Multiple Relaxation Processes Research Articles

Four ways to interpret temporal memory operators in the wave equation

Arbitrary power law attenuation and dispersion in medical ultrasound and elastography can be modeled with temporal memory operators in the wave equation. Here four alternative interpretations are given. Power laws for attenuation with exponents other than 2 correspond to the use of convolution operators expressible as fractional derivatives. The corresponding constitutive equation can be verified by time domain measurements. A framework with multiple relaxation processes can be formulated via the complex compressibility. The constitutive equation can also be expressed with higher order derivatives.

Cu(II)-Dy(III) and Co(III)-Dy(III) based single molecule magnets with multiple slow magnetic relaxation processes in the Cu(II)-Dy(III) complex.

Two dinuclear Schiff-base complexes [Cu(II)Dy(III)] and [Co(III)Dy(III)] have been synthesized and structurally characterized. The AC susceptibility measurements taken at BDC = 0.2 T show a slow magnetic relaxation typical for single-molecule magnets. Unusual is the presence of three relaxation branches in [Cu(II)Dy(III)]; the slowest (low-frequency) process possesses the barrier to spin reversal of U/kB = 2.8 K and an extrapolated relaxation time as slow as τ0 = 0.11 s. The intermediate-frequency process is typical for SMM of this class with U/kB = 122 K and τ0 = 9.9 × 10(-7) s; an onset of the high-frequency process is evidenced and this is the fastest. In contrast, the [Co(III)Dy(III)] complex free of exchange coupling exhibits only a single relaxation path with SMM parameters U/kB = 113 K and τ0 = 7.0 × 10(-9) s.

Field-induced multiple relaxation mechanism of Co(III)2Dy(III) compound with the dysprosium ion in a low-symmetrical environment.

A defective cubane-shaped heterometallic trinuclear Co(III)2Dy(III) compound with only one magnetically interesting ion (Dy(III)) has been assembled by virtue of a multifunctional acylhydrazone ligand. Because of the nonaxial ground state of Dy(III) ion derived from a low-symmetrical crystal field, the title compound displays field-induced multiple relaxation processes which are of molecular and a dipolar-dipolar coupling origin, as revealed by combined experimental and theoretical investigations. The results demonstrate that such a mononuclear dysprosium(III) compound with a low-symmetrical environment of magnetic center appears to be a model system for further investigations to shed light on the complex relaxation mechanism of lanthanide-based single ion magnets.

Shell thickness-dependent microwave absorption of core-shell Fe3O4@C composites.

Core-shell composites, Fe3O4@C, with 500 nm Fe3O4 microspheres as cores have been successfully prepared through in situ polymerization of phenolic resin on the Fe3O4 surface and subsequent high-temperature carbonization. The thickness of carbon shell, from 20 to 70 nm, can be well controlled by modulating the weight ratio of resorcinol and Fe3O4 microspheres. Carbothermic reduction has not been triggered at present conditions, thus the crystalline phase and magnetic property of Fe3O4 micropsheres can be well preserved during the carbonization process. Although carbon shells display amorphous nature, Raman spectra reveal that the presence of Fe3O4 micropsheres can promote their graphitization degree to a certain extent. Coating Fe3O4 microspheres with carbon shells will not only increase the complex permittivity but also improve characteristic impedance, leading to multiple relaxation processes in these composites, thus the microwave absorption properties of these composites are greatly enhanced. Very interestingly, a critical thickness of carbon shells leads to an unusual dielectric behavior of the core-shell structure, which endows these composites with strong reflection loss, especially in the high frequency range. By considering good chemical homogeneity and microwave absorption, we believe the as-fabricated Fe3O4@C composites can be promising candidates as highly effective microwave absorbers.

Dielectric Spectroscopy of Pristine and O7+ Ion Irradiated NCO‐Terminated Polybutadiene‐Based Liquid Crystalline Polyurethane

AbstractThe dielectric constant (ε′) and loss factor (ε′′) have been measured in NCO‐terminated polybutadiene‐based pristine and 100 MeV O7+ ion irradiated liquid crystalline polyurethane in the temperature region of 80–300 K at frequencies ranging from 1 KHz to 1 MHz. The variation in ε′with temperature in different temperature regions has been analyzed in relation to the dipole structure of the molecules. The ε′′–T plots of pristine liquid crystalline polyurethane (LCPU) reveal the presence of multiple relaxation processes associated with the crankshaft motion of but‐2‐ene groups, dipolar nature of carbonyl groups, and glass transition temperature, respectively. An additional dielectric loss peak is observed in irradiated LCPU samples associated with the Maxwell–Wagner–Sillars (MWS) polarization. There is an overall increase in ε′ in irradiated samples due to the dominance of MWS polarization arising from the large number of radiation‐induced defect sites and free radicals. The loss in γ relaxation due to chain scissions of but‐2‐ene groups and the formation of new subpolar groups providing a new dipolar relaxation process is observed in irradiated LCPU samples. The variation in ε′ with fluence shows the occurrence of a secondary radiation induced crystallization in irradiated LCPU samples. The X‐ray diffraction analysis also shows the effect of fluence on the crystalline nature of LCPU samples.

