Role of the Pair Correlation Function in the Dynamical Transition Predicted by Mode Coupling Theory

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Theoretical Chemistry

Background:

• Configurational entropy at the pair level (S_c2) is linked to the pair correlation function.
• S_c2 vanishes at the dynamical transition temperature (T_c) in many systems.
• This suggests a connection between a liquid's structure and its dynamical behavior.

Purpose of the Study:

• To investigate if the dynamical transition temperature (T_c) is determined by the liquid's structure.
• To develop a theoretical framework linking T_c to the pair correlation function.

Main Methods:

• Described system dynamics at the mean-field level.
• Applied concepts from dynamical density functional theory.
• Analyzed the dependence of T_c on the pair correlation function.

Main Results:

• The dynamical transition temperature (T_c) was shown to depend exclusively on the pair correlation function.
• The developed theory predicts T_c values consistent with experimental observations.
• This contrasts with microscopic Mode Coupling Theory (MCT) which overestimates T_c.

Conclusions:

• The dynamical transition temperature (T_c) is fundamentally embedded within the liquid's pair correlation function.
• Dynamical Density Functional Theory provides a successful framework for predicting T_c based on structural information.
• The findings offer a new perspective on the relationship between structure and dynamics in liquids.