A master equation investigation of coagulation reactions: Sol-gel transition
✍ Scribed by Matthias Thorn; Heinz-Peter Breuer; Francesco Petruccione; Josef Honerkamp
- Publisher
- John Wiley and Sons
- Year
- 1994
- Tongue
- English
- Weight
- 691 KB
- Volume
- 3
- Category
- Article
- ISSN
- 1022-1344
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✦ Synopsis
Abstract
The kinetics of irreversible coagulation phenomena in spatially homogeneous systems is formulated in terms of a multivariate stochastic process. The latter is governed by a master equation for the joint probability distribution of the numbers of reacting species. An efficient numerical algorithm is used to simulate the complete time evolution of the stochastic process. The method is illustrated by simulating the coagulation reaction with configuration‐dependent reaction kernels, K~ij~ = (ij)^ω^, for clusters of mass i and j with 1/2 < ω ⩽ 1, which are designed to model gelation phenomena. It is demonstrated that the stochastic simulation allows the determination of critical exponents and the gel point directly from the master equation. The results are compared to predictions of the rate equation approach to the sol‐gel transition.