Debye Relaxation Process Research Articles

Dynamics of supercooled liquid and plastic crystalline ethanol: Dielectric relaxation and AC nanocalorimetry distinguish structural α- and Debye relaxation processes.

Physical vapor deposition has been used to prepare glasses of ethanol. Upon heating, the glasses transformed into the supercooled liquid phase and then crystallized into the plastic crystal phase. The dynamic glass transition of the supercooled liquid is successfully measured by AC nanocalorimetry, and preliminary results for the plastic crystal are obtained. The frequency dependences of these dynamic glass transitions observed by AC nanocalorimetry are in disagreement with conclusions from previously published dielectric spectra of ethanol. Existing dielectric loss spectra have been carefully re-evaluated considering a Debye peak, which is a typical feature in the dielectric loss spectra of monohydroxy alcohols. The re-evaluated dielectric fits reveal a prominent dielectric Debye peak, a smaller and asymmetrically broadened peak, which is identified as the signature of the structural α-relaxation and a Johari-Goldstein secondary relaxation process. This new assignment of the dielectric processes is supported by the observation that the AC nanocalorimetry dynamic glass transition temperature, Tα, coincides with the dielectric structural α-relaxation process rather than the Debye process. The combined results from dielectric spectroscopy and AC nanocalorimetry on the plastic crystal of ethanol suggest the occurrence of a Debye process also in the plastic crystal phase.

The Lorenzo–Hartley’s function for fractional calculus and its applications pertaining to fractional order modelling of anomalous relaxation in dielectrics

Considering the applications and a great significance of the study pertaining to generalized functions in applied sciences, the author investigated the Lorenzo–Hartley’s function which is a generalization of classical functions widely used in fractional calculus. The Laplace transform pairs are derived and the requirements for the Lorenzo–Hartley’s function $$G_{\nu , \mu ,\delta }(a,c,t)$$ to be completely monotonic (for $$t > 0$$ ) are investigated. The author has shown the applications of this generalized function to describe the relaxation models, particularly in dielectrics. The Lorenzo–Hartley’s function $$G_{\nu , \mu ,\delta }(a,c,t)$$ of a real variable t is considered to investigate a computable mathematical framework for standard Debye and non-Debye relaxation processes in dielectric materials. The non-negative spectral distribution function is obtained for the corresponding response function. It is also demonstrated that the classical models like Cole–Cole (C–C), Davidson–Cole (D–C), and Havriliak–Negami (H–N) for non-Debye relaxation and standard Debye relaxation are the particular cases of the Lorenzo–Hartley’s function. Some of the study cases are also worked out to visualize the effects of variations of parameters on the response function and corresponding spectral distribution function. A generalized and unified fractional relaxation differential equation which governs response functions for classical dielectrics models pertaining to non-Debye relaxation (C–C, D–C, and H–N) is also established in the present investigation.

Broadband terahertz dielectric spectroscopy of alcohols

We have studied the complex dielectric properties of a series of alcohols in 0.5–10THz frequency range using THz time-domain spectroscopy. The dielectric response observed has contribution from a Debye relaxation process and three damped harmonic oscillators. Combination of experimental observations, all-atom molecular dynamics simulations and ab initio quantum calculations reveals that the complex dielectric spectra of alcohols result from a complex dynamics involving vibrational motions of several atoms across multiple interacting alcohol molecules. The major contribution comes from the fast hydrogen-bond rupture and reformation dynamics, the motion of alkyl chains, and the motions of the H-bonded OH groups.

High temperature structural phase transition and dielectric relaxation in an organic–inorganic hybrid compound: (4-methylpiperidinium)CdCl3

A new organic–inorganic hybrid perovskite-type compound, (4-MPD)CdCl3 (1, 4-MPD = 4-methylpiperidinium), demonstrating high temperature phase transition at around 364 K and prominent dielectric relaxation behavior, can be considered as a potential high temperature relaxor-type dielectric material. Systematic characterization techniques have been performed including variable-temperature structural analyses, differential scanning calorimetry (DSC) measurements, dielectric measurements and powder X-ray diffraction (PXRD) measurements. The structural phase transition coupled with the dielectric relaxation property is mainly ascribed to the order–disorder changes of organic cations. The studies of dielectric relaxation between 25 kHz and 1000 kHz disclose a significant Debye relaxation process above room temperature, which is well fitted by the Cole–Cole function.

