About 600 BC, the Greeks discovered [1] static electricity. Amber rods rubbed with cloth were found to attract feathers, the amber given the name elektron. Shortly thereafter, the Greeks postulated the existence of the atomos, the smallest indivisible scale for matter. In the context of the explanation of static electricity presented in this paper, however, the answer to the question why the rubbed amber rod attracted feathers would await knowledge that came some 2000 years later. This knowledge included Thompson’s discovery of the electron in 1896 that showed that the atom was indeed divisible, in combination with the liberation of electrons by the photoelectric effect discovered by Becquerel in 1839 and explained by Einstein in 1905, culminating with the formulation of QED by Purcell in 1946.

Today, all matter is known [2,3] to contain positively charged particles called protons and negatively charged particles called electrons. In an uncharged atom, the number of protons and electrons balance each other and the atom is neutral. If a neutral atom loses an electron, it has an excess of protons and is positively charged; whereas, if a neutral atom gains an electron, it is negatively charged. We know the rubbing of materials produces static electricity, but the mechanism by which electrons are produced in the rubbing of materials has remained a mystery since the early Greeks.

Static electricity is usually characterized by the of rubbing of cloth against an amber rod, although rubbing of any combination of materials may produce static electricity. Since the early Greeks, the rubbed material that charge positive or negative is given by the tribolectric series, a representative list of which is shown in Table 1. The material that charges positive is the one that is closer to the positive end of the series and the material closer to the negative end is charged negative.

Recently, the work function, which quantifies how readily a material loses electrons, was proposed [4] to explain the tribolectric series. Table 1 shows the work functions [5] of the conductor materials generally increase in the direction of the negative end of the tribolectric series, but for insulators the correlation of the tribolectric series with work function can not be confirmed because of the lack of available data.

Table 1. Tribolectric series and work functions

Generally, it is thought that the mechanism underlying static electricity is mechanical, the electrons physically removed by the rubbing of material surfaces. For example, if pieces of tape with the sticky side of one pressed against the smooth side of the other are quickly pulled apart, the mechanical action is described as the ripping [3] of electrons from one side of the tape by the other. If the work function is the basis of the tribolectric series, the physical removal of electrons would suggest that the work function may be quantified by mechanical energy. But since Einstein, the work function has been defined by the electromagnetic energy necessary to free an electron from the surface of a material by the photoelectric effect. Mechanical removal of electrons is excluded, although the work function may quantify [5] other electromagnetic phenomena such as thermionic and secondary electron emission. Without a doubt, the electromagnetic basis to the work function is unequivocal, and therefore it is reasonable to hypothesize that a mechanical mechanism does not underlie static electricity, a hypothesis that may be tested by comparing the binding energy of electrons and atoms.

Electrons are tightly bound to atoms. Atoms and molecules in most insulator materials are bound to each other by van der Waals forces [6] having typical binding energies of about 0.1 eV; whereas, conductor materials with metal bonds have binding energies at about 3 eV. But metal bonds in the presence of defects break at much lower energy. The mechanical energy necessary to separate a pair of atoms by an atomic diameter may be estimated by ½ s d ³ , where s is the macroscopic yield stress and d is the diameter of the atom. For example, Ni having s ~ 400 MPa and d ~ 0.248 nm gives a separation energy of about 0.02 eV, far less than the 4.97 eV work function. Similar to conductors, atoms and molecules in insulators separate at bond energies less than the work functions. It may therefore be concluded that a mechanical mechanism can not underlie static electricity because rubbing of surfaces whether conductors or insulators produces clusters of atoms and molecules rather than free electrons, the electrons remaining bound to the atoms and molecules as the clusters separate from the rubbed surfaces.

Given that rubbing of materials produces clusters of atoms and molecules - not free electrons - it is difficult to reconcile the fact that static electricity has been observed since the time of the early Greeks unless electromagnetic radiation is somehow produced from clusters of atoms and molecules in the gap between the rubbed materials. If so, static electricity may be readily explained by the electromagnetic radiation producing electrons from the surfaces of the rubbed materials by the photoelectric effect.

The purpose of this paper is to propose that the mechanism that underlies static electricity is electromagnetic - the mechanism called the cavity QED induced photoelectric effect. This electromagnetic mechanism, if eventually proven, would provide a common basis by which diverse areas of electrification may be unified, the areas including steam electricity, contact electrification, flow electrification, atmospheric electricity and lightning, the Leidenfrost phenomenon, sprites, ball lightning, and St. Elmo's fire.

