Chang T., Zhang H., Guo Z., Guo X.
Gao Huajian
2014.04.22
All pics from internet
Provides the most straightforward way for actuation and energy conversion.
Water flow
Waterwheels
Hydroelectric
turbines
Generally induced by an external source of energy.
Lack of intrinsic mechanism similar to downhill flow of water.
Thermal
Barreiro et al., Science 320, 775 (2008)
Electronic
Fennimore et al.,
Nature 424, 408 (2003)
Kudernac et al., Nature
479, 208 (2011)
kvdW
kvdW
VvdW  V0  kvT
kBkvdW
kν 
2m0
Potential coefficients (eV/atom/K)
0.5kvdW
8
7
e
6
kv
5
i
4
3
0.0
kv
0.5
1.0
1.5
Stiffness coefficient  (kvdW)


1
1
   zo (ql , qm )2  za (ql , qm )2  dql dqm
Guo Z, Chang T, Guo, X, Gao H, J Mech Phys Solids 60, 1676 (2012).
2.0
B
C
Soft
D
Hard
Displacement (nm)
50
B
25
0
kc = 0.48/4.8/7.7/9.6/12.0/14.4/14.4 nN/nm
k = 0.0096/0.096/0.144/0.192/0.24/0.288/0.096 nN/nm
2
A
A larger driving force can be
generated by a larger stiffness
gradient or a smaller local
stiffness.
Velocity (nm/ns)
-25
30
C
15
0
-15
-30
0.0
2.5
5.0
Time (ns)
7.5
10.0
Hard
Soft
8
24
6
18
4
12
2
6
0
0.0
0.2
0.4
Time (ns)
Superposition
Temperature
0.60.0
0.2
0.4
Time (ns)
0
0.6
C
30
30
300K
300K
300K
500K
12
15
6
0
0
-15
-6
-30
-12
0
2
4
6
Time(ns)
Accel – Stable – Deaccel
Shuttles like a pendulum
8
Displacement(nm)
0.801/2.403
2.403/4.005
0.801/4.005
0.801/4.005
Velocity(nm/ns)
10
36
B
A
Velocity (nm/ns)
Displacement (nm)
12
Nanodurotaxis:
Neither active sensing nor wetting
Durotaxis was
first observed in
living cells.
Water droplets undergo
reverse durotaxis.
Wetting
Active sensing
Lo et al., Biophys J 79, 144 (2000)
Discher et al, Science 310, 1139 (2005)
Style et al., Proc. Natl. Acad. Sci. U.S.A. (2013)
Interlayer Potential (meV/atom)
A
-48.42
-48.45
-48.48
-48.51
0
3
6
9
12
15
Stiffness (nN/nm)
Stiffness gradient induces a bias van der Waals potential
1st/2nd/3rd/4th ring
at the rear end
Inner part
4th/3rd/2nd/1st ring
at the front end
B
Interlayer Force (pN)
21.23
20
Unbalanced edge force/Net driving force
15
6.29 pN/5.48 pN
1.27 pN/0.93 pN
10
5
13.19
1st/2nd/3rd/4th rings
(52 atoms each)
on softer side
-10
5.995.43
2.371.91
0.63
0
-5
Stiffness jump
Stiffness gradient
-0.20
-1.72
-3.04
-5.49
-6.79
-0.34 -0.30
-0.66
-0.81
Inner region
1st/2nd/3rd/4th rings
(52 atoms each)
on harder side
-15
Driving force comes mainly from the unbalance edge force
-12.02
-12.97
Partly (less) from thermal atomic vibration, as shown by Guo et al, JMPS (2012).
Substrate Deformation (nm)
Partly (more) from out-of-plane deformation of substrate.
0.020
0.015
Soft
Hard
0.801 nN/nm
4.005 nN/nm
0.010
0.005
Contact area
0.000
-0.005
-0.010
Longitudinal position
Contributions to edge force from
substrate atoms at different position.
~4 pN (320 kPa)
Functional graded material
~5 pN (100 kPa)
Intrinsically
motivated
No external
power
needed
~10 pN (400 kPa)
Marerial interface
~2 N (2 kPa)
Nanoporous array
No biological
activity
involved
Durotaxis！
Stiffness
Engineering?
?
A fundamental law of nanoscale
directional motion
Mechanism & mechanics
General implications
*Chang T., Zhang H., Guo Z., Guo X.
*Gao Huajian
*2014.04.22