Cyclization kinetics of Gaussian semiflexible polymer chains

Area of Science:

• Polymer Physics
• Chemical Kinetics
• Computational Chemistry

Background:

• Gaussian semiflexible chains exhibit complex dynamics and cyclization behavior.
• Classical theories like Wilemski-Fixman often neglect non-Markovian effects crucial for accurate kinetic predictions.

Purpose of the Study:

• To develop a comprehensive theory for the dynamics and cyclization kinetics of Gaussian semiflexible chains.
• To incorporate non-Markovian effects and analyze their impact on polymer conformation and reaction rates.
• To provide accurate analytical expressions for key dynamic and kinetic parameters.

Main Methods:

• Derivation of asymptotic expressions for cyclization time, eigenvalues, eigenfunctions, and mean square displacement.
• Calculation of the distribution of reactive polymer conformations to account for non-Markovian effects.
• Comparison of theoretical predictions with numerical simulations for validation.

Main Results:

• Asymptotic expressions derived for dynamics and cyclization kinetics across all time and length scales.
• Explicit dependence on capture radius, reactive monomer positions, and finite bead number identified.
• The developed non-Markovian theory shows improved accuracy compared to classical models.

Conclusions:

• The novel non-Markovian theory accurately describes Gaussian semiflexible chain dynamics and cyclization.
• This work provides a more refined understanding of polymer reaction kinetics beyond classical approximations.
• The findings have implications for polymer science and related fields requiring precise dynamic predictions.