CFDLs Caused by EDP
© Charles Chandler
Figure 1. Charge Separation Under Pressure
At left is an abstract representation of a normal crystal lattice, using the familiar icon for an atom, and showing connections of electron shells. At right, extreme pressure has forced the expulsion of one of the electrons from the atom in the center. The expelled electron is to be found just outside, wherever there is room for it, while attracted to the positive ion by the electric force.
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 (See Figure 1.)
The same is true even for supercritical fluids — even though they're too hot for crystal lattices, and thus have a plasticity uncharacteristic of their subcritical solid regimes, once compressed down to the density of a solid, they become just as incompressible as subcritical solids.5,6 This fact isn't salient in the larger body of studies that have been done on supercritical fluids at less extreme pressures, and there's actually one place in the phase diagram where supercritical fluids are compressible beyond even the ideal gas laws — just above the critical temperature. (See the Nelson-Obert charts, and the closely spaced density lines just above the CP in Figure 2.) Nevertheless, the fluid is as incompressible as ever once it achieves its solid density. (See Figure 3.) CO2 at its critical temperature of 31 °C, when subjected to 300 GPa (i.e., 3 million bars), 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 beginning at the solid density, but that isn't what we'd call compressibility, certainly not in line with the ideal gas laws.
Figure 2. Carbon dioxide phase diagram, courtesy FutureChem.
Figure 3. Another representation of the density of the various states.7 In the solid regime, increasing pressure doesn't further compress the matter — it simply enables the closest packed arrangement even at increasing temperatures.
Electron Degeneracy Pressure
P = pressure
h = Planck's constant
me =
mp =
ρ = density
μe = electron/proton ratio
Thus the Pauli Exclusion Principle holds even for supercritical fluids. Monoatomic matter above the critical point isn't constrained by covalent bonds. But when two atoms are forcibly pushed together, the first conflict will be between the outer electrons. If the pressure is greater than the ionization potential of the atoms, the conflict results in the expulsion of electrons, leaving a strong electrostatic repulsion between the positively charged atomic nuclei, and further compression has to fight the Coulomb force. This marks the transition from compressibility to elasticity, which is very different. The Quantum Mechanics term for this effect is electron degeneracy pressure (EDP), though the Pauli Exclusion Principle predated QM, and is not reliant on it.
If the pressure is coming from gravitational loading, it increases with depth, meaning greater compression, and atoms packed closer together. At the threshold for EDP, electrons are expelled, and they have nowhere to go but up, where they will find room between atoms that aren't as tightly packed. Thus the expelled electrons are forced to a higher altitude, leaving positive ions below.
The implication not typically considered is that a charge separation has occurred, creating current-free double-layers (CFDLs) — they are layers of opposite charges, with a powerful electric field between them, but there is no current responding to the field, because something prevents it. In this case, it's gravity & EDP preventing charge recombination.


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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