Dielectric Theory Research Articles

Viscoelastic effects on frequency tuning of a dielectric elastomer membrane resonator

As a recent application of dielectric elastomers (DEs), DE resonators have become an alternative to conventional silicon-based resonators used in MEMS and have attracted much interest from the research community. However, most existing modeling works for the DE resonators ignore the intrinsic viscoelastic effect of the material that may strongly influence their dynamic performance. Based on the finite-deformation viscoelasticity theory for dielectrics, this paper theoretically examines the in-plane oscillation of a DE membrane resonator to demonstrate how the material viscoelasticity affects the actuation and frequency tuning processes of the resonator. From the simulation results, it is concluded that not only the applied voltage can change the natural frequency of the resonator, but also the inelastic deformation contributes to frequency tuning. Due to the viscoelasticity of the material, the electrical loading rate influences the actuation process of the DE resonator, while it has little effect on the final steady frequency tuned by the prescribed voltage within the safety range. With the consideration of the typical failure modes of the resonator and the evolution process of the material, the tunable frequency range and the safe range of the applied voltage of the DE membrane resonator with different dimension parameters are determined in this work, which are found to be dependent on the electrical loading rate. This work is expected to provide a better understanding on the frequency tuning of viscoelastic DE membrane resonators and a guideline for the design of DE devices.

Energy-loss function including damping and prediction of plasmon lifetime

An approach to include plasmon damping in the energy-loss function is described within the dielectric theory. Use of the energy-loss function included damping for calculating the electron inelastic mean free path yields results in good agreement with the experimental data and other theoretical results at medium–high energies. At a few eV above the Fermi energy, the present results are entirely consistent with those obtained from other measurements for Au. Also, a simple way to predict the values of damping and lifetime at low energies is described. Two values of lifetime for an electron with energy (above the Fermi energy) of 5eV in Al and 6eV in Au are predicted to be 2.18fs and 1.70fs, respectively. These predicted values are in reasonable agreement with those estimated from other measurements at the corresponding energies: 2.16 ± 0.22fs in Al, and 1.91 ± 0.32fs in Au.

Energy dependence of the energy loss function parametrization of indium in the Drude–Lindhard model

The energy loss function (ELF) is a key parameter for the calculations of energy losses undergone by electrons in matter. It is often the only input in the calculations performed within the models based on the semi‐classical dielectric response theory. Its perfect knowledge is thus of primordial importance. To evaluate the ELF, it is usual to consider as a model an expansion in Drude–Lindhard (DL) type oscillators with fixed values of the strength, width, energy and dispersion for the various oscillators. However, for materials that are characterized by a single sharp oscillator as aluminium or indium, it has been shown [Phys. Rev. B 46 (1992) 2486] that the damping parameter that corresponds in the DL model to the width of the oscillator increases for decreasing incident electron energy. To emphasize this effect, we perform in this work systematic calculation of the ELF for an indium target and for incident electron energies between 200 and 2000 eV. The ELF is determined by comparing REELS (reflection electron energy loss spectroscopy) experimental inelastic electron scattering cross sections with cross sections calculated within the semi‐classical dielectric response model, which is implemented in the QUEELS‐ε(k,ω)‐REELS software (Quantitative analysis of Electron Energy Losses at Surfaces) [Surf. Interface Anal. 36 (2004) 824]. We also perform measurements and calculations for varying incident and exit angles of the electron, namely for angles to the surface normal between 15o and 75o, to check the validity of our results for all geometries. Our results show that the damping parameter of indium in the DL model for electron energy of 200 eV is three times larger than for energy of 2000 eV. Copyright © 2014 John Wiley & Sons, Ltd.

One-dimensional potential for image-potential states on graphene

In the framework of dielectric theory, the static non-local self-energy of an electron near an ultra-thin polarizable layer has been calculated and applied to study binding energies of image-potential states near free-standing graphene. The corresponding series of eigenvalues and eigenfunctions have been obtained by numerically solving the one-dimensional Schrödinger equation. The image-potential state wave functions accumulate most of their probability outside the slab. We find that the random phase approximation (RPA) for the non-local dielectric function yields a superior description for the potential inside the slab, but a simple Fermi–Thomas theory can be used to get a reasonable quasi-analytical approximation to the full RPA result that can be computed very economically. Binding energies of the image-potential states follow a pattern close to the Rydberg series for a perfect metal with the addition of intermediate states due to the added symmetry of the potential. The formalism only requires a minimal set of free parameters: the slab width and the electronic density. The theoretical calculations are compared with experimental results for the work function and image-potential states obtained by two-photon photoemission.

