Chemistry in noninteger dimensions between two and three. II. Fractal surfaces of adsorbents

Abstract

The concept of fractal dimension D of surfaces, advanced as natural measure of surface irregularity in part I of this series, is shown to apply to a remarkable variety of adsorbents: graphites, fume silica, faujasite, crushed glass, charcoals, and silica gel. The D values found for these examples vary from two to almost three (for smooth and very irregular surfaces, respectively), thus covering the whole possible range. They quantify the intuitive picture that surface inhomogeneities are minor, e.g., in graphites, but dominant, e.g., in charcoal. The analysis is based on adsorption data, with main focus on adsorbates of varying molecular cross section. They include N2, alkanes, polycyclic aromatics, a quaternary ammonium salt, and polymers. The straight-line plots so obtained confirm also a number of reported on-surface conformations of specific adsorbates. The converse method to get D from varying the size of adsorbent particles is exemplified for fume silica and crushed glass.

Surface analysis of cryofixation-vacuum-freeze-dried polyaluminum chloride–humic acid (PACl–HA) flocs

“…In fact, the physical and chemical properties of floc surface have an important effect on the kinetic growing process of flocs, and more irregular and rough surfaces will imply more collision and attachment rates between different flocs in flocculation/flotation and filtration. However, the surface fractal dimension as an indication on the irregularity and roughness of surfaces [12][13][14][15][16][17][18][19][20] has rarely been reported in above coagulation process. In order to calculate the surface fractal dimension of floc, we must get the data matrix of surface irregularity from fine floc images or of micro-pore structure.…”

Fabrication and Fractality of Fe2O3-CeO2/ZSM-5 Composites for High-Temperature Desulfurization

“…In recent decades, fractal analysis has been widely applied in a few fields of scientific researches to characterize the geometric and structural properties of fractal surfaces and pore structures [33,34]. Fractal dimension is often adopted to quantitatively evaluate the irregularities of the fractal surface and pore structures.…”

Effect of polyferric chloride (PFC) doses and pH on the fractal characteristics of PFC–HA flocs

“…These pore surface fractal dimensions (D s ) were calculated with nitrogen adsorption data based on fractal FHH equations. However, the D s values of greater than three were observed based on nitrogen adsorption data and thermodynamic equation, and exceeded the range of surface fractal dimensions [18,20,[21][22][23][24][25][26][27].…”

“…More irregular and rough surfaces will imply greater collision and attachment rates between different flocs during treatment processes such as flocculation, flotation and filtration. However, the surface fractal dimension of flocs, which is an indication of surface irregularity and roughness [18][19][20][21][22][23][24][25][26][27], has rarely been investigated.…”