Subdiffusion-assisted reaction kinetics in disordered media
- Authors
- Kim, Ji-Hyun; Huh, Dann; Lee, Jinuk; Lee, Sangyoub; Sung, Jaeyoung; Seki, Kazuhiko; Tachiya, M.
- Issue Date
- Feb-2007
- Publisher
- IOP PUBLISHING LTD
- Citation
- JOURNAL OF PHYSICS-CONDENSED MATTER, v.19, no.6
- Journal Title
- JOURNAL OF PHYSICS-CONDENSED MATTER
- Volume
- 19
- Number
- 6
- URI
- https://scholarworks.bwise.kr/cau/handle/2019.sw.cau/24149
- DOI
- 10.1088/0953-8984/19/6/065116
- ISSN
- 0953-8984
1361-648X
- Abstract
- We present a theory for describing the reaction process occurring in disordered media with energetically disordered trapping sites and spatial constraints. The theory is based on a generalized fractional reaction-diffusion equation, which describes the time evolution of the mean distribution of a particle performing a continuous time random walk on a fractal network. The motion of a particle is subdiffusive because of the spatial constraints and/or the random detrapping times described by a waiting time distribution given by psi(t) similar to t(-(1+alpha)) with 0 < a < 1. Assuming that the reaction occurs at a separation of contact, the reaction and transport processes are decoupled and the kinetic information for the reaction is expressed in terms of the reaction-free Green's function obtained with the reflecting boundary condition at the separation of contact. The survival probability of a reactant pair is shown to decay asymptotically as tau(-alpha vertical bar ds/2-1 vertical bar), where d(s) is the fracton dimension of the fractal network under consideration. We also check the validity of the analytical results by comparison with Monte Carlo simulation results.
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Collections - College of Natural Sciences > Department of Chemistry > 1. Journal Articles
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