The Independent Reaction Time Model

The independent reaction time (1RT) model was introduced as a shortcut Monte Carlo simulation of pairwise reaction times without explicit reference to diffusive trajectories (Clifford et al, 1982b). At first, the initial positions of the reactive species (any number and kind) are simulated by convolving from a given (usually gaussian) distribution using random numbers. These are examined for immediate reaction—that is, whether any interparticle separation is within the respective reaction radius. If so, such particles are removed and the reactions are recorded as static reactions. 

Great simplification is achieved by introducing the hypothesis of independent reaction times (IRT) that the pairwise reaction times evolve independendy of any other reactions. While the fundamental justification of IRT may not be immediately obvious, one notices its similarity with the molecular pair model of homogeneous diffusion-mediated reactions (Noyes, 1961 Green, 1984). The usefulness of the IRT model depends on the availability of a suitable reaction probability function W(r, a t). For a pair of neutral particles undergoing fully diffusion-con-trolled reactions, Wis given by (a/r) erfc[(r - a)/2(D t)1/2] where If is the mutual diffusion coefficient and erfc is the complement of the error function. 

Green and Pimblott (1989) have extended the IRT model to partially diffusion-controlled reactions between neutrals. They derive an analytical expression that involves an additional parameter, namely the reaction velocity at encounter. For reactions between charged species, W generally cannot be given analytically but must be obtained numerically. Furthermore, numerical inversion to get t then 

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