Showing papers on "Debye published in 1989"

Outer‐sphere electron transfer reactions in non‐Debye solvents. Theory and numerical results

Abstract: In this paper we present a theory that predicts, for a wide range of reaction adiabaticity, the time evolution of the reactants’ population, σR(t), for outer‐sphere electron transfer reactions in polar solvents exhibiting a non‐Debye relaxation behavior. A number of stochastic trajectory studies have been performed to test the validity of the theory in the limit where solvent relaxation constitutes the rate‐limiting step. The agreement between the numerical and theoretical results is excellent. The theory is then used to study a number of different reactive regimes ranging from nonadiabatic to solvent‐controlled adiabatic limits. The studies performed show that the character of the decay of σR(t) for low activation barrier reactions constitutes a useful qualitative way of identifying a priori the dielectric relaxation properties of the solvent: For a non‐Debye solvent the decay of σR(t) is strongly nonexponential in contrast to the results for Debye solvents where σR(t) decays mainly exponentially. The so...

Modal characteristics of three-layered optical fiber waveguides: a modified approach

Abstract: By invoking Debye potentials, we formulate exact eigenvalue equations and the corresponding field distributions for general, three-layered, radially stratified, dielectric, and nonferromagnetic metal, optical fibers. By using cross products of Bessel functions, which may be regarded as the basic functional elements of the eigenvalue equations, a comparison is made between the properties of a three-layer structure and a simple step-index profile, and a simple graphical solution is obtained. The technique is applied to several practical structures, including two-layer fibers having a central index depression in the core, ring-core fibers, W fibers, and progressively stepped three-layered structures. The mathematical procedure is simple, and the results are of interest to optical fiber designers.

Time resolved Stark spectroscopy in NaK(B 1Π; V=1–14). Measurement of permanent electric dipole, radiative lifetimes, and collisional rate constants

Abstract: The permanent dipole moment μ of NaK(B 1Π) has been determined for several vibrational levels by observing the electric field induced e–f mixing using either cw or pulsed laser excitation. In the latter case the spectrally resolved fluorescence decay is modulated by ‘‘Stark quantum beats.’’ We find μ(Re) =2.4 (2) Debye. The measurement of the fluorescence decay rates in zero electric field vs buffer gas pressure (rare gases, N2) yields radiative lifetimes and depopulation cross sections. The dependence of the lifetime τ with the vibrational index V can be represented by the expression: τ(V)=12.8+0.46 V ns. It is consistent with a transition dipole moment between the B 1Π and X 1Σ+ states almost independent of the internuclear distance, close to the value of the K(4P–4S) transition which corresponds to the dissociation limits of the molecular states.

Casimir force on a solid ball when epsilon ( omega ) micro( omega )=1. Finite temperatures.

Abstract: The Casimir surface force on a solid ball is calculated, assuming the material to be dispersive and to be satisfying the condition epsilon(..omega..)..mu..(..omega..) = 1, epsilon(..omega..) being the spectral permittivity and ..mu..(..omega..) the spectral permeability. A recent paper by Brevik and Einevoll (Phys. Rev. D 37, 2977 (1988)) discussed this problem at zero temperature. In this paper, the case of finite temperatures is covered. The analysis is based upon use of the Debye expansion of the modified Bessel functions. This expansion, being an asymptotic one, is limited in accuracy. At general temperatures, the expansion shows an oscillatory variation on the second-order level. Such a variation is unphysical, so that the physical information that one can extract from second-order theory is limited. On the zeroth-order level, the formalism is, however, found to work well. We discuss the zeroth-order approximation in complete form and comment upon the second-order correction. Although numerical methods are in general necessary, useful analytic approximations can be obtained in the limiting cases of very low, or very high, nondimensional temperatures. At low temperatures, the dispersive effect induces a strong, attractive contribution to the force. At high temperatures, the force becomes small.

Non-Debye enhancements in the Mie scattering of light from a single water droplet.