Evaluation of superconducting gaps in optimally doped Ba(Fe1−xCox)2As2/Fe bilayers by ultrafast time-resolved spectroscopy

Measurements of nonequilibrium quasi-particle relaxation dynamics by using ultrafast pump and probe technique in optimally Co-doped Ba(Fe2As2)/Fe thin film has been reported. Multiple relaxation processes are present with BCS-like temperature-dependent superconducting gaps Δ0=(3.67±0.13) meV and Δ1=(6.1±0.1) meV, which are calculated considering the conventional electron-boson and spin fluctuations pairing mechanism. Then, the value of the electron–phonon coupling constant of λ=0.18 has been obtained.

Structural Rearrangement Through Lanthanide Contraction in Dinuclear Complexes

A new series of lanthanide complexes was synthesized, and the geometry and preliminary magnetic measurements of the complexes were explored. The specific ligand used (N'-(2-hydroxy-3-methoxybenzylidene)benzhydrazide) (H2hmb) was synthesized using a Schiff-base approach and was employed due to the presence of a coordination pocket that is able to accommodate magnetically selective lanthanide ions. The series can be divided into two groups that are categorized by a drastic structural rearrangement. The first group, Type I, contains six analogous complexes with the formula [M(III)2(Hhmb)3(NCS)3]·2MeOH·py (M = Y 1, Eu 2, Gd 3, Tb 4, Dy 5, Ho 6), while the second group, Type II, contains two dinuclear complexes with formula [M(III)2(Hhmb)2(NCS)4(MeOH)2] (M = Er 7, and Yb 8). Single-crystal X-ray analysis revealed that all M(III) ions in Type I exhibit monocapped distorted square antiprismatic geometries, while those of Type II exhibit distorted dodecahedron geometry. The direct current and alternating current magnetic measurements were carried out on all complexes, with 5, 7, and 8 exhibiting slow relaxation of the magnetization under an applied optimum dc field. Furthermore, complex 8 is the first example of a dinuclear Yb-based single-molecule magnet showing field-dependent multiple relaxation processes.

Molecular Dynamics of the Supercooled Pharmaceutical Agent Posaconazole Studied via Differential Scanning Calorimetry and Dielectric and Mechanical Spectroscopies

This paper presents comprehensive studies on the molecular dynamics of a pharmaceutically important substance, posaconazole. In order to characterize relaxation dynamics in the supercooled liquid and glassy states, dielectric and mechanical spectroscopies were applied. Dielectric data have indicated multiple relaxation processes that appear above and below the glass transition temperature Tg (τα=100 s) of posaconazole. From the curvature of the dielectric log10(τα) versus inverse of temperature dependence, we determine so-called "fragility", being a very popular parameter for classifying the structural dynamics of supercooled liquids and polymers. From the calculations, we get m=150, which means that is one of the most fragile glass-forming liquids. In this paper, the relaxation dynamics of supercooled posaconazole extracted from the dielectric response function was also confronted with shear-mechanical relaxation. Finally, we have also presented a direct comparison of the fragility and the number of dynamically correlated molecules Nc determined from dynamic calorimetry curves and dielectric and mechanical spectroscopies, showing a clear deviation in the picture of glass-transition dynamics generated by calorimetric and spectroscopic techniques.

Slow Magnetic Relaxation in Condensed versus Dispersed Dysprosium(III) Mononuclear Complexes

