The semi-empirical rate law for geminate-ion recombination by van den Ende, Warman, and Hummel, which predicts a linear dependence of the ion concentration with t−0.6, is modified to include simultaneous ion fragmentation. The theory is applied to the kinetics, as observed by pulse radiolysis of liquid methylcyclohexane (MCH) solutions of N2O, CHCl3, or tert-butylchloride (t-BuCl) at low temperatures. In MCH saturated with N2O (−130 °C), the solvent cation (MCH+, λmax = 550 nm) moves about 400 times faster than prediced by diffusion. With the known conductivity data at room temperature, an activation energy of about 2.7 kJ/mol can be derived. The solvent cation MCH+ does not appear to fragment. With t-BuCl added to MCH (−134 °C), MCH+ (λmax = 550 nm) and t-BuCl− (λmax = 450 nm) are observed simultaneously. The initial kinetics corresponds to the parent ion (MCH+) recombination with t-BuCl−. Then the MCH+ fragmentation with k1(−134 °C) = 3 × 105 s−1 is observed, followed by the geminate recombination of some fragment cation with t-BuCl−. The fragment cation recombines 300 times slower than the parent cation. With CHCl3 added to MCH (−130 °C), the MCH+ absorption is hidden within the [Formula: see text] band (λmax = 470 nm); however, the fragmentation is detected from kinetic analysis to occur in about 2 × 106 s−1. The modified t−0.6 rate law appears to be a very useful tool to study simultaneous ion recombination and ion fragmentation.
Calculation of the ion–ion recombination rate coefficient via a hybrid continuum-molecular dynamics approach