Phase-field approach to fracture for finite-deformation contact problems

The present contribution deals with a variationally consistent Mortar contact algorithm applied to a phase-field fracture approach for finite deformations, see [4]. A phase-field approach to fracture allows for the numerical simulation of complex fracture patterns for three dimensional problems, extended recently to finite deformations (see [2] for more details). In a nutshell, the phase-field approach relies on a regularization of the sharp (fracture-) interface. In order to improve the accuracy, a fourth-order Cahn-Hilliard phase-field equation is considered, requiring global C¹ continuity (see [1]), which will be dealt with using an isogeometrical analysis (IGA) framework. Additionally, a newly developed hierarchical refinement scheme is applied to resolve for local physical phenomena e.g. the contact zone (see [3] for more details). The Mortar method is a modern and very accurate numerical method to implement contact boundaries. This approach can be extended in a straightforward manner to transient phase-field fracture problems. The performance of the proposed methods will be examined in a representative numerical example. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Position-specific isotope analysis of the methyl group carbon in methylcobalamin for the investigation of biomethylation processes

In the environment, the methylation of metal(loid)s is a widespread phenomenon, which enhances both biomobility as well as mostly the toxicity of the precursory metal(loid)s. Different reaction mechanisms have been proposed for arsenic, but not really proven yet. Here, carbon isotope analysis can foster our understanding of these processes, as the extent of the isotopic fractionation allows to differentiate between different types of reaction, such as concerted (S_N2) or stepwise nucleophilic substitution (S_N1) as well as to determine the origin of the methyl group. However, for the determination of the kinetic isotope effect the initial isotopic value of the transferred methyl group has to be determined. To that end, we used hydroiodic acid for abstraction of the methyl group from methylcobalamin (CH₃Cob) or S-adenosyl methionine (SAM) and subsequent analysis of the formed methyl iodide by gas chromatography (GC) isotope ratio mass spectrometry (IRMS). In addition, three further independent methods have been investigated to determine the position-specific δ ¹³C value of CH₃Cob involving photolytic cleavage with different additives or thermolytic cleavage of the methyl-cobalt bonding and subsequent measurement of the formed methane by GC-IRMS. The thermolytic cleavage gave comparable results as the abstraction using HI. In contrast, photolysis led to an isotopic fractionation of about 7 to 9 ‰. Furthermore, we extended a recently developed method for the determination of carbon isotope ratios of organometal(loid)s in complex matrices using hydride generation for volatilization and matrix separation before heart-cut GC and IRMS to the analysis of the low boiling partly methylated arsenicals, which are formed in the course of arsenic methylation. Finally, we demonstrated the applicability of this methodology by investigation of carbon fractionation due to the methyl transfer from CH₃Cob to arsenic induced by glutathione.

Quantum‐Chemical and Electrochemical Investigation of the Electrochemical Windows of Halogenated Carborate Anions

The range of electrochemical stability of a series of weakly coordinating halogenated (Hal=F, Cl, Br, I) 1‐carba‐closo‐dodecaborate anions, [1‐R‐CB₁₁X₅Y₆]^? (R=H, Me; X=H, Hal, Me; Y=Hal), has been established by using quantum chemical calculations and electrochemical methods. The structures of the neutral and dianionic radicals, as well as the anions, have been optimized by using DFT calculations at the PBE0/def2‐TZVPP level. The calculated structures are in good agreement with existing experimental data and with previous calculations. Their gas‐phase ionization energies and electron affinities were calculated based on their optimized structures and were compared with experimental (cyclic and square‐wave) voltammetry data. Electrochemical oxidation was performed in MeCN at room temperature and in liquid sulfur dioxide at lower temperatures. All of the anions show a very high resistance to the onset of oxidation (2.15–2.85 V versus Fc^0/+), with only a minor dependence of the oxidation potential on the different halogen substituents. In contrast, the reduction potentials in MeCN are strongly substituent dependent (?1.93 to ?3.32 V versus Fc^0/+). The calculated ionization energies and electron affinities correlate well with the experimental redox potentials, which provide important verification of the thermodynamic validity of the mostly irreversible redox processes that are observed for this series. The large electrochemical windows that are afforded by these anions indicate their suitability for electrochemical applications, for example, as supporting electrolytes.     

Relaxing mixed integer optimal control problems using a time transformation

Mixed integer control systems are used to model dynamical behavior that can change instantly, for example a driving car with different gears. Changing a gear corresponds to an instant change of the differential equation what is achieved in the model by changing the value of the integer control function. The optimal control of a mixed integer control system by a discretize-then-optimize approach leads to a mixed integer optimization problem that is not differentiable with respect to the integer variables, such that gradient based optimization methods can not be applied. In this work, differentiability with respect to all optimization variables is achieved by reformulating the mixed integer optimal control problem (MIOCP). A fixed integer control function and a time transformation are introduced. The combination of both allows to change the sequence of active differential equations by partially deactivating the fixed integer control function. In contrast to other works, here different fixed integer control functions are taken into account. Advantages of so called control consistent (CC) fixed integer control functions are discussed and confirmed on a numerical example. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Parallel solution of volume-coupled multi-field problems using an Abaqus-PANDAS software interface