Electron Inelastic Mean Free Path Theory and Density Functional Theory Resolving Discrepancies for Low-Energy Electrons in Copper

We develop the many-pole dielectric theory of UV plasmon interactions and electron energy losses, and couple our advances with recent developments of Kohn-Sham density functional theory to address observed discrepancies between high-precision measurements and tabulated data for electron inelastic mean free paths (IMFPs). Recent publications have demonstrated that a five standard error difference exists between longstanding theoretical calculations and measurements of electron IMFPs for elemental solids at energies below 120 eV, a critical region for analysis of electron energy loss spectroscopy (EELS), X-ray absorption spectroscopy (XAS), and related technologies. Our implementation of improved optical loss spectra and a physical treatment of second-order excitation lifetimes resolves this problem in copper for the first time for energies in excess of 80 eV and substantially improves agreement for lower energy electrons.

Nonadiabatic dynamics of electron transfer in solution: explicit and implicit solvent treatments that include multiple relaxation time scales.

The development of efficient theoretical methods for describing electron transfer (ET) reactions in condensed phases is important for a variety of chemical and biological applications. Previously, dynamical dielectric continuum theory was used to derive Langevin equations for a single collective solvent coordinate describing ET in a polar solvent. In this theory, the parameters are directly related to the physical properties of the system and can be determined from experimental data or explicit molecular dynamics simulations. Herein, we combine these Langevin equations with surface hopping nonadiabatic dynamics methods to calculate the rate constants for thermal ET reactions in polar solvents for a wide range of electronic couplings and reaction free energies. Comparison of explicit and implicit solvent calculations illustrates that the mapping from explicit to implicit solvent models is valid even for solvents exhibiting complex relaxation behavior with multiple relaxation time scales and a short-time inertial response. The rate constants calculated for implicit solvent models with a single solvent relaxation time scale corresponding to water, acetonitrile, and methanol agree well with analytical theories in the Golden rule and solvent-controlled regimes, as well as in the intermediate regime. The implicit solvent models with two relaxation time scales are in qualitative agreement with the analytical theories but quantitatively overestimate the rate constants compared to these theories. Analysis of these simulations elucidates the importance of multiple relaxation time scales and the inertial component of the solvent response, as well as potential shortcomings of the analytical theories based on single time scale solvent relaxation models. This implicit solvent approach will enable the simulation of a wide range of ET reactions via the stochastic dynamics of a single collective solvent coordinate with parameters that are relevant to experimentally accessible systems.

A variational formulation for electroelasticity of microcontinua

The governing equations for a micromorphic theory of electromagneto-elastic dielectrics are derived by a variational formulation. Balance equations and boundary conditions are obtained assuming the internal energy as dependent on macro and micro-strain variables. A micropolar linear model is derived and the evolution equations for dipole and quadrupole are exploited to arrive at an expression for the polarization density. The present model is applied to the simple shear static problem for an isotropic dielectric layer subject to an external field. The resulting shear displacement and electric potential noticeably differ from the classical elastic case.

Chemical bond properties and charge transfer bands of O(2-)-Eu(3+), O(2-)-Mo(6+) and O(2-)-W(6+) in Eu(3+)-doped garnet hosts Ln3M5O12 and ABO4 molybdate and tungstate phosphors.

