Showing papers on "Debye published in 2022"

A Method to Measure Complex Dielectric Permittivity With Open-Ended Coaxial Probes

Abstract: This work presents a new method to measure the complex dielectric permittivity (CDP) variation of materials under test (MUTs) with open-ended coaxial probes. The CDP variation of an MUT is a continuous function of frequency as modeled with various dielectric relaxation models. Hence, the accuracy and the repeatability of CDP measurements can be improved by enforcing such spectral continuity. Here, we derive a new formulation that explicitly enforces the spectral continuity via the Debye relaxation model. In particular, we construct a cost functional based on an admittance integral at the tip of an open-ended coaxial probe. The Debye model parameters are substituted into the admittance integral to form a set of nonlinear equations. Later, these equations are iteratively minimized by a Gauss–Newton-based minimization scheme, for measured reflection coefficients when the tip of the probe is in contact with the MUT. The presented method differs from the conventional CDP measurement techniques in two aspects. First, the method looks for a global solution across the investigated frequency spectrum instead of solving CDP values individually at each frequency step. Second, the Debye parameters are directly retrieved without any data-fitting. The presented method is experimentally verified with various liquid samples, and the accuracy of obtained results is compared against the literature.

Li+ Conductivity of Space Charge Layers Formed at Electrified Interfaces Between a Model Solid-State Electrolyte and Blocking Au-Electrodes.

Abstract: The formation of space charge layers in solid-state ion conductors has been investigated as early as the 1980s. With the advent of all-solid-state batteries as an alternative to traditional Li-ion batteries, possibly improving performance and safety, the phenomenon of space charge formation caught the attention of researchers as a possible origin for the observed high interfacial resistance. Following classical space charge theory, such high resistances result from the formation of the depletion layers. These layers of up to hundreds of nanometers in thickness are almost free of mobile cations. With the prediction of a Debye-like screening effect, the thickness of the depletion layer is expected to scale with the square root of the absolute temperature. In this work, we studied the temperature dependence of the depletion layer properties in model solid Ohara LICGC Li+ conducting electrolytes using electrochemical impedance spectroscopy. We show that the activation energy inside the depletion layer increases to ca 0.42 eV compared to ca 0.39 eV in the bulk electrolyte. Moreover, the proportionality between temperature and depletion layer thickness, correlating to the Debye length, is tested and validated.

On the derivations of the Debye–Hückel equations

Abstract: This work presents the derivations of basic thermodynamic properties and activity coefficients equations from the linearised Poisson–Boltzmann equation. We consider two main approaches, the first one is based in classical thermodynamics, which has been used in the original work of Debye and Hückel, leading to the model which has been an important cornerstone of electrolyte thermodynamics since its original publication in 1923. The second approach relies on more modern derivations based on statistical mechanics, the so-called charging approaches. Both derivation routes have differences and shortcomings. We demonstrate the necessary steps to reach all original models derived from the Debye–Hückel model and further explore their capabilities and limitations concerning individual ion, and mean ionic activity coefficients for different size dissimilarities scenarios between ions. One immediate conclusion is that there is an unnecessary consideration in the Debye and Hückel derivation which is cancelled by another one they have made, leading to a correct expression for the activity coefficient. Also, the long-lasting consideration that both the Debye and Güntelberg charging processes lead to the same thermodynamic properties is demonstrated to be inaccurate, as it is rigorously true only when a common distance of closest approach is used. GRAPHICAL ABSTRACT

