Showing papers on "Debye published in 1998"

Electric modulus and interfacial polarization in composite polymeric systems

Abstract: The applicability of the electric modulus formalism is investigated on a Debye-type relaxation process, the interfacial polarization or Maxwell–Wagner–Sillars effect. Electric modulus, which has been proposed for the description of systems with ionic conductivity and related relaxation processes, presents advantages in comparison to the classical approach of the real and imaginary part of dielectric permittivity. In composite polymeric materials, relaxation phenomena in the low-frequency region are attributed to the heterogeneity of the systems. For the investigation of these processes through electric modulus formalism, hybrid composite systems consisting of epoxy resin–metal powder–aramid fibres were prepared with various filler contents and their dielectric spectra were recorded in the frequency range 10 Hz–10 MHz in the temperature interval 30–150°C. The Debye, Cole–Cole, Davidson–Cole and Havriliak–Negami equations of dielectric relaxation are expressed in the electric modulus form. Correlation between experimental data and the various expressions produced, shows that interfacial polarization in the systems examined is, mostly, better described by the Davidson–Cole approach and only in the system with the higher heterogeneity must the Havriliak–Negami approach be used. © 1998 Chapman and Hall

Debye-scale plasma structures associated with magnetic-field-aligned electric fields

Abstract: We report a new type of spatially coherent plasma structure that is associated with quasistatic, magnetic-field-aligned electric fields in space plasmas. The solitary structures form in a magnetized plasma, are multidimensional, and are highly supersonic. The size along ${\mathbf{B}}_{0}$ is a few ${\ensuremath{\lambda}}_{D}$ and increases with increasing amplitude, unlike a classical soliton. The perpendicular size appears to be influenced by ion motion. We show that the structures facilitate ion-electron momentum exchange and suggest that an aggregate of structures may play a role supporting large-scale, parallel electric fields.

Measuring the broken phase sphaleron rate nonperturbatively

Abstract: We present details for a method to compute the broken phase sphaleron rate (rate of hot baryon number violation below the electroweak phase transition) nonperturbatively, using a combination of multicanonical and real time lattice techniques. The calculation includes the ``dynamical prefactor,'' which accounts for prompt recrossings of the sphaleron barrier. The prefactor depends on the hard thermal loops, getting smaller with increasing Debye mass; but for realistic Debye masses the effect is not large. The baryon number erasure rate in the broken phase is slower than a perturbative estimate by about $\mathrm{exp}(\ensuremath{-}3.6).$ Assuming the electroweak phase transition has enough latent heat to reheat the universe to the equilibrium temperature, baryon number is preserved after the phase transition if the ratio of (``dimensionally reduced'' thermal) scalar to gauge couplings $\ensuremath{\lambda}{/g}^{2}$ is less than 0.037.

Electron transfer reaction dynamics in non-Debye solvents

Abstract: The dynamics of electron transfer in a non-Debye solvent is described by multidimensional Markovian reaction-diffusion equation. To highlight differences with existing approaches in the simplest possible context, the irreversible outer-sphere reaction in a solvent with a biexponential energy-gap autocorrelation function, Δ(t), is studied in detail. In a Debye solvent, Δ(t)=exp(−t/τL) and the rate can be rigorously expressed as an explicit functional of exp(−t/τL). It has been suggested that the exact rate in a non-Debye solvent can be found by replacing exp(−t/τL) with the appropriate (nonexponential) Δ(t). For a “biexponential” solvent, our approach is based on an anisotropic diffusion equation for motion on a harmonic surface in the presence of a two-dimensional delta function sink. Three approximations, which reduce the solution of this equation to effective one-dimensional ones, are considered and compared with exact Brownian dynamics simulation results. The crudest approximation replaces the non-Deby...

