The separation of chemical reactivity and Heisenberg spin-exchange effects in a radical-radical reaction by avoided level crossing μSR

The effect of Heisenberg spin exchange on the avoided level crossing (ALC) μSR spectra of organic free radicals is discussed within the framework of a two-state jump model. Numerical expressions are derived which also apply to chemical exchange processes. A simple expression relating ALC amplitude and linewidth to the exchange and chemical reaction rates is inferred from numerical calculations. The theory is applied to the kinetics of the radical-radical reaction between the muonated cyclohexadienyl radical and the diphenylpicrylhydrazyl radical (DPPH • ) which is investigated by means of transverse field (TF) and ALC μSR. A total rate constant of 4.7 (5) × 10 9 M −1 s −1 is found. ALC experiments allow its separation into a spin exchange contribution of ≈ 75% and a chemical contribution of ≈ 25%. The efficiency of the chemical reaction amounts to ≈ 1 3 per encounter of electron singlet radical pairs. The strong exchange-coupling limit holds true, and 10 −10 s is obtained as an upper limit for the radical pair lifetime at room temperature.