Dielectric Properties of Water in Charged Nanopores

Abstract: In this study, we examine the spectral dielectric properties of liquid water in charged nanopores over a wide range of frequencies (0.3 GHz to 30 THz) and pore widths (0.3 to 5 nm). This has been achieved using classical molecular dynamics simulations of hydrated Na-smectite, the prototypical swelling clay mineral. We observe a drastic (20-fold) and anisotropic decrease in the static relative permittivity of the system as the pore width decreases. This large decrement in static permittivity reflects a strong attenuation of the main Debye relaxation mode of liquid water. Remarkably, this strong attenuation entails very little change in the time scale of the collective relaxation. Our results indicate that water confined in charged nanopores is a distinct solvent with a much weaker collective nature than bulk liquid water, in agreement with recent observations of water in uncharged nanopores. Finally, we observe remarkable agreement between the dielectric properties of the simulated clay system against a compiled set of soil samples at various volumetric water contents. This implies that saturation may not be the sole property dictating the dielectric properties of soil samples, rather that the pore-size distribution of fully saturated nanopores may also play a critically important role.

The ω^3 scaling of the vibrational density of states in quasi-2D nanoconfined solids

Abstract: Atomic vibrations play a vital role in the functions of various physical, chemical, and biological systems. The vibrational properties and the specific heat of crystalline bulk materials are well described by Debye theory, which successfully predicts the quadratic $\omega^{2}$ low-frequency scaling of the vibrational density of states (VDOS) in bulk ordered solids from few fundamental assumptions. However, the analogous framework for nanoconfined materials with fewer degrees of freedom has been far less well explored. Using inelastic neutron scattering, we characterize the VDOS of amorphous ice confined to a thickness of $\approx 1$ nm inside graphene oxide membranes and we observe a crossover from the Debye $\omega^2$ scaling to an anomalous $\omega^3$ behaviour upon reducing the confinement size $L$. Additionally, using molecular dynamics simulations, we confirm the experimental findings and also prove that such a scaling of the VDOS appears in both crystalline and amorphous solids under slab-confinement. We theoretically demonstrate that this low-frequency $\omega^3$ law results from the geometric constraints on the momentum phase space induced by confinement along one spatial direction. Finally, we predict that the Debye scaling reappears at a characteristic frequency $\omega_\times= v L/2\pi$, with $v$ the speed of sound of the material, and we confirm this quantitative estimate with simulations. This new physical phenomenon, revealed by combining theoretical, experimental and simulations results, is relevant to a myriad of systems both in synthetic and biological contexts and it could impact various technological applications for systems under confinement such as nano-devices or thin films.

Diffusiophoresis of a highly charged dielectric fluid droplet induced by diffusion potential

Abstract: Diffusiophoresis of a dielectric fluid droplet in electrolyte solutions is investigated theoretically, focusing on the electrophoresis component resulting from the induced diffusion potential in the electrolyte solution when the diffusivities of cations and anions there are different. The resultant electrokinetic equations are solved with a pseudo-spectral method based on the Chebyshev polynomials. We found, among other things, that the electrophoresis component dominates at a larger Debye length, whereas the chemiphoresis component at a smaller Debye length for a dielectric droplet of a constant surface charge density. The two components are of comparable magnitudes in the NaCl solution. The dual between the spinning electric driving force tangent to the droplet surface and the hydrodynamic drag force reinforced by the motion-deterring electrokinetic Maxwell traction from the surrounding exterior osmosis flow is crucial in the determination of the ultimate droplet motion. Unlike the chemiphoresis component, which is independent of the sign of charges carried by the droplet, the droplet moving direction as well as its magnitude in the electrophoresis component depends on the sign of charges carried by the droplet as well as the direction of the electric field induced by the diffusion potential. This gives the electrophoresis component excellent maneuverability in practical applications like drug delivery and enhanced oil recovery, where migration of droplets toward regions of higher solute concentrations is often desired.

Classical Quantum Friction at Water–Carbon Interfaces

Abstract: Friction at water–carbon interfaces remains a major puzzle with theories and simulations unable to explain experimental trends in nanoscale waterflow. A recent theoretical framework—quantum friction (QF)—proposes to resolve these experimental observations by considering nonadiabatic coupling between dielectric fluctuations in water and graphitic surfaces. Here, using a classical model that enables fine-tuning of the solid’s dielectric spectrum, we provide evidence from simulations in general support of QF. In particular, as features in the solid’s dielectric spectrum begin to overlap with water’s librational and Debye modes, we find an increase in friction in line with that proposed by QF. At the microscopic level, we find that this contribution to friction manifests more distinctly in the dynamics of the solid’s charge density than that of water. Our findings suggest that experimental signatures of QF may be more pronounced in the solid’s response rather than liquid water’s.

