Numerical studies of electron tunnelling in liquids

Abstract

The diffusion equation, derived from Fick's second law, with an added exponential sink term to simulate electron tunnelling, is integrated numerically to determine the rate of electron decay at times greater than 1 ps. The effect of a coulomb interaction with a charged scavenger is examined and the steady-state rate constant shown to approximate closely to that obtained by combining the separate effects of tunnelling and charge-affected diffusion, which can be expressed analytically. Diffusion in the presence of a charge-induced dipole interaction is investigated for the case of scavenging of localised electrons in alkanes. The rate constant is shown to be dominated by random diffusion and tunnelling and the bias induced by the interaction is of little consequence. The sensivity of the rate constant to changes in the pre-exponential factor in the sink term is shown to be most favourable at short times.