Abstract: The glare spots usually seen on a single water droplet which has been illuminated by a plane wave are produced by geometrical rays which correspond to the different terms of the Debye series expansion of the Mie scattered field. Recently other glare spot enhancements have been predicted which correspond to scattering resonances coupling to the orbiting rays associated with high-order geometrical rainbows. We observed the non-Debye enhancement of the eleventh-order rainbow glare spot at an observation angle of 90° on a 3.5-mm water droplet illuminated by polarized He–Ne laser light.

Water concentration and dielectric permittivity in molecular crevices

Abstract: The behaviour of electric dipoles (water molecules) under the action of a high and nonuniform electric field is investigated. The model incorporates all the features of Clausius-Mossotti’s Debye’s, Onsager’s and Kirkwood’s approaches, and assumes, as a novel feature, that the dielectrophoretic drift of dipoles is balanced by dipole diffusion. A new relationship among local permittivity, electric field and water density is found that could explain why water molecules are rejected by charged molecular crevices which can engineer the binding of ionized ligands at very high rates as compared to bulk water.

Diffuse inelastic scattering of atoms from surfaces

Abstract: We consider the large-angle diffuse scattering of thermal-energy atoms by defects or adsorbates on a surface. We obtain the Debye-Waller factor for the thermal attenuation of the incoherent elastic peak. When the Debye exponent is small, the diffuse inelastic contribution is dominated by the single-phonon exchange, and is proportional to the frequency distribution function of the defect or adsorbate. We discuss its magnitude compared to the multiphonon background.

On the Role of Inertial Effects and Dipole-Dipole Coupling in the Theory of the Debye and Far-Infrared Absorption of Polar Fluids III. The Cosine Potential Itinerant Oscillator Model

Abstract: The polarizability and dynamic mobility for the itinerant oscillator model are calculated when the restriction to small oscillations is removed so that effects due to the cosine potential may be evaluated. The calculation is effected by expressing the Fokker-Planck equation for equal frictions per unit inertia in terms of sum and difference angular variables. The sum angle, $\chi$, yields the Fokker-Planck equation for a free rotator, the correlation functions of which are available in closed form. The difference angle, $\eta$, yields the Fokker-Planck equation for a rotator in a cosine potential. This equation is solved by the method of separation of the variables. The resulting set of differential-difference equations for the time responses is solved by using Reid's numerical algorithm. The complex polarizability is then evaluated from the numerical results by assuming that the moment of inertia of the dipole is very much less than that of the cage in accordance with the basic concept of the model. Unlike the complex polarizability, the dynamic mobility may be evaluated from the numerical results without any assumption about the inertia ratios.The polarizabilities computed for the cosine potential are compared with the small oscillation polarizabilities for the same parameter values. It is found that the cosine potential gives rise to (i) substantial absorption at frequencies between the microwave and far-infrared (Fro), bands (ii) an increase in the frequency of the maximum microwave absorption (iii) a decrease in the frequency of the maximum Pm absorption (iv) a much more rapid fall-off of the FIR absorption. If the barrier height parameter becomes large, the intermediate frequency absorption disappears and the effect of the cosine potential manifests itself as a shoulder on the FIR absorption. An approximate formula for the polarizability in terms of the Fourier transform of the angular velocity correlation function is shown to be satisfactory for small oscillations only. The theoretical results are in qualitative agreement with experimental observations on methyl chloride.

The low-temperature behaviour of the pyroelectric coefficient

Abstract: The results of both theoretical and experimental investigations of the temperature dependence of the pyroelectric coefficient γδ (T) are given. It is shown that in ideal crystals the γδ (T) may be represented by the sum of Debye's and Einstein's functions, which describe the contributions of acoustic and optical modes, respectively. Experimentally obtained γδ (T) dependences for different kinds of linear pyroelectrics and ferroelectrics are listed. The experimental data for linear pyroelectrics (except the region of the lowest temperatures) are described well by the mentioned sum of Debye's and Einstein's functions. In ferroelectrics the acoustic modes contribution to the γδ (T) is not found out in the frames of the accuracy of measurements. The simple estimations of the coefficient of anharmonicity and of the nonlinear dipole moment show that in ferroelectrics the relative contribution of the optical modes is greater than of the acoustic ones to the extent of the ratio (ω D /ω oj )2, where ω D i...