Orientation Polarization Spectroscopy—Toward an Atomistic Understanding of Dielectric Relaxation Processes

Abstract: The theory of orientation polarization and dielectric relaxation was developed by P. Debye more than 100 years ago. It is based on approximating a molecule by a sphere having one or more dipole moments. By that the detailed intra- and intermolecular interactions are explicitly not taken into consideration. In this article, the principal limitations of the Debye approximation are discussed. Taking advantage of the molecular specificity of the infrared (IR) spectral range, measurements of the specific IR absorption of the stretching vibration υ(OH) (at 3370 cm−1) and the asymmetric υas(CH2) (at 2862.9 cm−1) are performed in dependence on the frequency and the strength of external electric fields and at varying temperature. The observed effects are interpreted as caused by orientation polarization of the OH and the adjacent CH2 moieties.

The Debye temperatures of the constituents of a composite superconductor

Abstract: Born and Karman had pointed out a long time ago that a composite anisotropic solid must be characterized by multiple Debye temperatures (DTs). Since all non-elemental superconductors (SCs) are similar materials, we deal here with the problem of resolving the DT of a composite SC– usually given as single value --- into the DTs of its constituents. These DTs are a primary requirement for the application of the generalized BCS equations which have been shown to shed light on several properties of not only the high-Tc SCs, but also a variety of others such as SrTiO3 and the so-called exotic Fe-based heavy-fermion SCs which have been a serious concern for theoreticians for a long time. The SCs dealt with here are MgB2, YBCO, Tl-2212 and Bi-2212.

Critical screening parameters of one-electron systems with screened Coulomb potentials: high Rydberg limit

Abstract: We develop an efficient numerical method to directly calculate the critical screening parameters for one-electron systems with Hulthén and Debye–Hückel screened Coulomb potentials (SCPs). Compared to indirect methods, which locate the critical screening parameters via searching the potential parameters with near-zero energy, the method developed in this work directly calculates the critical screening parameters as eigenvalues of a generalized eigenvalue problem. This feature allows us to simultaneously determine the critical parameters for bound states from low-lying excitation to high-lying Rydberg limit with high accuracy. The method is applied to SCPs to investigate the asymptotic behavior of critical screening parameters as the principal quantum number n approaches infinity. It has been shown that the critical screening parameters in Hulthén and Debye–Hückel potentials follow the 2n −2 and 4n −2/π asymptotic laws, respectively, and that the orbital angular momentum affects the higher-order coefficients linearly.

Structural Universalities in a Two-Dimensional Yukawa Fluid

Abstract: The structural properties of a two-dimensional fluid in a wide range of the screening parameter κ are considered by example of a Debye–Hückel (Yukawa) system. The behavior of structural indicators appears universal and is independent of the screening parameter κ. This property makes it possible, in particular, to easily and noninvasively determine the key parameters of the interparticle interaction from the configuration of particles observed in experiments with complex (dusty) and colloidal plasmas.

Atomic Processes, Including Photoabsorption, Subject to Outside Charge-Neutral Plasma

Abstract: We present in this review our recent theoretical studies on atomic processes subject to the plasma environment including the α and β emissions and the ground state photoabsorption of the one- and two-electron atoms and ions. By carefully examining the spatial and temporal criteria of the Debye–Hückel (DH) approximation based on the classical Maxwell–Boltzmann statistics, we were able to represent the plasma effect with a Debye–Hückel screening potential VDH in terms of the Debye length D, which is linked to the ratio between the plasma density N and its temperature kT. Our theoretical data generated with VDH from the detailed non-relativistic and relativistic multiconfiguration atomic structure calculations compare well with the limited measured results from the most recent experiments. Starting from the quasi-hydrogenic picture, we were able to show qualitatively that the energy shifts of the emission lines could be expressed in terms of a general expression as a function of a modified parameter, i.e., the reduced Debye length λ. The close agreement between theory and experiment from our study may help to facilitate the plasma diagnostics to determine the electron density and the temperature of the outside plasma.

