charge-dipoleaccelerationofpolargas ...the high electrostatic charge of lightning balls could play a...

Hindawi Publishing CorporationJournal of NanomaterialsVolume 2010, Article ID 654389, 38 pagesdoi:10.1155/2010/654389

Research Article

Charge-Dipole Acceleration of Polar GasMolecules towards Charged Nanoparticles: Involvement inPowerful Charge-Induced Catalysis of HeterophaseChemical Reactions and Ball Lightning Phenomenon

Oleg Meshcheryakov

Wing Ltd Company, 33 French Boulevard, 65000, Odessa, Ukraine

Correspondence should be addressed to Oleg Meshcheryakov, [email protected]

Received 27 July 2010; Revised 6 November 2010; Accepted 10 November 2010

Academic Editor: Donglu Shi

Copyright © 2010 Oleg Meshcheryakov. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.

In humid air, the substantial charge-dipole attraction and electrostatic acceleration of surrounding water vapour moleculestowards charged combustible nanoparticles cause intense electrostatic hydration and preferential oxidation of these nanoparticlesby electrostatically accelerated polar water vapour molecules rather than nonaccelerated nonpolar oxygen gas molecules.Intense electrostatic hydration of charged combustible nanoparticles converts the nanoparticle’s oxide-based shells into thehydroxide-based electrolyte shells, transforming these nanoparticles into reductant/air core-shell nanobatteries, periodically short-circuited by intraparticle field and thermionic emission. Partially synchronized electron emission breakdowns within trillions ofnanoparticles-nanobatteries turn a cloud of charged nanoparticles-nanobatteries into a powerful radiofrequency aerosol generator.Electrostatic oxidative hydration and charge-catalyzed oxidation of charged combustible nanoparticles also contribute to a self-oscillating thermocycling process of evolution and periodic autoignition of inflammable gases near to the nanoparticle’s surface.The described effects might be of interest for the improvement of certain nanotechnological heterophase processes and to betterunderstand ball lightning phenomenon.

1. About the Possible Magnitude and Polarity ofa Net Electrostatic Charge of Ball Lightning

Despite numerous attempts, including the most recent ones[1–7], an adequate theoretical and experimental simulationof ball lightning still remains incomplete. At the same time, asimple analysis of the numerous witness descriptions of thisphenomenon [8, 9] can provide us with useful information,in particular, concerning the possible magnitude and polarityof a net electrostatic charge of lightning balls. Some witnessesdescribed a strong attraction of their hair towards lightningballs flying in immediate proximity to them (at distances ofabout two-three feet). It is interesting that such a strictlydirected attraction of human hair to lightning balls withdiameters of ∼10–20 centimetres was repeatedly observedby different witnesses indoors [9]. Our own experience of

experimental work, both with highly charged water-basedartificial clouds and with megavoltage equipment, shows thatan attraction of human hair towards such highly chargedobjects becomes apparent when an average electrostaticintensity reaches ∼1-2 kV/cm. Therefore, in the above cases,one can assume that a potential difference between the visiblesurfaces of lightning balls and the witnesses’ hair could beat least ∼60–120 kV, and so, a net electrostatic charge ofsuch lightning balls could be at least ∼1 microcoulomb.The most probable polarity of these lightning balls wasnegative with respect to the grounded witnesses. Severaldescriptions from other witnesses of ball lightning [9] showthat lightning balls can sometimes relatively uniformly andslowly fall from thunderclouds, only appreciably acceleratingdownwards when approaching the earth’s surface. Thissudden acceleration, which takes place not far from the

2 Journal of Nanomaterials

earth’s surface, and the lightning balls’ final elongation to theform of an ellipse before they touch the earth’s surface, canindirectly indicate that these balls were charged negativelyrather than positively—the earth’s surface is almost alwayspositively charged with respect to the base of thundercloudsduring a thunderstorm.

There are also several detailed descriptions of directobservations of a relatively low-temperature process of balllightning formation, that is, ball lightning formation withouta previous visible stroke of normal lightning [8, 9]. Inparticular, such ball lightning formation was repeatedlyobserved on grounded metal objects, for example, oncast-iron and steel pins of previously destroyed pin-typeinsulators that were found on pylons of old inoperativeelectric lines [8, 9]. During a thunderstorm, these groundedrusty pins could probably generate invisible positive stream-ers, simultaneously electrostatically spraying the positivelycharged iron/carbon-based aerosol particles. Such an intenseselective corrosion process accompanied by electrosprayingof combustible particles from relatively cold corona-formingmetal emitters along with a synchronous local generation of awater gas-based reducing atmosphere could be named “field-assisted metal dusting corrosion” because of its high physicalsimilarity to ordinary metal dusting corrosion processes [10–16]. At this point, however, it is only important to notethat a cloud of the unipolar charged combustible nano-ormicroparticles, which are possibly produced in this high-voltage corrosion-electrospraying process, could be a mate-rial basis of lightning balls, generated from the groundedconductors during thunderstorms, and probably such light-ning balls could be charged positively rather than negatively.

The positive polarity of the charged lightning ballsgenerated from grounded conductors can also explain theirtypical horizontal flying trajectories at relatively low heightsof about 0.5–2 metres above the ground.

In these cases, the identical polarity of the chargedlightning balls and the ground might be responsible for aCoulomb repulsion of these balls from grounded objects.Having analyzed various witness observations, we canassume the following.

(a) The net electrostatic charge of lightning balls can beboth positive and negative.

(b) Sometimes lightning balls can be exposed to a partialdischarging due to corona or spark discharges fromtheir surface; the discharging processes can perhapsreduce the magnitude of an initial electrostatic chargeof lightning balls.

(c) Sometimes a corona discharge from the surfaceof lightning balls can cause a corona charging ofneighbouring low conducting objects with a polaritysimilar to the polarity of these balls; such a processcan cause a subsequent immediate electrostatic repul-sion these balls from neighbouring low conductingobjects.

(d) A net electrostatic charge of the lightning balls, whichattract human hair at distances of about two-threefeet, can perhaps reach at least ∼1 microcoulomb.

(e) The lightning balls that are frequently describedas avoiding contact with grounded conductors andmaintaining their approximately constant low flyingheights above the ground can be charged with thesame polarity as the ground (i.e., positively ratherthan negatively during thunderstorms), consequentlythe force of electrostatic repulsion of these balls fromthe ground and grounded objects at short distancescan partially compensate for their weight, contribut-ing to a buoyancy of these balls; a net electrostaticcharge of such relatively long-living lightning ballswith typical diameters of ∼10–20 centimetres can bemuch higher than it was supposed in [17]; thus, themagnitude of the net electrostatic charge of lightningballs avoiding contact with grounded conductors canprobably also reach at least ∼1 microcoulomb, beingin fact limited by a voltage of corona ignition fromtheir surface.

It was repeatedly assumed, for example in [18, 19], thatthe high electrostatic charge of lightning balls could playa major role in the existence of ball lightning. Equally weshare this opinion, and in the present paper, we will examinethe possible role electrostatic charge plays in the life of balllightning, still assuming that ball lightning is a cloud ofcombustible aerosol particles that are exposed to a slow,predominantly electrochemical oxidation [20]. Such a pro-cess of the electrochemical oxidation of nano or submicronaerosol particles converts these combustible particles intoaerosol batteries—further, for short “nanobatteries”—thatare periodically (and perhaps with very high frequencies)short-circuited by intra-particle breakdowns.

According to [20], we can assume the following.

(a) The aerosol particles-batteries can exist either in theform of nano or submicron aggregates, or in theform of nano or submicron core-shell capsules, or ina more realistic combination of these two simplesttypes, that is, in the form of aerosol aggregatesconsisting of mixed nano or submicron core-shellparticles.

(b) The aerosol particles-batteries can contain at leastone reductant component, for example, a metal orcarbon-based component, and at least one electrolytecomponent.

(c) These aerosol particles can use either an internalcompact oxidant or external oxidant from ambientair, that is, oxygen gas and/or water vapour.

(d) During the electrochemical oxidation the aerosolparticles automatically turn into aggregated or core-shell structured aerosol nanobatteries periodicallyshort-circuited by the intra-particle breakdowns dueto both field and thermoionic electron emissiontaking place within and on the surface of particles-batteries.

(e) The short-circuited aerosol nanobatteries are freemagnetic dipoles, and so they can be exposed toan intense mutual magnetic dipole-dipole attraction,

Journal of Nanomaterials 3

forming ball-shaped clouds with high magneticpolarizability.

(f) The non-short-circuited aerosol nanobatteries arefree electric dipoles with substantial electric dipolemoments, and so they can be exposed to an intensemutual electric dipole-dipole attraction, formingball-shaped self-assembling clouds with high electricpolarizability (Figure 1).

(g) The repeating processes of the short circuits withinthe separate aerosol nanobatteries can be partiallyor totally synchronized within a ball lightning cloud;such repeating synchronized collective short circuitsof trillions of nanobatteries can generate powerfulelectromagnetic radiation, which could explain therepeatedly observed cases of red heat of incandescentbulbs’ filaments switched off from power sources;such a temporary red heat of the filaments repeatedlywas distantly induced during the slow flying of balllightning at distances of about one-two feet from theswitched off bulbs [9].

