Some surface effects in porous fractals

2014 Certain porous media have been claimed to be fractals in a broad range of scales a l L. The fractal dimension Df of the solid/void interface influences various surface effects characterized by a penetration length ls. If ls can be varied (by suitable external agents) through the interval (a, L), some information on Df can be extracted. We construct a tentative list of static physical processes leading to a variable ls : a) adsorption of latex spheres (of charge opposite to the wall) of different radii (R = ls); b) depletion layers in a polymer solution, where the polymer is repelled by the wall, with specific implications for gel permeation chromatography ; c) grafting of chains, in the (usual) regime where the grafting reaction stops whenever neighbouring chains begin to overlap ; d) preferential adsorption of one species in a binary mixture near criticality. Whenever the fractal dimension of the critical clusters Dc (~ 2.5) is larger than Df, the excess adsorption is controlled by the correlation length 03BE(= ls) and diverges near the critical point. J. Physique 46 (1985) 2117-2123 DTCEMBRE 1985, Classification Physics Abstracts 61.25 68.20 64.70 82.65 1. Surface fractals. Porous media with high specific areas play an important role in many fields : hydrology, oil sciences, oil technology, heterogeneous catalysis, chromatography, electrochemistry and so on. Sometimes the high area systems have a relatively narrow distribution of pore sizes (say, over less than a decade). In certain other cases, the distribution of pore sizes is extremely broad (say, over three decades or more). Certain porous media of the second group can be described as fractals in a certain range of lengths a I L. This means that they are statistically self-similar, or, in more concrete terms, that it is not possible to discriminate between two photographs of the same medium taken with two very different frame sizes (11, 12) (with 11, l2 in the fractal interval a, L). (*) Unite Associee au C.N.R.S. no 792 (U.A. 792). It often happens that the upper limit L is the size of the grains out of which the macroscopic structure is built The lower limit a may be as small as a molecular size. Various experiments suggest the possible existence of fractal structures in certain porous media, e.g. sandstones [1], industrial aluminas or silicas [2-3], or coals [4]. Some of these experiments will be reviewed later in this section after a brief reminder of the fractal dimension Df. * 1.1 DEFINITION OF Df. D f is the fractal dimension of the interface (2 D f 3). D~ can be defined in the following way. We generate spheres of radius 8 . with their centres around every point of the interface of one grain (size L). The volume spanned by the spheres per grain is Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198500460120211700