First-principles and classical molecular dynamics simulation of shocked polymers

Density functional theory (DFT) molecular dynamics (MD) and classical MD simulations of the principal shock Hugoniot are presented for two hydrocarbon polymers, polyethylene (PE) and poly(4-methyl-1-pentene) (PMP). DFT results are in excellent agreement with experimental data, which is currently available up to 80 GPa. Further, we predict the PE and PMP Hugoniots up to 350 and 200 GPa, respectively. For comparison, we studied two reactive and two nonreactive interaction potentials. For the latter, the exp-6 interaction of Borodin et al. showed much better agreement with experiment than OPLS. For the reactive force fields, ReaxFF displayed decidedly better agreement than AIREBO. For shocks above 50 GPa, only the DFT results are of high fidelity, establishing DFT as a reliable method for shocked macromolecular systems.

Figure 1

(Color online) Nonbonded contributions to the OPLS and exp-6 potential for C-C, C-H, and H-H. For C-H and H-H pairs, the OPLS repulsive component is significantly larger than for exp-6 potential, with the largest difference being in H-H.

Figure 2

(Color online) Electronic energy in meV per atom as a function of timestep in a DFT-AM05 simulation when starting from a PMP configuration taken from a classical MD run with the exp-6 potential (blue full line). Velocities were reinitialized randomly at 300 K. The black dashed line is the average energy over the entire 4000 step simulation. The adjustment in energy when going from the exp-6 potential to DFT-AM05 is less than 10 meV/atom.

Figure 3

(Color online) Hugoniot for polyethylene in $U_s\text{−}{U}_p$ (top) and $\text{P-}\rho$ (bottom). Experiments: shock handbook (Ref. 14) scaled to $0.955\text{g}/{\text{cm}}^3$ (black filled circles) and Nellis et al. (Ref. 10) (blue filled triangle up). Simulations: AIREBO (gray square), OPLS (purple filled triangle down), exp-6 (magenta circle), ReaxFF (brown diamond), tight-binding (Ref. 4) (pink triangles), DFT-AM05 temperature-ramp (red filled square), and DFT-AM05 steady-state (green filled diamond).

Figure 4

(Color online) Hugoniot for poly(4-methyl-1-pentene) in $U_s\text{−}{U}_p$ (top) and $\text{P-}\rho$ (bottom). Experiment: shock handbook (Ref. 14) (black filled circle). Simulations: AIREBO (gray square), OPLS (purple filled triangle down), exp-6 (magenta circle), ReaxFF (brown diamond), DFT-AM05 geometry 1 (red filled square), and DFT-AM05 geometry 2 (blue filled triangle up).

Figure 5

(Color online) Calculated temperatures as a function of pressure along the polyethylene principal Hugoniot. AIREBO (gray square), OPLS (purple filled triangle down), exp-6 (magenta circle), ReaxFF (brown diamond), DFT-AM05 temperature-ramp (red filled square), and DFT-AM05 steady-state (green filled diamond).

Figure 6

(Color online) Calculated temperatures as a function of density along the polyethylene principal Hugoniot (top) and relative to the DFT-AM05 temperature (bottom). AIREBO (gray square), OPLS (purple filled triangle down), exp-6 (magenta circle), ReaxFF (brown diamond), DFT-AM05 temperature-ramp (red filled square), and DFT-AM05 steady-state (green filled diamond).

Figure 7

(Color online) Average fraction of carbon atoms bound in the backbone in the DFT-AM05 simulations as a function of density along the Hugoniot. When there are two points at the same density, they are for two different temperatures bracketing the Hugoniot state. The error bars are one standard deviation. The cutoff distances used to define bonded atoms were $1.9\text{Å}$ for C–C, $1.3\text{Å}$ for C-H, and $0.8\text{Å}$ for H-H. Results are shown for two cutoff times: 20 fs (large blue circle) and 50 fs (small red circle).

Figure 8

(Color online) Distribution of carbon as a function of time in the DFT-AM05 simulation at $2.2\text{g}/{\text{cm}}^3$ along the Hugoniot at 3100 K presented as sliding averages over 10 fs intervals. Carbon in the backbone (red line $+$), carbon at the end of a strand (green line $\ast$), and carbon with three carbon neighbors (blue line ◇). The dashed lines show the fractions of perfect chains with 87.5% of carbon atoms in the backbone (red dashed triangle up) and 12.5% at the end of a strand (green dashed square). After 6 ps of equilibration, the backbone fraction has been reduced to 45% while 24% is bonded to three other carbons; the fraction of carbon atoms at the end of a strand fluctuates above the initial value. The composition changes over the first 3 ps as the system reaches equilibrium. During the last 3 ps, the count of backbone carbon atoms shows no trend, suggesting that the system can reach equilibrium over the time scale accessible in the first-principles simulations.