Kohlrausch Williams Watts Research Articles

Effect of temperature and frequency on the dielectric behaviour of cellulose nanocrystals

Nanocellulose is a promising material for advanced applications due to its renewable nature, non-toxicity, eco-friendliness, mechanical strength and other unique properties. This study investigates the dielectric properties of cellulose nanocrystals (CNCs) derived from wastepaper through acid hydrolysis, across a temperature range of 30°C to 100°C and a frequency range of 1 Hz to 10 MHz. Using theoretical models such as the modified Cole-Cole model, Jonscher's universal dielectric response (UDR) model and modified Kohlrausch-Williams-Watts (KWW) model, a detailed analysis is performed. The results indicate that the dielectric properties depend on temperature, with the frequency dispersion of the real (ε′) and imaginary parts (ε″) of the dielectric permittivity fitting the modified Cole-Cole equation. These values show an initial increase up to 70°C (ε′∼ 6000 and dielectric loss <1) followed by a decrease at higher temperatures, which is linked to the hydroxyl groups. A temperature dependence is also observed in space charge conductivity, free charge conductivity and relaxation time. Non-Debye type behaviour is attributed to asymmetrical features in the electric modulus spectra, as explained by the modified KWW model at various temperatures. The frequency variation of AC conductivity adheres to Jonscher’s power law and the temperature variation of the frequency exponent (0≤ s ≤1) indicates a correlated barrier hopping conduction mechanism for charge carriers. Overall, these findings highlight CNCs as excellent candidate for antistatic applications, demonstrating conductivity ranging from 10−5 to10−9 Scm−1. The results also suggest CNCs can be used in energy storage applications due to their outstanding dielectric properties and low dielectric loss (<1).

Thickness-dependent structural and growth evolution in relation to dielectric relaxation behavior and correlated barrier hopping conduction mechanism in Ni0.5Co0.5Fe2O4 ferrite thin films.

Ferrite thin films are explored due to their promising properties, which are essential in various advanced electronic devices. However, depositing a film with pure phase and uniform microstructure is challenging. The Ni0.5Co0.5Fe2O4 ferrite thin films are deposited using pulsed laser deposition (PLD) technique to explore the effect of thickness on structural properties, growth evolution, temperature-dependent dielectric behavior, and conduction mechanisms. Microstructural analysis revealed that the films are uniformly grown, exhibiting surface roughness ranging from  2 to 4 nm. The dielectric response, adhering to a modified Debye model, exhibited multiple relaxation processes, with notable changes in the dielectric constant and loss as film thickness increased. Impedance spectra exhibited both space charge and dipolar relaxation phenomena, corroborated by Cole-Cole and electrical modulus plots. The analysis of the imaginary electric modulus using the Kohlrausch-Williams-Watts (KWW) function revealed non-Debye-type relaxation in all deposited films, characterized by thermally activated broad peaks. Conductivity decreased up to a certain film thickness, and the frequency exponent derived from Jonscher's power law suggested a correlated barrier hopping model for AC conduction. Activation energies improved with film thickness up to 125 nm, consistent with a constant energy barrier for polarons during relaxation and conduction phases. The film with 125 nm thickness exhibited the optimal dielectric properties, with the maximum dielectric constant, minimum dielectric loss, and highest activation energy. These findings highlight the potential of dense, uniformly grown films with high dielectric constants and low dielectric losses for advanced electronic device applications.

Direct Identification of the Continuous Relaxation Time and Frequency Spectra of Viscoelastic Materials

