Fundamentals of Nonexponential Relaxation in Glass Forming Systems
Open Access
- Author:
- Doss, Karan
- Graduate Program:
- Materials Science and Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- June 03, 2022
- Committee Members:
- Seong Kim, Outside Unit & Field Member
Susan Sinnott, Major Field Member
John Mauro, Chair & Dissertation Advisor
Ismaila Dabo, Major Field Member
Clive Randall, Major Field Member
John Mauro, Program Head/Chair - Keywords:
- Glass Relaxation
Kinetics
Viscosity
Stretched Exponentials
Complex Systems - Abstract:
- The remarkable complexity in the emergent behaviors exhibited by glass-forming systems have captivated physicists for the better half of the 20th century and continue to be at the forefront of condensed matter research today. Glass-forming systems are atomically disordered and relax nonexponentially when perturbed out of equilibrium. Nonexponential relaxation attracts research interest from disparate fields and has been studied across multiple levels of abstraction. The complex nature of its origins has thus far precluded the derivation of first-principles models that establish a well-defined relationship between the glass-former chemistry and corresponding macroscopic properties of interest. This has inevitably yielded numerous phenomenological models that do not stand on strong theoretical foundations. The work presented herein establishes the thermodynamic foundations of structural relaxation and elucidates the origins of heuristic mathematical models that have been successful in modeling nonexponential relaxation in glass. In this dissertation, the mean relaxation time predicted by the Maxwell relation for stress relaxation is examined. The Maxwell relation is derived within the Markov Network Model framework which is rooted in the energy landscape description of a material. An expression for the average relaxation time under equilibrium and nonequilibrium conditions are presented. It is shown that relaxation time calculated using the Maxwell relation is mismatched with the structural relaxation time. Experimental evidence is presented to show that the relaxation time obtained from shear viscosity measurements must correspond to the stress relaxation time. Subsequently, a fundamental thermodynamic description of structural relaxation in glasses is developed by establishing a link between the Prony series solution to structural relaxation derived from the principles of irreversible thermodynamics and asymmetric Lévy stable distribution of relaxation rates. Additionally, it is shown that the bulk viscosity of glass, and not the shear viscosity, is the transport coefficient that is kinetically coupled to the structural relaxation process. The distribution of relaxation times and energy barrier heights underpinning stretched exponential relaxation are derived. It is shown that a stretched exponential response necessitates the generation of a power-law or fractal distribution of relaxation times, indicating an underlying symmetry of scale-invariance in time arising from heterogeneous dynamics. The presence of large scatter in linear response data has cast doubt on the existence of an inverse correlation between liquid fragility and nonexponentiality. In this light, a model for the temperature dependence of the stretching exponent is presented based on the MYEGA model for supercooled liquid viscosity. The factors impacting the relationship between fragility and the stretching exponent at the glass transition are elucidated using this model. It is shown that the dispersion in topological degrees of freedom is proportional to the deviation from exponential behavior at the glass transition for glass formers with identical fragilities. Lastly, this dissertation lays the groundwork for disambiguating the complex dynamics of glass through the use of data-driven modeling. While molecular dynamics simulations have provided invaluable insights into the atomic-scale dynamics underpinning a broad range of glass chemistries, they offer no direct insight into the collective modes underpinning the dynamics. Dynamic Mode Decomposition, an emerging data-driven technique, is used to recover the collective modes embedded in high-dimensional time-series data obtained from molecular dynamics simulations. The recovered modes are mined to study the relationship between structure and the dynamics using pressure quenched Silica as a model system. The proposed technique is easy to implement, scalable, and easily adapted to study the relationship between glass chemistry, thermal, and pressure histories, and the underlying dynamics.