Fractal Reaction Kinetics
Abstract
Classical reaction kinetics has been found to be unsatisfactory when the reactants are spatially constrained on the microscopic level by either walls, phase boundaries, or force fields. Recently discovered theories of heterogeneous reaction kinetics have dramatic consequences, such as fractal orders for elementary reactions, selfordering and selfunmixing of reactants, and rate coefficients with temporal ``memories.'' The new theories were needed to explain the results of experiments and supercomputer simulations of reactions that were confined to low dimensions or fractal dimensions or both. Among the practical examples of ``fractallike kinetics'' are chemical reactions in pores of membranes, excitation trapping in molecular aggregates, exciton fusion in composite materials, and charge recombination in colloids and clouds. Diffusioncontrolled reactions with geometrical constraints, as found in heterogeneous kinetics, may be described by reactions on fractal domains. The hallmarks of ``fractallike'' reactions are anomalous reaction orders and timedependent reaction rate ``constants.'' These anomalies stem from the nonrandomness of the reactant distributions in low dimensions. For homobimolecular reactions (A + A > Pr) the distribution is partially ordered, for example, quasiperiodic. However, for heterobimolecular reactions (A + B > Pr) the reactants segregate. Theory, simulations, and experiments are interrelated through the formalism of fractal reaction kinetics (42).
 Publication:

Science
 Pub Date:
 September 1988
 DOI:
 10.1126/science.241.4873.1620
 Bibcode:
 1988Sci...241.1620K