Surface fractal dimensions of some industrial minerals from gas-phase adsorption isotherms
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Serge Lacelle and Carmel Jolicoeura) Departement de chimie, Universite de Sherbrooke, Sherbrooke (Quebec), Canada J1K 2R1 (Received 5 July 1991; accepted 27 February 1992)
A high precision gravimetric method was used to investigate the adsorption of nitrogen (N2) and carbon tetrachloride (CC14), respectively, at 77 and 298 K, onto various industrial minerals. The solids investigated include silica isomorphs, blast furnace slags, an Y-zeolite, and several naturally occurring fibrous minerals. The adsorption isotherms were analyzed to derive surface areas, BET constants (C), and surface fractal parameters (D). The latter were obtained through an approach recently suggested by Avnir and Jaroniec,1 using multilayer adsorption data; D values obtained for the various gas-solid systems investigated cover the range 2.1-3.0. A systematic comparison between D values inferred from N2 and CCI4 adsorption data shows that the CCI4 molecule probes the surface roughness in a more discriminate fashion than N 2 . In most cases, the differences between D(N 2 ) and D(CC14) appear to reflect changes due to sample preparation more than intrinsic differences amongst the various solids. I. INTRODUCTION The surface fractal dimension, D, of a solid can be determined experimentally and serves to characterize its surface roughness or irregularities.2'3 Considering such irregularities at the atomic or molecular level, solid surfaces may exhibit fractal dimensions ranging from D = 2, for perfectly smooth surfaces, to D = 3, for sponge-like surfaces. It is interesting to note, from a practical point of view, that some of the solids whose surfaces lead to these limiting values are important synthetic minerals; cases in point are aerosil (D ~ 2) and silica gel (D = 3). The magnitude of the surface fractal dimensions of solids is relevant to many important physico-chemical processes, namely adsorption, surface diffusion, and catalysis.3 However, the measurement of D values is usually tedious and time consuming; typically, one needs to obtain a series of adsorption isotherms, either for a homologous series of adsorbate molecules on the solid of interest or for a single adsorbate on different particle size preparations of the solid.4 Recently, Avnir and Jaroniec1 proposed a convenient method to determine surface fractal dimensions from a single adsorption isotherm. Their approach is an extension of the Frenkel-Halsey-Hill (FHH) model for multilayer adsorption, and leads to the following equation:
0= — = k[ln(PQ/P)Y
(1)
"'Address correspondence to this author. 1888 http://journals.cambridge.org
J. Mater. Res., Vol. 7, No. 7, Jul 1992 Downloaded: 14 Mar 2015
As usual, 0 represents the surface fractional coverage (the number of adsorbed molecules N over the number of molecules adsorbed at monolayer coverage Nm); k is a constant, P and PQ are, respectively, the equilibrium and saturation pressures of the adsorbate, and v is a "critical" exponent. The latter is related to the surface fractal dimension of the adsorbent according to D =3- v
(2)
The
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