Reaction of the ligands 4,5-bis(propylthio)tetrathiafulvalene-2-(2-pyridyl)benzimidazole (L(1)) and 4,5-bis(propylthio)tetrathiafulvalene-2-(2-pyridyl)-3-(2-pyridinylmethyl)benzimidazole (L(2)) with Dy(hfac)3⋅2 H2O (hfac = 1,1,1,5,5,5-hexafluoroacetylacetonate) gave mononuclear complexes [Dy(hfac)3(L(1))] (1) and [Dy(hfac)3(L(2))] (2). In both compounds the Dy(III) ion is surrounded by six oxygen and two nitrogen atoms. Complex 1 displays single-ion magnet (SIM) behaviour only in solution (Δ=12(1) K and τ0 =1.9(4)×10(-6) s), while complex 2 is a SIM in both solution (Δ=15(2) K and τ0 =1.5(3)×10(-6) s) and solid state (Δ=17(2) K and τ0 =9.5(2)×10(-6) s). The SIM behaviour is obtained if the hydrogen bond is broken by dissolution (1 in solution) or by alkylation (2). Multiple relaxation processes were identified for 2 with two competing processes: a fast one in zero field and a slow one for fields higher than 500 Oe. The two processes coexist for intermediate applied magnetic field. Magnetic-dilution and frozen-solution measurements led to the conclusion that the origin of these multiple relaxation processes is not due to the property of a single molecule.

Molecular dynamics in liquid and glassy states of non-steroidal anti-inflammatory drug: Ketoprofen

Ketoprofen is a well known nonsteroidal anti-inflammatory drug (NSAID) with analgesic and antipyretic effects. It acts by inhibiting the body’s production of prostaglandin. The molecular mobility of amorphous ketoprofen has been investigated by broadband dielectric spectroscopy (BDS) covering wide temperature and frequency range. Multiple relaxation processes were observed. Besides the primary α-relaxation, one secondary relaxation, γ-have been identified. The γ-process visible in the dielectric spectra at very low temperature is non-JG relaxation, and has an activation energy E=37.91kJ/mol typical for local mobility. Based on Ngai’s coupling model smaller n or a larger Kohlrausch exponent (1−n) of the α-relaxation associated with larger τβ (Tg). In the case of ketoprofen we conclude that the secondary relaxation (β) emerging from intermolecular motions, is hidden under the dominant α-peak. The temperature dependence of the relaxation time of the α-process can be described over the entire measured range by a single Vogel–Fulcher–Tammann (VFT) equation. From VFT fits, the glass transition temperature (Tg) was estimated as 267.07K, and a fragility or steepness index m=86.57 was calculated, showing that ketoprofen is a fragile glass former. Our differential scanning calorimetry (DSC) study shows that ketoprofen is a non-crystallizing compound. To confirm the hydrogen bond patterns of ketoprofen FTIR spectroscopy was applied in both crystalline and amorphous phases. Solubility test performed at 37°C proved that amorphous phase is more soluble than the crystalline phase.

Modeling the glass transition of amorphous networks for shape-memory behavior

In this paper, a thermomechanical constitutive model was developed for the time-dependent behaviors of the glass transition of amorphous networks. The model used multiple discrete relaxation processes to describe the distribution of relaxation times for stress relaxation, structural relaxation, and stress-activated viscous flow. A non-equilibrium thermodynamic framework based on the fictive temperature was introduced to demonstrate the thermodynamic consistency of the constitutive theory. Experimental and theoretical methods were developed to determine the parameters describing the distribution of stress and structural relaxation times and the dependence of the relaxation times on temperature, structure, and driving stress. The model was applied to study the effects of deformation temperatures and physical aging on the shape-memory behavior of amorphous networks. The model was able to reproduce important features of the partially constrained recovery response observed in experiments. Specifically, the model demonstrated a strain-recovery overshoot for cases programmed below Tg and subjected to a constant mechanical load. This phenomenon was not observed for materials programmed above Tg. Physical aging, in which the material was annealed for an extended period of time below Tg, shifted the activation of strain recovery to higher temperatures and increased significantly the initial recovery rate. For fixed-strain recovery, the model showed a larger overshoot in the stress response for cases programmed below Tg, which was consistent with previous experimental observations. Altogether, this work demonstrates how an understanding of the time-dependent behaviors of the glass transition can be used to tailor the temperature and deformation history of the shape-memory programming process to achieve more complex shape recovery pathways, faster recovery responses, and larger activation stresses.

Constitutive modeling of the rate-dependent resilient and dissipative large deformation behavior of a segmented copolymer polyurea

Phase-separated segmented copolymers comprised of hard and soft segments can be tailored to offer hybrid mechanical performance including a highly dissipative yet resilient large strain behavior. The phase-separated morphology provides multiple relaxation processes which lead to a rate-dependent stress–strain behavior with a transition in rate sensitivity. In addition to the viscoelastic–viscoplastic dissipation pathways, stretch-induced softening due to microstructural breakdown provides a significant source of dissipation as evident in the hysteresis observed during cyclic loading. Extensive shape recovery is observed upon unloading, showing a highly resilient behavior in tandem with extensive dissipation. Here a microstructurally informed three-dimensional constitutive model is developed to capture the remarkable features of the large strain behavior of the segmented copolymers. The model employs multiple micro-rheological mechanisms to capture the time-dependent nonlinear constitutive responses of both hard and soft domains as well as the stretch-induced softening of the hard domains. In direct comparison to experimental data, the model is found to successfully capture the behavior of an exemplar polyurea copolymer over least six orders of magnitude in strain rate (10−3 to 103 s−1) including a transition in rate sensitivity at 1 s−1. The model is also shown to be predictive of the highly dissipative yet resilient stress–strain behavior under a variety of cyclic loading conditions. The microstructurally informed nature of the model provides insights into tailoring copolymeric microstructures to provide tunable energy storage and dissipation mechanisms in this important class of material.

