SCALING PROPERTIES OF DIFFUSION-LIMITED REACTIONS - FRACTALS

We have generalized our previous scaling arguments [Sheu, Lindenberg, and Kopelman, Phys. Rev. A 42, 2279 (1990)] for diffusion-limited A + B --> 0 reactions to encompass various possible connectivity properties and reaction conditions on fractal structures. The theory now allows for a more complete range of possible reaction surface configurations. While our original result (which is a special case) places a bound that is consistent with very recent simulations on critical percolation clusters, the generalization is needed to account for the behavior on finitely ramified structures such as Sierpinski gaskets and Peano curve fractal constructions. Our results yield upper and lower bounds for the oscillations of the reactant decay exponent which are typical for hierarchical structures. Our approach unites under a single framework situations such as the A + B --> 0 reaction and the A + A --> 0 reaction that were previously treated separately.