How Different Molecular Architectures Influence the Dynamics of H-Bonded Structures in Glass-Forming Monohydroxy Alcohols.

Primary alcohols have been an active area of research since the beginning of the 20th century. The main problem in studying monohydroxy alcohols is the molecular origin of the slower Debye relaxation, whereas the faster process, recognized as structural relaxation, remains much less investigated. This is because in many primary alcohols the structural process is strongly overlapped by the dominating Debye relaxation. Additionally, there is still no answer for many fundamental questions concerning the origin of the molecular characteristic properties of these materials. One of them is the role of molecular architecture in the formation of hydrogen-bonded structures and its potential connection to the relaxation dynamics of Debye and structural relaxation processes. In this article, we present the results of ambient and high-pressure dielectric studies of monohydroxy alcohols with similar chemical structures but different carbon chain lengths (2-ethyl-1-butanol and 2-ethyl-1-hexanol) and positions of the OH- group (2-methyl-2-hexanol and 2-methyl-3-hexanol). New data are compared with previously collected results for 5-methyl-2-hexanol. We note that differences in molecular architecture have a significant influence on the formation of hydrogen-bonded structures, which is reflected in the behavior of the Debye and structural relaxation processes. Intriguingly, studying the relaxation dynamics in monohydroxy alcohols at high pressures of up to p = 1700 MPa delivers a fundamental bridge to understand the potential connection between molecular conformation and its response to the characteristic properties of these materials.

Electrospun SnO2 submicron fibers for broadband microwave absorption

Reflection loss and absorbing width are two important parameters to estimate the performance of microwave absorbing materials. Previous research has often paid much attention on the former but limited interest has been gained for the later. Here we present electrospun SnO2 submicron fibers as a broadband microwave absorbing material in this paper. SnO2 fibers and tubes were prepared by the electrospinning method, and their microwave absorption properties are investigated in detail. It is found that various Debye relaxation processes and conducting loss contribute to the attenuation of the microwave. Besides, the reflection loss is affected by the impedance match. SnO2 fibers displayed an effective absorbing width (reflection loss lower than −10 dB) of 6 GHz with the thickness of 2 mm, and an absorbing width of 14 GHz was obtained by adjusting the thickness of the absorber from 2 to 5 mm. This study thus presents a novel and promising microwave absorbing material with broad absorbing width.

ChemInform Abstract: On the Existence of and Mechanism for Microwave‐Specific Reaction Rate Enhancement

AbstractReview: 59 refs.

Fractional models of anomalous relaxation based on the Kilbas and Saigo function

We revisit the Kilbas and Saigo functions of the Mittag-Leffler type of a real variable $$t$$ , with two independent real order-parameters. These functions, subjected to the requirement to be completely monotone for $$t>0$$ , can provide suitable models for the responses and for the corresponding spectral distributions in anomalous (non–Debye) relaxation processes, found e.g. in dielectrics. Our analysis includes as particular cases the classical models referred to as Cole–Cole (the one-parameter Mittag-Leffler function) and to as Kohlrausch (the stretched exponential function). After some remarks on the Kilbas and Saigo functions, we discuss a class of fractional differential equations of order $$\alpha \in (0,1]$$ with a characteristic coefficient varying in time according to a power law of exponent $$\beta $$ , whose solutions will be presented in terms of these functions. We show 2D plots of the solutions and, for a few of them, the corresponding spectral distributions, keeping fixed one of the two order-parameters. The numerical results confirm the complete monotonicity of the solutions via the non-negativity of the spectral distributions, provided that the parameters satisfy the additional condition $$0<\alpha +\beta \le 1$$ , assumed by us.

Effect of water absorption on pristine and ion-irradiated kapton-H polyimide using thermally stimulated depolarization current technique

In this paper we report the effect of water absorption on pristine and 75 MeV oxygen ion-irradiated kapton-H polyimide by using the thermally stimulated depolarization current (TSDC) technique. The TSDC spectra reveal two significant peaks at low and intermediate temperatures around 30°C and 110°C termed as γ-peak (absorbed water-relaxation) and β-peak (dipolar-relaxation), respectively. The strength of the low-temperature peak (γ-peak) is affected in the opposite mode for pristine and ion-irradiated samples. A current reversal has been observed at 60°C almost in all the cases; this can be associated with the presence of homocharges. The current reversal that appears here can be correlated with the internally developed field in the sample as the applied electric field is not very high. Activation energy has been calculated by using the Debye relaxation process. The value of activation energy for the γ-peak varies from 0.4 to 0.8 eV. Cole-Cole distribution, a relaxation process, is associated with distribution of relaxation time which can be measured using a distribution function. The enhancement in the distribution of τ can be associated with the dipolar relaxation process owing to the formation of some new radiation-induced sub-polar groups.

