Relaxation Domains Research Articles

Post-consumer high density polyethylene/zirconium phosphate and aluminum hydroxide composites: Assessment of physico-mechanical and flame retardancy properties

Regarding environmental preservation, the upcycling of plastics from petroleum source is a consistent alternative. This work intended to investigate melting extruded composites of post-consumer HDPE (rHDPE) filled with pristine zirconium phosphate (ZrP), aluminum hydroxide [Al(OH)3] and aluminum hydroxide modifying-zirconium phosphate [ZrPOct/Al(OH)3]. Physico-mechanical and flame retardancy were assessed. FTIR revealed that rHDPE brought some degree of oxidative degradation probably from its cleaning process and/or processing. By nuclear magnetic resonance at time domain, rHDPE showed three relaxation domains. Fillers induced the lowering of rHDPE relaxation time owing to polymer/filler by hydrogen bonds. Diffraction pattern of rHDPE/Al(OH)3 and rHDPE/ZrPOct/Al(OH)3 indicated better fillers’ dispersion. Fillers changed rHDPE crystallinity degree and thermal stability but rheologic properties were invariable. For all composites, elastic modulus increased (up to 17%) indicating stiffening. Yield strength did not change but stress and strain at break decreased. For the composites, SEM/EDS showed better dispersion and distribution of ZrP and ZrPOct/Al(OH)3 particles. It was assumed that ZrP and ZrPOct/Al(OH)3 greatly increased the flame retardancy. The work corroborates the importance of polymers’ upcycling, and it is in consonance with the objectives of 2030 Agenda released by United Nations.

Multilayered Atomic Relaxation in van der Waals Heterostructures

When two-dimensional van der Waals materials are stacked to build heterostructures, moir\'e patterns emerge from twisted interfaces or from mismatch in lattice constant of individual layers. Relaxation of the atomic positions is a direct, generic consequence of the moir\'e pattern, with many implications for the physical properties. Moir\'e driven atomic relaxation may be naively thought to be restricted to the interfacial layers and thus irrelevant for multi-layered heterostructures. However, we provide experimental evidence for the importance of the three dimensional nature of the relaxation in two types of van der Waals heterostructures: First, in multi-layer graphene twisted on graphite at small twist angles ($\theta\approx0.14^\circ$) we observe propagation of relaxation domains even beyond 18 graphene layers. Second, we show how for multi-layer PdTe$_2$ on Bi$_2$Se$_3$ the moir\'e lattice constant depends on the number of PdTe$_2$ layers. Motivated by the experimental findings, we developed a continuum approach to model multi-layered relaxation processes based on the generalized stacking fault energy functional given by ab-initio simulations. Leveraging the continuum property of the approach enables us to access large scale regimes and achieve agreement with our experimental data for both systems. Furthermore it is well known that the electronic structure of graphene sensitively depends on local lattice deformations. Therefore we study the impact of multi-layered relaxation on the local density of states of the twisted graphitic system. We identify measurable implications for the system, experimentally accessible by scanning tunneling microscopy. Our multi-layered relaxation approach is not restricted to the discussed systems, and can be used to uncover the impact of an interfacial defect on various layered systems of interest.

The use of fast field cycling to evaluate the time domain relaxation of starches from tropical fruit seeds

ABSTRACTA proton NMR relaxation study of the molecular dynamics in flour samples of ‘Eugenia uniflora’ (‘Pitanga’), ’Citrus reticulate’ (‘Tangerine’), ‘Prunus persica’ (‘Peach’), ‘Vitis vinifera’ (‘Grape’), and ‘Cucumis melo’ (‘Honeydew melon’) seeds is presented. The spin–lattice relaxation time was obtained over a broad frequency range from 100 kHz to 100 MHz using both conventional and fast field-cycling NMR techniques. This relaxometry study made possible a comparison between the molecular dynamics behaviour of starch from different fruit seeds and from potatoes. I was possible to conclude that the spin–lattice dispersion presents slightly differences for all samples, in particular at low frequencies. All relaxation dispersions could be well interpreted in terms of power-law relaxation models and domains with different power-law relaxation exponents. For the Peach seeds flour the relaxation dispersion at low frequencies was very similar to that observed for potato’s starch incorporated with 5% organoclay Viscogel B8 nanoparticles.

