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CFDLs Caused by EDP
 
© Charles Chandler
 
It is well-known that at high pressures, matter gets ionized.1 This is because of the Pauli Exclusion Principle, whereby no two identical fermions (i.e., particles with half-integer spins, such as electrons) may simultaneously occupy the same quantum state in the same location. If atoms are pressed too close together, the electron shells of neighboring atoms overlap, and the conflict forces the liberation of one of the electrons. The extra force required to do this accounts for the incompressibility of liquids and solids.2,3,4
 
Figure 1. Carbon dioxide phase diagram, courtesy FutureChem.
The same is true even for supercritical fluids.5,6 Above the critical point, the fluid loses the distinction between gas & liquid. (See Figure 1, and the representation of atomic spacing just below.7) Still at the critical temperature but with increasing pressure, the fluid is more easily compressed than the ideal gas laws predict. (See the Nelson-Obert charts, and the closely spaced density lines just above the CP in Figure 1.) With increasing temperature, the compressibility falls back in line with the ideal gas laws. Nevertheless, the fluid is as incompressible as ever appoaching its solid density. CO2 at its critical temperature of 31 °C, when subjected to 300 GPa (i.e., 3 megabars), has a density of 1400 kg/m3, which isn't much above its solid density below the triple point. So supercritical fluids still have a modulus of elasticity in the solid regime, but they are not compressible per the ideal gas laws.
 
 
Electron Degeneracy Pressure
$$P=\frac{h^2}{20m_em_p^{5/3}}\left(\frac{3}{\pi}\right)^{2/3}\left(\frac{\rho}{\mu_e}\right)^{5/3}$$
where:
P = pressure
h = Planck's constant
me = mass of electron
mp = mass of proton
ρ = density
μe = electron/proton ratio
Under moderate pressures, the electrons liberated by the compression don't go far. They are still attracted to the atomic nuclei by the electric force, and as soon as they can find adequate space between two atoms without shell conflicts, they come to rest. This space is provided by the random motions of atoms at any temperature above absolute zero. But under extreme pressures, even the widest gaps afforded by random motions do not provide sufficient space for the electrons. At this point, the Pauli Exclusion Principle forces the expulsion of the electrons, leaving positive ions behind. The Coulomb force between the ions then opposes further compression of the matter. This phenomenon is commonly called electron degeneracy pressure (EDP).
 
If the prime mover is gravity, hydrostatic pressure increases with depth, and the available space for electrons is only to be found at a higher altitude, where less gravitational loading enables greater distances between atoms. Thus the expelled electrons bubble up to higher altitudes, leaving positive ions below.
 
The implication not typically considered is that a charge separation has occurred, creating current-free double-layers (CFDLs), where a powerful electric field attracts the layers to each other, but EDP prevents recombination. Thus there is a resting potential, which ordinarily would be an electromotive force, but there is no current, even if there is no electrical resistance, because something else (i.e., EDP) opposes it.
 
 

References

1. Saumon, D.; Chabrier, G. (1992): Fluid hydrogen at high density: Pressure ionization. Physical Review A, 46 (4): 2084-2100

2. Dyson, F. J.; Lenard, A. (1967): Stability of Matter. I. Journal of Mathematical Physics, 8 (3): 423-434

3. Lenard, A.; Dyson, F. J. (1968): Stability of Matter. II. Journal of Mathematical Physics, 9 (5): 698-711

4. Dyson, F. J. (1967): Ground‐State Energy of a Finite System of Charged Particles. Journal of Mathematical Physics, 8 (8): 1538-1545

5. Otles, S. (2016): Supercritical Fluids — Density Considerations.

6. Tosatti, E. et al. (2009): High-pressure polymeric phases of carbon dioxide. Proceedings of the National Academy of Sciences, 106 (15): 6077-6081

7. Weill, F. et al. (1999): Supercritical fluid processing: a new route for materials synthesis. Journal of Materials Chemistry, 9 (1): 67-75


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