Amplitude dependence of filler-reinforced rubber: Experiments,constitutive modelling and FEM – Implementation

The focus of the present paper is the experimental investigation, the constitutive representation and the numerical simulation of the amplitude dependence of filler-reinforced elastomers. A standard way to investigate the dynamic properties of viscoelastic materials is via the dynamic modulus which is obtained from stress signals due to harmonic strain excitations. Based on comprehensive experimental data, an amplitude-dependent constitutive model of finite viscoelasticity is developed. The model is based on a modified Maxwell chain with process-dependent viscosities which depend on additional internal state variables. The evaluation of this thermodynamically consistent model is possible in both the time domain, via stress-time signals, and in the frequency domain, via the dynamic modulus. This property is very profitable for the parameter identification process. The implementation of the constitutive model into the commercial finite element code ANSYS with the user-programmable feature (UPF) USERMAT for large deformations in updated Lagrange formulation is presented. This implementation allows simulating the time-dependent behaviour of rubber components under arbitrary transient loading histories. Due to physical and geometrical nonlinearities, these simulations are not possible in the frequency domain. But, transient FEM computations of large loading histories are sometimes not possible in an acceptable time. In the context of the parameter identification the fundamental ideas are presented, how this problem has been solved. Transient FEM simulations of real rubber components are also shown to visualize the properties of the model in the context of the transient material behaviour.     

Molecular understanding of alumina supported single-site catalysts by a combination of experiment and theory

The nature and structure of grafted organometallic complexes on gamma-alumina are studied from a combination of experimental data (mass balance analysis, IR, NMR) and density functional theory calculations. The chemisorptive interactions of two complexes are analyzed and compared. The reaction of [Zr(CH2tBu)4] with alumina dehydroxylated at 500 degrees C gives {[(AlsO)2Zr(CH2tBu)]+[(tBuCH2)(Als)]-}, a bisgrafted cationic complex as major surface species. The DFT calculations show that the reaction with surface hydroxyls is very exothermic and that alkyl transfer on Al atoms is favored. In contrast, [W(CtBu)(CH2tBu)3] reacts with an alumina treated under identical conditions to give selectively a monografted neutral surface complex, [(AlsO)W(CtBu)(CH2tBu)2]. This was inferred by the evolution of 1 equiv of tBuCH3 per grafted W and the presence of remaining hydroxyls. The calculations show that the reaction of [W(CtBu)(CH2tBu)3] with surface hydroxyls is in fact less exothermic and has a considerably higher activation barrier than the one of the Zr complex. Additionally, the transfer of an alkyl ligand onto an adjacent Al center is disfavored, and hence cationic species are not formed. Some ligands of this monoaluminoxy surface complex interact with remaining surface hydroxyls, which explains the complexity of the experimental NMR and IR data.     

Solid-state NMR of a paramagnetic DIAD-FeII catalyst: sensitivity, resolution enhancement, and structure-based assignments

A general protocol for the structural characterization of paramagnetic molecular solids using solid-state NMR is provided and illustrated by the characterization of a high-spin Fe(II) catalyst precursor. We show how good NMR performance can be obtained on a molecular powder sample at natural abundance by using very fast (>30 kHz) magic angle spinning (MAS), even though the individual NMR resonances have highly anisotropic shifts and very short relaxation times. The results include the optimization of broadband heteronuclear (proton-carbon) recoupling sequences for polarization transfer; the observation of single or multiple quantum correlation spectra between coupled spins as a tool for removing the inhomogeneous bulk magnetic susceptibility (BMS) broadening; and the combination of NMR experiments and density functional theory calculations, to yield assignments.     

