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

Zhang, Shuai; Driver, Kevin P.; Soubiran, Francois; Militzer, Burkhard

doi:10.1103/PhysRevE.96.013204

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 × 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.

Authors:

Zhang, Shuai ^[1]; Driver, Kevin P. ^[1]; Soubiran, Francois ^[2]; Militzer, Burkhard ^[2]

Univ. of California, Berkeley, CA (United States); Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Univ. of California, Berkeley, CA (United States)

Publication Date:: Mon Jul 10 00:00:00 EDT 2017

Research Org.:: Lawrence Livermore National Laboratory (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; TRN: US1801320

Grant/Contract Number:: AC52-07NA27344; SC0010517; SC0016248; NA0001859

Resource Type:: 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.

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                    Zhang, Shuai, Driver, Kevin P., Soubiran, Francois, & Militzer, Burkhard. First-principles equation of state and shock compression predictions of warm dense hydrocarbons.  United States.  https://doi.org/10.1103/PhysRevE.96.013204

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                    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.  https://doi.org/10.1103/PhysRevE.96.013204.  https://www.osti.gov/servlets/purl/1418960.

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@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}

}

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Here, we study nonideal mixing effects in the regime of warm dense matter (WDM) by computing the shock Hugoniot curves of BN, MgO, and MgSiO₃. First, we derive these curves from the equations of state (EOS) of the fully interacting systems, which were obtained using a combination of path integral Monte Carlo calculations at high temperature and density functional molecular dynamics simulations at lower temperatures. We then use the ideal mixing approximation at constant pressure and temperature to rederive these Hugoniot curves from the EOS tables of the individual elements. We find that the linear mixing approximation works remarkably wellmore »« less
https://doi.org/10.1063/5.0023232

Full Text Available
First-principles simulations of warm dense lithium fluoride

Journal Article Driver, K. P. ; Militzer, B. - Physical Review. E

Here we perform first-principles path integral Monte Carlo (PIMC) and density functional theory molecular dynamics (DFT-MD) calculations to explore warm dense matter states of LiF. Our simulations cover a wide density-temperature range of 2.08–15.70g cm^-3 and 10⁴–10⁹ K. Since PIMC and DFT-MD accurately treat effects of atomic shell structure, we find a pronounced compression maximum and a shoulder on the principal Hugoniot curve attributed to K-shell and L-shell ionization. The results provide a benchmark for widely used EOS tables, such as SESAME, LEOS, and models. In addition, we compute pair-correlation functions that reveal an evolving plasma structure and ionization processmore »« less
Cited by 26
https://doi.org/10.1103/physreve.95.043205

Full Text Available
First-principles prediction of the softening of the silicon shock Hugoniot curve

Journal Article Hu, S. X. ; Militzer, B. ; Collins, L. A. ; ... - Physical Review B

Here, whock compression of silicon (Si) under extremely high pressures (>100 Mbar) was investigated by using two first-principles methods of orbital-free molecular dynamics (OFMD) and path integral Monte Carlo (PIMC). While pressures from the two methods agree very well, PIMC predicts a second compression maximum because of 1s electron ionization that is absent in OFMD calculations since Thomas–Fermi-based theories lack inner shell structure. The Kohn–Sham density functional theory is used to calculate the equation of state (EOS) of warm dense silicon for low-pressure loadings (P < 100 Mbar). Combining these first-principles EOS results, the principal Hugoniot curve of silicon formore »« less
Cited by 37
https://doi.org/10.1103/PhysRevB.94.094109

Full Text Available

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

Abstract

Citation Formats

Experimental and ab initio investigations of microscopic properties of laser-shocked Ge-doped ablator journal, December 2015

Heats of combustion of high temperature polymers journal, January 2000

Shock compressibility of polystyrene of variable initial density journal, January 1972

Characterization of the State of Hydrogen at High Temperature and Density journal, January 1999

High-precision measurements of the equation of state of hydrocarbons at 1–10 Mbar using laser-driven shock waves journal, May 2010

Equation of State of Polystyrene and Polymethylmethacrylate from Ultrasonic Measurements at Moderate Pressures journal, March 1972

First-principles equation of state and electronic properties of warm dense oxygen journal, October 2015

Synthesis of the elements in stars: forty years of progress journal, October 1997

Properties and computation of the Coulomb pair density matrix journal, December 1988

Molecular Dissociation in Hot, Dense Hydrogen journal, February 1996

A simulation-based and analytic analysis of the off-Hugoniot response of alternative inertial confinement fusion ablator materials journal, September 2016

