Anomalous diffusion and stretched exponentials in heterogeneous glass-forming liquids: low-temperature behavior

Area of Science:

• Condensed matter physics
• Materials science
• Statistical mechanics

Background:

• Understanding the dynamics of glass-forming liquids is crucial for materials science.
• Heterogeneity in liquids significantly impacts molecular motion and relaxation processes.
• Previous models often simplify liquid structures, limiting their predictive power.

Purpose of the Study:

• To develop a model for heterogeneous glass-forming liquids.
• To investigate the low-temperature dynamics of a tagged molecule within this heterogeneous environment.
• To analyze the wave-number-dependent, self-intermediate scattering function and its time dependence.

Main Methods:

• Development of a computational model for heterogeneous glass-forming liquids.
• Calculation of the low-temperature behavior of a tagged molecule.
• Analysis of the wave-number-dependent, self-intermediate scattering function (self-ISF).

Main Results:

• The model demonstrates stretched-exponential decay of the self-ISF at long times.
• Near the glass transition, the self-ISF exhibits a crossover from stretched-exponential (b=1/2) at high wave numbers to diffusive (b=1) at low wave numbers.
• Distinct beta (cage-breaking) and alpha (late-stage) relaxation processes were observed.
• Anomalously broad, non-Gaussian tails were found in the spatial representation of the self-ISF for large molecular displacements.

Conclusions:

• The proposed model accurately captures key features of molecular dynamics in heterogeneous glass-forming liquids.
• The observed crossover in scattering function behavior highlights the role of length scales in relaxation dynamics near the glass transition.
• The findings provide insights into the complex relaxation mechanisms governing supercooled liquids and glasses.