Microstructure aspects of radiation-cured networks: Cationically polymerized aromatic epoxy resins

The thermo-mechanical properties and nanostructural features of epoxy aromatic resins cationically cured by UV–visible or electron beam radiation have been studied by FT-NIR spectroscopy, dynamic mechanical analysis (DMA), dielectric spectroscopy (DS), and atomic force microscopy (AFM). The influence of formulation (nature and content of onium salt) and of curing parameters (doses, thermal treatment) on the thermophysical have been investigated. The presence of several relaxation domains observed by DMA and DS analysis confirms the presence of heterogeneities in the cured materials. Network formation is described by the percolation of glassy nanoclusters which are evidenced by AFM analyses. AFM probing by quantitative nanomechanical measurements confirms the gradual build-up of the local Young's modulus in good agreement with the macroscopic value.

Field effects to slow magnetic relaxation in a mononuclear Ni(ii) complex.

A mononuclear Ni(ii) complex [Ni(NCS)2(nqu)2(H2O)2]·2nqu (nqu - 5-nitroquinoline) shows a field induced slow magnetic relaxation with three relaxation domains. The relaxation time for the low-frequency mode is as slow as τ = 0.3 s at T = 1.9 K and BDC = 0.4 T.

Hydrazone‐Ligand‐Based Homodinuclear Lanthanide Complexes: Synthesis, Structure, and Magnetism

A series of dinuclear lanthanide complexes, [Dy2(LH)2(µ2‐Piv‐κ2O,O′)2(NO3‐κ2O,O′)2] (1), [Tb2(LH)2(µ2‐Piv‐κ2O,O′)2(NO3‐κ2O,O′)2] (2), [Gd2(LH)2(µ2‐Piv‐κ2O,O′)2(NO3‐κ2O,O′)2] (3), and [Ho2(LH)2(µ2‐Piv‐κ2O,O′)2(NO3‐κ2O,O′)2] (4) have been synthesized by the reaction of Ln(NO3)3·nH2O with the multidentate hydrazone‐based Schiff‐base ligand, N′‐(2‐hydroxy‐3‐methoxybenzylidene)acetohydrazide (LH2) in the presence of pivalic acid. X‐ray crystallography data reveals that 1–4 are isostructural, neutral, and contain two mono‐deprotonated ligands, two pivalates, and two chelated nitrates. Within the dinuclear assembly, the two lanthanides are bridged by two phenolate and two pivalate oxygens. Each of the two lanthanide ions is nine‐coordinated and possesses a distorted monocapped square‐antiprism geometry. Detailed magnetochemical analysis revealed the presence of weak antiferromagnetic coupling at low temperature for all complexes. The DyIII analogue displayed SMM behavior in the absence of a dc field with two relaxation domains in which the thermally activated domain exhibits an energy barrier of 40 K and relaxation time of 6.5 × 10–5 s.

Investigação da influência do processamento na dinâmica molecular de nanocompósitos de policarbonato e argila organofílica obtidos via intercalação por fusão

Nanocompósitos baseados em policarbonato e argila organofílica foram obtidos pelo método de intercalação por fusão em câmara de mistura sob diferentes valores de torque e temperatura. A influência desses parâmetros na qualidade da dispersão da argila na matriz polimérica foi investigada por ressonância magnética nuclear (RMN) de baixo campo, empregando o tempo de relaxação longitudinal, T1H, e por difração de raios X. As diferenças nos tempos de relaxação longitudinal e nos padrões de difração de raios X foram correlacionadas com a formação de domínios com mobilidades distintas. O nanomaterial formado apresentou morfologia intercalada com afastamento crescente das camadas de argila, conforme as condições de processamento se tornavam mais severas. A RMN ¹H mostrou que tanto o cisalhamento quanto a temperatura afetaram a mobilidade das cadeias poliméricas, explicitando a homogeneidade crescente da distribuição dos domínios de relaxação, de acordo com o aumento do torque e da temperatura.

