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The frequency spectrum of the depolarized light scattered from a dilute solution of large, rigid molecules can give information about their principal axis of inertia and therefore their symmetries. It is shown that, for spherical molecules, one finds a single Lorentzian line. In the case of axial symmetry, the spectrum is the sum of two Lorentzian lines. Linewidths and relative intensities of lines are calculated as a function of the optical polarizability tensor and rotational diffusion coefficients of the molecule.

Possible transitions are discussed for a smectic A film placed between two plates with homeotropic boundary conditions in a magnetic field parallel to the plates. It is predicted that in a central region the molecules will be aligned and that, close to each plate, a periodic pattern of disclinations will allow for folding the layers. The critical field is expected to be approximately 10 4 oe for a 1 cm thick sample and to vary as the inverse square root of the sample thickness.

A unified hydrodynamic theory is presented that is appropriate for crystals; smectic, cholesteric, and nematic liquid crystals; glasses; and normal fluids. In the theory, the increased spatial degeneracy as the system progresses from crystalline and mesomorphic phases to the isotropic fluid phase is marked by successive reductions in the number of firstorder elastic constants and in the number of transport coefficients. Distinction between local lattice dilations and local mass changes, and recognition of processes like vacancy diffusion that this difference makes possible, are crucial for understanding the connection between theories in different phases. Formulas are derived that give the number of hydrodynamic modes and the frequencies, lifetimes, and intensities of these modes in all of the above systems. In the nematic and cholesteric phases, the results agree with some found previously. In more complex systems, they are new. An attempt is made to explain the differences between the present hydrodynamic theory and other phenomenological proposals.

On etudie la structure de gouttelettes de cristal liquide nematique en emulsion dans un liquide isotrope. Suivant la tension superficielle, les molecules sont normales ou tangentes a la surface. Les configurations stables sont alors soit en etoile, soit bipolaires. On calcule l'energie de telles configurations en champ magnetique faible et eleve. Dans le cas de molecules normales a la surface, on s'attend a une transition de phase du premier ordre lors de l'application d'un champ magnetique intense. On etudie aussi les repartitions de charges dues aux effets piezoelectriques autour d'une ligne de disclination dans un milieu infini, et pour des gouttelettes.

On introduit les notions de theorie des groupes utiles pour l'etude des champs cristallins (classes — representation — caracteres). On montre comment le theoreme de Wigner permet de prevoir a priori les levees de degenerescence dans un entourage cristallin. Le produit direct de deux representations permet d'aborder le couplage spin-orbite ou le couplage de plusieurs electrons en champ cristallin fort. On definit les operateurs tensoriels irreductibles, et on montre comment le theoreme de Wigner-Eckart permet d'etablir a priori les regles de selection.

A phenomenological analysis of the polyene optical excitation spectra is presented. The successive absorption bands are interpreted in terms of odd and even exciton levels. An extrapolation of the experimental data on the whole polyene series gives the exciton levels of an infinite chain, and the energy gap between the filled bonding band and the empty antibonding band. The dependence of the absorption frequencies on the length of the chain allows for a calculation of the effective masses for these bands; they turn out to be small, which implies that the degree of alternation between the simple and double bonds is weak.

Constitutive equations for nematic liquid crystals were first established by Ericksen and Leslie. They used a stress tensor with six viscosity coefficients αi (i = 1...6). It is shown in this paper that the Onsager reciprocal relations lead to the relation α2 + α 3 = α6 - α5 . Hence there are only five independent viscosity coefficients for a nematic liquid crystal.

We present an extension of the Helfrich theory of hydrodynamic instabilities to the case of alternating electric fields. The electrohydrodynamic effects are described by two coupled equations for the charge density (q) and the local curvature of the molecular alignment (ψ). The relaxation time for q is the dielectric relaxation time τ (∼ 10-2 s in typical samples). The relaxation time T for ψ is strongly dependent on the field magnitude. Provided that the sample thickness d is above a certain limit dc, the nature of the instability is very different, depending on the ratio of the field frequency ω to a critical frequency ω c. For ω < ωc the onset of instability corresponds to a charge q which oscillates at the frequency ω, while the curvature ψ is essentially time independent. For ω > ωc the situation at threshold corresponds to a constant q and an oscillating ψ. These predictions, together with the calculated curves of threshold voltage vs ω and d, are in reasonable agreement with a number of recent experiments.

In a smectic sample, the layers must be equidistant, but they may be curved. When the boundary conditions are not compatible with flat layers, one obtains a focal conic texture. We consider here the most familiar case where each unit in this texture fills a certain cone. The interstices between these cones are filled by smaller cones, etc. We discuss some features of this iterative filling of space, and show that it should persist down to a few molecular lengths. An estimate of the energy associated with the iterated structure indicates, that (in the absence of all external fields) focal conic textures are less expensive than grain boundaries, in agreement with the standard optical aspect of smectic samples. We discuss the scattering of light by an iterated focal conic texture, in terms of a simple scaling law ; the resulting angular dependence of the scattered intensity is anomalous and may allow for a direct determination of the « scaling index » n associated with the iterative process.