Kinetics of two-dimensional diffusion-controlled reactions: A Monte Carlo simulation of hard-disk reactants undergoing a Pearson-type random walk

The Monte Carlo method has been used for simulating two-dimensional diffusi ve motion of hard disks as a Pearsonian random walk (in which each displace ment is of equal length but in a random direction) and for analyzing the ki netics of a diffusion-controlled irreversible bimolecular reaction between the diffusing entities. The results are compared with predictions based on hydrodynamic theory (the diffusion equation), which was recently shown to b e consistent with the experimental data on the self-quenching of 1-palmitoy l-2(1-pyrenedecanoyl)-sn-glycero-3 -phosphocholine (py(10)- PC) in 1-palmit oyl-2-oleoyl-sn-gycero-3-phosphocholine (POPC) fluid bilayers (Martins et a l. J. Phys. Chem. 1996, 100, 1889). Regardless of the time range analyzed a nd of the physical characteristics (diffusion constants and radii) of the r eactants, the agreement between the random walk picture and the hydrodynami c treatment improves as the magnitude of the step of the diffusive displace ment becomes smaller and one approaches the continuum limit. The study conf irms earlier deductions about the limits of validity of the hydrodynamic th eory (for reactions in 2D space) and reveals the need for more comprehensiv e experimental data.