Free energy of an inhomogeneous polymer-polymer-solvent system

Abstract: The free energy of an inhomogeneous polymer-polymer-solvent system has been obtained by extending Debye's approach for a polymer-solvent system. Our ternary result reduces to Debye's result for a binary polymer-solvent system and to McMaster's result for a binary polymer-polymer system at the appropriate limits. Like Debye's work, we neglect the entropic gradient contribution to free energy. Based on the ternary result we suggest a generalized expression for the free energy of multiple polymers dissolved in a common solvent. This expression is used to find the free energy of an inhomogeneous polydispersed polymer-solvent system.

Temperature dependence of static heavy quark potential

Abstract: T-dependence of the static heavy quark potential has been studied by an extensive numerical simulation of lattice QCD. The potential is measured from the correlations of Wilson lines. The potential below T c fits the expectation of the string picture very well and it is of the form of a linear-type plus a Coulomb term ( N t ≥6). A Yukawa potential from a Debye screening picture replaces it above the phase transition, which seems to agree with the expectation based on perturbative results, especially when T is much larger than T c .

Approximate solution of the Debye-Smoluchowski equation for geminate ion recombination in solvents of low permittivity

Abstract: The time-dependent geminate ion recombination probability is investigated under conditions suitable for describing recombination in low permittivity solvents. A ‘reverse’ diffusion process is introduced, whose spatial distribution function is identical to the reaction time distribution function conditioned on ultimate reaction. This process is used to provide various orders of deterministic approximation, which are compared with the median reaction time. The reverse process is also used to obtain short time asymptotic formulae for the spatial moments, which allow the introduction of a variance. The variance found by this method is found to be anomalously small, but to be in good agreement with numerical solution. An interpretation of this result is proposed.

Dispersion and dynamics of third-order electric polarisation in liquids within Smoluchowski-Debye theory☆

Abstract: Dispersion and absorption of third-order nonlinear electric susceptibilities in liquids as well as their time-transients are analyzed applying Smoluchowski's equation of rotational diffusion in the form proposed by Debye in his known dielectric relaxation theory of dipolar liquids. On the basis of solutions derived by method of statistical perturbation calculus, the real and imaginary components of nonlinear susceptibility are plotted versus the frequency of the externally applied cosine reorienting field.

Microwave dielectric dispersion in diglycine nitrate

Abstract: The paper presents the results of the investigation of the dielectric dispersion in diglycine nitrate crystals over the frequency range 1 MHz to 54 GHz. It is shown that the ferroelectric dispersion of the Debye type along the polar [101] direction is in the frequency range 108 to 1011 Hz and it is caused by the single relaxational soft mode. The frequency of the “flipping” proton mode in the paraelectric phase on approaching Tc varies according to γs = 0.34 (T - Tc ) GHz and makes the main contribution to the static permittivity which fits the Curie-Weiss law with the Curie constant C = 845 K. The magnitude of the activation energy of dipole reversal is found to be δU = 1.6 kTc . The results confirm the order-disorder type of ferroelectric phase transition.

Dielectric dispersion in Li2Ge7O15

Abstract: The complex dielectric constant of Li2Ge7O15 crystal has been measured at frequencies from 21 MHz to 7 GHz around the Curie temperature Tc. The dielectric dispersion of the Debye type has been found. A critical slowing-down of dielectric response has been observed, and the relaxation frequency decreases to about 1 GHz at Tc. The origin of the Debye dispersion observed in the vicinity of Tc is discussed in connection with the resonant type dispersion of soft optical phonon mode.

Low frequency vibrational modes in the glassy state of 1-cyanoadamantane: The density of states from incoherent neutron scattering

Abstract: From inelastic neutron scattering the density of vibrational states of 1-cyanoadamantane has been measured both in its low-temperature monoclinic phase and its glassy phase. A strong increase in the low-frequency part of the spectrum in the glassy state with respect to the ordered state is shown. While in the monoclinic state, the power dependence as a function of the energy exchange agrees with the usual Debye law, in the glassy state a noticeable deviation appears.

