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Abstract: This thesis explores the dynamics and sensing performance of silicon quantum dot (SiQD) ensembles coupled to the whispering gallery modes (WGMs) of spherical and cylindrical microcavities. The first project investigated the possibility of observing Purcell effects in an ensemble of QDs coupled to a microsphere resonator. However, no convincing evidence for rate modifications was found. Several possible reasons for this negative result were outlined and future experimental improvements were suggested. Next, the SiQDs were coupled to the WGMs of cylindrical cavities (fibers and microcapillaries) in order to investigate and optimize their refractive-index sensing performance. These sensors register a WGM wavelength shift in response to changes in local index of refraction. Using an SiQD coated optical fiber, the detection limit of the sensor was improved by projecting the WGM spectrum onto a full 2 dimensional CCD array. However, noise from various experimental sources limited the detection limit of the fiber sensor to a value of 2.4E-3 RIU. In order to further improve the ultimate limit of detection, a more mechanically stable device was constructed. This consisted of a microcapillary whose channel was coated with a layer of SiQDs embedded in a protective oxide matrix. By controlling the SiQD channel film thickness via an etching procedure, the device sensitivity to refractometric changes was maximized. Using the techniques developed to minimize the wavelength shift resolution, a detection limit of 1.7E-4 RIU was experimentally measured, which is less than a factor 2 larger than the calculated optimum theoretical limit of detection. This represents one of the best experimentally-observed detection limits reported for fluorescent WGM devices.

Statisticians are often called upon to analyze censored data. Environmental and toxicological data is often left-censored due to reporting practices for measurements that are below a statistically defined detection limit. Although there is an abundance of literature on univariate methods for analyzing this type of data, a great need still exists for multivariate methods that take into account possiblecorrelation amongst variables. Two methods are developed here for that purpose. One is a Markov Chain Monte Carlo method that uses a Gibbs sampler to estimate censored data values as well as distributional and regression parameters. The second is an expectation maximization (EM) algorithm that solves for the distributional parameters that maximize the complete likelihood function in the presence of censored data. Both methods are applied to bivariate normal data and compared to each other and to two commonly used simple substitution methods with respect to bias and mean squared error of the resulting parameter estimates. The EM method is the most consistent for estimating all distributional and regression parameters across all levels of correlation and proportions of censoring. Both methods provide substantially better estimates of the correlation coefficient than the univariate methods.

Trace level perchlorate analysis in water initiated a new development in the Ion Chromatography (IC) technology. Maintenance of a low detection limit may be highly affected by the operating conditions of the IC system. In this study the homoscedasticity of the IC system within the calibration concentration range was evaluated by Cochran’s test, the effect of the system drift on the calibration curve was investigated by lack of fit test. The detection limit of the system was obtained from Method Detection Limit (MDL) and the calibration curve separately. The effect of self regeneration suppressor (SRS) current on the detection limit was also investigated. The results revealed the homoscedasticity of the IC system. The effect of system drift on the calibration curve was noticed. An acceptable detection limit can be achieved under the lower SRS current (100 mA). Perchlorate remediation by zero valent iron was also studied in this research. Acid treatment of iron filings significantly enhanced the reduction rate of perchlorate and the reduction rate was correlated reasonably well by pseudo first order reaction kinetics. A linear correlation relating the reaction rate constant to the square of iron dosage was developed which predicted reasonably well the performance of flow through experiments. Flow-through column experiments were conducted to test a permeable reactive barrier at a laboratory scale. Effluent perchlorate concentration was below 4 μg L-1 for a 4.27 days retention time. The experimental results revealed that perchlorate was adsorbed on the iron surface before being reduced. In simulated ground water study, background anions decreased perchlorate reduction due to competitive behavior on the iron surface. In order to verify the catalytic effect of iron filing surface, batch experiments using zinc metal to reduce perchlorate were also conducted. The undetectable perchlorate reduction by zinc revealed that iron served as a reducing agent and catalyst simultaneously. The mechanism of perchlorate reduction on iron filings surface was also discussed.