Calculation of dynamics properties

WX Wenjie Xia NH Nitin K. Hansoge WX Wen-Sheng Xu FJ Frederick R. Phelan Jr. SK Sinan Keten JD Jack F. Douglas

This protocol is extracted from research article:

Energy renormalization for coarse-graining polymers having different segmental structures

**
Sci Adv**,
Apr 19, 2019;
DOI:
10.1126/sciadv.aav4683

Energy renormalization for coarse-graining polymers having different segmental structures

Procedure

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 〈*u*^{2}〉 was determined from the MSD 〈*r*^{2}(*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 *P*_{2}(*t*): ${\mathit{P}}_{2}(\mathit{t})=\frac{3}{2}\u3008{\text{cos}}^{2}\mathrm{\theta}(\mathit{t})\u3009-\frac{1}{2}$, 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 *D*_{s}, we calculated the MSD of the center of mass of polymer chains via the Einstein relation of the form: ${\mathit{D}}_{\mathrm{s}}={\text{lim}}_{\mathit{t}\to \infty}\frac{1}{6\mathit{t}}\u3008{[{\mathit{r}}_{\text{CM}}(\mathit{t})-{\mathit{r}}_{\text{CM}}(0)]}^{2}\u3009$, where *r*_{CM}(*t*) is the position of the center of mass of each chain at time *t*.

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