Statistical theory for polymer elasticity: From molecular kinematics to continuum behavior

Area of Science:

• Polymer Physics
• Materials Science
• Statistical Mechanics

Background:

• Predicting polymer mechanical behavior from microstructure is challenging.
• Existing models use nonphysical assumptions, limiting accuracy.
• Bridging molecular and continuum mechanics in polymers remains an open problem.

Purpose of the Study:

• Develop a unified theoretical framework for polymer networks.
• Accurately predict macroscopic mechanical behavior from microstructural features.
• Establish a physically grounded model for polymer elasticity.

Main Methods:

• Constructed a Hamiltonian for polymer chain segments.
• Utilized thermodynamic observables to derive chain kinematics (stretch, orientation).
• Developed a unified statistical description for individual chains and continuum networks.

Main Results:

• Chain kinematics are retrieved without phenomenological assumptions.
• Chain stretch is related to spatial direction and Eulerian logarithmic strain.
• Model accurately predicts hyperelastic response of elastomers.
• The model relies on minimal, physically grounded parameters.

Conclusions:

• The new Hamiltonian model offers a unified approach to polymer mechanics.
• It overcomes limitations of previous theoretical models.
• Provides accurate predictions for elastomer hyperelasticity using fundamental parameters.