Fractal bet and FHH theories of adsorption: a comparative study

Abstract

Two theories of multilayer adsorption of gases, namely the BrunauerEmmett-Teller (bet) theory and the Frenkel-Halsey-Hill (fhh) theory, have recently been extended to the case of fractal substrates in a number of different ways. We present a critical evaluation of the various predictions. The principal results are the following. At high coverage, the fractal bet and fhh isotherms apply to mass and surface fractals, respectively. Both give characteristic power laws with D -dependent exponents ( D = fractal dimension of the substrate). The bet isotherm additionally depends on the topological dimension D top of the substrate. For fractal aggregates ( D top = 1) with D < 2, the adsorbed phase exists only in a highly disordered state. The bet theory is sensitive to multiple-wall effects (they affect prefactors); the fhh theory is not. For the fhh theory, detailed assessments of the approximations in the model are available. The predictions of the fhh theory have been observed on fractal silver surfaces.

Fractal Characterization of Wide Pore Range Catalysts: Application to Pd–Ag/SiO2 Xerogels

“…5), experimental points are very fuzzy and Eq. [8] is not clearly verified. The fractal dimensions obtained from SAXS measurements are in good agreement with the values obtained from mercury porosimetry, in the overlapping region ( Table 2).…”

“…(6)(7)(8)(9) to fractal surfaces is the most popular method for determining the fractal dimension from N 2 adsorptiondesorption measurements. In this approach a film thickness of more than 1.5 layers is used to probe the geometry of the surface.…”

“…In all cases, a power law with η = (D s ) SAXS ≈ 3 (Eq. [8]) is verified on a length scale which broadens with increasing Ag concentration in the Pd-Ag alloy.…”

Pickett Equation for the Description of Adsorption on Arbitrary Surfaces

“…In Equation 20, there is no singularity for D = 2 because of the limit of the product of (D-2) and the integral when D = 2 is finite. Equation 20is studied in detail in [6]. However, its practical application is related to computational difficulties.…”

“…The topological-based fractal BET theory is based on the three-parameter equation. As shown by Pfeifer et al, this equation has a number of drawbacks [6]. Both approaches employ the fundamental principles of the BET theory.…”