Molecular Simulations of Liquid Jet Explosions and Shock Waves Induced by X-Ray Free-Electron Lasers

X-ray free-electron lasers (XFELs) produce x-ray pulses with high brilliance and short pulse duration. These properties enable structural investigations of biomolecular nanocrystals, and they allow one to resolve the dynamics of biomolecules down to the femtosecond timescale. Liquid jets are widely used to deliver samples into the XFEL beam. The impact of the x-ray pulse leads to vaporization and explosion of the liquid jet, while the expanding gas triggers the formation of shock wave trains traveling along the jet, which may affect biomolecular samples before they have been probed. Here, we used molecular dynamics simulations to reveal the structural dynamics of shock waves after an x-ray impact. Analysis of the density and temperature in the jet revealed shock waves that form close to the explosion center, travel along the jet with supersonic velocities, and decay exponentially with an attenuation length proportional to the jet diameter. A trailing shock wave formed after the first shock wave, similar to the shock wave trains in experiments. High shock wave velocities in our simulations are compatible with the phenomenon of "fast sound," as emerging at large sound frequencies. Although using purely classical models in the simulations, the resulting explosion geometry and shock wave dynamics closely resemble experimental findings, and they highlight the importance of atomistic details for modeling shock wave attenuation.