Reactive fractal surfaces

Abstract

We extend our finding that the surfaces of most materials are fractal on a molecular scale to chemically reactive surfaces: We report that in many cases the reaction rate, v, between a surface and reactant molecules diffusing to it from the bulk (Eley-Rideal type process) scales with particle radius, R, as v <*-R0*'3 45678, in which Dr, the reaction dimension, is a characteristic parameter of the reaction. It is suggested that, quite often, DR can be interpreted as the fractal dimension of the subset of reactive sites of the surface. The relation between DR and the surface fractal dimension, D, reflects a rich mechanistic phenomenology of this type of reaction, such as the effects of diffusional screening and trapping, of chemical surface site selectivity, and of morphology changes during the reaction. Examples include reactive dissolution of various natural materials, dissolution of drugs, thermal decomposition, and coal gasification. Wenzel's very early law (1777) on surface reactivity is generalized. It is shown that the efficiency of a reaction can be increased by controlling the geometrical parameters of the

Molecularly-Limited Fractal Surface Area of Mineral Powders

“…The form of Equation (3b) confirms the validity of the mutual experimentally observed linear relation between log(SSA) and log(x) or the linear relation between log(SSA) and log(s), with slopes equal to (D´3) and (2´D) respectively [7,19], as mentioned in the introduction. It seems that such experimentally determined dependences with a significant linear theoretical fit imply a fractal (or self-similar) character of measured surfaces.…”

“…The s parameter may even reach a lattice dimension of crystals, i.e., 10´1 0 m. Because of an experimentally found paradox that D variables depend on the type of adsorbate (size of s), the researchers [7] introduced a new parameter, the "reaction fractal dimension" D R (see Table 1). It means that the same powder may have different fractal dimensions according to the type of adsorbate molecules interacting with the powder surface.…”

“…In several works dealing with the fractal dimension of surfaces, the scale parameter was omitted in spite of the fact that it is not possible to perform fractal analysis without it (see Discussion). [7]. The D R is the reaction fractal dimension and D is the true fractal dimension.…”

“…Alternatively, a dissolution process allows the SSA determination [6,7]. The "geometric" SSA can be derived from sieve or laser measurements of particle size distribution [8,9] or from capillary elevation of liquid through powder [10,11].…”

Stratospheric solar geoengineering without ozone loss

“…Calcite particles are treated the same as alumina particles, forming fractal aggregates upon coagulation. We use a monomer radius of 275 nm and take the fractal dimension D f to be 2.1 (29). Compared with the alumina particles of 240 nm radius studied in Weisenstein et al (2), pure calcite particles in this study sediment about 15% slower due to their larger radius but lower density of 2.7 g·cm −3 .…”