Charge transfer (CT) energy from the ligand to the central ions is an important factor in luminescence properties for rare earth doped inorganic phosphors. The dielectric theory of complex crystals was used to calculate chemical bond properties. Combining the photoluminescence and the dielectric theory of complex crystals, the CT bands of O(2-)-Eu(3+), O(2-)-Mo(6+) and O(2-)-W(6+) for Eu(3+)-doped inorganic phosphors have been investigated experimentally and theoretically. Taking Eu(3+)-doped Ln3M5O12 (Ln = Y, Lu and M = Al, Ga), Gd3Ga5O12, MMoO4 (M = Ca, Sr, Ba) and MWO4 (M = Ca, Sr, Ba) as typical phosphors, we investigated the effects of the cation size on the CT bands and chemical bond properties including the bond length (d), the covalency (fc), the bond polarizability (αb) and the environmental factor (he) of O(2-)-Eu(3+), O(2-)-Mo(6+) and O(2-)-W(6+), respectively. For systematic isostructural Ln3M5O12 (Ln = Y, Lu and M = Al, Ga) phosphors, with the increasing M ion radius, the bond length of Ln-O decreases, but fc and αb increase, which is the main reason that the environmental factor increased. For the isostructural MMoO4:Eu, with the increasing M ion radius, the Mo-O bond length increases, but fc and αb decrease, and thus he decreases. However, in the compound system MWO4:Eu (M = Ca, Ba) with the increasing M ion radius, the O-W bond length increases, but fc and αb increase, and thus he increases and the O-W CT energy decreases. Their O(2-)-Eu(3+), O(2-)-Mo(6+) and O(2-)-W(6+) CT bands as well as their full width at half maximum (FWHM) were directly influenced by he. And with the increasing he, CT bands of O-Eu or O-Mo or O-W decrease and their FWHM increases. These results indicate a promising approach for changing the material properties, searching for new Eu(3+) doped molybdate, tungstate or other oxide phosphors and analyzing the experimental result.

Wake Potential for Dust Grains in a Flowing Plasma

The wake effect among dust grains in a flowing plasma is studied by the linear-response dielectric theory within the linear hydrodynamics model. The expression of potential is derived, and it can be divided into two parts: one is the screened Coulomb short-ranged repulsive potential, and the other is the long-ranged oscillatory wake potential. The numerical results show that both the amplitude and wavelength of the wake potential depend on the Mach number, in such a manner that the wavelength of the oscillating potential increases, while its amplitude decreases, with increasing Mach number.

Electric field induced sheeting and breakup of dielectric liquid jets

We report experimental observations of the controlled deformation of a dielectric liquid jet subjected to a local high-voltage electrostatic field in the direction normal to the jet. The jet deforms to the shape of an elliptic cylinder upon application of a normal electrostatic field. As the applied electric field strength is increased, the elliptic cylindrical jet deforms permanently into a flat sheet, and eventually breaks-up into droplets. We interpret this observation—the stretch of the jet is in the normal direction to the applied electric field—qualitatively using the Taylor-Melcher leaky dielectric theory, and develop a simple scaling model that predicts the critical electric field strength for the jet-to-sheet transition. Our model shows a good agreement with experimental results, and has a form that is consistent with the classical drop deformation criterion in the Taylor-Melcher theory. Finally, we statistically analyze the resultant droplets from sheet breakup, and find that increasing the applied electric field strength improves droplet uniformity and reduces droplet size.

Numerical Study on Deformation and Interior Flow of a Droplet Suspended in Viscous Liquid under Steady Electric Fields

A model based on the volume of fluid (VOF) method and leaky dielectric theory is established to predict the deformation and internal flow of the droplet suspended in another vicious fluid under the influence of the electric field. Through coupling with hydrodynamics and electrostatics, the rate of deformation and internal flow of the single droplet are simulated and obtained under the different operating parameters. The calculated results show that the direction of deformation and internal flow depends on the physical properties of fluids. The numerical results are compared with Taylor's theory and experimental results by Torza et al. When the rate of deformation is small, the numerical results are consistent with theory and experimental results, and when the rate is large the numerical results are consistent with experimental results but are different from Taylor's theory. In addition, fluid viscosity hardly affects the deformation rate and mainly dominates the deformation velocity. For high viscosity droplet spends more time to attain the steady state. The conductivity ratio and permittivity ratio of two different liquids affect the direction of deformation. When fluid electric properties change, the charge distribution at the interface is various, which leads to the droplet different deformation shapes.

Complex Microwave Permittivity of Secondary High Explosives

AbstractWe aim to understand how microwaves interact with high explosives by studying the complex permittivity from 1–18 GHz of HMX, RDX, TNT, TATB, PETN, Octol, Comp B, 95 % RDX/5 % Viton A (PBX‐RDX), PBX 9404, PBXN‐5, PBXN‐7, PBXW‐14, PBX 9501, and PBX 9502. The combination of a resonant cavity perturbation technique for determining the room‐temperature complex dielectric constant at discrete frequencies and a wide band open circuit method (1–18 GHz) provides an accurate, broadband measurement that describes the dielectric properties in the frequency range of interest. While the values of the real and imaginary permittivity components did not vary significantly as a function of frequency, we found the real part of the permittivity to be highly dependent on relatively small changes in the material density. We used dielectric mixing theory, specifically the linear‐law approximation, to compare the predicted values based on the dielectric properties of individual components with those of the resulting formulation measured experimentally for a select number of samples; the prediction agrees well within the observed variability of the experimentally measured values.

