The reversible reaction A+B⇔C in solution. A system-size expansion approach on the base of reactive many-particle diffusion equations
The diffusion-influenced reaction A+B■C is reconsidered by using an approach which starts directly from the reactive many-particle diffusion equations which govern the change in time of system states with a defined number of reactive particles. The classical problem is transformed into a more compac...
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Veröffentlicht in: | The Journal of chemical physics 1993-02, Vol.98 (3), p.2353-2365 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | The diffusion-influenced reaction A+B■C is reconsidered by using an approach which starts directly from the reactive many-particle diffusion equations which govern the change in time of system states with a defined number of reactive particles. The classical problem is transformed into a more compact ‘‘quantum’’ one by using a second quantization procedure. In this way, by straightforward operator manipulations, exact state-specific evolution equations can be derived. To prove the conditions for an approximate deterministic description of macroscopic systems, a system-size expansion in the sense of van Kampen is applied to these equations. By approximating the triplet and quadruplet terms in the evolution equations, a rate equation, a Fokker–Planck equation for the particle number fluctuations, and an evolution equation for the AB-pair distribution function can be derived which are consistent with one another. The results of this approach are compared with those of other recent studies including the stochastic approach I used in [Chem. Phys. 150, 187 (1991)]. |
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ISSN: | 0021-9606 1089-7690 |
DOI: | 10.1063/1.465074 |