Molecular dynamics of shock waves in one-dimensional chains

The behavior of shock waves in one-dimensional chains has been explored in a series of molecular-dynamics computer experiments. Three "realistic" nearest-neighbor pair potentials were considered—Lennard-Jones 6-12, Toda, and Morse—as well as three truncated forms—harmonic, cubic, and quartic. Over a wide range of shock strengths the particle velocity profiles and shock speeds for a given form of potential can be characterized in strength by $\alpha \nu$, where $\alpha$ is the cubic anharmonicity coefficient and $\nu$ is the particle velocity in units of the long-wavelength sound speed. For strong shocks ($\alpha \nu >1\mathrm{}$), steady hard-rod-like velocity profiles are observed for the "realistic" potentials and the quartic truncated form, but not for the harmonic or cubic forms. The shock thickness in the harmonic chain grows as the cube root of time, while the shock thickness in the anharmonic chain grows linearly with time, in proportion to shock strength. This evolution of the shock thickness is unaffected by initial equilibration of the chain at finite temperature. If either a heavy- or light-mass defect is included, the shock wave is reflected and the relaxation process is slowed behind the defect.