Kinetic regimes and cross-over times in many-particle reacting systems
Department of Chemical Engineering, Columbia University New York, NY 10027, USA
2 Department of Physics, Columbia University - New York, NY 10027, USA
Accepted: 21 December 1998
We study kinetics of single-species reactions ("") for general local reactivity Q and dynamical exponent z (rms displacement .) For small molecules z=2, whilst z=4,8 for certain polymer systems. For dimensions d above the critical value , kinetics are always mean field (MF). Below dc, the density nt initially follows MF decay, . A 2-body diffusion-controlled regime follows for strongly reactive systems () with . For , MF kinetics persist, with . In all cases at the longest times. Our analysis avoids decoupling approximations by instead postulating weak physically motivated bounds on correlation functions.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 05.70.Ln – Nonequilibrium and irreversible thermodynamics / 82.35.+t – Polymer reactions and polymerization
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