When discussing the simplest possible processes of spon-taneous formation of the short-circuited aerosol nanobat-teries from combustible aerosol nanoparticles in a stormatmosphere, it was assumed in [20] that a high concentrationof water vapour in the air can significantly modify themechanism of oxidation of many metal aerosol nanopar-ticles, converting a normal process of direct oxidationof these nanoparticles by neutral oxidizing species intothe predominantly electrochemical, that is, ion-mediatedoxidation process in this highly humid atmosphere. Duringsuch an electrochemical oxidation, water vapour from humidair contributes to the formation of the hydrated, hydroxideor oxyhydroxide-based, thermolabile porous layers on thesurface of metal nanoparticles rather than contributing to theformation of more thermostable layers of mixed anhydrousmetal oxides [19], normally growing on the surface ofnanoparticles either at very high, dehydrating temperaturesor only in dry oxygen [21–26].

In humid air, a quick diffusion transfer of ions can takeplace through the hydroxide-based electrolyte layers growingon the surface of the nanoparticles due to their oxidation bywater vapour. The quick processes of the diffusion of ionizedoxidizing species, such as ions OH−, O2−, CO32−, that easilymigrate through the dynamic surface electrolyte layers of themixed hydroxides towards the metal core of the nanoparticle,can considerably prevail above the much slower alternativeprocesses of the inward diffusion of neutral oxidizing species,such as molecular O2, H2O, CO2, or neutral radicals like OH.

Similarly, the quick processes of the diffusion of ions ofmetal core, such as Fe2+, Fe3+, Fe(OH)+, or Fe(OH)2+, tothe nanoparticle surface also can significantly prevail abovemuch slower alternative processes of diffusion of neutralatoms from the metal core to the surface of the nanoparticle.

Thus, at relatively low temperatures, while electrolytelayers growing on the surface of metal nanoparticles remainthermostable, a process of the water vapour -inducedelectrochemical oxidation of combustible nanoparticles canbecome a most preferable process of their oxidation in humid

air because of the possibility of the quick intra-particletransport of ions, and particularly because of the possibilityof the quick transport of ionized oxidizing species throughthe hydrated surface electrolyte layers towards oxidable coresof the combustible nanoparticles.

It seems that in addition to high air humidity anotherextremely important complementary condition is necessaryin order that the process of electrochemical oxidation ofcombustible aerosol nanoparticles can substantially prevailover the alternative process of their normal oxidation by neu-tral oxidizing species from ambient air. We suppose that sucha complementary condition, radically changing the processof oxidation of combustible nanoparticles in humid air, canbe a high electrostatic charge of these nanoparticles. Furtherit will be shown how and why a presence of electrostaticcharges on combustible aerosol nanoparticles can make animportant contribution to their preferential oxidation bywater vapour molecules but not by much more numerousoxygen gas molecules in humid air that is, how and why elec-trostatic charges distributed on the surface of combustibleaerosol nanoparticles can become powerful selective catalystsof water vapour-induced oxidation of these nanoparticles.

2. Electrostatic Hydration of Atmospheric Ionsand Charged Aerosol Nanoparticles

As is well known, in normal, humid air, intense charge-dipole interaction between atmospheric ions and highlypolar molecules of water vapour causes immediate hydrationof the ions. A hydrated ion includes a central ion and awater shell normally consisting of several H2O molecules.The hydrated ions are extremely stable because of the hugeelectrostatic energy which keeps polar water moleculesin immediate proximity to the central ion (the typicalenergies of complete dehydration of atmospheric ions canbe ∼several electron-volts). Therefore the hydrated ions area standard form of gaseous ions in the lower troposphere[8, 18, 27]. The charge-dipole interaction between gaseousions and surrounding polar gas molecules is a powerful andlong-range attraction, and intense hydration of gas ionscaused by the ion-dipole attraction finds useful applications,for example for an effective operation of the Wilson chamberwhere gaseous ions generated by ionizing radiation act ascondensation nuclei in order to visualize tracks of ionizingparticles. In this well known case, hydrated or alcohol-solvated gaseous ions quickly turn into water or alcoholbased charged nanoparticles. These charged nanoparticlesquickly grow into micrometre-sized droplets due to theirfurther intense electrostatic hydration/solvation undersupersaturation conditions.

Electrostatically charged aerosol nanoparticles, especially“small” nanoparticles with characteristic sizes of aboutseveral nanometres, almost do not differ from gaseousions in their ability to attract surrounding polar gasmolecules, including water vapour molecules, from ambientatmosphere due to the powerful long-range charge-dipoleinteraction. In humid air, a surplus electrostatic charge ofsuch nanoparticles is almost always localized to trapping


−C−

−C−

−C−

−C−

−C−

−C−

−C−

−C−

−C−

−C−

−C−

−C−

−C−

+Ag2O

+

+Ag2O

+

+Ag2O

+

+Ag2O

+

+Ag2O

+

+Ag2O

+

+Ag2O

+

+Ag2O

+

+Ag2O

+

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+

+Ag2O

+

+Ag2O

+

+Ag2O

+

−C−

+Ag2O

+

−C−

+Ag2O

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−C−

+Ag2O

+

−C−

+Ag2O

+

−C−

−C−

+Ag2O

+

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−C−

+Ag2O

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−C−

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−C−

+Ag2O

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+Ag2O

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−C−

+Ag2O

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+Ag2O

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−C−

+Ag2O

+

−C−

−C−

−C−

−C−

+Ag2O

+

+Ag2O

+

+Ag2O

+CaSO4

+CuO

+

← Cu(OH)2 nanoporous surface layer← hydrated thermolabile dynamic porous surface layers of copper hydroxide and copperhydroxo-carbonate are the interphase electrolyte substances, which contribute to the

preferential electrochemical mechanism of air oxidation of the soot carbon nanoparticles

+

+

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+

+

−−−−−−−−−−−−−

← AgOH nanoporous surface layer

Between spontaneously aggregated soot carbon smoke nanocomponents and silver oxide smoke

nanocomponents can proceed by way of an electrochemical mechanism. forming C/Ag2O

nanobatteries short-circuited by surface discharges.

Subsequent high-exothermal intra-particle reactionsC + Ag2O→ CO + Ag −79 kJ or

C + 2Ag2O→ CO2 + 4Ag −331 kJ

Natural molten or hydrated electrolyte nanocomponents of these nanobatteries can consist of:

(1) the smoke nanoparticles of the evaporated and then co-condensed carbonate or sulphate fillers,

commonly applied in arc-resistant plastic (phenol-formaldehyde) insulation;

(2) hydrated surface layers of silver hydroxide AgOH spontaneously formed on a fresh surface of the

Ag2O smoke nanoparticles in humid air.

An alternative reaction between soot carbon CuO smoke nanocomponents:

C + 2CuO → CO2 + 2Cu− 63.5 kJ → 2Cu + O2 → 2CuO-330 kJ

K2CO3

K2CO3 K2CO3

K2CO3

K2CO3

K2CO3

K2CO3K2CO3

K2CO3

K2CO3 K2CO3

K2CO3 K2CO3

K2CO3 K2CO3

K2CO3

K2CO3 K2CO3 K2CO3

K2CO3K2CO3

K2CO3 K2CO3 K2CO3

K2CO3 K2CO3

K2CO3

K2CO3

CaCO3

The soot carbon smoke nanoparticles and silver oxide smoke nanoparticles. and also composite

two-component C/Ag2O nanoparticles, can sometimes be co-formed as a result of a high-power electric arc

discharge within electrocontact equipment.

Figure 1: electrostatic fields and the high initial concentration of aggregated aerosol nanoparticles-nanobatteries facilitate electrostaticaggregation of individual nanobatteries and automatic conversion of these composite aerosol aggregates to microscopic nanoparticle-based high-voltage generators. Ball lightning can contain some hundreds of billions of individual nanobatteries per cubic centimetre.Every such individual nanobattery is an electric dipole and every short-circuited individual nanobattery is also a magnetic dipole. If theinitial concentration of the aerosol nanobatteries is high enough, these nanobatteries can spontaneously form metastable micrometre-sizedaerosol chains aggregates due to the mutual electrostatic dipole-dipole attraction. However, an external electrostatic field, for example athunderstorm electrostatic field, can modify this self-assembling process. The electrostatic aggregation of the nanobatteries enables theperiodic formation of relatively long electric circuits consisting of many nanobatteries temporarily connected in series. The micrometre-sized chain aggregates, which contain only ten thousand individual particles-nanobatteries, can locally generate a ten kilovolt voltage withcorresponding macroscopic spark discharges. In particular, the aggregated composite aerosol nanobatteries can be spontaneously formedfrom soot aerosol nanoparticles-nanoanodes and metal oxide oxidant nanoparticles-nanocathodes. Unipolar charged aggregated aerosolnanobatteries consisting, for example, of the soot carbon-reductant nanoparticles and CuO oxidant nanoparticles (or also of the soot carbonreductant nanoparticles and Ag2O or PdO oxidant nanoparticles) could be one of the most probable components of lightning balls frequentlygenerated from electrical equipment during thunderstorms.

sites on the nanoparticles surface (in the form of either oneor several adsorbed hydrated ions), that is, very close tosurrounding polar gas molecules.

If the charged nanoparticles are conducting, surpluselectrostatic charges can migrate around their surface ina random manner. In addition, both the conducting andnonconducting charged aerosol nanoparticles can freely andirregularly revolve on their axes due to continuous stochasticBrownian collisions with surrounding gas molecules. In thiscase, a time-average density of surplus electrostatic chargeon the nanoparticle surface can be practically equivalent tothe time-average charge density on the surface of the same

charged nanoparticle whose surplus electrostatic charge islocalized in its centre that is, the surplus electrostatic chargeis quasidistributed on the surface of the nanoparticle.