Scaling of the non-phononic spectrum of two-dimensional glasses.

Abstract: Low-frequency vibrational harmonic modes of glasses are frequently used to rationalize their universal low-temperature properties. One well studied feature is the excess low-frequency density of states over the Debye model prediction. Here, we examine the system size dependence of the density of states for two-dimensional glasses. For systems of fewer than 100 particles, the density of states scales with the system size as if all the modes were plane-wave-like. However, for systems greater than 100 particles, we find a different system-size scaling of the cumulative density of states below the first transverse sound mode frequency, which can be derived from the assumption that these modes are quasi-localized. Moreover, for systems greater than 100 particles, we find that the cumulative density of states scales with the frequency as a power law with the exponent that leads to the exponent β = 3.5 for the density of states. For systems whose sizes were investigated, we do not see a size-dependence of exponent β.

Comment on “Stark shift and width of x-ray lines from highly charged ions in dense plasmas”

Abstract: We point out in this Comment a misleading remark made by Gu and Beiersdorfer [Phys. Rev. A 101, 032501 (2020)] that the Debye-H\"uckel (DH) model ``performs rather poorly'' compared with the ion sphere model is due to their questionable use of the Debye length by assuming the same mobility for the plasma electrons and ions. Actually, our recent works based on a judicious application of the DH approximation, which meets the spatial and temporal criteria, have led to good agreements with all the available line shift experimental measurements on $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ emission lines of He-like ions.

Boson-peak vibrational modes in glasses feature hybridized phononic and quasilocalized excitations.

Abstract: A hallmark of structural glasses and other disordered solids is the emergence of excess low-frequency vibrations on top of the Debye spectrum DDebye(ω) of phonons (ω denotes the vibrational frequency), which exist in any solid whose Hamiltonian is translationally invariant. These excess vibrations-a signature of which is a THz peak in the reduced density of states D(ω)/DDebye(ω), known as the boson peak-have resisted a complete theoretical understanding for decades. Here, we provide direct numerical evidence that vibrations near the boson peak consist of hybridizations of phonons with many quasilocalized excitations; the latter have recently been shown to generically populate the low-frequency tail of the vibrational spectra of structural glasses quenched from a melt and of disordered crystals. Our results suggest that quasilocalized excitations exist up to and in the vicinity of the boson-peak frequency and, hence, constitute the fundamental building blocks of the excess vibrational modes in glasses.

The Effect of Dielectric Relaxation Processes on the Complex Dielectric Permittivity of Soils at Frequencies From 10 kHz to 8 GHz—Part I: Experimental

Abstract: This is the first of two articles that present experimental spectra of six soil samples with varying clay contents ranging from 0 to 55% and organic carbon levels ranging from 0 to 3.9%, measured at a small step of moisture change at a temperature of 25°C. The study was carried out using a method that enables measurements of the same sample over a wide frequency range of 1 kHz to 8.5 GHz, and in some cases up to 20 GHz. The relative effective complex dielectric permittivity (RCP) is strongly influenced by dielectric relaxation processes due to the Maxwell-Wagner effect in the frequency range of 10 kHz to 8.5 GHz, as demonstrated. These processes are aided by the presence of clay in the soil. Up to frequencies of 4-5 GHz, these processes have a weak influence, mainly on the imaginary part of the RCP. This explains why in the dielectric models of Dobson and Mironov, where relaxation processes are ignored, free and physical bound water have high specific conductivity. We demonstrated that organic carbon, even at low content, reduces the real and imaginary parts of the RCP when all other factors are equal. Part II will present the results of using the Debye and Cole-Cole formulas to model relaxation processes.

