Mathematical foundations of an ultra coarse-grained slip link model

Area of Science:

• Polymer physics
• Computational modeling
• Statistical mechanics

Background:

• EcoSLM is an ultra-coarse-grained slip link model.
• Understanding polymer dynamics requires accurate modeling.
• Bridging coarse-grained and fine-grained models is crucial.

Purpose of the Study:

• Present the master equation for the ecoSLM model.
• Validate ecoSLM against established theoretical frameworks.
• Provide a method for mapping ecoSLM to fine-grained models and experiments.

Main Methods:

• Derivation of the discrete master equation for ecoSLM.
• Comparison with the continuous Fokker-Planck equation for Brownian dynamics.
• Development of a single-chain microscopic model with inter-slip-link repulsion.

Main Results:

• The discrete master equation for large chains shows equilibrium and dynamic properties similar to the continuous Fokker-Planck equation.
• The microscopic model is approximately consistent with ecoSLM's fluctuation potential.
• Effective friction as a function of molecular weight is identified as key for mapping.

Conclusions:

• The mathematical framework enables extreme coarse-graining using ecoSLM.
• EcoSLM can serve as an interface for fine-grained slip link models.
• The study provides a foundation for applying ecoSLM to complex polymer systems.