Oriented polymer dispersed discotic liquid crystals

Polymer dispersed discotic liquid crystals (PDDLCs) were prepared using the hexa-n-octanoate of rufigallol (RHO) and three polymer matrices: polystyrene (PS), poly(methyl methacrylate) (PMMA) and poly(ethyl methacrylate) (PEMA). The molecular orientation of RHO in stretched PDDLC films was characterized by means of infrared dichroism. It was found that the stretching of films that contain RHO in both the columnar D1 and crystalline phase can effectively align columns of RHO along the stretching direction, with the short axes of the rigid cores lying in the plane of the film. By contrast with stretched polymer dispersed nematic liquid crystals, no orientation of RHO is induced for films stretched with RHO in the isotropic phase, followed by rapid cooling to room temperature. However, if stretched films are cooled under strain into the columnar D1 phase, orientation of RHO can develop with time.     

Electronic structure calculations of 1,3-dipolar cycloadditions using density functional and Hartree–Fock methods

Local spin density (LSD ) methods were used to study the concerted 1,3-dipolar cycloadditions for fulminic acid plus acetylene, fulminic acid plus ethylene, and nitrone plus ethylene. Cartesian Gaussian double-zeta split-valence basis sets augmented with one set of polarization functions (DZVP ) were used for the LSD calculations. The LSD calculations were performed with the LSD exchange functional (Dirac) and with the Vosko, Wilk, and Nusair correlation energy functional (VWN ). Nonlocal spin-density corrections (NLSD ) were estimated with the exchange functional of Becke and the correlation energy functional of Perdew (VWN + BP ) and Becke, and the correlation energy functional of Lee, Yang, and Parr (B-LYP ). Vibrational frequencies were computed at the VWN and B-LYP levels by numerical differentiation of the analytical first derivatives of the energy. Each of these reactions was examined using Hartree–Fock and Møller–Plesset perturbation theory for comparison. Geometry optimizations were carried out at the Hartree–Fock level with the 6-311G (d,p) basis set, and correlation energies were computed up to the MP 4SDTQ /6-311G (d,p) level of theory. For the reactions of fulminic acid plus acetylene, fulminic acid plus ethylene, and nitrone plus ethylene, our best estimated density functional barrier heights are 7.8 ± 1.5, 8.9 ± 0.3, and 11.05 ± 1.9 kcal/mol, respectively. These results are in reasonable agreement with the correlated wave-function calculations and experimental estimates. © 1994 John Wiley & Sons, Inc.     

A family of enneanuclear iron(II) single-molecule magnets

Complexes [Fe₉(X)₂(O₂CMe)₈{(2‐py)₂CO₂}₄] (X^?=OH^? ( 1 ), N₃^? ( 2 ), and NCO^? ( 3 )) have been prepared by a route previously employed for the synthesis of analogous Co₉ and Ni₉ complexes, involving hydroxide substitution by pseudohalides (N₃^?, NCO^?). As indicated by DC magnetic susceptibility measurements, this substitution induced higher ferromagnetic couplings in complexes 2 and 3 , leading to higher ground spin states compared to that of 1 . Variable‐field experiments have shown that the ground state is not well isolated from excited states, as a result of which it cannot be unambiguously determined. AC susceptometry has revealed out‐of‐phase signals, which suggests that these complexes exhibit a slow relaxation of magnetization that follows Arrhenius behavior, as observed in single‐molecule magnets, with energy barriers of 41 K for 2 (τ₀=3.4×10^?12 s) and 44 K for 3 (τ₀=2.0×10^?11 s). Slow magnetic relaxation has also been observed by zero‐field ⁵⁷Fe Mössbauer spectroscopy. Characteristic integer‐spin electron paramagnetic resonance (EPR) signals have been observed at X‐band for 1 , whereas 2 and 3 were found to be EPR‐silent at this frequency. ¹H NMR spectrometry in CD₃CN has shown that complexes 1 – 3 are stable in solution.     

An efficient preparation of beta-aryl-beta-ketophosphonates by the TFAA/H3PO4-mediated acylation of arenes with phosphonoacetic acids

Beta-aryl-beta-ketophosphonates can be efficiently prepared in good yield by using a TFAA/85% H 3PO 4-mediated acylation of electron-rich arenes with phosphonoacetic acids. The conditions offer advantages over existing methods of preparing these useful compounds by not requiring the use of strong base, cryogenics, or an anhydrous and inert atmosphere. Furthermore, some functional groups not tolerated with the reaction conditions used in existing methods are compatible with the herein described conditions.     

Multifractal analysis of the divergence of Fourier series: The extreme cases

We study the size, in terms of the Hausdorff dimension, of the subsets of T such that the Fourier series of a generic function in L ¹(T), L ^p (T), or C(T) may behave badly. Genericity is related to the Baire Category Theorem or the notion of prevalence. This paper is a continuation of [3].     

The Validity of the Multifractal Formalism: Results and Examples

By obtaining a new sufficient condition for a valid multifractal formalism, we improve in this paper a result developed by L. Olsen (1995, Adv. Math.116, 82-196). In particular, we describe a large class of measures satisfying the multifractal formalism and for which the construction of Gibbs measures is not possible. Some of these measures are not unidimensional but have a nontrivial multifractal spectrum, giving a negative answer to a question asked by S. J. Taylor (1995, J. Fourier Anal. Appl., special issue). We also describe a necessary condition of validity for the formalism which is very close to the sufficient one. This necessary condition allows us to describe a measure μ for which the multifractal packing dimension function B_μ(q) is a nontrivial real analytic function but the multifractal formalism is nowhere satisfied. This example gives also a solution to a problem posed by Taylor (cited above).     

Weierstrass functions with random phases

Consider the function

where 1$">, , and is a non-constant 1-periodic Lipschitz function. The phases are chosen independently with respect to the uniform probability measure on . We prove that with probability one, we can choose a sequence of scales such that for every interval of length , the oscillation of satisfies . Moreover, the inequality is almost surely true at every scale. When is a transcendental number, these results can be improved: the minoration is true for every choice of the phases and at every scale.

     

Metal silanolates: organic soluble equivalents for O−2

Alkali metal trimethylsilanolates, M^⊕?OSiMe₃, convert carboxylic acid derivatives into their corresponding anhydrous acid salts under mild non-aqueous conditions.     

Stabiliser partitioning and oxidative degradation in rubber-toughened polypropylene

Solubility measurements on an antioxidant and a UV stabiliser in polypropylene and an ethylene/propylene rubber are correlated with partitioning between the two bulk polymers and between the phases of a blend. At low concentrations, partitioning concentrates the additive in the rubber; the effect increases with temperature, so that most of the additive will be in this phase at processing temperatures. Calculations suggest that the additives can diffuse between phases fast enough to compensate for consumption in either at service temperatures. At processing temperatures, diffusion of antioxidant from the more stable rubber phase to the polypropylene phase may be slow enough to limit protection from oxidation.