Large deviations of Rouse polymer chain: First passage problem.

Area of Science:

• Polymer Physics
• Statistical Mechanics
• Computational Chemistry

Background:

• The Rouse model is a fundamental tool for understanding polymer dynamics.
• First passage (FP) problems are crucial for characterizing molecular processes like unzipping or diffusion.
• Solving FP problems for polymer models often involves complex multi-dimensional Kramers' problems.

Purpose of the Study:

• To investigate analytical methods for solving the first passage problem for the Rouse model.
• To analyze the behavior of mean first-passage time (τ(z)) as a function of chain length and extension.
• To develop and validate a new theoretical approach for polymer FP problems.

Main Methods:

• Direct and forward-flux sampling (FFS) simulations were employed to measure mean first-passage times.
• Two theoretical approaches were tested: a zero-temperature asymptotic theory and a new theory based on Freidlin-Wentzell theory.
• The dynamics were projected onto the minimal action path in the proposed theoretical framework.

Main Results:

• Mean first-passage time decreases with an increasing number of beads in the Rouse chain.
• Two distinct scaling regimes for τ(z) were identified, with a transition dependent on chain length.
• The new Freidlin-Wentzell-based theory accurately predicts both scaling regimes but struggles with the numerical prefactor in the first regime.

Conclusions:

• A combination of the new theory and FFS simulations yields a simple, accurate analytical expression for polymer FP times across all extensions and chain lengths.
• The study provides insights into the arm-retraction mechanism in branched polymer rheology, mapping it to the solved Rouse model.
• The proposed model significantly improves upon the Milner-McLeish theory, reducing overestimation of FP times by over tenfold.