Multisite reversible geminate reaction

摘要

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 Laplacedomain, for two different initial conditions, is valid for the case when the sites are overlappingspheres with no long-range interactions with the diffusing particle. The possibility to invert into thetime domain is determined by a characteristic polynomial. When all its roots are distinct, it ispossible to apply the Lagrange interpolation formula and obtain a partial-fraction expansion that canbe termwise inverted. At long times the occupancy of all sites, and for all initial conditions, decaysas t-(3/2).The behavior at short times depends on the initial condition: when starting from contact, thebinding probability rises as t1/2, but if the particle is initially bound to one of the sites, the occupancyof the others rises as t312. In between these two power laws we observe an intermediate-time kineticsconsisting of N decaying exponentials. Those which are slower than a characteristic diffusion timeare in the reaction-control regime and fit a discrete-state kinetic approximation with no adjustableparameters, whereas the faster kinetic steps are diffusion controlled. The model solved herein maydepict a wide range of physical situations, from multisite proton transfer kinetics to hydrogen-bonddynamics of liquid water.