| This thesis addresses the application of statistical mechanics to problems in anomalous transport and combinatorial chemistry.; For two anomalous transport problems, statistical field theoretic techniques have been employed. In the investigation of disorder-induced time-dependent diffusion in zeolites, it is suggested that disordered framework aluminums and non-framework cations can create a random electrostatic potential in zeolites that can lead to a discrepancy between diffusivities measured by microscopic and macroscopic experimental techniques. The value of the discrepancy and the characteristic time scale at which it occurs is calculated for several ionic and polarizable species diffusing in zeolites. For ionic species, a discrepancy is almost inevitable. For polarizable species, a significant discrepancy may occur in some zeolites only for long alkanes or large species such as benzene. In another application of statistical field theory, the A + A → reaction is considered, where the transport of the particles is given by Lévy flights in a quenched random potential. With a common literature model of the disorder, the random potential can only increase the rate of reaction. With a model of the disorder that obeys detailed balance, however, the rate of reaction initially increases and then decreases as a function of the disorder strength. The physical behavior obtained with this second model is in accord with that for reactive turbulent flow, indicating that Lévy flight statistics can model aspects of turbulent fluid transport.; By analogy with Monte Carlo algorithms, new strategies are proposed for design and redesign of high-throughput experiments, or combinatorial chemistry. For small molecule libraries, several Monte Carlo methods are examined, including Metropolis, three types of biased schemes, and composite moves that include swapping or parallel tempering. Among them, the biased Monte Carlo schemes exhibit particularly high efficiency in locating optimal compounds. The Monte Carlo strategies are compared to a genetic algorithm approach. Although the best compounds identified by the genetic algorithm are comparable to those from the better Monte Carlo schemes, the diversity of favorable compounds identified is reduced by roughly 60%. In another problem, how best to design and redesign high-throughput experiments for templated zeolite synthesis is addressed. A model that relates materials function to chemical composition of the zeolite and the structure directing agent is introduced. Using this model, several Monte Carlo-like design protocols are evaluated. Multi-round protocols are found to be effective, and strategies that use a priori information about the structure-directing libraries are found to be the best. |