Miscibility Calculations for Water and Hydrogen in Giant Planets journal, June 2015

Absolute Equation-of-State Data in the 10–40 Mbar (1–4 TPa) Regime journal, February 1998

The Rankine–Hugoniot relation for shock waves in very porous media journal, August 1978

Equation of state for partially ionized carbon at high temperatures journal, October 2005

Equation of state of CH 1.36 : First-principles molecular dynamics simulations and shock-and-release wave speed measurements journal, September 2012

First-principles investigations on ionization and thermal conductivity of polystyrene for inertial confinement fusion applications journal, April 2016

Very-high-temperature molecular dynamics journal, January 2006

First-principles equation of state of polystyrene and its effect on inertial confinement fusion implosions journal, October 2015

Equation of state data experiments for plastic foams using smoothed laser beams journal, August 1999

Ab initio calculation of thermodynamic, transport, and optical properties of CH2 plastics journal, May 2015

Equation-of-state measurements of polyimide at pressures up to 5.8 TPa using low-density foam with laser-driven shock waves journal, May 2003

Computation of the high temperature Coulomb density matrix in periodic boundary conditions journal, July 2016

Absolute measurements of the equations of state of low-Z materials in the multi-Mbar regime using laser-driven shocks journal, May 1997

Natural widths and blackbody radiation induced shift and broadening of Rydberg levels in magnesium ions journal, January 2015

National direct-drive program on OMEGA and the National Ignition Facility journal, October 2016

Path integral Monte Carlo and density functional molecular dynamics simulations of hot, dense helium journal, April 2009

A unified formulation of the constant temperature molecular dynamics methods journal, July 1984

Brominated plastic equation of state measurements using laser driven shocks journal, March 1998

First-principles and classical molecular dynamics simulation of shocked polymers journal, February 2010

First-principles simulations and shock Hugoniot calculations of warm dense neon journal, January 2015

Purgatorio—a new implementation of the Inferno algorithm journal, May 2006

Shock velocity and temperature measurements of plastic foams compressed by smoothed laser beams journal, January 2005

A new quotidian equation of state (QEOS) for hot dense matter journal, January 1988

A new global equation of state model for hot, dense matter journal, September 1995

The Properties of Heavy Elements in Giant Planet Envelopes journal, September 2016

Studies of Plastic-Ablator Compressibility for Direct-Drive Inertial Confinement Fusion on Omega journal, May 2008

Hydrogen–Helium Mixtures at High Pressure journal, June 2005

X-ray Thomson scattering as a temperature probe for Gbar shock experiments journal, May 2014

Properties of warm dense polystyrene plasmas along the principal Hugoniot journal, June 2014

Precision equation-of-state measurements on National Ignition Facility ablator materials from 1 to 12 Mbar using laser-driven shock waves journal, May 2012

Inertial-confinement fusion with lasers journal, May 2016

Shock Hugoniot and temperature data for polystyrene obtained with quartz standard journal, June 2009

Equation of state and optical luminosity of benzene, polybutene, and polyethylene shocked to 210 GPa (2.1 Mbar) journal, March 1984

Gigabar Spherical Shock Generation on the OMEGA Laser journal, January 2015

Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set journal, October 1996

Probing matter at Gbar pressures at the NIF journal, March 2014

THE INTERIORS OF GIANT PLANETS: Models and Outstanding Questions journal, May 2005

X-ray scattering measurements on imploding CH spheres at the National Ignition Facility journal, July 2016

Strong Coupling and Degeneracy Effects in Inertial Confinement Fusion Implosions journal, June 2010

Hugoniot and mean ionization of laser-shocked Ge-doped plastic journal, December 2013

Thermophysical properties for shock compressed polystyrene journal, August 2011

Equations of State for Ablator Materials in Inertial Confinement Fusion Simulations journal, May 2016

Path integrals in the theory of condensed helium journal, April 1995

Ground State of the Electron Gas by a Stochastic Method journal, August 1980

Using neutrons to measure keV temperatures in highly compressed plastic at multi-Gbar pressures journal, December 2016

Simulations of dense atomic hydrogen in the Wigner crystal phase journal, September 2006

Optical properties of highly compressed polystyrene using laser-driven shockwaves journal, July 2003

Equation-of-state measurements for polystyrene at multi-TPa pressures in laser direct-drive experiments journal, December 2005

Dissociation along the principal Hugoniot of the Laser Mégajoule ablator material journal, August 2016

Gigabar material properties experiments on nif and omega conference, January 2012

