Variational integration in endochronic theory for small strain elastoplastodynamics

This paper presents a basic endochronic plasticity model with isotropic hardening for small strain theory according to Valanis. The key point of this model is a convolution integral over an intrinsic time scale involving past values of the strain measure and a so-called memory kernel which leads to a smooth evolution equation for the internal variable. For the temporal discretization of the underlying constitutive equations and the resulting evolution equation we use higher order accurate variational integrators (VI). The remarkable feature is the fact that we approximate the position vector in terms of velocities according to partitioned Runge-Kutta methods (pRK). As a representative model problem serves a quasistatic, uniaxial tensile testing as well as a dynamic, elastoplastic cantilever beam with a smooth plasticity model according to the Valanis framework. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Spectral Assignment of Phenanthrene Derivatives Based on 6H-Dibenzo[C,E][1,2] Oxaphosphinine 6-Oxide by NMR and Quantum Chemical Calculations

Abstract

Organophosphorus compounds such as 6H-dibenzo[c,e][1,2]oxaphosphinine 6-oxide (DOPO, 1) and its derivatives are important and versatile compounds for a broad field of applications. However, a thorough spectral assignment is often subordinate to its chemical properties. This article presents and unambiguously attributes the ¹H and ¹³C NMR spectra of DOPO (1), selected products yielded from the Atherton–Todd reaction (2–4), DOPO-HQ (5) as well as sulfur derivatives (6–7) via a set of 1D- and 2D-NMR experiments. The complex P-C and P-H coupling patterns are discussed and compared with the derivatives possessing different chemical environments around the phosphorus atom. In addition, we compared our results with density functional theory calculations. Even though the prediction of NMR data of organophosphorus compounds via molecular modeling is limited, this study presents a method that yields good results for this class of heterocycles. This knowledge should help to quickly assign NMR spectroscopic data of other DOPO (1) derivatives and can be extrapolated to organophosphorus compounds in general.

Supplemental materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfur, and Silicon and the Related Elements for the following free supplemental resource: NMR Spectra of Compounds 1-7 (Figures S1 - S15).     

Phospha-alkynes - Useful Building Blocks in Organic Chemistry1

Abstract

The syntheses of phospholes (7, [3+2]-cycloaddition), bicyclophosphaalkenes (17, [4+2]-cycloaddition), and phosphabenzenes (15, [4+2]-cycloaddition followed by an extrusion process) starting from the phosphaalkynes (4) are described. The 2–Dewar phosphabenzene 18, obtained from the cyclobutadiene 21 and 4 (R =^tBu), is the starting material for the synthesis of the valency isomers 19, 20, 22, and 23.     

Hexa-Coordinated Silicon Complexes Derived from Regioisomeric Aminotriphenylethanols and Their use as Dopants for Liquid Crystals

Abstract

Tridentate imine ligands that are obtained from the chiral, regioisomeric amino alcohols 2-amino-1,1,2-triphenyethanol and 2-amino-1,2,2-triphenylethanol serve for the formation of bis-chelated silicon complexes. Whereas the complex based on the former amino alcohol is obtained as a diastereomeric mixture, the complex that is derived from 2-amino-1,2,2-triphenylethanol forms in a completely diastereoselective manner, and its configuration is determined as (A,R,R), according to a crystal structure analysis. The new silicon complexes are found to be efficient dopants for the conversion of nematic liquid crystals into cholesteric phases.

GRAPHICAL ABSTRACT