Measurement of the solubility of metal complexes in supercritical carbon dioxide using a UV–vis spectrometer

A new apparatus based on the circulation method was developed to measure the solubility of metal complexes in supercritical carbon dioxide (scCO₂) at a wide range of temperatures and pressures. A UV–vis spectrometer, which was connected to a small saturation cell through optical fibers, was used to determine solubility. The solubilities of cobalt(III) acetylacetonate (Co(acac)₃) and chromium(III) acetylacetonate (Cr(acac)₃) in scCO₂ were measured to check the validity of both the apparatus and the method and to accumulate new solubility data. The solubility data for Cr(acac)₃ obtained in this study were in good agreement with the data reported in the literature.The measured solubilities of Co(acac)₃ and Cr(acac)₃ were also correlated with the empirical equation including the three adjustable parameters, based on the equation proposed by Chrastil. The parameters were determined by fitting the equation to the experimental data for each metal complex and the calculated results closely replicated the experimental data.     

Perturbation method for determining the group of invariance of hierarchical models

We propose a perturbation method for determining the (largest) group of invariance of a toric ideal defined in [S. Aoki, A. Takemura, The largest group of invariance for Markov bases and toric ideals, J. Symbolic Comput. 43 (5) (2008) 342–358]. In the perturbation method, we investigate how a generic element in the row space of the configuration defining a toric ideal is mapped by a permutation of the indeterminates. Compared to the proof by Aoki and Takemura which was based on stabilizers of a subset of indeterminates, the perturbation method gives a much simpler proof of the group of invariance. In particular, we determine the group of invariance for a general hierarchical model of contingency tables in statistics, under the assumption that the numbers of the levels of the factors are generic. We prove that it is a wreath product indexed by a poset related to the intersection poset of the maximal interaction effects of the model.     

Wolfram

Ohne Zusammenfassung     

Comparison of Differently Bound Molecules in the Gel and Subgel Phases of a Phospholipid Bilayer System

The thermal behavior associated with the melting of ice was investigated by differential scanning calorimetry (DSC) for the gel and L-subgel phases of dipalmitoylphosphatidylcholine (DPPC)-water system of varying water contents up to a full hydration. By calorimetric analysis previously developed by us, the numbers of differently bound water molecules were estimated, and used to construct water distribution diagrams (i.e., a plot of the cumulative numbers of these water molecules vs. water content) for the two phases. A comparison of the diagrams revealed the critical role of interlamellar water which changes from freezable to non-freezable one in a conversion of the gel to the L-subgel phase by the thermal annealing. This revised version was published online in July 2006 with corrections to the Cover Date.     

Theory of the steady-state current of a redox couple at interdigitated array electrodes of which pairs are insulated electrically by steps

The possibility of constructing an interdigitated array electrode (IDA) with a submicrometre gap is proposed in which adjacent microband electrodes are separated from each other by an insulated step. Then the IDA is an assembly of protrusive and hollow microband electrodes. The unit model of the IDA consisted of half of the lower (hollow) microband electrode, an insulated step and half of the upper (protrusive) microband electrode with a finite thickness on the step. The boundary value problem involving the two-dimensional Laplace equation is presented for redox cycling at the IDA under diffusion control and is solved numerically by a boundary element method. The steady-state current was computed as a function of the height of the step and the thickness of the upper electrode. It was larger than the current at the ordinary IDA, partly because the true electrode area was larger than the area of the ordinary IDA. The current varied linearly with the logarithm of the step height. It was expressed by a simple approximate equation in order to facilitate prediction of its numerical value.