One way or another, it is very likely that the surpluscharges distributed on the surface of the hydrophobic orhydrophilic nanoparticles will make a major contribution totheir local or total surface hydration in humid air due tothe powerful charge-dipole attraction of surrounding polarmolecules of water vapour, which is very similar to thehydration of atmospheric ions mentioned above.

In fact, in this case the charge-dipole attraction ofwater vapour molecules towards the charged surface of the


nanoparticle plays the role of a powerful electrostatic waterpump.

If the charged nanoparticle is cold enough, the electroad-sorbed water molecules can strongly hold on to the coldcharged surface of the nanoparticle.

If the charged nanoparticle is heated to a high enoughtemperature, the water vapour molecules previously elec-troadsorbed on the charged surface of this nanoparticle canbe thermally desorbed when heating.

If the electroadsorbed water molecules are not consumedon the surface of the cold charged nanoparticle, for exampledue to some possible surface reactions, the surface of thecharged nanoparticle will remain highly hydrated till thenanoparticle is cold enough.

If the charged nanoparticle consists of a substance thatcan be oxidized by water vapour at a given temperature, thewater vapour-induced oxidative reactions will inevitably takeplace on the surface of such a charged nanoparticle.

In many cases, during water vapour-induced oxidationof combustible nanoparticles, for example metal nanopar-ticles, a complete cascade of the primary and secondaryoxidative reactions accompanying the water vapour-inducednanoparticle oxidation can be highly exothermal, and so,because of the series of such highly exothermal oxidativereactions, a temperature of the charged “electrohydrated”nanoparticle will grow to some limiting value, while theelectroadsorbed water vapour molecules will be subject tothermal desorption from the heated nanoparticle surface,despite the continuous functioning of the “electrostatic waterpump”. The thermal desorption of the water moleculeswill reduce the rate of the water vapour-induced oxidativesurface reactions, consequently the charged nanoparticlewill quickly cool, and so the process of the electrostatic,charge-dipole adsorption of the water vapour molecules willrecommence. Again, the rate of the exothermal oxidativereactions will grow, and it will again cause the growth oftemperature of the charged nanoparticle and so on. Thiscyclical oxidative process will repeat until the combustiblecharged nanoparticle is completely oxidized. Probably afrequency of such a self-oscillating oxidative process mightbe very high, as possible rates of heating/cooling of thenanoparticles are extremely high.

Clearly, a balance between the competing processes of theelectrostatic oxidative adsorption of water vapour moleculeson the surface of the charged nanoparticle and thermaldesorption of water molecules from this surface can beachieved either in a mode of a synchronous running ofboth these processes, or in the self-oscillating mode of asuccessive alternation of these processes, or in a combinationof these two modes. It seems, however, that the self-oscillating mode of the successive alternation of the processesof the electrostatic oxidative adsorption of the water vapourmolecules on the surface of the charged nanoparticle andtheir thermal desorption from this surface would be oneof the most probable modes. The additional reasons forthe high probability of such a self-oscillating mode ofwater vapour induced oxidation of combustible chargednanoparticles will be discussed in the next section.

3. The Mechanisms and Products of WaterVapour-Induced Oxidation of CombustibleNanoparticles Radically Differ from theMechanisms and Products of Their Oxidationby Oxygen Gas

At least two main gas oxidants with substantial partial pres-sures are available in the air to oxidize combustible aerosolnanoparticles, irrespective of whether these nanoparticles areelectrostatically charged, and consequently, they can activelyelectroadsorb polar molecules of water vapour from ambientair, or these nanoparticles are electrostatically neutral, andconsequently, they will be much more indifferent to sur-rounding water vapour.

These two main atmospheric oxidants are the following:

(a) oxygen gas, O2, with a mole fraction of oxygenmolecules in the air at Sea level, nO, ∼0.21 (i.e., ∼0.21 mol of oxygen gas per one mol of air),

(b) water vapour, H2O, with a mole fraction of watermolecules, nW , ranging in the air at sea level between∼0.002 (at very low air temperatures, in particular,in Antarctica) to ∼0.01-0.02 (at normal summertemperatures in temperate latitudes), to ∼0.03 airhumidity maximum (in the tropics or during sum-mer thunderstorms in temperate latitudes).

In this paper, we will use the term “humid air” for normalair atmosphere, where a mole fraction of molecules of watervapour, nW , ranges from 0.01 to 0.03 mol of water vapour perone mol of air.

Thus, the term “humid air” will be in fact equivalent tothe term “normal air”, as the humidity of such “humid air” istypical not only for most thunderstorms, but also practicallyfor any summer weather.

In this paper, we also conditionally use the term“combustible nanoparticles”, which requires a more precisedefinition. This term is used by us to denote aerosolnanoparticles or substrate-integrated/substrate-precipitatednanostructures consisting of condensed materials, which areable to be oxidized by surrounding molecules of both oxygengas, and water vapour, irrespective of the specific mechanism,rate and optimal temperature of such oxygen-gas or watervapour-induced oxidation.

And so the term “combustible nanoparticles” can be,in particular, applied to aerosol nanoparticles or substrate-integrated/substrate-precipitated nanostructures consistingof the overwhelming majority of metals, metalloids, sulfides,hydrides, carbides, phosphides, nitrides, silicides, borides,lower oxides, many organic compounds, particularly unsat-urated organic compounds, many polymer and biopolymerstructures. A lot of carbon-based nanoparticles, for examplesoot nanoparticles, fullerenes, or carbon nanotubes can alsobe considered as “combustible nanoparticles”, because theycan be theoretically oxidized by both surrounding oxygengas molecules and/or water vapour molecules. Thus, in thispaper, a wide range of nanoparticles will be conditionallyconsidered as “combustible nanoparticles” in the aboveaspect.


The mechanisms of oxidation of combustible aerosolnanoparticles by each of the two competing atmosphericoxidants are radically differing. As mentioned above, reac-tions of the dry oxygen oxidation of many combustible(e.g., metal or metalloid) aerosol nanoparticles can givereaction products in the form of solid or molten layers ofmixed oxides, growing on the surface of the nanoparticlesduring the process of their oxidation. Alternatively, reactionsof oxidation of the combustible aerosol nanoparticles bymolecules of pure water vapour usually give simultaneouslytwo types of different reaction products:

(a) solid reaction products in the form of the more orless hydrated, more or less thermostable, more or lessporous metal hydroxide shells on the surface of thenanoparticles, and in addition,

(b) combustible gases, in particular, hydrogen gas, whenoxidizing the nanoparticles of the great number ofreactive metals or metalloids, for example, when oxi-dizing the nanoparticles of such different substancessuch as aluminium, iron, tungsten, molybdenum,zirconium, calcium, cadmium, and silicon

As an example, let us compare the reaction products synthe-sized when oxidizing the silicon based aerosol nanoparticleseither in dry oxygen, or in pure water vapour, or in humidair.

Aerosol nanoparticles that consist of pure silicon can beoxidized in dry oxygen to generate nanolayers of the mixedsilicon oxides growing on their surface

Si(nanoparticle core) + O2

= SiO2(surface nanolayer) (dielectric).(1)

2Si(nanoparticle core) + O2

= 2SiO(surface nanolayer)(volatile combustible dielectric)(2)

At high temperatures (∼700–1300◦C), either in pure watervapour or in humid air the silicon aerosol nanoparticles canbe oxidized to generate growing surface layers of the mixeddielectric silicon oxides plus the evolved hydrogen gas

Si(nanoparticle core) + 2H2O(vapour)

= SiO2(surface nanolayer) (dielectric) + 2H2 ↑,(3)

SiO(surface nanolayer) + H2O(vapour)

= SiO2(surface nanolayer) (dielectric) + H2 ↑ .(4)

At relatively low temperatures, in humid air products of thewater vapour-induced oxidation of silicon nanoparticles caninclude the evolved hydrogen gas and mixed layers of silicicacids, growing on the nanoparticles surface instead of mixedanhydrous silicon oxides. These dynamic porous surfacenanolayers can consist of either metasilicic acid H2SiO3,orthosilicic acid H4SiO4, disilicic acid H2Si2O5, or pyrosilicicacid H6Si2O7, or of the mixed silicic acids. Such hydrated

surface nanolayers are water-soluble electrolytes with arelatively low thermal stability and low ionic conduction,which, nevertheless, can probably make some contributionto the process of low temperature electrochemical oxidationof silicon nanoparticles [20]:

Si(nanoparticle core) + H2O(vapour) + O2

= H2SiO3(water-soluble volatile electrolyte

),

(5)

SiO2(surface nanolayer) + H2O(vapour)

= H2SiO3(water-soluble volatile electrolyte

).

(6)

Silicon-containing aerosol nanoaggregates, which in addi-tion to nanoparticles of pure silicon contain some mineralnanocomponents, such as co-aggregated nanoparticles ofeither NaOH, or KOH, or Ca(OH)2, or Ba(OH)2 canbe co-condensed from the plasma-evaporated silicate oraluminosilicate minerals in a carbon monoxide reducinglocal atmosphere, which is almost identical with the processdescribed in [19].

In humid air, products of the water vapour-inducedoxidation of such silicon containing aerosol nanoaggregates,can include evolved hydrogen gas and surface nanolay-ers of thermostable water-soluble and/or molten silicatebased electrolytes, automatically forming silicon/air core-shell nanobatteries with silicon core, silicate electrolyte shelland external air oxidant

Si(nanoparticle) + 2NaOH(mineral nanoimpurity) + H2O(vapour)

= Na2SiO3(electrolyte

)+ 2H2 ↑,

(7)

Si(nanoparticle) + 2KOH(mineral nanoimpurity) + H2O(vapour)

= K2SiO3(electrolyte

)+ 2H2 ↑ .

