skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

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

Abstract

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 0.07–22.4gcm –3 and 6.7 × 10 3 – 1.29 × 10 8K. 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. Lastly, 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.

Authors:
 [1];  [1];  [2];  [2]
  1. Univ. of California, Berkeley, CA (United States); Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  2. Univ. of California, Berkeley, CA (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1418960
Alternate Identifier(s):
OSTI ID: 1369103
Report Number(s):
LLNL-JRNL-736348
Journal ID: ISSN 2470-0045; PLEEE8
Grant/Contract Number:
AC52-07NA27344; SC0010517; SC0016248; NA0001859
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review E
Additional Journal Information:
Journal Volume: 96; Journal Issue: 1; Journal ID: ISSN 2470-0045
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 70 PLASMA PHYSICS AND FUSION

Citation Formats

Zhang, Shuai, Driver, Kevin P., Soubiran, Francois, and Militzer, Burkhard. First-principles equation of state and shock compression predictions of warm dense hydrocarbons. United States: N. p., 2017. Web. doi:10.1103/PhysRevE.96.013204.
Zhang, Shuai, Driver, Kevin P., Soubiran, Francois, & Militzer, Burkhard. First-principles equation of state and shock compression predictions of warm dense hydrocarbons. United States. doi:10.1103/PhysRevE.96.013204.
Zhang, Shuai, Driver, Kevin P., Soubiran, Francois, and Militzer, Burkhard. Mon . "First-principles equation of state and shock compression predictions of warm dense hydrocarbons". United States. doi:10.1103/PhysRevE.96.013204.
@article{osti_1418960,
title = {First-principles equation of state and shock compression predictions of warm dense hydrocarbons},
author = {Zhang, Shuai and Driver, Kevin P. and Soubiran, Francois and Militzer, Burkhard},
abstractNote = {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 0.07–22.4gcm–3 and 6.7 × 103 – 1.29 × 108K. 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. Lastly, 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.},
doi = {10.1103/PhysRevE.96.013204},
journal = {Physical Review E},
number = 1,
volume = 96,
place = {United States},
year = {Mon Jul 10 00:00:00 EDT 2017},
month = {Mon Jul 10 00:00:00 EDT 2017}
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on July 10, 2018
Publisher's Version of Record

Citation Metrics:
Cited by: 2works
Citation information provided by
Web of Science

Save / Share:
  • Cited by 2
  • Cited by 5
  • As one of the simple alkali metals, sodium has been of fundamental interest for shock physics experiments, but knowledge of its equation of state (EOS) in hot, dense regimes is not well known. By combining path integral Monte Carlo (PIMC) results for partially ionized states at high temperatures and density functional theory molecular dynamics (DFT-MD) results at lower temperatures, we have constructed a coherent equation of state for sodium over a wide density-temperature range of 1.93-11.60 g/cm 3 and 10 3–1.29×10 8 K. We find that a localized, Hartree-Fock nodal structure in PIMC yields pressures and internal energies that aremore » consistent with DFT-MD at intermediate temperatures of 2×10 6 K. Since PIMC and DFT-MD provide a first-principles treatment of electron shell and excitation effects, we are able to identify two compression maxima in the shock Hugoniot curve corresponding to K-shell and L-shell ionization. Our Hugoniot curves provide a benchmark for widely used EOS models: SESAME, LEOS, and Purgatorio. Due to the low ambient density, sodium has an unusually high first compression maximum along the shock Hugoniot curve. At beyond 10 7 K, we show that the radiation effect leads to very high compression along the Hugoniot curve, surpassing relativistic corrections, and observe an increasing deviation of the shock and particle velocities from a linear relation. Here, we also compute the temperature-density dependence of thermal and pressure ionization processes.« less
  • The equation of states (EOS) and electronic structures of argon with temperatures from 0.02 eV to 3 eV and densities from 0.5 g/cm{sup 3} to 5.5 g/cm{sup 3} are calculated using the pair potential and many-body potential molecular dynamics and the density functional theory (DFT) molecular dynamics with van der Waals (vdW) corrections. First-principles molecular dynamics is implemented above 2.0 g/cm{sup 3}. For the cases of low densities below 3 g/cm{sup 3}, we performed pair potential molecular dynamics in order to obtain the ionic configurations, which are used in density functional theory to calculate the EOS and electronic structures. Wemore » checked the validity of different methods at different densities and temperatures, showing their behaviors by comparing EOS. DFT without vdW correction works well above 1 eV and 3.5 g/cm{sup 3}. Below 1 eV and 2.0 g/cm{sup 3}, it overestimates the pressure apparently and results in incorrect behaviors of the internal energy. With vdW corrections, the semi-empirical force-field correction (DFT-D2) method gives consistent results in the whole density and temperature region, and the vdW density functional (vdW-DF2) method gives good results below 2.5 g/cm{sup 3}, but it overestimates the pressure at higher densities. The interactions among the atoms are overestimated by the pair potential above 1 eV, and a temperature dependent scaled pair potential can be used to correct the ionic configurations of the pair potential up to 3 eV. The comparisons between our calculations and the experimental multi-shock compression results show that the Hugoniot line of DFT-D2 and DFT tends to give larger pressure than the results of the self-consistent fluid variational theory, and the difference increases with the density. The electronic energy gap exists for all our cases up to 5.5 g/cm{sup 3} and 1 eV. The effect of vdW interactions on the electronic structures are also discussed.« less