Limited Range Fractality of Randomly Adsorbed Rods

Multiple resolution analysis of two dimensional structures composed of randomly adsorbed penetrable rods, for densities below the percolation threshold, has been carried out using box-counting functions. It is found that at relevant resolutions, for box-sizes, $r$, between cutoffs given by the average rod length and the average inter-rod distance $r_1$, these systems exhibit apparent fractal behavior. It is shown that unlike the case of randomly distributed isotropic objects, the upper cutoff $r_1$ is not only a function of the coverage but also depends on the excluded volume, averaged over the orientational distribution. Moreover, the apparent fractal dimension also depends on the orientational distributions of the rods and decreases as it becomes more anisotropic. For box sizes smaller than the box counting function is determined by the internal structure of the rods, whether simple or itself fractal. Two examples are considered - one of regular rods of one dimensional structure and rods which are trimmed into a Cantor set structure which are fractals themselves. The models examined are relevant to adsorption of linear molecules and fibers, liquid crystals, stress induced fractures and edge imperfections in metal catalysts. We thus obtain a distinction between two ranges of length scales: $r$ where the internal structure of the adsorbed objects is probed, and $< r < r_1$ where their distribution is probed, both of which may exhibit fractal behavior. This distinction is relevant to the large class of systems which exhibit aggregation of a finite density of fractal-like clusters, which includes surface growth in molecular beam epitaxy and diffusion-limited-cluster-cluster-aggregation models.Comment: 10 pages, 7 figures. More info available at http://www.fh.huji.ac.il/~dani/ or http://www.fiz.huji.ac.il/staff/acc/faculty/biham or http://chem.ch.huji.ac.il/employee/avnir/iavnir.htm . Accepted for publication in J. Chem. Phy

On the correlation between the enantiomeric excess of L-isovaline and the level of aqueous alteration in carbonaceous meteorites

A positive correlation was observed between the enantiomeric excess (ee) of L-isovaline (L-iVal) and the degree of aqueous alteration (AqA) of carbonaceous meteorites. The origin of this remarkable phenomenon has remained enigmatic from two points of view: First, the correlation is between seemingly unrelated observables–nothing about AqA is of chiral characteristics; and second, following the accepted assumption that circularly polarized light (CPL) was the origin of the observed meteoritic ee of L-amino acids (AAs), it remined unclear why some of the observed levels of the ee of L-iVal in that correlation are significantly higher than those observed in laboratory simulations or those obtained from circular dichroism (CD) g-factor calculations. The current proposition accounting for this picture attributes late AqA conditions of the meteoritic parent bodies as providing the grounds for amplification of early initially CPL-generated low levels of L-ee. For reasons summarized below, this interpretation, which treats the CPL event and the AqA process as occurring in wide-time separated eras, is re-visited. An alternative interpretation of the observed correlation and of the high ee-values, is provided. It focuses on hydrophilic dust-aggregates clouds in wet star-forming regions in early pre-solar times, where both the CPL event and the grounds leading to the later AqA processes of the parent bodies, occurred. This mechanism removes the time separation between the initial ee formation and the AqA of the parent body, and replaces it with parallel processes, providing a scenario to the observation of high ee’s without total destruction, and to the apparent AqA/L-ee correlation. Although iVal is at the focus of this report, the steps of the development of the alternative mechanism and the conclusions that arise from it, are relevant and applicable to the general observations of L-ee’s of meteoritic AA’s

Apparent Fractality Emerging from Models of Random Distributions

The fractal properties of models of randomly placed $n$-dimensional spheres ($n$=1,2,3) are studied using standard techniques for calculating fractal dimensions in empirical data (the box counting and Minkowski-sausage techniques). Using analytical and numerical calculations it is shown that in the regime of low volume fraction occupied by the spheres, apparent fractal behavior is observed for a range of scales between physically relevant cut-offs. The width of this range, typically spanning between one and two orders of magnitude, is in very good agreement with the typical range observed in experimental measurements of fractals. The dimensions are not universal and depend on density. These observations are applicable to spatial, temporal and spectral random structures. Polydispersivity in sphere radii and impenetrability of the spheres (resulting in short range correlations) are also introduced and are found to have little effect on the scaling properties. We thus propose that apparent fractal behavior observed experimentally over a limited range may often have its origin in underlying randomness.Comment: 19 pages, 12 figures. More info available at http://www.fh.huji.ac.il/~dani

Exact stoichiometry high surface area mesoporous AlPO4 glass for efficient catalysis

Mesoporous AlPO4 materials have attracted much attention in catalysis due to their high thermal and chemical stability. Of particular interest for catalysis is the pure stoichiometry high surface area (> 500 m2/g) mesoporous AlPO4 (mAlPO4) glass prepared via a template-free aqueous sol–gel synthetic route. Toward the application of this material for catalysis, we have developed methods for loading it with nanoparticles (NPs) of catalytic metals—Pd and Rh—and carried out a detailed characterization study of the resulting doped materials by a wide array of analytical methods, including synchrotron X-ray absorption spectroscopy, inelastic neutron scattering and more. The applicability of this material for catalysis, both by itself and as a support for catalytic NPs, was then evaluated. The pure mAlPO4 exhibited excellent acid-catalyzed [3 + 2] cycloaddition of nitriles and sodium azide. mAlPO4 loaded with the Pd NPs catalyzed very efficiently deoxygenation reactions of benzyl alcohols. mAlPO4 loaded with Rh NPs catalyzed with high selectivity, the hydrogenation of phenols and cresols and full conversion the hydrogenation of the industrially very high-volume toluene to methylcyclohexane. The materials-science aspects of these successful catalysts were studied in detail, leading, for instance, to the understanding of the important role of the interfacial Rh/Pd–O-P bonds. Graphical abstract: [Figure not available: see fulltext.