Static electricity by the cavity QED induced photoelectric effect occurs by the Two-step model [7] that comprises contact and separation as illustrated in Fig. 1 (a) and (b), respectively.

Fig. 1 Static electricity: Two-step model

(a) Contact (b) Separation

Fig. 1(a) shows rubbing contact produces clusters of atoms of Materials 1 and 2. Each atom in the clusters contains low frequency IR radiation of magnitude 3 x ½ kT, the average energy of which may be represented by a harmonic oscillator with a broad range of frequencies. The instant of separation is depicted in Fig. 1(b). Briefly, the gap is a high frequency QED cavity, and therefore the low frequency IR emission from each atom in the clusters is suppressed, a condition referred to [8] as inhibited cavity QED. To conserve energy, the inhibited IR energy is promptly absorbed and accumulates to VUV levels in the atoms of the material surfaces forming the gap.

Electrons are not liberated by the photoelectric effect unless the Planck energy of the IR radiation accumulates to the threshold given by the work function of the materials. If the materials have different work functions, the one with the lower work function is the first to liberate electrons and acquire a positive charge, a condition consistent with the proposal [4] that the material in the tribolectric series with the lower work function charges positive and the material with a higher work function charges negative. Fig. 1(b) depicts Material 2 having a work function lower than Material 1. Hence, VUV radiation is shown liberating electrons from Material 2, the electrons donated to Material 1. Material 2 acquires positive charge and Material 1 negative charge.

Static electricity observed in the rubbing of materials, the rubbing comprising a repetitive sequence of the gap between rubbed surfaces undergoing contact and separation is proposed similar to a bubble collapsing and nucleating during ultrasonic vibration in water. The IR radiation from suspended atoms and molecules in both the gap and bubble inhibited by the respective high resonant frequency QED cavities. Nucleation and collapse of bubbles in water is discussed in Appendix A.

The IR radiation inhibited in the cavity QED induced photoelectric effect accumulates to VUV levels as clusters break away from surface of the rubbed materials. Both attached and free clusters are illustrated in Fig. 2.

Fig. 2 Cavity QED induced photoelectric effect - Inhibited IR radiation

Before separation, the attached cluster to the surface of Material 1 emits uninhibited IR radiation, the wavelength l of which exceeds the size of the gap g between the surfaces of the materials, i.e., l >> g. However, at the instant of separating from the surface, the IR radiation from atoms in the free cluster is suppressed by cavity QED, the wavelength l constrained within the confines of the gap g. Assuming a spherical cluster of radius R_o, the inhibited IR energy U_IR is,

(1)

where, Y is the IR energy density, Y ~ N_dof x ½ kT / D ³, k is Boltzmann’s constant, T is absolute temperature, N_dof is the number of degrees of freedom of the atoms or molecules in the cluster, and D is the solid density spacing between atoms or molecules in the cluster, D ~ 0.3 nm.

The momentary suppression of IR radiation from atoms and molecules within the clusters is a loss of EM energy. But energy conservation requires the suppressed EM energy be promptly released to the surrounding space, the energy release taking the form of multi-IR photons that collectively combine to VUV levels. In Fig. 2, the cluster rubbed from Material 1 is shown to move into the evacuated space between the surfaces, the Planck energy E of the EM radiation at a distance R from the center of the cluster acting over the adjacent rubbed surfaces comprised of molecules of dimension D is,

(2)

where, R ~ g /2. The optical band-gap of Material 2 is assumed less than that of Material 1, and therefore the Material 1 is depicted in Fig. 2 to lose electrons and acquire positive charge while Material 2 gains electrons and acquires negative charge.

In the cavity QED induced photoelectric effect, the number N_e of electrons produced depends on the number N_p of photons and the photoelectric yield g_P of electrons per photon,

(3)

Since the released EM radiation is coherent and comprised of multi-IR photons, the number N_p of VUV photons having Planck energy E_VUV may be written,

(4)

Most metals illuminated with visible and ultraviolet [9] light have low electron yields ( g_P < 10^-3 ) while reasonable yields ( g_P < 10^-1) are only obtained with VUV light. Generally, the inhibited IR accumulates to VUV levels and so the photoelectric yield is taken as, g_P < 0.1.

