## Sunday, October 08, 2017

### The Abnormal Force

How does the chair actually hold you up when you sit down?  What is keeping your car tires from sinking through the road surface?  What is keeping my coffee mug from falling through my desk?  In high school and first-year undergrad physics, we teach people about the normal force - that is a force that acts normal (perpendicular) to a surface, and it takes on whatever value is needed so that solid objects don't pass through each other.

The microscopic explanation of the normal force is that the electrons in the atoms of my coffee mug (etc.) interact with the electrons in the atoms of the desk surface, through a combination of electrostatics (electrons repel each other) and quantum statistics (the Pauli principle means that you can't just shuffle electrons around willy-nilly).  The normal force is "phenomenological" shorthand.  We take the observation that solid objects don't pass through each other, deduce that whatever is happening microscopically, the effect is that there is some force normal to surfaces that touch each other, and go from there, rather than trying to teach high school students how to calculate it from first principles.  The normal force is an emergent effect that makes sense on macroscopic scales without knowing the details.  This is just like how we teach high school students about pressure as a useful macroscopic concept, without actually doing a statistical calculation of the average perpendicular force per area on a surface due to collisions with molecules of a gas or a liquid.

You can actually estimate the maximum reasonable normal force per unit area.  If you tried to squeeze the electrons of two adjacent atoms into the volume occupied by one atom, even without the repulsion of like charges adding to the cost, the Pauli principle means you'd have to kick some of those electrons into higher energy levels.  If a typical energy scale for doing that for each electron was something like 1 eV, and you had a few electrons per atom, and the areal density of atoms is around 1014 per cm2, then we can find the average force $F_{\mathrm{av}}$ required to make a 1 cm2 area of two surfaces overlap with each other.   We'd have $F_{\mathrm{av}} d \sim 10^{15}$eV, where $d$ is the thickness of an atom, around 0.3 nm.   That's around 534000 Newtons/cm2, or around 5.3 GPa.   That's above almost all of the yield stresses for materials (usually worrying about tension rather than compression) - that just means that the atoms themselves will move around before you really push electrons around.

Very occasionally, when two surfaces are brought together, there is a force that arises at the interface that is not along the normal direction.  A great example of that is in this video, which shows two graphite surfaces that spontaneously slide in the plane so that they are crystallographically aligned.  That work comes from this paper.

As far as I can tell, there is no official terminology for such a spontaneous in-plane force.  In the spirit of one of my professional heroes David Mermin, who coined the scientific term boojum, I would like to suggest that such a transverse force be known as the abnormal force.  (Since I don't actually work in this area and I'm not trying to name the effect after myself, hopefully the barrier to adoption will be lower than the one faced by Mermin, who actually worked on boojums :-)  ).

#### 1 comment:

Anonymous said...

Tangential force doesn't do the job?