General Relations between Stress Fluctuations and Viscoelasticity in Amorphous Polymer and Glass-Forming Systems

Area of Science:

• Physics
• Materials Science
• Polymer Science

Background:

• Mechanical stress is crucial for viscoelastic polymer systems and supercooled liquids.
• Long-range stress correlations contribute to dynamic heterogeneity in these systems.
• Existing relations between stress correlations and relaxation moduli are not fully understood.

Purpose of the Study:

• To rigorously derive exact fluctuation-dissipation theorem (FDT) relations between stress correlations and relaxation moduli.
• To derive new approximate relations valid in the hydrodynamic regime for arbitrary dimensions.
• To provide a comprehensive framework for interconverting stress-correlation and relaxation functions.

Main Methods:

• Rigorous derivation of exact FDT relations.
• Derivation of new approximate relations incorporating thermal conductivity and composition fluctuations.
• Verification of approximate relations using simulation data on 2D systems.

Main Results:

• Three exact FDT relations and two new exact relations were derived.
• Several new approximate relations for the hydrodynamic regime were established.
• A method to obtain stress-correlation functions from relaxation moduli and vice versa in any dimension was provided.

Conclusions:

• The study establishes exact and approximate relationships between stress correlations and relaxation moduli.
• These findings offer a unified theoretical framework for viscoelastic materials.
• The derived relations are applicable across various spatial dimensions and material types.