TINY BUBBLES
(C)1995 Alan M. Schwartz
Classical physics lacks only exact measurement for exact
description. Quantum mechanics elaborates wave properties of
reality - a universe of eerie diffraction phenomena, Heisenberg
Uncertainty, non-local interactions... extending to spectacles
like electrical superconductivity and superfluid helium.
Experiments verify subtle attributes of the counter-intuitive
quantum world. Can we shove a macroscopic crochet hook through
quantum mechanical loopholes?
The wave nature of particles is subject to resonant properties of
cavities. If an integral number of half-wavelengths do not fit
(one half-wavelength at the minimum), the wave is excluded.
Cavity shape and dimensions dictate the distribution and spacing
of wave energy levels. Quantum reality can be customized.
When liquid helium boiling at 4.2 degrees Kelvin and 760 torr
(one atmosphere pressure) is pumped below 383 torr, its
temperature passes 2.174 degrees Kelvin and it undergoes a Bose-
Einstein condensation. Superfluid helium is a bulk, extended
correlated minimum energy wavefunction. It has no viscosity, for
instance, flowing with unimpeded ease through a mass of tightly
packed jeweler's rouge in the classic heat-driven "helium
fountain." Suppose a random assembly of microscopic interstices
in packed rouge were replaced with a crystalline lattice of
naughtily-dimensioned cavities. Here comes the crochet hook!
Aluminosilicate (rock) is readily assembled about organic
molecule templates to create synthetic zeolites or "molecular
sieves." Burn off the organic. The remaining crystalline
ceramics can be 40% by volume empty space - interconnected
molecule-sized cavities arranged in a repeating three dimensional
lattice. Thousands of tons of zeolites are manufactured
annually. Standard pore sizes are 0.3 nanometer (passing water
and ammonia, but not ethane), 0.4 nm (sulfur dioxide and ethane,
not propane), 0.5 nm (butanol, not branched hydrocarbons), and
1.0 nm (dibutylamine, not tributylamine). Mesoporous molecular
sieves are templated about surfactant micelles to have pores and
channels in the range of 2-10 nm. Room temperature helium atoms
have a diameter of 0.19 nm from viscosity behavior. What size
cavity, or heap of 10^20 cavities, bedevils superfluid helium?
Louis de Broglie posited that a particle possesses an intrinsic
wavelength equal to Planck's constant divided by its momentum
(mass times velocity). Electrons, neutrons, and even helium
atoms have been diffracted from crystals. They each exhibit the
expected de Broglie wavelength. Double slit diffraction also
works, one particle at a time fired, and go rationalize that!
What is the velocity, hence wavelength, of a helium atom at 2.7
degrees Kelvin? No problem! Maybe. Let us start with a
classical description of a monoatomic gas at 2.7 degrees Kelvin.
Helium is very cooperative. At least we avoid confounding
rotational and vibrational degrees of freedom.
James Clerk Maxwell and Ludwig Boltzmann derived statistical
velocity distributions for atomic and molecular systems dependent
upon their temperature and mass only. Helium atoms mass
6.6465x10^(-27) kg. At 2.7 degrees Kelvin they chug along at
root-mean square, arithmetic mean, and most probable velocities
of 129.7, 119.5, and 105.9 meters/second (1245 meters/second
average velocity at room temperature). The corresponding de
Broglie wavelengths are 0.769, 0.834, and 0.941 nm. Lower
temperatures mean lower velocities and longer wavelengths.
Common molecular sieves have pores well-sized to contain
classical helium and confound quantum mechanical helium with half
wavelength resonant cavity restrictions. Mesoporous molecular
sieves ought to enforce "particle in a box" behavior upon very
tiny drops. Place your bets and take your chances.
(There is the complication that we have a liquid, not a gas. And
a Bose condensation has no energy distribution - all particles
reside at a correlated degenerate lowest energy state unless they
are excited, as a unit, to the next quantum level. And that zero
point energy becomes significant compared to thermal energy. Is
there a physicist about? This is fun!)
Monitor the superfluid transition for liquid helium held within
the interior cavities of a mass of molecular sieve crystals. We
expect profound changes in transition temperature and specific
heat behavior when cavity constraints alter the physics of the
system. It seems like an exemplary and not difficult experiment.
Similar procedures performed without the presence of sieves in
the pot birthed reams of published results (K. Onnes, Nature 78
370 (1908) and F. London, J. Phys. Chem. 43 49 (1939)). I have
not heard of the molecular sieve experiment yet being performed.
Progress occurs when accepted boundary conditions are violated.
Euclid's Fifth Postulate, the Parallel Postulate, disturbed
Euclid and every geometer following. Attempts to prove the Fifth
Postulate by counter-example - assuming either an infinite number
or no lines parallel to a given line - gave birth to hyperbolic
and elliptic geometries. What happens when we attempt to put a
0.38 nm half-wavelength in a 0.3 nm cavity? What are the
properties of a tiny drop of superfluid liquid helium constrained
by quantum limits? Inquiring minds want to know!