| Summary: | Single-molecule spectroscopy has provided a means to uncover pathways and heterogeneities that were previously hidden beneath the ensemble average. Such
heterogeneity, however, is often obscured by the artifacts of experimental noise and
the occurrence of undesired processes within the experimental medium. This has
subsequently caused in the need for new analytical methodologies. It is particularly
important that objectivity be maintained in the development of new analytical
methodology so that bias is not introduced and the results improperly characterized.
The research presented herein identifies two such sources of experimental uncertainty,
and constructs objective approaches to reduce their effects in the experimental results.
The first, photoblinking, arises from the occupation of dark electronic states within the
probe molecule, resulting in experimental data that is distorted by its contribution. A
method based in Bayesian inference is developed, and is found to nearly eliminate
photoblinks from the experimental data while minimally affecting the remaining data
and maintaining objectivity. The second source of uncertainty is electronic shot-noise,
which arises as a result of Poissonian photon collection. A method based in wavelet
decomposition is constructed and applied to simulated and experimental data. It is
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found that, while making only one assumption, that photon collection is indeed a
Poisson process, up to 75% of the shot-noise contribution may be removed from the
experimental signal by the wavelet-based procedure. Lastly, in an effort to connect
model-based approaches such as molecular dynamics simulation to model-free
approaches that rely solely on the experimental data, a coarse-grained molecular model
of a molecular ionic fluorophore diffusing within an electrostatically charged polymer
brush is constructed and characterized. It is found that, while the characteristics of the
coarse-grained simulation compare well with atomistic simulations, the model is lacking
in its representation of the electrostatically-driven behavior of the experimental system.
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