[Paper Review] Glass transition theory based on stress relaxation

Kostya Trachenko|arXiv (Cornell University)|Dec 3, 2005

Material Dynamics and Properties16 references4 citations

TL;DR

This paper proposes that the glass transition onset is defined by a supercooled liquid acquiring the solid glass's stress relaxation mechanism, using local relaxation events (LREs) to derive both stretched-exponential relaxation and the Vogel-Fulcher law simultaneously. The theory quantifies fragility via the number of retarded LREs, reproducing experimental correlations with non-exponentiality and bonding type.

ABSTRACT

We propose that an onset of glass transition can be defined as the point at which a supercooled liquid acquires the stress relaxation mechanism of a solid glass. We translate this condition into the rate equation for local relaxation events. This equation simultaneously gives two main signatures of glass transition, stretched-exponential relaxation and the Vogel-Fulcher law. The proposed theory quantifies system fragility in terms of the number of retarded local relaxation events and reproduces its correlation with the non-exponentiality of relaxation and bonding type.

Motivation & Objective

• To define the glass transition onset based on stress relaxation dynamics rather than thermodynamic or kinetic thresholds.
• To explain the simultaneous emergence of stretched-exponential relaxation (SER) and the Vogel-Fulcher (VF) law in supercooled liquids.
• To provide a unified theoretical basis for two universal features of glassy dynamics: non-exponential relaxation and non-Arrhenius viscosity.
• To quantify system fragility in terms of the number of retarded local relaxation events (LREs), linking it to experimental observables like β and bonding type.

Proposed method

• Introduces local relaxation events (LREs) as microscopic quanta of stress relaxation, each involving atomic jumps and structural reorganization.
• Derives a rate equation for LREs under external stress, modeling how stress redistribution affects activation barriers.
• Uses a master equation approach to describe the time evolution of the number of unrelaxed LREs, leading to a solution that yields stretched-exponential relaxation.
• Relates the system's fragility to the number of retarded LREs (n_r), with temperature and pressure encoded in the parameter C.
• Applies the fluctuation-dissipation theorem to connect stress relaxation under pressure to correlation function decay in equilibrium systems.
• Solves the rate equation to derive both the stretched-exponential form and the Vogel-Fulcher law, showing their simultaneous emergence.

Experimental results

Research questions

• RQ1 Can the onset of the glass transition be defined by the acquisition of a solid-like stress relaxation mechanism in a supercooled liquid?
• RQ2 How can both stretched-exponential relaxation and the Vogel-Fulcher law be derived from a single underlying mechanism?
• RQ3 Why is the non-exponentiality parameter β invariant under different combinations of pressure and temperature that fix the relaxation time τ?
• RQ4 How is system fragility related to the number of retarded local relaxation events and the nature of chemical bonding?

Key findings

• The proposed theory simultaneously reproduces the stretched-exponential relaxation (SER) and the Vogel-Fulcher (VF) law through a single rate equation for local relaxation events.
• The non-exponentiality parameter β decreases with increasing fragility, which is quantified by the number of retarded local relaxation events (n_r), matching experimental data for over 70 systems.
• The theory predicts that β remains invariant under different combinations of pressure and temperature that fix τ, consistent with recent experimental observations.
• Fragility increases with n_r, and the model predicts that covalent systems are stronger (less fragile) than ionic systems due to higher activation barriers from breaking stable electronic configurations.
• The model explains the correlation between fragility and bonding type: ionic systems have higher n_r and thus greater fragility, while covalent systems have lower n_r and are more strong.
• The theory provides a microscopic basis for the observed relationship between β and fragility, showing that higher n_r leads to greater non-exponentiality and stronger deviation from Arrhenius behavior.