaCl, KCl, and CsCl solutions in water. When lithium salt of PTAA is mixed with LiCl ΔHmix is positive. For mixing experiments with other alkali chlorides the effect is exothermic. In addition, the enthalpies of mixing of PTALi with tetramethyl-, tetraethyl-, tetrapropyl-, and tetrabutylammonium chloride were measured at T = 278.15 K, 298.15 K, and 318.15 K. Popular polyelectrolyte theories, such as Manning's limiting law, predict for the heat to be released upon dilution, and consumed upon mixing; the agreement between this purely electrostatic theory and experiments is at best qualitative. The ΔHmix values are correlated with the enthalpies of hydration of the cations of the low molecular mass salts added to the solution.

Modeling and Validating the Optimal Routes of a Sensor Network Using the Electrostatic Field Equations

In this paper, the analogy between the optimal routes within a sensor network and the electrostatic field lines is utilized successfully. In other words, partial differential equations similar to those of the electrostatic field theory are solved using Finite Difference Method (FDM) to find the optimal routes of the network. For the purpose of validation, an Opnet program based on the generated optimal routes is written to find the throughput and delay of the sensor network, a similar program is then applied to some arbitrary routing scenarios. The results show that the throughput and delay performance of the proposed method is better than that of the chosen arbitrary routing scenarios. It is also found from the results that the throughput of some scenarios is 50 % lower than that of the proposed method.

Moderated PEF from Transitioning between the Micro and Macroscopic Usage of Coulomb’s Law

The dielectric constant in Coulomb’s Law, D, can quantify an empirical reduction of force. It can also quantify a reduction of electrostatic field as seen in classical electrostatic theory where the induced charge layer is assumed to be infinitely thin. The two approaches exemplify two traditions that have been used in parallel for decades. They produce Potential Energy Functions (PEFs) that differ by a factor of the permittivity, er. The classical electrostatic theory result can be incorporated into force field models with an effective dielectric function, Deff, which spans the induced charge layer and accommodates both traditions. The Deff function increases the magnitude of local terms as compared with cumulative long distance terms. It is shown that the Deff function reduces distance dependence of the radial PEF within the induced charge layer and improves computational stability for some systems including substrate in dilute salt solution. End use applications include pharmaceutical development (e.g. protein calculations with docking), materials development, solvation energy calculations and QM/MM calculations.

Russian

In present review article are considered methods of preparation of microdispersed colloid silver nanoparticles and scopes of its practical application in nanoindustry, bionanotechnology, medicine and allied industries, including water processing and water purification. The mechanisms of bactericidal influence of colloid silver on a microbic cell are considered from the point of view of absorptive, electrostatic, enzyme and mutagen theories. Silver exerts both bactericidal and bacteriostatic effect against more than 500 species of microorganisms. Effect of bacterial destruction by silver drugs is 1,500 times more than the same concentration of phenol and 3,5 times more than the action of mercuric chloride. It is shown that effects of colloid silver are defined by concentration, the sizes of microdispersed nanoparticles and their stabolity in warer solutions, which are being prepared by means of various physico-chemical, biochemical and biotechnological methods.

A novel approach to improving the quality of chitosan blended yarns using static theory

Chitosan is a desirable material for several reasons, including its biocompatibility, biodegradability, non-toxicity, and excellent absorption. Rapid progress in material science has resulted in the development and widespread use of chitosan in the textile industry primarily because it is polycationic and can inhibit microorganism activity. However, high electrostatic, poor mechanical properties, and the polycationic property of chitosan materials, which are the main reason for the electro-static generation of chitosan fibers, have a negative impact on the spinning process and lower the quality of chitosan yarns. Therefore, there is a critical need to reduce production losses and improve the poor spinnability. A new spinning approach exploits triboelectric electrostatic theory to efficiently remove the electric charge and to promote yarn formation under optimum conditions precisely and controllably, thereby minimizing waste and achieving a high utilization ratio of the chitosan fibers. Lagrange interpolation is used to systematically analyze the basic mechanical properties of the developed materials. The results show that the tenacity of chitosan/PAN blended yarns is superior to that of chitosan/cotton blended yarns because of the complementary effect of positive and negative charges; and the novel application of static theory can be used to effectively resolve the high static and reduce material cost problems in the yarn production process. This new approach is expected to promote the usage of chitosan fibers in the textile industry and in medical applications.

