Electronic Resource
College Park, Md.
:
American Institute of Physics (AIP)
The Journal of Chemical Physics
92 (1990), S. 5235-5238
ISSN:
1089-7690
Source:
AIP Digital Archive
Topics:
Physics
,
Chemistry and Pharmacology
Notes:
The radiation boundary condition was originally proposed by Collins and Kimball as a means of avoiding the unphysical prediction of the Smoluchowski model for reaction rates that the calculated rate in three dimensions k(t) has the property k(0)=∞. A microscopic model that can be used to derive the boundary conditions uses the tacit assumption that an encounter between two molecules A and B gives rise to a reaction with a probability α〈1. We consider a non-Markovian model in which the probability that exactly n encounters between A and B are required to produce a reaction is equal to θn. We show that when the expected number of such encounters is finite, one gets the usual radiation boundary condition. When the expected number is infinite, one finds a boundary condition that is nonlocal in time. The extension of our analysis to higher dimensions as well as to the Smoluchowski equation is readily generated.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.458530
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