Non-classical reaction kinetics in low dimensional systems: Experiments and Monte Carlo simulations.

The common goal among the different projects discussed in this thesis is the development of a better understanding of the behavior of diffusion-limited elementary reaction processes under less than ideal conditions, i.e. the conditions of real chemical and physical systems. This thesis is a compilation of the results obtained from both Monte Carlo computer simulations and laboratory experiments for systems in which a variety of non-ideal conditions are either introduced purposefully or are intrinsically present. Three processes: Diffusion, described by the number of distinct sites visited in time ($S\sb{t}$) as well as the A + A $\to$ 0 and the A + B + 0 diffusion-limited reaction processes, are studied via Monte Carlo simulations on isotropic lattices and on tubular lattices. Asymptotic scalings of $S\sb{t}$ and the reaction processes were determined. Finite size scaling was also investigated. The finite size effect temporal expression scaled with lattice-width squared for all processes on isotropic one, two or three dimensional lattices. However, the finite size scaling with the short dimension(s) in tubular lattices was observed to be more complicated, with scaling exponents which depend on the process occurring and the dimensionality of the embedding space. Algebraic scaling arguments are given but may not be strictly valid for some cases. The heterogeneous reaction kinetics of two competing chemical reaction fronts was investigated experimentally using the chemical reaction of $Cr\sp{3+}$ with xylenol orange. The qualitative experimentally measured behavior of the local reaction rate across the length of the front, as well as the scaling in time of both the width of the front and the global reaction rate, reproduced the behavior predicted by Taitelbaum and Vilensky's computer model for the case of two competing reaction fronts under heterogeneous reactant conditions. A set of experiments employed confocal microscopy to measure the instantaneous concentration of fluorescein free acid in a focused laser beam phototrap. The imperfect trapping process in these experiments was the photobleaching of the fluorescein molecules that diffused into the phototrap. Quasi-1-dimensional and quasi-2-dimensional samples were studied and the experimentally determined scalings of the trapping rate with time were found to be in agreement with the non-classical rate laws predicted theoretically. On the other hand, stirred samples yielded classical results, as expected. A chemical trapping reaction was investigated using the catalytic oxidation of glucose. Experiments were performed in capillary tubes filled with a glucose/$O\sb2$ solution, with the catalyst embedded in a polyacrylamide matrix at one end of the tube. A non-classical reaction rate was observed by measuring, with respect to time, the change in the size of the depletion mass of the $O\sb2$ surrounding the trap.Ph.D.Physical chemistryPure SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/130294/2/9722030.pd