Dielectric Boundary Research Articles

Dielectric relaxation behavior and energy storage properties in Ba 0.4 Sr 0.6 Zr 0.15 Ti 0.85 O 3 ceramics with glass additives

Abstract Ba 0.4 Sr 0.6 Zr 0.15 Ti 0.85 O 3 ceramics with SrO–B 2 O 3 –SiO 2 glass additives were prepared via the solid state reaction route. The effects of glass contents on the sintering behavior, dielectric properties, microstructures, and energy storage properties of BSZT ceramics were investigated. Dielectric breakdown strength of 22.4 kV/mm was achieved for BSZT ceramics with 20 wt% glass addition. Dielectric relaxation behavior was observed in dielectric loss versus temperature plots. In order to investigate the mechanism of dielectric breakdown performance, the relationship between dielectric breakdown strength and grain boundary barrier was studied by the measurements of breakdown strength and activation energy. A discharged energy density of 0.45 J/cm 3 with an energy efficiency of 88.2% was achieved for BSZT ceramics with 5 wt% glass addition.

Charging Free Energy Calculations Using the Generalized Solvent Boundary Potential (GSBP) and Periodic Boundary Condition: A Comparative Analysis Using Ion Solvation and Oxidation Free Energy in Proteins

Free energy simulations using a finite sphere boundary condition rather than a periodic boundary condition (PBC) are attractive in the study of very large biomolecular systems. To understand the quantitative impact of various approximations in such simulations, we compare charging free energies in both solution and protein systems calculated in a linear response framework with the Generalized Solvent Boundary Potential (GSBP) and PBC simulations. For simple ions in solution, we find good agreements between GSBP and PBC charging free energies, once the relevant correction terms are taken into consideration. For PBC simulations with the particle-mesh-Ewald for long-range electrostatics, the contribution (ΔG(P-M)) due to the use of a particle rather than molecule based summation scheme in real space is found to be significant, as pointed out by Hünenberger and co-workers. For GSBP, when the inner region is close to be charge neutral, the key correction is the overpolarization of water molecules at the inner/outer dielectric boundary; the magnitude of the correction (ΔG(s-pol)), however, is relatively small. For charging (oxidation) free energy in proteins, the situation is more complex, although good agreement between GSBP and PBC can still be obtained when care is exercised. The smooth dielectric boundary approximation inherent to GSBP tends to make significant errors when the inner region is featured with a high net charge. However, the error can be corrected with Poisson-Boltzmann calculations using snapshots from GSBP simulations in a straightforward and robust manner. Because of the more complex charge and solvent distributions, the magnitudes of ΔG(P-M) and ΔG(s-pol) in protein simulations appear to be different from those derived for solution simulations, leading to uncertainty in directly comparing absolute charging free energies from PBC and GSBP simulations for protein systems. The relative charging/oxidation free energies, however, are robust. With the linear response approximation, for the specific protein system (CueR) studied, the effect of freezing the protein structure in the outer region is found to be small, unless a very small (8 Å) inner region is used; even in the latter case, the result is substantially improved when the nearby metal binding loop is allowed to respond to metal oxidation. The implications of these results to the applicability of GSBP to complex biomolecules and in ab initio QM/MM simulations are discussed.

Motion of a Cylindrical Dielectric Boundary

The interplay between geometry and electrostatics contributes significantly to hydrophobic interactions of biomolecules in an aqueous solution. With an implicit solvent, such a system can be described macroscopically by the dielectric boundary that separates the high-dielectric solvent from low-dielectric solutes. This work concerns the motion of a model cylindrical dielectric boundary as the steepest descent of a free-energy functional that consists of both the surface and electrostatic energies. The effective dielectric boundary force is defined and an explicit formula of the force is obtained. It is found that such a force always points from the solvent region to solute region. In the case that the interior of a cylinder is of a lower dielectric, the motion of the dielectric boundary is initially driven dominantly by the surface force but is then driven inward quickly to the cylindrical axis by both the surface and electrostatic forces. In the case that the interior of a cylinder is of a higher dielectric, the competition between the geometrical and electrostatic contributions leads to the existence of equilibrium boundaries that are circular cylinders. Linear stability analysis is presented to show that such an equilibrium is only stable for a perturbation with a wavenumber larger than a critical value. Numerical simulations are reported for both of the cases, confirming the analysis on the role of each component of the driving force. Implications of the mathematical findings to the understanding of charged molecular systems are discussed.