Instantaneous x-ray radiation energy from laser produced polystyrene plasmas for shock ignition conditions journal, October 2013

First-principles equation-of-state table of deuterium for inertial confinement fusion applications journal, December 2011

Shock Hugoniot measurements of CH at Gbar pressures at the NIF journal, March 2016

Time‐resolved measurements of laser‐induced shock waves in deuterated polystyrene porous targets by x‐ray backlighting journal, March 1991

Improved tetrahedron method for Brillouin-zone integrations journal, June 1994

Indirect drive ignition at the National Ignition Facility journal, October 2016

Amorphization-induced surface electronic states modulation of cobaltous oxide nanosheets for lithium-sulfur batteries journal, May 2021

Synthesis of the elements in stars: forty years of progress text, January 1997

Development of Path Integral Monte Carlo Simulations with Localized Nodal Surfaces for Second-Row Elements text, January 2015

First-Principles Equation of State and Electronic Properties of Warm Dense Oxygen text, January 2016

The properties of heavy elements in giant planet envelopes text, January 2016

Ab initio calculation of thermodynamic, transport, and optical properties of CH$_2$ plastics text, January 2016

Calculation of a Deuterium Double Shock Hugoniot from Ab initio Simulations text, January 2001

Simulations of Dense Atomic Hydrogen in the Wigner Crystal Phase text, January 2005

First Principles Calculations of Shock Compressed Fluid Helium text, January 2006

Equation of state for partially ionized carbon at high temperatures text, January 2005

Experimental and ab initio investigations of microscopic properties of laser-shocked Ge-doped ablator
journal, December 2015

Heats of combustion of high temperature polymers
journal, January 2000

Shock compressibility of polystyrene of variable initial density
journal, January 1972

Characterization of the State of Hydrogen at High Temperature and Density
journal, January 1999

High-precision measurements of the equation of state of hydrocarbons at 1–10 Mbar using laser-driven shock waves
journal, May 2010

Equation of State of Polystyrene and Polymethylmethacrylate from Ultrasonic Measurements at Moderate Pressures
journal, March 1972

First-principles equation of state and electronic properties of warm dense oxygen
journal, October 2015

Synthesis of the elements in stars: forty years of progress
journal, October 1997

Properties and computation of the Coulomb pair density matrix
journal, December 1988

Molecular Dissociation in Hot, Dense Hydrogen
journal, February 1996

A simulation-based and analytic analysis of the off-Hugoniot response of alternative inertial confinement fusion ablator materials
journal, September 2016

Miscibility Calculations for Water and Hydrogen in Giant Planets
journal, June 2015

Absolute Equation-of-State Data in the 10–40 Mbar (1–4 TPa) Regime
journal, February 1998

The Rankine–Hugoniot relation for shock waves in very porous media
journal, August 1978

Equation of state for partially ionized carbon at high temperatures
journal, October 2005

Equation of state of CH $_{1.36}$ : First-principles molecular dynamics simulations and shock-and-release wave speed measurements
journal, September 2012

First-principles investigations on ionization and thermal conductivity of polystyrene for inertial confinement fusion applications
journal, April 2016

Very-high-temperature molecular dynamics
journal, January 2006

First-principles equation of state of polystyrene and its effect on inertial confinement fusion implosions
journal, October 2015

Equation of state data experiments for plastic foams using smoothed laser beams
journal, August 1999

Ab initio calculation of thermodynamic, transport, and optical properties of CH2 plastics
journal, May 2015

Equation-of-state measurements of polyimide at pressures up to 5.8 TPa using low-density foam with laser-driven shock waves
journal, May 2003

Computation of the high temperature Coulomb density matrix in periodic boundary conditions
journal, July 2016

Absolute measurements of the equations of state of low-Z materials in the multi-Mbar regime using laser-driven shocks
journal, May 1997

Natural widths and blackbody radiation induced shift and broadening of Rydberg levels in magnesium ions
journal, January 2015

National direct-drive program on OMEGA and the National Ignition Facility
journal, October 2016

Path integral Monte Carlo and density functional molecular dynamics simulations of hot, dense helium
journal, April 2009

A unified formulation of the constant temperature molecular dynamics methods
journal, July 1984

Brominated plastic equation of state measurements using laser driven shocks
journal, March 1998

First-principles and classical molecular dynamics simulation of shocked polymers
journal, February 2010

First-principles simulations and shock Hugoniot calculations of warm dense neon
journal, January 2015