A Finite-Difference Frequency-Domain (FD-FD) Approach To Electromagnetic Scattering Problems

Abstract: A finite-difference, frequency-domain (FD-FD) approach to electromagnetic wave scattering is presented. This approach evolved from recent progress that features the concept of generalized scattering amplitudes, the application of boundary-fitted curvilinear coordinate systems, and the use of Debye potentials for 3-D obstacle scatterings. The introduction of the radially non-oscillatory generalized scattering amplitudes circumvents the difficulties in dealing with oscillatory field quantities in the infinite exterior scattering region and allows the finite-difference method to be applied to scattering problems in an effective manner. The radiation condition in terms of the generalized scattering amplitude is very simple in form and can be enforced exactly in the far field. For a 3-D scattering problem the formulation in terms of Debye potentials, expressed as functions of body-fitted coordinates, not only decouples the vector scattering problem into a combination of two independent scalar scattering proble...

On the influence of Debye shielding on the Stark broadening of ion lines within the classical model

Abstract: The influence of Debye shielding on the Stark lineshift to width ratio is demonstrated in the case of ion lines. The Coulomb cut-off potential, especially suitable for a non-ideal plasma and for higher densities, has been used.

The Shape of the Multi‐Plasmon Radiation Band in Direct Gap Semiconductors

Abstract: The form-functions of the multi-plasmon light absorption spectra are obtained using the fluctuation-dissipation theorem. Transitions with photon and plasmon absorption leads to the absorption edge shift into the longwavelength spectrum region obeying Urbach's rule. It is shown, that the ground state exciton interaction with plasmons is weak due to the smallness of the Bohr radius compared to the Debye screening radius. The band shape of the multi-plasmon own radiation of the nondegenerative electron—hole plasma is calculated. Multiplasmon transitions are direct ones whereas the radiation band consists of the superposition of equidistant Maxwell bands being apart from each other by the plasmon frequency. The amount of the multi-plasmon satellites depends on the value of the plasma emission constant and plasma temperature. Indirect multiplasmon transitions lead to more abrupt radiation intensity decay at the short wave edge of the band. It is shown that plasmon dispersion leads to the shift of the peak value positions of the single-plasmon satellites. The theory of multi-plasmon transitions in semiconductors developed with account of the LO phonon replicas coincides with experimental data. [Russian Text Ignored].

Large-Debye-distance effects in a homogeneous plasma

Abstract: The classical phenomenon of electron plasma oscillations has been investigated from new aspects. The applicability of standard normal-mode analysis of plasma perturbations has been judged from comparisons with exact numerical solutions to the linearized initial-value problem. We consider both Maxwellian and non-Maxwellian velocity distributions. Emphasis is on perturbations for which αλD is of order unity, where α is the wavenumber and λD the Debye distance. The corresponding large-Debye-distance (LDD) damping is found to substantially dominate over Landau damping. This limits the applicability of normal-mode analysis of non-Maxwellian distributions. The physics of LDD damping and its close connection to large-Larmor-radius (LLR) damping is discussed. A major discovery concerns perturbations of plasmas with non-Maxwellian, bump-in-tail, velocity distribution functions f0(ω). For sufficiently large αλD (of order unity) the plasma responds by damping perturbations that are initially unstable in the Landau sense, i.e. with phase velocities initially in the interval where df0/dw > 0. It is found that the plasma responds through shifting the phase velocity above the upper velocity limit of this interval. This is shown to be due to a resonance with the drifting electrons of the bump, and explains the Penrose criterion.

Crystal Dynamics of F.C.C. Inert Gas Solids

Abstract: Results for the phonon dispersion curves along the [ζ00], [ζζ0], [ζζζ], symmetry directions and the Debye characteristic temperatures for Ne, Ar, Kr, and Xe rare gas solids are obtained on the basis of a five-parameter non-central force model. These results are compared with the experimental values with remarkable success. The Cauchy discrepancy is also explained on the basis of the model.