Self-propelled jump of droplets is among the most striking phenomena in droplet collisions on substrates. Self-propelled jump phenomena of droplets have been observed in experiments, which have also been reproduced in macro- or mesoscale numerical simulations. However, there have been few previous studies on the phenomena at nanoscales. To unravel the dynamics and mechanisms of nanoscale binary droplet collisions on substrates, head-on collision processes of two identical water droplets with diameters of 10nm on graphite substrates are investigated by molecular dynamics (MD) simulations. By varying the impact Reynolds number of binary droplet collisions on hydrophilic or hydrophobic substrates, we successfully reproduce self-propelled jump of droplets on a super-hydrophobic surface with a contact angle of 143^◦ and a relatively high impact Reynolds number of 17.5. Parametric studies indicate that both high impact Reynolds numbers and high hydrophobicity promote self-propelled jump. Moreover, the criterion based on the Ohnesorge number derived from the mesoscopic self-propelled jump regime is insufficient to precisely predict a nanoscale self-propelled jump phenomenon. For this reason, our study includes the impact Reynolds number and the substrate properties like contact angle as additional criteria to refine and extend the current theory for the self-propelled jump behaviours to nanoscales. The study provides insight into the mechanism of self-propelled jump phenomenon at nanoscales.