Purgatorio—a new implementation of the Inferno algorithm
journal, May 2006

Shock velocity and temperature measurements of plastic foams compressed by smoothed laser beams
journal, January 2005

A new quotidian equation of state (QEOS) for hot dense matter
journal, January 1988

A new global equation of state model for hot, dense matter
journal, September 1995

The Properties of Heavy Elements in Giant Planet Envelopes
journal, September 2016

Studies of Plastic-Ablator Compressibility for Direct-Drive Inertial Confinement Fusion on Omega
journal, May 2008

Hydrogen–Helium Mixtures at High Pressure
journal, June 2005

X-ray Thomson scattering as a temperature probe for Gbar shock experiments
journal, May 2014

Properties of warm dense polystyrene plasmas along the principal Hugoniot
journal, June 2014

Precision equation-of-state measurements on National Ignition Facility ablator materials from 1 to 12 Mbar using laser-driven shock waves
journal, May 2012

Inertial-confinement fusion with lasers
journal, May 2016

Shock Hugoniot and temperature data for polystyrene obtained with quartz standard
journal, June 2009

Equation of state and optical luminosity of benzene, polybutene, and polyethylene shocked to 210 GPa (2.1 Mbar)
journal, March 1984

Gigabar Spherical Shock Generation on the OMEGA Laser
journal, January 2015

Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set
journal, October 1996

Probing matter at Gbar pressures at the NIF
journal, March 2014

THE INTERIORS OF GIANT PLANETS: Models and Outstanding Questions
journal, May 2005

X-ray scattering measurements on imploding CH spheres at the National Ignition Facility
journal, July 2016

Strong Coupling and Degeneracy Effects in Inertial Confinement Fusion Implosions
journal, June 2010

Hugoniot and mean ionization of laser-shocked Ge-doped plastic
journal, December 2013

Thermophysical properties for shock compressed polystyrene
journal, August 2011

Equations of State for Ablator Materials in Inertial Confinement Fusion Simulations
journal, May 2016

Path integrals in the theory of condensed helium
journal, April 1995

Ground State of the Electron Gas by a Stochastic Method
journal, August 1980

Using neutrons to measure keV temperatures in highly compressed plastic at multi-Gbar pressures
journal, December 2016

Simulations of dense atomic hydrogen in the Wigner crystal phase
journal, September 2006

Optical properties of highly compressed polystyrene using laser-driven shockwaves
journal, July 2003

Equation-of-state measurements for polystyrene at multi-TPa pressures in laser direct-drive experiments
journal, December 2005

Dissociation along the principal Hugoniot of the Laser Mégajoule ablator material
journal, August 2016

Gigabar material properties experiments on nif and omega
conference, January 2012

Instantaneous x-ray radiation energy from laser produced polystyrene plasmas for shock ignition conditions
journal, October 2013

First-principles equation-of-state table of deuterium for inertial confinement fusion applications
journal, December 2011

Shock Hugoniot measurements of CH at Gbar pressures at the NIF
journal, March 2016

Time‐resolved measurements of laser‐induced shock waves in deuterated polystyrene porous targets by x‐ray backlighting
journal, March 1991

Improved tetrahedron method for Brillouin-zone integrations
journal, June 1994

Indirect drive ignition at the National Ignition Facility
journal, October 2016

Amorphization-induced surface electronic states modulation of cobaltous oxide nanosheets for lithium-sulfur batteries
journal, May 2021

Synthesis of the elements in stars: forty years of progress
text, January 1997

Development of Path Integral Monte Carlo Simulations with Localized Nodal Surfaces for Second-Row Elements
text, January 2015

First-Principles Equation of State and Electronic Properties of Warm Dense Oxygen
text, January 2016

The properties of heavy elements in giant planet envelopes
text, January 2016

Ab initio calculation of thermodynamic, transport, and optical properties of CH$_2$ plastics
text, January 2016

Calculation of a Deuterium Double Shock Hugoniot from Ab initio Simulations
text, January 2001

Simulations of Dense Atomic Hydrogen in the Wigner Crystal Phase
text, January 2005

First Principles Calculations of Shock Compressed Fluid Helium
text, January 2006

Equation of state for partially ionized carbon at high temperatures
text, January 2005

Multi-charge-state molecular dynamics and self-diffusion coefficient in the warm dense matter regime
journal, January 2018

Path integral Monte Carlo simulations of dense carbon-hydrogen plasmas
journal, March 2018

Development and modeling of a polar-direct-drive exploding pusher platform at the National Ignition Facility
journal, July 2018