Screening Nitrides with High Debye Temperatures as Nonlinear Optical Materials

Abstract: Nitrides, in which P in pnictides is substituted by N, are proposed as nonlinear optical (NLO) materials. Herein, 34 asymmetric nitrides collected in the Inorganic Crystal Structure Database (ICSD) are evaluated and predicted by first-principles calculations. As a result, three Si-nitrides possessing wide band gaps and large NLO coefficients are screened out: BeSiN2 (6.66 eV, d24 = −1.09 pm/V), LiSi2N3 (6.51 eV, d15 = −1.38 pm/V), and LaSi3N5 (4.73 eV, d14 = −0.98 pm/V). In addition, LiGaS2-like structure MoZn3N4 is a promising infrared NLO material with a large NLO coefficient d24 = −16.70 pm/V, which is 1.2 times that of the infrared benchmark AgGaS2 (d36 = 13.4 pm/V); meanwhile, its band gap of 3.05 eV is better than that of AgGaS2 (2.73 eV). Moreover, MoZn3N4 with a higher Debye temperature of 795.5 K, which suggests higher sound speeds and longer phonon lifetimes, thus should exhibit higher thermal conductivity. These nitrides represent a new exploration family of NLO materials.

Small-angle X-ray scattering: characterization of cubic Au nanoparticles using Debye's scattering formula

Abstract: A versatile software package in the form of a Python extension, named CDEF (computing Debye's scattering formula for extraordinary form factors), is proposed to calculate approximate scattering profiles of arbitrarily shaped nanoparticles for small-angle X-ray scattering (SAXS). CDEF generates a quasi-randomly distributed point cloud in the desired particle shape and then applies the open-source software DEBYER for efficient evaluation of Debye's scattering formula to calculate the SAXS pattern (https://github.com/j-from-b/CDEF). If self-correlation of the scattering signal is not omitted, the quasi-random distribution provides faster convergence compared with a true-random distribution of the scatterers, especially at higher momentum transfer. The usage of the software is demonstrated for the evaluation of scattering data of Au nanocubes with rounded edges, which were measured at the four-crystal monochromator beamline of PTB at the synchrotron radiation facility BESSY II in Berlin. The implementation is fast enough to run on a single desktop computer and perform model fits within minutes. The accuracy of the method was analyzed by comparison with analytically known form factors and verified with another implementation, the SPONGE , based on a similar principle with fewer approximations. Additionally, the SPONGE coupled to McSAS3 allows one to retrieve information on the uncertainty of the size distribution using a Monte Carlo uncertainty estimation algorithm.

Single molecule demonstration of Debye–Stokes–Einstein breakdown in polystyrene near the glass transition temperature

Abstract: Rotational-translational decoupling, in which translational motion is apparently enhanced over rotational motion in violation of Stokes-Einstein (SE) and Debye-Stokes-Einstein (DSE) predictions, has been observed in materials near their glass transition temperatures (Tg). This has been posited to result from ensemble averaging in the context of dynamic heterogeneity. In this work, ensemble and single molecule experiments are performed in parallel on a fluorescent probe in high molecular weight polystyrene near its Tg. Ensemble results show decoupling onset at approximately 1.15Tg, increasing to over three orders of magnitude at Tg. Single molecule measurements also show a high degree of decoupling, with typical molecules at Tg showing translational diffusion coefficients nearly 400 times higher than expected from SE/DSE predictions. At the single molecule level, higher degree of breakdown is associated with particularly mobile molecules and anisotropic trajectories, providing support for anomalous diffusion as a critical driver of rotational-translational decoupling and SE/DSE breakdown.

