Stochastic models of diffusion-controlled ionic reactions in radiation-induced spurs. 1. High-permittivity solvents

Alternative theories for the kinetics of diffusion-controlled reactions between ions in radiation-induced spurs are considered for solvents of high permittivity, such as water. A Monte-Carlo (MC) technique for simulating the paths of the diffusing ions and their encounters is developed and shown to provide an accurate description of the time-dependent reaction probability for the case of a single pair, by comparison with numerical solutions of the Debye-Smoluchowski equation. The MC simulations are then used to test the application of more approximate theories for the kinetics of multipair spurs. Two models are examined: (i) prescribed diffusion, which is conventionally applied in radiation chemistry, and (ii) the independent reaction times (IRT) model in which reaction times are associated independently with each ion pair. The IRT model is shown to describe the kinetics better than prescribed diffusion for a two-pair Gaussian, showing time-dependent reaction probabilities that are close to those obtained from the MC simulations. Good agreement is also found for the regular tetrahedron, where the effects of competition are maximized. The performance of both approximate models improves as the number of pairs in an initially Gaussian spur is increased and prescribed diffusion copes better with ionic reactions than it does with reactions between neutral species. Finally, a comparison between ionic and neutral spurs demonstrates that it is necessary to include charge in any model of spur kinetics involving ions, even in a high-permittivity solvent such as water.