(8)

Thus, the described above example of the possible alternativepathways of the dry oxygen and humid air-induced oxidationof the silicon or silicon-based nanoparticles illustrates a sim-ple fact: in humid air, reactions of oxidation of combustibleaerosol nanoparticles by water vapour frequently can beaccompanied by an evolving of combustible gases, most oftenhydrogen gas. Such an evolving of combustible gases can takeplace through the process of water vapour induced oxidationof very different nanoparticles. Naturally, this water vapour-induced gradual evolving of the combustible gases on thenanoparticle surface in turn can be accompanied by theirperiodical spontaneous ignition in humid air.

4. Partially Synchronized Collective Processesof Electrostatic Oxidative Hydration ofCombustible Nanoparticles, Evolution, andAutolgnition of Combustible Gases andGeneration of Electromagnetic Radiation in aCloud of Unipolar ChargedNanoparticles-Nanobatteries

Within a small cloud of predominantly unipolar chargedred-hot nanoparticles-nanobatteries, that is, within ball


lightning, there are several potential reasons for the con-tinuous or repeating processes of spontaneous ignition ofevolved combustible gases. For example, such a spontaneousignition of combustible gases can occur due to the repeatingcollective discharge processes of short circuits taking placewithin and on the nanoporous surface of the aggregatedaerosol nanobatteries. On the other hand, such repeatingprocesses of auto-ignition of the combustible gases canoccur due to contact of the evolved gases with a fractionof micrometre-sized permanently red-hot aerosol particles—“permanent aerosol igniters”—that in turn were previouslyheated by the preceding intracloud exothermal oxidativereactions, including for example oxygen gas-induced oxida-tive reactions; these substantially slowed oxygen-inducedoxidative reactions can still proceed in humid air on arelatively low-hydrated surface of a fraction of minimallycharged or uncharged particles co-aggregated with highlycharged particles in order to form composite charged aerosolaggregates, perhaps constituting ball lightning.

It would be reasonable to assume that if ball light-ning really is a cloud of charged combustible particles-nanobatteries subjected to slow, predominantly electro-chemical oxidation, this cloud most probably contains anextremely polydisperse ensemble of highly aggregated andvariously charged particles. One hypothetical fraction ofaerosol particles constituting ball lightning could includenano or submicron particles positively charged with pos-sible charge limits of ∼1 up to ∼10 surplus elementarycharges per one nano/submicron particle. Another fractionof aerosol particles, which initially form ball lightningcloud, could include nano or submicron particles negativelycharged with the same charge limits. Gradual electrostaticaggregation of the first and second aerosol fractions canresult in gradual mutual recombination of opposite chargeswithin ball lightning. As mentioned above, the positiveand negative charges are substantially unbalanced in balllightning, totally generating a net electrostatic charge ofball lightning that can reach ∼0.1–1 microcoulomb. Athird hypothetical fraction of combustible aerosol particlesconstituting ball lightning could contain minimally chargedor neutral nano-, submicron, or micrometre-sized aerosolparticles, which can be aggregated in the form of chains[19] by both a charge-dipole and dipole-dipole electrostaticinteraction. A fourth fraction of aerosol particles constitutingball lightning could include relatively large, micrometre-sized highly charged particles, which play the role of localelectrostatic collectors precipitating numerous surroundingchain aerosol aggregates consisting of minimally charged orpolarized nano- and submicron particles. A large surfaceof such an aerosol collector can be charged with tens oreven hundreds of surplus elementary charges. These charges,that is, adsorbed hydrated ions, relatively evenly distributedon the surface of the micrometre-sized particles, are localcentres of intense attraction of the surrounding polarizedchain aerosol aggregates. Electrostatic precipitation of theoppositely charged chain nanoaggregates radially directed tothe surface of the micrometre-sized particles-collectors, cancontribute to a formation of the sea—urchin/hedgehog-likestructures, such as those described in [6].

Surplus charges, distributed on the surface of themicrometre-sized particles-collectors, are centres of elec-trostatic attraction not only for surrounding chain aerosolnanoaggregates but also for surrounding polar molecules ofwater vapour. Therefore, the highly charged surface of suchmicrometre-sized particles can play the role of a catalyticsurface where the combustible nano or submicron particlesconstituting chain aggregates will consecutively react withelectroadsorbed (and locally electrostatically accelerated)molecules of water vapour (Figure 2). In this case, electro-static charges permanently fixed on the surface of the highlycharged particles-collectors in the form of adsorbed ions,such as H3O+(H2O)n, OH−(H2O)n or O2− (H2O)n, can playthe role of selective catalysts of local water vapour inducedoxidation of surrounding nano- or submicron combustibleparticles, either oppositely charged or only polarized.

So, during the electrostatic precipitation of the chainsof the aggregated nano- and submicron aerosol particleson the charged surface of the large particles collectors, thecombustible particles from these chains can be exposed tointense water vapour-induced oxidation, locally catalyzed bythe surplus electrostatic charges fixed on this surface. Sucha scenario of the water vapour induced oxidation of theminimally charged or even neutral but polarized combustiblenanoparticles really could require the presence of the fourthhypothetical fraction consisting of the micrometre-sizedhighly charged aerosol particles—natural catalytically activeelectrostatic aerosol collectors of both water vapour andsurrounding combustible nanoparticles.

Alternatively, surplus electrostatic charges, capable ofcatalyzing the water vapour induced oxidation of com-bustible aerosol nanoparticles, could move along chainaggregates, step-by-step contributing to the consecutiveoxidation of nanoparticles within chains. Such consecutivecharge-catalyzed water vapour-induced oxidation of aggre-gated combustible nanoparticles by a stepped shift of surpluscharge along the chain of the aggregated nanoparticles couldresemble the process of Bickford’s fuse combustion (Figures3, 4).

Clearly, if characteristic sizes of a combustible particle areof ∼10–1000 nm or greater, unipolar surplus charges (i.e.,adsorbed hydrated ions) distributed on the surface of suchan aerosol particle can form only local mobile surface spotsof extremely high electrostatic intensity.

The charge-dipole interaction will cause intense attrac-tion and local acceleration of the surrounding water vapourmolecules to these highly charged surface spots, conse-quently such intense electrostatic hydration of the chargedspots on the surface of a combustible particle will resultin active water vapour induced oxidation of these smallcharged sites of the surface of a combustible particle. Beingthermally activated during the oxidative process, the surpluselectrostatic charges (adsorbed hydrated ions) can jump onthe surface of the heated particle in a random manner.And so, this consecutive electrostatic water vapour induced“charge spot corrosion” of the submicron- or micrometre-sized particles step-by-step can oxidize even such largecharged particles-particularly when their surface is highlyhydrophilic and so locally electroadsorbed water vapour


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Micrometre-sized highly charged aerosol particlesare natural electrostatic collectors of numeroussurrounding chain aggregates consisting ofpolarized/charged combustible nanoparticles.Water vapour molecules, substantially acceleratedby a charge-dipole attraction, attack both the chargednanoparticles and also uncharged nanoparticleslocalized in immediate proximity to bound chargeson the surface of the micrometre-sized highlycharged particle

Figure 2: Radius of the nanoparticle surface zone, most intensively attacked by surrounding electrostatically accelerated water vapourmolecules, can reach ∼1-2 nm in immediate proximity to the site where the surplus charge (i.e., adsorbed hydrated ion) is located at thismoment.

molecules can be next distributed on all the surface of theparticle by wetting (Figure 5).

Thus, a water vapour induced oxidation of combustiblenanoparticles, and particularly the charge-catalyzed watervapour induced oxidation of combustible nanoparticles, isalmost always accompanied by an evolution of combustiblegases.

Only when a concentration of the evolved combustiblegases reaches a lower flammability limit within the nanopar-ticles cloud, the gases can locally ignite, and a radiallyspreading deflagration wave can then ignite the whole cloud.Such high-temperature deflagration waves can periodicallypropagate within the cloud of combustible aerosol nanopar-ticles and contribute to the periodic thermal dehydrationof the electrohydrated nanoparticles. This periodic thermaldehydration of the combustible nanoparticles can temporar-ily retard their water vapour induced oxidation. Howeverif aggregated combustible nanoparticles constituting thissmall cloud contain a fraction of charged nanoparticles,the powerful electrostatically induced adsorption of polar

molecules of water vapour from ambient humid air willcontinuously rehydrate these charged nanoparticles, con-tributing to reactivation of their water vapour induced oxi-dation, as well as probably to an intra-cloud cyclization andsynchronization of the successive processes of electrostaticoxidative hydration and thermal dehydration of the chargedcombustible nanoparticles.

Each repeating cycle of such intra-cloud collective pro-cesses can consist of successive stages:

(a) electrostatic oxidative hydration of the chargedcombustible nanoparticles accompanied by evolvingcombustible gases,

(b) autoigniting the evolved gases, for example by theircontact with a fraction of the permanently red-hot“igniter” micrometre-sized aerosol particles,

(c) thermal dehydration of the majority of the com-bustible nanoparticles.

Within a bal lightning cloud, these three-stage cycles canrecur repeatedly in the form of a self-oscillating process.


