Europhys. Lett.
Volume 69, Number 2, January 2005
Page(s) 177 - 183
Section General
Published online 01 January 2005
Europhys. Lett., 69 (2), pp. 177-183 (2005)
DOI: 10.1209/epl/i2004-10333-0

Reversible diffusion-limited reactions: "Chemical Equilibrium" state and the Law of Mass Action revisited

R. 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 $A+A
\rightleftharpoons B$ reactions. We consider a general model with long-ranged elementary reaction rates, such that any pair of A particles, separated by distance $\mu$, may react at a rate $k_{+}(\mu)$, and any B may dissociate at a rate $k_{-}(\lambda)$ into a geminate pair of A's separated by distance $\lambda$. Within an exact analytical approach, we show that the state attained by reversible DLR at $t = \infty$ 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 $k_{+}(\mu)/k_{-}(\mu)$ is independent of $\mu$ for any $\mu$.

05.70.Ln - Nonequilibrium and irreversible thermodynamics.
05.45.-a - Nonlinear dynamics and nonlinear dynamical systems.
82.20.-w - Chemical kinetics and dynamics.

© EDP Sciences 2005