The dissociative phase transition of fluid nitrogen at pressures in the range 30–110 GPa (0.3–1.1 Mbar), temperatures in the range 4000–14 000 K, densities up to 3.5 g/cm3, and internal energies up to 1 MJ/mol was investigated by shock compression. Equation‐of‐state, shock‐temperature, and electrical‐conductivity experimental data are presented and analyzed in detail.

Equation‐of‐state, shock‐temperature, and electrical‐conductivity data of dense fluid nitrogen in the region of the dissociative phase transition

The exponential-6 potential model is widely used in fluid equation of state studies. We have developed an accurate and efficient complete equation of state for the exponential-6 fluid based on HMSA integral equation theory and Monte Carlo calculations. Our equation of state has average fractional error of 0.2% in pV/NkBT and 0.3% in the excess energy Uex/NkBT. This is a substantial improvement in accuracy over perturbation methods, which are typically used in treatments of dense fluid equations of state. We have applied our equation of state to the problem of dense supercritical N2. We find that we are able to accurately reproduce a wide range of material properties with our model, over a range 0.01⩽P⩽100 GPa and 298⩽T⩽15 000 K.

An accurate equation of state for the exponential-6 fluid applied to dense supercritical nitrogen

Vibrational spectra of liquid nitrogen shock compressed to several high pressure/high temperature states were recorded using single‐pulse multiplex coherent anti‐Stokes Raman scattering. Vibrational frequencies, third‐order susceptibility ratios, and linewidths are presented for the fundamental and several excited‐state transitions. Vibrational frequencies were found to increase monotonically up to ≈17.5 GPa single shock and ≈30 GPa double shock. Above these pressures, the vibrational frequencies were observed to decrease with further increases in pressure. The decrease in vibrational frequency occurs in a pressure regime where the shocked nitrogen is becoming optically opaque. The consequence of the decrease in vibrational frequency on the Gruneisen mode gamma and its effect on the N2 equation of state is discussed. The transition intensity and linewidth data suggest that thermal equilibrium of the vibrational levels is attained in less than 10 ns at these high pressures and temperatures. Finally, the measured linewidths exhibit an almost linear dependence on shock temperature, and also suggest that the vibrational dephasing time has decreased to less than 1 ps at the highest pressures.

Coherent anti‐Stokes Raman spectroscopy of shock‐compressed liquid oxygen

Coherent anti‐Stokes Raman scattering (CARS) and spontaneous Raman spectroscopy have been used to obtain vibrational spectra of shock‐compressed and static high‐pressure fluid nitrogen, respectively. Vibrational frequencies were obtained from the CARS data using a semiclassical model for these spectra. Spontaneous Raman vibrational frequencies were determined by fitting data using a Lorentz‐shape line. A functional form was found for the dependence of the vibrational frequency on pressure and temperature to 40 GPa and 5000 K, respectively. By fitting the vibrational data to this form, a pressure scale based on the fluid nitrogen vibron has been calibrated for use at very high temperature. The nitrogen vibron pressure scale was used to determine the fluid‐δ nitrogen phase boundary up to 20 GPa and 900 K.

Calibration of the nitrogen vibron pressure scale for use at high temperatures and pressures

A theory is presented for calculating the bond length and vibrational frequency shifts in dense molecular fluids. We combine equation‐of‐state calculations based on the effective spherical potentials of Shaw, Johnson, and co‐workers with a simple model for the interactions of a molecule with the surrounding fluid. The repulsive interactions are approximated with the hard‐sphere model of Schweizer and Chandler. We extend their model by including an improved treatment of the long‐range attractive interactions and the centrifugal forces. We apply this model to fluid nitrogen and compare with static and shock wave experimental frequency shifts, as well as computer simulation data, over a wide range of pressures and temperatures. We find that while the results using this simple model are reasonably close to experiment in the region appropriate to shock conditions, agreement with data taken under static high‐pressure conditions (at lower temperatures) is not as good. Inadequacies of the model and possible improvements are discussed.

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Vibrational frequency shifts in dense molecular fluids

For a certain class of thermodynamic perturbation theories, a generalization of the Gibbs–Bogoliubov inequality holds through second order of perturbation theory and for a subset of terms the inequality is true to infinite order. Using this approximate variational principle, a perturbation theory is chosen for which the Helmholtz free energy of the reference system is minimized under the constraint that the first order term is identically zero. We apply these ideas to the determination of effective spherical potentials that accurately reproduce the thermodynamics of nonspherical molecular potentials. For a diatomic‐Lennard‐Jones (DLJ) potential with l/σ=0.793, the resulting spherical reference potential is identical to the median average over angles for the repulsive part of the potential, but differs in the attractive well. The variational effective spherical potential leads to more accurate thermodynamics than the median, however, particularly in the triple point region.

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J. D. Johnson

Papers

An approximate variational method for improved thermodynamics of molecular fluids