Relaxation time and frequency spectra are not directly available by measurement. To determine them, an ill-posed inverse problem must be solved based on relaxation stress or oscillatory shear relaxation data. Therefore, the quality of spectra models has only been assessed indirectly by examining the fit of the experiment data to the relaxation modulus or dynamic moduli models. As the measures of data fitting, the mean sum of the moduli square errors were usually used, the minimization of which was an essential step of the identification algorithms. The aim of this paper was to determine a relaxation spectrum model that best approximates the real unknown spectrum in a direct manner. It was assumed that discrete-time noise-corrupted measurements of a relaxation modulus obtained in the stress relaxation experiment are available for identification. A modified relaxation frequency spectrum was defined as a quotient of the real relaxation spectrum and relaxation frequency and expanded into a series of linearly independent exponential functions that are known to constitute a basis of the space of square-integrable functions. The spectrum model, given by a finite series of these basis functions, was assumed. An integral-square error between the real unknown modified spectrum and the spectrum model was taken as a measure of the model quality. This index was proved to be expressed in terms of the measurable relaxation modulus at uniquely defined sampling instants. Next, an empirical identification index was introduced in which the values of the real relaxation modulus are replaced by their noisy measurements. The identification consists of determining the spectrum model that minimizes this empirical index. Tikhonov regularization was applied to guarantee model smoothness and noise robustness. A simple analytical formula was derived to calculate the optimal model parameters and expressed in terms of the singular value decomposition. A complete identification algorithm was developed. The analysis of the model smoothness and model accuracy for noisy measurements was carried out. The equivalence of the direct identification of the relaxation frequency and time spectra has been demonstrated when the time spectrum is modeled by a series of functions given by the product of the relaxation frequency and its exponential function. The direct identification concept can be applied to both viscoelastic fluids and solids; however, some limitations to its applicability have been pointed out. Numerical studies have shown that the proposed identification algorithm can be successfully used to identify Gaussian-like and Kohlrausch–Williams–Watt relaxation spectra. The applicability of this approach to determining other commonly used classes of relaxation spectra was also examined.

Controlled Sol-Gel Transitions of Metal-Organic Membrane-Enveloped Cellulose Nanofibrils via Metal Coordination in Aqueous Media.

We report a metal coordination-driven sol-gel transition system where cellulose nanofibrils are enveloped by a rationally designed metal-organic membrane (MOM) in an aqueous medium. Specifically, 2,2,6,6-tetramethylpiperidine-1-oxyl (TEMPO)-oxidized bacterial cellulose (TOBC) is encapsulated within an MOM comprising Zn2+ and the chelator phytic acid (PA), denoted TOBCMOM. Using the DLVO theory, we elucidate how tuning the metal ion valence in TOBCMOM modulates the sol-gel transition by controlling interfibrillar attractive forces. Notably, TOBCMOM fluids exhibit relaxation times consistent with the Kohlrausch-Williams-Watts (KWW) function. Significantly, we demonstrate reversible, sustainable sol-gel transitions in TOBCMOM under stepwise mechanical strain. This facile approach enables rheological tailoring of aqueous media, promising for the development of advanced stimuli-responsive smart fluids for applications in cosmetics, food science, and pharmaceutical formulations.

Physical aging of a glassy polymer in cultural heritage conservation

AbstractArtworks, particularly easel paintings, are multi‐component materials intended to last indefinitely. The protective coatings applied to these artworks often consist of amorphous glass‐like polymers, which undergo slow physical aging and structural recovery below their glass transition temperature. This process alters key physical properties such as mechanical strength, optical clarity, and thermal stability over extended periods. This study investigates the time‐dependent evolution of these properties in Laropal A81, a widely used synthetic resin for cultural heritage conservation, particularly as a replacement for ancient varnishes. The investigation involves characterization of enthalpy recovery via differential scanning calorimetry, refractive index evolution via refractometry, and creep compliance evolution via rheological measurements. The aging behavior of Laropal A81 is further analyzed using the Kohlrausch–Williams–Watts function and the Tool–Narayanaswamy–Moynihan model, enabling the quantification of critical dynamic parameters such as activation energy, nonlinearity, partition coefficients, and non‐exponentiality. The gained insights into the long‐term behavior of this coating's properties can be valuable for improving preservation and restoration strategies for cultural heritage.

