View source for VdW suck-in

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[[File:Hinge self assisted assembly demo.png|200px|thumb|right|VdW force is "sucking" the pin into the sleeve. No retention structures neded as they would be needed for the macroscale.]]
[[Van der Waals force]] can be very useful in advanced [[gemstone]] based nanosystems to hold things in place 
* during assembly processes or 
* even in final products.

In particular the VdW force can be uses to hold axles withing chains. <br>
'''Axles literally get "sucked" into their sleeves''' as the higher surface contact area means lower energy. <br>
This is very similar to surface tension energy.
So unlike a (hooks law) linear spring where force is proportional to displacement
one gets a near constant force over displacement.

By choosing contact area profiles (easier for planar surfaces) one can emulate all kind on nonlinear spring behaviors. 

* {{wikitodo|Add image of extendable soap bubble skin in rectangular wireframe}}
* {{wikitodo|Add math showing that at room-temperature thermally activated axle displacements are negligible even for very small crystolecules}}

== A note on sticking strength ==

The strength of VdW bonds is not to be underestimated. <br>
Weak bonds can be shaken open by thermal motion from heating. But ... <br>
It does not take much contact surface area at all such that <br>
the required temperature would be so high that <br>
the [[gemstone]] base material would start to melt (or decompose) before the contact sticking becomes shaken apart.

Much boosted by the situation that the wole [[crystolecule]] made from many many atoms <br>
does just get kT energy for each of it's few DOFs of motion. 

* {{wikitodo|Make a temperature vs area chart for diamond to diamond planar contact}}

== Estimating thermally driven slide-out quantitatively ==

Let's assume a pin with a diameter of ⌀1nm: <br>
From [[Nanosystems]] we know that the <br>
VdW-energy surface-energy-density between diamonds is <br>
ε = 200zJ/nm² (for silicon instead it is: ε = 700zJ/nm²) <br>
'''Question:''' What is the expectation for the <br>
axial slide-out h corresponding to E = k * 300K? <br>
d * π * h * ε = k T <br>
h = k T / (d * π * eps)  <br>
h = 4.14zJ / (1nm * π * 200zJ/nm^2)  <br>
h = 6.6pm (crudely!) <br>

Van der Waals alone is more than sufficient. <br>
Even for smallest axles and all nondestructive temperatures. <br>
Tenfold room temperature in Kelvin (300K => 3000K) still <br>
gives only a mere 66pm expectation for the slide-out distance. <br>
For reference the length of a (C–C) bond in diamond is 154pm. <br>
Even short pins will be significantly longer.

== Related ==

* [[Van der Waals force sticking]] - {{wikitodo|fator parts out to this page}}
* '''[[Van der Waals force]]'''
* [[Energy, force, and stiffness]]
* [[Comparison of mechanical character of different bonds types]]
* [[Intuitive feel]]
* [[Crystolecules]]

== External links ==

Surface tension is a good intuition for sliding type VdW forces: <br>
Here's a [https://www.youtube.com/watch?v=nKKS3qQGR8w short video on YouTube @FluidDynamics] <br>
Here's another longer [https://www.youtube.com/watch?v=GMoVKSvUkt8 video demo on youtube @fyzlab]. <br>
Note that in the video due to the small area and large relative area change the membrane gets thinned out by a lot <br>
this leads to a non-constant increasing force and rather than a constant force<br>
which in turn allows for balancing with the constant force that is gravity. <br>
VdW force on the other hand has no such thinning out effect and is constant.

* Wikipedia: [https://en.wikipedia.org/wiki/Surface_tension Surface tension]
* Wikipedia: [https://en.wikipedia.org/wiki/File:Surface_growing.png growing surface graphic]

* Tweet about related math: https://twitter.com/mechadense/status/1529798765854564352?s=20&t=CM0IGEpcOo67KRC3eG7dMA