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The pH of water by QED radiation from Nanobubbles
Self-ionization of the water molecule as the extremely unlikely source of H ions in the pH of water is superseded by the dissociation of water by the QED induced UV radiation produced in nanobubbles
Historically, acid-base chemistry assumes water molecules dissociate into hydrogen and hydroxyl ions through self-ionization:
Self-ionization aside, once the water molecule is dissociated, the recombination of H and OH ions is very rapid. Indeed, the H ion having a lifetime of about 1 picosecond only moves a distance of a few hydrogen bonds. Yet over this time, the concentration of H ions is required to define the steady pH observed in water. Indeed, MD simulations  claim to support self-ionization as a rare breaking of hydrogen bonds where H and OH ions recombine very quickly within tens of femtoseconds. MD stands for molecular dynamics. By self-ionization, the pH of water is required to be defined in the brief transient of the H ion population during recombination.
The MD simulation in support of self-ionization as the rare breaking of hydrogen bonds does not overcome the fact the Boltzmann distribution requires the probability of dissociation to be extremely unlikely. Alternatively, MD can never explain self-ionization because it is contrary to the Boltzmann distribution.
Given that self-ionization is extremely unlikely, nanobubble dissociation is proposed as the source of H ions that define the pH of water. Nanobubbles are nearly spherical < 100 nm air-containing cavities in liquid water. Generally, bubbles collapse by surface tension that increases as the diameter decreases, and therefore nanobubbles are thought to dissolve in a few microseconds. Contrarily, nanobubbles are found to remain stable for hours and even days, defying the expectation of prompt dissolution.
Recently, the stability of nanobubbles is shown  to depend on the charge repulsion of OH ions in the bubble that opposes surface tension, while the H ions form hydronium H[sub]3[/sub]
QED induced UV radiation
Water molecules continually evaporate from the nanobubble wall. In the bubble wall, the water molecules have thermal kT energy, as they are a part of the liquid continuum. But in the EM confinement of the bubble, QM precludes the H and OH ions in the bubble from having the heat capacity to increase in temperature. QM stands for quantum mechanics. Conservation of the thermal energy of the evaporated water molecules therefore proceeds by the creation of non-thermal EM radiation at the TIR mode of the bubble by QED. TIR stands for total internal reflection and QED for quantum electrodynamics.
The Planck energy E of the QED induced EM radiation is, E = hc/λ, where h is Planck’s constant and c the velocity of light.The EM radiation has wavelength λ = 2nd, where n is the refractive index of water vapor, n ~ 1 and d the bubble diameter. For diameters d < 100 nm, the QED radiation is in the UV having a wavelength λ < 250 nm that by the photoelectric effect provides a steady source of H and OH ions. Unlike self-ionization that produces a local transient source of H ions, UV radiation provides a steady source of H-ions over an extended region consistent with pH measurements. The thumbnail shows the absorbance in water for UV at 250 nm is ~ 0.001/cm corresponding to an extended region of about 10 m. See “Nanobubbles in acid-base chemistry,” at http://www.nanoqed.org 2014
Unlike self-ionization where the water molecule is unlikely to dissociate, QED radiation produces a large number of H and OH ions in the nanobubble, but in the small volume the number of recombinations is also very large resulting in a low net charge. Regardless, the Planck energy of QED radiation in the UV produces ion fragments: the light H ions having high velocities are absorbed in the bubble wall to form H[sub]3[/sub]
Summary and Conclusions
1. By QM, nanobubbles under TIR confinement preclude H and OH ions in the bubble from having the heat capacity to increase in temperature to conserve the thermal energy of molecules evaporating from the bubble wall. Because of QM, conservation proceeds by QED creating UV radiation that propagates into the extended surroundings to dissociate water molecules. Given the ubiquity of nanobubbles, QM may be considered to provide water with a source of low level UV to dissociate surrounding water molecules, the H ions of which are detected in pH measurements. The self-ionization of water is therefore an unnecessary requirement in acid-base chemistry.
2. Classical physics always allows water molecules to have the heat capacity to conserve EM energy by an increase in temperature, and therefore bubble wall molecules evaporating into the bubble are mistakenly thought to change the nanobubble temperature. QM differs.
3. By QM, the temperature of H and OH ions in the bubble cannot increase to conserve the thermal energy of evaporating bubble wall molecules. Instead, conservation proceeds by creating steady QED induced EM radiation that dissociates the evaporating wall molecules or is emtted into the water surroundings. For d < 100 nm nanobubbles, continuous UV radiation is produced that dissociates water molecules over an extended region consistent with steady pH measurements
4. Nanobubbles arc characterized by long-lived stability from the QED induced repulsion of OH ions in the bubble opposing the collapse of the bubble by surface tension.
5. The pH of water is the consequence of H ions created by QED induced UV radiation produced in nanobubbles.
 P. L. Geissler, et al., “Autoionization in Liquid Water,” Science 2001, 291, 2121.
 T. Prevenslik, “Stability of nanobubBles by Quantum Mechanics.“ Topical Problems of Fluid Mechanics, Inst. Thermomechanics, Prague, 19-21 February, 2014.