Logarithmic relaxation in glass-forming systems.

Area of Science:

• Condensed Matter Physics
• Theoretical Physics

Background:

• Mode-coupling theory (MCT) is a key framework for understanding ideal glass transitions.
• Glass-forming systems exhibit complex dynamics near transition singularities.

Purpose of the Study:

• Analyze correlation functions near higher-order glass-transition singularities within MCT.
• Investigate asymptotic solutions of equations of motion for these systems.

Main Methods:

• Asymptotic expansion of solutions in polynomials of the logarithm of time (t).
• Analysis of correlation functions and their interpolation between different dynamic scenarios.

Main Results:

• A leading-order logarithmic decay law (ln(t)) is identified.
• Leading corrections are described by a fourth-order polynomial.
• Three distinct scenarios for structural relaxation dynamics are elucidated, including vanishing corrections, reduced von Schweidler's law validity, and replacement of beta-process decay.

Conclusions:

• The study provides a detailed theoretical description of dynamics near glass transition singularities.
• Findings offer explanations for phenomena like strong alpha relaxation stretching and two-peak susceptibility spectra.
• The results advance the understanding of structural relaxation in glass-forming materials.