Optical properties of highly compressed polystyrene: An ab initio study

Using all-electron density functional theory, we have performed an ab initio study on x-ray absorption spectra of highly compressed polystyrene (CH). We found that the $K$-edge shifts in strongly coupled, degenerate polystyrene cannot be explained by existing continuum-lowering models adopted in traditional plasma physics. To gain insights into the $K$-edge shift in warm, dense CH, we have developed a model designated as “single mixture in a box” (SMIAB), which incorporates both the lowering of the continuum and the rising of the Fermi surface resulting from high compression. This simple SMIAB model correctly predicts the $K$-edge shift of carbon in highly compressed CH in good agreement with results from quantum molecular dynamics (QMD) calculations. Traditional opacity models failed to give the proper $K$-edge shifts as the CH density increased. Based on QMD calculations, we have established a first-principles opacity table (FPOT) for CH in a wide range of densities and temperatures [$\rho =0.1-100\mathrm{g}/\mathrm{c}{\mathrm{m}}^3$ and $T=2000-1000000\mathrm{K}$]. The FPOT gives much higher Rosseland mean opacity compared to the cold-opacity–patched astrophysics opacity table for warm, dense CH and favorably compares to the newly improved Los Alamos atomic model for moderately compressed CH (${\rho }_{\mathrm{CH}}\le 10\mathrm{g}/\mathrm{c}{\mathrm{m}}^3$), but remains a factor of 2 to 3 higher at extremely high densities (${\rho }_{\mathrm{CH}}\ge 50\mathrm{g}/\mathrm{c}{\mathrm{m}}^3$). We anticipate the established FPOT of CH will find important applications to reliable designs of high-energy-density experiments. Moreover, the understanding of $K$-edge shifting revealed in this study could provide guides for improving the traditional opacity models to properly handle the strongly coupled and degenerate conditions.

Figure 1

Results of convergence tests for polystyrene (CH) at $\rho =4.0\mathrm{g}/\mathrm{c}{\mathrm{m}}^3$ and $T=125000\mathrm{K}$: (a) pressure and (b) internal energy as a function of the energy cutoff ($E_{\max }$) and the number of atoms ($N$) in the supercell. The pure Coulombic potentials are used in our all-electron quantum molecular dynamics (QMD) calculations. The convergence of static properties is generally reached for $E_{\max }\ge 40\mathrm{keV}$ and $N\ge 16$.

Figure 2

Convergence testing results of x-ray absorption spectra for CH at $\rho =4.0\mathrm{g}/\mathrm{c}{\mathrm{m}}^3$ and $T=125000\mathrm{K}$: (a) $E_{\max }$ varying from 20 to 60 keV with 16-atom and Г-point calculations; (b) changing the number of atoms and $k$ point with $=40\mathrm{keV}$. Convergence of x-ray absorption calculations is generally reached for $E_{\max }\ge 40\mathrm{keV}$ and $N\ge 16$.

Figure 3

The electrical conductivity and the refractive index are plotted as functions of the photon energy (frequency) for the case of polystyrene at $\rho =4.0\mathrm{g}/\mathrm{c}{\mathrm{m}}^3$ and $T=125000\mathrm{K}$.

Figure 4

The x-ray absorption coefficient ${\alpha }_K$ is plotted as a function of the photon energy (frequency) for CH at a higher density of $\rho =10\mathrm{g}/\mathrm{c}{\mathrm{m}}^3$ with temperatures varying from $T=31250\mathrm{K}$ to $T=500000\mathrm{K}$. The small $K$-edge movement is seen for the highest-temperature case of $T=500000\mathrm{K}$ (dashed red line).

Figure 5

The density of state (DOS) is plotted for each corresponding case shown in Fig. 4. The Fermi-energy levels are marked by the vertical lines for each case. The downshift of the Fermi surface at $T=500000\mathrm{K}$ explains the $K$-edge movement seen in Fig. 4 (dashed red line) at this higher temperature.

Figure 6

The x-ray absorption spectra are plotted as a function of the photon energy (frequency) for CH at different densities varying from (a) $\rho =10\mathrm{g}/\mathrm{c}{\mathrm{m}}^3$ to (d) $\rho =100\mathrm{g}/\mathrm{c}{\mathrm{m}}^3$ with a fixed temperature of $T=125000\mathrm{K}$. The $K$-edge upshifting with CH density increasing is clearly seen.

Figure 7

The DOS for each corresponding case shown in Fig. 6. Again, the vertical dashed line in each panel marks the Fermi surface location for each case.

Figure 8

The QMD-predicted $K$ edges of carbon are plotted as a function of CH density. Predictions from five different continuum-lowering models, including the Stewart-Pyatt [7], Ecker-Kröll [8], modified ion-sphere [9], and Crowley models [11], and the newly improved atomic code (Los Alamos) using the Hummer-Mihalas continuum-lowering model [10] with the consideration of Pauli blocking, are also drawn in the same figure by dashed lines with open symbols. The “single mixture in a box” (SMIAB), developed in this work, is indicated by the blue solid line.

Figure 9

Comparisons of the absorption coefficient ${\alpha }_K$ of polystyrene as a function of photon energy hν between our QMD calculations and LANL's newly improved atomic model are made for densities of (a) $\rho =4\mathrm{g}/\mathrm{c}{\mathrm{m}}^3$ and (b) $\rho =10\mathrm{g}/\mathrm{c}{\mathrm{m}}^3$, both at $T=125000\mathrm{K}$.

Figure 10

Similar to Fig. 9 but for CH densities of (a) $\rho =50\mathrm{g}/\mathrm{c}{\mathrm{m}}^3$ and (b) $\rho =100\mathrm{g}/\mathrm{c}{\mathrm{m}}^3$ both at $T=125000\mathrm{K}$.

Figure 11

Comparisons of Rosseland mean opacity ($K_{\mathrm{R}}$) as a function of CH temperature, among our QMD calculations, the LANL's atomic model, and the cold-opacity–patched astrophysics opacity table (AOT), are made for CH densities of (a) $\rho =0.5\mathrm{g}/\mathrm{c}{\mathrm{m}}^3$ and (b) $\rho =4.0\mathrm{g}/\mathrm{c}{\mathrm{m}}^3$.

Figure 12

Similar to Fig. 11 but for CH densities of (a) $\rho =10\mathrm{g}/\mathrm{c}{\mathrm{m}}^3$ and (b) $\rho =50\mathrm{g}/\mathrm{c}{\mathrm{m}}^3$.

Figure 13

The grouped Rosseland opacities, from both our QMD calculations and AOT, are plotted as a function of x-ray photon energy (hν) for a fixed CH density of $\rho =4\mathrm{g}/\mathrm{c}{\mathrm{m}}^3$, but at different temperatures of (a) $T=62500\mathrm{K}$, (b) $T=125000\mathrm{K}$, (c) $T=500000\mathrm{K}$, and (d) $T=1000000\mathrm{K}$.

Figure 14

The grouped Rosseland opacities, from both our QMD calculations and AOT, are plotted as a function of x-ray photon energy (hν) for a much higher CH density of $\rho =50\mathrm{g}/\mathrm{c}{\mathrm{m}}^3$ and at different temperatures of (a) $T=125000\mathrm{K}$, (b) $T=250000\mathrm{K}$, (c) $T=500000\mathrm{K}$, and (d) $T=1000000\mathrm{K}$.