Structure des savons alcalins

Summary This is a systematic X-ray diffraction study of the structure of the mesomorphic phases occurring with potassium soaps ranging from C₈ to C₂₂.Four types of structure have been identified. The first is lamellar with both polar groups and paraffin chains in the crystalline state. The second is also lamellar, but with both polar groups and paraffin chains in the liquid state. The third corresponds to the localization of indefinitely long ribbons on a two-dimensional oblique lattice; polar groups are crystalline and paraffin chains desorganized. The fourth corresponds to the localization of discs on a three-dimensionnalB-faces centered orthorhombic lattice; polar groups are crystalline and paraffin chains disorganized.The structural parameters and the polymorphism of the polar groups have been discussed.

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Zusammenfassung Wir beschreiben hier eine systematische Röntgenstrahlendiffraktionsforschung der Struktur der mesomorphen Phasen von Kalium Seifen von C₈ bis C₂₂.Vier Strukturtypen wurden gefunden. Die erste Struktur ist lamellar; beides, die polaren Gruppen und die Paraffinketten sind kristallisiert. Die zweite Struktur ist auch lamellar; aber in diesem Falle sind beides, die polaren Gruppen und Paraffinketten geschmolzen. Die dritte Struktur entspricht einer Lokalisation von Seifenbändern in einem zweidimensionalen monoklinen Gitter; die polaren Gruppen sind kristallisiert und die Paraffinketten geschmolzen. Die vierte Struktur entspricht einer Lokalisation von Seifenscheiben in einemB-flächenzentrierten orthorhombischen Raumgitter; die Polargruppen sind kristallisiert und die Paraffinketten geschmolzen.Wir haben aus den experimentellen Resultaten einige Schlußfolgerungen gezogen.

     

ETUDE DE LA FRAGMENTATION DE N-ARYL ET DE N-ALKYL AMINOCETONES EN SPECTROMETRIE DE MASSE

A Comparison of the chemical ionisation and elctron-impact mass spectra of alkyl and aryl aminoketones has bee carried out. This has revealed the particular stabilization of the N-aryl grops in all cases.     

Interactions électriques dans les phases mésomorphes des systèmes amphiphile-eau: Rôle de la teneur en eau,de la longueur de la chaîne paraffinique,de la nature du cation,et de la température

Summary Using X-ray diffraction techniques, we have determined the specific surface of polar groups in the two structures observed for binary soap-water systems in the mesomorphic state: the cylindrical structure and the lamellar one.This parameter depends upon the temperature, the nature of the polar group, the type of structure of the system and the quantity of water present in the mixture. It is, on the contrary, independent of the length of the paraffin chain of the soap. This result suggests that the role of the electrical state of the aqueous regions is by far the most important.

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Zusammenfassung Mit Hilfe der Röntgenstrahlen-Diffraktion wurde die spezifische Fläche polarer Gruppen der zwei wichtigsten Strukturen der binären Seifen/Wasser-Systeme im mesomorphen Zustand bestimmt: die zylindrische und die lamellare Struktur.Diese Größe ist von der Temperatur, der Natur der polaren Gruppen, der Struktur des Systems und des Wassergehaltes der Mischung abhängig. Die spezifische Fläche ist jedoch von der Länge der Seifen-Paraffin-Kette unabhängig. Der elektrische Zustand des wässerigen Teiles scheint also sehr wichtig zu sein.

     

Acetylenic and diacetylenic liquid-crystalline monomers: towards ordered conjugated polymers

Abstract

Acetylenic and diacetylenic mesomorphic monomers have been prepared in order to obtain long conjugated polymers able to give high non-linear optical hyperpolarizabilities. Here we report the synthesis of such monomers incorporating cholesteryl and methoxybiphenyl groups; their structural and thermal behaviour are described. The occurrence of mesophases in the acetylenic and diacetylenic derivatives is discussed as a function of the spacer length and of the size of the mesogen moiety. The diacetylenic derivatives containing the methoxybiphenyl groups do not exhibit any liquid-crystalline behaviour but are able to polymerize under U.V. radiation.     

Rate Optimality of Wavelet Series Approximations of Fractional Brownian Motion

Consider the fractional Brownian motion process $B_H(t), t\in [0,T]$, with parameter $H\in (0,1)$. Meyer, Sellan and Taqqu have developed several random wavelet representations for $B_H(t)$, of the form $\sum_{k=0}^\infty U_k(t)\epsilon_k$ where $\epsilon_k$ are Gaussian random variables and where the functions $U_k$ are not random. Based on the results of Kühn and Linde, we say that the approximation $\sum_{k=0}^n U_k(t)\epsilon_k$ of $B_H(t)$ is optimal if $$ \displaystyle \left( E \sup_{t\in [0,T]} \left| \sum_{k=n}^\infty U_k(t) \epsilon_k\right|^2 \right)^{1/2} =O \left( n^{-H} (1+\log n)^{1/2} \right), $$ as $n\rightarrow\infty$. We show that the random wavelet representations given in Meyer, Sellan and Taqqu are optimal.     

Spin waves transport across a ferrimagnetically ordered nanojunction of cobalt-gadolinium alloy between cobalt leads

A model calculation is presented for the spin wave scattering and coherent transport at the ferrimagnetically ordered cobalt-gadolinium alloy nanojunction between cobalt leads. The structural model for the amorphous alloy nanojunction [Co_1/2Gd_1/2]₃ is considered as an ordered alloy hcp structure of three (0001) atomic planes between the leads. To analyze the spin dynamics and spin wave scattering at the nanojunction boundary, the phase field matching method (PFMT) is implemented over the ground state of the system, in the Heisenberg Hamiltonian representation. The coherent reflection and transmission probabilities of spin waves from the cobalt leads incident onto the nanojunction boundary are calculated, and numerical results are presented for the coherent SW transport across the nanojunction over the entire range of their frequencies. The results are especially valid in the interval between nanometric SW wavelengths greater than the nanojunction width and macroscopic wavelengths. They demonstrate in particular, the possibility of the resonance assisted maxima for the SW transmission spectra owing to the interactions between the incident spin waves and the localized spin resonances on the nanojunction. This effect is general and may be observed at different characteristic frequencies and corresponding incident angles.     

McMullen's conditions and some lower bounds for general convex polytopes

We give a lower bound for the number of vertices of a generald-dimensional polytope with a given numberm ofi-faces for eachi = 0,..., d/2 – 1. The tightness of those bounds is proved using McMullen's conditions. Form greater than a small constant, those lower bounds are attained by simpliciali-neighbourly polytopes.     

Ehrenfest's theorem reinterpreted and extended with Wigner's function

For a wave packet evolving quantum mechanically, the rates of change of the expectations and uncertainties of the position and momentum are exactly the same as if Wigner's function instantaneously obeyed a classical Liouville equation (whatever the Hamiltonian). This extension of Ehrenfest's theorem should be useful for dealing with the evolution and manipulation of quantum states.     

Classical Yang-Mills-Dirac equations: Qualitative analysis of some solutions with a noncompact symmetry group

We consider classical Yang-Mills and Yang-Mills-Dirac equations on Minkowski space, with gauge group SU(2), and look for solutions invariant (up to a gauge transformation) under SO(3)×SO₀(1, 1) and SO₀(2, 1)×SO(2), respectively. In each case, we analyze the qualitative features of the solutions, in particular the asymptotic behavior as the solution approaches its singularities. The method is based on standard theorems from the theory of nonlinear ordinary differential equations.