Far-infrared spectra and associated dynamics in acetonitrile-water mixtures measured with femtosecond THz pulse spectroscopy

Abstract: We report the frequency-dependent absorption coefficient and index of refraction in the far-infrared region of the spectrum for mixtures of acetonitrile and water. The mixtures do not behave ideally, and deviate from ideality most noticeably for mixtures that are between 25% and 65% acetonitrile by volume. Two implementations of the Debye model for describing the dielectric relaxation behavior of mixtures are compared, and we show that these mixtures are better treated as uniform solutions rather than as two-component systems. We find an enhanced structure in the mixtures, relative to ideal mixtures, but we do not find direct evidence for microheterogeneity. The Debye time constant for the primary relaxation process for the mixtures is up to 25% longer than that for an ideal mixture.

Charge distribution from a simple molecular orbital type calculation and non-bonding interaction terms in the force field MAB.

Abstract: A simple and fast method to calculate charge distributions in organic molecules is presented. The method is based on charge shifts within the saturated σ-system, driven by orbital electronegativities, coupled to a modified Huckel treatment of the unsaturated π-systems. Experimental molecular dipole moments of a set of 119 molecules are reproduced with a root mean square deviation of 0.36 Debye units. Furthermore, the obtained charge distribution is used to describe hydration free energies in terms of hydrogen-bonding donor and acceptor strengths of polar groups. Least square fitting to experimental data of 281 compounds leads to values for these strengths with accuracy limits of ±4.3% and ±2.5%, respectively. Properly normalized values are taken to parametrize the hydrogen bonding terms in our MAB force field. The method is sufficiently fast to be used in the preparatory phase of interactive force-field calculations.

Impact of new permittivity measurements on sea surface emissivity modeling in microwaves

Abstract: As part of a measuring program dedicated to the analysis of the dielectric properties of seawater in the frequency range 3–89 GHz, a new dielectric permittivity model based on the standard Debye theory has been developed for remote sensing applications over the ocean below 40 GHz, together with polynomial interpolations at the millimeter frequencies 85.5 and 89 GHz. The aim of this paper is to test the relevance of these new dielectric measurements through statistical comparisons of radiative transfer predictions with satellite and airborne radiometric data between 18 and 89 GHz. A radiometric sensitivity analysis to the permittivity measurement errors is proposed, which yields a sea surface brightness temperature accuracy of at least 0.5 K below 20 GHz, 1 K at 24 GHz, and 1.5 K at 37 and 89 GHz. At frequencies less than 40 GHz, superiority of the revised Debye model is pointed out over the most commonly used model of Klein and Swift [1977]. At millimeter frequencies the new permittivity expressions deviate significantly from the standard Debye predictions, especially at low temperature, suggesting the influence of a second “high-frequency” Debye relaxation. Our comparisons with radiometric data at 89 GHz and in the channel 85.5V of the special sensor microwave imager tend to support this hypothesis. The results emphasize the importance of an adequate modeling of the complex permittivity of seawater as input to the surface emissivity models, at any frequency of the microwave spectrum, and augur interesting outputs in both in-flight calibration and interpretation of satellite data.

An Easy Method for the Determination of Debye Temperature from Thermal Expansion Analyses

Abstract: A combination of the early approaches of the Debye model for specific heat and the Gruneisen theory of the thermal expansion of solids is used to interpolate the thermal variation of lattice parameters. From this analysis, relevant parameters such as the Debye temperature and the value of lattice parameters extrapolated at 0 K are deduced. This method and its limitations are reported. A program has been developed which can be readily used with any computer. Practical applications are given as an illustration. The method is first applied to an ideal cubic compound Na2Ca3Al2F14, which we propose as a standard for thermal expansion calibrations. Then, magnetoelastic phenomena, which occur at very low temperature, are displayed in cubic rare earth garnets by comparison of experimental and extrapolated data. The model is extended to an anisotropic hexagonal system, where the values of lattice parameters extrapolated at 0 K are determined within 10−5. Debye temperatures are estimated within a relative error of 10% and are in good agreement with those calculated from specific heat data; they prove the relevance of this easy method.

