Jingyuan Li 1,a) , Xiaofeng Wang 1 , Lina Zhao 1 , Xingfa Gao 1 , Yuliang Zhao 1,4,b) and Ruhong Zhou 2,3,5,c)
1. CAS Key Laboratory for Biomedical Effects of Nanomaterials and Nanosafety, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, 100049, China
2. IBM Thomas J. Watson Research Center, Yorktown Heights, New York 10598
3. Department of Chemistry, Columbia University, New York, New York 10027
4. CAS Key Laboratory for Biomedical Effects of Nanomaterials and Nanosafety, National Center for Nanoscience and Technology of China, Beijing, 100190, China
5. Institute of Quantitative Biology and Medicine, SRMP and RAD-X, Soochow University Medical College; Jiangsu Provincial Key Laboratory of Radiation Medicine and Protection,
Suzhou 215123, China a) Electronic mail: lijingyuan@ihep.ac.cn
b) Electronic mail: zhaoyuliang@ihep.ac.cn
c) Electronic mail: ruhongz@us.ibm.com
Δ P , osmotic pressure; n, total number of water molecules; f, constant force applied to each water molecule; A, the area of unit cell
For a = 0.001 nm/ps 2 , n = 11639; f = m ×a = 2.99
×10 -14 N ; A = 3.63×10 -17 m 2 ;
Δ P = 9.59 MPa
We calculated the averaged force of water exerting on the blade over a period of time, denoted by time-average driving force.
The instant force of water exerting to the blade highly fluctuates, while the fluctuation of time-average driving force is depressed by increasing the time window size. The corresponding force distribution also becomes narrower, and the probability of having the net driving forces along the -z direction increases. For the system with the flow velocity of 1.82×10 -3 nm/ps, the probability of driving force being along -z direction increase to 70 % as the window size increases to 50 ps. In this way, the designed nanoscopic water turbine can rotate largely unidirectionally as driven by the seemingly weak water flow.
FIG. S1 Interaction force of water with the nano-turbine blade in the system with the flow velocity of 1.82
× 10 -3 nm/ps. (a) The fluctuation of time-average interaction force with the window size of 10 (black), 20 (red), 50 (green) and 100 ps (blue). (b) The fitting and the distribution of time-average interaction force with the window size of 1 (black), 10 (red) and 50 ps (green). The tendency towards the mean force along the -z direction becomes profound as the window size increases.
FIG. S2 The dependence of flow rate on the acceleration rate of water. The flow rate increases linearly as the increase of the acceleration rate of water.

FIG. S3 The rotation rate of nano-turbine, ω, with respect to the average water velocity (denoted by flow velocity, V
Z
) in 300K.
The linear fit (red) of the results obtained from the original system with the size of 6
6
nm 3 , using velocity-rescaling thermostat method (black square). The results obtained from the simulation using Nose-Hoover thermostat method (green circle) and the system with the size of 9
9
15 nm 3 (blue triangle) are also plotted. Linear relationship between the rotation rate and flow velocity in these two systems are similar to the original system.
FIG. S4 The fluctuation amplitude of nano-turbine’s rotation is characterized by the root mean square of the extent of reverse rotation.
FIG. S5 The frequency of net rotation of nano-turbine. The frequency of reversal rotation exhibits the linear dependence on the water flow velocity.
FIG. S6 The distribution of V
Z
, the water flow velocity over the whole x-y region, (black) and the average smoothing curve (red) in the system with the flow velocity of -1.82×10 -3 nm/ps (dash line). The total water flow velocity remains conserved throughout the z-axis.

FIG. S7 The distribution of average velocity of water within 2Å water slab in the system with the flow velocity of 2.01×10 -3 nm/ps, T = 360K. (a) The distribution of instant-average velocity of water (b) The fitting and the distribution of time-average velocity of water with the window size of 1 (black), 10 (red) and 50 ps (green).
FIG. S8 Scaling plot of the relationship among the flow velocity, driving force and rotation rate at 300 K and 360 K. (a) The dependence of the ration rate on the driving force F z
in scaling plot can also be fit to the linear functions very well. Similarly, the relationship between the driving force and the flow velocity (b) can be fit to the linear function.