## Equilibration

## Multiscale approach to equilibrating model polymer melts

We present an effective and simple multiscale method for equilibrating Kremer Grest model polymer melts of varying stiffness. In our approach, we progressively equilibrate the melt structure above the tube scale, inside the tube and finally at the monomeric scale. We make use of models designed to be computationally effective at each scale. Density fluctuations in the melt structure above the tube scale are minimized through a Monte Carlo simulated annealing of a lattice polymer model. Subsequently the melt structure below the tube scale is equilibrated via the Rouse dynamics of a force-capped Kremer-Grest model that allows chains to partially interpenetrate. Finally the Kremer-Grest force field is introduced to freeze the topological state and enforce correct monomer packing. We generate 15 melts of 500 chains of 10.000 beads for varying chain stiffness as well as a number of melts with 1.000 chains of 15.000 monomers. To validate the equilibration process we study the time evolution of bulk, collective, and single-chain observables at the monomeric, mesoscopic, and macroscopic length scales. Extension of the present method to longer, branched, or polydisperse chains, and/or larger system sizes is straightforward.

FIGURE. Visualization of a melt of 1000 chains of 15 000 beads each during the equilibration process. All the polymers are shown on the left hand side of the box, while the same ten randomly selected polymers are shown on the right hand side of the box. Conformation just after lattice annealing (a), after 0.1τe (b), and 1τe (c) of Rouse dynamics simulation with the force-capped KG model, and final melt configuration after KG warmup (d).

FIGURE. Mean-square internal distances of equilibrated melts (colored symbols) compared to brute force equilibrated melts (dashed black lines) and Kuhn length (dotted black line) for varying stiffness.

C. Svaneborg, H.A Karimi-Varzeneh, N. Hojdis, F. Fleck, R. Everaers "Multiscale approach to equilibrating model polymer melts" Phys. Rev. E. **94**, 032502 (2016) DOI: 10.1103/PhysRevE.94.032502