Low-Temperature Photochemistry of Previtamin D: A Hula-Twist Isomerization of a Triene

What is the standard course of the cis – trans isomerization of nonpolar polyenes? Many results support a pathway in which only a central CH group rotates out of the plane, while the remaining parts of the molecule reorient within the plane (“hula-twist” mechanism). The intermediate structure through which the molecule passes corresponds to the geometry predicted for the conical intersection of the S₁ and S₀ potential energy surfaces (see picture).     

Light scattering and dielectric relaxation studies of glass forming liquids

Extended Abstract: Glass forming organic liquids and polymers exhibit long range density fluctuations with correlation length ξ in the range of 10–300 nm at temperatures above T_g (1 - 6). This follows from dynamic and static light scattering experiments revealing some unexpected features, which cannot be explained on the basis of conventional liquid state theories: (i) In static light scattering the intensity I(q → 0) is no longer proportional to the isothermal compressibility, (ii) This excess scattering I_exc shows a strong q-dependence (q = (4π/Λ.)sin(θ/2)) corresponding to a correlation length ξ in the above mentioned range, (iii) The Landau-Placzek ratio I_Rayleigh/2I_Brillouin is much too high compared with the results of light scattering theories, (iv) In photon correlation spectroscopy a new ultraslow hydrodynamic mode (Γ ˜ q²) is detected with relaxation rates Γ about 10⁻⁶ to 10⁻⁹ lower than those of the α-process at a given temperature. In order to explain these observations, a two-state fluid model is proposed, which starts from the coexistence of “liquid-like” and “aperiodic solid-like” regions within the liquids. Such ideas have been discussed many times before, so for example A.R. Ubbelohde (7) speculates about “anticrystalline” clusters in liquids. Molecular dynamics simulations of atomic liquids showed that long range orientational fluctuations appear upon supercooling (8). A preferred icosahedral ordering is observed (9) and the number of icosahedral clusters increases with decreasing temperature (10). In connection with the interpretation of the dynamics of supercooled liquids different “two-state” models have been proposed (11 - 15). For the explanation of the light scattering results we propose that the molecules in the different dynamic states (“liquid” or “solid”) aggregate during annealing of the liquid at temperatures above T_g. Experiments showed that the equilibration times can be rather long (3 - 5), but nevertheless the liquids exhibiting long range density fluctuations are in the state of lowest free energy. We claim that our observations are the first experimental proof of the existence of such different dynamic states, which have been discussed many times before. The extended secondary clusters can also be detected by ultra small angle X-ray scattering.     

Optimal Domains for Kernel Operators via Interpolation

The problem of finding optimal lattice domains for kernel operators with values in rearrangement invariant spaces on the interval [0,1] is considered. The techniques used are based on interpolation theory and integration with respect to C([0, 1])–valued measures.