ISSN:
1089-7690
Source:
AIP Digital Archive
Topics:
Physics
,
Chemistry and Pharmacology
Notes:
This paper analyzes diffusion controlled reactions between Brownian particles in d dimensions separated by a d−1-dimensional hyperplane. We calculate the rate coefficient k(t) defined by N(overdot)=k(t)ρAρB, where N(overdot) is the reaction rate per unit interface area, ρi is the number density of i far from the interface on the side containing i, and t is the reaction time. k(t) is expressed in terms of the particle diffusion coefficients Di and the distance of closest approach between the components before a reaction. The critical dimension dc at which reaction kinetics cross over from compact (d〈dc) to noncompact (d〉dc) behavior is reduced by the presence of an interface to dc =1 from dc =2 for reactions without an interface. Thus, for d〉1, k(t) exhibits all the characteristics of noncompact reactions. For example, k(t) has a constant long time limit k. For noncompact cases with d〉2 we find that when DA/DB(very-much-greater-than)1 the more mobile species dominates (k∝DA) while for d=2 the slow species enters logarithmically and k vanishes in the limit DB →0 [k∝DA/ln(DA/DB)]. The crossover case d=dc =1 is very different and exhibits some features of compact behavior; e.g., k(t) is quenched logarithmically at long times. In this case we find, as in the d=2 noncompact case, that k(t) vanishes in the limit DB/DA→0. This effect is entirely absent for reactions without an interface and results from the rate being limited by diffusion of the slow species to the interface.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.454362
Permalink