Single molecule demonstration of Debye–Stokes–Einstein breakdown in polystyrene near the glass transition temperature

Abstract: Rotational-translational decoupling, in which translational motion is apparently enhanced over rotational motion in violation of Stokes-Einstein (SE) and Debye-Stokes-Einstein (DSE) predictions, has been observed in materials near their glass transition temperatures (Tg). This has been posited to result from ensemble averaging in the context of dynamic heterogeneity. In this work, ensemble and single molecule experiments are performed in parallel on a fluorescent probe in high molecular weight polystyrene near its Tg. Ensemble results show decoupling onset at approximately 1.15Tg, increasing to over three orders of magnitude at Tg. Single molecule measurements also show a high degree of decoupling, with typical molecules at Tg showing translational diffusion coefficients nearly 400 times higher than expected from SE/DSE predictions. At the single molecule level, higher degree of breakdown is associated with particularly mobile molecules and anisotropic trajectories, providing support for anomalous diffusion as a critical driver of rotational-translational decoupling and SE/DSE breakdown.

Debye-series expansion of T-matrix for light scattering by non-spherical particles computed from Riccati-differential equations.

Abstract: A new formulation of the Debye series based on the Riccati-differential equations was developed to compute electromagnetic wave scattering by non-spherical particles. In this formulation, the T-matrix was expanded in terms of the Debye series. The zeroth-order term, which corresponds to a combination of diffraction and external reflection, is given by unity minus the external reflection matrix. The higher-order terms are generated from the transmission matrix from the medium to the particle, the internal reflection matrix within the particle and the transmission matrix from the particle to the medium. We demonstrate that the aforementioned four reflection-transmission matrices satisfy the Riccati-differential equations, which can be numerically solved by the fourth-order Runge-Kutta method. The present algorithm can be applied to generalized convex non-spherical particles. The differential equations were analytically validated in the case of a homogeneous sphere. Representative results were given in the case of spheroids. The impacts of the Debye series with various orders on the optical properties of spheroids were revealed with significant details.

A semi-empirical correction for the Rayleigh-Debye-Gans approximation for fractal aggregates based on phasor analysis: Application to soot particles

Abstract: • The internal electric field of fractal aggregates is studied with a phasor approach. • Internal coupling and absorption explain the RDG-FA discrepancies for large aggregates. • Aggregate size, monomer radius, refractive index, and wavelength dependencies are investigated. • Semi-empirical corrections for the RDG-FA derived forward-scattering and absorption are proposed. The Rayleigh Debye-Gans approximation for Fractal Aggregates (RDG-FA) is commonly used for the evaluation of the radiative properties of fractal aggregates of nanometer-scale nearly spherical particles as soot particles. The cost of its simplicity, however, is the precision of the aggregate cross sections when the refractive index deviates from unity and when the aggregate’s spheres, or monomers, are not sufficiently small compared to the wavelength. While correction factors have been highlighted before, their physical origin is not clear and no universal correction factors are proposed. The present study develops an approach based on phasor analysis of the aggregate’s internal electric field rigorously determined by the discrete dipole approximation. Aggregates representative of the Diffusion Limited Cluster Aggregation (DLCA) regime having a fractal dimension of D f = 1.78 are considered as representative of a soot aggregate. The results reveal that correction factors to the RDG-FA for forward scattering ( A ) and the absorption cross section ( h ) are due to a competition between internal-field hot-spots caused by point contact between the spherical monomers and a decrease of the field amplitude as the field propagates through the aggregate. Both phenomena are neglected in the RDF-FA by definition. The absorption phenomenon explains the aggregate-size dependence of A and h . These effects are then studied as the aggregate size varies according to the number of monomers N m ranging from 10 to 1000, as the monomer radius varies from R m = 5 nm - 30 nm , and as the wavelength varies from λ = 266 nm - 1064 nm . Both constant and wavelength dependent refractive indices for organic, graphitic, and amorphous soot are considered. Finally, a semi-empirical model is proposed intended to correct the RDG-FA theory based on the analysis.