Dielectric study of hot-pressed nanocomposite polymer electrolytes

Ion-conducting nanocomposite polymer electrolyte films based on poly(ethylene oxide)-NaPO3 3: 1 with up to 15 wt % of SiO2 have been prepared using recently developed hot-press technique instead of conventional solution cast method. With 7 wt % of SiO2, the film conductivity has been enhanced by an order of magnitude. The materials have been characterized by Fourier transform infrared spectrometry and thermogravimetric analysis. For the composition with the highest conductivity, the temperature dependences of ionic mobility, mobile ions concentration, ionic transference number, and ionic drift velocity have been determined. Dielectric constant and dielectric loss have been measured. The conductivity enhancement has been discussed on the basis of existing theories of dielectrics.

Stopping and Straggling of Swift Hydrogen-Dicluster Ions Using Energy-Loss Function of Harmonic Oscillator Model

In the present work we analyze our theoretical investigation of various aspects of the random and aligned stopping power of hydrogen-dicluster H_2^+ moving in close but variable vicinity of each other in a dilute and dense stopping targets, which being modeled by a harmonic oscillator (HO) with generalized oscillator strength (GOS).This model combined with a free electron gas (FEG) using dielectric theory to calculate the energy loss function (ELF) of dense medium which treated by harmonic oscillator model. We have made comprehensive investigation of single and vicinage stopping power, and related quantities for hydrogen-dicluster ions H_2^+ in (C, Al, Ar and Xe) targets.

Inelastic Cross Sections for Low-Energy Electrons in Liquid Water: Exchange and Correlation Effects

Low-energy electrons play a prominent role in radiation therapy and biology as they are the largest contributor to the absorbed dose. However, no tractable theory exists to describe the interaction of low-energy electrons with condensed media. This article presents a new approach to include exchange and correlation (XC) effects in inelastic electron scattering at low energies (below ∼10 keV) in the context of the dielectric theory. Specifically, an optical-data model of the dielectric response function of liquid water is developed that goes beyond the random phase approximation (RPA) by accounting for XC effects using the concept of the many-body local-field correction (LFC). It is shown that the experimental energy-loss-function of liquid water can be reproduced by including into the RPA dispersion relations XC effects (up to second order) calculated in the time-dependent local-density approximation with the addition of phonon-induced broadening in N. D. Mermin's relaxation-time approximation. Additional XC effects related to the incident and/or struck electrons are included by means of the vertex correction calculated by a modified Hubbard formula for the exchange-only LFC. Within the first Born approximation, the present XC corrections cause a significantly larger reduction (∼10-50%) to the inelastic cross section compared to the commonly used Mott and Ochkur approximations, while also yielding much better agreement with the recent experimental data for amorphous ice. The current work offers a manageable, yet rigorous, approach for including non-Born effects in the calculation of inelastic cross sections for low-energy electrons in liquid water, which due to its generality, can be easily extended to other condensed media.

Determination of the Cu 2p primary excitation spectra for Cu, Cu2O and CuO

The shape and intensity of photoelectron peaks are strongly affected by extrinsic excitations due to electron transport out of the surface (including bulk and surface effects) and to intrinsic excitations due to the sudden creation of the static core hole. These effects must be included in the theoretical description of the emitted photoelectron spectra. We have calculated the effective energy-differential inelastic electron scattering cross section for XPS, including both surface and core hole effects, within the dielectric response theory by means of the QUEELS-XPS software (QUantitative analysis of Electron Energy Losses at Surfaces for XPS). The full XPS spectrum is then modeled by convoluting this energy loss cross section with the primary excitation spectrum that accounts for all effects which are part of the initial photo-excitation process, i.e. lifetime broadening, spin–orbit coupling, and multiplet splitting. The shape of this primary excitation spectrum is determined by requiring close agreement between the resulting theoretical spectrum and the experimental XPS spectrum. These calculations were performed for Cu 2p peaks of Cu, Cu2O, and CuO. For CuO, we compare the obtained primary excitation spectra with first principle calculations performed with the CTM4XAS software (Charge Transfer Multiplet program for X-ray Absorption Spectroscopy) for the corresponding emissions and we find good quantitative agreement.