Laminated magnetic graphene with enhanced electromagnetic wave absorption properties

Graphene is highly desirable as an electromagnetic wave absorber because of its high dielectric loss and low density. Nevertheless, pure graphene is found to be non-magnetic and contributes to microwave energy absorption mostly because of its dielectric loss, and the electromagnetic parameters of pure graphene, which are out of balance, result in a bad impedance matching characteristic. In this paper, we report a facile solvothermal route to synthesize laminated magnetic graphene. The results show that there have been significant changes in the electromagnetic properties of magnetic graphene when compared with pure graphene. Especially the dielectric Cole–Cole semicircle suggests that there are Debye relaxation processes in the laminated magnetic graphene, which prove beneficial to enhance the dielectric loss. We also proposed an electromagnetic complementary theory to explain how laminated magnetic graphene, with the combined advantages of graphene and magnetic particles, helps to improve the standard of impedance matching for electromagnetic wave absorbing materials. Besides, microwave absorption properties indicate that the reflection loss of the as-prepared composite is below −10 dB (90% absorption) at 10.4–13.2 GHz with a coating layer thickness of 2.0 mm. This further confirms that the nanoscale surface modification of magnetic particles on graphene makes graphene-based composites have a certain research value in electromagnetic wave absorption.

Graphene/polyaniline nanorod arrays: synthesis and excellent electromagnetic absorption properties

In the paper, we find that graphene has a strong dielectric loss, but exhibits very weak attenuation properties to electromagnetic waves due to its high conductivity. As polyaniline nanorods are perpendicularly grown on the surface of graphene by an in situ polymerization process, the electromagnetic absorption properties of the nanocomposite are significantly enhanced. The maximum reflection loss reaches −45.1 dB with a thickness of the absorber of only 2.5 mm. Theoretical simulation in terms of the Cole–Cole dispersion law shows that the Debye relaxation processes in graphene/polyaniline nanorod arrays are improved compared to polyaniline nanorods. The enhanced electromagnetic absorption properties are attributed to the unique structural characteristics and the charge transfer between graphene and polyaniline nanorods. Our results demonstrate that the deposition of other dielectric nanostructures on the surface of graphene sheets is an efficient way to fabricate lightweight materials for strong electromagnetic wave absorbents.

Dielectric Relaxation Studies of the Fast Lithium-Ion Conductor La2/3-xLi3xTiO3 (x=0.06, 0.11)

The diffusion processes of lithium ions in La2/3-xLi3xTiO3 (x=0.06, 0.11) compounds were investigated by dielectric relaxation method. Prominent relaxation dielectric loss peaks, peaks P1 and P2 in La0.56Li0.33TiO3 and peaks P3 and P4 in La0.61Li0.18 TiO3, were observed. From the shift of peak position with frequency, the activation energy of 0.36~0.42 eV and the pre-exponential factor of relaxation time in the order of 10-14 ~ 10-13 s were obtained if one assumes Debye relaxation processes. The activation energies of lithium ion diffusion in La2/3-xLi3xTiO3 compounds and the characteristic vibration frequency for the ionic hopping motion are higher than those measured by 7Li nuclear magnetic resonance (NMR) spectroscopy and that of the typical phonon frequency (about 1013Hz). These values of relaxation parameters strongly suggest the existence of interaction between the relaxation species (here lithium ions or vacancies). Basing on the coupling model, the decoupled relaxation parameters of the dielectric relaxation peaks is: P1 (0.14 eV, 2×10-13 s), P2 (0.25 eV, 1.8×10-13 s), P3 (0.17 eV, 4×10-13 s) and P4 (0.3 eV, 2.7×10-13 s). These decoupled parameters are very close to the NMR measurement results and the reciprocal of the typical phonon frequency. Judging from the relaxation parameter of the peaks and combining with the crystallographic characterization, it is suggested that the P1 (P3) and P2 (P4) peaks are associated with the lithium ion diffusion in the ab planes and between the adjacent ab planes, respectively.

