Resolving Dynamic Properties of Polymers through Coarse-Grained Computational Studies

Coupled length and time scales determine the dynamic behavior of polymers and underlie their unique viscoelastic properties. To resolve the long-time dynamics it is imperative to determine which time and length scales must be correctly modeled. Here we probe the degree of coarse graining required to simultaneously retain significant atomistic details and access large length and time scales. The degree of coarse graining in turn sets the minimum length scale instrumental in defining polymer properties and dynamics. Using linear polyethylene as a model system, we probe how the coarse-graining scale affects the measured dynamics. Iterative Boltzmann inversion is used to derive coarse-grained potentials with 2–6 methylene groups per coarse-grained bead from a fully atomistic melt simulation. We show that atomistic detail is critical to capturing large-scale dynamics. Using these models we simulate polyethylene melts for times over $500\mu \mathrm{s}$ to study the viscoelastic properties of well-entangled polymer melts.

Figure 1

A single ${\mathrm{C}}_{96}{\mathrm{H}}_{194}$ PE chain represented with increasing degree of coarse graining $\lambda =2$, 3, 4, and 6 methylene groups per CG bead. Bead diameter corresponds to the minimum in the nonbonded interaction for each CG model.

Figure 2

Tabulated pair potential between CG beads. The UA and $\mathrm{CG}4\text{−}M$ potentials are included for comparison.

Figure 3

(a) The MSD of the inner 24 -${\mathrm{CH}}_2$- groups of each polymer chain at 500 K. (b) Same data as in (a), scaled by $\alpha$. The solid lines represent the scaling predictions $t^1$ for the diffusive regime and $t^{1/4}$ for the reptation regime.

Figure 4

MSD of center of mass scaled with the same $\alpha$ scale factor as for the inner -${\mathrm{CH}}_2$- groups in Fig. 3. The solid line has slope $t^1$. Inset: The alpha scale factor for different coarse-grained models and the UA and Martini models.

Figure 5

Modulus $G(t)$ for each of the CG polymer models at 500 K. Closed and open symbols represent the $n=96$ and $n=480$ chain length, respectively. Solid lines represent the $n=1920$ length, while $n=960$ chains are omitted for clarity.

Figure 6

Density versus temperature for the $n=96$ samples cooled at $1.4\mathrm{K}/\mathrm{ns}$.