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How to Build Casimir Molecules

Certain nanoparticles ought to form stable molecular clusters because the Casimir forces between them repel at short distances but attract at larger ones.

The Casimir effect is a constant source of fascination to physicists. The effect exists because of the quantum nature of the vacuum which is filled with electromagnetic waves leaping in and out of existence.

Place two parallel conducting plates close together in this vacuum and the larger waves cannot fit between them. So the waves outside push the plates together. That’s the famous Casimir force which was first measured accurately in 1997.

In recent years, however, physicists have calculated that the combination of various different materials in various different shapes should generate repulsive forces (although this force has yet to be measured).

Today, Alejandro Rodriguez and buddies at the Massachusetts Institute of Technology in Cambridge say that by carefully choosing nanoparticles of different materials and sizes, the attractive and repulsive Casimir forces should lead to a stable configuration; a Casimir molecule, you might say.

In an impressive analyse, Rodriguez and co do calculate the Casimir forces for combinations of infinite slabs made alternately of silicon and silicon dioxide, for nanoparticles and for alternating slabs and spheres.

But their most interesting analysis is on the forces between Teflon and silicon nanospheres immersed in ethanol. By choosing the radii of these spheres carefully the can be suspended against the force of gravity above an infinite slab. It turns out that the forces between the particles is repulsive at separations closer than 100 nm but becomes attractive as the distance increases.

Clearly, this is a fascinating situation in which the spheres should form a stable, nontouching “dicluster”. What’s more, this is an experiment that could be done relatively easily today, provided the size of the nanoparticles can be controlled with the required precision.

That’s exciting stuff but these experiments will be fraught with difficulty. The MIT team acknowledge that calculating even the sign of the Casimir force in complex geometries is famously tricky.

That’s partly because Casimir forces are not additive like conventional forces. So when more than one force has to be considered, the complexity of the calculations rapidly increases. (In this case, there is the repulsive and attractive forces between the spheres as well as the suspending force over the infinite slab.)

That’s why it is not possible to easily generalise the effect further, perhaps to create an entire sheet of stable nanoparticles. Whether that kind of stable 2D Casimir crystal is even possible is not known.

But the MIT team say this Teflon-silicon nanoparticle arrangement should be a good starting point for experimental investigation. Good luck to them!

One question the team does not address in this paper is what Casimir molecules and crystals might be useful for. Any suggestions gratefully received.

Ref: arxiv.org/abs/0912.2243: Non-touching Nanoparticle Diclusters Bound By Repulsive and Attractive Casimir Forces

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