Relaxation Model of Lithium Ions in the Garnet-Like Li&lt;sub&gt;5&lt;/sub&gt;La&lt;sub&gt;3&lt;/sub&gt;Bi&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;12&lt;/sub&gt;Lithium-Ion Conductor

The relaxation mechanism of lithium ions in Li5La3Bi2O12 electrolyte was investigated by internal friction (IF) method. A prominent relaxation-type IF peak was observed. From the shift of peak position with frequency, the activation energy of E=1.0-1.1 eV and the pre-exponential factor of relaxation time in the order of τ0 =10-25 ~10-18 s were obtained if one assumes a distributed Debye relaxation process. These values of relaxation parameters strongly suggest the existence of interaction between the relaxation species (here lithium ions or vacancies). Basing on the coupling model, the values of E and τ0 were determined as 0.5-0.6 eV and 10-17 ~ 10-15 s, which still deviated from the typical values for point defect relaxation. A new phenomenological model was used to describe the relaxation process, and the values of E and τ0 were determined as 0.46 eV and 3.6×10-14 s, which is in agreement with the typical values for point defect relaxation.

Dielectric Relaxation Studies of the Fast Lithium-Ion Conductor La&lt;sub&gt;2/3-x&lt;/sub&gt;Li&lt;sub&gt;3x&lt;/sub&gt;TiO&lt;sub&gt;3&lt;/sub&gt; (x=0.06, 0.11)

The diffusion processes of lithium ions in La2/3-xLi3xTiO3 (x=0.06, 0.11) compounds were investigated by dielectric relaxation method. Prominent relaxation dielectric loss peaks, peaks P1 and P2 in La0.56Li0.33TiO3 and peaks P3 and P4 in La0.61Li0.18 TiO3, were observed. From the shift of peak position with frequency, the activation energy of 0.36~0.42 eV and the pre-exponential factor of relaxation time in the order of 10-14 ~ 10-13 s were obtained if one assumes Debye relaxation processes. The activation energies of lithium ion diffusion in La2/3-xLi3xTiO3 compounds and the characteristic vibration frequency for the ionic hopping motion are higher than those measured by 7Li nuclear magnetic resonance (NMR) spectroscopy and that of the typical phonon frequency (about 1013Hz). These values of relaxation parameters strongly suggest the existence of interaction between the relaxation species (here lithium ions or vacancies). Basing on the coupling model, the decoupled relaxation parameters of the dielectric relaxation peaks is: P1 (0.14 eV, 2×10-13 s), P2 (0.25 eV, 1.8×10-13 s), P3 (0.17 eV, 4×10-13 s) and P4 (0.3 eV, 2.7×10-13 s). These decoupled parameters are very close to the NMR measurement results and the reciprocal of the typical phonon frequency. Judging from the relaxation parameter of the peaks and combining with the crystallographic characterization, it is suggested that the P1 (P3) and P2 (P4) peaks are associated with the lithium ion diffusion in the ab planes and between the adjacent ab planes, respectively.

Molecular dynamics changes induced by solvent in 2-ethyl-1-hexanol

Apart from other classes of materials, supramolecular structures may exist in H-bonded liquids due to the existence of hydrogen bonding. The dynamics of these structures remains one of the most exciting topics of interest of modern science because of its crucial meaning for the behavior of water and its participation in biological processes. A special group of these liquids form monohydroxy alcohols due to their similarity to water, their ability to vitrification, and the existence of the Debye relaxation process in dielectric loss spectra reflecting the dynamics of H-bond structures. Dynamics of these structures can be studied by changes of thermodynamic conditions, by immersion of the liquid into the constraint geometry, and by dilution in a nonassociated solvent. Herein we studied the behavior of relaxation dynamics of mixtures of 2-ethyl-1-hexanol with bromobutane using broadband dielectric spectroscopy. Analysis of the results exhibits the existence of crossover in temperature dependence of static permittivity of the Debye process at some particular temperature T(c). This temperature shifts to lower values with increasing concentration of bromobutane. Moreover, below some "critical" concentration of alcohol in the mixture the shape of the Debye process loses exponentiality and the temperature dependence of relaxation times starts to change. This change was illuminated based on the analysis of the steepness index. For the lowest concentration, the value of this parameter becomes the same as the value of the steepness index of faster relaxation, called process II, of pure alcohol at ambient pressure. The observed change in relaxation dynamics with lowering concentration of alcohol is astonishingly similar to the behavior observed in the same material at elevated pressure. A possible origin of these similarities is also discussed.

