REACTION-KINETICS OF CLUSTER IMPURITIES

We study the kinetics of clustered immobile reactants in diffusion-con trolled single-species annihilation. We consider the initial condition s where the immobile reactants occupy a subspace of dimension d(i), wh ile the rest of the d-dimensional space is occupied by identical mobil e particles. The Smoluchowski rate theory suggests that the immobile r eactant concentration s(t) exhibits interesting behavior as a function of the codimension, (d) over bar = d - d(i). This survival probabilit y undergoes a survival-to-extinction transition at (d) over bar(c) = 2 . For (d) over bar < (d) over bar(c), a finite fraction of the immobil e reactants survives, while for (d) over bar greater than or equal to (d) over bar(c), s(t) decays indefinitely. The corresponding asymptoti c properties of the concentration are discussed. The theoretical predi ctions are verified by numerical simulations in two and three dimensio ns.