M. Borkovec et al., SURFACE-AREA AND SIZE DISTRIBUTIONS OF SOIL PARTICLES, Colloids and surfaces. A, Physicochemical and engineering aspects, 73, 1993, pp. 65-76
Small-angle X-ray scattering was employed to show that the surface of
soil particles is rough and scales as A is-proportional-to r(D)s where
A is the surface area of a given size fraction of radius r and D(s) i
s the surface fractal dimension (D(s) = 2.4 +/- 0.1). This relation ha
s been confirmed by independent surface-area measurements on fractiona
ted soil samples using nitrogen-gas adsorption and Methylene Blue adso
rption from solution. These results bear an interesting relationship t
o recent size-distribution measurements of soil particles. The number
of particles per unit volume with a radius larger than r has been show
n to follow a power law N(r) is-proportional-to r(-D) where the expone
nt D is the fragmentation fractal dimension (D = 2.8 +/- 0.1). The pow
er law is typically valid between two cut-off radii r1 << r << r2 with
values around r1 almost-equal-to 10-100 nm and r2 almost-equal-to 10-
5000 mum. The specific surface area of the unfractionated soil sample
depends critically upon the position of the lower cut-off r1 and can b
e accurately estimated from size-distribution data and the knowledge o
f D(s). These features can be related to a class of fragmented fractal
s which are characterized by the two fractal dimensions D and D(s). Th
ese fractal dimensions obey the inequalities 2 < D(s) < D < 3 and 2D(s
) - D less-than-or-equal-to 2 which are also satisfied by the present
experimental estimates.