BASES NORMALES AUTODUALES ET GROUPES UNITAIRES EN CARACT ÉRISTIQUE 2

Let k be a field of characteristic 2, and let L/k be a finite Galois extension, with Galois group G. We show the equivalence of the following two properties: (?) The group G is generated by elements of order 2 and by elements of odd order. (??) There exists x ∈ L such that Tr(x) = 1 and Tr(x.g(x)) = 0 for every g ∈ G, g = 1.     

Orientational ordering in some nematogens deviating from the classical rod-shape

Several new laterally substituted liquid crystalline compounds have been synthesized. They have the same main core which contains four rings (two aromatic, two alicyclic) with two lateral substituents introduced on the same side of one of the inner rings. One of the substituents is a 4-X-benzyloxy group (X=CH3,CN,Cl) and the other is a hexyloxy chain. The presence of the lateral aromatic substituent makes these compounds deviate markedly from the classical rod-shape. However, a wide enantiotropic nematic phase is present for all the compounds. The order parameters of the chain and the para -disubstituted aromatic rings were obtained by using a 2D 13C NMR technique with variable angle spinning. The temperature dependence of the order parameters was estimated using 13C chemical shifts with slow spinning of the sample parallel to the magnetic field. The results indicate that the two lateral substituents are more or less folded back along the mesogenic core. Thus, the flexible lateral chain is found to be roughly aligned with the molecular long axis, whereas the para axis of the less flexible aromatic branch makes a considerable angle with the molecular long axis imposed by the core, substantially increasing the mean width of the molecule. The core ordering does not seem to be influenced by the type and position of the substituents. The folding back of the lateral chain and the substantial tilt of the lateral aromatic branch with respect to the core main axis are confirmed by the X-ray structure of a parent compound.     

Brownian dynamics with constraints

Systems possessing degrees of freedom operating on widely separated timescales, where the effects of those operating on the smaller timescales are relatively unimportant, may be modelled by the use of the Langevin equation. In order to study such systems containing complex polyatomic particles, holonomic constraints may be used. Though there is no lack of published algorithms for the numerical solution of the Langevin equation, few of them have been developed with sufficient rigour to ensure their precision, nor to demonstrate their compatibility with constraints. This study recapitulates an approach based upon Runge-Kutta equations which has the advantage of being perfectible to any desired order in the time-step, and shows how it may be combined with the SHAKE method in order to perform constrained Brownian dynamics simulations. Results are presented for some simple systems with a third order algorithm, and it is found that the correct dynamic and statistical behaviour is recovered.     

Onsager model for a variable dielectric permittivity near an interface

Using a generalization of an Onsager type approach, we are able to predict a dielectric permittivity profile of an inhomogeneous dipolar fluid in the presence of a dielectric interface. The reaction and cavity fields are calculated semi-analytically using bispherical coordinates. An asymptotic expression for the local permittivity is derived as a function of distance from the interface.     

ABSORPTION INTENSITIES, PRESSURE-BROADENING AND LINE MIXING PARAMETERS OF SOME LINES OF NH3 IN THE ν4 BAND

The intensities and foreign gas broadening coefficients of 57 selected lines of the ν₄ band of NH₃ have been measured in the region of 1550 cm^-1 using a high resolution Brucker Fourier transform spectrometer. The line intensities were obtained by using the methods of absorbance at the line center and by fitting Voigt profiles to the measured shapes of the lines. The latter method also provides the collisional widths of the lines. In addition, collision cross relaxation coefficients of O₂ and air foreign gases were measured for 9 doublets of NH₃ in the ν₄ band. The J and K quantum numbers dependencies of pressure-broadening coefficients and line intensities are discussed. The observed air broadening and cross relaxation coefficients were found to be in reasonable quantitative agreement with the concentration-weighted average of the N₂ and O₂ broadening coefficients. The comparison of our present and previous results obtained for the NH₃–H₂, NH₃–air, NH₃–N₂ and NH₃–CO₂ collisions shows an increase of the pressure broadening and cross relaxation coefficients with quadrupole moment of the foreign gas. The analysis of the line intensities was based on the third-order theory of line strengths and yields effective transition moments, vibrational band strengths and correction parameters of the symmetric and antisymmetric partial bands of the fundamental ν₄ band.     

Effects of size polydispersity on depletion interactions

The depletion potentials between two infinite planes, and between two large spheres, due to polydisperse mixtures of non-interacting polymer coils and of interacting small hard spheres, are calculated over a wide range of polydispersities and of polymer or colloid concentrations. The case of non-interacting polymers can be treated analytically within a generalization of the Asakura-Oosawa model. The more difficult case of a polydisperse bath of hard spheres is treated within Rosenfield's ‘fundamental measure’ formulation of density functional theory. Polydispersity is found to have little effect on the depletion attraction, but to strongly reduce the repulsive barrier due to correlation and to damp the subsequent oscillations in the depletion potential.     

Electrostatic interactions of charges and dipoles near a polarizable membrane

A variational method is used to determine the polarization charge density induced on the surfaces of a dielectric slab (a coarse-grained model of a membrane) by electric point charges and extended dipoles. The results are used to obtain analytic expressions for the polarization energy and the resulting forces acting on and between pairs of charges positioned in various geometries relative to the membrane. The polarization effects are shown to be substantial and often non-trivial on the nanometre scale, compared to direct Coulomb interactions.     

O2 broadening of carbon disulphide 12C32S2 in the v 3 and v 3—v 1 bands

Using a tunable diode laser spectrometer, we have measured O₂ broadening coefficients of ¹²C³²S₂ for 31 lines in the v ₃ fundamental band near 6.5 μm and 12 lines in the v ₃—v ₁ band near 11.4 μm. The collisional halfwidths are obtained by fitting the spectral lines with a Voigt and a Rautian profile. The broadening coefficients of ¹²C³²S₂-O₂ are also calculated from semiclassical theory involving, in addition to electrostatic interactions, successively the atom-atom Lennard-Jones model and a simple formulation for the anisotropic dispersion forces, leading to more satisfactory results.