Structural properties, dielectric relaxation, and impedance spectroscopy of NASICON type Na3+xZr2−xPrxSi2PO12${\rm Na}_{3+x} {\rm Zr}_{2-x} {\rm Pr}_{x} {\rm Si}_2 {\rm PO}_{12}$ ceramics

AbstractWe investigate the dielectric and impedance spectroscopic investigation of Pr‐doped NASICON type () samples as a function of temperature and frequency. The Rietveld refinement of X‐ray diffraction patterns confirms the monoclinic phase having C2/c space groups for all the samples. The scanning electron microscopy shows the granular‐like structure and energy dispersive X‐ray analysis confirms the desired compositions. The temperature (90–400 K) and frequency (20 Hz–2 MHz) dependence of electric permittivity are explained using Maxwell–Wagner–Sillars (MWS) polarization and space charge polarization mechanisms. The dielectric relaxation shows nearly equal activation energy for all the samples with a non‐Debye type of relaxation in the measured temperature range. The complex impedance analysis shows the presence of broad grain and grain boundary relaxation peaks. The stretched exponent analysis of electric modulus using the Kohlrausch–Williams–Watts (KWW) function further confirms the non‐Debye type of relaxation. Moreover, scaling analysis of the electric modulus shows a similar type of relaxation for all the samples. The ac conductivity data are fitted using modified power law, where the temperature dependence of exponent () confirms the correlated barrier hopping (CBH) type conduction for all the samples. Our results indicate that the Pr‐doped NASICON samples are potential candidates for charge storage devices due to their large electric permittivity.

Electrical transport characteristics of rare earth ions (Er³⁺, Sm³⁺) exchanged cobalt-manganese ferrite using impedance spectroscopy

This study presents findings on the AC impedance characteristics of rare earth-doped Co0.5Mn0.5RExFe2-xO4 ferrites (where RE = Er and Sm, and 0.0 ≤ x ≤ 0.1), synthesized utilizing the citrate auto-combustion process. Employing impedance spectroscopy at frequencies ranging from (100 −1 MHz) and temperatures between 30°C and 120°C, we distinguished the impact of grains (Gs) and grain boundaries (GBs) in these compositions. The Jonscher power law was applied to characterize the AC conductivity results. The dielectric constant έ and dielectric loss ε” decline as the frequency rises and reach a stable state at higher frequencies, indicating the characteristic dielectric dispersion. This phenomenon manifests the Maxwell-Wagner polarization, as described by Koop's hypothesis. The modified Debye formula provides a good match for the frequency-dependent dielectric permittivity fluctuation. The Cole-Cole plots revealed a single semicircle for the unaltered sample and lower Er³⁺ concentrations (up to x=0.02), but two semicircles appeared at higher Er³⁺ concentrations and in the Sm³⁺ doped samples. The G and GB resistances increased with higher concentrations of Er³⁺/ Sm³⁺ but showed a decrease at x=0.1 in Sm³⁺-doped samples. The data examination designates that the resistive and capacitive possessions are predominantly affected by G and GB processes. A relaxation phenomenon in the existing samples is shown by the frequency-dependent of the imaginary portion of impedance (Z"). Remarkably, the relaxation time (τz) showed linear temperature dependence. Additionally, studies of the electrical modulus (M’ and M”) highlighted non-Debye sort dielectric relaxation in all compositions, with peaks in the imaginary modulus indicating a shift in charge carrier mobility from long-range toward short-range. The investigation focused on the non-Debye relaxation, which was analyzed by determining the stretching exponential parameter (β). This factor was obtained by fitting the modified Kohlrausch-Williams-Watts (KWW) formula to the graph of the imaginary electric modulus. The substitution of Fe3+ by Er3+ and Sm3+ ions substantially enhanced the dielectric properties, particularly Co-Mn-Sm ferrite series, suggesting their potential use in high-frequency devices.

Study of temperature-dependent interface with viscoelastic behavior through shear testing and modeling

In this work, the effect of temperature on interfaces with viscoelastic behavior was investigated using experimental and theoretical means. In particular, rubber/woven fabrics with thickness of 0.5 mm were subjected to self-designed shear tests at temperatures ranging from 263.15 to 383.15 K. Derived interface cyclic regeneration was observed through shear tests. Subsequently, a bi-linear cohesive zone model (CZM) was used to describe the shear test data. A novel image processing algorithm was developed to analyze the damaged morphology of the rubber/weave interface. It was found that hairniness amount decreased by 68.4 % when the temperature increased from 263.15 to 383.15 K. In addition, by combining the bi-linear CZM with the Kohlrausch–William–Watts law, Wiliams-Landel-Ferry equation and BK criterion, a 3D temperature-dependent constitutive model (KBW) was developed. The model successfully simulated the viscoelasticity of interfaces at different temperatures with margin of error less than 9 %. Thus, this study provides a strategy for elucidating the temperature dependence of interfaces with viscoelastic behavior.

