Plateau moduli of Kremer-Grest models for commodity polymer melts

TL;DR

This work targets the plateau (entanglement) moduli of highly entangled Kremer-Grest polymer melts with $Z=100$ and $Z=200$ by analyzing the time evolution of the elastic response to a step strain, extrapolating to infinite time and zero strain. It employs two deformation routes: conventional melts under strain and the inverse primitive-path analysis (iPPA) route that deforms a primitive-path mesh, then returns to Kremer-Grest interactions, enabling a cross-check of the modulus estimates. The analysis uses Likhtman–McLeish theory to extract $G_e$ and $G_N^{(0)}$, and demonstrates that end-pinned melts and iPPA-derived results agree closely and are consistent with experimental data when mapped onto Kuhn-scale units, validating a common rheological interpretation. The study also assesses the computational efficiency of the iPPA approach, showing substantial speedups over brute-force relaxation, thereby providing a robust framework to connect molecular topology with macroscopic rubber-elastic moduli for commodity polymers.

Abstract

We estimate the plateau moduli of highly entangled end-pinned bead-spring polymer melts with Z = 100 and Z = 200 from the time-dependent elastic response to a step strain, which we first extrapolate to infinite time and then interpolate to zero strain. We present data for systems deformed in the melt state as well as for systems deformed at the primitive path level following the recent iPPA protocol. We observe excellent agreement between the plateau moduli obtained via the two deformation protocols and good agreement with the available experimental data for commodity polymer melts using a common mapping on the Kuhn scale.

Figures (2)

• Figure 1: Illustration of the present methodology. The tiny system visualized here was designed for illustrative purposes only and comprise $M=30$ chains with $Z=3$ entanglements. In each visualization the left side shows the whole melt, and the right side only the same three representative chains. We use two methods for stress relaxation: brute force (blue arrows, bottom row) and primitive-path acceleration (green arrows, top row). The brute force approach starts with an unstrained melt state (bottom left), which is rapidly step strained (bottom center), and followed by a very long stress relaxation at constant strain simulation (bottom right). The primitive path accelerated method start by generating the equilvalent primitive path mesh (top left), the mesh is step strained and equilibrated (top center). An inverse PPA push-off is performed whereby excess contour length is reintroduced while switching back to the KG force field (top right). The resulting (unphysical) conformation is equilibrated in a relatively short constant strain simulation.
• Figure 2: Illustration of the step-wise transformation Svaneborg2024IPPA between the KG and PPA force fields, which allows for a reversible interconversion between topologically equivalent melt states and primitive path meshes. The central red bead has WCA interactions with blue beads (KG, $\eta=0$), no pair interactions with green beads (PPA, $\eta=1$), and force capped interactions with magenta beads to switch WCA interactions on or off (iPPA, $0<\eta<1$). The PPA window in the illustration is $W=4$, in PPA applications $W\propto \sqrt{N_{eK}}$.