Diffusion-limited binary reactions in low-dimensional systems: Monte Carlo simulations.

Abstract

The main task of this dissertation was to study the macroscopic kinetic laws and the particle distributions of binary diffusion-limited reactions in low dimensional systems by means of computer simulations. The effects of diffusion, reaction, particle landing processes, geometry, and electric field were investigated. The Random Walk method was used to model the diffusion process, and fractal geometries were employed to model disordered systems. Particle distributions were analyzed mainly using interparticle distance distributions, nearest neighbor distance distributions, and segregation parameters. Kinetic laws were obtained by comparing the kinetic data with the theoretical predictions, by using empirical methods to obtain the reaction orders, and by examining the particle distributions. Our simulation results agree with most of the theoretical predictions. These simulations have extended the current model to new parameter regimes and new sets of parameters. For systems far from equilibrium, self-organization was observed, and anomalous kinetics prevails. Reactant distributions were determined based on the dimension-dependent transport properties of the random walker, the selectivity of reactions between the members of neighboring pairs, and the correlation of landing particles. The kinetics was found to be directly related to the reactant distributions. For A + A $\to$ 0 reactions, a correspondence of the inter-particle distance distribution to the kinetic rate law was found. The effective reaction order, X, is equal to 1 + 2/d$\sb{\rm s}$ (d$\sb{\rm s} < 2)$ for transient reactions and for steady state reactions with random landing. However, X = 2 for steady state reactions with geminate landing. For A + B $\to$ 0 reactions, a correspondence of reactant segregation to the kinetic rate laws was found. Segregation is initiated by spatial fluctuations, and grow as fluctuations are amplified. In general, segregation decreases as the dimension increases. Thus, a variety of rate equations are obtained depending on the geometry and the details of the particle landing process. Some experiments on A + A $\to$ 0 reactions were also performed: Exciton fusion kinetics was measured for one-dimensional crystalline wires of naphthalene, with ordered and disordered domain structures. The experimental results support our simulation results.