Van der Waals
(forces ≥ Casimir-Polder)
The Casimir effect can be viewed as a manifestation of the quantum-mechanical zero-point energy of the vacuum, and has recently been hyped as if it were something new and mysterious that will assist or maybe ruin advanced nanomechanical systems. It has inflamed the minds of something-for-nothing energy enthusiasts, too.
In reality, what Casimir described is a 60-year-old idealized case of a 50-year-old correction to an 80-year-old theory — a correction that decreases the predicted forces. Let’s take a closer look a Casimir forces and their practical significance.
Van der Waals, London, and Casimir
Since the early publications of Johannes Diderik van der Waals more than a century ago, it has been known that molecules attract one another when close together, even if they have no electric charge or dipole moment. In 1930, Fritz London provided a quantum mechanical description of this interaction, now termed the “van der Waals” or “London dispersion” force. London formulated his description in terms of correlated zero-point fluctuations in the distribution of electric charge (and hence of the electromagnetic field).
In 1948, Dutch physicists Hendrik Casimir and Dirk Polder predicted an attractive force between parallel, perfectly conductive plates; they formulated the theory in terms of zero-point fluctuations in the electromagnetic field, without explicitly describing the corresponding fluctuations in the distribution of electric charge in the plates. Casimir-Polder theory was not entirely satisfactory, inasmuch as no such material exists, or can exist. (Note that a perfect conductor in the relevant sense would be a perfect gamma-ray reflector.)
The unification: Lifshitz theory
In 1956, Evgeny Lifshitz remedied this situation by unifying the London and Casimir descriptions and extending the analysis to materials with realistic electromagnetic properties. Lifshitz theory is equivalent to London theory at short range, but takes account of the finite speed of light: this retards the propagation of fluctuations in the electromagnetic field and thereby weakens the correlation of charge fluctuations at greater distances.
Lifshitz’s result is identical to Casimir’s in the idealized case of perfect conductive plates, and it is effectively identical to London’s at distances of a few nanometers or less. At short range, the forces between pairs of atoms decline with distance in proportion to r–7; at longer range, the decline steepens to r–8. In brief, Lifshitz subsumes Casimir, and both correct London downward.
Dispersion forces and nanomachines
In London’s terminology, the van der Waals/London/Casimir-Polder/Lifshitz interaction is a dispersion force, but it sounds far more exciting and mysterious when called “the Casimir effect” and described in terms of zero-point energy and quantum-mechanical vacuum fluctuations. Cranks find it fascinating and hucksters profit.
Dispersion forces have great practical importance. They ubiquitous, and are (for example) almost entirely responsible for the cohesion of hydrocarbons like polyethylene. They resist the separation of atomically flat plates of ordinary materials with a force on the order of 108 N/m2 (0.1 nN/nm2). Dispersion forces forces affect (but don’t oppose) the motion of nanomechanical parts that roll or slide over one another.
Nanomachines and authoritative misinformation
I included a detailed, atomistic analysis of rolling and sliding interfaces in my MIT dissertation; this can be found as part of the broader physics-based analysis in Nanosystems: Molecular Machinery, Manufacturing, and Computation (Wiley/Interscience, 1992). I used standard molecular mechanics models in this work. Such models uniformly use the simple London r–7 approximation, and I note the Casimir correction in a footnote on page 65.
Years later, I was surprised to encounter false but authoritative statements suggesting that my work neglects dispersion forces, implying that all this advanced-nanotechnology stuff is very dubious and that I lacked even freshman-level familiarity with molecular physics. I leave it to the reader to consider what frame of mind and level of knowledge might lead someone to say this, and to consider the effects.
I’m glad this sort of nonsense has been in decline.
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Uncle Al 04.29.09 at 5:39 pm UTC
Lamellar solids are common: smectite clays, graphite, molybdenum and tantalum disulfides, zirconium phosphonates, magnesium diboride, optical coatings. No thermodynamic anomalies appear even when superconducting, e.g., MgB2). The layers don’t form mirrored etalons. If you’re feeling clean and wholesome, science has the cure – casimatter!
A 70 nm aluminum layer, 2.7 g/cm^3, reflects 93% (99% of theoretical) between 100 and 120 nm. MgF2, 3.177 g/cm^3 and RI = 1.63 at 121 nm, has 80% transmittance at 115 nm. LiF, 2.639 g/cm^3 and RI = 1.777 goes to 110 nm. Aluminum’s coefficient of thermal expansion, 23.1 ppm/K, is matched by 60:40 MgF2:LiF alloy, RI = 1.628 at 121 nm.
Spin a flat wide deposition torus over alternating sectors of magnetron sputtered Al metal and 60:40 MgF2:LiF alloy to lay down an endless alternate bifilar spiral deposit of 70 nm Al and 37 nm fluoride alloy to half-wave cancel a 120 nm optical pathlength. Cool, cut out pieces of casimatter: average density 2.79 gm/cm^3 of which 37 wt-% is ZPF-depleted fluoride alloy.
Examine casimatter cleverly.
frank 04.30.09 at 12:01 pm UTC
Eric, I don’t disagree with your numbers but my point is that the signifigance of “up conversion” of vacuum fluctuations is being overlooked. they do not just magically become higher in frequency as the gap closes. They twist on the time axis making this a relativistic effect at the opposite end of the spectrum from an event horizon. I humbly submit that the engine for catalytic action is a Casimir time detour where reactants “do their time” before returning from the cavity or outcropping of Casimir geometry to our plane.
V/R
Fran