Probing the Fractal Character of Pore Surfaces in Shale with Adsorption Technique
- PDF / 896,842 Bytes
- 6 Pages / 417.6 x 639 pts Page_size
- 69 Downloads / 154 Views
ABSTRACT We report on an adsorption study on two shale samples that have previously been investigated by small-angle neutron scattering (SANS). The scattering data indicate that these samples can be characterized as surface fractals in length from 5 A to 500 A, with the fractal dimension D between 2.83 and 2.75. Using the existing models for adsorption on fractal surfaces, the values of D deduced from the adsorption data appear to be consistently lower than the SANS results. We discuss these findings. INTRODUCTION In recent years it has been shown that the geometric irregularities in many natural porous materials are statistically scale invariant over several decades of length scales, that is, they can be described as self-similar fractals with the fractal dimension D between 2 and 31. Considerable effort has been directed towards an understanding of adsorption on fractal surfaces. To date, however, there have been few adsorption experiments performed on well-characterized fractal systems. The purpose of this article is to report such a study, so that the theoretical predictions can be tested. An adsorption isotherm experiment measures the amount of gas adsorbed on a substrate as a function of the equilibrium vapor pressure P at a fixed temperature T. The surface area (S) of the underlying substrate is determined by the number of adsorbed molecules (Nm ) required to cover the surface with a monolayer blanket and the cross-sectional area (om-) of the molecule. For a fractal surface of linear size L and dimension D, if the adsorbed molecules are of size f, the combination of two basic relationships, Nm - (L /f)D and r. t 2 , yields S~j2 (L /f) D _-
(1)
In any real system, the above power-law behavior extends only over a finite range of length scales, say, from f_ to f+, where the lower limit f may be as small as a few angstroms and the upper limit t+ can be as large as the pore radius. In their pioneer work, Avnir et al used the standard BET adsorption technique 4 to measure the surface area S as a function of the adsorbed molecule size f and found that the fractal dimension D varied between 2 and 3 for a variety of porous materials'. This so-called yardstick method, though appealing in its simplicity, suffers several shortcomings. Most notably, the range of length scales probed by changing molecular size is very limited; the shape of adsorbed molecules and their interactions with an heterogeneous surface can alter the apparent area even in the absence of geometric roughness. For a multilayer film adsorbed on a fractal surface, many of the limitations in the original work of Avnir et al. might be avoided. Chemical heterogeneity on the surface should be unimportant because the substrate becomes mostly shielded after the completion of the first 243
Mat. Res. Soc. Symp. Proc. Vol. 543 © 1999 Materials Research Society
monolayer; and the thermodynamics of the liquid-like film and the vapor is the key consideration here. Moreover, the film thickness z should set the minimum radius of curvature of the liquidvapor inte
Data Loading...