A model of a local dielectric constant in proteins

Abstract: A model for the calculation of the scalar, position-dependent static dielectric function of an ensemble consisting of polarizable sites and of free relaxing point dipoles at fixed positions is proposed. It is based on classical electrostatics and leads to an iteration equation or nonlinear partial differential equation for the local dielectric constant. The expressions contain the equations of Debye, Onsager, and Neumann as special cases and thus might be considered as an extension to inhomogeneous matter. The model may have applications in the case of biological macromolecules in particular proteins where the polar side chains can be identified with the model’s dipoles. The algorithm leads to a position dependent dielectric constant in the protein interior in contrast to the assumption of a homogeneous permittivity throughout the protein. By taking into account the dielectric fine structure inside the macromolecules we hope that our approach may help to improve continuum electrostatic models of these molecules. The relevant polarizabilities and dipole moments of the amino acids are given and their corresponding local dielectric constants are estimated as a first approximation based on the Onsager and Kirkwood equations.

Pulsed-beam propagation in lossless dispersive media. I. Theory

Abstract: This first part of a two-part investigation is concerned with the effects of dispersion on the propagation characteristics of the scalar field associated with a highly localized pulsed-beam (PB) wave packet in a lossless homogeneous medium described by the generic wave-number profile k(ω)=ω/c(ω), where c(ω) is the frequency-dependent wave propagation speed. While comprehensive studies have been performed for the one-dimensional problem of pulsed plane-wave propagation in dispersive media, particularly for specific c(ω) profiles of the Lorentz or Debye type, even relatively crude measures tied to generic k(ω) profiles do not appear to have been obtained for the three-dimensional problem associated with a PB wave packet with complex frequency and wave-number spectral constituents. Such wave packets have been well explored in nondispersive media, and simple asymptotic expressions have been obtained in the paraxial range surrounding the beam axis. These paraxially approximated wave objects are now used to formulate the initial conditions for the lossless generic k(ω) dispersive case. The resulting frequency inversion integral is reduced by simple saddle-point asymptotics to extract the PB phenomenology in the well-developed dispersive regime. The phenomenology of the transient field is parameterized in terms of the space–time evolution of the PB wave-front curvature, spatial and temporal beam width, etc., as well as in terms of the corresponding space–time-dependent frequencies of the signal, which are related to the local geometrical properties of the k(ω) dispersion surface. These individual parameters are then combined to form nondimensional critical parameters that quantify the effect of dispersion within the space–time range of validity of the paraxial PB. One does this by performing higher-order asymptotic expansions beyond the paraxial range and then ascertaining the conditions for which the higher-order terms can be neglected. In Part II [J. Opt. Soc. Am. A15, 1276 (1998)], these studies are extended to include the transitional regime at those early observation times for which dispersion is not yet fully developed. Also included in Part II are analytical and numerical results for a simple Lorentz model that permit assessment of the performance of various nondimensional critical estimators.

An FDTD algorithm for transient propagation in biological tissue with a Cole-Cole dispersion relation

Abstract: The finite difference time domain (FDTD) method has become a popular numerical technique for analyzing the propagation of electromagnetic fields in the human body. Because of the high water content in many biological tissues, a Debye dispersion relation has often been used to describe the frequency variation in their dielectric properties. However, an accurate representation over a broad frequency range usually requires using a linear combination of several Debye functions. An alternative is to describe the frequency dependence using the Cole-Cole dispersion relation. While a number of frequency dependent FDTD formulations have been developed for Debye and Lorentz media, the Cole-Cole dispersion relation has not received nearly as much attention. In the approach presented here, the Cole-Cole dispersion relation is transformed into a time domain relation between the electric field and polarization current which involves a convolution integral. A recursive update of the convolution integral is made possible by approximating a time series by a sum of decaying exponentials.

Theoretical study of synthetic bianisotropic materials

Abstract: The electromagnetic properties of artificial molecules composed of small linearly loaded antennas embedded in a host medium are derived and discussed. It is demonstrated that the electromagnetic characteristics of these artificial materials can be designed by carefully selecting their loads. Various previously known material models (Debye, Lorentz) are recovered and their properties are generalized to more complex behaviors (Time Derivative Debye and Lorentz). Inherent duality between the dielectric and magnetic molecules allows us to derive a matched material satisfying ∈r =μr over broad frequency bandwidths. The electromagnetic properties of bianisotropic molecules composed of two antennas in tandem are presented. The electromagnetic characteristics of composite materials derived from these bianisotropic molecules are derived through an application of the Maxwell-Garnett Law.