Brownian Dynamics Study of Current and Selectivity of Calcium Channels

Brownian Dynamics (BD) simulation is a powerful approach to investigate ion permeation properties through protein ion channels. BD does not require the explicit evaluation of the motion of all the particles in the system. Only ions' trajectories are computed. This results in a small computational burden that allows micro-second scale simulations, long enough for the reliable estimate of ionic currents. We studied ion permeation properties and estimated ion currents through calcium channels, using a simplified channel model and Brownian Dynamics. We modeled the carboxylate-rich selectivity filter of calcium channels with 8 independent half-charged oxygens confined in the central region of the pore. We computed ions' trajectories self-consistently evaluating the electrostatic forces acting on the ions at every timestep. Such forces were evaluated solving Poisson's equation with a Boundary Element Method to deal with dielectric boundaries, called Induced Charge Computation method (ICC). A transmembrane potential was included as a spatially constant component of the electric field, a good approximation to a fully consistent treatment, see Crozier et al. (Biophys. J. 81:3077) and Hollerbach and Eisenberg (Langmuir, 18:3626). Boundary conditions for ionic concentrations in the intra- and extra-cellular domain were imposed by a Grand Canonical-Monte Carlo algorithm. We simulated different concentrations of CaCl2 added to NaCl solution only on one side of the membrane. Ion permeation was investigated under physiological conditions, using different sub-millimolar calcium concentrations and different transmembrane potentials. Channel selectivity and conductance were determined by electrostatic forces, steric repulsion due to charge crowding, and gradients of concentration and potential.

Variational Implicit Solvation with Solute Molecular Mechanics: From Diffuse-Interface to Sharp-Interface Models

Central in a variational implicit-solvent description of biomolecular solvation is an effective free-energy functional of the solute atomic positions and the solute-solvent interface (i.e., the dielectric boundary). The free-energy functional couples together the solute molecular mechanical interaction energy, the solute-solvent interfacial energy, the solute-solvent van der Waals interaction energy, and the electrostatic energy. In recent years, the sharp-interface version of the variational implicit-solvent model has been developed and used for numerical computations of molecular solvation. In this work, we propose a diffuse-interface version of the variational implicit-solvent model with solute molecular mechanics. We also analyze both the sharp-interface and diffuse-interface models. We prove the existence of free-energy minimizers and obtain their bounds. We also prove the convergence of the diffuse-interface model to the sharp-interface model in the sense of Γ-convergence. We further discuss properties of sharp-interface free-energy minimizers, the boundary conditions and the coupling of the Poisson-Boltzmann equation in the diffuse-interface model, and the convergence of forces from diffuse-interface to sharp-interface descriptions. Our analysis relies on the previous works on the problem of minimizing surface areas and on our observations on the coupling between solute molecular mechanical interactions with the continuum solvent. Our studies justify rigorously the self consistency of the proposed diffuse-interface variational models of implicit solvation.

Surface states in photonic crystals

Among many unusual and interesting physical properties of photonic crystals (PhC), in recent years, the propagation of surface electromagnetic waves along dielectric PhC boundaries have attracted considerable attention, also in connection to their possible applications. Such surfaces states, produced with the help of specialized defects on PhC boundaries, similarly to surfaces plasmons, are localized surfaces waves and, as such, can be used in various sensing applications. In this contribution, we present our recent studies on numerical modelling of surface states (SS) for all three cases of PhC dimensionality. Simulations of these states were carried out by the use of plane wave expansion (PWE) method via the MIT MPB package.

Poisson-Boltzmann Calculations: van der Waals or Molecular Surface?

The Poisson-Boltzmann equation is widely used for modeling the electrostatics of biomolecules, but the calculation results are sensitive to the choice of the boundary between the low solute dielectric and the high solvent dielectric. The default choice for the dielectric boundary has been the molecular surface, but the use of the van der Waals surface has also been advocated. Here we review recent studies in which the two choices are tested against experimental results and explicit-solvent calculations. The assignment of the solvent high dielectric constant to interstitial voids in the solute is often used as a criticism against the van der Waals surface. However, this assignment may not be as unrealistic as previously thought, since hydrogen exchange and other NMR experiments have firmly established that all interior parts of proteins are transiently accessible to the solvent.

