Self-diffusion in melts of statistical copolymers: The effect of changes in microstructural composition

We have used nuclear reaction analysis to measure diffusion coefficients D in couples consisting of hydrogenated polybutadienes of structure (C₂H₃(C₂H₅))_x(C₄H₈)_1?x and their partly deuterated counterparts. The 1,2- and 1,4-olefinic isomers are randomly distributed along the chains and the mean vinyl fraction x varies between 0.38 and 0.94. We find that the effective monomeric mobility D₀ [defined by D = D₀(N_e/N²) for each copolymer, where N is the backbone length and N_e the entanglement spacing] decreases monotonically with increasing vinyl content x. Over the range of microstructures and temperatures T (?14?40°C) investigated we find log(D₀/T) varies smoothly with (T ? T_g), where T_g is the glass transition temperature of the respective melts. An analysis of our data in terms of a simple activated rate process model suggests that D₀ is controlled by thermally activated hopping of segments whose effective volume is close to that of the respective statistical segment lengths of the copolymeric chains. ©1995 John Wiley & Sons, Inc.     

A fully variational strong discontinuity approach at finite strains

A novel, fully variational three-dimensional finite element formulation for the modeling of locally embedded strong discontinuities at finite strains is presented. The proposed numerical model is based on the Enhanced Assumed Strain concept with an additive decomposition of the displacement gradient into a conforming and an enhanced part. The discontinuous component of the displacement field which is associated with the failure in the modeled structure is isolated in the enhanced part of the deformation gradient. In contrast to previous works, a variational constitutive update is used. The internal variables are determined by minimizing a pseudo-elastic potential. The advantages of such a formulation are well known, e.g. the tangent stiffness matrix is symmetric, standard optimization algorithms can be applied and it represents a natural basis for error estimation and mesh adaption. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling of material failure by combining the advantages of embedded strong discontinuity approaches and classical interface elements

A finite element formulation within the framework of the Strong Discontinuity Approach suitable for the simulation of crack growth is presented. The formulation allows for intersecting discontinuities and similarly to classical interface elements, the cracks are introduced parallel to the element facets. However and in contrast to interface elements, the discontinuities are directly embedded in finite elements, based on the Enhanced Assumed Strain concept. It is shown that a realistic prediction of the mechanical response requires the consideration of more than one crack within each finite element. The proposed formulation is suitable to overcome locking effects and it automatically fulfills crack path continuity. The approach is strictly local yielding an efficient numerical formulation. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Neighboring group effect in Pd-catalyzed carbonylation terminated by lactonization: a need for a protective group and/or DMF

Synthesis of analogues of antifungal podolactones via Pd-catalyzed processes revealed that tandem 6-exo-alkyne carbopalladation/carbonylative lactonization sequence is strongly solvent-dependent. Contrary to earlier reports, premature esterification was the predominant pathway when the starting enynes derived from (Z)-2-iodohex-2-en-1,4-diol were subjected to Pd-catalyzed carbonylation in MeOH. Apparently, irreversible complexation of Pd by the OH group prevented decarbonylation and hence 6-exo-alkyne carbopalladation. Similarly, the influence of the chelation was also evident when the reaction was applied to the analogous preparation of 3-hydroxymethylbutenolides. The neighboring group effect can be efficiently overcome through using DMF as the solvent in combination with protection of the OH function.     

Variational approach to formation of misoriented microstructures in plastic deformation

The formation of misoriented microstructures in plastic deformation is explained within the framework of continuum mechanics as a result of the reduction of the energetically costly hardening in multislip by local lattice rotations. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A basis for the Stickelberger ideal and the system of circular units of a cyclotomic field

A basis for the Stickelberger ideal is constructed, along with a system of independent units that, together with-, where =exp(2i/m), m 2, m 2 (mod 4), generate the group of circular units of the field Q(). As an application, it is possible to obtain a representation for the first and second factors of a number of classes of divisors of the field Q() in the form of determinants.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 175, pp. 69–74, 1989.     

Simultaneous excitation of long and short range surface plasmons in an asymmetric structure

An asymmetric multilayer structure allowing nearly 100% simultaneous excitation of both symmetric and antisymmetric surface plasmons is proposed. It is shown that the two surface plasmons can be excited at a fixed angle of incidence with polychromatic light or with monochromatic light at different angles of incidence, depending on the design. The structure can be of interest in high-performance surface plasmon resonance sensing and in all-optical signal processing.     

Syntheses, structures and Raman spectra of Cd(BF4)(AF6) (A = Ta, Bi) compounds

The compounds, Cd(BF₄)(TaF₆) and Cd(BF₄)(BiF₆), have been synthesized and characterized by single-crystal X-ray diffraction and Raman spectroscopy. Both isostructural compounds crystallize in the monoclinic P2₁/c space group with a = 8.2700(6) Å, b = 9.3691(6) Å, c = 8.8896(7) Å, β = 94.196(3)°, V = 686.94(9) Å³ for Cd(BF₄)(TaF₆) and a = 8.3412(8) Å, b = 9.4062(8) Å, c = 8.9570(7) Å, β = 93.320(5)°, V = 701.58(11) Å³ for Cd(BF₄)(BiF₆). Eight fluorine atoms (4 BF₄⁻ + 4 AF₆⁻) form a surrounding around the cadmium atom in the shape of distorted square antiprism. These compounds are not isostructural with mixed-anion analogues of Ca, Sr, Ba and Pb studied earlier.     

Plastic slip distribution in two-phase laminate microstructures: Dislocation-based versus generalized-continuum approaches

The size-dependent mechanical response of a simple model microstructure is investigated using continuum dislocation-based, Cosserat and strain-gradient models of crystal plasticity. The governing equations and closed-form analytical solutions for plastic slip and lattice rotation are directly compared. The microstructure consists of a periodic succession of hard (elastic) and soft (elastoplastic single-crystal) layers, subjected to single glide perpendicular to the layers. In the dislocation-based approach, inhomogeneous plastic deformation and lattice rotation are shown to develop in the soft channels, either because of bowing of dislocations or owing to pile-up formation. The generalized continuum non-local models are found to be able to reproduce the plastic slip and lattice rotation distribution. In particular, a correspondence was found between the generalized-continuum results and line tension effects; the additional or higher- order balance equations introduced in the non-local models turn out to be the counterparts of the equilibrium equation for bowed dislocations. The relevance and possible physical interpretation of additional or higher-order interface conditions responsible for the inhomogeneous distribution of plastic slip and lattice rotations are discussed.