TY - JOUR
T1 - Scaling behavior of surface irregularity in the molecular domain
T2 - From adsorption studies to fractal catalysts
AU - Pfeifer, Peter
AU - Avnir, David
AU - Farin, Dina
PY - 1984/9
Y1 - 1984/9
N2 - For an unexpected variety of solids, the surface topography from a few up to as many as a thousand angstroms is very well described by fractal dimension, D. This follows from measurements of the number of molecules in surface monolayers, as function of adsorbate or adsorbent particle size. As an illustration, we present a first case, amorphous silica gel, where D has been measured independently by each of the two methods. (The agreement, 3.02±0.06 and 3.04±0.05, is excellent, and the result is modeled by a "heavy" generalized Menger sponge.) The examples as a whole divide into amorphous and crystalline materials, but presumably all of them are to be modeled as random fractal surfaces. The observed D values exhaust the whole range between 2 and 3, suggesting that there are a number of different mechanisms by which such statistically self-similar surfaces form. We show that fractal surface dimension entails interfacial power laws much beyond what is the source of these D values. Examples are reactive scattering events when neutrons of variable flux pass the surface (this is of interest for locating fractal substrates that may support adlayer phase transitions); the rate of diffusion-controlled chemical reactions at fractal surfaces; and the fractal implementation of the traditional idea that the active sites of a catalyst are edge and apex sites on the surface.
AB - For an unexpected variety of solids, the surface topography from a few up to as many as a thousand angstroms is very well described by fractal dimension, D. This follows from measurements of the number of molecules in surface monolayers, as function of adsorbate or adsorbent particle size. As an illustration, we present a first case, amorphous silica gel, where D has been measured independently by each of the two methods. (The agreement, 3.02±0.06 and 3.04±0.05, is excellent, and the result is modeled by a "heavy" generalized Menger sponge.) The examples as a whole divide into amorphous and crystalline materials, but presumably all of them are to be modeled as random fractal surfaces. The observed D values exhaust the whole range between 2 and 3, suggesting that there are a number of different mechanisms by which such statistically self-similar surfaces form. We show that fractal surface dimension entails interfacial power laws much beyond what is the source of these D values. Examples are reactive scattering events when neutrons of variable flux pass the surface (this is of interest for locating fractal substrates that may support adlayer phase transitions); the rate of diffusion-controlled chemical reactions at fractal surfaces; and the fractal implementation of the traditional idea that the active sites of a catalyst are edge and apex sites on the surface.
KW - adsorption
KW - catalysis
KW - fractal structures
KW - interfacial diffusion
KW - neutron scattering
KW - Solid surfaces
UR - http://www.scopus.com/inward/record.url?scp=34250135036&partnerID=8YFLogxK
U2 - 10.1007/BF01012933
DO - 10.1007/BF01012933
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AN - SCOPUS:34250135036
SN - 0022-4715
VL - 36
SP - 699
EP - 716
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 5-6
ER -