Some thoughts on bioimpedance and biodielectrics

From early on we learnt that a dielectric is an insulator, and a practical way to measure it was to place it between two capacitor plates. The plates were dry and so was the dielectric – the resistance between the plates was very high. With living tissue it was quite different, the material was not dry and the capacitor plates had wet contact with the tissue. At the wet plates polarization impedance appeared constituting an important source of error. The discipline of bioimpedance had one problem more than the discipline of dielectrics. Even so it became more and more common to classify tissue as a dielectric instead of a conductor. The terms melted together, but not completely. Taking a closer look at the theory of Bioimpedance and Biodielectrics we discover that both disciplines suffer from a lack of consistency. Dielectric theory emerged much earlier than impedance theory; it started more than 200 years ago with Coulomb’s law (1795): ,

Calculations of stopping powers and inelastic mean free paths for 20 eV–20 keV electrons in 11 types of human tissue

Systematic calculations are performed for determining the stopping powers (SP) and inelastic mean free paths (IMFP) for 20eV–20keV electrons in 11 types of human tissue. The calculations are based on a dielectric model, including the Born−Ochkur exchange correction. The optical energy loss functions (OELF) are empirically evaluated, because of the lack of available experimental optical data for the 11 tissues under consideration. The evaluated OELFs are examined by the f-sum rule expected from the dielectric response theory, and by calculation of the mean excitation energy. The calculated SPs are compared with those for PMMA (polymethylmethacrylate, a tissue equivalent material) and liquid water. The SP and IMFP data presented here are the results for the 11 human tissues over the energy range of 20eV–20keV, and are of importance in radiotherapy planning and for studies of various radiation effects on human tissues.

Flow patterns and deformation modes of coaxial liquid columns in transverse electric fields

Steady-state flow patterns and deformation modes of coaxial liquid columns in transverse electric fields are studied analytically. The governing creeping flow equations are solved for Newtonian and (mutually) immiscible fluids in the framework of leaky dielectric theory. A detailed analysis of the electric and flow fields is presented and it is shown that there will be four possible flow patterns in and around the columns, in terms of the direction of the external flow (top-to-sides/bottom-to-sides vs. sides-to-top/sides-to-bottom) and the number of vortices (single vortex vs. double vortices) in the shell, and that the senses of the net electric shear stresses at the inner and the outer interfaces and their relative importance are the key parameters in setting these patterns. Equilibrium shapes of the interfaces are also found and it is shown that there are four distinct modes of deformation, depending on the governing nondimensional parameters of the problem. The instability of the jet is also examined qualitatively using the observations pertaining the instability of single-phase drops and jets and the scaling arguments based on the present solution.

Beyond the Continuum: How Molecular Solvent Structure Affects Electrostatics and Hydrodynamics at Solid–Electrolyte Interfaces

Standard continuum theory fails to predict several key experimental results of electrostatic and electrokinetic measurements at aqueous electrolyte interfaces. In order to extend the continuum theory to include the effects of molecular solvent structure, we generalize the equations for electrokinetic transport to incorporate a space dependent dielectric profile, viscosity profile, and non-electrostatic interaction potential. All necessary profiles are extracted from atomistic molecular dynamics (MD) simulations. We show that the MD results for the ion-specific distribution of counterions at charged hydrophilic and hydrophobic interfaces are accurately reproduced using the dielectric profile of pure water and a non-electrostatic repulsion in an extended Poisson-Boltzmann equation. The distributions of Na(+) at both surface types and Cl(-) at hydrophilic surfaces can be modeled using linear dielectric response theory, whereas for Cl(-) at hydrophobic surfaces it is necessary to apply nonlinear response theory. The extended Poisson-Boltzmann equation reproduces the experimental values of the double-layer capacitance for many different carbon-based surfaces. In conjunction with a generalized hydrodynamic theory that accounts for a space dependent viscosity, the model captures the experimentally observed saturation of the electrokinetic mobility as a function of the bare surface charge density and the so-called anomalous double-layer conductivity. The two-scale approach employed here-MD simulations and continuum theory-constitutes a successful modeling scheme, providing basic insight into the molecular origins of the static and kinetic properties of charged surfaces, and allowing quantitative modeling at low computational cost.