SURFACE-AREA AND SIZE DISTRIBUTIONS OF SOIL PARTICLES

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) is the surface fractal dimension (D(s) = 2.4 +/- 0.1). This relation has been confirmed by independent surface-area measurements on fractionated soil samples using nitrogen-gas adsorption and Methylene Blue adsorption from solution. These results bear an interesting relationship to recent size-distribution measurements of soil particles. The number of particles per unit volume with a radius larger than r has been shown to follow a power law N(r) is-proportional-to r(-D) where the exponent D is the fragmentation fractal dimension (D = 2.8 +/- 0.1). The power 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 be accurately estimated from size-distribution data and the knowledge of D(s). These features can be related to a class of fragmented fractals which are characterized by the two fractal dimensions D and D(s). These 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.