Trends in the temperature dependence of dynamical heterogeneity in strong and fragile supercooled liquids

The temperature dependence of the Kohlrausch-Williams-Watts (KWW) stretching exponent β of shear relaxation kinetics is determined for a wide variety of deeply supercooled glass-forming liquids with fragility index m ranging between ∼ 30 and 90 using small amplitude oscillatory shear parallel plate rheometry. Intriguingly, and contrary to conventional wisdom, β and m are observed to be uncorrelated at temperatures close to the glass transition Tg. However, a clear pattern emerges when the variation of β is considered as a function of the α-relaxation timescale τα. In particular, β is observed to increase rapidly (slowly) for relatively strong (fragile) liquids with decreasing τα upon increasing temperature above Tg. Consequently dβ/d(log τα) is found to be negatively correlated with m near and above Tg. A possible origin of this intriguing trend is discussed within the frameworks of the energy landscape and the elastic facilitation models of relaxation of supercooled liquids.

Magnetic exchange interactions and non-Debye relaxation in spin-3/2 frustrated Kagomé magnet Co3V2O8

We report the experimental determination of the magnetic exchange parameter ( J/kB = 2.88 ± 0.02 K) for the Spin-3/2 ferromagnetic (FM) Kagomé lattice system: Co3V2O8 using the temperature dependence of dc-magnetic susceptibility χ(T) data by employing the fundamental Heisenberg linear chain model. Our results are quite consistent with the theoretically reported nearest neighbor dominant FM exchange coupling strength Jex−NN∼ 2.45 K. Five different magnetic phase transitions (6.2–11.2 K) and spin-flip transitions (9.6–7.7 kOe) have been probed using the ∂ ( χT )/ ∂T vs. T, heat capacity (CP -T) and differential isothermal magnetization curves. Among such sequence of transitions, the prominent ones being incommensurate antiferromagnetic (AFM) state at 11.2 K, commensurate AFM state at 8.8 K, and commensurate FM state across 6.2 K. All the successive magnetic phase transitions have been mapped onto a single H-T plane through which one can easily distinguish the above-mentioned different phases. The magnetic contribution of the CP -T near TN (11.2 K) has been analyzed using the power-law expression CM = A|T — TN|−α resulting in the critical exponent α = 0.18 ± 0.01 (0.15 ± 0.003) for T < TN (T > TN ), respectively for the Co3V2O8. It is interesting to note that non-Debye type dipole relaxation is quite prominent in Co3V2O8 and was evident from the Kohlrausch–Williams–Watts analysis of complex modulus and impedance spectra (0 ⩽β⩽ 1). Mott’s variable-range hopping of charge carriers process is evident through the resistivity analysis ( ρac -T −1/4 ) in the temperature range 275 ∘C–350 ∘C. Moreover, the frequency-dependent analysis of σac (ω) follows Jonscher’s power law yielding two distinct activation energies ( Ea∼ 0.37 and 2.29 eV) between the temperature range 39 ∘C–99 ∘C and 240 ∘C–321 ∘C.

The Ageing of μPlasma-Modified Polymers: The Role of Hydrophilicity.

Thermoplastic polymers exhibit relatively limited surface energies and this results in poor adhesion when bonded to other materials. Plasma surface modification offers the potential to overcome this challenge through the functionalisation of the polymer surfaces. In this study, three polymers of differing hydrophobicity (HDPE, PA12, and PA6) were subjected to a novel, atmospheric, μPlasma surface treatment technique, and its effectiveness at increasing the surface energies was evaluated via measurement of the contact angle. To characterise the physical and chemical changes following μPlasma surface modification, the surface morphology was observed using atomic force microscopy (AFM), and the functionalisation of the surface was evaluated using infrared spectroscopy. Immediately after treatment, the contact angle decreased by 47.3° (HDPE), 42.6° (PA12), and 50.1° (PA6), but the effect was not permanent in that there was a pronounced relaxation or ageing phenomenon in operation. The ageing process over five hours was modelled using a modified stretched exponential function Kohlrausch-Williams-Watts (KWW) model, and it was found that the ageing rate was dependent on the hydrophilicity of polymers, with polyamides ageing more rapidly than polyethylene.