The Ngai coupling model of relaxation: Generalizations, alternatives, and their use in the analysis of non-Arrhenius conductivity in glassy, fast-ionic materials

Abstract: The ionic conductivity of glassy, fast-ion-conducting materials can show non-Arrhenius behavior and approach saturation at sufficiently high temperatures [J. Kincs and S. W. Martin, Phys. Rev. Lett. 76, 20 (1996)]. The Ngai coupling model was soon applied to explain some of these observations [K. L. Ngai and A. K. Rizos, Phys. Rev. Lett. 76, 1296 (1996)], but detailed examination and generalization of the coupling model suggested the consideration of a related, yet different, approach, the cutoff model. Although both the coupling and cutoff models involve a shortest nonzero response time, τc, and lead to single-relaxation-time Debye response at limiting short times and high frequencies, they involve different physical interpretations of their low- and high-frequency response functions. These differences are discussed; the predictions of both models in the frequency and time domains are compared; and the utility of both models is evaluated for explaining the non-Arrhenius conductivity behavior associated w...

Ab initio single- and multiple-scattering exafs debye-waller factors : raman and infrared data

Abstract: The extended x-ray-absorption fine structure (EXAFS) Debye-Waller factor is an essential term appearing in the EXAFS equation that accounts for the molecular structural and thermal disorder of a sample. Single- and multiple-scattering Debye-Waller factors must be known accurately to obtain quantitative agreement between theory and experiment. Since the total number of fitting parameters that can be varied is limited in general, data cannot support fitting of all relevant multiple-scattering Debye-Waller factors. Calculation of the Debye-Waller factors is typically done using the correlated Debye approximation, where a single parameter (Debye temperature) is varied. However, this procedure cannot account in general for Debye-Waller factors in materials with heterogeneous bond strengths, such as biomolecules. As an alternative procedure in this work, we calculate them ab initio directly from the known or hypothetical three-dimensional structure. In this paper we investigate the adequacy of various computational approaches for calculating vibrational structure within small molecules. Detailed EXAFS results will be presented in a subsequent paper. Analytical expressions are derived for multiple scattering Debye-Waller factors, based on the plane wave approximation. Semiempirical Hamiltonians and the ab initio density functional method are used to calculate the normal mode eigenfrequencies and eigenvectors. These data are used to calculate all single- and multiple-scattering Debye-Waller factors up to a four atom cluster. These ab initio Debye-Waller factors are compared to those calculated from experimental infrared and Raman frequencies. As an example comparison with experimental EXAFS data from ${\mathrm{GeCl}}_{4}, {\mathrm{GeH}}_{3}\mathrm{Cl}$ gases are also reported. Good agreement is observed for all cases tested.

Debye-Hueckel-Bjerrum theory for charged colloids

Abstract: We formulate an extension of the Debye-Hueckel-Bjerrum theory [M. E. Fisher and Y. Levin, Phys. Rev. Lett. 71, 3826 (1993)] to the fluid state of a highly asymmetric charged colloid. Allowing for the formation of clusters consisting of one polyion and n condensed counterions, the total Helmholtz free energy of the colloidal suspension is constructed. The thermodynamic properties, such as the cluster-density distribution and the pressure, are obtained by the minimization of the free energy under the constraints of fixed number of polyions and counterions. In agreement with the current experimental and Monte Carlo results, no evidence of any phase transition is encountered.

Magnetic multipole transitions of a stripped carbon ion in a variety of Debye plasmas

Abstract: Survival of the excited triplet states and the spin-forbidden transitions including the magnetic dipole (M1) and magnetic quadrupole (M2) decays in the two-electron ion embedded in a variety of Debye plasmas are investigated theoretically. The dependence of the transition energy on the plasmas screening strength exhibits remarkably opposite patterns for the principal quantum number conserving and the non-conserving transitions. The magnetic multipole decay rates of the lower-lying states are seen to remain less affected at lower values of the screening magnitude.

