Fractional Integro-Differential Equations for Electromagnetic Waves in Dielectric Media

We prove that the electromagnetic fields in dielectric media whose susceptibility follows a fractional power-law dependence in a wide frequency range can be described by differential equations with time derivatives of noninteger order. We obtain fractional integro-differential equations for electromagnetic waves in a dielectric. The electromagnetic fields in dielectrics demonstrate a fractional power-law relaxation. The fractional integro-differential equations for electromagnetic waves are common to a wide class of dielectric media regardless of the type of physical structure, the chemical composition, or the nature of the polarizing species (dipoles, electrons, or ions)

Subordination model of anomalous diffusion leading to the two-power-law relaxation responses

We derive a general pattern of the nonexponential, two-power-law relaxation from the compound subordination theory of random processes applied to anomalous diffusion. The subordination approach is based on a coupling between the very large jumps in physical and operational times. It allows one to govern a scaling for small and large times independently. Here we obtain explicitly the relaxation function, the kinetic equation and the susceptibility expression applicable to the range of experimentally observed power-law exponents which cannot be interpreted by means of the commonly known Havriliak-Negami fitting function. We present a novel two-power relaxation law for this range in a convenient frequency-domain form and show its relationship to the Havriliak-Negami one.Comment: 5 pages; 3 figures; corrected versio

Fractional Equations of Curie-von Schweidler and Gauss Laws

The dielectric susceptibility of most materials follows a fractional power-law frequency dependence that is called the "universal" response. We prove that in the time domain this dependence gives differential equations with derivatives and integrals of noninteger order. We obtain equations that describe "universal" Curie-von Schweidler and Gauss laws for such dielectric materials. These laws are presented by fractional differential equations such that the electromagnetic fields in the materials demonstrate "universal" fractional damping. The suggested fractional equations are common (universal) to a wide class of materials, regardless of the type of physical structure, chemical composition or of the nature of the polarization.Comment: 11 pages, LaTe

Counterflow Regolith Heat Exchanger

A problem exists in reducing the total heating power required to extract oxygen from lunar regolith. All such processes require heating a great deal of soil, and the heat energy is wasted if it cannot be recycled from processed material back into new material. The counterflow regolith heat exchanger (CoRHE) is a device that transfers heat from hot regolith to cold regolith. The CoRHE is essentially a tube-in-tube heat exchanger with internal and external augers attached to the inner rotating tube to move the regolith. Hot regolith in the outer tube is moved in one direction by a right-hand - ed auger, and the cool regolith in the inner tube is moved in the opposite direction by a left-handed auger attached to the inside of the rotating tube. In this counterflow arrangement, a large fraction of the heat from the expended regolith is transferred to the new regolith. The spent regolith leaves the heat exchanger close to the temperature of the cold new regolith, and the new regolith is pre-heated close to the initial temperature of the spent regolith. Using the CoRHE can reduce the heating requirement of a lunar ISRU system by 80%, reducing the total power consumption by a factor of two. The unique feature of this system is that it allows for counterflow heat exchange to occur between solids, instead of liquids or gases, as is commonly done. In addition, in variants of this concept, the hydrogen reduction can be made to occur within the counterflow heat exchanger itself, enabling a simplified lunar ISRU (in situ resource utilization) system with excellent energy economy and continuous nonbatch mode operation

Non-intrinsic origin of the Colossal Dielectric Constants in CaCu3Ti4O12

The dielectric properties of CaCu3Ti4O12, a material showing colossal values of the dielectric constant, were investigated in a broad temperature and frequency range extending up to 1.3 GHz. A detailed equivalent circuit analysis of the results and two crucial experiments, employing different types of contacts and varying sample thickness, provide clear evidence that the apparently high values of the dielectric constant in CaCu3Ti4O12 are non-intrinsic and due to electrode polarization effects. The intrinsic properties of CaCu3Ti4O12 are characterized by charge transport via hopping of localized charge carriers and a relatively high dielectric constant of the order of 100.Comment: 4 pages, 4 figure

Beta relaxation in the shear mechanics of equilibrium viscous liquids: Phenomenology and network modeling of the alpha-beta merging region

The phenomenology of the beta relaxation process in the shear-mechanical response of glass-forming liquids is summarized and compared to that of the dielectric beta process. Furthermore, we discuss how to model the observations by means of standard viscoelastic modeling elements. Necessary physical requirements to such a model are outlined, and it is argued that physically relevant models must be additive in the shear compliance of the alpha and beta parts. A model based on these considerations is proposed and fitted to data for Polyisobutylene 680.Comment: 8 pages, 6 figures, Minor correction

Plastic-crystalline solid-state electrolytes: Ionic conductivity and orientational dynamics in nitrile mixtures

Many plastic crystals, molecular solids with long-range, center-of-mass crystalline order but dynamic disorder of the molecular orientations, are known to exhibit exceptionally high ionic conductivity. This makes them promising candidates for applications as solid-state electrolytes, e.g., in batteries. Interestingly, it was found that the mixing of two different plastic-crystalline materials can considerably enhance the ionic dc conductivity, an important benchmark quantity for electrochemical applications. An example is the admixture of different nitriles to succinonitrile, the latter being one of the most prominent plastic-crystalline ionic conductors. However, until now only few such mixtures were studied. In the present work, we investigate succinonitrile mixed with malononitrile, adiponitrile, and pimelonitrile, to which 1 mol% of Li ions were added. Using differential scanning calorimetry and dielectric spectroscopy, we examine the phase behavior and the dipolar and ionic dynamics of these systems. We especially address the mixing-induced enhancement of the ionic conductivity and the coupling of the translational ionic mobility to the molecular reorientational dynamics, probably arising via a "revolving-door" mechanism.Comment: 9 pages, 7 figures; revised version as accepted for publication in J. Chem. Phy

Dielectric properties of charge ordered LuFe2O4 revisited: The apparent influence of contacts

We show results of broadband dielectric measurements on the charge ordered, proposed to be mul- tiferroic material LuFe2O4. The temperature and frequency dependence of the complex permittivity as investigated for temperatures above and below the charge-oder transition near T_CO ~ 320 K and for frequencies up to 1 GHz can be well described by a standard equivalent-circuit model considering Maxwell-Wagner-type contacts and hopping induced AC-conductivity. No pronounced contribution of intrinsic dipolar polarization could be found and thus the ferroelectric character of the charge order in LuFe2O4 has to be questioned.Comment: 4 pages, 3 figure

Dielectric behavior of Copper Tantalum Oxide

A thorough investigation of the dielectric properties of Cu2Ta4O12, a material crystallizing in a pseudo-cubic, perovskite-derived structure is presented. We measured the dielectric constant and conductivity of single crystals in an exceptionally broad frequency range up to GHz frequencies and at temperatures from 25 - 500 K. The detected dielectric constant is unusually high (reaching values up to 105) and almost constant in a broad frequency and temperature range. Cu2Ta4O12 possesses a crystal structure similar to CaCu3Ti4O12, the compound for which such an unusually high dielectric constant was first observed. An analysis of the results using a simple equivalent circuit and measurements with different types of contact revealed that extrinsic interfacial polarization effects, derived from surface barrier capacitors are the origin of the observed giant dielectric constants. The intrinsic properties of Cu2Ta4O12 are characterized by a (still relatively high) dielectric constant in the order of 100 and by charge transport via hopping conduction of Anderson-localized charge carriers.Comment: 18 pages, 6 figures, submitted to Jouranl of Physical Chemestr