Chang T., Zhang H., Guo Z., Guo X. Gao Huajian

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Provides the most straightforward way for actuation and energy conversion. Water flowWaterwheels Hydroelectric turbines

Generally induced by an external source of energy. Lack of intrinsic mechanism similar to downhill flow of water. Barreiro et al., Science 320, 775 (2008) Fennimore et al., Nature 424, 408 (2003) Kudernac et al., Nature 479, 208 (2011) Thermal Electronic

Guo Z, Chang T, Guo, X, Gao H, J Mech Phys Solids 60, 1676 (2012).

A A larger driving force can be generated by a larger stiffness gradient or a smaller local stiffness.

Superposition Temperature Accel – Stable – Deaccel Shuttles like a pendulum

Durotaxis was first observed in living cells. Active sensing Lo et al., Biophys J 79, 144 (2000) Water droplets undergo reverse durotaxis. Wetting Discher et al, Science 310, 1139 (2005) Style et al., Proc. Natl. Acad. Sci. U.S.A. (2013) Nanodurotaxis: Neither active sensing nor wetting

Stiffness gradient induces a bias van der Waals potential

Driving force comes mainly from the unbalance edge force Unbalanced edge force/Net driving force 6.29 pN/5.48 pN 1.27 pN/0.93 pN

Partly (less) from thermal atomic vibration, as shown by Guo et al, JMPS (2012). Partly (more) from out-of-plane deformation of substrate. Contributions to edge force from substrate atoms at different position.

Functional graded material Marerial interface Nanoporous array ~4 pN (320 kPa) ~5 pN (100 kPa) ~10 pN (400 kPa) ~2  N (2 kPa) Intrinsically motivated No external power needed 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 *