Eur. Phys. J. E 1, 159-177
Interfacial reaction kinetics
B. O'Shaughnessy1 - D. Vavylonis2
1 Department of Chemical Engineering, Columbia University, 500 West 120th
Street, New York, NY 10027, USA
2 Department of Physics, Columbia University, 538 West 120th Street, New
York, NY 10027, USA
bo8@columbia.edu,
dvav@phys.columbia.edu
Received 8 June 1998 and Received in final form 10 September 1999
Abstract
We study irreversible A-B reaction kinetics at a fixed interface
separating two immiscible bulk phases, A and B. Coupled equations are
derived for the hierarchy of many-body correlation functions.
Postulating physically motivated bounds, closed equations result without
the need for ad hoc decoupling approximations. We consider general
dynamical exponent z, where
is the rms diffusion
distance after time t. At short times the number of reactions per unit
area,
,
is 2nd order in the far-field reactant densities
.
For spatial dimensions dabove a critical value
,
simple mean field (MF) kinetics
pertain,
where
Qb is the local reactivity. For low dimensions
,
this MF
regime is followed by 2nd order diffusion controlled (DC) kinetics,
,
provided
.
Logarithmic corrections
arise in marginal cases. At long times, a cross-over to 1st order
DC kinetics occurs:
.
A density
depletion hole grows on the more dilute A side. In the symmetric case
(
), when
the long
time decay of the interfacial reactant density,
,
is
determined by fluctuations in the initial reactant distribution, giving
.
Correspondingly, A-rich and B-rich
regions develop at the interface analogously to the segregation effects
established by other authors for the bulk reaction
.
For
fluctuations are
unimportant: local mean field theory applies at the interface (joint
density distribution approximating the product of A and B densities) and
.
We apply our results to simple
molecules (Fickian diffusion, z=2) and to several models of short-time
polymer diffusion (z>2).
PACS
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian
motion -
68.45.Da Adsorption and desorption kinetics; evaporation and
condensation -
82.35.+t Polymer reactions and polymerization
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