A Multifractal Approach to Patchwise Adsorption

✍ Scribed by Marcel Ovidiu Vlad

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 295 KB
• Volume: 159
• Category: Article
• ISSN: 0021-9797
• DOI: 10.1006/jcis.1993.1292

✦ Synopsis

A fractal approach to patchwise adsorption is suggested. Although the geometrical structure of the surface is not explicitly considered, some fractal features are included by assuming that a broad distribution of patches exists. A Markovian scenario for generating such a distribution is introduced. We assume that the actual distribution of patches is the result of a growth process, characterized by two different probabilities: the probability (\alpha) that a growth event takes place and the probability (\lambda) that during a growth event an active site from a patch is replaced by at least two active sites. The size distribution (\xi(M)) of the patches can be explicitly evaluated. It has a long tail for large patches (\xi(M)) (\cong M^{-(1+H)} \Xi(\ln M)) as (M \rightarrow \infty), where the fractal exponent (H) is equal to (\ln \alpha / \ln (1-\lambda)) and (\Xi(\ln M)) is a periodic function of (\ln M) with a period (-\ln (1-\lambda)). Concerning the adsorption equilibrium, we show that the probability (P(N)) that (N) molecules are adsorbed on a patch has a multifractal behavior (P(N) \cong) (\int d Q \rho(Q) N^{-(1+/)} \Lambda(\ln N)) as (N \rightarrow \infty), where (\rho(Q)) is the distribution function of the adsorption heat and (\Lambda(\ln N)) is a periodic function of (\ln N). The relationships with the other fractal approaches as well as with the classical homotattic patch model are atso considered. 1993 Acadcmic Press, Inc.