The clustering of carbon in the detonation regime is studied with the assumption of a diffusion-limited clustering process. The diffusion constants are determined from modified Enskog theory and the Stokes–Einstein relation. With the size dependence of the cluster energy treated with a surface term, the energy difference between clusters and bulk carbon has an asymptotic time dependence of t−1/3. That is, for any given time it takes 1000 times as long to release the next 90% of the carbon energy. This leads to a very slow ‘‘reaction rate’’ which can couple to the reaction zone to produce nonideal time-dependent detonations on the scale of microseconds and centimeters. In addition, any ‘‘bottleneck’’ in the clustering process due to a sticking coefficient of less than one leads to a temporary delay in energy release that persists out to times several orders of magnitude larger than the time scale of the initial effect of the ‘‘bottleneck.’’
We present an extensive set of molecular dynamics results for the thermodynamics of dense fluid N 2 • The density and temperature regime is 1.3 g/cm3 s'p S, 2.3 g/cm3 and 500 K S, TS, 12000 K.These data are then analyzed to study the effects of internal degrees offreedom on the N 2 equation of state. Most importantly, we demonstrate the existence of an effective spherical potential that models very accurately (to 1.5% or better in pressure and energy) the true equation of state for the anisotropic N2 potential. We discuss the relation of this effective potential to the median average over angles and other averaging methods, including the arithmetic mean.
Sets of pressures and their corresponding specific volumes and internal energies are derived from measurements on steadily propagating, planar shock waves propelled by explosively driven metal assemblies into a 1:1 atomic mixture of the elements nitrogen and oxygen in each of two liquid initial states. One of these is the equimolar solution of O2 and N2, at T≂85 K, v0≂1.06 cm3/g; the other is the pure explosive compound NO, at T≂122 K, v0≂0.79 cm3/g. Results for this system are calculated with effective spherical potentials and presented graphically for comparison with the measurements. Single- and reflected-shock states are reported, as are incidental new results on pure liquid N2 at 85 K. The method of measurement is described, with reference to its previous applications to liquid O2 and Ar. First-shock pressures from both initial forms lie between 10 and 30 GPa, and the Hugoniots intersect at a common state, near 21 GPa, where a single reflected-shock Hugoniot is centered. Concordant measured state variables at this intersection provide novel confirmation of the expectation, inherently incorporated into theory, that unique equilibrium states are reached. Accounting for densities of these states by theory indicates a significant amount of oxidized nitrogen, in reversible equilibrium with major, but not exclusive, N2 and O2 components. This is treated as residual NO only, although the uncertainty in the potentials for other oxides does not assure their absence.
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 Grüneisen 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.
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