Modeling and Simulation of Viscoelastic Behavior of Three-Phase Polymer Blends with Multiple Droplet Morphology

Three-phase polymer blends with ``multiple droplet" morphology are important industrially. They are referred to as ``double emulsions" as the droplets of these blends themselves contain a number of smaller droplets inside. In this work, the dynamic viscoelastic behavior of double emulsions composed of three immiscible polymeric liquids is modeled. Simulations show that such double emulsions exhibit three relaxation domains due to relaxation of two different interfaces (internal and external) and the matrix polymer. The factors affecting the dynamic viscoelastic behavior of double emulsions composed of three immiscible polymeric liquids are discussed.

On the viscoelastic behavior of multiple emulsions

The dynamic viscoelastic behavior of multiple emulsions is investigated. A modified Palierne model is used to predict the storage and loss moduli of multiple emulsions. The multiple emulsions exhibit two relaxation domains due to relaxation of two different interfaces—internal and external. The internal interface is the interface between internal droplets and their suspending medium (primary emulsion continuous-phase). The external interface is the interface between multiple-emulsion droplets and their suspending medium (external continuous-phase). The factors affecting the dynamic viscoelastic behavior of multiple emulsions are discussed.

Viscoelastic Relaxation of Cross-Linked, Alternating Copolymers in the Free-Draining Limit

We study theoretically the viscoelastic relaxation of cross-linked copolymers in the framework of generalized Gaussian structures (GGS), which are extensions of the Rouse model to arbitrary geometries. The model holds for general homogeneous copolymers under free-draining conditions; it is especially suitable for treating alternating copolymers. We calculate the storage G‘(ω) and the loss G‘‘(ω) moduli both for un-cross-linked and for cross-linked copolymer chains, and observe a variety of features: alternating copolymers differ from homopolymers in the high-frequency domain, where G‘‘(ω) may display two maxima. Cross-linking alternating A−B copolymer chains into regular networks (lattices) leads to the appearance of a network-dominated, low-frequency relaxation domain. In the case of very large differences in the mobility of the A monomers, of the B monomers, and of the cross-links, G‘(ω) is very structured, displaying three relaxation domains, separated by two plateaus. G‘‘(ω) shows three peaks. We exp...

Relaxation phenomena in AOT-water-decane critical and dense microemulsions

We report on extensive measurements of the low and high frequencies sound velocity and sound absorption in AOT-water-decane microemulsions deduced from ultrasonic and, for the first time as far as the absorption is concerned, from Brillouin scattering experiments. New experimental results on dielectric relaxation are also reported. Our results, which include data taken for critical as well as dense microemulsions, show new interesting relaxation phenomena. The relaxation frequencies deduced from very high frequency acoustical measurements are in good agreement with new high frequency dielectric relaxation measurements. We show that along the critical isochore, sound dispersion, relaxation frequency, and static dielectric permittivity can be accurately fitted to power laws. The absolute values of the new exponents we derived from experimental data are nearly equal, and they are very close to β=0.33 characterising the shape of the coexistence curve. The exponent characterising the infinite frequency permittivity is very close to 0.04 relevant to the diverging shear viscosity. For dense microemulsions, two well defined relaxation domains have been identified and the temperature variations of the sound absorption and the zero frequency dielectric permittivity bear striking similarities. We also show that the relaxation frequency of the slow relaxation process is almost independent of temperature and volume fraction and so cannot be attributed to percolation phenomena, whereas it can more likely be attributed to an intrinsic relaxation process probably connected to membrane fluctuations.