Analytical solutions for rotational diffusion in the mean field potential: application to the theory of dielectric relaxation in nematic liquid crystals

Abstract: A theory of dielectric relaxation in nematics is developed for a molecular dipole moment directed at an arbitrary angle to the molecular long axis. Both exact and simple approximate analytical formulae for the longitudinal and transverse components of the complex dielectric permittivity tensor are obtained for the non-inertial rotational Brownian motion of a molecule in the mean field potential of Maier and Saupe. It appears that both longitudinal and transverse relaxation processes are effectively described by two Debye type mechanisms with corresponding relaxation times and dielectric strengths expressed in terms of the order parameter. The generalization of the theory for an arbitrary axially symmetric mean field potential is given.

Mixing formulas in time domain

Abstract: The dispersive properties of dielectric materials in both the time and the frequency domains are discussed. Special emphasis is placed on the treatment of heterogeneous materials, particularly two-phase mixtures. A time-domain Maxwell–Garnett rule is derived that differs from the corresponding frequency-domain formula in that it is expressed in terms of convolutions and inverse operators of the susceptibility kernels of the materials. Much of the analysis deals with the question of how the temporal dispersion of the dielectric responses of various physical materials is affected by the mixing process. Debye, Lorentz, Drude, and modified Debye susceptibility models are treated in detail.

Ionic transitions and oscillator strengths in Debye plasma - a case study

Abstract: Stability and energy of the excited states of the \(\) ion in plasmas are investigated theoretically using the Debye model. The transition energies of \(\) and \(\) transitions are seen to follow completely opposite trends of variation with the plasma screening strength. The dependence of absorption oscillator strength values on the screening strength is also discussed.

Structure and structure relaxation

Abstract: A discrete-dynamics model, which is specified solely in terms of a system's equilibrium structure, is defined for the density correlators of a simple fluid. This model yields results for the evolution of glassy dynamics which are identical with the ones obtained from the mode-coupling theory for ideal liquid–glass transitions. The decay of density fluctuations outside the transient regime is shown to be given by a superposition of Debye processes. The concept of structural relaxation is given a precise meaning. It is proven that the long-time part of the mode-coupling theory solutions is structural relaxation, while the transient motion merely determines an overall time scale for the glassy dynamics.

High output capacitative gas/liquid detector

Abstract: A gas or liquid detector that includes a capacitative sensor and a capacitance detector. The capacitative sensor includes a first electrode and a second electrode separated from one another, and additionally includes Debye elements extant in the liquid adjacent such portions of the electrodes that are in contact with the liquid. The Debye elements each include a Debye capacitor with an associated shunt conductor. The shunt conductor has an exponentially-increasing conductance versus voltage characteristic. The Debye element adjacent the first electrode and the Debye element adjacent the second electrode are connected in series by conduction through the liquid. The Debye element adjacent at least the first electrode has a substantially greater capacitance than the capacitance between the electrodes absent the Debye elements. The capacitance detector is connected to the capacitative sensor and measures the capacitance of the capacitative sensor by applying an alternating voltage between the electrodes. The alternating voltage has a voltage amplitude less than the voltage amplitude at which the Debye element extant adjacent at least the first electrode ceases to be predominantly capacitative. By measuring the capacitance of the capacitative sensor using an alternating voltage having a voltage amplitude less than the voltage amplitude at which the Debye element ceases to be predominantly capacitative, the capacitances measured are one or more orders of magnitude greater than the capacitances conventionally measured between electrodes in contact with a liquid.

Unified solution of the inverse capacity problem

Abstract: The inverse specific heat problem has played a significant role in physics. But there is no satisfactory solution for this inherently ill-posed inverse problem. The present work shows a concise and unified solution based on the M\"obius inversion technique and the Poisson-Abel process. This solution can explain both Debye's and Einstein's approximations very well. All the mathematical deductions are shown in the Appendixes; they are deduced in an elementary way for physicists.