On the gravitational energy associated with Earth's changing oblateness

Relative to the gravitational potential energy of the Earth's monopole, the multipole energy has received far less attention. In this paper, we recapitulate the basic physics from first principles and derive the formulas for multipole energies in analogy to classical electrostatic theory. We focus on the zonal quadrupole energy associated with the Earth's oblateness, the dominant term in Earth's gravity field apart from the monopole. We find the gravitational energy Eoblateness ≈ 10−6 |Emonopole| = +2.5 × 1026 J. We examine the implications of Eoblateness and its changes associated with long-term ‘secular’ decreases in the oblateness parameter J2. We find the rate of loss of Eoblateness due to the Earth rounding induced by the present-day GIA is about –200 GW, an amount quite significant in the kinetic energy budget of the mantle heat engine that drives the plate tectonics that has been estimated to be ∼1 TW. We also assert that the tidal braking and the global earthquake dislocations, both resulting in Earth rounding on long-term geological timescales, are accompanied with a secular decrease of Eoblateness at nearly the same rate of several GW.

Models and mechanisms of Hofmeister effects in electrolyte solutions, and colloid and protein systems revisited.

Specific effects of electrolytes have posed a challenge since the 1880's. The pioneering work was that of Franz Hofmeister who studied specific salt induced protein precipitation. These effects are the rule rather the exception and are ubiquitous in chemistry and biology. Conventional electrostatic theories (Debye-Hückel, DLVO, etc.) cannot explain such effects. Over the past decades it has been recognised that additional quantum mechanical dispersion forces with associated hydration effects acting on ions are missing from theory. In parallel Collins has proposed a phenomenological set of rules (the law of matching water affinities, LMWA) which explain and bring to order the order of ion-ion and ion-surface site interactions at a qualitative level. The two approaches appear to conflict. Although the need for inclusion of quantum dispersion forces in one form or another is not questioned, the modelling has often been misleading and inappropriate. It does not properly describe the chemical nature (kosmotropic/chaotropic or hard/soft) of the interacting species. The success of the LMWA rules lies in the fact that they do. Here we point to the way that the two apparently opposing approaches might be reconciled. Notwithstanding, there are more challenges, which deal with the effect of dissolved gas and its connection to 'hydrophobic' interactions, the problem of water at different temperatures and 'water structure' in the presence of solutes. They take us to another dimension that requires the rebuilding of theoretical foundations.

The Physical Origins of the Chemical Bond

The properties of the chemical bond are the same as those of the electrostatic flux that links the cores of two bonded atoms via their bonding electrons. Both the bond and the flux depend only on the number of electrons that form the bond, and significantly, neither depends on how the electron density is distributed. This allows the rules of chemical bonding to be developed using classical electrostatic theory without the need to know how the electron density is distributed. The magnitude of the flux is equal to the bond order (bond valence) and hence correlates with the bond length [1]. A network of bonds is equivalent to a capacitive electric circuit which allows one to predict the bond fluxes, hence also the bond lengths. Bond angles are determined by the spherical symmetry of the flux around each atom, and the resulting bonding geometry can be predicted using little more than a pocket calculator. The rules of all the predictive bond models: the VSEPR model, the ionic model, the covalent bond model and the bond valence model can be derived using classical electrostatics without introducing problematic concepts such as hypervalency, dative bonding, hybridization and the dichotomy between ionic and covalent bonding, thus eliminating the paradoxes created by the physically questionable Lewis and orbital models. Quantum effects are rarely important except in the transition metals where in some cases they perturb the bonding geometry.

Averaging of Multivalued Integral Equations

Integral equations are extensively used in various fields of knowledge, such as the theory of elasticity, heat and mass transfer, the theory of oscillations, fluid dynamics, the theory of filtration, electrostatics, electrodynamics, biomechanics, game theory, control theory, voting theory, electrical engineering, economics, and medicine. The investigations of actual processes based on idealized mathematical models often lead to equations with small parameters. For their investigation, various asymptotic methods are extensively used. The choice of a specific asymptotic method depends on the structure of the equation used to describe the dynamics of an object. In recent years, averaging methods are rapidly developed in the nonlinear mechanics and in the theory of oscillations. The mathematical substantiation of the averaging method for ordinary differential equations was originated in 1937 by Krylov–Bogolyubov in their fundamental work [1]. The works by Grebenikov, Mitropol’skii, Moiseev, Perestyuk, Plotnikov, Samoilenko, Filatov, and other researchers [2–4, 7–11, 14] played a great role in the development of the averaging method for different classes of differential equations. Later, the ideas of the averaging method were generalized for differential equations with multivalued and fuzzy right-hand sides (see [5, 6, 9, 12, 13] and the references therein). In the present paper, we substantiate the averaging method for a multivalued integral equation. Let conv .R/ be a metric space of nonempty compact convex subsets R with the Hausdorff metric h.F;G/: Consider a multivalued integral equation

