Van der Waals - Empirical Studies

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Here are some experimental numbers for van der Waals force:

For the spider species Evarcha arcuata, the contact elements (setules) each have an average contact area of 1.7 × 105 nm2 and produce an adhesive force of 41 nN per setule. http://www.iop.org/EJ/abstract/0964-1726/13/3/009/

For geckos, "Each seta ends in up to 1000 even tinier tips. The tips are only 200 billionths of a meter wide... A single seta can lift the weight of an ant 200 µN" 200 µN per tip/ 1000 tips per seta = 200 nN per seta (About 5 times more than the spiders can do.) http://www.lclark.edu/~autumn/dept/geckostory.html See also http://www.me.cmu.edu/faculty1/sitti/nano/publications/PNAS_sitti.pdf

And then there's the synthetic stuff: "Each synthetic hair is made from a material called kapton and measures 2.0 microns in height and 0.2 microns in diameter - the same as gecko hairs. A piece of tape one centimeter square holds around 100 million of these artificial setae and could support a weight of one kilogram." 314000000/4*200*200=78500000*40000= 3,140,000,000,000 nm2 .000,003,140,000,000,000 .000,003,140 m2; For comparison, 1 centimeter is .01*.01=.0001 m2 so there's not too much actual surface area. 1 kilogram of weight in Earth’s gravity field exerts a force of 9.807 N (F=ma) 9.807N / 3,140,000,000,000 nm2 = X N / ((3.14/4)*200*200) nm2 31400 * 9.807 / 3140000000000 = 98.07 nN per setae. Andre Geim, Nature Materials (DOI: 10.1038/nmat917) http://www.newscientist.com/news/news.jsp?id=ns99993785

"Perpendicular force was 181 +/- 9 nN for PDMS spatulae with tip radius of 230–440 nm and 294 +/- 21 nN for polyester spatulae with tip radius of ~350 nm." http://www.me.cmu.edu/faculty1/sitti/nano/publications/PNAS_sitti.pdf

This is definitely good enough agreement for our calculations, to find out if the robotic gripper can grab parts, pull them off the conveyer belt, move them at particular velocities (TBD), and release (one finger at a time, or all at once) once the nanocube is in place.

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