# First-principles Equation of State and Shock Compression Predictions of Warm Dense Hydrocarbons

## TL;DR

This study uses advanced simulations to predict the equation of state and shock compression behavior of various hydrocarbon materials under extreme conditions, revealing the effects of ionization and radiation on their properties.

## Contribution

It provides the first-principles EOS and shock compression predictions for multiple hydrocarbon ratios, highlighting the impact of radiation and electronic structure on shock behavior.

## Key findings

- Shock Hugoniot curves show a single compression maximum due to K-shell ionization.
- Radiation effects significantly increase shock compression ratios above 2 Gbar.
- The linear mixing rule for EOSs is accurate within 1% for stellar-core conditions.

## Abstract

We use path integral Monte Carlo and density functional molecular dynamics to construct a coherent set of equation of state 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 $0.07-22.4$ g/cm$^{3}$ and $6.7\times10^3-1.29\times10^8$ 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 EOSs is a reasonable approximation with errors better than 1% for stellar-core conditions.