Fig. 3 shows the number N_e of electron charges produced by a single cluster with the multi-IR photons combining to a Planck energy E_VUV ~ 4.9 eV. The radius R₀ is limited to 5 mm because if the evacuated space of thickness D is treated as a 1D QED cavity, the EM resonant wavelength is, l ~ 2D. To suppress most of the EM energy, Fig. A-1 shows l < 20 mm, and therefore D < 10 mm, or the largest cluster that can fit in the 1D space has a radius R₀ < 5 mm. Hence, static electricity by the cavity QED induced photoelectric effect may be upper bound by a 5 mm radius cluster. Taking a yield g_P < 0.1, the electronic charge e N_e ~ 3 nC.

The amount of charge accumulated as a person walks across the floor has been measured [10] to be about 3x10^-8 C per step. Hence, a lower bound of about 10 clusters of the upper bound 5 micron radius clusters are required to produce the observed charge. Actual numbers of clusters may be much be at least 2 orders of magnitude larger because of lower electron yields.

Fig. 3 Static-electrification - Electronic charge and cluster radius

Asymmetric charging [11] occurs if identical materials are rubbed with one stationary and the other moving in such a way that contact takes place between a small area of the stationary material and a larger area of the moving material. The cavity QED induced photoelectric effect predicts the stationary material heated to a higher temperature than the moving material is always charged positive. Clusters of atoms rubbed from the stationary material have higher thermal kT energy than those rubbed from the moving material. As clusters break away from the stationary material, the accumulated Planck energy liberates electrons from the adjacent atoms in the stationary material surface, the stationary material acquiring a positive charge, the moving material acquiring a negative charge. Clusters rubbed from the moving material give the moving material a positive charge. But because of the lower kT energy of the clusters rubbed from the moving material, the number of electrons lost is small compared to number gained from the stationary material, and therefore the moving material acquires a net negative charge.

The work function correlation [4] with the tribolectric series is consistent with the cavity QED induced photoelectric effect. However, because of the sparse work function data it is tempting to consider approximations to the work function based on bulk material properties. Correlation's with atomic, surface, and bulk properties [12] include: atomic number, atomic ionization energy, electronegativity, and surface energy. For example, the electronegativity as the power of an atom in a molecule to attract electrons to it was found to describe roughly the trend in work function, although the deviations from linearity were considerable. Insulator work functions were not correlated.

With regard to insulators, the work function was proposed [13] related to tribolectric charge exchange by Coehn's rule:

However, experiments [14] showed the sign of the tribolectric charge after polishing to depend on the charge of the ZnO face and not the dielectric constant of ZnO and the friction material.

In the cavity QED induced photoelectric effect, the parameter of interest is the photoelectric yield of the material surfaces rather than the work function. That the work function may not be the underlying parameter in the tribolectric series is suggested from multi-IR photon induced photo-emission studies of insulators, the yield [15] found to correlate with the optical band-gap rather than the work function, the band-gap achieved by the accumulation of IR photons. This data supports the notion of IR photons accumulating to VUV levels in the cavity QED induced photoelectric effect.

A preliminary assessment of the cavity QED induced photoelectric effect as the mechanism that underlies static electricity is shown to be tenable. The photoelectric process relies on the fact that the energy loss from the inhibited IR radiation of the atomic clusters is compensated by an increase in Planck energy of the material surfaces. The Planck energy may be estimated by 3 x ½ kT of low frequency IR energy for every atom that separates from material surfaces.The Planck energy in the VUV is sufficient to liberate free electrons.

Work function and photoelectric yield data of insulators is required to confirm the correctness of the cavity QED induced photoelectric effect. This will also confirm which parameter best correlates with the tribolelectric series.

[1]The New Encyclopaedia Britannica, Encyclopaedia Britannica Inc., USA, 1998.

[2]A.D. Moore, Electrostatics and its Applications, John Wiley, 1973.

[3]C.K. Adams, Nature's Electricity, Tab Books inc., Blue Ridge Summit, PA, 1987.

[4]T.B. Jones, Triboelectric Series, WWW Homepage.

[5]CRC Handbook of Chemistry and Physics, CRC Press,1998.

[6]H.C. Ohanian, Modern Physics, Prentice-Hall, 1987.

[7]Z.Z. Yu, K. Watson, Two-step model for contact charge accumulation, J. Electrostat. 51-52 (2001) 319-325.

[8]S. Harouche,J-M Raimond, Cavity quantum electrodynamics, Scientific American (1993) 54-62.

