Aging and Failure of a Polymer Chain under Tension

Area of Science:

• Polymer physics
• Statistical mechanics
• Materials science

Background:

• Polymer chain rupture under constant stress is a model for system failure.
• Previous studies focused on average collapse rates, neglecting the distribution of these rates.
• The probability distribution function (PDF) of collapse rates has not been analytically calculated.

Purpose of the Study:

• To develop a theory for the probability distribution function (PDF) of polymer chain collapse rates.
• To specifically analyze the tail of the PDF, representing fast collapse events.
• To provide a theoretical framework for understanding rare but critical failure events.

Main Methods:

• Analytical theory development.
• Focus on the tail of the probability distribution function (PDF).
• Extensive numerical simulations for validation.

Main Results:

• The tail of the PDF follows a power law.
• The exponent of this power law is universal and theoretically determined.
• Numerical results strongly support the developed theory.

Conclusions:

• The study provides the first analytical theory for the PDF of polymer chain collapse rates.
• The identified power-law tail with a universal exponent offers new insights into system failure dynamics.
• The findings have implications for a broader range of systems experiencing stress-induced failure.