Dielectric relaxation of nonionic microemulsion: influence of the salinity

Study of dielectric properties of a quaternary microemulsion system composed of water, oil, a nonionic surfactant, and an alcohol, in the frequency range 100 kHz – 15 GHz is reported as a function of salt (NaCl) concentration. Depending on the salinity, the decomposition of the dielectric spectra shows the presence of two or three main relaxation domains. The lower relaxation frequency and the corresponding spectral amplitude increase as a function of salinity. The other observed relaxation mechanisms are shown to be dipolar in origin.PACS No.: 97.22Gn

Dielectric properties of faujasites: comparison between types X and Y during dehydration

The dielectric properties of two faujasites, X and Y, were studied in a wide range of frequencies (10–10 6 Hz) at several temperatures and for various outgassing temperatures TT (100–400°C). Conductivity measurements were undertaken with the aim of describing the possible mechanisms of conduction in these materials. The polarization conductivity is ascribed to the cations in the large cages (supercages). The d.c. conductivity is related to the migration of the exchangeable cations over relatively large distances. The corresponding activation energies vary from 0.58 to 0.9 eV for NaX and from 0.61 to 0.85 eV for NaY. These energies vary with TT in a different way for each zeolite. Two relaxation domains, attributed to the cations on sites II and III′, are a function of the dehydration temperature. The activation energies are 0.41–0.58 eV. These two processes are shown by the technique of the thermally stimulated currents–relaxation map analysis.

Determination of the molecular weight distribution of linear polymers by inversion of a blending law on complex viscosities

The method presented in this paper allows to calculate the molecular weight distribution (MWD) of linear homopolymer melts from the complex shear modulus data measured in a wide frequency domain. An empirical blending law on complex viscosities is first developed; as a consequence, the variations of the storage and loss modulus as a function of MWD are presented. This simulation demonstrates also the role of the shape of the MWD itself, and shows that one should not postulate a priori the shape of the MWD. An efficient numerical approach based on a Tikhonov regularization method with constraint is used to solve this ill-posed problem; the MWD is hence derived without any assumption on its shape. This method is first applied on simulated data to prove its numerical efficiency. Then the inversion method is applied on complex moduli data of various commercial polymers (polypropylene, polyethylene and polystyrene) and on an artificial mixture of polystyrene that have been presented in the literature. For amorphous polymers, the coupling of the terminal relaxation domains with the transition region at higher frequency leads to errors in the low molecular weight tail: one way to solve this problem is to cut off the experimental data at the high frequencies. This general method needs only a few physical parameters, namely the scaling law for the Newtonian viscosity η0=f(M w ) and the plateau modulus G N 0, and leads to reasonable results with respect to the simplicity of the viscoelastic model used.

Dielectric Properties of a Faujasite Y as a Function of the Hydration State

The evolution of conduction and polarization phenomena is studied as a function of dehydration temperature (TT varying from 100 up to 400 °C) on a faujasite Y zeolite. The measurements are carried out as a function of frequency at different temperatures. In all cases, the conductivity is ascribed to the migration of cations in large cages involving energies varying from 0.61 to 0.85 eV. Two relaxation domains are observed. It is assumed that they are due to the movement of cations of sites III‘ and II. The existence of these two domains is confirmed by the technique of the thermally stimulated currents. The spreading domain of relaxation depends on the dehydration state of the zeolite.

Ionic conductivity and dielectric response of dehydrated zeolites

A classical hopping model is applied to cation motion in zeolites. Fifteen dielectric relaxation modes and non-zero conductivity are found in zeolite NaA. Using data from previous molecular dynamics simulations, the temperature dependence of activation energies, relaxation frequencies and amplitudes is numerically calculated. Strong deviations from Arrhenius behavior are obtained. These results are consistent with room temperature experimental data and predict two relaxation domains and a lower conductivity activation energy at higher temperatures.