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Figure 3: Stepped movement of an electrostatic charge (e.g., a hydrated ion) along a chain of combustible aerosol nanoaggregates successivelycatalyzes water vapour-induced oxidation of these nanoparticles, step-by-step burning the nanoaggregates.

An intra-cloud synchronization of the repeating stages ofwater vapour-induced oxidation of charged combustiblenanoparticles is probably only one of the possible scenarios,but a tendency to such an intra-cloud thermodynamic stagesynchronization can arise from at least six interconnectedcircumstances: (1) relatively slow evolving combustible gaseswithin the ball lightning cloud; (2) relatively fast intra-cloudpropagation of the deflagration waves, which consequentlycan contribute to practically synchronous thermal dehydra-tion of almost all the nanoparticles within the cloud; (3)extremely low thermal inertia of the majority of nanopar-ticles within the cloud; (4) relatively high thermal inertiaof the small fraction of micrometer sized permanently red-hot aerosol particles-igniters within the cloud; (5) existenceof the lower flammability limits of evolved combustiblegases; (6) existence of the relatively prolonged ignition delaytime, including ignition hydrogen/air mixtures by high-frequency streamer discharges [28]. If the gas evolved bycharged combustible nanoparticles-nanobatteries during theprocess of their water vapour-induced oxidation is hydrogen,this combustible gas can be periodically autoignited eitherby collective discharge short circuits within and on thesurface of the aerosol particles-nanobatteries or by contact

of the hydrogen with the fraction of the large, micrometre-sized aerosol particles-igniters permanently heated to atemperature higher than ∼585◦C, which is the autoignitiontemperature of air-hydrogen mixtures, or even at a lowertemperature—as a result of potential catalytic effects of thehighly developed oxidized surface of the heated nanoparticles(such as iron based nanoparticles, which can substantiallycatalyze the air-hydrogen oxidation reactions).

If the cloud of metal aerosol nanoparticles is exposed toa preferential oxidation by water vapour, the evolving hydro-gen can be either autoignited or nonautoignited dependingon the concrete local temperature and concentration condi-tions.

The evolving hydrogen gas can react with ambientatmospheric oxygen both directly on the surface of the metalaerosol nanoparticles and partially in the surrounding gasphase. When the evolving hydrogen is autoignited by oxygenfrom ambient humid air, we do not see a flame directly,because the air-hydrogen flame is visible only in ultravioletand not in visual range. However, the ball lightning cloud ofelectrostatically charged red-hot nanoparticles can play therole of a relatively low-quality natural aerosol visualizer ofthe air-hydrogen flame generated by this cloud during the


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+−Figure 4: Branched chain aggregates of combustible soot or metal nanoparticles are a frequent aerosol product of high-temperaturecondensation of carbon/metal vapour evaporated by an electric arc. These aggregates can contain a lot of small nanoparticles. Every suchaggregate can be charged with several elementary charges. An elementary charge (a hydrated ion) located on a peripheral combustiblenanoparticle in the chain is a powerful point catalyst of its oxidation by surrounding polar molecules of water vapour. When the firstperipheral nanoparticle is entirely oxidized, the elementary charge jumps onto the next nanoparticle in the chain catalyzing its water vapour-induced oxidation, then the process repeats again, and so forth. During such a charge-catalyzed successive oxidation of nanoparticles inaerosol nanoaggregates, the elementary charge moves along the chain of the oxidizable nanoparticles linked with a wave of water vapour-induced oxidation of the nanoparticles in a similar way to how a flame front moves along a Bickford’s fuse. Thus, even a single elementarycharge can enable the successive catalytic oxidation of a lot of the small combustible nanoparticles, when moving this charge along theaerosol nanoaggregate. The stepped movement of adsorbed ions along the chains of combustible aggregates successively catalyzes their watervapour induced oxidation, ultimately, completely burning off these aggregated aerosol particles.

process of the preferential water vapour induced oxidation ofthe charged metal nanoparticles. If the combustible aerosolnanoparticles are strongly interconnected within the cloudby a long-range mutual attraction, for example by thedipole-dipole magnetic attraction, they can form a relativelyheavy stable ball-shaped cloud, and so convection currentsproduced by the air-hydrogen flame cannot appreciably

influence both the motion and shape of this heavy stableaerosol cloud [20].

Thus, in this case, we can only see a luminous ball-shaped cloud of the distantly interconnected red-hot aerosolnanoparticles, but not an air-hydrogen flame cone.

In addition to hydrogen, the different combustible gasescan also be generated through the process of the water


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Figure 5: Successive “jumping” of the surplus charge—a local catalyst of water vapour-induced oxidation of combustible nanoparticle—between the charge trapping sites on the surface of the relatively large (i.e., ∼5–100 nm in diameter) combustible nanoparticle causesnumerous successive events of local corrosion of this surface with a final water vapour-induced oxidation of the whole nanoparticle.

vapour-induced oxidation of different combustible aerosolnanoparticles, including nonmetallic ones. For example, acombustible mixture of carbon monoxide and hydrogen, so-called water gas, can be evolved during the process of pref-erential water vapour-induced oxidation of carbon-basednanoparticles, such as soot nanoparticles, fullerenes, carbonnanotubes, or metal carbide nanoparticles. A completedwater vapour induced oxidation of these nanoparticles willgenerate gas reaction products in the form of carbon dioxideand combustible hydrogen. Alternatively, the completeddry oxygen-induced oxidation of these nanoparticles wouldgenerate only noncombustible carbon dioxide. Similarly, acombustible gas mixture of phosphine and hydrogen canbe evolved through the process of water vapour-inducedoxidation of calcium phosphide aerosol nanoparticles. Thesenanoparticles can be generated as aerosol products ofplasma-chemical reduction of organic calcium phosphateby organic carbon. A formation of such a small cloud ofcalcium phosphide nanoparticles can, for example, arisewhen a bird is struck by regular lightning. Similarly, inhumid air a combustible hydrogen sulphide can be generatedthrough the process of the water vapour-induced oxida-tion of many metal sulfide nanoparticles, such as naturalparticles of weathered iron sulfide minerals and also someorganic sulfide nanoparticles. Alternatively, a completed dryoxygen-induced oxidation of metal sulfide nanoparticles cangenerate only noncombustible solid metal sulphates, metaloxides, as well as the sulphur dioxide and sulphur trioxidegases. Thus, as one can see the mechanisms and productsof water vapour-induced oxidation of many absolutely

different combustible nanoparticles radically differ from themechanisms and products of their oxidation by oxygen gas.

Although a cone of flame is as a rule invisible overball lightning, in the literature, there are several alternativedescriptions of observations of lightning balls combinedwith tongues of flame emerging from them [8, 9]. On theone hand, these rare observations can show that sometimesforces of a dipole-dipole attraction between separate aerosolparticles-nanobatteries constituting ball lightning are inad-equate to keep all the particles inside the ball cloud, andsome part of the hot aerosol particles can be captured byascending convective currents. On the other hand, theserare observations show that sometimes combustible gases,evolved during the process of water vapour-induced oxida-tion of aerosol particles-batteries constituting ball lightning,contain components, which are able to generate visuallydistinguishable tongues of combustion products.

In our preliminary experiments, small burning clouds ofcombustible, ethanol and methanol-based, droplets with thedroplets diameters of ∼1–3 micrometres were generated. Aflow of these droplets suspended in the air was generatedwith the help of a simple ultrasonic drug inhalator with anoscillator frequency of ∼1 megahertz. The ethanol and/ormethanol-based solutions contained from 2 up to 5 percentby weight of acetyl salicylic acid (99.0%, Sigma-Aldrich) plusfrom 2 to 3 percent by weight of calcium nitrate tetrahydrate(98.0%, Sigma-Aldrich) and plus from 2 to 5 percent byweight of cupric nitrate hemipentahydrate (98.0%, Sigma-Aldrich). It is important to note that in these experimentsthe micrometre-sized droplets of the combustible solutions


were not exposed to additional artificial electrostatic charg-ing. Only minimal spontaneous bipolar charging of themicrometre-sized combustible droplets took place duringtheir ultrasonic generation.

When burning, the droplets of the ethanol and/ormethanol based solutions were subjected to immediateevaporation, initially turning into solid particles of acetylsalicylic acid mixed with calcium nitrate and copper nitrate.These solid aerosol particles in turn were exposed to athermal oxidative decomposition to form small flame cloudsconsisting of submicron soot particles impregnated with acombination of calcium nitrate/calcium hydroxide/calciumoxide and copper nitrate/copper hydroxide/copper oxides.Obviously, the final target products of the thermal oxidativedecomposition form as aggregated soot-based combustiblesubmicrometre particles consisting of amorphous carbonmixed with the calcium and copper oxides. In addition, someother organic/inorganic solution compositions originallycontaining nitrates of alkaline metals also were investigatedwith the purpose of formation of the clouds of suchcarbon/air aerosol nanobatteries.

Several fragments of video of these almost electrostat-ically neutral burning small clouds are shown in Figure 6.As one can see, the clouds have a high-temperature stableball-shaped core and a relatively cold and transparent coneof flame. Diameters of the ball-shaped cores of these smallburning clouds were from ∼10 to 35 mm. These ball-shapedflame clouds could be retained as long as the aerosol flowof the micrometre-sized droplets was directed into the zoneof combustion. The time of independent life of such ball-shaped small flame clouds was only of∼50–120 milliseconds.

