First-principles equation of state and shock compression predictions of warm dense hydrocarbons

We use path integral Monte Carlo and density functional molecular dynamics to construct a coherent set of equations of state (EOS) for a series of hydrocarbon materials with various C:H ratios (2:1, 1:1, 2:3, 1:2, and 1:4) over the range of $0.07–22.4\mathrm{g}{\mathrm{cm}}^{-3}$ and $6.7\times {10}^3–1.29\times {10}^8\mathrm{K}$. The shock Hugoniot curve derived for each material displays a single compression maximum corresponding to $K$-shell ionization. For C:H = 1:1, the compression maximum occurs at 4.7-fold of the initial density and we show radiation effects significantly increase the shock compression ratio above 2 Gbar, surpassing relativistic effects. The single-peaked structure of the Hugoniot curves contrasts with previous work on higher-$Z$ plasmas, which exhibit a two-peak structure corresponding to both $K$- and $L$-shell ionization. Analysis of the electronic density of states reveals that the change in Hugoniot structure is due to merging of the $L$-shell eigenstates in carbon, while they remain distinct for higher-$Z$ elements. Finally, we show that the isobaric-isothermal linear mixing rule for carbon and hydrogen EOS is a reasonable approximation with errors better than 1% for stellar-core conditions.

Figure 1

Temperature-density profile of the principal Hugoniot curve of polystyrene CH (initial density ${\rho }_0=1.05\mathrm{g}{\mathrm{cm}}^{-3}$) with and without radiation correction, obtained from the equation of state calculated in this work. Isobar and isentrope profiles are coplotted. The symbols mark the simulation conditions.

Figure 2

Pressure-compression profile of the principal Hugoniot curve of polystyrene derived from this work in comparison with different theoretical and experimental methods: OF-DFT [50], SESAME 7593 [41], Nova [14, 15], Omega [20, 50] and Gekko [19] for CH, and LEOS 5400 [89] for GDP.

Figure 3

(a) Hugoniot curves of C-H compounds calculated from first principles in comparison with those from ideal mixtures of carbon and hydrogen. (b) Hugoniot curves of polystyrene for different initial densities (in $\mathrm{g}{\mathrm{cm}}^{-3}$) and other materials.

Figure 4

Density of state of polystyrene in comparison with that of oxygen at ${10}^5\mathrm{K}$. The dashed curves denote the occupied states, and the dotted lines are extrapolations of the free-electron density of state. The Fermi energies are aligned at $E=0\mathrm{eV}$.