Harveen Kaur

Date of Award

Fall 2020

Document Type

Open Access Dissertation


Chemistry and Biochemistry

First Advisor

Mark A. Berg


Heterogeneity in relaxation rates is a well-established feature of supercooled liquids. It implies the existence of a rate-exchange process to restore ergodicity, but the experimental characterization of that exchange has been incomplete and controversial. This dissertation develops three-dimensional (3D) correlation functions that provide a well-defined measure of rate exchange from single-molecule measurements. This approach is demonstrated on both single-molecule dichroism measurements and atomistic simulations of molecular rotation in ortho-terphenyl.

The first project develops non-parametric analysis of nonexponential and multidimensional kinetics. The quantification of nonexponential (dispersed) kinetics has relied on empirical functions, which yield parameters that are neither unique nor easily related to the underlying mechanism. Multidimensional kinetics provide more information on dispersed processes, but a good approach to their analysis is even less clear than for standard, one-dimensional kinetics. This method analyzes kinetic data in one or many dimensions with a nonparametric scheme: it quantifies nonexponential decays without relying on a specific functional form. The quantities obtained are directly related to properties of the mechanism causing the rate dispersion.

The second project applies ensemble-based multidimensional analysis and non-parametric approach on state-of-the-art single-molecule dichroism data to extract a detailed correlation function for rotational-rate exchange. Rate exchange near the glass transition is measured with unprecedented detail. Exchange is distinctly slower than alpha relaxation, implying the existence of a corresponding long-lived structure that is not accounted for in current theories. A fast phase of exchange is also observed and is assigned to molecules in the boundaries of rate-correlated spatial regions.

The third project measures the dynamics in the crossover region. In a supercooled liquid, the crossover temperature Tc separates a high-temperature region that is described by mode-coupling theories from a low-temperature region where random first-order transition theory applies. An all-atom molecular-dynamics simulation of o-terphenyl well below Tc (α-relaxation time > 14 μs) is analyzed with new statistical methods to reveal the molecular features associated with this change in mechanism. At Tc and below, a distinct state emerges that immediately precedes a rotational jump. Rate heterogeneity is already the dominant cause of nonexponential decays at the crossover. Exchange within the distribution of rates exchange is faster than α-relaxation at Tc (290 K), becomes the same at lower temperatures (272.5 K), trending toward a recent experimental observation of exchange slower than α-relaxation near the glass transition (244.5 K). The results of this project are described in chapters 4 and 5.

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