Mechanochemical treatment of kaolinite

Kaolinite surfaces were modified by mechanochemical treatment for periods of time up to 10 h. X-ray diffraction shows a steady decrease in intensity of the d(001) spacing with mechanochemical treatment, resulting in the delamination of the kaolinite and a subsequent decrease in crystallite size with grinding time. Thermogravimetric analyses show the dehydroxylation patterns of kaolinite are significantly modified. Changes in the molecular structure of the kaolinite surface hydroxyls were followed by infrared spectroscopy. Hydroxyls were lost after 10 h of grinding as evidenced by a decrease in intensity of the OH stretching vibrations at 3695 and 3619 cm−1 and the deformation modes at 937 and 915 cm−1. Concomitantly an increase in the hydroxyl stretching vibrations of water is found. The water-bending mode was observed at 1650 cm−1, indicating that water is coordinating to the modified kaolinite surface. Changes in the surface structure of the OSiO units were reflected in the SiO stretching and OSiO bending vibrations. The decrease in intensity of the 1056 and 1034 cm−1 bands attributed to kaolinite SiO stretching vibrations were concomitantly matched by the increase in intensity of additional bands at 1113 and 520 cm−1 ascribed to the new mechanically synthesized kaolinite surface. Mechanochemical treatment of the kaolinite results in a new surface structure.

Time-Dependent Density Functional Molecular Orbital and Excited State Calculations on Bis(porphyrinyl)butadiynes in the Monocationic, Neutral, Monoanionic, and Dianionic Oxidation States

We report a theoretical study of the multiple oxidation states (1+, 0, 1−, and 2−) of a meso,meso-linked diporphyrin, namely bis[10,15,20-triphenylporphyrinatozinc(II)-5-yl]butadiyne (4), using Time-Dependent Density Functional Theory (TDDFT). The origin of electronic transitions of singlet excited states is discussed in comparison to experimental spectra for the corresponding oxidation states of the close analogue bis{10,15,20-tris[3‘,5‘-di-tert-butylphenyl]porphyrinatozinc(II)-5-yl}butadiyne (3). The latter were measured in previous work under in situ spectroelectrochemical conditions. Excitation energies and orbital compositions of the excited states were obtained for these large delocalized aromatic radicals, which are unique examples of organic mixed-valence systems. The radical cations and anions of butadiyne-bridged diporphyrins such as 3 display characteristic electronic absorption bands in the near-IR region, which have been successfully predicted with use of these computational methods. The radicals are clearly of the “fully delocalized” or Class III type. The key spectral features of the neutral and dianionic states were also reproduced, although due to the large size of these molecules, quantitative agreement of energies with observations is not as good in the blue end of the visible region. The TDDFT calculations are largely in accord with a previous empirical model for the spectra, which was based simplistically on one-electron transitions among the eight key frontier orbitals of the C4 (1,4-butadiyne) linked diporphyrins.

Implicit difference approximation for the time fractional diffusion equation

In this paper, we consider a time fractional diffusion equation on a finite domain. The equation is obtained from the standard diffusion equation by replacing the first-order time derivative by a fractional derivative (of order $0<\alpha<1$ ). We propose a computationally effective implicit difference approximation to solve the time fractional diffusion equation. Stability and convergence of the method are discussed. We prove that the implicit difference approximation (IDA) is unconditionally stable, and the IDA is convergent with $O(\tau+h^2)$, where $\tau$ and $h$ are time and space steps, respectively. Some numerical examples are presented to show the application of the present technique.