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Impingement of binary droplets at the nanoscale is very important and is ubiquitous in daily life and practical applications, such as lab-on-a-chip and digital microfluidics. The current work performs molecular dynamics (MD) simulations to simulate free evolution of impacting deposited droplets with incoming ones with different height differences. The representative dynamics under different given conditions have been directly captured with the help of MD simulations. We observe that the targeted systems initially experienc primary spreading followed by secondary spreading, and ultimately, merged droplets can deposit upon the surface or form bouncing ones. Through recordation of the maximal spreading factor over primary and secondary spreading, the law of spreading at various separated distance (Dsep) and impacting Weber number (We) is investigated. The increasing Dsep can obviously postpone the collision obviously while the increasing We allows the collision to be advanced. The external factor of Dsep can not affect the primary spreading but shows a significant influence on the secondary spreading. The prefactor of the secondary spreading at low-velocity impingement is 0.06 whose value is the same as that for primary spreading. On further increasing We, the high-velocity impingement alters the secondary spreading with prefactor increasing from 0.06 to 0.09. This is attributable to the fact that the collision between incomplete retracting droplets and incoming ones resists the secondary spreading. But at high velocity, the pattern of incomplete-retraction collision can promote the secondary spreading. The variation of contact time at a wide range of Dsep and We is recorded, and the effect of these two mentioned parameters is investigated. This work can help researchers to understand the impact of binary nanodroplets with various Dsep, which is very suitable for guiding the practical applications that need different impacting conditions.