Effect of the topology on the gaussian elasticity of a network. The example of a fractal topology

By considering fractal topologies of polymer networks, we show that one can obtain much smaller values of the elastic modulus than predicted by classical models for the same density of crosslinks. In a regular fractal such as the Sierpinski gasket, one can replace the segments joining the modes by Gaussian chains. This allows one to draw some micronetworks of rank k = 1, 2 etc., with no dangling ends except for the few external points (3 for any rank). Within the frame of the phantom network model, we calculate the elastic modulus of the micronetwork. It varies as p^k−1 for p < 1, which leads, even for rather small orders k such as 2, 3, to values lower than the classical James and Guth modulus, which actually corresponds to the connectivity of a tree. Thus there is an influence of the topology. Fluctuations of the positions of crosslinks and of the distance between two crosslinks are estimated and are found to correspond to a lower deformation of the chains. Whether these topologies are more than an example and could explain the anomalies observed experimentally is a postponed discussion.     

Recent developments in heterocyclic systems with a Si–M′–Ge or Ge–M′–Ge linkage (M′ = Fe,Ru, or Co)

The present review describes recent work on the synthesis, spectroscopic analysis, and investigation of the chemical behaviors of new polynuclear heterocyclic complexes 1–7 having M–M′–M catenation. Various CO substitution, cleavage, expansion, and adducts decomposition reactions are described.     

Enhancement of inhomogeneities in gels upon swelling and stretching

In this paper, it is shown how a percolation process can be used to describe the inhomogeneities of polymer concentration, appearing in gels prepared by random crosslinking of a semi-dilute solution, and how they are modified by swelling or stretching of the network. Neutron scattering experimental data are compared to the predictions of this model in the isotropic and anisotropic cases. A good agreement is found. In particular, “abnormal” butterfly patterns in the iso-intensity curves have been detected, as expected from the model.     

Chemometrics in chromatography

The impact of chemometrics in chromatography is presented. The development of systematic experiments is encouraged to exploit simultaneously the richness of teh chromatographic data and the possibilities of complementary data processing techniques.     

Expedient BINOL derivative arylations

A dramatic improvement of our previous methodology based on a Suzuki–Miyaura cross-coupling to access 3,3′-disubstituted H₈-BINOLs using microwave heating is reported herein. These new conditions represent a large gain in term of atom-economy, reaction time, catalyst loading, and excess of reagents employed.     

Electrical Conductivity in TCNQ Salts of Bis(4-dimethylaminophenylimino) sulfur and its Structural Analogues

Four compounds, N,N,N',N'-tetramethyl-p-phenylene diamine, N,N,N',N'-tetramethyl-benzidine, 4,4'-bis(dimethylamino)azobenzene and bis(4-dimethylaminophenylimino)sulfur (BAPIS) were examined electrochemically and spectroscopically. Each was shown to be a fairly good donor forming in its first oxidation state a radical-cation. The latter two materials surprisingly exhibited only single one-electron oxidations. Conformational flexibility about the -NSN- unit was studied by NMR spectroscopy and ab initio molecular orbital theory. The experimental ΔG* for a cis-trans to trans-cis interconversion in BAPIS was found to be 11.9 kcal/mole.

The four donors all form 1:1 adducts with TCNQ. The compaction resistances of the complexes have been measured as a function of temperature. Of the four, (BAPIS)(TCNQ) appears to be a one-dimensional material. The other three complexes behave as typical mixed stack organic semiconductors.     

The Combinatorics of Laguerre,Charlier, and Hermite Polynomials

This paper describes several combinatorial models for Laguerre, Charlier, and Hermite polynomials, and uses them to prove combinatorially some classical formulas. The so-called “Italian limit formula” (from Laguerre to Hermite), the Appel identity for Hermite polynomials, and the two Sheffer identities for Laguerre and Charlier polynomials are proved. We also give bijective proofs of the three-term recurrences. These three families form the bottom triangle in R. Askey's chart classifying hypergeometric orthogonal polynomials.     

Anisotropic surface effects in Au and Cu monocrystals

Electroreflectance spectra at normal incidence of (100) and (110) faces of gold and copper monocrystals are given, in the spectral range from 0.22–0.7 μm. The fractional change in reflectance is different with (110) faces when light is polarized parallel to the [001] direction and parallel to the [$\text{1}\text{10}$] direction while no anisotropy is seen on (100) faces. This shows that electroreflectance is a powerful tool to investigate metal surfaces where the optical electrons are sensitive to the distribution of the surface atoms.     

Spin asymmetry in γe ↑→e+2 jets: A laboratory for final state interactions

We isolate final state interactions not parametrized by fragmentation functions and yet present in QCDO(α _s ) corrections to two-jet production in photon-longitudinally polarized electron scattering. Our calculation focuses on dynamical imaginary (absorptive) corrections that are absent in any tree diagrams. We explicitly demonstrate cancellation of imaginary infinities in the sum over graphs. The resulting asymmetry is predicted to be small. Such a quantity should be soon measured in experiments exploiting the naturally large electron polarization occurring in standard high energy storage rings.