Introducing Charge Hydration Asymmetry in the Realm of Continuum Solvation

Charge hydration asymmetry (CHA) manifests itself in the experimentally observed strong dependence of free energy of ion hydration on the sign of the ion charge. This asymmetry is not consistently accounted for by popular models of solvation; its magnitude varies greatly between the models. While it is clear that CHA is somehow related to charge distribution within a water molecule, the exact nature of this relationship is unknown. We propose a simple, yet general and rigorous criterion that relates rotational and charge inversion properties of a water molecule's charge distribution with its ability to cause CHA. We show which electric multipole components of a water molecule are key to explain its ability for asymmetric charge hydration. We then test several popular water models and explain why specific models show none, little, or strong CHA in simulations. We use the gained insight to derive an analogue of the Born equation that includes the missing physics necessary to account for CHA and does not rely on redefining the continuum dielectric boundary. The proposed formula is as simple as the original, does not contain any fitting parameters, and predicts hydration free energies and entropies of spherical cations and anions within experimental uncertainty. We further incorporate CHA into the framework of Generalized Born continuum solvation model; our findings suggest that the gap between the practical continuum electrostatics framework and the more fundamental explicit solvent treatment can be reduced considerably by explicitly introducing CHA into the existing framework.

Light extraction by directional sources within optically dense media

Light extraction efficiency (LEE) from a light-emitting diode is commonly referenced against an isotropic radiator within a dense dielectric medium. However, this description is not necessarily accurate for photonic devices with directional source elements. We therefore derive exact solutions for the LEE of a directive radiating source next to a planar dielectric boundary, accounting for any Fresnel reflections at the interface. These results can be used to validate numerical simulations and to quantify the baseline LEE for different source models. Four variations are explored, including the isotropic radiator, parallel and perpendicular orientations of the Hertzian dipole, and Lambertian scattering. Due to index matching, Fresnel reflections are generally negligible for materials with large escape cones, but reduce LEE by 20 % or more when critical angle is below 25°.

Three-dimensional numerical prediction of domain walls in class-A ring lasers

We carefully numerically simulate the full three-dimensional (3D), two-level Maxwell Bloch equations in a ring configuration, beyond the rotating wave and slowly varying envelope approximations. The 3D electromagnetic spatial and temporal variations are then well described up to the micrometer and femtosecond scales. Genuine dielectric waveguide boundary conditions together with no-reflection, perfectly matching layers are implemented. Besides the already known and well-described transverse instabilities of a traveling-wave solution, we observe steady zipper-state configurations characterized by the coexistence, in the laser transverse plane, of two longitudinal counter-propagating waves, with their separation plane parallel to the ring laser optical axis. The direction of propagation of the traveling wave is observed to change slowly and periodically with time.

Implementation of the Solvent Macromolecule Boundary Potential and Application to Model and Realistic Enzyme Systems

The implementation of the solvent macromolecule boundary potential (SMBP) by Benighaus and Thiel (J. Chem. Theory Comput. 2009, 5, 3114) into the program package CHARMM is presented. The SMBP allows for the efficient calculation of solvent effects for large macromolecules using irregularly shaped dielectric boundaries. In contrast to the generalized solvent boundary potential (GSBP) by Roux et al. (J. Chem. Phys. 2001, 114, 2924) from which it is derived, the SMBP is targeted for quantum mechanical/molecular mechanical (QM/MM) setups using ab initio methods for the QM part. After presenting benchmark results for simple model systems, applications of the SMBP for the calculation of geometries, reaction energy barriers, and vibrational frequencies for an alkaline phosphatase (AP) enzyme are discussed. Although the effect of the boundary potential on optimized structures (including the transition state) and vibrational frequencies is relatively small, the energetics of the phosphoryl transfer catalyzed by AP depend significantly on the boundary potential. Finally, to emphasize a unique feature of our implementation, we apply both SMBP and GSBP to the calculation of the energy barrier for a proton transfer reaction in a simple model channel, where the effect of an external transmembrane potential is studied. Due to the dipolar response of the polar environment, the effective charge displacement estimated based on the effect of the membrane potential on the proton transfer energetics deviates from the net charge that passes the membrane.

Effect of grain boundary on the electromechanical response of ferroelectric polycrystals

The effect of grain boundaries on the electromechanical response of a ferroelectric polycrystal subjected to an electric field or stress is investigated numerically by using a phase field model. The grain boundaries in the phase field model are regarded as dielectrics in which the ferroelectric properties are degraded completely. The phase field simulations show that the presence of dielectric grain boundaries results in a large build-in depolarizing field in grains. The depolarizing field has a significant influence on the coercive field, the switching behaviour of ferroelectric domain under an electric field or stress, and the piezoelectric and dielectric properties of the ferroelectric polycrystal. It is found that both coercive field and remnant polarization decrease with the increase of the thickness of dielectric grain boundary. However, the piezoelectric coefficient and permittivity of the ferroelectric polycrystal become larger when the thickness of dielectric grain boundary increases. The enhancement of dielectric and piezoelectric properties by the dielectric grain boundary suggests a new degree of freedom to tune the electromechanical response of ferroelectric polycrystalline materials.