Synthesis and characterization of polyaniline nanoparticles with enhanced microwave absorption

A series of polyaniline (PANI) materials have been prepared by a reverse dropping method with the assistance of polyvinylpyrrolidone (PVP). It can be found that PVP and the dropping rate play critical roles in determining the morphology evolution of PANI, and the restriction of PVP is highly dependent on the dropping rate. Well dispersed PANI nanoparticles can only be obtained under moderate conditions. Thanks to the unique preparative process, these samples show significant changes in the length and oxidation state of conjugated chains, as proved by the results of UV/vis absorption spectra and FT-IR spectra, which result in their distinguishable conductivity and microwave absorption. Very interestingly, PANI nanoparticles exhibit substantially enhanced microwave absorption properties. In particular the optimum one, PANI-NP2, presents very strong reflection loss (−40.5 dB at 5.8 GHz) and wide response bandwidth (3.2–18 GHz over −10 dB), which are indeed comparable to those composites of PANI with various magnetic particles, implying promising applications as a kind of light-weight and highly effective microwave absorber. By systematically investigating the electromagnetic parameters, it can be concluded that suitable complex permittivity, improved characteristic impedance and multiple relaxation processes in PANI nanoparticles should be responsible for their good microwave absorption.

New insight into the kinetic behavior of the structural formation process in agar gelation

Experimental investigations based on our custom-built torsion resonator were carried out on the kinetics and relaxation of the structural formation process in three agar–water solutions with agar concentrations of 0.75, 1.0, and 2.0 % w/w under natural cooling. An interesting temperature-dependent oscillatory decaying behavior of the structure development rate (SDR) in the agar gelation process is observed. This oscillatory SDR-decaying behavior is indicative of a sum of multiple SDR-determining relaxation processes and could be quantitatively described by a multiple-order Gaussian-like equation, i.e., $dG^{\prime }/dt\equiv \sum \nolimits _{n=0}^{m}{dG^{\prime }/dt}^{(n)}=\sum \nolimits _{n=0}^{m}K_{n}{\rm exp}[-2(T-T_{n})^{2}/W_{n}^{2}]$ . The ${\rm T}_{n}$ dependences of ${\rm W}_{n}$ in the gelation zone were also found to follow the Arrhenius law with activation energies of 39–74 kJ/mol for three investigated samples, indicating the important role of formation or fission of the hydrogen bonding interaction playing in the agar structural network formation. These findings provide insights into the mechanical properties and distinctive structure development rates of agar sols that dynamically and naturally evolve to form gels.

Dielectric Studies on Molecular Dynamics of Two Important Disaccharides: Sucrose and Trehalose

Broadband dielectric measurements were carried out in the supercooled as well as in the glassy state of two very important disaccharides: trehalose and sucrose. Multiple relaxation processes were observed. Above the glass transition temperatures of examined disaccharides structural relaxation of cooperative origin was detected, where in the glassy state more local motions (secondary modes) appeared. Our data were discussed in light of the findings reported by other groups. We pointed out that sample preparation might impact mobility and, thus, dielectric loss spectra in a significant way. Consequently, it may lead to misinterpretation of the dielectric relaxation processes. Moreover, impact of physical aging and pressure on dynamics of two secondary relaxation processes observed in the glassy state of trehalose and sucrose has been investigated. Additionally, we have demonstrated that, in contrast to the calorimetric measurements (DSC), activation energies of the β- and γ-relaxation processes observed in the glassy state of sucrose and trehalose do not change as a result of physical aging. Finally, we found out that the β-relaxation process slows down as pressure increases. We interpreted this fact in view of increasing rigidity of the structures of disaccharides.