Investigation of liquid–liquid transition process in atactic polystyrene by means of thermally stimulated depolarization current

Thermally stimulated depolarization current (TSDC) measurement was used to investigate the liquid–liquid transition process of atactic polystyrene (aPS). There are four distinct peaks (α, ρ 1, LL and ρ 2) showed in TSDC spectrum in the range of 300–480 K. Compared with the result of differential scanning calorimetry for aPS, the TSDC spectrum showed that the peak LL located at 422 K could be attributed to the movement of entire chain related to liquid–liquid transition. The isolated peak LL was separated from TSDC spectrum of aPS by curve fitting procedure of the kinetics equation. The distribution of relaxation time of liquid–liquid transition was obtained in terms of the principle of Debye relaxation process. Based on analysis of calculated results, it was confirmed that the relaxation time during the liquid–liquid transition of aPS changed gradually from following Vogel–Fulcher equation to Arrhenius rule with increasing temperature.

Internal friction study on the lithium ion diffusion of Li 5La 3M 2O 12 (M = Ta, Nb) ionic conductors

The diffusion processes of lithium ions in Li 5La 3M 2O 12 (M = Ta, Nb) electrolytes were investigated by internal friction (IF) method. Prominent relaxation IF peaks, peaks P 1 and P 2 in Li 5La 3Ta 2O 12 and peaks P Nb1 and P Nb2 in Li 5La 3Nb 2O 12, were observed. From the shift of peak position with frequency, the activation energy of 1.0 eV and the pre-exponential factor of relaxation time in the order of 10 −22–10 −26 s were obtained if one assumes Debye relaxation processes. These values of relaxation parameters strongly suggest the existence of interaction between the relaxation species (here lithium ions or vacancies). Basing on the coupling model, the activation energy was determined as 0.6–0.7 eV. Judging from the relaxation parameter of the peaks and combining with the crystallographic characterization, it is suggested that the P 1 ( P Nb1) and P 2 ( P Nb2) peaks are associated with the lithium ion diffusion between different octahedral sites.

Mechanical relaxation studies of α and slow β processes in Nd65Fe15Co10Al10 bulk metallic glass

The relaxation dynamics of the primary α and secondary β processes in Nd65Fe15Co10Al10 bulk metallic glass has been investigated by using low-frequency mechanical spectroscopy, differential scanning calorimetry (DSC) and x-ray diffraction. From the shift of internal friction peaks by the frequency change, the activation energy of β relaxation (Eβ) is found to be about 1.01 eV, and a correlation between Eβ and glass transition temperature (Tg) is found Eβ ≈ 24 RTg, indicating that the β relaxation is intrinsic in metallic glasses. According to the coupling model, the uncoupled activation energy of α relaxation (Eα*) is found to be about 1.38 eV, still larger than the value of Eβ corresponding to a simple Debye relaxation process. The possible mechanism and the connection between α and β relaxations are discussed.

Comment on “Slow Debye-type peak observed in the dielectric response of polyalcohols” [J. Chem. Phys. 132, 044504 (2010)

as dipolar De-bye relaxation process observed previously in some alcohols.As pointed out herein, the Debye-like peak reported in Ref. 1is simply associated with dc-conduction process. In fact, thedetermined relaxation time for this new process gives onlyapparent information on translational diffusion coefficient ofthe mobile charges presented in almost any liquid. Conse-quently, any considerations on dynamics of “larger hydrogenbonded structures” based on analysis of the Debye peak thatis generated by using a blocking electrode do not make anysense.As a starting point, we will calculate the compleximpedance of the equivalent electrical circuit for measuringcell used in Ref. 1. As shown in electrical scheme in Inset inFig. 1, it is represented by two capacitors:

Nonlinear response and two stable electroconducting states in transparent plasticized PVC films

The electric conductivity of transparent plasticized poly(vinyl chloride) (PVC) films with thicknesses about 30–50 μm has been studied in electric fields with strengths significantly below the breakdown level. It is established that the PVC films exhibit spontaneous reversible transitions between two stable states—with high and relatively low conductivities, in which the bulk resistivity amounts to ∼103 and 106 Ω m, respectively. Relaxation current-voltage characteristics have been measured in a continuous regime, which allowed the Debye relaxation processes to be taken into consideration and effects related to the nonlinearity and transitions between indicated states to be separated. A regime with deterministic switching between the two conducting states has been observed. A simple qualitative model that describes the anomalous character of conductivity in polymer films is proposed.