Thermodynamic consistency in variable-level coarse graining of polymeric liquids

Area of Science:

• Computational chemistry and physics
• Polymer science and engineering
• Statistical mechanics

Background:

• Reduced descriptions (coarse-graining) of macromolecular liquids often lack thermodynamic consistency with atomistic models.
• Discrepancies arise despite agreement in structural properties like the total correlation function.

Purpose of the Study:

• To derive an analytical expression for the effective potential between coarse-grained units in polymer liquids.
• To ensure thermodynamic consistency between reduced and atomistic descriptions.
• To identify key features of the effective potential essential for accurate modeling.

Main Methods:

• Utilized the first-principles Ornstein-Zernike equation.
• Modeled polymer chains as collections of interpenetrating blobs with variable number (n(b)) and size (N(b)).
• Derived an analytical expression for the pair potential between these coarse-grained units.

Main Results:

• The derived effective potential exhibits a long, slowly decaying repulsive tail.
• The tail's decay follows a characteristic scaling exponent of N(b)(1/4).
• This finding is general for coarse-grained models of polymer melts with units larger than the persistence length.

Conclusions:

• The inclusion of a long, repulsive potential tail is critical for coarse-grained models.
• This feature enables accurate prediction of both structural and thermodynamic properties of macromolecular liquids.
• The derived analytical expression provides a foundation for developing more consistent coarse-grained models.