The one dimensional Lorentz gas - A model for geminate recombination reactions

In order to gain insight into the phenomenon of the solvent cage effect, which plays an important role in the dynamics of geminate recombination reactions, we present some studies on a simplified model - the one dimensional Lorentz gas. In this model fixed, point scatterers are placed at random along a line and a single point particle moves amongst them. On colliding, the traveller may be reflected or transmitted with a certain probability. We use computer simulation to calculate the velocity correlation function (VCF) and the distribution of first return times to a given scatterer (J(t)) for three reflection probabilities. We also consider an approximate theory, whereby the traveller remembers, after every collision, the position of the previous scatterer and the fact that there is a region of free space between the last and the present scatterer. This theory correctly predicts there to be a negative well in the VCF but underestimates its magnitude. For the first-return time problem, however, it gives very good agreement with the full simulation results. We also analyse the short and long time behaviour of J(t) and compare with predictions from the Lorentz- Boltzmann equation. © 1995.