It is necessary to note that video fragments shown inFigure 6 are used here only to experimentally illustrate thepossibility of coexistence (and a visual observation) of aball-shaped cloud (consisting of the burning hot submi-cron soot particles impregnated with inorganic electrolytecomponents) and visually distinguishable tongues of flameover this spherical cloud. Thus, the above illustration willnot be connected to our further discussion, because burningparticles constituting ball-shaped flame clouds shown abovewere only slightly charged with negligible bipolar charges,and the low bipolar charges of these aerosol particles wereprobably generated due to:

(1) thermoionic electron emission from the surface ofhot particles during combustion,

(2) adsorption of negative gas ions to the surface ofrelatively cold aerosol particles.

The same type of thermoionic bipolar electrostatic chargingof nanoparticles takes place in many processes involvingdusty plasma, and probably also in the processes describingmicrowave-induced formation of ball-shaped dusty plasmain [5, 6].

Undoubtedly, due to an intense charge-dipole attraction,in humid air both the positively and negatively chargedcombustible nanoparticles suspended either in a flame or inlow-temperature air dusty plasma can be actively attackedand oxidized by the surrounding highly polar molecules of

water vapour rather than by non-polar molecules of oxygen.However, parallel with the nanoparticle charging processes,active synchronous processes of neutralization of the bipolarcharges of the flame/plasma suspended particles (causedeither by cooling of the particles or by mutual recombinationof opposite charges of the co-aggregated bipolar particles)can strongly reduce the final charges of these particles.

Consequently, because of gradual recombination ofbipolar charges, within such practically quasineutral, flameor dusty plasma clouds containing overwhelming majorityof uncharged or minimally charged combustible nanopar-ticles, the electrostatic delivery of polar molecules of watervapour to the reactive surface of these hot particles will besignificantly slowed down, and so the charge-catalyzed watervapour-induced oxidation of these quasi-neutral aerosolparticles will be finally minimized.

Thus, if we wish to accomplish a continuous processof predominantly water vapour-induced oxidation of per-manently charged combustible aerosol particles, a surplus,uncompensated electrostatic charge is necessary for a cloudof such particles.

So, as assumed above and as it will be quantitativelyproved later, in humid air, electrostatically charged com-bustible particles can be exposed to preferential oxidationby surrounding polar molecules of water vapour rather thanto alternative oxidation by non-polar molecules of oxygengas due to intense charge-dipole attraction of the polargas molecules to the charged aerosol particles. During theprocess of preferential water vapour induced oxidation ofthe charged aerosol nanoparticles, the evolving and auto-igniting of combustible gases, in particular, hydrogen gas,on the one hand, and a synchronous growing of thehydroxide-based dynamic thermolabile electrolyte layers onthe surface of these charged nanoparticles, on the otherhand, can take place within the cloud of such nanoparticles.Both the surface growth of the hydroxide-based porouselectrolyte layers and evolution of the combustible reducinggas on the nanoparticles surface hamper oxidation of thenanoparticles by external neutral oxidizing species, firstof all such as molecules O2, but at the same time, thehydrated surface electrolyte layers can effectively transporteither metal ions from reductant cores to the nanoparticlessurface or negatively charged, ionized oxidizing species fromthe outer surface of the nanoparticles to their reductantcores, contributing to predominantly electrochemical, thatis, ion-mediated oxidation of these combustible nanoparti-cles. Consequently, the electrostatically charged, periodicallyelectrohydrated combustible aerosol particles, being co-aggregated with numerous surrounding polarized neutralparticles, spontaneously transform into aerosol nanobatter-ies periodically short-circuited by the field and thermoionicelectron emission from their reductant/metal cores (theelectron emitting anodes of these nanobatteries) towardsexternal surfaces of their porous thermolabile electrolyteshells (the air depolarized cathodes of these nanobatteries)[20].

The repeating processes of auto-ignition and combustionof evolved combustible gases can make an important con-tribution to synchronously repeating processes of heating of


Figure 6: Practically neutral burning small clouds with a high-temperature ball-shaped core and a relatively cold and transparent coneof flame consist of billions of submicron soot-based aerosol particles, which can be only minimally charged with almost balanced bipolarcharges.

the charged nanoparticles-nanobatteries and consequently totheir repeating flame thermal dehydration.

During such “thermocycling,” consisting of alternatingstages of the electrostatic, charge-dipole hydration of thenanoparticles and their subsequent flame thermal dehy-dration, electrophysical properties of the interphase con-tact between a reductant, for example metal core of thenanoparticle-nanobattery and its growing, either metal oxideor metal hydroxide, shell periodically will radically change,with an alternation from the metal-semiconductor (metal-dielectric) core-shell junction (in the stage of thermal dehy-dration of the nanoparticle shell) to the metal-electrolytecore-shell junction (in the stage of electrostatic surface re-hydration of the temporarily cooled nanoparticle).

These fast cyclic changes of the electrophysical character-istics of the interphase core-shell contacts will result in cyclicprocesses of the interphase electron-ion transfer (electron-ion jumping), forming strong local interphase core-shellelectrostatic fields, which in turn will control the specificstage-dependent mechanisms of the nanoparticles oxidation,in particular, from the Cabrera-Mott oxidation mechanism-in the stage of flame thermal surface dehydration of thecombustible nanoparticle—to the electrochemical oxidationmechanism—in the stage of electrostatic surface rehydrationof this nanoparticle [20, 29, 30].

It is important to note that in the case of both theCabrera-Mott mechanism of the nanoparticle oxidationand the electrochemical mechanism of its oxidation, eachinstantaneous event of gradual oxidation of combustiblemetal/metalloid aerosol nanoparticle will necessarily resultin the generation of a powerful instantaneous local core-shell electrostatic field and consequently the generation of aninstantaneous electric dipole moment of this nanoparticle.

Clearly, when a combustible aerosol particle is nano-or submicrometre sized, each instantaneous event of its gasphase oxidation from one side cannot be compensated bythe same synchronous event of its oxidation from the otherside (stochastic nature of such successive spotty oxidationof small aerosol particles is absolutely similar to a locallyunbalanced character of Brownian collisions). Therefore,individual nano- or submicrometre combustible aerosol par-ticles will always possess the instantaneous uncompensatedelectric dipole moments generated during their gas phaseoxidation.

The Cabrera-Mott oxidation mechanism assumesprimary migration of electrons from a metal core into a

nanoporous dielectric or semiconductor metal-oxide shell.In this case, the initial electron migration generates a localelectrostatic field between the metal core and the metal oxideshell, and this field further contributes to intense outwardelectrodiffusion of the metal ions with their followingsurface oxidation.

The alternative electrochemical mechanism of oxidationassumes primary diffusion migration of metal ions from ametal core into a nanoporous surface electrolyte, for exampleinto a more or less hydrated metal hydroxide shell. In thiscase, initial outward migration of the metal ions generates alocal electrostatic field between the metal core and the metalhydroxide shell, and this field further contributes to intensefield/ thermoionic electron emission from the metal core tothe outer surface of the nanoparticle, with following surfaceelectrochemical oxidation of the metal ions (naturally, onlywhen these ions recombine with emitted electrons).

In fact, both these mechanisms of oxidation are elec-trochemical, because diffusion (or electrodiffusion) of ionsthrough porous surface layers is a key process that precedesthe events of the metal ion oxidation in both cases.

Both these types of oxidation of metal or metalloidbased aerosol nanoparticles can generate powerful momen-tary electrostatic fields, high instantaneous electric dipolemoments and strong instantaneous relaxation electron/ioncore-shell currents within the nanoparticles irrespective ofwhether these nanoparticles are extra charged or not.

Consequently, both these mechanisms of oxidationcan convert combustible aerosol nanoparticles into short-circuited nanobatteries.

It is possible to assume, however, that if a processof the metal/metalloid oxidation takes place in the real,that is, humid air, then a local negative surface chargegenerated by electrons, which migrate from a metal core intogrowing metal oxide surface layers (according to the Cabrera-Mott oxidation mechanism) will always cause immediateelectrostatic hydration of such highly charged surface sites,locally transforming these surface sites from their purelymetal oxide (i.e., dielectric or semi-conductor) state intoa hydrated, for example metal-hydroxide (i.e., electrolyte)state.

Thus, it seems that a process of atmospheric oxidation ofmany metals or metalloids can frequently be automaticallyconverted from the Cabrera-Mott oxidation mode into thetrue electrochemical mode of oxidation only due to pow-erful fast spontaneous electrostatic hydration of oxidatively


charged surface sites, which is inevitable in the conditions ofthe real, humid air oxidation.

It is important to emphasize that such a predominantlyelectrochemical mode of atmospheric oxidation of manymetal structures, including metal nanoparticles, can ariseonly owing to natural redistribution of electrons between ametal core and a dielectric or semi-conductor metal oxidesurface layer (i.e., without additional electrostatic chargingof a metal object exposed to atmospheric oxidation).

Probably, in many cases, within a ball lightning cloud theheat of combustion of evolved combustible gases e.g., hydro-gen gas) can considerably exceed the heat that is generatedor is consumed in primary heterophase reactions of watervapour-induced oxidation of metal, or metalloid, or carbon-based combustible particles constituting ball lightning.

Thus, the highly endothermic stage of the thermaldehydration of the electrostatically charged combustiblenanoparticles can be appreciably delayed in time with respectto the stage of their electrostatic oxidative hydration—onlythe heat of combustion of the evolved gases can effectivelytemporarily dehydrate the charged nanoparticles.