Anisotropy in the dielectric spectrum of hydration water and its relation to water dynamics

Proteins, molecules, and macromolecular assemblies in water are surrounded by a nanometer-sized hydration layer with properties very different from bulk water. Here, we use classical molecular dynamics simulations to study the dielectric response of hydration water next to hydrophobic and hydrophilic planar surfaces. We find the interfacial dielectric absorption of water to be strongly anisotropic: compared to bulk water, which shows a broad dielectric absorption maximum around 15 GHz in the imaginary part of the dielectric function, the absorption for electric fields parallel to the surface is of similar strength and shows a slight redshift, while for perpendicular electric fields it is strongly attenuated and blueshifted. This anisotropy is generic for hydrophobic and hydrophilic surfaces. From our spatially resolved dielectric functions and a modified Maxwell-Garnett theory that accounts for anisotropic hydration layers around spherical particles, the dielectric absorption of solutions of organic molecules and micelles is derived to exhibit the experimentally known attenuation in combination with a redshift. These two features are traced back to the subtle interplay of interfacial depolarization effects and the dielectric anisotropy in the hydration layer. By a detailed analysis of the individual water molecule dynamics the perpendicular blueshift is shown not to be linked to accelerated water reorientation, but rather to dielectric boundary effects. Carefully conducted angularly resolved experiments at planar aqueous interfaces will be able to resolve this dielectric anisotropy and thus to confirm the subtle connection between spectral absorption features and the molecular water dynamics in hydration layers.

Optimized optomechanical crystal cavity with acoustic radiation shield

We present the design of an optomechanical crystal nanobeam cavity that combines finite-element simulation with numerical optimization, and considers the optomechanical coupling arising from both moving dielectric boundaries and the photo-elastic effect. Applying this methodology results in a nanobeam with an experimentally realized intrinsic optical Q-factor of 1.2x10^6, a mechanical frequency of 5.1GHz, a mechanical Q-factor of 6.8x10^5 (at T=10K), and a zero-point-motion optomechanical coupling rate of g=1.1MHz.

Charge Hydration Asymmetry: The Basic Principle and How to Use It to Test and Improve Water Models

Charge hydration asymmetry (CHA) manifests itself in the experimentally observed strong dependence of free energy of ion hydration on the sign of the ion charge. This asymmetry is not consistently accounted for by popular models of solvation; its magnitude varies greatly between the models. While it is clear that CHA is somehow related to charge distribution within a water molecule, the exact nature of this relationship is unknown. We propose a simple, yet general and rigorous criterion that relates rotational and charge inversion properties of a water molecule's charge distribution with its ability to cause CHA. We show which electric multipole components of a water molecule are key to explain its ability for asymmetric charge hydration. We then test several popular water models and explain why specific models show none, little, or strong CHA in simulations. We use the gained insight to derive an analogue of the Born equation that includes the missing physics necessary to account for CHA and does not rely on redefining the continuum dielectric boundary. The proposed formula is as simple as the original, does not contain any fitting parameters, and predicts hydration free energies and entropies of spherical cations and anions within experimental uncertainty. Our findings suggest that the gap between the practical continuum electrostatics framework and the more fundamental explicit solvent treatment may be reduced considerably by explicitly introducing CHA into the existing continuum framework.

Electron magneto-hydrodynamic waves bounded by magnetic bubble

The propagation of electron magneto-hydrodynamic (EMHD) waves is studied experimentally in a 3-dimensional region of low magnetic field surrounded by stronger magnetic field at its boundaries. We report observations where bounded left hand polarized Helicon like EMHD waves are excited, localized in the region of low magnetic field due to the boundary effects generated by growing strengths of the ambient magnetic field rather than a conducting or dielectric material boundary. An analytical model is developed to include the effects of radially nonuniform magnetic field in the wave propagation. The bounded solutions are compared with the experimentally obtained radial wave magnetic field profiles explaining the observed localized propagation of waves.

