LIMITED RANGE FRACTALITY OF RANDOMLY ADSORBED RODS

Multiple resolution analysis of two dimensional structures composed of randomly adsorbed penetrable rods, for densities below the percolatio n 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 r(l), these systems exhibit apparent fractal behavior. It is shown th at unlike the case of randomly distributed isotropic objects, the uppe r cutoff r(l) 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 orientati onal distributions of the rods and decreases as it becomes mon anisotr opic. For box sizes smaller than [l] the box counting function is dete rmined by the internal structure of the rods, whether simple or itself fractal. Two examples are considered-one of regular rods of one dimen sional structure and rods which are trimmed into a Canter set structur e which are fractals themselves. The models examined are relevant to a dsorption of linear molecules and fibers, Liquid crystals, stress indu ced fractures, and edge imperfections in metal catalysts. We thus obta in a distinction between two ranges of length scales: r<[l], where the internal structure of the adsorbed objects is probed and (l)<r<r(l), where their distribution is probed, both of which may exhibit fractal behavior. This distinction is relevant to the large class of systems w hich 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. (C) 1997 American Institu te of Physics.