High-precision estimate of the hydrodynamic radius for self-avoiding walks

Area of Science:

• Polymer Physics
• Statistical Mechanics
• Computational Chemistry

Background:

• Self-avoiding walks (SAWs) are fundamental models for polymer chains in solution.
• Understanding the relationship between different chain dimensions, like gyration radius (R_G) and hydrodynamic radius (R_H), is crucial for predicting polymer behavior.
• Accurate estimation of universal ratios and critical exponents requires advanced simulation techniques.

Purpose of the Study:

• To accurately determine the universal asymptotic amplitude ratio between the gyration radius and the hydrodynamic radius of self-avoiding walks.
• To provide improved estimates for other universal properties characterizing polymer chain dimensions.
• To refine the estimation of the Flory exponent (ν) by mitigating scaling corrections.

Main Methods:

• Utilizing high-resolution Monte Carlo simulations.
• Employing a novel sampling scheme for efficient estimation of various observables.
• Analyzing chains with lengths up to N=2^25 (approximately 34 million monomers).

Main Results:

• The universal ratio R_G/R_H was estimated to be 1.5803940(45), significantly improving upon previous results.
• Competing corrections to scaling for the hydrodynamic radius were clearly identified.
• A highly accurate estimate for the Flory exponent, ν=0.58759700(40), was obtained by eliminating leading scaling corrections.

Conclusions:

• The study provides the most accurate determination to date of key universal properties for self-avoiding walks.
• The developed sampling scheme offers a general approach for precise estimation of polymer properties.
• These findings contribute to a deeper understanding of polymer physics and statistical mechanics.