강진규Views: 248, 2016.03.04 15:51:42
- Journal of Physics: Condensed Matter 19 (2007) 065116 (14pp)
Ji-Hyun Kim1, Dann Huh1, Jinuk Lee1, Sangyoub Lee*1,4, Jaeyoung Sung2, Kazuhiko Seki3 and M Tachiya3,4
1 Department of Chemistry, Seoul National University, Seoul 151-747, Korea
2 Department of Chemistry, Chung-Ang University, Seoul 156-756, Korea
3 National Institute of Advanced Industrial Science and Technology (AIST), AIST Tsukuba Central 5, Higashi 1-1-1, Tsukuba, Ibaraki 305-8565, Japan
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 ψ(t)~t−(1+α) with 0<α<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 τ−α|ds/2−1|, where ds 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.