Limited range fractality of randomly adsorbed rods

Daniel A. Lidar*, Ofer Biham, David Avnir

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

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 〈l〉 and the average inter-rod distance r1, these systems exhibit apparent fractal behavior. It is shown that unlike the case of randomly distributed isotropic objects, the upper cutoff r1 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 〈l〉 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<〈l〉, where the internal structure of the adsorbed objects is probed and 〈l〉<r<r1, 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.

Original languageAmerican English
Pages (from-to)10359-10367
Number of pages9
JournalJournal of Chemical Physics
Volume106
Issue number24
DOIs
StatePublished - 22 Jun 1997

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