Molecular dynamics of detonation. I. Equation of state and Hugoniot curve for a simple reactive fluid.

Abstract

A simple microscopic model of chemical reactions is explored for diatomic exchange reactions 2AB?${\mathit{A}}_{2}$+${\mathit{B}}_{2}$. A pair of atoms bind chemically when they lie within a ``square'' attractive well. The presence of a bond, however, leaves the bound atoms in a state in which they have only hard-sphere repulsion for other atoms. A calculation combining the canonical-ensemble Monte Carlo technique with molecular dynamics is used to determine the equilibrium composition and thermodynamic properties of equimolar binary mixtures of A and B atoms, subject to this square-well, hard-sphere interaction potential for temperatures and densities accessible to detonation waves in a fluid consisting of metastable AB molecules at an initial temperature ${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{A}\mathit{B}}$/20${\mathit{k}}_{\mathit{B}}$ (in which ${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{a}\mathit{b}}$ is the well depth of the ab interaction and ${\mathit{k}}_{\mathit{B}}$ is the Boltzmann constant), with ${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{A}\mathit{A}=3}$${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{A}\mathit{B}}$ and ${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{B}\mathit{B}}$=${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{A}\mathit{B}}$. The calculations for systems of both 216 and 1728 atoms include the pressure, the internal energy, and the mean free times for various types of collisions. The Hugoniot curve for states behind detonation waves is determined for six values of the density for the smaller systems and one value for the larger; finite-system effects are found to be small. The Hugoniot curve is shown to have a concave shape in the pressure-volume plane, typical of exothermic materials, and the Chapman-Jouguet state is determined.