So, within ball lightning electrostatically charged com-bustible nanoparticles can be subjected to preferential oxi-dation by polar molecules of water vapour rather than non-polar molecules of oxygen gas. A periodic fast alternatingof the processes of electrostatic hydration and thermaldehydration of the charged nanoparticles in humid air can bepartially or totally synchronized with the repeating processesof evolution of combustible gases, their auto-ignition, andfollowing quick flame extinction.

Naturally, the fast alternating processes of electro-static oxidative hydration and thermal dehydration of thecharged aerosol particles constituting ball lightning cancause periodic melting and hydrogen gas-induced foamingthese particles; formation of submicron or micrometre-sizedelectrostatically charged metal/metal oxide/metal hydroxidehollow globules can be a natural outcome of such remelt-ing/refoaming.

Many witnesses who observed ball lightning at veryshort distances described ball lightning as a relatively low-temperature object, which did not radiate intensive thermalradiation [8, 9]. Indeed a time-average temperature of thecharged nanoparticles can be relatively low owing to a quickalternating of the processes of their intense heating andcooling. At the same time, peak “colour” temperatures ofthe hot nanoparticles, which are periodically reached inthe quickly repeating processes of their oxidative or flamereheating, could be ∼750–950◦C (for most typical red ororange lightning balls), and so these nanoparticles couldthermally emit a pulsating red or orange light with a ripplefrequency high enough so that the light from ball lightningdid not flicker.

Probably, however, total luminous radiation of nano-particles-nanobatteries within ball lightning could arise froma combination of all three main light emitting processes:(1) nanoparticles-nanobatteries can emit faint light (faintthermal radiation) due to their direct oxidative heatingor due to their periodic heating caused by a flame fromcombustion of combustible gases evolved in water vapour

induced oxidative reactions; (2) nanoparticles-nanobatteriescan emit pulsating luminous and ultra-violet radiation (aswell as powerful pulsating wideband radio/micro waves) atmoments of their partially or totally synchronized shortcircuits; (3) nanoparticles-nanobatteries can probably some-times contain (or produce during oxidation) fluorescent orphosphorescent materials (e.g., some mixed metal oxidesor sulphides), consequently, these particles-batteries cangenerate relatively low-temperature ultra-violet inducedphotoluminescence, also electroluminescence or cathodolu-minescence.

Equally, many semi-conductor-based nanoparticles-na-nobatteries can probably possess properties of quantum dots.In particular, the highly charged silicon based nanopa-rticles—silicon/air core-shell nanobatteries [20], continu-ously retransformed from the high-temperature, thermallydehydrated, Si/SiO2 core/shell nanostructure into the low-temperature, electrohydrated, Si/Si(OH)4 core/shell nanos-tructure, can possess properties of quantum dots [31]. Suchsemi-conductor-based nanoparticles-nanobatteries, possess-ing properties of quantum dots, could be able to an intenselow-temperature photo-, cathodo- and electroluminescencestimulated either by ultra-violet radiation of air-hydrogenflame or by collective discharge electron emission processeswithin the short-circuited nanobatteries.

Thus, a time-average temperature of many lightning ballscan be relatively low, and consequently a light intensity fromthe ball lightning can practically be not connected with thetime-average temperature of ball lightning.

5. Steel Containing Objects and AluminiumContaining Objects Were Frequently Involvedin the Directly Observed Processes of BallLightning Formation

The involvement of iron/carbon-, and/or aluminium-basedobjects in ball lightning formation processes was repeatedlymentioned in numerous witnesses’ reports [8, 9].

In particular, a lot of these reports were devoted todescriptions of a “high-temperature” ball lightning forma-tion, in which a high-voltage arc evaporation of iron/carbon-based materials and further condensation of the evaporatedmaterials in the form of a small smoke cloud could be themost probable events. At the same time, alternative, relatively“low-temperature” processes of ball lightning formation,that is those without the involvement of a visible electricarc, also were repeatedly described as connected with thefrequent participation of the cast iron-based or steel basedobjects [8, 9].

Probably, it would be reasonable to assume that theunipolarly charged, iron-, and/or carbon-, and/or alumi-nium-based combustible aerosol particles could be initiallygenerated from the electrode materials in all such balllightning formation phenomena.

Therefore special attention to the process of water vapourinduced oxidation of the electrostatically charged iron-,or carbon-, or aluminium-based aerosol nanoparticles, ortheir compositions in the form of electrostatically hydrated


aggregated nanobatteries (or additionally in the form ofelectrostatically hydrated aggregated nanothermites/nano-pyrotechnics) will be pertinent to our further discussion.

6. Some Quantitative Estimations ofa Charge-Dipole Interaction betweena Charged Aerosol Nanoparticleand Surrounding Polar Gas Molecules

It seems that on the one hand, a charge-dipole inter-action between a charged aerosol nanoparticle and polargas molecules from ambient air, for example, surroundingmolecules of water vapour, can increase the number ofcollisions of these polar gas molecules with the chargednanoparticle, without a similar influence on the number ofcollisions of this particle with non-polar gas molecules.

On the other hand, it would be reasonable assume thatthe charge-dipole interaction between the charged aerosolnanoparticle and the surrounding polar gas moleculescan in addition to increase kinetic energy of the polarmolecules, accelerating these gas molecules towards thecharged nanoparticle at a short distance of their mean freepath from the charged nanoparticle.

Let us consider a simple case of oxidation of a com-bustible aerosol nanoparticle charged with the minimumpossible charge, that is, charged with either a positive ornegative elementary charge, Q = |e| = 1.6 · 10−19(C).

Again, with the purpose of simplification, let us assumethat:

(a) this charged aerosol nanoparticle is spherical andit can freely and irregularly revolve on its axis dueto continuous stochastic Brownian collisions withsurrounding gas molecules;

(b) a time-average density of surplus electrostatic chargeon the surface of this nanoparticle is practicallyequivalent to the time-average charge density onthe surface of the same charged nanoparticle whosesurplus electrostatic charge is localized in its centre,that is, the surplus electrostatic charge is quasi-distributed on the surface of the nanoparticle, withthe possibility of free fast migration of this charge onthe nanoparticle surface.

In humid air, the majority of possible oxidative reactionson the surface of the discussed combustible nanoparticlecan be caused by molecules of the two main competingatmospheric oxidants, oxygen gas and water vapour.

A flux of oxygen molecules incident upon the surface ofthe charged combustible nanoparticle suspended in humidair determines the frequency of collisions of the oxygengas molecules with the surface of the charged nanoparticle,fO(mol/s). Correspondingly, this molecular flux determinesalso the rate of oxidative surface reactions caused by afraction of the high-energy oxygen molecules possessingenough kinetic energy to climb the activation energy barriersof such oxygen induced oxidative surface reactions.

Similarly, a flux of water vapour molecules incidentupon the surface of the charged combustible nanoparticle

suspended in humid air determines the frequency of col-lisions of the water vapour molecules with the surface ofthe charged nanoparticle, fW (mol/s). And correspondingly,this molecular flux also determines the rate of oxidativesurface reactions caused by a fraction of the high-energywater vapour molecules possessing enough kinetic energy toclimb the activation energy barriers of such water vapourinduced oxidative surface reactions.

7. Humid Air Oxidation of a Spherical (∼2 nmin Diameter) Iron Metal Aerosol NanoparticleCharged with the Minimum Positive ChargeQ = |e| = 1.6 · 10−19(C) at a Relatively LowTemperature of about 300 K.

As a first example, let us consider a relatively low-temperature process of humid air oxidation of a spherical(∼2 nm in diameter) iron metal-based aerosol nanoparticlecharged with the minimum possible positive charge Q =|e| = 1.6 · 10−19(C), that is, with a single lost electron.

Let us assume that exothermic oxidation of this ironmetal nanoparticle in the humid air is slow enough, becausethe water vapour and oxygen gas-induced intense growthof the passivating layers consisting of the mixed hydratediron hydroxides, iron oxy-hydroxides, and iron oxides takesplace on the surface of the iron metal nanoparticle during itshumid air oxidation.

Assuming that the process of the mixed, water vapourand oxygen gas-induced exothermic oxidation of the dis-cussed charged nanoparticle is slow enough, we could alsosuppose, for the first example, that both a time-averagetemperature of the nanoparticle surface, Ts, and a time-average temperature of ambient humid air around thisnanoparticle, T , can remain approximately constant, andboth these temperatures are approximately equal to theinitial temperature of the nanoparticle oxidation process,that is, to ∼300 K.

Ts = T = 300(K). (9)First, let us compare the flux of oxygen molecules with thecompeting flux of water vapour molecules incident upon thesurface of the discussed charged nanoparticle in the humidair.

As oxygen molecules are non-polar and their permanentelectric dipole moment, pO, is zero, a flux of oxygenmolecules incident upon the surface of an uncharged aerosolnanoparticle is practically equal to a flux of oxygen moleculesincident upon the surface of the same charged nanoparticle.In other words, the frequency of collisions of non-polaroxygen molecules with the surface of an uncharged nanopar-ticle, fO unch (mol/s), is practically equal to the frequencyof collisions of the oxygen molecules with the surface of asimilar but charged aerosol nanoparticle, fO (mol/s), whichcould be written as follows:

fO unch = fO = AnOvσO = AnOvπR2, (10)where A—a numerical factor, nO = 0.21—the mole fractionof oxygen molecules in humid air (mol/mol), v—the mean


speed of gas molecules at a given temperature (m/s), σO =πR2—the cross section for collisions of surrounding non-polar oxygen molecules with the charged (or also uncharged)aerosol nanoparticle (m2), R—the radius of the nanoparticle(m).

