Reversible diffusion-limited reactions: "Chemical Equilibrium" state and the Law of Mass Action revisitedR. Voituriez1, M. Moreau1 and G. Oshanin1, 2, 3
1 Laboratoire de Physique Théorique des Liquides, Université Paris 6, Tour 16 4 place Jussieu, 75252 Paris Cedex 05, France
2 Max-Planck-Institut für Metallforschung - Heisenbergstr. 3 D-70569 Stuttgart, Germany
3 Institut für Theoretische und Angewandte Physik, Universität Stuttgart Pfaffenwaldring 57, D-70569 Stuttgart, Germany
received 14 September 2004; accepted in final form 10 November 2004
Two fundamental notions of classical chemical kinetics -the "Chemical Equilibrium" and the "Law of Mass Action"- are re-examined here for reversible diffusion-limited reactions (DLR), on the example of association/dissociation reactions. We consider a general model with long-ranged elementary reaction rates, such that any pair of A particles, separated by distance , may react at a rate , and any B may dissociate at a rate into a geminate pair of A's separated by distance . Within an exact analytical approach, we show that the state attained by reversible DLR at is generally not a true thermodynamic equilibrium, but rather a non-equilibrium steady state, and that the Law of Mass Action is invalid. The classical picture holds only in case when the ratio is independent of for any .
05.70.Ln - Nonequilibrium and irreversible thermodynamics.
05.45.-a - Nonlinear dynamics and nonlinear dynamical systems.
82.20.-w - Chemical kinetics and dynamics.
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