Comparison of three-dimensional Poisson solution methods for particle-based simulation and inhomogeneous dielectrics

Particle-based simulation represents a powerful approach to modeling physical systems in electronics, molecular biology, and chemical physics. Accounting for the interactions occurring among charged particles requires an accurate and efficient solution of Poisson's equation. For a system of discrete charges with inhomogeneous dielectrics, i.e., a system with discontinuities in the permittivity, the boundary element method (BEM) is frequently adopted. It provides the solution of Poisson's equation, accounting for polarization effects due to the discontinuity in the permittivity by computing the induced charges at the dielectric boundaries. In this framework, the total electrostatic potential is then found by superimposing the elemental contributions from both source and induced charges. In this paper, we present a comparison between two BEMs to solve a boundary-integral formulation of Poisson's equation, with emphasis on the BEMs' suitability for particle-based simulations in terms of solution accuracy and computation speed. The two approaches are the collocation and qualocation methods. Collocation is implemented following the induced-charge computation method of D. Boda et al. [J. Chem. Phys. 125, 034901 (2006)]. The qualocation method is described by J. Tausch et al. [IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 20, 1398 (2001)]. These approaches are studied using both flat and curved surface elements to discretize the dielectric boundary, using two challenging test cases: a dielectric sphere embedded in a different dielectric medium and a toy model of an ion channel. Earlier comparisons of the two BEM approaches did not address curved surface elements or semiatomistic models of ion channels. Our results support the earlier findings that for flat-element calculations, qualocation is always significantly more accurate than collocation. On the other hand, when the dielectric boundary is discretized with curved surface elements, the two methods are essentially equivalent; i.e., they have comparable accuracies for the same number of elements. We find that ions in water--charges embedded in a high-dielectric medium--are harder to compute accurately than charges in a low-dielectric medium.

A second-order scheme for Maxwell's equations with dielectric permittivity discontinuities and total field-scattered field boundaries

A finite volume scheme for numerical solution of Maxwell's equations in regions with dielectric permittivity discontinuities and total field-scattered field (TFSF) boundaries is proposed. The scheme is second-order accurate in space and time. The key idea is to choose stencils for approximation of derivatives used to increase the order of approximation so that they do not cross dielectric permittivity discontinuities or TFSF boundaries. Computational results verify second order of approximation of the proposed scheme.

Investigation of two discharge configurations in the CAMILA Hall thruster by the particle-in-cell method

The CAMILA (co-axial magneto-isolated longitudinal anode) concept was introduced to improve the ionization efficiency in low-power Hall thrusters. With relatively large coaxial anode surfaces and longitudinal magnetic strength, the CAMILA represents a significant departure from conventional Hall thrusters. In order to investigate the physical processes inside the CAMILA thruster, a two-dimensional particle-in-cell simulation of the thruster channel is used. The discharge parameters are analysed in two magnetic configurations: simplified CAMILA with a conventional magnetic field and full CAMILA with strengthened longitudinal component of the magnetic field. The simulation is fully kinetic with electrons, ions and gas atoms (xenon) represented as particles. Electron–neutral interactions are included together with particle–boundary interactions such as recombination and secondary emission. In addition, dielectric boundaries float and the cathode is represented as a free-space boundary, emitting electrons to satisfy quasi-neutrality on its surface. The high anode efficiency, observed in experiments, can be explained by several mechanisms found in this work. In the simplified case (magnetic configuration similar to the experiments) a focusing potential is created near the anode–dielectric boundary that directs ions away from the walls. It is created due to a combination of anode placement, in parallel with the channel, penetration of the plasma inside the anode cavity and the shape of magnetic force lines. Simulated steady-state results show good agreement with experimental measurements. In the full CAMILA case we demonstrate that the ionization region is found in the anode cavity. The electric field inside the anode cavity is substantial and it is directed towards the anode cavity centreline. Electrons are heated sufficiently to reach a high degree of ionization inside the anode cavity while ion currents to the anode surfaces are reduced significantly.

Dynamic electric potential redistribution and its influence on the development of a dielectric barrier plasma jet

We investigate the initiation and development of a streamer-like plasma jet generated in a single-electrode dielectric barrier configuration at atmospheric pressure. The influence of dielectric boundary conditions on discharge propagation dynamics, morphology and current distribution was studied using spatially and temporally resolved emission spectroscopy and wide-bandwidth current measurements. A Phantom high-frame-rate camera system was used to visualize discharge inception as a function of pulse repetition frequency, which was varied between 1 and 20 kHz. At discharge inception, with the copper ring anode located 20 mm behind the capillary tip, the discharge propagated along the 2 mm diameter inner wall of the glass capillary regardless of pulse repetition frequency. The steady-state morphology remained annular below 6 kHz, but gradually transitioned to an axial morphology with the expansion of a dark wall sheath towards the anode as the pulse repetition frequency was increased to 10 kHz. In the axial mode, the ionization front steadily decelerated with a corresponding decrease in peak emission intensity, while emission from the residual plasma channel increased. This indicated a dynamic redistribution of electric potential from the ionization front into the residual plasma channel that was attributed to charge accumulation on the dielectric surface between discharge pulses.