Electrical conductivity and hopping conduction mechanism by VRH model in halide modified tellurite glasses

Electrical properties of halide doped tellurium glasses with composition 60TeO2-(25-x) Bi2O3-15B2O3-x ZnCl2, where x varies from 0 to 20 with step-size 5 has been studied in frequency range 10-1 Hz–105 Hz and temperature range of 200°C–300°C. The frequency-dependent conductivity was found to obey Almond-West's universal powers law and parameters such as frequency exponent (s), DC conductivity, and crossover frequency were obtained by fitting the ac conductivity experimental data with Almond-West's universal powers law. Based on estimated s values the electrical conduction model was depicted, and it was found that the correlated barrier hopping (CBH) model provides a pretty realistic depiction of the primary AC conduction mechanism. Further, the migratory enthalpy (Hm) and the enthalpy required to remove the cation from its initial position near a charge-compensating centre (Hf) were calculated. Further, Variable range hopping, or VRH, was found to be the process by which charges move between localized states.The electric modulus (M″) fitting with the Kohlrausch-Williams-Watts (KWW) function revealed non-Debye-type relaxation in the examined glass samples. Activation energy estimated from conductivity (1.13–1.20 eV), and electric modulus (1.13–1.22 eV) analysis are in good agreement indicating that polarons had to overcome a constant energy barrier throughout both the relaxation and conduction phases. One master curve was produced for all compositions and temperatures as a result of an impressive convergence in the scaling spectra of the AC conductivity and electric modulus (M′ and M″). Therefore, it was concluded that neither temperature nor composition impacted the conduction or relaxation mechanisms seen in the glass samples under study. The dielectric properties studies suggested non-debye type behavior.

PREFACE — SPECIAL ISSUE ON FRACTALS AND LOCAL FRACTIONAL CALCULUS: RECENT ADVANCES AND FUTURE CHALLENGES

Fractal geometry plays an important role in the description of the characteristics of nature. Local fractional calculus, a new branch of mathematics, is used to handle the non-differentiable problems in mathematical physics and engineering sciences. The local fractional inequalities, local fractional ODEs and local fractional PDEs via local fractional calculus are studied. Fractional calculus is also considered to express the fractal behaviors of the functions, which have fractal dimensions. The interesting problems from fractional calculus and fractals are reported. With the scaling law, the scaling-law vector calculus via scaling-law calculus is suggested in detail. Some special functions related to the classical, fractional, and power-law calculus are also presented to express the Kohlrausch–Williams–Watts function, Mittag-Leffler function and Weierstrass–Mandelbrot function. They have a relation to the ODEs, PDEs, fractional ODEs and fractional PDEs in real-world problems. Theory of the scaling-law series via Kohlrausch–Williams–Watts function is suggested to handle real-world problems. The hypothesis for the tempered Xi function is proposed as the Fractals Challenge, which is a new challenge in the field of mathematics. The typical applications of fractal geometry are proposed in real-world problems.

CALCULUS OPERATORS AND SPECIAL FUNCTIONS ASSOCIATED WITH KOHLRAUSCH–WILLIAMS–WATTS AND MITTAG-LEFFLER FUNCTIONS

In this paper, many important formulas of the subtrigonometric, subhyperbolic, pretrigonometric, prehyperbolic, supertrigonometric, and superhyperbolic functions sin Wiman class are developed for the first time. The subsine, subcosine, subhyperbolic sine, and subhyperbolic cosine associated with Kohlrausch–Williams–Watts (KWW) function and their scaling-law ODEs are proposed. The supersine, supercosine, superhyperbolic sine, and superhyperbolic cosine functions associated with Mittag-Leffler (ML) function and their fractional ODEs are obtained. The conjectures for the supercosine functions containing ML function are presented in detail.