Dielectric properties of an NaX zeolite as a function of the hydration state

The dielectric properties of the NaX zeolite (Si/Al=1.3) have been measured after different thermal treatments in the temperature range 100–400°C. The frequency domain was varied from 10 to 106 Hz, the measuring temperature being in the range 80–150°C. Independent of the outgassing temperature (i.e. the number of water molecules), the ac conductivity is ascribed to migration of the supercage cations. The variation in the migration energy (Edc) as a function of the adsorbed water molecules (0.9–0.58 eV) shows their influence on the conduction process. Two relaxation domains are observed: ‘low-frequency’ and ‘high frequency’ relaxations, which are due to local hops of cations located in sites II and III, respectively. These two relaxations are confirmed by thermally stimulated current measurements. The energies associated with these relaxations vary with the outgassing temperature.

Synergistic effect of zeolite in an intumescence process: study of the carbonaceous structures using solid-state NMR

This work deals with the chemical effect of zeolite 4A added to the intumescent ammonium polyphosphate (APP)–pentaerythritol (PER) system [fire retardant (FR) polyethylene-based formulation]. The study of the thermal behaviour of the system using thermogravimetric (TG) analysis shows that the presence of the zeolite leads to an increase in the stability of the material at high temperature (T > 500 °C). Chemical analysis and cross-polarisation dipolar-decoupled magic-angle spinning (CP–DD–MAS)13C NMR reveals that the materials resulting from the thermal treatment of the APP–PER and APP–PER/4A systems are formed by carbonaceous and phosphocarbonaceous species and that the zeolite enhances the stability of the phosphocarbonaceous species. DD–MAS 31P NMR indicates that this stability may be due to an absence of pyrophosphate species in the heat-treated APP–PER/4A system. Micro-Raman spectroscopy and 1H NMR of the solid state provides information on the structure of the carbonaceous material. Thermal treatment led to the formation of a ‘turbostatic carbon’ with a local structure of this ‘carbon species’, with the zeolite permitting retention of the comparatively unorganised carbon species in the high-temperature range. Moreover, a low-resolution solid-state 1H NMR study of the spin–lattice and spin–spin relaxations of the samples allows an evaluation of the size of the slow relaxation domains using the Goldman–Shen procedure. It is shown that the zeolite hinders the formation of small molecules in the polyaromatic network. Finally, the relationship between the formation of a coherent macromolecular network and the improved FR performance of the APP–PER/4A system is proposed.

A thermally stimulated current/relaxation map analysis of the relaxation processes in aromatic polyester, liquid crystal polymer film

AbstractThermally stimulated current (TSC) and relaxation map analysis (RMA) have been applied to the examination of dynamics of thermally induced relaxation processes in highly oriented, wholly aromatic, polyester liquid crystalline polymer films. Films of two compositions were examined. A primary distinction in composition was the difference in level of 6‐hydroxy‐2‐napthoic acid. Following an analysis protocol developed by Sauer et al., it was found that values of activation enthalpy were well above the zero entropy value at temperatures well below the Sauer “Tg.” This indicates a high level of cooperativity in rotational relaxation processes even at low temperatures. Cooperative rotational relaxation domains were postulated to account for this behavior. The persistence of cooperativity above the Sauer “Tg.” is evidence that these materials did not undergo a conventional glass transition at any temperature in the range–80 to 200°C. The behavior of these materials as a model system of “loosely bundled rods” was examined using a modified Barker–Crine analysis. This type of model behavior seemed to fall off at relatively low temperatures. The occurrence of rotational processes at high temperatures with little or no loss in orientation suggests that polymer chains are physically constrained to maintain their relative positions. © 1994 John Wiley & Sons, Inc.

FRACTAL RELAXATION SYSTEMS. PART III: STRUCTURE AND VIEW SCALES

Abstract This is the third and last part of a series of articles concerned with the study of fractal relaxation systems in the linear range. The article focuses on the discussion of the self-similar and affine features of fractal relaxation systems in the linear range. The singularity structure is shown to be scale invariant, hence it can be reconstructed by applying a given generator, which consists of a simple recursive rule, to an initiator. The related concepts of view scale and structure scale are introduced to investigate the invariants of the singularity structure both in the frequency and relaxation domains.