  Carbon-hydrogen plasmas and hydrocarbon materials are of broad interest to
laser shock experimentalists, high energy density physicists, and
astrophysicists. Accurate equations of state (EOS) of hydrocarbons are valuable
for various studies from inertial confinement fusion (ICF) to planetary
science. By combining path integral Monte Carlo (PIMC) results at high
temperatures and density functional theory molecular dynamics (DFT-MD) results
at lower temperatures, we compute the EOS for hydrocarbons at 1473 separate
($\rho,T$)-points distributed over a range of compositions. These methods
accurately treat electronic excitation and many-body interaction effects and
thus provide a benchmark-quality EOS that surpasses that of semi-empirical and
Thomas-Fermi-based methods in the warm dense matter regime. By comparing our
first-principles EOS to the LEOS 5112 model for CH, we validate the specific
heat assumptions in this model but suggest that the Grueneisen parameter is too
large at low temperature. Based on our first-principles EOS, we predict the
Hugoniot curve of polystyrene to be 2-5% softer at maximum compression than
that predicted by orbital-free DFT and SESAME 7593. By investigating the atomic
structure and chemical bonding, we show a drastic decrease in the lifetime of
chemical bonds in the pressure interval of 0.4-4 megabar. We find the
assumption of linear mixing to be valid for describing the EOS and the shock
Hugoniot curve of the dense, partially ionized hydrocarbons under
consideration. We make predictions of the shock compression of glow-discharge
polymers and investigate the effects of oxygen content and C:H ratio on their
Hugoniot curve. Our full suite of first-principles simulation results may be
used to benchmark future theoretical investigations pertaining to hydrocarbon
EOS, and should be helpful in guiding the design of future gigabar experiments.
