Simple Model for Dynamic Heterogeneity in Glass-Forming Liquids

Area of Science:

• Condensed Matter Physics
• Soft Matter Physics
• Statistical Mechanics

Background:

• Liquids near the glass transition exhibit dynamical heterogeneity, characterized by significant spatial and temporal fluctuations in local relaxation rates.
• Understanding these dynamics is crucial for predicting material properties and behavior in complex fluids.

Purpose of the Study:

• To introduce a simple continuum model for quantitatively predicting correlators of dynamical heterogeneity.
• To validate the model's predictions against numerical simulations of well-established liquid models.

Main Methods:

• Development of a continuum model to describe fluctuations in dynamical heterogeneity.
• Comparison of model predictions for dynamic susceptibility (χ4(t)) with numerical results.
• Analysis of the effect of heterogeneity lifetime (τex) on the dynamic susceptibility decay.

Main Results:

• The model shows remarkable agreement with numerical results for both binary hard-sphere and Kob-Andersen Lennard-Jones liquids.
• The lifetime of dynamic heterogeneities (τex) minimally impacts the peak position of χ4(t) (t=t4∼τα).
• τex significantly controls the decay of χ4(t) after its peak, providing a method for its estimation.

Conclusions:

• The proposed continuum model offers a powerful tool for quantitatively analyzing dynamical heterogeneity in glass-forming liquids.
• The study elucidates the distinct roles of heterogeneity lifetime and relaxation time in shaping dynamic susceptibility.
• The findings provide a pathway to estimate heterogeneity lifetimes from experimental or simulation data.