If a combustible aerosol nanoparticle suspended inhumid air is uncharged, non-polar molecules of atmosphericoxygen have a significant quantitative advantage over polarmolecules of atmospheric water vapour when colliding (andalso when reacting) with this nanoparticle, because the molefraction of oxygen gas molecules is approximately tenfoldgreater than the mole fraction of water vapour moleculesin humid air. Therefore, non-polar oxygen molecules can bea principal gas oxidant of uncharged combustible nanopar-ticles in humid air, while relatively few polar moleculesof water vapour probably play a secondary role in theprocesses of humid air oxidation of uncharged nanoparticles(Figure 7).

The high-energy oxygen molecules possessing enoughkinetic energy to climb the activation energy barriers of theoxidative surface reactions also can collide and react with thesurface of uncharged combustible nanoparticle suspendedin the humid air much more often in comparison with therelatively few high-energy water vapour molecules.

The preferential formation of the mixed, iron oxide layerson the surface of an uncharged iron nanoparticle could be anatural outcome of such a significant quantitative advantageof oxygen gas molecules over water vapour molecules inhumid air. Indeed, it seems that oxygen induced formationof layers consisting predominantly of mixed iron oxides onthe surface of the uncharged iron nanoparticle in humid airis a much more probable process than an alternative processof water vapour-induced formation of mixed hydrated, ironhydroxide, and/or iron oxy-hydroxide, surface layers.

However, it would also be reasonable to suppose thatintense electrostatic hydration that locally converts ironoxides into iron hydroxides and iron oxy-hydroxides inhumid air can still take place on oxidatively charged sitesof the iron oxide surface of the originally uncharged ironnanoparticle, because electron migration from the iron metalcore into the iron oxide Fe3O4/Fe2O3 semiconductor shellwill continuously generate new negative surface charges evenduring a predominantly oxygen gas-induced oxidation of thisoriginally uncharged iron nanoparticle.

At the same time, it seems that a different situationcan arise when the discussed minimally charged ironnanoparticle is exposed to oxidation in humid air. Becausewater vapour molecules are high-polar, in contrast to non-polar oxygen molecules, and the permanent electric dipolemoment of a water vapour molecule is

pW = 1.84(D) = 0.6 · 10−29(C ·m), (11)

the intense charge-dipole attraction between the chargednanoparticle and surrounding polar molecules of watervapour can make an important contribution to the pro-cess of intense electrostatic nanoparticle hydration and,correspondingly, to a predominantly water vapour inducedoxidation of the nanoparticle. Owing to the substantial

charge-dipole attraction between the charged nanoparticleand surrounding polar molecules of water vapour, boththe frequency and the intensity of collisions of the watervapour molecules with the surface of the charged aerosolnanoparticle can considerably exceed the correspondingfrequency and intensity of collisions of these molecules withthe surface of a similar uncharged nanoparticle (Figure 8).

The frequency of collisions of polar molecules of watervapour with a surface of the charged aerosol nanoparticle,fW , can be represented as follows:

fW = AnWvσW , (12)where A—a numerical factor, nW ∼ 0.02—the molefraction of water vapour molecules in the humid atmosphere(mol/mol), v—the mean speed of gas molecules at agiven temperature (m/s), σW—an effective cross section forcollisions of surrounding polar molecules of water vapourwith the charged aerosol nanoparticle (m2).

The collision cross section σW = πr∗2 can be determinedestimating the value of potential energy of the charge-dipoleinteraction between the charged aerosol nanoparticle andpolar molecule of water vapour from a gas microenviron-ment of the aerosol nanoparticle (taking into account thatthe size of the molecular dipole, that is, polar molecule ofwater vapour, is only about 0.2 nm)

U(r) = − 14πε0

pQr2

, (13)

where 1/4πε0 = 9 · 109 (m/F), p = pW = 0.6 · 10−29—thepermanent electric dipole moment of water vapour molecule(C·m), Q = 1.6 · 10−19—the charge of the nanoparticle (C),r—the distance between the centre of the charged aerosolnanoparticle and the given molecule of water vapour froma gas microenvironment of the nanoparticle, (m).

An electrostatic capture of the surrounding polarmolecules of water vapour with a mean kinetic energy, W ∼3/2 kT , by the aerosol nanoparticle charged with a charge, Q,can take place at an effective distance—the effective captureradius—r∗, such that

32kT = 1

4πε0

pQr∗2

, (14)

where k ≈ 1.38 · 10−23—the Boltzmann constant (J/K),T—the temperature of ambient humid air around the

nanoparticle (K).As we assume that the temperature around the nanopar-

ticle remains about 300 K, the mean kinetic energy of the airmolecules is about

W = 1.5 · 1.38 · 10−23 (J/K) · 300(K) = 6.21 · 10−21(J).(15)

Correspondingly, a spherical volume of the radius of r∗

around the iron metal aerosol nanoparticle with an initialdiameter of 2 nm, suspended in humid air and charged witha minimum positive charge Q = |e| = 1.6 · 10−19(C), is anarea where an effective electrostatic, charge-dipole capture ofthe surrounding polar water vapour molecules takes place at


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In standard air atmosphere

A noncharged combustible aerosol nanoparticle,for example, a metal/carbon/organic/virus aerosol nanoparticle,

Mean free path of molecules is ∼65–100 nanometers

∼1–20 nanometers in diameter

Figure 7: Even in a high humid air atmosphere, a high concentration of oxygen gas molecules creates the prerequisites for a preferentialoxidation of uncharged combustible aerosol nanoparticles by oxygen molecules but not water vapour molecules. Water vapour, beinganother major air oxidant, with its much lower air concentration usually plays a secondary role in oxidative reactions on the surface ofuncharged combustible nanoparticles. However, this situation can completely change during humid air oxidation of electrostatically chargednanoparticles.

the temperature of about 300 K and at a mean atmosphericpressure at sea level, P, equal to 101,325 (Pa).

As one can see the value of the effective radius ofthe electrostatic capture of the surrounding water vapourmolecules by the minimally charged iron nanoparticle

r∗ =√

pQ

4πε03/2kT

=√

9 · 109 0, 6 · 10−29 · 1, 6 · 10−19

3/2 · 4, 1 · 10−21 = 1.19 · 10−9(m),

(16)

only slightly exceeds the 1 nm radius of the discussed chargednanoparticle and also it is much less than the mean free pathof the ambient gas molecules, l ≈ 10−7(m), under the givenconditions of temperature and pressure.

The corresponding cross section for collisions of thesurrounding polar molecules of water vapour with thediscussed charged iron nanoparticle (and probably also for

electrostatic capture of these polar molecules by the chargediron nanoparticle) is

σW ∼ πr∗2 = 4.5 · 10−18(m2). (17)

This cross section also only slightly (approximately one and ahalf times) exceeds a “geometrical” cross-section for possiblecollisions of this charged nanoparticle with the surroundingnon-polar oxygen molecules:

σO ∼ 3.14 · 10−18(m2). (18)

Indeed as one can see the cross-section for collisions ofthe surrounding polar molecules of water vapour witha minimally charged 2 nm diameter aerosol nanoparticlecan only slightly exceed the cross-section for collisions ofthis aerosol nanoparticle with the surrounding non-polarmolecules of oxygen gas due to a contribution of thecharge-dipole attraction between such a charged aerosolnanoparticle and surrounding polar molecules of watervapour.

However, the situation strongly changes when the diam-eter of the minimally charged nanoparticle becomes less


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+− +−

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Mean free path of molecules is ∼ 65–100 nanometers In standard air atmosphere

A minimally (plus or minus one electron) charged combustible aerosol nanoparticle,

for example, a metal/carbon/organic/virus aerosol nanoparticle, generates a powerful electrostatic field

E ∼ 105–109 V/m in the vicinity of the nanoparticle, strongly attracting and accelerating neighbouring polarmolecules, in particular, water vapor molecules at a distance of the mean free path of molecules

∼1–20 nanometers in diameter

Figure 8: Powerful charge-dipole attraction between charged aerosol nanoparticles and the surrounding molecules of water vapour inhumid air bends the trajectories of the polar molecules and also additionally accelerates these polar molecules in the direction of the chargednanoparticles at a distance of the air molecules’ mean free path. On the other hand, nonpolar air molecules, such as oxygen gas molecules(or nitrogen gas, or carbonic gas) are practically not subject to the influence of charge-dipole attraction in the vicinity of charged aerosolnanoparticles, and so the absolute values of kinetic energy and the directions of movement of the nonpolar air molecules around the chargednanoparticles are practically not changed by forces of the charge-dipole attraction. A significant electrostatic acceleration of water vapourmolecules in the vicinity of the charged combustible aerosol nanoparticles substantially increases reactivity of these molecules. Thus, theoxidizing efficiency of the polar molecules of water vapour in relation to the charged combustible nanoparticles considerably exceeds thealternative oxidizing efficiency of nonpolar, correspondingly electrostatically nonaccelerated molecules of oxygen gas, though approximatelya tenfold excess of oxygen gas molecules’ concentration, in comparison with the concentration of water vapour molecules, normally takesplace in air atmosphere.

than 1 nm. For example, it is easy to estimate that a crosssection for collisions of a minimally charged 1 nm diameteraerosol nanoparticle with the surrounding water vapourmolecules can approximately by sixfold exceed the crosssection for collisions of

charge-dipoleaccelerationofpolargas ...the high electrostatic charge of lightning balls could play a...

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