Degree Type

Dissertation

Date of Award

2005

Degree Name

Doctor of Philosophy

Department

Chemistry

First Advisor

John J. Kozak

Second Advisor

Mark Gordon

Abstract

The effect of imposing different constraints (biases, boundary conditions) on the mean time to trapping (or mean walklength) for a particle (excitation) migrating on a finite dendrimer lattice with a centrally-positioned trap is explored. By mobilizing the theory of finite Markov processes, one is able to obtain exact analytic expressions for site-specific walklengths as well as the overall walklength for both nearest-neighbor and second-nearest-neighbor displacements. A novel feature of this work is the establishment of a connection between the random walk models studied here and percolation theory. The full dynamical behavior was also determined via solution of the stochastic master equation, and the results obtained compared with recent spectroscopic experiments.

DOI

https://doi.org/10.31274/rtd-180813-16436

Publisher

Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/

Copyright Owner

Jonathan Lee Bentz

Language

en

Proquest ID

AAI3184583

File Format

application/pdf

File Size

96 pages

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