Enumeration of three-dimensional convex polygons

A self-avoiding polygon (SAP) on a graph is an elementary cycle. Counting SAPs on the hypercubic lattice ℤ ^d withd≥2, is a well-known unsolved problem, which is studied both for its combinatorial and probabilistic interest and its connections with statistical mechanics. Of course, polygons on ℤ ^d are defined up to a translation, and the relevant statistic is their perimeter. A SAP on ℤ ^d is said to beconvex if its perimeter is “minimal”, that is, is exactly twice the sum of the side lengths of the smallest hyper-rectangle containing it. In 1984, Delest and Viennot enumerated convex SAPs on the square lattice [6], but no result was available in a higher dimension. We present an elementar approach to enumerate convex SAPs in any dimension. We first obtain a new proof of Delest and Viennot's result, which explains combinatorially the form of the generating function. We then compute the generating function for convex SAPs on the cubic lattice. In a dimension larger than 3, the details of the calculations become very cumbersome. However, our method suggests that the generating function for convex SAPs on ℤ ^d is always a quotient ofdifferentiably finite power series.     

Ruthenium nanoparticles in ionic liquids: structural and stability effects of polar solutes

Ionic liquids are a stabilizing medium for the in situ synthesis of ruthenium nanoparticles. Herein we show that the addition of molecular polar solutes to the ionic liquid, even in low concentrations, eliminates the role of the ionic liquid 3D structure in controlling the size of ruthenium nanoparticles, and can induce their aggregation. We have performed the synthesis of ruthenium nanoparticles by decomposition of [Ru(COD)(COT)] in 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide, [C(1)C(4)Im][NTf(2)], under H(2) in the presence of varying amounts of water or 1-octylamine. For water added during the synthesis of metallic nanoparticles, a decrease of the solubility in the ionic liquid was observed, showed by nanoparticles located at the interface between aqueous and ionic phases. When 1-octylamine is present during the synthesis, stable nanoparticles of a constant size are obtained. When 1-octylamine is added after the synthesis, aggregation of the ruthenium nanoparticles is observed. In order to explain these phenomena, we have explored the molecular interactions between the different species using (13)C-NMR and DOSY (Diffusional Order Spectroscopy) experiments, mixing calorimetry, surface tension measurements and molecular simulations. We conclude that the behaviour of the ruthenium nanoparticles in [C(1)C(4)Im][NTf(2)] in the presence of 1-octylamine depends on the interaction between the ligand and the nanoparticles in terms of the energetics but also of the structural arrangement of the amine at the nanoparticle's surface.     

A novel ruthenium(II) complex for two-photon absorption-based optical power limiting in the near-IR range

In this article, the synthesis of a novel high-conjugated ligand and its corresponding Ru(II) complex PTFTF:Ru is reported, along with the linear and nonlinear optical characterizations. Two-photon absorption based optical power limiting properties (OPL), especially in the near infrared, are described and compared to those of the analogous complexes previously published. Combined with a preliminary theoretical approach, this allows us to highlight several key parameters for OPL optimization in such molecular systems and more particularly the spectral overlap between TPA and excited-state absorption.     

NMR Study of Water Distribution inside Tomato Cells: Effects of Water Stress

Tomato pericarp tissue was studied by low-field nuclear magnetic resonance (NMR) relaxometry. Two kinds of experiments were performed to investigate the correlation between multi-exponential NMR relaxation and the subcellular compartments. The longitudinal (T ₁) versus transverse (T ₂) relaxation times were first measured on fresh samples and then the transverse relaxation time was measured on samples exposed to water stress. Four signal components were found in all experiments. The results showed that all signal components corresponded to the water in different cell compartments, and that no signal from non-exchangeable protons was present. Moreover, we demonstrated that NMR relaxation is suitable for the continuous monitoring of water rebalancing between subcellular compartments of plant tissues.     

Co(II)5(OH)6(SO4)2(H2O)4: the first ferromagnet based on a layered cobalt-hydroxide pillared by inorganic...OSO3-Co(H2O)4-O3SO..

The synthetic mineral Co(II)5(OH)6(SO4)2(H2O)4 (1), obtained by hydrothermal reaction of CoSO4.7H2O and NaOH at 165 degrees C and consisting of brucite-like Co4(OH)6O2 layers pillared by OSO3-Co(H2O)4-O3SO, is a ferromagnet (T(Curie)= 12 K, Hc= 580 Oe).     

Constitutive equations for an electroactive polymer

Ionic electroactive polymers can be used as sensors or actuators. For this purpose, a thin film of polyelectrolyte is saturated with a solvent and sandwiched between two platinum electrodes. The solvent causes a complete dissociation of the polymer and the release of small cations. The application of an electric field across the thickness results in the bending of the strip and vice versa. The material is modeled by a two-phase continuous medium. The solid phase, constituted by the polymer backbone inlaid with anions, is depicted as a deformable porous media. The liquid phase is composed of the free cations and the solvent (usually water). We used a coarse grain model. The conservation laws of this system have been established in a previous work. The entropy balance law and the thermodynamic relations are first written for each phase and then for the complete material using a statistical average technique and the material derivative concept. One deduces the entropy production. Identifying generalized forces and fluxes provides the constitutive equations of the whole system: the stress–strain relations which satisfy a Kelvin–Voigt model, generalized Fourier’s and Darcy’s laws and the Nernst–Planck equation.     

Coadsorption of carbofuran and lead at the water/silica interface. Possible impact on environment

Despite its extremely weak adsorption at the water/silica interface, carbofuran can, however, induce the coadsorption of metallic salts, like, for example, lead nitrate, and thus enhance its adsorption. We quantitatively studied this phenomenon with a depletion method and under concentration conditions close to the environmental ones. Heavy metal salt was found to positively adsorb, whereas carbofuran relative adsorption is generally slightly negative. This study provides evidence that considering these facts is of paramount importance in environmental prospects. To cite this article: G. Elmanfe et al., C. R. Chimie 9 (2006).