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Multisite reversible geminate reaction Soohyung Park and Noam Agmona

Summary: Multisite reversible geminate reaction
Soohyung Park and Noam Agmona
Institute of Chemistry and the Fritz Haber Research Center, The Hebrew University of Jerusalem,
Jerusalem 91904, Israel
Received 2 October 2008; accepted 5 January 2009; published online 20 February 2009
We provide an analytic solution for diffusion-influenced geminate reaction with multiple N
reversible binding sites of which one may be irreversible . The solution obtained in the Laplace
domain, for two different initial conditions, is valid for the case when the sites are overlapping
spheres with no long-range interactions with the diffusing particle. The possibility to invert into the
time domain is determined by a characteristic polynomial. When all its roots are distinct, it is
possible to apply the Lagrange interpolation formula and obtain a partial-fraction expansion that can
be termwise inverted. At long times the occupancy of all sites, and for all initial conditions, decays
as t-3/2
. The behavior at short times depends on the initial condition: when starting from contact, the
binding probability rises as t1/2
, but if the particle is initially bound to one of the sites, the occupancy
of the others rises as t3/2
. In between these two power laws we observe an intermediate-time kinetics
consisting of N decaying exponentials. Those which are slower than a characteristic diffusion time
are in the reaction-control regime and fit a discrete-state kinetic approximation with no adjustable


Source: Agmon, Noam - Institute of Chemistry, Hebrew University of Jerusalem


Collections: Chemistry