About Nonlinear Classic Field Theory of Connected Charges

On the basis of an exact solution for the field of a charge in a uniformly accelerated noninertial frame of reference (NFR) and formulated Equivalent Situation Postulate the nonlinear electrostatic theory of bound charges has been constructed. Proposed method is outside of the flat space-time, however the curvature is not directly connected with the Einstein gravitational theory. The method proposed eliminates divergence of the proper energy and makes classical electrodynamics consistent at any sufficiently small distances.

Oscillations of nonspherical and spherical bubbles

Murray Strasberg maintained an interest in bubble oscillations throughout his career and frequently offered an incisive perspective. His early bubble research includes [Strasberg, J. Acoust. Soc. Am. 25, 536–537 (1952); Strasberg, Acustica 4, 450 (1954)]. His pertinent application of an electrostatic potential theory analogy expands interests of some of James Clerk Maxwell's students. In addition some related discussions with Murray will be recalled and experiments from the 1980s and 1990s at Washington State University pertaining to bubbles and their associated dynamics reviewed. Those experiments concern the response of bubbles to steady and modulated optical radiation forces [Unger and Marston, J. Acoust. Soc. Am. 83, 970–975 (1988); Unger and Marston, Ocean Optics IX, Proc. SPIE 925, 326–333 (1988)] and to modulated acoustical radiation forces [Asaki et al., Phys. Rev. Lett. 75, 2686–2689, (E) 4336 (1995); Asaki and Marston, J. Fluid Mech. 300, 149–167 (1995); Asaki and Marston, J. Acoust. Soc. Am. 102, 3372–3377 (1997)]. The latter papers pertain to the simultaneous measurement of the frequency and damping of bubble shape oscillations. [Work supported by ONR.]

Electrostatic forces or structural scaffolding: What stabilizes the lattice spacing of relaxed skinned muscle fibers?

The filament lattice in relaxed striated muscle is thought to be stabilized by electrostatic forces between charged filaments; electrostatic theories based on known filament charge densities do predict that the lattice spacing drops slightly with sarcomere length when actin and myosin filaments overlap. However, at sarcomere lengths with no overlap, electrostatic forces are reduced to a very low level and electrostatic models predict that the lattice collapses to a much smaller spacing. This collapse is not observed, which suggests that the A-band and I-band lattices are stabilized mechanically by the M-band and Z-line. To determine which mechanisms operate, consider a model where charged-filament interactions are supplemented by elastic titin filaments and radially elastic M-bands and Z-lines. To make progress, this model is simplified by assuming that the areas of A-band and Z-line unit cells are equal. Published data for the length-dependence of the lattice spacing, in and out of overlap, can be fitted to a mechanical model with known titin elasticity and very weak M-band or Z-line stiffness (≈0.15pN/nm per unit cell), which implies that electrostatic interactions cannot be ignored. A better fit is obtained when electrostatic interactions are restored. Electrostatic interactions also explain why the lattice spacing of relaxed muscle is a decreasing function of temperature.

Variational Implicit Solvation with Poisson-Boltzmann Theory.

We incorporate the Poisson–Boltzmann (PB) theory of electrostatics into our variational implicit-solvent model (VISM) for the solvation of charged molecules in an aqueous solvent. In order to numerically relax the VISM free-energy functional by our level-set method, we develop highly accurate methods for solving the dielectric PB equation and for computing the dielectric boundary force. We also apply our VISM-PB theory to analyze the solvent potentials of mean force and the effect of charges on the hydrophobic hydration for some selected molecular systems. These include some single ions, two charged particles, two charged plates, and the host–guest system Cucurbit[7]uril and Bicyclo[2.2.2]octane. Our computational results show that VISM with PB theory can capture well the sensitive response of capillary evaporation to the charge in hydrophobic confinement and the polymodal hydration behavior and can provide accurate estimates of binding affinity of the host–guest system. We finally discuss several issues for further improvement of VISM.