Numerical simulations have proven to be a powerful tool in several engineering disciplines, such as mechanical, civil and biomechanical engineering, and are thus widely used. However, the reliability of the simulations strongly relies on the governing material model. These models are usually developed in academic or industrial research projects and are implemented into dedicated software packages to proof their concepts. A transfer of these models from the research into a production-related environment is often time consuming and prone to failures, and therefore a costly task. The present work introduces a general interface between the research code PANDAS, which is a dedicated multi-field finite-element solver based on a monolithic solution strategy, and the commercial finite-element package Abaqus. The coupling is based on the user-defined element subroutine (UEL) of Abaqus. This procedure, on the one hand, allows for a straight-forward embedding of the PANDAS material models into Abaqus. On the other hand, it provides, in comparison to the native UEL subroutine of Abaqus, a user-friendly programming environment for user-defined material models with an extended number of degrees of freedom. Furthermore, the coupling also supports the parallel-analysis capabilities for large-scale problems on high-performance computing clusters. The Abaqus-PANDAS linkage can be applied to various coupled multi-field problems. However, the present contribution addresses, in particular, volume-coupled multi-field problems as they arise when proceeding from the Theory of Porous Media (TPM) as a modelling framework. For instance, it can be used to model partially or fully saturated soils, or chemically or electro-chemically driven swelling phenomena as they appear, for example, within hydrogels. Additionally, discontinuities, such as cracks, can be described for instance via phase-field models or by the extended finite-element method (XFEM). (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stable and Storable N(CF3)2 Transfer Reagents

Fluorinated groups are essential for drug design, agrochemicals, and materials science. The bis(trifluoromethyl)amino group is an example of a stable group that has a high potential. While the number of molecules containing perfluoroalkyl, perfluoroalkoxy, and other fluorinated groups is steadily increasing, examples with the N(CF₃)₂ group are rare. One reason is that transfer reagents are scarce and metal-based storable reagents are unknown. Herein, a set of Cu^I and Ag^I bis(trifluoromethyl)amido complexes stabilized by N- and P-donor ligands with unprecedented stability are presented. The complexes are stable solids that can even be manipulated in air for a short time. They are bis(trifluoromethyl)amination reagents as shown by nucleophilic substitution and Sandmeyer reactions. In addition to a series of benzylbis(trifluoromethyl)amines, 2-bis(trifluoromethyl)amino acetate was obtained, which, upon hydrolysis, gives the fluorinated amino acid N,N-bis(trifluoromethyl)glycine.     

Pentafluoroethylaluminates: A Combined Synthetic,Spectroscopic, and Structural Study

Salts of the tetrakis(pentafluoroethyl)aluminate anion [Al(C₂F₅)₄]⁻ were obtained from AlCl₃ and LiC₂F₅. They were isolated with different counter-cations and characterized by NMR and vibrational spectroscopy and mass spectrometry. Degradation of the [Al(C₂F₅)₄]⁻ ion was found to proceed via 1,2-fluorine shifts and stepwise loss of CF(CF₃) under formation of [(C₂F₅)_4−nAlF_n]⁻ (n=1–4) as assessed by NMR spectroscopy and mass spectrometry and supported by results of DFT calculations. In addition, the [(C₂F₅)AlF₃]⁻ ion was structurally characterized.     

An Iterative Divergent Approach to Conjugated Starburst Borane Dendrimers

Using a new divergent approach, conjugated triarylborane dendrimers were synthesized up to the 2^nd generation. The synthetic strategy consists of three steps: 1) functionalization, via iridium catalyzed C−H borylation; 2) activation, via fluorination of the generated boronate ester with K[HF₂] or [N(nBu₄)][HF₂]; and 3) expansion, via reaction of the trifluoroborate salts with aryl Grignard reagents. The concept was also shown to be viable for a convergent approach. All but one of the conjugated borane dendrimers exhibit multiple, distinct and reversible reduction potentials, making them potentially interesting materials for applications in molecular accumulators. Based on their photophysical properties, the 1^st generation dendrimers exhibit good conjugation over the whole system. However, the conjugation does not increase further upon expansion to the 2^nd generation, but the molar extinction coefficients increase linearly with the number of triarylborane subunits, suggesting a potential application as photonic antennas.     

Boron: Its Role in Energy‐Related Processes and Applications

Boron's unique position in the Periodic Table, that is, at the apex of the line separating metals and nonmetals, makes it highly versatile in chemical reactions and applications. Contemporary demand for renewable and clean energy as well as energy‐efficient products has seen boron playing key roles in energy‐related research, such as 1) activating and synthesizing energy‐rich small molecules, 2) storing chemical and electrical energy, and 3) converting electrical energy into light. These applications are fundamentally associated with boron's unique characteristics, such as its electron‐deficiency and the availability of an unoccupied p orbital, which allow the formation of a myriad of compounds with a wide range of chemical and physical properties. For example, boron's ability to achieve a full octet of electrons with four covalent bonds and a negative charge has led to the synthesis of a wide variety of borate anions of high chemical and electrochemical stability—in particular, weakly coordinating anions. This Review summarizes recent advances in the study of boron compounds for energy‐related processes and applications.