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Calculation of dynamics properties
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Energy renormalization for coarse-graining polymers having different segmental structures

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The CG and AA-MD simulations were carried out using the Large-scale Atomic/Molecular Massively Parallel Simulator software (47). In our simulations, the Debye-Waller factor 〈u2〉 was determined from the MSD 〈r2(t)〉 of the center of mass of monomers of the AA and CG models at around t ≈ 4 ps, corresponding to a caging time scale estimated from our simulations. The segmental relaxation time τ was evaluated by calculating the second Legendre order parameter P2(t): $P2(t)=32〈cos2θ(t)〉−12$, where θ(t) is the angle of a pseudo “bond” vector—defined as CG beads “B-C” between the consecutive isopropylidene group (i.e., labeled as a B-type CG bead) and carbonate group (i.e., labeled as a C-type CG bead)—under consideration at a time t relative to its position at t = 0. For the calculation of self-diffusion Ds, we calculated the MSD of the center of mass of polymer chains via the Einstein relation of the form: $Ds=limt→∞16t〈[rCM(t)−rCM(0)]2〉$, where rCM(t) is the position of the center of mass of each chain at time t.

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