Predicting ion specific capacitances of supercapacitors due to quantum ionic interactions

A new theoretical framework is now available to help explain ion specific (Hofmeister) effects. All measurements in physical chemistry show ion specificity, inexplicable by classical electrostatic theories. These ignore ionic dispersion forces that change ionic adsorption.We explored ion specificity in supercapacitors using a modified Poisson–Boltzmann approach that includes ionic dispersion energies. We have applied ab initio quantum chemical methods to determine required ion sizes and ion polarisabilities. Our model represents graphite electrodes through their optical dielectric spectra. The electrolyte was 1.2M Li salt in propylene carbonate, using the common battery anions, PF6-,BF4- and ClO4- . We also investigated the perhalate series with BrO4- and IO4-.The capacitance C=dσ/dψ was calculated from the predicted electrode surface charge σ of each electrode with potential ψ between electrodes. Compared to the purely electrostatic calculation, the capacitance of a positively charged graphite electrode was enhanced by more than 15%, with PF6- showing >50% increase in capacitance. IO4- provided minimal enhancement. The enhancement is due to adsorption of both anions and cations, driven by ionic dispersion forces. The Hofmeister series in the single-electrode capacitance was PF6->BF4->ClO4->BrO4->IO4- . When the graphite electrode was negatively charged, the perhalates provided almost no enhancement of capacitance, while PF6- and BF4- decreased capacitance by about 15%.Due to the asymmetric impact of nonelectrostatic ion interactions, the capacitances of positive and negative electrodes are not equal. The capacitance of a supercapacitor should therefore be reported as two values rather than one, similar to the matrix of mutual capacitances used in multielectrode devices.

Electrocoalescence of binary water droplets falling in oil: Experimental study

The approaching movement and consequent coalescence of binary water droplets falling in stagnant oil and exposed to an external electric field are investigated using a high speed camera. Different situation of the droplets and electric field intensities are applied in the experiments. The qualitative results of the experimental observations are exhibited through the scaled images of the binary droplets snapshots in milliseconds. Furthermore, different approaching trends of the droplets are presented as quantitative plots and discussed based on the theoretical electrostatic and hydrodynamic models. The effect of the applied voltage amplitude, initial distance of the drop pair, and skew angle of the electric field are investigated. The experimental results prove the electrostatic theories; as acceleration in electrocoalescence demonstrated using a stronger electric field as well as closer distance between the droplets. It was also revealed that the skew angle of the electric field decelerates the electrocoalescence until alignment of the droplets.

Sorting Out the Structure of Single-Stranded DNA

The mechanical properties of single stranded nucleic acids play a vital role in such dynamic processes as DNA replication and RNA folding. While experiments have demonstrated that duplex DNA molecules behave as ideal worm-like chains with a persistence length that can be measured accurately, the unfolded single-stranded form of DNA (ssDNA) has been surprisingly recalcitrant: different biophysical techniques lead to different conclusions. Making matters worse, all-atom molecular dynamics simulations of ssDNA do not agree with experiment. This has motivated new experimental and theoretical work. In recent force spectroscopy and computational studies, McIntosh, Stevens and Saleh propose models where excluded volume influences long-ranged structure, while specific ion interactions induce wrinkles at short length scales (Single-stranded DNA is not a wormlike-chain, Biophys. J. 104, 28). However, direct structural evidence for these models is lacking. Thus, we perform detailed investigations of ssDNA homopolymers using x-ray scattering, single molecule FRET, and quantitative characterization of the ion atmosphere in mono- and di-valent salt. We develop a novel data-driven ensemble optimization technique that allows us to visualize the conformational adaptation of the DNA backbone to changes in the ion atmosphere, including the distinct effects of base stacking and ion valence. Correlation functions obtained from the structure ensembles, without reference to polymer or electrostatic theories, nonetheless show signatures of electrostatic excluded volume and strong ion effects at short distances. We discuss the implications for new polyelectrolyte theories of ssDNA and the biological role of electrostatics in these systems.

Demonstration of protein hydrogen bonding network application to microelectronics

Model of hydrogen bonding networks in active site of ?-lactamase during the last intermediate EY of acylenzyme reaction semicycle is presented. The I-V characteristics of each hydrogen bond are calculated following Marcus theory and theory of protein electrostatics. Simulations showed that HBN characteristics are similar to the characteristics of microelectronic devices such as amplifier, signal modulator, triangular pulse source. The results demonstrated the analogy of HBNs in the active site of ?-lactamase protein to microelectronic integrated circuit with multiple outputs each with different characteristics.