A modelling approach for the heterogeneous oxidation of elastomers

The influence of oxygen on elastomers, known as oxidation, is one of the most important ageing processes and becomes more and more important for nowadays applications. The interaction with thermal effects as well as antioxidants makes oxidation of polymers a complex process. Based on the polymer chosen and environmental conditions, the ageing processes may behave completely different. In a lot of cases the influence of oxygen is limited to the surface layer of the samples, commonly referred to as diffusion-limited oxidation. For the lifetime prediction of elastomer components, it is essential to have detailed knowledge about the absorption and diffusion behaviour of oxygen molecules during thermo-oxidative ageing and how they react with the elastomer. Experimental investigations on industrially used elastomeric materials are executed in order to develop and fit models, which shall be capable of predicting the permeation and consumption of oxygen as well as changes in the mechanical properties. The latter are of prime importance for technical applications of rubber components. Oxidation does not occur homogeneously over the entire elastomeric component. Hence, material models which include ageing effects have to be amplified in order to consider heterogeneous ageing, which highly depends on the ageing temperature. The influence of elevated temperatures upon accelerated ageing has to be critically analysed, and influences on the permeation and diffusion coefficient have to be taken into account. This work presents phenomenological models which describe the oxygen uptake and the diffusion into elastomers based on an improved understanding of ongoing chemical processes and diffusion limiting modifications. On the one side, oxygen uptake is modelled by means of Henry’s law in which solubility is a function of the temperature as well as the ageing progress. The latter is an irreversible process and described by an inner differential evolution equation. On the other side, further diffusion of oxygen into the material is described by a model based on Fick’s law, which is modified by a reaction term. The evolved diffusion-reaction equation depends on the ageing temperature as well as on the progress of ageing and is able to describe diffusion-limited oxidation.     

Double dynamers: molecular and supramolecular double dynamic polymers

The formation of double dynamers, polymers that are dynamic on both the molecular and supramolecular levels, was achieved in solution and corroborated by electron microscopy; NMR and mass spectrometry studies confirm their double molecular and supramolecular nature.     

Novel reaction products from the hypervalent iodine oxidation of hydroxylated stilbenes and isoflavones

Novel reaction pathways for the hypervalent iodine-mediated oxidation of bioactive phenols containing extended conjugated pi-systems are described. Oxidation of 4-hydroxystilbenes in methanol using a hypervalent iodine-based oxidant led to the formal 1,2-addition of methoxy groups across the central stilbene double bond. Treatment of the structurally related 4-hydroxyisoflavone with di(trifluoroacetoxy)iodobenzene leads to the surprising formation of 2,4'-dihydroxybenzil. Potential mechanisms for these new reaction pathways are discussed, and the X-ray crystal structure of 2,4'-dihydroxybenzil is presented. In contrast, oxidation of the corresponding 3-hydroxystilbenes and 3-hydroxyisoflavone led to conventional dienone oxidation products. The antitumour implications of these oxidation processes are briefly highlighted; the novel 4-substituted phenolic oxidation products were found to be inactive in terms of in vitro antitumour cellular activity, whereas the 3-substituted phenol products gave novel agents with potent and enhanced antitumour activity in the HCT 116 cancer cell line.     

Supramolecular polymers generated from heterocomplementary monomers linked through multiple hydrogen-bonding arrays--formation, characterization, and properties

Supramolecular polymers are described that are derived from the association of two homoditopic heterocomplementary monomers through sextuple hydrogen-bonding arrays. They form fibers and a variety of different materials depending on the conditions. The strong affinity of the DAD-DAD (D=donor, A=acceptor) hydrogen-bonding sites for double-faced cyanuric acid type wedges drives the supramolecular polymeric assembly in apolar and chlorinated organic solvents. The marked influence of stoichiometry, as well as end-capping and cross-linking agents upon fiber formation is revealed in solution and by electron microscopy (EM). The results further contribute to the development of a supramolecular polymer chemistry that comprises reversible polymers formed through recognition-controlled noncovalent connections between the molecular components. Such materials are, by nature, dynamic and present adaptive character in view of their ability to respond to external stimuli.     

Monitoring the differential ordering of enantiomers included into cyclodextrins through deuterium NMR in lyotropic liquid crystals

Deuterium NMR in an aqueous non-chiral liquid crystal allows the discrimination of enantiomers through their ordering inside beta-cyclodextrins.     

Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; A method for computing all of them. Part 2: Numerical application

Summary The present paper, together with the previous one (Part 1: Theory, published in this journal) is intended to give an explicit method for computing all Lyapunov Characteristic Exponents of a dynamical system. After the general theory on such exponents developed in the first part, in the present paper the computational method is described (Chapter A) and some numerical examples for mappings on manifolds and for Hamiltonian systems are given (Chapter B).

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Sommario Questo articolo, insieme con il precedente (Parte 1: Teoria, pubblicato in questa stessa rivista) è inteso a fornire un metodo esplicito per il calcolo di tutti gli esponenti caratteristici di Lvapunov per un sistema dinamico. Dopo la teoria generale su tali esponenti sviluppata nella prima parte, qui si illustra il metodo di calcolo (Capitolo A) e si danno esempi numerici per applicazioni di varietà in sè e per sistemi Hamiltoniani (Capitolo B).