The shift and rotational motions of nano-meter particle in unbounded flow region are analyzed by the singularity superposed method following low Reynolds number theory. The formulas of Stokes drag force and rotational drag torque under slip regime are derived

and accordingly Stokes-Einstein diffusion relationships are established. The theoretical analysis shows that the drag for shift motion and drag torque for rotational motion are less than both solutions under the condition of no-slip regime

and accordingly Stokes-Einstein diffusion coefficients are greater than the no-slip cases

which indicates that the diffusion capability increases for the particle motion at slip regime. The increasing diffusion capability is related to Knudsen number directly: the larger the Knudsen number

the greater the diffusion capability. The derived results can be used to describe particles motion in the unbounded liquid or gas flow with low concentration

and are applicable in the fields of chemical industry

environmental science

ore dressing

biomechanics

and so on.