## Stiff Kremer-Grest

The Kremer-Grest (KG) model is the defacto standard for coarse-grain modeling of polymers using Molecular Dynamics. It represents a polymer as a string of beads. The beads are essentially hard spheres and the springs increase in stiffness to prevent chains from passing through each other. So far there is somewhat more than 1500 papers studying various aspects of polymer physics using the KG model. The KG model is a generic model, and was not designed to match any particular specific polymer chemistry.

To adjust the KG model to match specific polymers, as a first step we added a tunable chain stiffness inspired by previous work of Roland Faller and Florian Müller-Plathe. In our publication ”Characteristic Time and Length Scales in Melts of Kremer-Grest Bead Spring Polymers with Wormlike Bending Stiffness” C. Svaneborg, R. Everaers. Macromolecules 53, 1917 (2020) we characterized the resulting models.

The two renderings shows the primitive path of a standard KG model (left) and a very stiff KG model (right). The small gray chains illustrate the density of entanglements along the primitive paths. Generated well equilibrated melts with in excess of Z=200 entanglements per chain for varying stiffness. We characterized the Kuhn length, entanglement length, Kuhn friction of the KG models as function of chain stiffness. To estimate the Kuhn length we invented a new extrapolation procedure that corrects due to effects for incompressibility. To estimate the entanglement length we invented a new estimator that corrects for the finite number of Kuhn segments between entanglements for semi-flexible chains. We also invented an estimator for bead friction and Kuhn time that corrected for entanglements.

Theoretical polymer models are typically formulated at the Kuhn scale, and neglect polymer effects such as the packing of monomers and melt incompressibility. They also include ad-hoc mathematical models of tube confinement. KG models offers an computational alternative that naturally include all these effects and in this sense are more realistic than theoretical models on one hand, and on the other hand KG models are computationally far more efficient and simple compared to atomistic polymer models. With the Kuhn mapping, we can use KG models to make accurate parameter-free predictions for real polymers. We can also use the KG models to learn how to make more more accurate theories since polymer physics emerges naturally from these models.