ANOMALOUS DIFFUSION MODELS AND MANDELBROT SCALING-LAW SOLUTIONS

In this paper, the anomalous diffusion models are studied in the framework of the scaling-law calculus with the Mandelbrot scaling law. A analytical technology analogous to the Fourier transform is proposed to deal with the one-dimensional scaling-law diffusion equation. The scaling-law series formula via Kohlrausch–Williams–Watts function is efficient and accurate for finding exact solutions for the scaling-law PDEs arising in the Mandelbrot scaling-law phenomena.

Understanding charge transport and dielectric relaxation properties in lead-free Cs2ZrCl6 nanoparticles.

In the exploration of perovskite materials devoid of lead and appropriate for capturing solar energy, a recent finding has surfaced concerning Cs2ZrCl6. This compound has attracted interest as a potential candidate, displaying advantageous optical and electrical features, coupled with remarkable durability under environmental stresses. This research outlines the effective production of non-toxic metal halide nanoparticles of Cs2ZrCl6 using the gradual cooling technique. Thorough examinations have been conducted to explore the structural, optical, and dielectric traits. Over the frequency range of 101-106 Hz, the dielectric constant, loss factor, electric modulus, and electrical conductivity of Cs2ZrCl6 exhibit a strong dependence on temperature. The Nyquist plot confirms the distinct contributions of grains and grain boundaries to the total impedance. In the high-frequency region, the dielectric constant tends to increase with temperature. In accordance with the modified Kohlrausch-Williams-Watts (KWW) equation, an asymmetric nature corresponding to the non-Debye type is observed in the electric modulus spectra at different temperatures. Furthermore, the imaginary part of the electric modulus spectrum shifts from the non-Debye type towards the Debye type with increasing temperature, despite not obtaining an exact Debye response. The frequency-dependent behavior of AC conductivity has been modeled using Joncher's universal law. The conduction mechanism within the Cs2ZrCl6 compound is attributed to the small polaron tunneling model (NSPT). Furthermore, Cs2ZrCl6 has the potential to function as an energy harvesting device due to its elevated dielectric constant combined with minimal dielectric loss.

Temperature dependent magnetic and electrical transport properties of lanthanum and samarium substituted nanocrystalline nickel ferrite and their hyperthermia applications

Structural, optical, temperature dependent magnetic and electrical properties have been investigated for the nanocrystalline NiFe1.97RE0.03O4 (RE = La3+ and Sm3+) compound. Without any signs of a secondary REFeO3 phase, the Rietveld refinement reveals a single-phase spinel structure possessing cubic symmetry for current samples. The decrease in lattice constant has been observed as a result of RE ions substitution. The TEM micrographs reveal nanosized particles with an average size of 35 ± 3 nm and 32 ± 3 nm for La3+ and Sm3+ substituted samples. EDX spectra of both samples show good compositional homogeneity. HRTEM micrographs of both samples show well resolved lattice fringes and their inter-planar spacing matches with that obtained from the Rietveld analysis of the XRD patterns. The concentration of Fe2+ and Fe3+ ions has been estimated from the XPS spectra analysis and it is found to be ∼ 22% and 78% for NiFe1.97La0.03O4 and, 20% and 80% for NiFe1.97Sm0.03O4 compound. The optical energy band gap for rare earth substituted samples is found to be more than that of pure nickel ferrite. The value of saturation magnetization (Ms) and magneto-crystalline anisotropy constant (K1) estimated from the “Law of Approach to Saturation” equation for rare earth substituted samples are found to be less than that of pure nickel ferrite. However, an enhanced value of coercivity has been observed with RE substitution. ZFC (zero field cooling) and FC (field cooling) DC magnetization curves measured at 100 Oe in the temperature range of 60–400 K reveal a combination of weak and intermediate forms of magnetic interaction between the particles for both samples. Temperature dependent analysis of saturation magnetization and coercivity employing modified Bloch’s law and Kneller’s relation supports the nanomagnetic behavior of both samples. Under an AC magnetic field of 14.92 kA/m and frequency 337 kHz, the SAR and ILP values have been found to be ∼ 331 W/g and 4.22 nHm2/kg for NiFe1.97La0.03O4 and, ∼ 241 W/g and 3.21 nHm2/kg for NiFe1.97Sm0.03O4. The dielectric relaxation data have been analyzed at various temperatures ranging from 40 to 300 0C over the frequency range 100 Hz-1 MHz using electrical impedance spectroscopy. The dielectric constant for rare earth substituted samples is found to be more and their AC conductivity is observed to be less than that of pure nickel ferrite. The analysis of temperature dependent AC conductivity employing Jonscher’s power law suggests that the charge carrier’s conduction mechanism of both samples follows the small polaron hopping mechanism below 200 0C, thereafter; it follows the correlated barrier hopping mechanism. The activation energy estimated by imaginary impedance spectra is found to be 0.411 eV and 0.398 eV for NiFe1.97La0.03O4 and NiFe1.97Sm0.03O4 which is more than that of pure nickel ferrite. The Cole-Cole plots at different temperatures suggest the presence of non-Debye-type relaxation. The modeling of Cole-Cole plots with equivalent circuits for both samples confirms the contribution of both grain and grain boundary in electrical conduction. The estimated stretching exponential factor by fitting the modified KWW (Kohlrausch-Williams-Watts) equation to the imaginary modulus curve reveals relatively more dipole-dipole interaction in NiFe1.97Sm0.03O4 than that of the La3+ substituted sample.

