Building a Framework for Analyzing Non-Linear and Multidimensional Kinetics

Many materials exhibit multiple rates of molecular relaxation due to structural complexities. Standard linear and one-dimensional kinetic cannot extract all the necessary dynamic information about these systems. This dissertation contributes to an overarching scheme to develop new non-linear and multidimensional kinetic experiments to obtain this information. The studies span computation and experiments, picosecond to second timescales, and both single-molecule and pulsed-laser kinetics Single-molecule kinetics experiments yield time series that contain information about unique structural and dynamic properties of materials. However, these time series are noisy, and data analysis is challenging. Parametric methods are computationally intensive and require strong, unverifiable assumptions about the system being studied. Existing nonparametric methods reduce the time resolution to milliseconds, even though photon-counting detectors with tens-of-nanosecond resolution are widely used for data collection. The first part of this dissertation addresses these problems by developing a signal-processing method using high-order correlation functions. The correlation method effectively removes detector noise without introducing a specific model for the system. It reduces large datasets into a few relevant statistical parameters, making subsequent computations efficient. These computations can yield complete kinetic information about the materials: the locations and populations of the states and the state-to-state transition rates. The method is agnostic about whether the state-space is continuous or discrete. Detector bias can be accurately corrected, even with high-count-rate photon counting. The numerical viability of this technique was demonstrated using several simulations with either additive, photon, or photon-counting noise. Its experimental practicality was demonstrated on benchmark experimental datasets. A theoretical analysis of the results establishes practical guidelines for the data quality required to carry out a successful recovery of the system’s kinetics. The analysis then leads to a proposal for and simulation of the conditions necessary to push single-molecule experiments into the submicrosecond regime. The second part of this dissertation focuses on the internal structure and dynamics of micelles. The rotation of a solute molecule in a micelle shows multiple rates, this is, rate dispersion. One-dimensional kinetics cannot conclusively confirm the mechanism behind this rate dispersion. We have gained additional information by probing the rotational dynamics of two solute molecules of different sizes and polarities inside CTAC micelles and by using a two-dimensional 2D ultrafast technique called Multiple Population-period Transient Spectroscopy (MUPPETS). The results are inconsistent with common models for surfactant micelles that invoke strong ordering: chain alignment, radial layering or solute localization. Rather, our results provide evidence that the internal structure of micelles is highly disordered, resulting in different solute molecules experiencing different local viscosities. The micelle is closer to a droplet of ordinary liquid with confinement effects arising from similarity in the length of the hydrocarbon chain and the micelle diameter.