Excluded volume effect on diffusion-influenced reactions in one dimension

Abstract

The excluded volume (EV) effect between nonreactive like-particles of diffusion-influenced pseudo-first-order reaction A + B-->C is investigated by the hierarchical Smoluchowski approach of Kuzovkov and Kotomin [Rep. Prog. Phys. 51, 1479 (1988)] and the many-particle kernel formalism of Lee [J. Chem. Phys. 113, 8686 (2000)] in one dimension. Contrary to the three-dimensional analysis, the latter theory can be formulated without additional approximations in one dimension so that more accurate results are obtained. Although formulations and resulting expressions are different, these two theories show almost identical results numerically. The EV effect becomes significant at higher concentrations of B molecules as in three dimensions. However, we found that the EV effect in one dimension is more pronounced than in three dimensions. A similar trend appears as the size of the B molecule increases. Theoretical results are compared with Monte Carlo simulations. The simulation results reveal much larger EV effect than that predicted by both theories. This behavior may be attributed to the cage effect which is not considered in both theories. (C) 2003 American Institute of Physics.