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Molecular Model for Linear Viscoelastic Properties of Entangled Polymer Networks.

Andrei A Gusev¹, Tim Bernhard¹

¹Department of Materials, ETH Zürich, CH-8093 Zürich, Switzerland.

|November 18, 2024

Summary

This study introduces a molecular Kuhn-scale model to simulate polymer network stress relaxation. The model accurately predicts material behavior by incorporating entanglements and comparing results with molecular dynamics simulations.

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Area of Science:

Polymer Physics
Materials Science
Computational Modeling

Background:

Entangled polymer networks exhibit complex stress relaxation dynamics.
Understanding these dynamics is crucial for designing advanced polymer materials.
Existing models often struggle to capture the effects of network topology.

Purpose of the Study:

To develop a novel molecular Kuhn-scale model for simulating stress relaxation in entangled polymer networks.
To incorporate entanglements as entropic springs within the network structure.
To validate the model's predictions against molecular dynamics (MD) simulations.

Main Methods:

Governing equation based on the linearized Langevin equation.
Derivation of stress relaxation modulus using the fluctuation-dissipation theorem and normal mode representation.
Finite element procedure to assemble network connectivity matrix and solve for eigenvalues.
Simulation of both perfect and imperfect polymer networks.

Main Results:

The molecular Kuhn-scale model successfully predicts stress relaxation modulus and viscoelastic moduli.
Model predictions show excellent agreement with MD simulation estimates over overlapping time and frequency ranges.
The model effectively captures the behavior of networks with varying structures, including defects and loops.

Conclusions:

The presented molecular Kuhn-scale model provides a robust framework for predicting the viscoelastic behavior of entangled polymer networks.
The model's accuracy, validated by MD simulations, makes it a valuable tool for polymer material design and analysis.
This approach offers insights into the relationship between network architecture and macroscopic mechanical properties.