The probe profile and lateral resolution of scanning transmission electron microscopy of thick specimens

Lateral profiles of the electron probe of scanning transmission electron microscopy (STEM) were simulated at different vertical positions in a micrometers-thick carbon sample. The simulations were carried out using the Monte Carlo method in CASINO software. A model was developed to fit the probe profiles. The model consisted of the sum of a Gaussian function describing the central peak of the profile and two exponential decay functions describing the tail of the profile. Calculations were performed to investigate the fraction of unscattered electrons as a function of the vertical position of the probe in the sample. Line scans were also simulated over gold nanoparticles at the bottom of a carbon film to calculate the achievable resolution as a function of the sample thickness and the number of electrons. The resolution was shown to be noise limited for film thicknesses less than 1 μm. Probe broadening limited the resolution for thicker films. The validity of the simulation method was verified by comparing simulated data with experimental data. The simulation method can be used as quantitative method to predict STEM performance or to interpret STEM images of thick specimens.     

Monte Carlo analysis of polymer translocation with deterministic and noisy electric fields

Polymer translocation through the nanochannel is studied by means of a Monte Carlo approach, in the presence of a static or oscillating external electric voltage. The polymer is described as a chain molecule according to the two-dimensional “bond fluctuation model”. It moves through a piecewise linear channel, which mimics a nanopore in a biological membrane. The monomers of the chain interact with the walls of the channel, modelled as a reflecting barrier. We analyze the polymer dynamics, concentrating on the translocation time through the channel, when an external electric field is applied. By introducing a source of coloured noise, we analyze the effect of correlated random fluctuations on the polymer translocation dynamics.     

Wetting properties at the surface of iota-carrageenan-based edible films

Surface properties of edible films composed of a polymeric matrix of carrageenan in association with hydrophobic material were studied by contact angle measurements. The use of this technique not only in a static mode but also in a dynamic way enables investigation of surface hydrophobicity as well as surface wettability. The absorption flux inside the material can be estimated from the wetting kinetic, which can be very useful to quickly compare water barrier efficiency of the tested films. Comparison of carrageenan films with films containing known amounts of additives enables understanding and correlation of changes of the surface properties with the nature of used additives (glycerol used as a plasticizer, glycerol monostearate used as a surfactant, and fat) and their influence on the orientation of polymer chains at the surface during film formation. Very different responses were observed from one surface of the film (film-casting-support interface) to the other (film-air interface), which could be also attributed to the influence of the support on the polymer and to macromolecular orientation during drying after casting.     

Approximations filaires pour les équations de Poisson et de Maxwell harmoniques

We are interested in the approximation of the Poisson and time harmonic Maxwell equations around a circular cylinder with a small radius. Numerical approximation requires a typical meshsize comparable to the radius of the cylinder, thus increasing the computational cost. In many applications (spacecraft charging computation, wire antennas modelling) the mesh size becomes too large to perform realistic computations. A mathematical study proves the convergence of the sequence $u_{\mathrm{?}}$ of Poisson equation solutions when the radius ? goes to 0 toward a limit problem with a convergence rate of $1/\ln (\mathrm{?})$. A wire approximation is proposed exhibiting a rate of convergence larger that $\sqrt{\mathrm{?}}$ without constraint of mesh refinement related to the radius size. This method is extended to the case of arbitrary wire cross section and also to the time harmonic Maxwell equations. To cite this article: F. Rogier et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006).     

Quantum scaling laws in the onset of dynamical delocalization

We study the destruction of dynamical localization experimentally observed in an atomic realization of the kicked rotor by a deterministic Hamiltonian perturbation, with a temporal periodicity incommensurate with the principal driving. We show that the destruction is gradual, with well-defined scaling laws for the various classical and quantum parameters, in sharp contrast to predictions based on the analogy with Anderson localization.     

On the groups of codes with empty kernel

An internal factor of a word x is a word v such that x=uvw for some nonempty words u,w. The kernel of a set X of words is the set of words of X which are internal factors of words of X. Let φ be the syntactic morphism of the submonoid X ^* generated by X. We prove that if X is a code with empty kernel, the groups contained in the image by φ of the complement of the set of internal factors of the words of X are cyclic. This generalizes a result announced by Schützenberger in 1964.     

On the use of graphs in discrete tomography

In this tutorial paper, we consider the basic image reconstruction problem which stems from discrete tomography. We derive a graph theoretical model and we explore some variations and extensions of this model. This allows us to establish connections with scheduling and timetabling applications. The complexity status of these problems is studied and we exhibit some polynomially solvable cases. We show how various classical techniques of operations research like matching, 2-SAT, network flows are applied to derive some of these results.     

Formation of nanometric HT-LiCoO(2) by a precipitation and aging process in an alcoholic solution

In this paper, we detailed the formation/evolution of precipitates in alcoholic media containing Co(II+) and Li(+) species, together with the evolution of the composition and structure/texture of the resulting solid phases during the aging process at controlled constant temperature. While the end product is found to be well-crystallized HT-LiCoO(2), its formation is shown to result from a two-step process enlisting the initial fast precipitation of β-HCoO(2) and then its slow dissolution followed by recrystallization of the lithium-containing material. These results were obtained through combined X-ray diffraction, Raman and IR spectroscopy, elemental and oxidation-state analysis, and high-resolution transmission electron microscopy/selected-area electron diffraction observations. Depending on the cationic concentration, the size of the precipitated material can be controlled within the nanometric range. The electrochemical performances of these aged materials are slightly improved compared to those of the directly precipitated ones that we previously reported. The main limitation of these materials remains the presence of surface protons.     

The relevance of the fluorine interactions in the supramolecular structure of a complex constructed from copper(II) hexafluoroacetylacetonate and the 4′-(3-pyridyl)-2,2′:6′,2″-terpyridine ligand. Novel C-F/π synthons involving the π-system of the terpyridine moieties and those of the hexafluoroacetylacetonate chelate rings

Reaction of 4′-(3-pyridyl)-2,2′:6′,2′′-terpyridine (pyterpy) with Cu(hfacac)₂ (hfacac = hexafluoroacetylacetonate) led to the formation of the novel compound [Cu₃(hfacac)₄(μ-pyterpy)₂][Cu(hfacac)₃]₂ (1). The structure is composed of a trinuclear [Cu₃(hfacac)₄(μ-pyterpy)₂]²⁺ cation and two [Cu(hfacac)₃]⁻ anionic species. The cation consists of a chain of three Cu^II atoms connected by bridging pyterpy ligands. The [Cu(hfacac)₃]⁻ anions have the hfacac ligands coordinated in their usual chelating manner through their carbonyl O donors. Besides the coulombian forces, the ionic species are fixed by C-H?O, C-H?F, F?F and a variety of unusual inter-ion C-F?π interactions that control the packing motif. These π-interactions involve the terpyridine groups from the pyterpy ligand and the five-membered rings of the chelating hexafluoroacetylacetonate anions.