Theoretical model for diffusion controlled reactions of solvated electrons, incorporating a tunnelling mechanism

Abstract

The effect on diffusion-controlled reactions, of electron tunnelling from a solvent cavity to a scavenger molecule, is examined. The radial diffusion equation is modified to include a sink term, which varies exponentially with distance from the origin, and thus simulates tunnelling behaviour. An analytical solution is obtained for the steady-state, and applied to diffusion controlled reactions of the solvated electron in media covering a wide range of viscosities. In low viscosity media (η∼10^–3 kg m^–1 s^–1) reaction can take place at a reactant separation of about two molecular diameters, this distance increases with viscosity, reaching about eight molecular diameters for η= 10⁹ kg m^–1 s^–1. The theory is also applied to energy transfer by an exchange mechanism; transfer only begins to take place from distances greater than the encounter distance when the viscosity reaches ∼10⁵ kg m^–1 s^–1.