[9]E.W. McDaniel, Collision Phenomenon in Ionized Gases, Wiley, New York, 1964.

[10]N. Jonassen, Charging by walking. Compliance Engineering 18 (2001) 22–26.

[11]N. Jonassen, How is static electricity generated? Compliance Engineering 12 (2001)34-40 .

[12]J. Holzl, F.K. Schulte, H. Wagner, Solid Surface Physics, Springer-Verlag, Berlin,1979.

[13]C.F. Gallo, W.L. Lama, Some charge exchange phenomena explained by a classical model of the work function, J. Electrostat. 2 (1976) 319-325.

[14]J. Halfdanarson, K. Hauffe, Triboelectric effects of Li_2/0- Zinc oxide. Photographic Science and Engineering 23 (1979) 33-37.

[15]W.J. Siekhaus, J.H. Kinney, D. Milam, K.K. Chase, Electron emission from insulator and semiconducor surfaces by multiphoton excitation below the optical damage threshold. Applied Physics A. 39 (1986) 163-166.

(A.1)

where, h is Planck's constant, u = c / l is the bubble resonant frequency, c is the speed of light, and l is the wavelength of the bubble resonance. In a spherical bubble of radius R, the bubble resonance may be considered to have a wavelength l ~ 4R and frequency u ~ c / 4R.

(A.2)

where, E_T = hu / ( exp (hu / kT ) - 1) is the usual temperature dependent Planck energy, k is Boltzmann's constant, and T is absolute temperature. E_G is the temperature independent Planck energy described by EM waves or cavity field modes, the standing waves depending on the bubble geometry G. The Planck energy E_T is observed to converge to kT at wavelengths l > 100 microns as shown at T ~ 300 K in Fig. A-1.

The cavity field modes correspond to standing EM waves having a Planck energy E_G = hu _f, where u _f is the fundamental resonant frequency of the bubble cavity. Since the Planck energy E_G is formed by pairs of harmonic-oscillators on opposing bubble wall surfaces, the ZPE of each harmonic-oscillator in the pair is half of the full Planck energy E_G,

ZPE = ½ E_G = ½ h u _f (A.3)

The ZPE is restricted by cavity QED. Since the bubble resonant frequency u _f varies from VUV to soft X-rays, low frequency ZPE is inhibited by QED from the bubble cavity, u < u _f. Only high frequency ZPE may exist in the bubble cavity, u > u _f .

In the Planck theory of SL, the surface water molecule VUV emission is not in equilibrium with the temperature of the bubble wall. Stimulation of VUV states of the surface molecules at ambient temperature occurs through the ZPE. Consistency [A4] is found with Planck's general blackbody spectrum density r (u ,T ) restricted here for cavity QED by,

where, u > u _f (A.4)

(A.5)

where, Y is the EM energy density, Y ~ 6 x ½ kT / D ³ for a liquid water molecule having 6 DOF and D is the spacing between molecules at liquid density. Figure A-1 shows the energy of the average harmonic oscillator to be concentrated at wavelengths l > 100 mm. Hence, the bubble need not be small to inhibit IR radiation. Since the wavelength l of a standing optical wave in a spherical bubble of radius R is, l ~ 4R, the condition for inhibited IR is R < l / 4 ~ 25 mm.

(A.6)

where, N_p is the number of photons that may be lower bound by the N_m of surface molecules, N_p > N_m ~ 4p R² / D ². If all the available EM energy U_EM inhibited during nucleation is conserved with the Planck energy U_Planck of the surface molecules,

(A.7)

Consider a bubble at T ~ 300 K having a radius R ~ R₀ = 1.4 mm corresponding to surface tension S ~ 0.072 Nt / m. Taking the spacing D = 0.3 nm as representative of water, the EM radiation accumulated in the bubble wall surface molecules in the VUV have a Planck energy E ~ 120 eV. Hence, the Planck energy is more than sufficient to promptly dissociate water molecules on the bubble surface to form excited hydroxyl states *OH. Since Ar atoms in the atmosphere dissolve in the water, Ar*OH excimers are produced from the *OH excited states on the bubble wall in the high pressures that accompany bubble collapse. In this arrangement, the light emission observed in bubble collapse is caused by decomposition of the Ar*OH excimers [A7] upon the pressure rarefaction wave, the excited *OH states produced [A8] by inhibited IR by cavity QED.