Summary
The effective rate of the diffusion-controlled irreversible reaction X+X→A (Smoluchowski process) is calculated with the use of a general theory based on the continuous stochastic equations for birth and death processes. In the region of small chemical rates the effective reaction rate is determined by the chemical reaction rate, while for the high rates (Smoluchowski limit) the diffusion-controlled kinetics will dominate. The kinetics of one- and two-dimensional processes is also briefly discussed.
riassunto
Si calcola con l’uso di una teoria generale basata sulle equazioni stocastiche continue per processi di nascita e morte il rateo effettivo di una reazione irreversiile controllata dalla diffusione X+X→A (processo di Smoluchowski). Nella regione di bassi ratei chimici, si determina il rateo effettivo della reazione mediante il rateo chimico di reazione, mentre per alti ratei (limite di Smoluchowski) dominerà la cinetica controllata dalla diffusione. Si discute inoltre brevemente la cinetica dei processi mono-e bidimensionali.
Резюме
На основе континуальной стохастической теории процессов рождениягибели рассчитана эффективная скорость необратимой диффузионно-ограниченной реакции X+X→A (процесс Смолуховского). В области малых значений химических скоростей реакции эффективная скорость определяется химическими скоростями реакции, в то время как при больших значениях (предел Смолуховского) будет доминировать диффузионно-ограниченная кинетика. Кратко рассмотрена также кинетика процессов в одном и двух измерениях.
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Chechetkin, V.R., Lutovinov, V.S. Continuous stochastic description of birth and death processes and diffusion-controlled reactions. Nuovo Cim B 99, 103–116 (1987). https://doi.org/10.1007/BF02726573
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DOI: https://doi.org/10.1007/BF02726573