Cyclization of a polymer: first-passage problem for a non-Markovian process

Area of Science:

• Polymer Physics
• Statistical Mechanics
• Theoretical Chemistry

Background:

• Understanding polymer chain dynamics is crucial for materials science.
• Polymer chain closure is a fundamental process influencing material properties.
• Existing models often rely on Markovian assumptions, limiting their applicability.

Purpose of the Study:

• To investigate the closure dynamics of a polymer chain released from a defined end-to-end distance.
• To model this process as a non-Markovian first passage problem.
• To explore the emergence and geometrical basis of the Wilemski-Fixmann approximation.

Main Methods:

• Formulating the problem as a first passage time problem for a non-Markovian process.
• Expressing survival probability via the three-time distribution of end-to-end distance.
• Numerically solving a Volterra integral equation.

Main Results:

• The survival probability of polymer chain closure was successfully evaluated.
• The Wilemski-Fixmann approximation was shown to emerge from the developed theoretical framework.
• The geometrical interpretation of this approximation was elucidated.

Conclusions:

• The non-Markovian first passage approach provides a robust framework for studying polymer chain closure.
• This work offers a deeper understanding of polymer relaxation dynamics.
• The findings contribute to the theoretical basis of approximations used in polymer physics.