Anomalous Kinetics of Photoluminescence from Degrading Organic Materials and Its Theoretical Rendition

The Photoluminescence (PL) degradation of thermally evaporated Alq3 thin films is described by four Kohlrausch-Williams-Watt (KWW) functions, which are solely mathematical expressions. The present contribution not only unfolds the physical meaning of the KWW function, but also reveals new mathematical tools. By introducing the concept of the material clock, the system has been described by a damped harmonic oscillator, which in certain conditions allows the expansion of the KWW function in the so-called Prony series. The terms of this series can be attributed to chemical and physical processes that really contribute to the decay, i.e., degradation of Alq3 thin films when interacting with internal and environmental agents. These insights unveiled the usefulness of proper mathematical procedures and properties, such as the monotonicity and the complete monotonicity, for investigating the PL of this ubiquitous organometallic molecule, which possesses one among the highest emission yield. Moreover, this method is also promising for describing the photoluminescent processes of similar organic molecules important both for basic research and optoelectronic applications.

Effect of carbon nanofibers on the viscoelastic response of carbon/epoxy composites

Carbon fibre reinforced polymer (CFRP) laminates nano-enhanced with carbon nanofibers (CNFs): 0.75 wt% and 0.5 wt% of epoxies Sicomin and Ebalta, respectively, were manufactured and their static and viscoelastic behaviour analyzed. After 180 min, the bending stress decreases and creep displacement increases over time, with Ebalta nano-enhanced resin laminates with CNFs showing the best results. A strong dependence of creep behaviour and stress relaxation is obtained with the applied stress level. The results show that laminates produced with pure Sicomin resin increased creep displacement by 1%, for a bending stress of 200 MPa, and 2 times greater for the bending stress of 700 MPa. The viscoelastic behaviour of CFRP composites nano-enhanced with CNFs was accurately predicted by the Kohlrausch-Williams-Watts (KWW) model and Findley power law.

Unexpected non-monotonic changing in the heterogeneity of glasses during annealing

The heterogeneity of glasses has critical influences on the properties. How heterogeneity evolves during annealing is an intriguing cutting-edge question. In this work, the heterogeneity of the annealed metallic and polymer glasses has been studied systematically by using stress relaxation and nanoindentation tests. The stress relaxation processes are analyzed using Kohlrausch-Williams-Watts (KWW) equation. We surprisingly find that the heterogeneous factor βKWW in KWW equation does not change monotonously but increases first and then decreases along with the annealing time. The two-stage process implies that glasses do not evolve as expected toward the more homogeneous glassy state but become homogeneous first and then more heterogeneous. This is further verified by the evolution of critical shear stress for local plasticity. It is revealed that the two-stage process is correlated with different relaxation modes, which is further interpreted using a phenomenological model. These findings not only give insights into understanding the nature of glasses, but also are useful for designing glasses with superior properties.