Scaling behavior of surface irregularity in the molecular domain: From adsorption studies to fractal catalysts

Peter Pfeifer*, David Avnir, Dina Farin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

135 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)699-716
Number of pages18
JournalJournal of Statistical Physics
Volume36
Issue number5-6
DOIs
StatePublished - Sep 1984

Keywords

  • adsorption
  • catalysis
  • fractal structures
  • interfacial diffusion
  • neutron scattering
  • Solid surfaces

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