A 3-D electromagnetic infinite element

Abstract: An ellipsoidal infinite element is used for the modeling of electromagnetic fields in exterior domains surrounding a structure. This infinite element is based on a multipole expansion that describes scattered and/or radiated fields exterior to the structure. The electromagnetic field is represented in the exterior domain by a pair of scalar potentials, referred to as the Debye potentials.

An advanced dielectric continuum approach for treating solvation effects: Time correlation functions. I. Local treatment

Abstract: A local continuum solvation theory, exactly treating electrostatic matching conditions on the boundary of a cavity occupied by a solute particle, is extended to cover time-dependent solvation phenomena. The corresponding integral equation is solved with a complex-valued frequency-dependent dielectric function e(ω), resulting in a complex-valued ω-dependent reaction field. The inverse Fourier transform then produces the real-valued solvation energy, presented in the form of a time correlation function (TCF). We applied this technique to describe the solvation TCF for a benzophenone anion in Debye (acetonitrile) and two-mode Debye (dimethylformamide) solvents. For the Debye solvent the TCF is described by two exponential components, for the two-mode Debye solvent, by three. The overall dynamics in each case is longer than that given by the simple continuum model. We also consider a steady-state kinetic regime and the corresponding rate constant for adiabatic electron-transferreactions. Here the boundary effect introduced within a frequency-dependent theory generates only a small effect in comparison with calculations made within the static continuum model.

A field theory study of the effect of specific interactions in ionic systems: A simple model

Abstract: The effect of specific ionic interactions on the Debye length has been studied using a simple model Hamiltonian for a binary mixture of anions and cations in the framework of the field theory. The Hamiltonian contains the Coulombic interaction and an independent non-Coulombic part describing a binary mixture of equivalent uncharged particles. We use a local and quadratic approximation to calculate the partition function via a functional integral. The Debye limiting law is obtained with a renormalized screening length. The screening is enhanced when the specific interactions favor demixion. This is illustrated on the example of an asymmetric hard sphere mixture.

Equation of state of MgSiO3 perovskite and its thermoelastic properties under lower mantle conditions

Abstract: A simple four-parameter model for calculating thermoelastic properties of MgSiO3 perovskite is presented based on the Vinet model for static lattice and the Debye approximation for lattice vibration. The input parameters are the volume of the unit cell, V0, the bulk modulus, K0, its pressure derivative, K0′, and the Debye temperature, Θ0, in the static lattice at zero pressure. For V0, K0 and K0′ the theoretical values by Stixrude and Cohen [1993] are used and Θ0 is determined to reproduce the experimental value at ambient conditions, 980 K, by Akaogi and Ito [1993]. The resulting isobars are in good agreement with experimental data to 1300 K and 11 GPa by Wang et al. [1994], with those to 1200 K at 20 GPa by Utsumi et al. [1995], and with those to 1500 K and to 2000 K, respectively, by Kato et al. [1995] and Funawori et al. [1996] both at 25 GPa. Using the present equation of state together with the method for calculating adiabatic Lame constants λS and μS for isotropic medium given in the present paper, density ρ, and sound velocities νp and νs of MgSiO3 perovskite under lower mantle conditions have been calculated where the constant-entropy model is assumed with the temperature at the core-mantle boundary being taken to be 3000 K. The results for ρ, νp, and νs are in agreement with the preliminary reference Earth model (PREM) within −2.4%∼ −3.7%, +3.3%∼+1.1%, and +0.8%∼−6.8%, respectively, over the lower mantle from 670 to 2891 km in depth. The calculated thermal expansivity under lower mantle conditions is in good agreement with that of the lower mantle estimated by Anderson [1982]. Using the present model with the parameters determined from experimental data at room temperature by Knittle and Jeanloz [1987], assuming Θ0 to be the same as that of MgSiO3 perovskite, thermoelastic properties of (Mg0.9, Fe0.1)SiO3 perovskite under lower mantle conditions have been calculated. The density becomes in much better agreement (+0.4%∼−0.8 %) with PREM and νp and νs remain almost unchanged from those of MgSiO3 perovskite.