Two New Dy3Triangles with Trinuclear Circular Helicates and Their Single-Molecule Magnet Behavior

Self-assembly of polydentate Schiff base 2,6-diformyl-4-methylphenol di(benzoy1hydrazone) (H(3)L), with dysprosium thiocyanate and sodium azide, affords two novel trinuclear triangular circular helicate dysprosium(III) complexes, [Dy(3)(μ(3)-OCH(3))(2)(HL)(3)(SCN)]·4CH(3)OH·2CH(3)CN·2H(2)O (1) or [Dy(3)(μ(3)-N(3))(μ(3)-OH)(H(2)L)(3)(SCN)(3)](SCN)·3CH(3)OH·H(2)O (2), depending on the presence or absence of base. Single-crystal X-ray analyses show that two μ(3)-methoxy oxygens cap the Dy(3) triangle in complex 1 and that one μ(3)-OH and one μ(3)-N(3)(-) cap the Dy(3) triangle of complex 2, representing the first example of a μ(3)-N(3)(-)-capped lanthanide complex reported to date. Ac susceptibility measurements reveal that multiple relaxation processes and the onset of slow magnetization relaxation occur for complex 1 and 2, respectively. Theoretical calculations are required to elucidate the underlying mechanism; however, the different magnetic anisotropy of the respective structures, which is dictated by the coordination environment of Dy(III) ions and structural parameters of the triangles, is mostly responsible for the distinctive relaxation dynamics observed.

Effect of attrition time on the microwave permeability of magnetic Fe-Si-Al flakes

Fe-Si-Al particles with irregular shapes have been successfully milled into flaky shapes by attrition for 10, 20, and 30 h, respectively. The attrition time has very small effect on the static magnetic properties, but shows strong effects on the high frequency properties (permittivity and permeability). With increasing the attrition time, the values of permeability can be obviously enhanced, especially at lower frequencies. The high frequency permittivity values of flakes milled for 30 h are much larger than those of particles milled for 10 or 20 h. A multiple relaxation processes model has been used to study the permeability dispersion behaviors. Analysis show the variation of shape anisotropy could be the main cause for the observed changes in permeability dispersion behaviors. However, the electromagnetic wave absorption properties of composites filled with these flaky shape Fe-Si-Al particles are found deteriorated when the particles have been milled for longer time.

A carbon-rich ruthenium decorated dysprosium single molecule magnet

The association of a carbon-rich ruthenium complex with an anisotropic dysprosium ion leads to a unique complex showing SMM behaviour with multiple relaxation processes.

Molecular dynamics and crystallization phenomenon of supercooled and glassy DNA and RNA nucleosides:β-adenosine,β-thymidine, andβ-uridine

Nucleosides are chemical compounds that have an extremely important biological role; they can be found in all types of living organisms. They are crucial components from which DNA and RNA acids are built. In addition, nucleosides are key regulators of many physiological processes. In this paper, the molecular dynamics in the liquid and glassy state of three selected nucleosides, β-adenosine, β-thymidine, and β-uridine, was investigated by means of dielectric spectroscopy. Our results revealed multiple relaxation processes associated with different types of molecular motions. Besides the primary α relaxation, two secondary modes in the glassy states of examined compounds were identified. Crystallization progress monitored by dielectric spectroscopy and x-ray diffraction technique at isostructural relaxation conditions revealed that the examined nucleosides possess completely different tendencies to recrystallize from the liquid as well as the glassy state. We have also made an attempt to predict the time scale of molecular motion below the glass transition temperatures of the respective nucleosides to discuss their potential stability at room temperature over prolonged storage time. Finally, combination of molecular mobility studies with evaluation of thermodynamic parameters from calorimetric measurements allowed us to discuss the fundamental roles of both kinetic and thermodynamic factors in governing the physical stability of the glassy state.

Multiple relaxation processes versus the fragile-to-strong transition in confined water

Broadband dielectric spectroscopy data on water confined in three different environments, namely at the surface of a globular protein or inside the small pores of two silica substrates, in the temperature range 140 K ≤ T ≤ 300 K, are presented and discussed in comparison with previous results from different techniques. It is found that all samples show a fast relaxation process, independently of the hydration level and confinement size. This relaxation is well known in the literature and its cross-over from Arrhenius to non-Arrhenius temperature behavior is the object of vivid debate, given its claimed relation to the existence of a second critical point of water. We find such a cross-over at a temperature of ~180 K, and assign the relaxation process to the layer of molecules adjacent and strongly interacting with the substrate surface. This is the water layer known to have the highest density and slowest translational dynamics compared to the average: its apparent cross-over may be due to the freezing of some degree of freedom and survival of very localized motions alone, to the onset of finite size effects, or to the presence of a calorimetric glass transition of the hydration shell at ~170 K. Another relaxation process is visible in water confined in the silica matrices: this is slower than the previous one and has distinct temperature behaviors, depending on the size of the confining volume and consequent ice nucleation.